IMS DOCUMENT

TRN

SIXTH INTERNATIONAL CONGRESS ON QUANTUM CHEMISTRY

Jerusalem, Israel August 21-25,1988

PROGRAM CONTENTS

Page

Acknowledgement s Ill

The Organizing Committee IV

General Information V

Social Program VII

Program for Accompanying Persons VIII

Travel and Accommodation IX

Timetable X

Congress Program XI

Abstracts (Posters) 1-122

Index 123

J.

II SIXTH INTERNATIONAL CONGRESS ON QUANTUM CHEMISTRY

JERUSALEM, ISRAEL

AUGUST 21-25, 1988

Under the auspices of:

The International Academy of Quantum Molecular Science The Israel Academy of Sciences and Humanities

Sponsored by:

Bar Han University Israel National Council for Research and Development Tel Aviv University The Hebrew University of Jerusalem The Technion, Israel Institute of Technology The Weizmann Institute of Science

Generously Supported by:

The Baron Edmond de Rothschild Foundation Paris, France

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III ISRAEL ORGANIZING COMMITTEE

Michael Baer Soreq Nuclear Research Center, Yavneh

Harold Basch Bar Ilan University, Ramat Gan

Maurice Cohen, Chairman, Local Committee The Hebrew University of Jerusalem

Robert B. Gerber The Hebrew University of Jerusalem

Amiram Goldblum The Hebrew University of Jerusalem

Amitai Halevi Technion - Israel Institute of Technology, Haifa

Joshua Jortner, Chairman Tel Aviv University

Uzi Kaldor Tel Aviv University

Raphael D. Levine, Vice-Chairman The Hebrew University of Jerusalem

Abraham Nitzan Tel Aviv University

Ruben Pauncz, Honorary Chairman Technion - Israel Institute of Technology, Haifa

Benjamin Scharf Ben Gurion University, Beer Sheva

Moshe Shapiro The Ueizmann Institute of Science, Rehovot

J.

IV GENERAL INFORMATION

CONGRESS VENUE The Hebrew University Campus, Givat Ram, Jerusalem. Please note that all plenary lectures will take place at the Wise Auditorium- The parallel Symposia will be in Maizer Building, Hall A & Hall B (adjacent to the Wise Auditorium).

LANGUAGE The Congress will be conducted in English.

REGISTRATION AND INFORMATION The registration and information desk will be open on Sunday, August 21, at the Sonesta Hotel, Jerusalem, between 16:00 - 21:00 hrs. From Monday, August 22, through Thursday, August 25, the desk will operate at the Wise Auditorium, the Hebrew University Campus, Givat Ram, between 08:00 - 18:00 hrs.

BADGE Please wear your name badge at all Congress sessions and events.

POSTERS The posters are arranged in three sessions, on Tuesday (Session A), Wednesday (Session B), and Thursday (Session C) (see program for details). Presentors are responsible for fixing their posters in the morning of the appropriate day and removing them no later than 19:00 hrs the same day.

SLIDE PREVIEWS Slide and overhead projectors will be available to speakers during the Congress breaks for those wishing to check their slides before submitting them to the projectionist.

PROJECTION Speakers are requested to hand their slides (in correct order) to the projectionist In the lecture hall, 20 minutes prior the beginning of the session, and to collect them immediately thereafter. The speaker's name and sequence of presentation of the slides must be marked on each slide.

V TRANSPORTATION The hotels are located at 7-10 minutes walking distance from the Hebrew University, Glvat Ram Campus, therefore no shuttle services will be provided. From the hotels take buses No. 9, 24 or 28. For details regarding transportation to social events please refer to the social events program.

MEALS Participants should make their own lunch arrangements. There are a number of possibilities within the Givat Ram Campus:

1. Topaz Cafeteria, in the basement of the Sherman Administration Building, next to the Wise Auditorium. Open: 08:00 - 16:00 hrs. A three course lunch including soft drink is available at the price of 13.- NIS per meal.

2. Belt Belgia, (the Faculty Club) a few minutes walk across the campus. The dining room serves full meals. Light refreshments are available in the soup and salad bar as well as in the coffee shop.

BANK AND POST-OFFICE These are to be found on the ground floor of the Sherman Administration Building.

CERTIFICATE OF ATTENDANCE Certificates of attendance will be available at the information desk, upon request.

SEMINAR ORGANIZERS AND TRAVEL AGENTS PELTOURS - CONVENTIONS 28, Ahad Ha'am St. Phone: (03) 650862 P.O.Box 394 Fax : (03) 660060 61003 Tel Aviv, Israel Telex: 33803, 35819 PELTG IL Cable: PELTOURS TELAVIV

VI SOCIAL PROGRAM

SUNDAY, AUGUST 21, 1988 21:00 Informal Get-together at the Sonesta Hotel, Jerusalem ' (Light refreshments will be served)

MONDAY, AUGUST 22, 1988 20:30 Reception and buffet dinner at the Israel Academy of Sciences and Humanities

Transportation: 20:10 - Departure from hotels 22:30 - Return to hotels

TUESDAY, AUGUST 23, 1988 19:45 Reception and visit to the Israel Museum, hosted by the Jerusalem Municipality. Light refreshments will be served on the balcony, after which participants are invited to visit the Museum and the Shrine of the Book.

Transportation: 19:30 - Departure from hotels 22:00 - Return to hotels

WEDNESDAY, AUGUST 24, 1988 Free Evening Participants wishing to attend the Sound & Light performance at the David Citadel, Jaffa Gate, could do so at the following hours: 20:30 - Performance in Hebrew 21:30 - Performance in English 22:30 - Performance in French Admission fees: 6.50«- NIS per person; 5.- NIS per person for groups of 5 people or more, to be paid on the spot. Participants are also advised to visit the Jewish Quarter with the newly opened Herod!an House (open until 21:00 hrs). Admission is free. i

THURSDAY, AUGUST 25, 1988 J 20:30 Farewell dinner at the Knesset (Israel Parliament) j| Participation by invitation only. Vf ' x Transportation: f. 20:10 - Departure from hotels .' 23:00 - Return to hotels

VII PROGRAM FOR ACCOMPANYING PERSONS

Registered accompanying persons are Invited to attend all social events of the Congress. In addition, the following half-day tours will take place during session times*

MONDAY, AUGUST 22, 1988

09:00 hrs Accompanying persons are invited to attend the bus departs opening session. Imediately thereafter, depart for from Givat a guided tour of Mount Scopus Campus and a short Ram Gate visit to the Old City. Return to hotels and/or Givat Ram Campus (about 13:30 hrs).

THURSDAY, AUGUST 25, 1988

09:45 hrs A visit to the breathtaking beauty of a stalactite bus departs from and stalagmite cave. Continue to Kibbutz Tzora where lobby of the you will be introduced to this unique way of Sonesta Hotel communal life. Enjoy a stroll around the Kibbutz. Return to hotels and/or Givat Ram Campus (about 13:30 hrs).

I

VIII TRAVEL AND ACCOMMODATION

Peltours Conventions will operate a travel desk at the Congress venue during the same hours as the registration & information desk. All tourist services such as hotel accommodation, excursions by buses or private cars, car rentals, departure transfers and other tourist services will be provided- Please pay attention to the Egged Tour Excursion booklet ant the Hertz special convention price list, which are included in your briefcase.

RECONFIRMATION OF FLIGHTS All overseas participants must reconfirm their return flight at least 72 hours before departure. Please complete the form enclosed in your envelope and hand it over to the Peltours1 Hospitality Desk by Tuesday.

BALANCE OF PAYMENT FOR HOTEL ACCOMMODATION AND TOURS Participants who made their hotel reservations directly with Peltours must settle their account at the Travel Desk. It is recommended to do so not later than Tuesday, August 23.

SATELLITE SYMPOSIA Participants attending either the Quantum Biology and Pharmacology or the Many-Body Methods in Quantum Chemistry Symposia may reserve accommodation at the hospitality desk.

POST SYMPOSIUM TOUR B Participants who registered for the Post Symposium tour B to the Galilee (August 26-29), are requested to be ready for departure with their luggage at the hotel lobby on August 26, after breakfast and after having settled their extra charges with the hotel.

Sonesta/Knesset Tower 07:30 hrs Ramada Renaissance 07:45 hrs

ORGANIZERS & TRAVEL AGENTS Phone: (03) 650862 | Peltours - Conventions Telex: 33803, 35819 M, P.O.Box 394 Cable: PELTOURS TELAVIV J 61003 Tel Aviv Fax : (03) 660060 'I%

IX TIMETABLE

SUNDAY, AUGUST 21, 1988 16:00 Registration - Sonesta Hotel, Jerusalem 21:00 Get-together - Sonesta Hotel

MONDAY, AUGUST 22, 1988 08:00 Registration (cont'd) 09:00-10:00 Opening Session - Wise Auditorium 10:00-10:30 Coffee Break 10:30-11:45 Plenary Lecture I - Wise Auditorium 11:45-13:00 Plenary Lecutre II - Wise Auditorium 13:00-15:00 Lunch 15:00-18:00 The Commemorative Massimo Simonetta Symposium 16:30-17:00 Coffee Break 20:30 Reception at the Israel Academy of Sciences and Humanities

TUESDAY, AUGUST 23, 1988 09:00-10: 15 Plenary Lecture III - Wise Auditorium 10:15-10:45 Coffee Break 10:45-12:00 Plenary Lecture IV - Wise Auditorium 12:00-13:30 Lunch 13:30-15:00 Poster Session A 15:00-18:00 Symposium 1 - Hall A (Maizer Building) 15:00-18:00 Symposium 2 - Hall B (Maizer Building) 16:00-16:30 Coffee Break 19:45 Reception at the Israel Museum

WEDNESDAY, AUGUST 24, 1988 09:00-10:15 Plenary Lecture V - Wise Auditorium 10:15-10:45 Coffee Break 10:45-12:00 Plenary Lecture VI - Wise Auditorium 12:00-13:30 Lunch 13:30-15:00 Poster Session B 15:00-18:00 Symposium 3 - Hall A (Maizer Building) 15:00-18:00 Symposium 4 - Hall B (Maizer Building) 16:30-17:00 Coffee Brsak Free Evening 21:30 Optional Sound & Light Performance at the David Citadel

THURSDAY, AUGUST 25, 1988 09:00-10:15 Plenary Lecture VII - Wise Auditorium 10:15-10:45 Coffee Break 10:45-12:00 Plenary Lecture VIII - Wise Auditorium 12:00-13:00 Lunch 13:00-14:00 Poster Session C 14:00-16:30 Symposium 5 - Hall A (Maizer Building) 14:00-16:30 Symposium 6 - Hall B (Maizer Building) 16:30-17:00 Coffee Break 17:00-18:30 Closing Session - Wise Auditorium 20:30 Farewell Dinner at the Israel Parliament.

X CONGRESS PROGRAM

MONDAY, AUGUST 22, 1988 WISE HODITORIUM

09.00 - 10.00 OPENING SESSION Chairperson: A. PULLMAN Institut de Biologie Physico-Chimique Paris, France

Addresses: A. PULLMAN, President of the International Academy of Quantum Molecular Science Y. BEN-PORATH, Rector of the Hebrew University J. JORTNER, President of the Israel Academy of Sciences and Humanities

Commemoration: In honored memory of the late L. de Broglie - B. PULLMAN Nobel Prize Laureate and member of the Institut de Biologie Physico- Academy of Quantum Molecular Science Chemique Paris, France

In honored memory of the late R.S. Mulliken - J.A. POPLE Nobel Prize Laureate and member of the Carnegie-Mellon University Academy of Quantum Molecular Science Pittsburgh, USA

10.00 - 10.30 Coffee Break

10.30 - 11.45 PLENARY LECTURE I MOLECULAR QUANTUM MECHANICS Chairperson: P.-O. LOWDIN University of Florida Gainesville, USA

Analytic Second and Third H.F. SCHAEFFER, III Derivative Methods for Post- University of Georgia Hartree-Fock Wavefunctions Athens, USA

11.45 - 13.00 PLENARY LECTURE II INTERMOLECULAR FORCES Chairperson: G. HALL University of Nottingham England, UK

Intermolecular Forces from D.P. CRAIG the Viewpoint of Quantum Australian National University Electrodynamics Canberra, Australia

13.00 - 15.00 Lunch I

XI Monday, August 22, 1988

15.00 - 18.00 THE COMMEMORATIVE MASSIMO SIMONETTA SYMPOSIUM Chairperson* R. PAUNCZ The Technion, Israel Institute of Technology, Haifa, Israel

15.00 - 15.30 The Valence Bond Theory M. RAIMONDI Universita di Milano Milano, Italy

15.30 - 16.00 Structure and Reactions E.R. DAVIDSON in Some Organic Systems Indiana University Bloomington, USA

16.00 - 16.30 Experimental Studies of J. DUNITZ Charge Densities in ETH Zurich Molecules and Crystals Zurich, Switzerland

16.30 - 17.00 Coffee Break 17.00 - 17.30 Symmetry in Catalysis: L. SALEM Symmetry in Molecular Universite de Paris-Sud Crystals Orsay, France 17.30 - 18.00 Proteins: Dynamics and M. KARPLUS Functions Harvard University Cambridge, USA

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TUESDAY, AUGUST 23, 1988 09.00 - 10.15 PLENARY LECTURE III DENSITY FUNCTIONAL METHODS Chairperson: R.G. PARR University of North Carolina Chapel Hill, USA

The Density Functional M. LEVY Theory Tulane University New Orleans, USA

10.15 - 10.45 Coffee Break

XII Tuesday, August 23, 1988

10.45 - 12.00 PLENARY LECTURE IV MOLECULAR DYNAMICS Chairperson: R. HOFFMAN Cornell University New York, USA

Molecular Dynamics R.D. LEVINE The Hebrew University Jerusalem, Israel

12.00 - 13.30 Lunch

B.30 - 15.00 POSTER SESSION A PARALLEL SYMPOSIA

15.00 - 18.00 SYMPOSIUM 1 - HALL A MOLECULAR QUANTUM MECHANICS Chairperson: J. PALDUS University of Waterloo Waterloo, Ontario, Canada

15.00 - 15.30 Advances with the Mflller- N.C. HANDY Plesset Theory The University Chemical Laboratory Cambridge, England, UK 15.30 - 16.00 Coupled-Cluster Methods R.J. BARTLETT for Molecular Structure University of Florida and Spectra Gainesville, USA

16.00 - 16.30 Coffee Break

16.30 - 17.00 Structure, Elementary K. MOROKUMA Reaction and Catalytic Institute for Molecular Cycle of Organometallic Science Compounds Okazaki, Japan 17.00 - 17.30 On the Second-Order C.-C. SUN Reduced Density Matrices Jilin University Changchung, P.R. of China

XIII Tuesday, August 23, 1988

15.00 - 18.00 SYMPOSIUM 2 - MLL B VAN DER WAALS MOLECULES AND CLUSTERS Chairperson: M. KARPLUS Harvard University Cambridge, USA

15.00 - 15.30 Three Dimensional Quantum J.A. BESWICK Mechanical Studies of Universite de Paris-Sud Dissociation Dynamics of Orsay, France van der Waals Systems

15.30 - 16.00 Solvent Clusters: Structures, S. LEUTWYLER Order-Disorder Transitions Universitat Bern of Spectra Bern, Switzerland

16.00 - 16.30 Coffee Break

16.30 - 17.00 Quantum Chemical Predictions V. BONACIC-KOUTECKY About the Structure and Freie Universitat Berlin Properties of Small Metallic Berlic, F.R. of Germany and Covalent Clusters

17.00 - 17.30 Intermolecular Interactions P. HOBZA Between Large Systems Czechoslovak Academy of Sciences Prague, Czechoslovakia

17.30 - 18.00 From Isolated Molecules A. TRAMER Through Clusters to Universite de Paris-Sud Matrices Orsay, France

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WEDNESDAY, AUGUST 24, 1988 - WISE AUDITCHIUM

"t 09.00 - 10.15 PLENARY LECTURE V QUANTUM MECHANICS OF i" CHEMICAL REACTIONS Chairperson: i J. KOOTECKY Freie UniversitSt Berlin !. l'1 Berlin , F.G. of Germany 1 Quantum Theory of Chemical W.H. MILLER ; Dynamics: Reactive Scattering University of California | and Path Integrals Berkeley, USA •f 10.15 - 10.45 Coffee Break

XIV Wednesday, August 24, 19S8

10.45 - 12.00 PLENARY LECTURE VI KINETICS IN CONDENSED PHASES Chairperson: R.D. LEVINE The Hebrew University Jerusalem, Israel

Charge Transfer Reaction J.T. HYNES Dynamics in Solution University of Colorado Boulder, USA

12.00 - 13.30 Lunch

13.30 - 15.00 POSTER SESSION B

PARALLEL SYMPOSIA

15.00 - 18.00 SYMPOSIUM 3 - HALL A SIMULATION OF QUANTUM PHENOMENA Chairperson: I. SHAVTTT Ohio State University Columbus, Ohio, USA

15.00 - 15.30 Mirror-Potential Methods M.H. KALOS for Many-Electron Problems New York University New York, USA

15.30 - 16.00 Quantum Simulations of P. WOLYNES Electron Transfer University of Illinois Processes Urbana, USA

16.00 - 16.30 Molecular Reactions R.B. GERBER in Crystalline Solids The Hebrew University Jerusalem, Israel

16.30 - 17.00 Coffee Break

17.00 - 17.30 Quantum Chemistry Via Path U. LANDMAN Integrals and Real-Time Georgia Institute of Physics Dynamics Simulations Atlanta, USA

17.30 - 18.00 Equilibrium Structures and W. ANDREONI Finite Temperature Properties IBM Zurich Research Laboratory of Microclusters from ab-initio Ruschlikon, Switzerland Molecular Dynamics Simulations

XV Wednesday, August 24, 1988

15.00 - 18.00 SYMPOSIUM 4 - HALL B MOLECULAR SPECTROSCOPY Chairperson: D.P. CRAIG Australian National University Canberra, Australia

15.00 - 15.30 Higher-Order Centrifugal J.K.C. WATSON Distortion and Quartic National Research Council Potential Constants of Canada Ottawa, Ontario, Canada

15.30 - 16.00 The Role of Doubly Excited Ch. JUNGEN States in Molecular Rydberg Universite de Paris-Sud Spectra Orsay, France

16.00 - 16.30 Calculation of Lifetimes S.D. PEYERIMHOFF of Molecules in Universitat Bonn Excited States Bonn, W. Germany 16.30 - 17.00 Coffee Break

17.00 - 17.30 Overview of Pyrazine J. KOMMANDEUR University of Groningen Groningen, The Netherlands

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THURSDAY, AUGUST 25, 1988 - WISE AUDITORIUM

09.00 - 10.15 PLENARY LECTURE VII SURFACE PHENOMENA Chairperson: K. RUEDENBERG Iowa State University Ames, USA

The Concepts of Modern G. SOMORJAI Surface Science and University of California Heterogeneous Catalysis Berkeley, USA

10.15 - 10.45 Coffee Break

XVI Thursday, August 25, 1988

10.45 - 12.00 PLENARY LECTURE VIII QUANTUM BIOCHEMISTRY Chairperson: K. FUKUI Kyoto Institute of Technology Kyoto, Japan

Molecular Mechanisms.of B. PULLMAN Specificity in DNA- Institut de Biologie Physico- Antitumor Drug Chemique Interactions Paris, France

12.00 - 13.00 Lunch

13.00 - 14.00 POSTER SESSION C - PARALLEL SYMPOSIA

14.00 - 16.30 SYMPOSIUM 5 MOLECULAR DYNAMICS Chairperson: M. SHAPIRO The Weizmann Institute of Science Rehovot, Israel

14.00 - 14.30 Dynamics of Weakly M.S. CHILD Bound Systems University of Oxford Oxford, England, UK 14.30 - 15.00 How to Control Chemical P. BRUMER Reactions with Lasers University of Toronto Toronto, Canada 15.00 - 15.30 Optical Spectroscopy R.L. WHETTON and Excitation Dynamics University of California of Large Molecular Clusters Los Angeles, USA 15.30 - 16.00 Time Dependent Quantum R. KOSLOFF Mechanical Methods for The Hebrew University Molecular Dynamics Jerusalem, Israel

16.00 - 16.30 Quantum Rate Constants J.C. LIGHT Using a Discrete University of Chicago Representation and the Chicago, USA Flux-Flux Autocorrelation 16.30 - 17.00 Coffee Break I

XVII Thursday, August 25, 1988

14.00 - 16.30 SYMPOSIUM 6 - HALL B THEORETICAL ORGANIC AND INORGANIC CHEMISTRY Chairperson A. VEILLARD University Louis Pasteur Strasbourg, France

14.00 - 14.30 Some Applications of the A.J. STONE Tensor Spherical Harmonic The University Chemical Theory to Properties of Laboratory Cluster Molecules Cambridge, England, UK.

14.30 - 15.00 New Theoretical Ideas and J.K. BURDETT the Structures of Solids University of Chicago Chicago, USA

15.00 - 15.30 Mechanistic Analysis of M. NEWTON Electron Transfer Kinetics: Brookhaven National The Role of the Electronic Laboratory Structure Theory Upton, L.I., New York, USA

15.30 - 16.00 The Electronic States and J. MICHL Photochemical Behavior of University of Texas Alkylated Polysilanes Austin, Texas, USA

16.00 - 16.30 Organic Reactions and W. JORGENSEN Interactions in Solution Purdue University West Lafayette, Indiana, USA

16.30 - 17.00 Coffee Break

17.00 - 18.30 CLOSING SESSION - WISE SIXTY YEARS SINCE THE AUDITORIUM HEITLER-LONDON PAPER Chairperson: J.A. POPLE Carnegie-Mellon University Pittsburgh, USA

The Origin, Development and W. KOLOS Significance of the Heitler- University of Warsaw London Approach Warsaw, Poland

CLOSING OF SYMPOSIUM

XVIII ABSTRACTS

I; POSTER SESSION A A-l ISOSCALAR FACTORS FOR MULTISHELL CALCULATIONS

A. NOVOSELSKY, M. VALLIERES, J.-Q. CHEN, R. GILMORE

DEPARTMENT OF PHYSICS & ATMOSPHERIC SCIENCE

DREXEL UNIVERSITY, PHILADELPHIA. PA 19104

JACOB KATREL

DEPARTMENT OF CHEMISTRY, TECHN10N - HAIFA 32000. ISRAEL

The algorithm of Bayman and Lande for computing single shell CFPs for Fermions (or Bosons) has been extended in three ways. First, the symmetry restriction to Fermions or Bosons has been relaxed, and CFPs between N-l and N particle states of arbitrary permuta- tional symmetry have been constructed. This allows efficient computation of CFPs for identical particles which carry two or more quantum numbers of angular momentum, or other unitary, type (e.g., Is, l-s-t) since much smaller computations are carried out separately within each subspace and combined only after their completion using permutation group Clebsch-Gordan coefficients. This procedure is described by J. Katriel in this conference. Second, matrix elements of single particle creation and annihilation opera- tors have been constructed between states of arbitrary permutational symmetry. These are used for the efficient construction of operator matrix elements between N-l and N particle Fermion (or Boson) states when each particle carries two or more quantum numbers of unitary type. A 'sum over path overlaps' method has been developed to construct matrix elements of products of single particle creation and annihilation operators. This procedure is described by A. Novoselsky in this conference. Third, restriction to a single shell has also been relaxed. This is done by computing the isoscalar factors for the permutation group using a variant of the Bayman-Lande method. In this variant, the operators diagonalized are class sums of two particle interchanges for the permutation group rather than second order Casimirs for the continuous groups. Since only the permutation group is involved, the results-are not restricted to shells with small angular momentum. Phase relations among the isoscalar factors have been systematically determined. This algorithm allows efficient multi- shell calculations required for configuration-interaction computations. A-2

MATRIX ELEMENTS OF STANDARD OPERATORS

IN THE L-S COUPLING SCHEME

AKIVA NOVOSELSKV. MICHEL VALLIERES. ROBERT GILMORE

DEPARTMENT OF PHYSICS AND ATMOSPHERIC SCIENCE

DREXEL UNIVERSITY, PHILADELPHIA . PENNSYLVANIA 19104

JACOB KATRIEL

DEPARTMENT OF CHEMISTRY. TECHNION, HAIFA 32000. ISRAEL

A new efficient algorithm for the calculation of standard one- and two-body operators in an L-S coupling scheme is presented. The second quantization formalism is used. Creation (annihilation) operators between states of mixed symmetry in the L (S) subspace are defined propotional to the CFPs between the two appropriate mixed symmetry states. The CFPs for mixed symmetry states are computed via a new and efficient method proposed by our group, reported here by Jacob Katriel. One- and two-body matrix elements are calculated separately in the L and S subspaces using the matrix elements of the creation (annihilation) operators. The matrix elements are then combined to yield L-S matrix elements by using Clebsh-Gordan coefficients of the permutation group and a new scheme of "sums over path overlaps". The computer code impit.nenting this algorithm calculates the matrix dements for shell-model calculations in the largest practical / shell with spin two orders of magnitude faster than the traditional state of the art codes. A-3 COEFFICIENTS OF FRACTIONAL PARENTAGE IN THE L-S COUPLING SCHEME A. NOVOSELSKY, J. KATRIEL* AND R. GILHORE DEPARTMENT OF PHYSICS AND ATOMSPHERIC SCIENCE DREXEL UNIVERISTY, PHILADELPHIA, PENNSYLVANIA 19104

An efficient procedure for the evaluation of the coefficients of frac- tional parentage (cfp's) for L-S coupled wavefunctions is presented. The cfp's are calculated separately for N particles, each with angular momentum I (s), coupled into a total angular momentum L (S). The N particle states formed can belong to any permutational symmetry. The procedure for the evaluation of the L and the S cfp's for arbitrary permutational symmetry is a generalization of the procedure proposed by Bayman and Lande for symmetric and antisymmetric states. It involves the construction and diagonalization of the matrices representing the quadratic Casimir operators for the appropriate special unitary and symplectic (or ortho- gonal) groups. The cfp's of the antisymmetric L-S coupled states are obtained in terms of products of cfp's for L and S corresponding to conju- gate representations of the symmetric group. This method is demonstrated to provide cfp's for L-S states for systems with a considerably larger number of particles than is feasible using the procedures heretofore available.

* Permanent address: Department of Chemistry, Technion - Israel Institute of Technology, 32000 Haifa, Israel A-4 TIGHT UPPER AHD LOWER BOUNDS TO THE SCHRODINGER EQUATION EIGEN-

VALUES

P.M. FERNANDEZ and E.A. CASTRO

Institute de Investigaclones Fisicoqulmicas Tefiricas y Aplicadas

(INIFTA), Facultad.de Cienclas Exactas, Universidad Nacional de

La Plata, Casilla de Correo 16, Sucursal 4, (1900} La Plata,

ARGENTINA

The purpose of this communication is to present a method for obtaining rapidly convergent upper and lover bounds to the Schrodigner equation eigenvalues. The procedure consists of wrl_t ing the logarithmic derivative of the wavefunction as a Pa.de approximant:. The coefficients of the denominator polynomial are obtained from a system of homogeneous linear equations and the roots of its determinant prove to be the above mentioned bounds. The method applies to one-dimensional and central—field models. A number of numerical examples are shown. A-5 CHARGE DENSITY BY THE USE OF THE HILLER-SUCHER-FEINBERG IDENTITY. PERTURBATIVE CORRECTIONS AND CONFIGURATION-INTERACTION EFFECTS

KAZUHIRO ISHIDA DEPARTMENT OF CHEMISTRY, FACULTY OF SCIENCE, SCIENCE UNIVERSITY OF TOKYO

The configuration-interaction (CI) calculations are carried out for He atom and several molecules in order to obtain the value of the charge density at the nucleus by the use of the Hiller-Sucher-Feinberg (HSF) identity. The HSF density can be also calculated with the double perturbation theory based on the M011er-Plesset-type theory and also on the Epstein-Nesbet- type. It is found that each value of these perturbative cor- rections (to the second-order with respect to the electron cor- relation effects) is very similar to that of the correction by the CI with single and double electron excitations for all of the present atom and molecules. Especially for the He atom, the HSF density by the full-CI wave function is in excellent agreement with the exact value to three significant figures. It can be shown that the superiority of the HSF density over the usual delta-function-type density Is excellently confirmed.

Key References 1) K. Ishida, Int. J. Quantum Chenw , 28^, 349 (1985).

2) K. Ishida, Int. J. Quantum Chem.t 3£, 543 (1986). 3) K. Ishida, Int. J. Quantum Chem. (to be published). A-6 TRENDS OF OSCILLATOR STRENGTHS IN THE LITHIUM ISOELECTRONIC SEQUENCE

C. BARRIENTOS, I. MARTIN and E. CHARRO DEPARTAMENTO DE QUIMICA FISICA. FACULTAD DE CIENCIAS. 47005 VALLADOLID. SPAIN

The study of atomic transition probabilities in highly ionized atoms is a subject of considerable interest for many fields, For example in studies of controlled thermonuclear reactions and in astrophysical studies. Selective searches have revealed many systematic trends of atomic tran- sition probabilities along isoelectronic sequences. These regularities are of great practical importance since they may be used for several applications: to estimate uncertainties in the data, to improve existing data and to find additional numerical data by simple interpolation and extrapolation techniques. Recently, the theoretical study of properties related to atomic transition probabilities in alkali-like systems has grown because of the continuing im- portance of the core polarization effects in systems with one valence-electron outside the spherical core. Since it was shown that the oscillator strengths for electric dipole tran- sitions in atoms calculated from exact wave functions could be written in several equivalent forms, there has been a controversy over which form to use for approximate calculations. In this communication we present oscillator strengths, for the principal series, of a number of elements (Lil-SiXII) in the lithium isoelectronic se- quence, evaluated through the Quantum Defect Orbital (QDO) method (1). The QDO formalism, based upon the exact solution of the one-electron SchrUdinger equation containing an effective potential, has been previously applied to the study of several atomic properties (i.e. 2-6), and in spite of its sim- plicity it offers a sensible compromise between easiness of calculation and accuracy of results. Oscillator strengths were computed in three ways: from the length and velocity forms of the dipole transition moment and with explicit inclusion of core-polarization effects in the transition moment operator. In addition, we have studied the systematic behaviour of the f-values along the lithium isoelectronic sequence. A comparison of our oscillator strengths with available values and a detailed study of the trends of f-values along the sequence show that the results are reliable. From the graphs presented, it is possible to derive new values either for ions not considered or for types of transitions not studied in this work.

(1) G. Simons, J. Chem. Phys. 60 (1974) 645 (2) I. Martin and G. Simons, J. Chem. Phys. 62 (1975) 4799 (3) I. Martin and G. Simons, Mol. Phys. 32 (1976) 1017 (4) C. Barrientos and I. Martin, Can. J. Phys. 63 (1985) 1441 (5) I. Martin and C. Barrientos, Can. J. Phys. 64 (1986) 867 (6) C. Barrientos and I. Martin, Can. J. Phys. 65 (1987) 435 A-7 PSEUDOPOTENTIAL INVESTIGATION OF SOME ALKALI METAL MOLECULES

I. TAMASSY-LENTEI and A. DERECSKEI-KOVACS Institute of Theoretical Physics Kossuth Lajos University H-4O1O Debrecen, Hungary

The alkali metal elements play very important part in the chemistry. Investigation was performed for the ground state of some alkali dimer and alkali hydride mo- lecules using the pseudopotential method. In this appro- ximation the core and valence electrons of the atom are treated separately, so the alkali atoms are considered as one-electron systems. At present they are described by a simple analytical pseudopotential; the dimers are two- electron systems. This approach simplifies the quantum- mechanical description very much. According to the variational method different floa- ting-type wave functions completed with correlated fac- tors were applied. The consideration of the electron- . correlation proved to be very important. jj Geometrical data, electronic structures, stabilities J of the systems were determined for the ground state of the alkali metal molecules. A-8 Accurate Numerical Study of the RHF Energy Bands and Density of States of Regular and Alternating Infinite Chains of Hydrogen Atoms. J.G. FRIPIAT. J. DELHALLE, J.M. ANDRE, Jl. CALAIS Laboratoire de Chinrie Thdorique Appliqu6c Facultes Universitaires N.D. de la Paix, Namur (Belgium)

The RHF formalism, either at the full db initio level or transcribed in logically related approximate schemes (e.g. PPP,CNDO, INDO, MNDO, etc.), is fundamentally inappropriate to study cases with partially occupied bands. In the RHF Scheme, the orbital energy of the uppermost partially filled bands has an infinite derivative at the Fermi energy which yields a vanishing (unphysical) DOS at the Fermi energy. This behavior of the RHF approximation, well known for the electron gas and the nearly-free electron (NFE) gas, was recently reinvestigated to trace its roots by Monkhorst1 and by Delhalle and Calais^ who have found that the pathology is due to the combination of two factors: the discontinuous character of the occupation function and the long-range nature of the Coulombic interactions. A formal analysis has shown that the k-dependent exchange lattice sums occuring in the RHF formalism belongs to the class of the kernel series which exhibit strong variations with respect to k in the vicinity of the Fermi level, and require huge numbers of terms to let the singular behavior at the Fermi level fully develop. Appropriate techniques will be described to conduct all the involved summations • (Coulomb and exchange) to their limit These procedures are applied to infinite chain of \ H atoms and H2 molecules and provide efficient and reliable tools to render obsolete \ the empirical and unsettled procedure of guessing the number of interactions to be IS U included in actual calculations.

1. H.J. Monkhorst, Phys. Rev. B 20,1504 (1979). 2. J. DelhaUe and J.L. Calais, J. Chem. Phys., 85,5286 (1986). J. DelhaUe and JX. Calais, Phys. Rev., B 35,9460 (1987). A-9 CONVERGENCE OF FINITE CHAIN APPROXIMATION FOR LINEAR AND NON-LINEAR POLARIZABILITIES OF POLYMERIC POLYENES

BERNARD KIRTMAN

DEPARTMENT OF CHEMISTRY

UNIVERSITY OF CALIFORNIA, SANTA BARBARA, CA. 93106, USA

ABSTRACT

Static longitudinal polarizabilities, azz, and hyperpolarizabilities, 7ZZZZ, are determined for finite polyene chain models of polyacetylene, polydiacetylene and polybutatriene. For small chains, comparison with ab initio calculations shows very good agreement. The convergence with chain length of azz/N and, particularly, 7ZZZZ/N is slow with polybutatriene being the worst offender. At 62 carbons the deviation from the limiting infinite N value is still substantial. For the hyperpolarizability there can be orders of magnitude difference between our values and PPP results even when the chains are small.

. i

!r * A-10 MULTIPHOTON BOUND-BOUND ELECTRONIC TRANSITIONS OF H2O: A THEORETICAL INVESTIGATION V. GALASSO DIPARTIMENTO DI SCIENZE CHIMICHE, UNIVERSITA' DI TRIESTE, 1-34127 TRIESTE (ITALY)

The low-lying electronic excited states of H2O, when accessed by multiphoton absorption, have been investigated at ab-initio level utilising RPA vertical transition energies and amplitudes obtained with a large Gaussian-type orbital basis set, [4s3pld| 3slp] + 5s5p4d diffuse functions on oxygen, and performing appropriate rotational averages in order to take random orienta- tion of the molecules into account. The transition probability coefficients W for two-, three-, and four-photon single-frequency absorption from plane (P) polar- ised, circularly (C) polarised, and unpolarised (U) light and the polarisation ratios Q =(C)/(P) have been calculated. The W_ 2 values are spread over a larger interval than W_ f^_O (4) f« O and W . The most intense transitions are calculated for excitation to the 3 Ax (two-photon), 2 Az and 3 Bx (three- photon), and 2 Alt 2 B1, 3 Bx, and 4 B2 (four-photon) states. Irrespective of the number of absorbed photons, all the transi- tions to A^ excited states show considerably different polar- isation ratios. The molecular response to simultaneous, concerted absorption of two and three photons from two laser beams under various polar- isation conditions has been also examined as a function of the laser frequencies. Unlike in the double-beam two-photon experi- ment, no frequency of (near-)true transparency is predicted for the excitation channels in the double-beam three-photon experi- ment. The resonant peaks in three-photon absorption are expect- ed to be narrower than in the case of two-photon absorption. The different variation of the various polarisation ratios pro- vides further experimentally observable features that can be used to verify the location of the excited states.

10 A-ll

COMPLETION OF LOW-ENERGY e-N2 SCATTERING CALCULATIONS

USING THE HYBRID THEORY

C. A. Weatherford* and A. Temkin** •Department of Physics, Florida A. & M. University, Tallahessee, Florida, U.S.A.

**Laboratory for Astronomy and Solar Physics, NASA/Goddard Space Flight Center Greenbelt, Maryland, U.S.A.

We shall exhibit final results of a hybrid theory calculation of low energy electron scattering from the ground electronic state ( Eg*) of N£. The calculation embodies all the developments we have made over the years starting from the hybrid theory itself,*• in which dynamical aspects of vibrational motion are simultaneously included with adiabatic aspects of rotational motion both in the formal expressions for the scattering amplitude as well as the equations, wherein the fixed-and adiabatic-nuclei approximations are intermixed with vibrational close coupling. The present calculation incorporates the non-iterative partial differential equation-technique* together with non-iterative exchange^ and a static e-N2 potential based on an MCSCF ground state^ and a polarization potential generalized from the recent calculation of Morrison et al. We expect our final (15 vibrational closely coupled state) calculation to refine our presently completed 10 state calculation,^ and confirm its main conclusion: giving for the first time the correct peak to valley ratio of the substructure of the ng resonance (centered at 2.4 eV). We also hope that it will resolve the discrepancy that now exists in experimental results'.° at very low energy (E

1. N. Chandra and A. Temkin, Phys. Rev. A 13, 188 (1976) 2. E. C. Sullivan and A. Temkin, Comp. Phys. Comm. 25, 97 3620 (1985) 3. C. A. Weatherford, K. Onda, A. Temkin, Phys. Rev. A 11 4. C. A. Weatherford, F. B. Brown, A. Temkin Phys. Rev. A 35, 4561 '; (1987) 5- 5. M. A. Morrison, B. C. Saha, T. L. Gibson, Phys. Rev. A 36, 3682 (1987) I 6. C. A. Weatherford and A. Terakin, Proc. of 15th ICPEAC Satellite

11 A-12

THEORETICAL COLLISION SPECTROSCOPY INVOLVING ALIGNED AND ORIENTED ATOMS

P.SALAS+, C.COtJRBIN* and P.WAHNON+

+DEPT. DE QOIMICA, E-T .S . I.TELECOMUNICACION UNIVERSIDAD POLITECNICA DE MADRID, 28040 MADRID SPAIN *LPOC, UNIVERSITE DE PARIS VI, 75005 PARIS PRANCE

The aim of this investigation is to study collision proce- sses in which the initial angular momentum of the active elec- tron can be completely controlled. This project has been initiated in the frame of an Euro— pean Collaboration Program of Research devoted to the study of electronic transition like direct excitation, electron capture and electron detachment induced in collisions involving initia Lly prepared excited targets in the medium energy range. For the both systems investigated presently here: (1) H+ + Na*(3p,m) *• H*(n=2) + Na+ AE = 0.36 eV. 2 2 (2) He(ls ) + Na*(3p,m) »- Heds ) + Na(3s) AE = 2.1 eV. v only the reaction (1) is experimentally in progress now [1 ] . The available results disagree with recent calculations [2] of total cross sections for charge transfer from Na(3s) to H(2p) and Na(3p) to H(2p). In the present work we use a model poten- tial method [2jto calculate total and differential cross sec- tions, by including rotational coupling and Stark effect due to degenerate final states of H. The relative importance'of this long-range processes against direct dynamical charge transfer must be considered. For the reaction (2) a simple model has been recently pro- posed [4]to predict excitation/deexcitation probabilities by using a stationary phase argument, obtaining a "propensity ru- le" which predicts that for a given impact parameter the deex- citation of Na (3p) is small for one and large for the other one of the two orientations of the atom, near the excitation maximum. It is interesting to see to which degree a more ela- borate model will confirm or modify this result. We are perfor ming accurate calculations of ab-initio adiabatic potentials . energies and coupling matrix elements to determine the rele-- | vant electronic wave functions and to solve the close coupling j equations that yield the scattering amplitudes [3] . •'

REFERENCES ' [l] T.Royer,D.Dowek,J.C.Houver,J.Pommier, XV ICPEAC, Brighton • (England), book of abstracts, 110 (1987) ;, t2] R.J.Allan, J.Phys. B 19_ 321 (1986) j [3] P.Wahn<5n,P.Salas,C.Courbin, Z.Phys. D (1988) (accepted) ill [4J N.Andersen,S-E.Nielsen, Z.Phys. D, At.Mol. and Clusters i j> 309 (1987) 1 12 A-13 A CLASSICAL PATH APPHDACH TO REACTIVE SCATTERING.

G.D. BILLING CHEMISTRY LABORATORY III H.C. 0RSTED INSTITUTE UNIVERSITY OF COPENHAGEN 2100 COPENHAGEN 0, DENMARK

AND

J.T. MUCKERMAN CHEMISTRY DEPARTMENT BROOKHAVEN NATIONAL LABORATORY UPTON, NY 11973

A new classical path method for treating reactive three-body collisions has been formulated by the use of hyperspherical coordinates. These coordinates allow a definition of a classical and quantum subsystems which makes it possible to extend the classical path approach to reactive systems. Thus only that part of the system which asymptotically defines the correct spectroscopic eigenstates in the rearrangement channels is quantized. The remaining degrees of freedom are treated classically. As a result the quantum mechanical part of the problem reduces to a 2D problem. Total and state to state reactive cross sections will be presented for the D + H-- system.

References. J.T. Muckerman, 3.D. Gilbert and G.D. Billing. A Classical Path Approach to Reactive Scattering. I. Use of hyperspherical Coordinates, J.Chem.Phys. (in press). G.D. Billing and J.T. Muckerman A Classical Path Approach to Reactive Scattering. II. Apparatous for 3D applications. III.Reactive state to state cross sections for the D + H- system.

13 A-14 THE SOLVENTS INFLUENCE ON THE ELECTRONIC BAND, AT 281.6 n»,IN THE VAPOUR SPECTRUM OF ORTHQ - TOLUIDINE

TASILE HAG0V5I MIRCEA BUCUR, AND MARCEL OLTEAN

THE PHYSICAL CHEMISTRY LABORATORY THE FACULTY OF TSCHNOLOOICAL CHEMISTRY THE FOLITECHNICAL INSTITUTE,IASSY,ROUMANIA

The shifts in 27 solvents ef the electronic band, at 281.6 nm, in the vapour spectrum of ortho - toluidine are •easured* One try t» explain the shifts »y the intervention ef different kinds ef the solute - solvent interactions. The ••served displacements are compared with those calculated on the basis ef the McRao's theory /J.Phys.Chem.. Q , §62 (1957)/, and the anomalies are interpreted, Finally7~"the dipole moment ef the solute molecule in the excited state is evaluated,as a principal index ef reactivity.

14 A-15 The change in the dressed potential of a polyatomic molecule in intense photon fields: Simple rules based on the Nuclear Charge-Mass ratio

Nakaya Saito and George G. Hall

Division of Molecular Engineering- Faculty of Engineering, Kyoto University, Sakyo-ku, Kyoto 606, Japan

Abstract: An explicit expression for the dressed potential of a polyatomic molecule, in the adiabatic approximation, is derived. This expression clearly shows the importance of the nuclear charge-mass ratio (NCMR) for the change of potential due to photon fields. It is found from a simple calculation that the H atom is the only atom having an abnormal NCMR value, whereas all other atoms have similar or the same values. This means that only those molecules contain a H atom should ; be strongly affected by fields. On the basis of this new- physical insight, we postulate two rules, which enable us to ; classify molecules, in respect to their response to intense =? photon fields, into three classes: high-sensitive,low-sensitive I and insensitive molecules. Qualitative verification is also f given by using water isotopes. 3

is A-16 ANHARMONICITY EFFECTS ON THE VIBRATIONAL PREDISSOCIATION

3 OF THE Ne-I2(B H*,V) COMPLEX: A CLOSE-COUPLING INFI- NITE ORDER SUDDEN TREATMENT*.

G. DELGADO-BARRIO, 0. RONCERO, J. CAMPOS-MARTINEZ, A.M. CORTINA and P. VILLAREAL.

Institute de Estructura de la Materia, CSIC

Serrano, 123; 28006 Madrid, Spain

ABSTRACT. A model previously applied [13 to study the vibra- tional predissociation (VP) of the He-Ij^v), is exten- ded here to treat the VP of Ne-I2(B,v) in the region of initial vibrational excitations 28£v£ 34. Due to the an- harmonicity channel for VP,.dv=-1, becomes energetically forbidden. This gives rise to oscillations of the VP rate as function of v that, therefore, no longer follows the typical superlinear behaviour shown in the low diatomic excitations regime.

1 G, Delgado-Barrio, P. Mareca, P. Villareal, A.M. Cortina and S. Miret-ArtSs J. Chem. Phys., 84 (1986) 4268

16 A-17

A QtJANTAL STUDY OF THE RESONANCES IN THE Na-N2 SYSTEM

S. MIRET-ARTES, G. DELGADO-BARRIO, J. CAMPOS-MARTINEZ and P. VILLAREAL-HERRAN

Institute de Estructura de la Materia CSIC. Serrano, 123 28006 Madrid Spain

ABSTRACT In this work we study the rolejOf the resonances for the electronic quenching of Na( P) by N- in the T-shape configuration. The position of the resonances that appears in this collision and also their lifetimes are estimated by different quantal approaches. The approximations consist of a diabatic -CI model for obtaining the po- sitions. Afterthat, by using the golden rule expression the corresponding widths are obtained. Different re- suts are presented when the continuum-continuum — interaction is included or not.

17 A-18 DYNAMICAL AND SPECTROSCOPIC STUDY OF NON-RIGID MOLECULES. APPLICATIONS

TO THIOACETALDEHYDE AND THIOACETONE

Y.G. SMEYERS, A. NINO and M.N. BELLIDO

INSTITUO DE ESTRUCTURA DE LA MATERIA

SERRANO, N2 119, E-28006-MADRID, SPAIN.

Abstract

The phosphorescence spectra of thioacetaldehyde and thioacetone ex- hibit two long progressions that were attributed to two large amplitude out-of-plane modes, corresponding to the methyl torsion, and aldehydic hydrogen or carbonyl sulfur wagging. In order to study the internal dynamics of these molecules, the non- rigid groups for the methyl rotation and aldehydic hydrogen wagging in thioacetaldehyde, and for the two methyl rotation and carbonyl sulfur wagging in thioacetone, are deduced, as well as their character tables. From the symmetry properties of these motions, symmetry adapted functional forms are deduced. The potential energy surfaces are then calculated numerically resor- ting to electronic ab initio calculations, in the U-31G + d orbitals on the sulfur atom, in the RHF approximation for the singlet ground states, and in the UHF one for the first triplet excited states. Large conforma- tional and geometrical changes are observed with the excitation. The results are fitted to the symmetry adapted functional forms by a multiple regression method. From the character tables, the symmetry eigenvectors which diagonalize the Hamiltonian matrix in boxes, are deduced. The Schrodinger equations for the nuclear motion are then solved (in two dimensions) developing the solutions in the symmetry eigenvector basis. From the vibrational-torsional wave-functions of both fundamental and excited states, the Franck-Condon factors are deduced. Finally, from the Franck-Condon factors and the energy level differences, the phospho- rescence spectra of thioacetaldehyde and thioacetone are theoretically reconstructed, and compared with the experimental data. A reasonable agreement is encountered.

Bibliography Y.G. Smeyers and M.N. Bellido, Int. J. Quantum Chem., 19, 553 (1981) Y.C. Smeyers and A. Nino, J. Comp. Chem., 8, 381 (1987). Y.G. Smeyers, A. Nino and M.N. BelJido, Theoret. Chim. Acta, in press.

18 A-19 PROTON TRANSFER AND SOLITONIC EXCITATIONS IN HYDROGEN BONDED

SYSTEMS

H. CHOJNACKI, P. MISIAK, M. PYKA

INSTITUTE OF ORGANIC AND PHYSICAL CHEMISTRY, 1-4 WYB. WYSPIANSKIEGO 27, 50-370 WROCLAW, POLAND

The sequential and parallel proton transfer mechanism has been studied for some model hydrogen bonded systems. The results of quantum chemical calculations for linear one-dimensional chains and cetrosymmetric dimers distinctly show that the proton displacement within hydrogen bridges has to be considered as a coupled non-linear process. The influence of the crystal lattice on the proton motion has been considered as well. It seems to lead to the lowering of the potential barrier in the case of linear hydrogen bonded systems, whereas no essential changes in the potential shape was found for cyclic dimers. For interpretation of the charge transfer mechanism along the hydrogen bonded chains, the soliton model is invoked [1]. In the following paper dynamics of the proton motion in discrete finite chain has been analysed by numerical integration of equation of motion assuming different potential shape for the hydrogen bridges [2, 3, 5]. It was found that solitonic excitations are more stable with the Toda potential [4J than those with the harmonic interactions. The role of asymmetry of the potential barrier for the proton displacement has also been considered within the solitonic model.

[1] A. S. Davydov, Solitons in Molecular- Systems, Reidel, Dordrecht 1985. [2] Y. Kashimori, F. Chien, K. Nishimoto, Chem. Phys., 1O7. 389, 1986. [3] P. Misiak, H. Chojnacki, Theochem, in press. [4] M. Toda, Theory of Nonlinear Lattices, Springer, New York, 1981. [5] M. Peyrard, S. Pnevmatikos, N. Flytzanis, Phys. Rev., 36, 903, 1987.

19 A-20 OFF-CENTER SMALL POLARONS PI. GEORGIEV INSTITUTE OF SOLID STATE PHYSICS BULGARIAN ACADEMY OF SCIENCES 72 LENIN BLVD., 1784 SOFIA, BULGARIA

In his pioneering work on the small polaron, Kolstein had shown that coupling to an asymmetric intramolecular vibration could split the vibronic potential energy into a double-well potential type El]. This suggestion is now extended further by considering the vibronic mixing of two newly-degenerate diffe- rent-parity eigenstates of the polaron Hainiltonian in the loca- lized limit by virtue of the coupling to an odd vibrational mode (the pseudo-Jahn-Teller effect). As the coupling strength is gradually increased, strong mixing occurs which changes abruptly the shape of the vibronic potential energy curve from single to double well. At this instant an electric dipole occurs related to the eonfigurational transfigurement from centrosymmetric to noncentrosymmetric with the underlying pari- ty nonconservation. Its magnitude first increases but then sa- turates, as the Jahn-Teller energy (E™) is increased. The occurrence of a vibronic electric dipole associated with a small polaron can have a profound effect on the dielectric, transport, and optical properties of the host crystal. Estima- tes made for superconducting perovskites have yielded dipole magnitudes of several tens of Oebye pertinent to a s-p mixing. The associated off-center instability can reorientate through interwell tunneling or move across the crystal via a related translational mechanism. Neighboring off-center polarons can bind to form bipolaron molecules by virtue of dipole-dipole coupling of considerable magnitude LZ1 . Bipolaron formation may bring about superconductivity to the specimens. On the other hand, both the off-center instability and the related vibronic dipole are destroyed on optical excitation above a threshold energy of 4B_ which raises the vibronic system to an excited centrosymmetric hybrid electronic state. Specific problems related to the translational and rotational masses of itinerant off-center uni- and bi- polarons will also be dis- cussed. 1. T. Holstein, Ann. Phys. 8, 3*3 U959)- 2. M. Borissov and M. Georgiev, Z. Physik B (in press).

20 A-21 VIBRATIONAL SPECTRA OF GERMANE AND METHYL GERMANE : HARMONIC FORCE FIELD AND IR INTENSITIES FROM AB INITIO SECOND ORDER PERTURBATION THEORY

JAVIER FERNANDEZ-SANZ : DEPARTAMENTO DE QUIMICA FISICA FACULTAD DE QUIMICA SEVILLA - SPAIN AND CLAUDE POUCHAN : UA 474 - UNIVERSITE DE PAU 64000 PAU - FRANCE

The vibrational spectra and the associated harmonic force fields for germane and methyl germane have been calculated from ab initio second order perturbation theory using an effective core potential to describe the inner shell of Ge and Double ^ plus polarization basis sets for the valence electron. These calculations are completed at H.F. level by the determination of the I.R. intensities. Theoretical results agree with experiment for both molecules. A combination of experimental and theoretical values allows to propose the best available force field for methyl germane.

21 A-22

Title; THE LIPPMANN-SCHWINGER EQUATION FOR OBTAINING THE CONTINUUM ORBITAL IN AUGER PROBLEMS. APPLICATIONS TO ATOMIC AND MOLECULAR SPECTRA

Authors; RENATO COLLE, ALESSANDRO FORTUNELLI and STEFANO SIMONUCCI

Affiliationst SCUOLA NORMALS SUPERIORE, 56100 PISA, ITALY

and

ISTITUTO DI CHIMICA QUANTISTICA ED ENERGETICA MOLECOLARE DEL CNR, VIA RISORGIMENTO 35, 56100 PISA, ITALY

Abstract: A new method is proposed for obtaining the conti- nuum orbital representing the emitted electron in Auger problems, through the use of a Lippmann- Schwinger equation. The method has been tested by calculating the KLL Auger spectrum of atomic Ne and used to interpret the Auger spectrum of the LiF molecule. fr References: 1) R. Colle, A. Fortunelli and S. Simonucci I II Nuovo Cimento (1988) in press. ' 2) R. Colle, A. Fortunelli and S. Simonucci | Europhysics Letters (1988) submitted. i 3) R. Colle, S. Simonucci and T.O. Woodruff '* Phys. Rev. A (1988) in press. t

22

i-.!*•'• A-23 THE STOCHASTIC THEORY ANO ITS RELATIONS TO THE GENERAL REACTION RATE THEORY S.G. CHRISTOV INSTITUTE OF PHYSICAL CHEMISTRY BULGARIAN ACADEMY OF SCIENCES 1040 SOFIA, BULGARIA The simple classical one-dimensional stochastic model of Kramers £1] for an adiabatic decay reaction in solution has been extended to include many-dimensional systems [2-53 and non-adiabatic effects [6-8]. Some quantum generalizations of the stochastic theory are also made recently C9-H3 • The aim of the present paper is to show that these results follow directly from a general reaction-rate theory [12,131, based on quantum collision theory and statistical physics. For the purpose use is made of a many-frequency oscillator model [1^] that comprises the "reacting system" and the "medium" in a unique system. In this way it is shown that a quantum genera- lization of the stochastic theory is possible only at relative- ly high temperatures at which the nuclear tunneling plays only a moderate role. Below a well-defined temperature that determi- nes the range of large tunneling the distinction between "reac- tant" and "medium" completely loses its physical meaning so that.the stochastic approach becomes inapplicable. In this temperature range a full quantum-mechanical treatment of the entire system (reactant + bath) in the framework of the general reaction-rate theory is necessary [12-143. 1. H.A. Kramers, Physica 2, 284 (19^0). 2. R. Landauer and J.A. Swanson, Phys. Rev. 121, 1668 (I96I). 3. L.S. Langer, Ann. Phys. (N.Y.) 5J£. 258 (1959). 4. I.y. Alexandrov, Chem. Phys. il, ^9 (I98O). 5- L.D. Zusman, Chem. Phys. 42, 295 (I98O). j 6. J.L. Skinner and P.G. ..Wolynes, J. Chem. Phys. 62, 21^3 (I978) s 7' B.I. Yakobson and A.I. Burstein, Chem. Phys. ^2, 385 (I98O). 8. B.L. Terable, H.L. Friedman and M.D. Newton, J. Chem. Phys. i 26, 1490 (1982). j. 9- P-G. Wolynes, Phys. Rev. Lett. *£, 968 (I98I). ; 10. V.I. Melnikov and S.V. Meshkov, JETP Lett. 22, 382 (I983). I 11. Y.I. Dakhnovskii and A.A. Ovchinnikov, Mol. Phys. 5J, 237 )• 12. S.G. Christov, Ber. Bunsenges. phys. Chem. £6, 507 (1972); 13. S.G. Christov, Collision Theory and Statistical Theory of Chemical Reactions, Springer, Berlin, 1980. 14. S.G. Christov, Phil. Mag. B j|2, 71, 91 (I985).

23 A-24

EFFECTS OF DIFFUSE FUNCTIONS ON THE POTENTIAL SURFACES OF THE

X" + CH.F —» XCH_ + F" REACTION ( X" = CH~ , 0H~ , CoH_0")

J.BERTRANa and E.SANCHEZ MARCOSb

aDept.Chemistry.Universidad Autdnoma Barcelona.08193 Bellaterra. (Spain)

Dept.Physical Chemistry.Universidad Sevilla. 41071 Sevilla. (Spain)

Comparison between the stationary points of the 3-21G and 3-21+G potential surfaces for the reactions of the title have been performed. Inclusion of diffuse functions leads to more exothermic processes. This fact implies that the transition state appears earlier in the 3-21+G energy profiles than in the 3-21G. As a consequence, the deformation energy of reactants in reaching the transition structures is minor and the 3-21+G activation energy should be lower than the 3-21G one. This is found for the C- and O-alkylation of C-H,O~ and for the alkylation of CH~, which are the reactions where strong product relative stabilizations occur when diffuse functions are included : 46.3 Kcal/mol for the CH~ alkylation and - 52. Kcal/mol for the alkylations of theienolate anion.

Contrarily, the alkylation of OH is predicted to have an activation barrier higher at the 3-21+G level than at the 3-21G level. This may be explained by the degree of localization of the negative charge along the pathway, which leads to an increase in the barrier height. It must be * taken into account that this process has a low relative stabilization energy i- of products when diffuse functions are included in the basis set,14.5 Kcal t mol" , because of their similar effect upon F~ and 0H~. 'i t (1) K.N.Houk and M.N.Paddond-Row, J.Am.Chem.Soc., 108, 2659 (1986) f

24 A-25 TOWARD BLACK-BOX METHODS IN MULTICONFIGURATIONAL SCF AND CI THEORY J. M. BOFILL AND P. PULAY DEPARTMENT OF CHEMISTRY, UNIVERSITY OF ARKANSAS FAYETTEVILLE, ARKANSAS 72701 Research in the past decade has solved the convergence problem which plagued MC-SCF theory for a long time. Moreover, the introduction of the CAS/FORS method diminished the arbitrariness of the configuration selection. Three problems remain, however: (1} The selection of the active space is arbitrary to a certain extent. (2.S Second-order MC-SCF methods need accurate starting orbitals. (3) Large MC-SCF wavefunctions are too expensive for the difficult geometry optimization in transition states. In a recent paper [1], we have demonstrated that the natural orbitals (NOs) of the UHF wavefunction provide excellent approximations to the CAS-SCF orbitals. Orbitals with significant fractional occupancy should be included in the active space. Obviously, this approach works only if the UHF wave function differs from the RHF one. It can be shown that this is always the case for strong correlation (the occupancy of the correlated orbital exceeds about 0.12); in our opinion, MC-SCF techniques should be reserved for such cases. We have investigated a number of typical systems: stretched water, F2, H2O2, ethane, twisted ethylene, ozone, NO, N9O4, CH3...H, transition states on the HCNO+HCCH surface, NiC2H2, HeJ, formoxyl (CHOo), the allyl radical, and dichromium. In systems with several independent UHF solutions for the same state, the NOs of the average density should be used. In all cases, the fractionally occupied UHF NOs span a space very close to the CAS active space. Our scheme eliminates the difficulties at the start of the MC-SCF iteration, and defines a consistent active space. However, the active space defined this way may vary over the potential surface. In our opinion, the latter behavior is inevitable in any consistent definition. We are currently working on the generalization of this scheme to excited states. The excellent approximation of the CAS active orbitals by UHF NOs suggests that a full CI, carried out in the active space defined by the fractionally occupied UHF NOs, is a a good wave function without further orbital optimization. We call this method the Complete Active Space CI - UHF Natural Orbital (CAS-UNO) method. CAS-UNO is dramatically less expensive than CAS-SCF or even GVB wave functions. E.g. for the HCNO+C2H2 cydoaddition transition state (8x8 CAS) CAS-UNO is forty times less expensive than CAS-SCF (using the GAMESS program), and its energy is only 0.008 a. u. higher. CAS-UNO gradients can be readily formulated. We believe that CAS-UNO is an ideal method to search complicated potential surfaces for stationary points. We will compare CAS-UNO optimized structures with the corresponding MC-SCF ones. 1 P. Pulay and T. P. Hamilton, J. Chem. Phys., in press.

25 A-26

HYDRATION OF CO2 BY CARBONIC ANHYDRASE: A THEORETICAL STUDY

JIIN-YUN LIANG AND WILLIAM N. LIPSCOHB

DEPARTMENT OF CHEMISTRY, HARVARD UNIVERSITY CAMBRIDGE, MASSACHUSETTS 02138 USA ABSTRACT Quantum mechanical calculations have been applied to study the reaction mechanism of human carbonic anhydrase catalyzed CO, hydration: CO, + OH" > HCO,~ + H+. This reaction is responsible for fast metabolism of CO, in the human body . The entire enzymatic reaction is divided into five steps: (1) binding of CO, near Zn ; (2) conversion of CO, to HCO. by nucleophilic attack of Zn +-bound OH' on C of CO,; (3),internal pro- ton transfer of Zn -bound HCO-"; (4) binding of H,0 to Zn* +to facili- tate release of HCO-"; and (5) coordinated transfer of H from Zn - bound H,0 to a proton transfer group, then to buffer, and finally to solvent. For each of these reaction steps, possible catalytic effects of active site residues were examined. The results are summarized below:

(1) For the binding of substrate CO,, the experimentally measured fre- quency shift of CO, in the aqueous solution and in the enzyme is repro- duced in the theoretical calculations. This result is consistent with CO, binding to the zinc ion near a hydrophobic pocket in the enzyme's active site.

(2) For the internal proton transfer of zinc-bound HCO,~, the barrier of 35.6 kcal/mol for the direct internal proton transfer is reduced to 3.5 kcal/mol when one water molecule is included, and to 1.4 kcal/rcol when two such water molecules are included . This internal proton transfer is favored over a mechanism in which zinc-bound OH" attacks on 0 of CO,, a bindentate intermediate forms, and the OH" moiety of the resulting HCO," dissociates from zinc, thus leaving one of the oxygen of the ori- ginal CO, as a ligand to zinc.

(3) For the intramolecular proton transfer between zinc-bound H,0 and His 64, the zinc ion not only lowers the pK of zinc-bound water but also helps to repel the proton electostatically away from zinc. His 64 functions as proton receiver and helps to pull the proton towards it. The partially ordered active site water molecules are also important for proton relay .

In addition to quantum mechanical studies on enzyme catalysis, statisti- cal methods and molecular dynamics simulations have been applied to examine the origin of a 13 kcal/mol barrier for the reaction of CO, + 0H~ —> HCO," in the aqueous solution.

REFERENCES

1. Lindskog, S. (1983) in Zinc Enzymes (Splro, T.G., Ed.) p. 77 John Wiley & Sons, New York. 2. Liang, J.Y. and Lipscomb, W. N. Biochemistry, 26, 5293, 1987. 3. Liang, J.Y. and Lipscomb, W. N. Biochemistry, in preparation. Jj. 4. Brooks, B.R.; Bruccolerl, R.E.; Olafson, B.D.; States, D.J.; Swaminathan, S. and Karplus, M. J. Comput. Chew., 4, 187, 1983.

26 A-27

MOLECULAR FHOTODISSOCIATION AND REACTIVE SCATTERING

G.G. BALINT-KURTI

SCHOOL OF CHEMISTRY

UNIVERSITY OF BRISTOL, BRISTOL BS8 ITS

The theory of the photodissociation of molecules into fragments with internal structure has been formulated and applied to two photodissociation processes:

1) HCt • 2 ^ H( Si/2) •

2 2 The branching ratio of C«( P3/a)/C£( Pi/2) produced by photodissociation of HC£ in different vibrational levels is predicted to be a sensitive and structured function of photolysis frequency [1].

3 2) H20 * hi) -•H( S1/2) • OH(j,n,p)

In this process the OH fragment is produced in specific X-doublet states. The theory has been implemented in an approximate form and reproduces quantitatively the experimentally observed OH X-doublet quantum state distribution [2,3].

3) An approximate 3-dimensional quantum mechanical method for the calculation of reactive scattering cross sections has been formulated and tested [4]. The Fixed Angle Reactor Method (FARM) utilises classical trajectory calculations to determine the degree to which reactants are funnelled into a preferred geometry for reaction. These classical trajectory calculations are coupled to fixed angle quantum reactive scattering calculations, similar in spirit to the reactive infinite order sudden method [4], The method has been tested in calculations on the H+H2 and D+H2 systems and shown to provide reliable results at both low and high collision energies.

References

1. S.C. Givertz and G.G. Balint-Kurti, J. Chem. Soc. Faraday Trans. 2, 82, 1231 (1986). 2. G.G. Balint-Kurti, J. Chem. Phys., §4, 4443, (1986). 3. R. Schinke, V. Engle, P. Andersen, D. Hausler and G.G. Balint-Kurti, Phys. Rev. Letters 5§, 1180, (1985). 4. B.M.D.D. Jansen op de Haar and G.G. Balint-Kurti, J. Chem. Phys., 85, 2614,(1986): also ibid (in press).

27 A-28

THEORETICAL STUDY OF THE PHOTOCHEMICAL CLEAVAGE OF THE M FTAL-ALKYL BOND IN THE METHYLALUMINIUM PORPHYRIN AIPCH$

M.M. Rohmer

Laboratoire de Chimie Quantique ER 139 du CNRS Universite Louis Pasteur F 67000 Strasbourg, France

Potential energy surfaces have been obtained from ab initio CI calculations for the homolytical cleavage upon photolysis of the aluminium-alkyl bond in the methylaluminium porphyrin :

^ AlP + CH3

They provide a basis for the mechanism proposed for this photochemical reaction : • excitation to a spin-allowed singlet excited state I • conversion to the triplet photoactive state through intersystem crossing I. f • dissociation into the products of the reaction along the triplet potential energy \ surface \

28 A-29 A CLOSE COUPLING CALCULATION OF THE HD/Pt(111) SURFACE SCATTERING

S.MIRET-ARTES, G. DELGADO-BARRIO, A.M. CORTINA and P. VTLLAREAL Institutes de Estructura de la Materia CSIC. Serrano, 123 28006- Madrid, Spain N. MOISEYEV Department of Chemistry, Technion-Israel Institute of Technology." 32000 Haifa, Israel

ABSTRACT

There is much experimental and theoretical interest in the understanding of the dynamics of rotationally inelastic molecule~surface scttering. The HD/Pt(111) systems is a good prototype for — comparing experiment and theory because of its — characteristics: the rotational excitation proba- bilities are large due to the offset of the HD - center of mass from its geometric center, there one typically a small number of energetically open inelastic channels and the modeling can be done with only one degree of traslational freedom due -. to the low surface corrugation. In this work, we - calculate the rotational excitation probabilities of this system considering the influence of the — temperature and compare with previous works.

29 A-30 A TEMPERATURE DEPENDENT CLOSE-COUPLING STUDY OF THE INTERACTION BETWEN He ATOMS AND Cu (110) SURFACE

G. DELGADO-BARRIO, P. VILLAREAL, M. HERNANDEZ, O. RONCERO and S. MIRET-ARTES.

Instituto de Estructura de la Materia, CSIC. Serrano, 123; 28006 Madrid, Spain

ABSTRACT A great deal of experimental measurements about the interaction at thermal energies betwen helium — atoms and a now highly corrugated copper surface are available now in order to check different theoretical calculations. The (110) crystal face is essentially corrugated in one dimension and very simple close-cou- pling calculations are possible for an hypothetical - perfectly immobile surface lattice. The temperature - dependence of the difraction intensities is introduced by means of a modification of the parameters of the — corrugated Morse potential used initially. A comparison among the experimental diffraction intensities, those obtained by using the Debye-Waller factor and our results are presented.

30 A-31

Atom Scattering from Disordered Surfaces

A.T. Yinnon, R.Kosloffand RB Gerber Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics The Hebrew University of Jerusalem, Jerusalem 91904, Israel

ABSTRACT

Surface disorder often greatly affects the physical and chemical behaviour of the surfaces. Hence the determination of local surface structure is a major goal of surface science. Results in the last few years indicate that He scattering is a powerfull probe of surface disorder. In the case of scattering from isolated imperfections attenuation of the coherent scattering was observed. In addition non coherent off specular maxima were present in the scattering pattern. In this paper we present the results of a theoretical study of these systems and interpret the experimental and calculated scattering patterns. Calculations were done with the quantum mechanical wave packet method, the semi-classical sudden approxi- mation and the classical trajectory method. By employing these various methods, we succeeded to give a complete interpretation of the different scattering features, each method providing complementary information. Since no one method allowes for com- plete understanding of all features, we stress the importance of using a multiple method approach for gaining insight into the scattering dynamics. Our results indicate the incoherent scattering maxima to be Fraunhofer interfer- ences and rainbows. The intensity and location of which are sensitive to the gas phase atom /surface imperfection interaction. While the existence of these maxima have been experimentally verified in the case of atom scattering from an isolated imperfection (an CO atom adsorbed on Pt, a surface step) our theoretical results indicate that even for a randomly disordered surface like a mixed Kr-Xe (2% Xe) overlayer on an Ag(lll) sur- face, these maxima, although smoothed, still persist. A quantum mechanical calculation of the probability of the current density of the scat- tered atoms facilitated to picture the dynamics leading to these maxima and provides insight into the quantum mechanical scattering process.

31 A-32

QUANTUM CHEMISTRY STUDY OF BENZENE CHEMISORPTION ON THE Rh(lll)

SURFACE

CAO YANG ( Y. CAO ), WANG YOULIANG ( Y.-L. WANG )

DEPARTMENT OF CHEMISTRY, SUZHOU UNIVERSITY, SUZHOU, CHINA

The chemisorption of benzene on Rh(lll) surface is studied using quantum chemistry DV-X« method. The cluster model of 6 Rh atoms is used to represent the Rh(lll) surface, which is determined on the experimental result observed by LEED. It's electronic structure, the ground states valence levels, density of states, and the charge transfer between adsorbate and substrate, are obtained. The results of DOS show two Increased peaks at 8.17 and 14.68 ev contributed by

71 orbitals,are in good agreement with UPS experiment,supporting the

LEED structure analysis. The results of DV-Xet calculations indicate that the adsorbed benzene structure is unperturbed from its stable gas-phase structure; is /T-bonded to the Rh surface with the ring plane parallel to the plane, and has a C $v \ bonding symmetry.

The 71 electrons of benzene transfer to the d-orbitals of Rh, so its resonance stability decreases and is easy to be hydrogenated.

Besides, the equilibrium benzene-Rh surface distance is found to be about 2.IS A.

References

CU B.E.Koel, J.E.Crowell, CM.Mate and 0. A.Somorjai, J.Phys.Chem. ,

88,1988,<1984>.

123 M.Neumann, J.U.Mack, E.Bertel and F.P.Netser, Surf.Sci.,

199,629,(1989).

£33 A.B.Anderson,M.R.McDevitt.F.F.Urbach, Surf.Sci., 146,80,(1984). 32 A-33

NEW RESULTS IN NON-I.OC ,L QUANTUM TRANSPORT IN RESTRICTED GEOMETRIES

VIPINSRTVASTAVA CAVENDISH LABORATORY, CAMBRIDGE UNIVERSITY, CAMBRIDGE CB3 OHE AND SCHOOL OF PHYSICS, UNIVERSITY OF HYDERBAD, HYDERABAD 500134, INDIA

It is well recognised now that the quantum-mechanical phase-coherence can be hundreds of times larger than the average elastic scattering length in a normal condensed matter system at very low temperature - low enough to preclude inelastic scattering events. Electron transport under such situations in systems of size comparable to the phase-coherence length becomes non-local and reveals interesting new effects. The observation of Aharanov-Bohm and certain other related effects in these resistive systems has stirred up the activities at the 'mesoscopic level'. We report here the possibility of observing a Josephson-type effect arising due to the long-range phase order in such systems when subjected to the quantum-Hall-effect conditions. In the narrow quantum-Hall devices, the edge currents which carry most of the system current can fall near enough to be weakly linked. It is shown that under this condition the phase-slip at the two edges can drive a high frequency \ f alternating-current (a.c.) in the transvese direction i.e. parallel to the Hall field. To detect it,

one should resonate it by applying an a.c. voltage of appropriate frequency in addition to the I' % . i Hall voltage. Another new experimental result recently reported is that the Hall effect • I t quenches in the magnetic field range, O < B < B0"1. We show that this effect is caused by the low frequency phase-driven a.c. in the system that drives electrons against the Lorentz force.

33 A-34

Confluence of Localized and Extended States in Anderson Model

Vipin Srivastava Cavendish Laboratory, Cambridge University, Cambridge CB3 OHE, UK and School of Physics, University of Hyderabad, Hyderabad 500 134, India*

It is now well known that spatially localized and extended states, if coexist at the same energy, will get converted into an extended state. However, it is not generally realised that such a 'confluence' of degenerate localized and extended states may have important and interesting properties and may throw fresh light on the nature of states in disordered systems. We have examined this problem here from purely mathematical direction and have derived interesting physical consequences. While poles of the disordered system's Green's function represent localized states and its branch-cut represents continuum of extended states, we examine the possiblity and consequences of the presence of poles in the Riemann sheets obtained by analytically continuing 'inside' the cut. In such a situation, we find that the 'stay-put' probability for an electron approaches zero as time approaches infinity at a slow pace, so much so, that the time-integral of the stay-put probability diverges. This result has important implications in that it defines a new regime of transport in disordered electron systems. It also clarifies a subtle point about the original Anderson - criterion for localization.

"(* * Permanent address

I,

34 A-35 TRANSITION STATE STABILIZATION IN THE ACTIVE SITE OF AMINOACIL-tRNA SYNTHETASES A.A. VOITYUK, A.A. BLIZNYUK, O.I. LAVRIK INSTITUTE OF BIOORGANIC CHEMISTRY, NOVOSIBIRSK, 630090, "USSR

The mechanism of the transition state stabilization in the reaction of amino acid activation catalysed by aminoacyl-tRNA synthetases (EC 6.1.1) was suggested. The stabilization is due to the formation of hydrogen bonds between the phosphoryl oxygen of ATP a-phosphate and the enzyme group, which are tfc.

References 1. A.A. VoityuK, A.A. BliznyuK (1987) Theor. Chem. Acta 72, 223 2. R.J. Leatherbarrow, A.R. Fersht, G. Winter (1985) Proc Natl. Acad. Sci. USA 82, 7840.

35 A-36 TOWARDS A QUANTUM MECHANICAL TREATMENT OF SUBSTRATE-ENZYME INTERACTIONS: A REACTION LIGAND FIELD APPROACH. ROMAN OSMAN, Department of Physiology and Biophysics, Mount Sinai School of Medicine, New York, NY 10029, USA. WALTER J. STEVENS, Molecular Spectroscopy Division, National Bureau of Standards, Gaithersburg, MD 20899, USA. HAROLD BASCH, Department of Chemistry, Bar-Han University, Ramat-Gan, Israel. We study the enzymatic mechanism of action of superoxide dismutation in the presence of Mn- or Fe- containing superoxide dismutase. Approximate models of the active iites of these enzymes have been constructed based on their crystal structure. The apexes of the trigonal bipyramid, that serves as a model of the active site, are occupied by an ammonia and water in the axial positions and by two ammonia molecules and a hydroxyl ion in the equatorial plane. In the simulation of the enzymatic mechanism the superoxide ion is interacting with the metal in the axial position replac- ing the water molecule. In order to be able to perform high quality MCSCF calculations of the interaction between the active site model and superoxide we replace the ligands around the metal (i.e., the three ammo- nias and the hydroxyl) by a reaction ligand field. The reaction ligand field is constructed from three components: electrostatic, polarization and repulsion. The electrostatic ligand field is represented by an expan- sion of the charge distribution in monopoies, quadrupoles and octupoies positioned on the nuclear centers and on the centroids of the localized orbitals of the separated ligands. The polarization is represented by polarizability tensors obtained from a CPHF calculation of the ligands and are positioned at the centroids of the localized orbitals. The repulsion is represented by a three term linear combination of gaussian repulsive : potentials of a similar form as the effective core potentials. The repul-, ; sive potentials are fitted to reproduce the repulsion energy between the • ligands and the metal in both oxidation states (i.e., 3+ and 2+ for Fe and ,/' Mn). We will present and compare results of structure optimization of i several electronic states of the metal-superoxide complexes obtained with * the complete-SCF representation and the one in which the ligands have been 'f replaced by their reaction field. The agreement between the all-SCF and f the reaction ligand field calculations indicates that such replacements "'• can be very useful in designing a quantum mechanical approach to the cal- ;. culations of substrate-enzyme Interactions.

'{• I\

36 A-37

EFFECT OF ELECTRON CORRELATION ON THE RELATIVE STABILITY OF WINSTEIN AND MOBIUS STRUCTURES OF THE HOMOTROPYLIUM CATION.

Mario BAR2AGHI and Carlo GATTI C.N.R. Center for the Study of Structure/Reactivity Relations, c/o Department of Physical Chemistry and Electrochemistry, University of Milano, Via Golgi 19, 1-20133 Italy.

Recent crystallographic investigations of Childs and coworkers indicated that the homotropylium cation may adopt either a Wlnstein homoaromatic structure, J_, or a MObius aromatic structure, 2_, depending on the appropriate placement of electron donor substituents (1). Our recent MO ab initio calculations with the small split-valence 3-21G basis set and the 6-31G* basis set, which includes d orbitals on carbon, definitely indicate the cyclo- octatrienylium cation 2_ as the global minimum on the C.H.+ potential energy surface (2). A local minimum corresponding to. the homoaromatic structure ]_ can be found at the 6-31G* level. It is 4.3 kcal/mol less stable than 2 and can rearrenge to 2_ through a barrier lower than 10 hartrees. Inclusion of electron correlation effects in the wave functions by single-point MP2 and HP3 calculations (2,3) indicates a single minimum on the potential energy profile in the Mobius structural region. The importance of electron correlation corrections for a proper description of delocalization and aromatic character has been emphasized (3), but Moller-Plesset perturbative corrections are known to converge very slowly. Therefore we have evaluated the full Coulomb correlation contribution to the total energy of C.H + by integrating the Colle-Salvetti density functional at the 6-31G* level. The results indicate two minima at R = 1-700 A and R,. _ = 2.267 A for structures J_ and 2_ respectively, being' 2 less stable than 2_ by 1.3 kcal/mol. A small energy barrier of 0.5 kcal/mol separates 2 from 2_. The estimated planarization energy of 2_ is 21.3 kcal/mol, in good agreement with the experimental value of 22.3 kcal/mol. This value is underestimated at the HF level (18.7 kcal/mol)(2) and overestimated at the MP2 (31.7 kcal/mol)(2) and MP3 (25.4 kcal/mol)(3) levels. The effect of electron correlation on the three carbon membered ring • closure reaction path has been also investigated by means of one-pair GVB and CISD(8e) calculations. A topological analysis of the correlated charge ; density distributions derived therefrom is presented.

;,L 1) (a) R.F. Childs, A. Varadarajan, C.J.L. Lock, R. Faggiani, C.A. Fyfe, . I R.E. Wasylishen, J. Am. Chem. Soc. J_04, ,2452 (1982). (b) R.F. Childs, .' •(* R. Faggiani, C.J.L. Lock, M. Mahendran, J. Am. Chem. Soc. 108, 3613 • s? (1986). • 2) (a) M. Barzaghi and C. Gatti, J. Chimie Physique 8£, 783 (1987). k (b) M. Barzaghi and C. Gatti, La Chitiica e l'Industria j>£, 98 (1987).. I' (c) C. Gatti and H. Barzaghi, Abstracts of the 1987 American Conference on Theoretical Chemistry, Gull Lake, Minnesota, (d) M. Barzaghi and C. Gatti, Abstracts of the 1987 World Congress of Theoretical Organic Chemists, Budapest, (e) M. Barzaghi and C. Gatti, J. Mol. Struct. (Theochem), in press. 3) R.C. Haddon, J. Am. Chem. Soc. 110, 1108 (1988).

37 A-38 ELECTRONIC CONFIGURATION OP THE PEPTIDE BOND IN GROUND AND EXCITED STATE IN THE DINAMIC OP THE PEITIDE STRUCTURES. R.L.PAVLOV, Y.I.DEICHEV, V.G.VEEEV INSTITUTE FOR NUCLEAR RESEARCH AND NUCIEAR ENERGY, BULGARIAN ACADEMY OP SGIEGES, 1784- SOFIA., BULGARIA. The peptide bond is connected with such fundamental pro- perties as the transfer of energy (1) and electron, the trans- fer of electron state of excitation (1,2), the formation of an additional delocalization system in the peptide establishments In the dynamics of the peptide establishments the peptide bond is being destroyed its electronic configuration is decisive for the formation of the type of conductivity of the peptide chains and the formation of energy zones* The presented work shows the uniform character and inter- dependence of those processes as a result of the specific fe- atures in ground state and in the process of exitation of the electron system of the peptide bond. Complex investigations are made on(,its o' - and % -electron systems in ICAO-MO approxi- mation of Huckel. Made are also calculations about the process of adding neighbouring hydrogen atoms and groups of atoms. Ground and first excited ^-electron states are presented. It is shown that when a #-electron system is excited, thei^-elec- tronic configuration is destroyed. Investigated is the poten- tial, created by the ^-electrons. Proved are the existence of a spherical potential hole with an oxygen atom in its centre and the formation of an enegy threshold along the C-N bond. Interpreted are : the transition to an excited $ -electron state of the peptide bond, the mechanism of its destruction, its electronic type of conductivity, its rolein the formation of energy zones in the peptide chains, as well as the trans- fer of energy and electron and the formation of an additional delocalization system as a consequence of the transfer of ex- cited electron states. • This work ts the continuation of our research made on the I. destruction of the peptide bond (2,5,4). X 1. J.G.Vassileva-Popova et al., In : Abstr.of 3rd int.Congr. f of Quantum Chem.,1979, Kyoto, Japan,1979, 31-S-3, p.29. !* 2* R.L.Pavlov et al., In : Biology. X National Youth Confe- ( rence* Sofia,1979i PP.293-296, ( in Bulgarian.). ' 3. J.G.Tassileva-Popova et al.. In J Abstr.of 6"* Int.Bioptu X. Congr.,1978, Kyoto, Japan.1978, p.416 ; Glasnik hemiskog >•• drustva, Beograd, 44 (1979) 1-2, 9^JI ( in Serbian ). f 4. R.L.Pavlov et al., In : Absbr.of 3ra int.Colog.Phys. and 1 Chem.Inform., Transfer in Regulation of Reproduction and % Ageins,1980, Varna, Bulgaria,1980, p.77 ; Abstr. of 16 *b % Europ.Congr.on Molecular Spectroscopy,1983, Sofia. Bulga- f ria,1983, P.275.

38 A-39

CRITICALLY HETEROSYHMETRIC BIRADICALOID GEOMETRIES AND THEIR

ROLE IN PHOTOCHEMISTRY.

VLASTA BONACIC-KOUTECKY1, JOSEF MICHL2 AND KLAUS SCHbFFEL1

1. FREIE UNIVERSITAT BERLIN

INSTITUT FUR PHYSIKALISCHE UNO THEORETISCHE CHEMIE,

TAKUSTR. 3, D-1OOO BERLIN 33.

2. DEPARTMENT OF CHEMISTRY, UNIVERSITY OF TEXAS AT AUSTIN,

AUSTIN, TEXAS 787 12 USA.

Ab initio large scale calculations confirm the existence of an So -Sl, conical intersection at orthogonally twisted double bond geometries in the protonated Schiff bases and substituted push- pull cyclobutadienes, originally predicted from the simple two- electron, two-orbital model. Influence of the polar environment on the S -S. energy gap has been in-estigated. The likely consequences of these results for the detailed description of the mechanisms of cis-trans isomerization, the formation of twisted internal charge-transfer (TICT) states, proton translocation , and possibly of the initial step in vision, as well as for the understanding of the regiospecifity of singlet photocycloaddition, are discussed.

f

39 A-40 Theoretical Studies on the Hydrolysis of Urea by Ikchoon Lee, Chang Kon Kim and Byung Choon Lee* Department of Chemistry, Inha University, Inchon, 160, Korea •Department of Science Education, Choongbuk National University, Chongju, 310, Korea

Mechanisms of the hydrolysis of urea have been investigated using the method. All geometries were fully optimized and the transition states were characterized by calculating force constants. The- results showed that : (i) The unimolecular decomposition process via the direct intra- molecular proton transfer is preferred to both the Al and the bimolecular nucleophilic attack by water, in agreement with the experimental results of Shaw et al- in the low acidity medium, (ii) The diprotonated form of urea exists as an equilibrium species, which undergoes the A2 type hydrolysis more favorably than the monoprotonated form, as Moodie et al. found in the intermediate acidity medium, (iii) The A2 hydrolysis of the monoprotonated form is very similar to those of acetamide(4' and methyl carbamate. (iv) As the number of the sclvate water molecule increases, the activation barrier for the A2 process of the monoprotonated form in- creases while that for the unimo'ecular decomposition of the free base form decreases, indicating a possibility of the barrier height reversal in the bulk sclvent in favor of the latter process, thus accommodating all the experimentally found trends in the urea hydrolysis. The Al mechanism involving a six-membered ring type transition state was found to be a high energy barrier process so that the mechanism may be ruled out as untenable. References : (1) (a) W. H. R- Shaw and J. J. Bordeaux, j. Am. chem. soc, 77, 4729 (1955); (b) W. H. R. Shaw and D. G. Walker, ibid., 79, 4329 (1957). (2) G. A. Olah and A. M. White, j. Am. Chem. Soc., 90, 6087 (1968). (3) D. W. Farlow and R. B. Moodie, J. Chem. soc. (B), 407 (1971). (4) I. Lee, C. K. Kim and H. S. Seo, Tetrahedron, 42, 6627 (1986). (5) 1. Lee, C. K. Kim and B. C._Lee, J. Comput. chem., 8, 794 (1987). (6) C. J. Siffney and C. J. O'Connor, j. chem. Soc. Perkin II, 362 (1976).

40 A-41

QUANTUM CHEMICAL AB INITIO INVESTIGATION OF MIXED BeLik AND

MgNak CLUSTERS.

VLASTA BONACIC-KOUTECKY1, PIERCARLO FANTUCCI2,

WOLFGANG PEWESTORF1 AND JAROSLAV KOUTECKY1

1. INSTITUT FÜR PHYSIKALISCHE UND THEORETISCHE CHEMIE,

FREIE UNIVERSITÄT BERLIN, D-1OOO BERLIN 33.

2. DIPARTIMENTO DI CHIMICA INORGANICA E METALLORGANICA,

UNIVERSITA DI MILANO, 1-20133 MILANO.

The optimal geometries of the mixed neutral BeLi], and cationic BeLi. clusters (k=2-8) have been determined using the analytical gradient method in the framework of all-electron Hartree-Fock procedure. The energies of the H-F optimized cluster have been calculated with the configuration interaction method. The "optimal" cluster geometries are very symmetric with the Be atom in the centrum of the cluster. The atomization energy per atom increases with the increasing number of Li atoms and reaches a maximum for the clusters with the 8 valence electrons in agreement with ideas of the cluster shell model. The electronic structure of MgNa. and MgNa. clusters have been investigated both with all-electron and effective core potential methods. The small MgNa. clusters are much less stable than the BeLij, clusters in analogy with the behaviour of the Mg clusters. The MgNa. cluster is stable towards dissocia- 3 n it ... tion only if both d functions are included in the basis set and § if the electron correlation among the valence electrons is % taken into account. MgNa. is already stable on the SCF level in 7 agreement with experimental findings. The calculated stabili- ' ties of MgNak and MgNa^ clusters increase if the intershell electron correlation is taken into account through the effect of the core polarization.

41 A-43

AB INITIO STUDIES ON ICOSAHEDRAL MOLECULES Y. JIANG OJ. YU M. ZHANG X. LI INSTITUTE OF THEORETICAL CHEMISTRY, JILIN UNIVERSITY, CHANGCHUN, CHINA

In this paper, we present the symmetry reductions of I. group, tabulating compre- hensively the irreducible bases as well as matrice for generators C~ C, and C,- which are sufficient for simplifying the ab initio or X

2- Tablei: Calculated results of (a.u.)

Population MO energy bond type occupancy Bs Bp H l.P.

19u -0.076 BB 8 0 8 0 0.046 -0.1 14 BH 10 0. 6.85 3.15 0.095 *B -0.216 BH 6 0.42 3.72 1.86 0.201 3t1u 2t -0.216 BH 6 2u 1.07 2.13 2.80 0.209

3a -0.316 BH 2 0.28 1.02 0.70 0.305 19 -0.341 BB 10 3.82 4.68 1.50 0.322 Zh9 2t1U -0.557 BB 6 4.87 0.78 0.56 0.523

2ag -0.757 BB 2 1.60 0.40 0 0.709 References (1) Scamehern.C.A., Hermiller.S.M. and Pitzer.R.M., J. Chem. Phys., 84, 833 (1986). (2) Goursot.A., Penigault.E., Chermette.H. and Fripiat.J.G., Can. J. Chem., 64, 1752 (1986). (3) Wunderlich.J.A. and Lipscomb.Ul.N., J. Am. Chem. Soc, 82, 4472 (1960). (4) Wade.K., Adv. Inorg. Chem. & Radiochem., 18, 1 (1976).

42 A-44

VIBRATIONAL SPECTRUM OF DISTANNANE, Sn2 Hg, FROM "AB INITIO" CORRELATED

WAVEFUNCTIONS.

A.A. MARQUEZ CRUZ AND J. FERNANDEZ SANZ.

DEPARTAMENTO DE QUIMICA FISICA. UNIVERSIDAD DE SEVILLA. 41012 SEVILLA.

SPAIN.

Theoretical harmonic force field, vibrational frequencies and infrared intensities of ethanelike distannane molecule are reported.

Calculations are carried out at HF-SCF level by using an ab initio relativistic effective core potential to describe the inner electrons of heavy atoms. For the valence electrons, a double £ basis set augmented by d orbitals on the tin atom is used. Electron correlation is taken into account by means of a second order perturbation approach.

Theoretical results are compared with experimental infrared spectrum (1) and alow us its full explanation.

The tin-tin stretching force constant is predicted to be 1.282 mdyn/A. This value reveals the weakness of this genuine metal-metal bond.

(1) W.H. Jolly, J. Am. Chem. Soc. 83 (1961) 335.

43 A-45

AB INITIO CI CALCULATIONS ON THE MOLYBDENUM-TIN DOUBLE BOND.

JULIO ANGUIANO, ANTONIO MARQUEZ CRUZ AND JAVIER FERNANDEZ SANZ.

DEPARTAMENTO DE QUIMICA FISICA. UNIVERSIDAD DE SEVILLA. 41012 SEVILLA.

SPAIN.

By using effective core potentials to describe the inner electrons of heavy atoms, we have carried out ab initio CI calculations on Mo (C0)_ Sn H structure.

Assuming a C_ symmetry, alternated and eclipsed conformations have been optimized at HF-SCF level. The former structure seems to be slightly favoured.

Our predicted Mo - Sn bond length agrees reasonably well with the experimental data.

Detailed analysis of molecular orbitals shows the existenee of a 77 bond between molybdenum and tin orbitals.

Effects of electron correlation on electronic structure of Mo - Sn bond and equilibrium distance have been reported.

44 A-46

MNDO INVESTIGATION OF THE FOUR DIASTEREOISOMERS OF RADIATION-INDUCED 5,6-DIHYDROXY-5,6-DIHYDROTHYMIDINE .

A. GRAND, J. CADET, V. BARONE, L. VOITURIEZ, C. VOISIN Laboratoires de Chimie, Departement de Recherche Fondamentale, Centre d'Etudes Nucleaires de Grenoble 85 X, F-38041 GRENOBLE CEDEX, France

The decomposition of thymidine upon exposure to ionizing radiations in aerated aqueous solutions is mostly mediated by OH radicals. One of the main degradation pathway of this DNA nucleoside leads to the formation of the four diastereoisomers of 5,6-dihydroxy-5,6-dihydrothymidine through transient hydroperoxides. The main aim of the present study was the determination of the major confoi'mational features of theses diols including puckering of the pyrimidine and osidic rings, and the orientation of the thymine moiety about the N-glycosidic bond. This theoretical investigation was carried out by using the MNDO formulation included in the MOPAC package.

The validity of this approach was demonstrated by the comparison of the MNDO optimized geometrical parameter with those obtained in the solid state as the result of the X-ray determination of the (-)cis-5R,6S diastereotner. The overall energy of this glycol was shown to be strongly dependent on the orientation of the base with respect to the N-glycosidic bond. Two energy minima which correspond to the expected syn and anti rotamers were observed, the anti conformer being the more favourable ; conformation. This is in agreement with NMR investigation in D_0 which ;-t showed a prefenrential anti orientation. ^ Other major physical properties, including dipolar moment, ionisation 5 energy, n -5lT* transition, charge densities on the reactives centers, may ] also be determined. The investigation was extended to the three other diastereomers and a classification in term of energetic stability can be improved, which seems !• in good agreement with the experimental results obtained by NMR \. spectroscopy. '

45 A-47

ELECTRONIC POPULATION IN Fe(CO)~ BY EHT AND X=< CALCULATIONS.

Andre GRAND1, Paul J. KRUSIC2 and Robert SUBRA3

^aboratoires de Chimie, D.R.F., CENG, 38401 GRENOBLE C4dex 2 Central Research and Development Department E.I. Du Pont de Nemours CIE WILMINGTON Delaware 19898 USA

3 LEDSS - Universite J. Fourier, 53X, 38041 GRENOBLE Cedex

An experimental and theoritical study of the transient Fe(C0)~ radical is presented. This radical, isoelectronic with Co(CO),, is obtained for the first time in solution, by X -irradiation of dilute Fe(CO) at 77K. The general features of its ESR spectrum are similar to those of Co(CO)^ ie. a nearly axial g tensor Cg// = 2.0.039, gl = 2.0707) but it was impossible to get further information on C couplings. On the basis of the experimental results for Co(CO),, we present a theoretical study by both Extended Huckel and X^ -nethods for Fe(CO) in trigonal pyramidal geometry.

The SOMO is found of A1 symmetry with a LUMO of E symmetry in both methods.

In both calculations the SOMO is made up mostly of a highlv directional part centered on the metal wich uses only metal s,pz and dz " orbitals and of a second part wich is strongly "IT delocalized over the equatorial CO ligands and uses almost exclusively the pz orbitals of the equatorial atoms. The apical CO's contribute negligiby to the SOMO.

The only carbon giving a substantial coupling with the unpaired electron is the apical one, in accordance with ESR results on Co(CO), 27 Gauss).

The calculations allow a complete understanding of the structure of the radical and achieve the experiments work.

46 POSTER SESSION

I B-l

THE MULTICONHGURATIONAL SPIN-TENSOR

TIME DEPENDENT HARTREE-FOCK METHOD

PROF. DANNY L. YEAGER, CHEMISTRY DEPARTMENT, TEXAS A&M UNIVERSITY,

COLLEGE STATION, TEXAS 77843-3255, USA

ABSTRACT

The multiconfigurational time-dependent Hartree-Fock (MCTDHF) approach [1] gives the correct linear response of a multiconfigurational wave- function to an external perturbation [2]. Hence, this method is sometimes called multiconfigurational linear response [3]. (It may also be derived from the multiconfigurational ph Green's function.) The single configurational approach is known as the time-dependent Hartree-Fock (TDHF). MC based pro- cedures have significant advantages over single configurational (+ perturba- tion theory) based methods in particular for highly correlated and open shell systems. Both the TDHF and MCTDHF satisfy the Thomas-Reiche-Kuhn sum rule and have equivalence between the length and velocity forms of the oscillator strength in the limit of a complete orbital basis. Since an MCSCF(SCF) state is the initial state in the MCTDHF(TDHF) all the variational parameters are opti- mized so the Hellman-Feynman and generalized Brillouin theorems are ful- filled. We have also recently shown that MCTDHF can mimic A full CI at a frac- tion of the cost [4].

We have been developing a new MC linear response method which explicitly includes spin tensor coupling. Hence states of pure symmetry are always generated by both the ph and transfer operators even for open shell systems. This is similar to our recently developed MCSTEP single particle Green's function approach for ionization potentials and electron affinities [5]. I will present this method and new applications for excitation energies, transition moments, and polarizabilities for the open shell systems O2 (ground state) and N2 in various triplet excited states.

References

[1J D.L. Yeager and P. Jorgensen, Chem. Phys. Lett. £5_, 77 (1979).

[2] R.Kubo, J. Phys. Soc. Japan 12, 570 (1959).

[3] J. Oddershede, P. Jorgensen, and D. Yeager, Comp. Phys. Rep. 2., 33 (1984).

[4] R. Graham, D. Yeager, J. Olsen, P. Jorgensew, R. Harrison, S. Zarabian, and R. Bartlctt, J. Chem. Phys. Bl, 6544 (1986). !| » [5] J. Golab and D. Yeager, J. Chem. Phys. 32, 2925 (1987). ' 47 B-2

GRAPHICAL REPRESENTATION OF MODEL SPACES:

APPLICATIONS TO VARIATIONAL AND PERTURBATION METHODS.

Wiodzislaw Duch

Institute of Physics, UMK ul. Grudzi^dzka 5, 87-100 Torun, Poland

Many-body equations are defined in the nany-particle Hilbert space. In practice the space is always finite-dimensional and built from primitive objects like one-particle functions (orbitals or spin- orbitals). It is possible to visualize such a space using graphs that represent in a global way the basis of the many particle model space. The architecture and structure of these graphs reflects the symmetries and relations of the basis functions thus taking a dis- cussion of an architecture of model spaces possible. Graphical rep- resentation allows us to see the structure of model spaces and to teach a computer how to use it. In general any kind of tensor space may be visualized graphically. Examples of graphs useful in molecular, atomic and nuclear physics, such as graphs representing determinants, spin eigenfunctions or angular momentum eigenfunctions, will be pre- sented [1]. A small graph aay represent a space of huge dimension.

Calculation of matrix elements is, from the practical point of view, central to most methods used in many-body problems. Graphs should be constructed in such a way that would allow calculation of matrix ele- ments directly from a graph, without additional algebraic manipulations, thus facilitating the mapping of differential or integral operators to their matrix representatives defined on the finite-dimensional space described by the graph. The structure of the matrix is then recognized with the help of a graph: non-zero matrix elements are identified and those elements that are the same or are related in a simple way are computed only once, making the many-body methods computationally very efficient.

Graphical methods were used with great success in the configuration interaction method and include graphical versions of the unitary group approach (GUGA) based on a four-slope graph (Shavitt's graph) and the symmetric group approach (SGGA) [2] based on a three-slope graph, as well as formulations employing determinants, based on two-slope spin-separated graphs [1]. Recently graphical methods were also applied to derivation of formulas in the open-shell RHF pertur- bation theory. Examples of such derivations will be presented.

[1] V. Ouch, GRHS or Graphical Representation of Hodel Spaces, Lecture Notes in Chemistry, Vol. 42 (1986) [2] V. Duch, J. Karwowski, Comp. Phys. Rep. 2 (1985) 92

48 B-3

THE FOCK EXPANSION IN ATOMIC AND MOLECULAR QUANTUM MECHANICS. P.C. ABBOTT Department of Physics, University of Western Australia, Nedlands 6009, Australia.

It is widely believed that the Schrodinger equation (SE) for the stationary states of molecules is intractable[l]. This belief is strengthened by the difficulty in solving the SE for the simplest atomic and molecular systems: exact solutions of the SE are known only for the hydrogen isoelectronic sequence and the hydrogen molecular ion.

The SE for H2+ is separable in confocal elliptic coordinates yielding a coupled set of ordinary second order differential equations. All of the precise calculations thus far have been based upon semi-analytical solution of these coupled differential equations using the method of Frobenius[2,3]. However, since the SE for all other atoms and molecules is non-separable, a method of solving the SE that does not rely on separability is of paramount importance.

In 1954, Fock[4] proposed that, in the neighbourhood of r = 0, the exact ]S-state helium cigcnfunctions have the Feck expansion (FE) [W2]

kpvvw'w/F p = 0 r, r,* r, as — COS 9 - rl rir2 Substitution of the FE into the SE yields a differential recurrence relation for the *Pkp(a,9). The FE was later extended to a sytem of N particles and states of any symmct v. Jid applies to a wide class of potentials[5,6]. In other words, the generalised FE applies ;. all stationary states of atoms and molecules.\7,8]

Progress on the solution of the SE for the 1S, 3S, 3P and ^-states of helium[9], the van der Waals interaction between two hydrogen atoms[10] and H2+, will be reported. In particular, it is shown that not only can the H2+ eigenfunction be written in terms of the FE, so can its energy[ll] viz.,

[I] Davidson, E R. 1979 Computational Methods for Molecular Structure Determination: Theory aid Technique. NRCC Proceedings No. 8,1-1 [2] Bates, DJt., Ledsham, K and Stewart, AX. 1953 Phil Trans. Roy. Sac. A246,216 [3] Bui, T.T. and Hunter, G. 1974 Them. Chin. Ada 33,169-76 [4] Fock, VA. 1954 Itv. Akad. Nauk. 18,161, 1958 K. Norske Vidensk. Selsk. Fork 31,138-52 [5] Ermolaev, A.M. 1958 Vest. Len. Univ. 14,48-64 [6] Dcmkov, Y.N. and Ermolaev, A.M. 1959 Sov. Phys.-JETP 9,633-5 [7] Leny.J. 1984 Lecture Nous in Physics vd 195 (Berlin: Springer) pp235-47 [8] Morgan, JD. 1986 Theor. Chun. Acla 69,181-223 [9] Abbott, P.C. and Mtslen EM. 1987 Whys. A. 20,2043-2075 Gouschalk, J.G., Abbott, P.C. and Matlen EH. 1987 J.Phys. A. 20,2077-2104 Gotuchalk, J.G. and Maslen E.N. 1987 J.Phys. A. 20,2781-2803 [10] Tulub,A.V. 1969 Sov. Phys.-Dokl. 13,936-8 Abbott, P.C. 1986 Thesis University of Western Australia [II] Klaus, M. 1983 J.Phys. A. 16, 2709-20 49 B-4

QCHEM1.0: A QUANTUM CHEMISTRY SOFTWARE PACKAGE FOR A WIDE RANGE OF COMPUTING ENVIRONMENTS.

P.C. ABBOTTt and G.S. CHANDLERtt

t Department of Physics, University of Western Australia, Nedlands 6009, Australia. tt Department of Physical and Inorganic Chemistry, University of Western Australia, Nedlands 6009, Australia.

QCHEM1.0 is the first version of a portable package for quantum chemistry calculations and has been developed over the last two years. QCHEM currently includes routines for the calculation of molecular geometry and atomic and molecular SCF. A variety of other routines are planned, e.g. geometry optimisation, one-electron properties, Moller-Plesset and Cf. The QCHEM system is based on the concepts of the XTAL system of crystallographic programs[l] and adheres strictly to the concepts of portability, generality and flexibility[2]. The failure of most other quantum chemistry packages to meet these goals has already been noted[3]. Portability is achieved through a kernel (or nucleus, based on that of XTAL) of machine-specific routines that have been written and tested on every machine from a CRAY to an IBM-PC over a period of five years. This range of hardware is especially relevant as quantum chemistry packages have been designed for bom extremes[4,5]. The source code is distributed as ratmac instructions to be converted to fortran77 code for the target machine by the preprocessor RFPP[6\. A portable version of RFPP is supplied with the QCHEM system.

QCHEM encourages collaborative development because the file structure and the system operations (e.g. input/output processing) have been specified precisely and are strictly enforced[7]. These specifications enable laboratories with diverse interests to use common software and to develop programs that interface easily with existing calculations. Separate calculations communicate with each other through a binary data file which also archives the results. Developers are encouraged, where possible, to write modular code in its most general form. Modularity and generality allow easy adaptation to specific requirements (e.g. the electron integral codes may be replaced with alternate algorithms). This allows direct comparison between algorithms. Good documentation is a very important component of the QCHEM system[6,7,8]. A sample of User and System documentation will be available for viewing. There is a simple pathway for exchanging atomic data between the QCHEM and XTAL systems. In addition, many of the tools of theXTAL system (e.g. plotting routines) may be incorporated into the QCHEM system with only minor modification. f 1] Hall, S.R., Stewart, J.M. and Munn, R.J. 1980 Ada Cryst. A36,979 [2] Hall, S.R. and Stewart, J.M. 1988 XTAL2.4 System Manual. University of Western Australia Report [3] Cisneros, G. and Bunge, C.F. 1986 Int. J. Quant. Chem. Symp. 19, 193 [4] Colwell, S.M., Marshall, A.R., Amos, R.D. and Handy, N.C. 1985 Quantum Chemistry on Microcomputers, Chemistry in Britain (July), 655-9 [5] Taylor, P.R. and Bauschlicher, C.W. Jr. 1987 Theor. Chan. Acta. 71, 105 [6] Hall, S.R., 1988 RFPP2.3: Ratmac-to-fortran77 User's Manual. University of Western Australia Report [6] Favas, M.C and Hall, S.R., 1988 QCHEM1.0 System Manual. University of Western Australia Report [7] Favas, M.C. 1988 QCHEMLO User's Manual. University of Western Australia Report 50 B-5

19 19 35 l AND HYPERFINE COUPLING CONSTANTS FOR F, F2~» °

OBTAINED BY UHF AND CI METHODS

F. GREIN AND S. P. KARNA

DEPARTMENT OF CHEMISTRY

UNIVERSITY OF NEW BRUNSWICK

FREDERICTON, N.B.

CANADA E3B 6E2

Using Gaussian basis sets, both isotropic (a^,) and nonisotropic (A,. ) 19 19 35 hyperfine coupling constants (hfcc) were calculated for F, F, , CS. and

C8-2 from projected unrestricted Hartree-Fock (PUHF) and MRD-CI wavefunctions. The basis sets were increased in size and function-type (d,f-functions) until the hfcc's no longer changed. As expected, A,, was fairly insensitive to the basis set, whereas aM changed a lot. 35 For C2._ , relatively small basis sets and PUHF methods were found to 19 - be sufficient for obtaining experimental hfcc values. For F_ , the PUHF results for aM are 12% too high, but agreement with experimental numbers is 19 35 easily obtained at the CI level. The atomic systems F and C& present much greater difficulties. The dependence of a^. on the basis set is strong, 19 and convergence is hard to reach. For F, PUHF results for a^ are ~75Z 35 higher than an experimental value. For C£, experimental or reliable theoretical hfcc's are not available.

i |

;.• ;

51 B-6

IMPROVED TREATMENT FOR MATRIX ELEMENT EVALUATION OF SPIN-DEPENDENT OPERATORS

QIANER ZHANG AND XIANGZHU LI (DEPARTMENT OF CHEMISTRY AND INSTITUTE OF PHYSICAL CHEMISTRY, XIAMEN UNIVERSITY, XIAMEN, FUJIAN, CHINA)

A general approach of obtaining matrix elements of spin- dependent operators for many-electron systems is developed to improved the treatment primitively suggested by Cooper and Musher. The approach is largely based on the recent results which the present authors have achieved in the representation theory of inner- and outer-product reduction of the symmetric group Sjr. The approach consists of (1) exploitation of the outer-product coupling coefficient (OPCC) to generalize the symmetry adapted linear combination of spin-dependent operators, (2) formulation of the irreducible tensor method of S^j, (3) presentation of a general expression for the matrix elements in terms of a Racah coefficient of SN together with a reduced matrix element, (4) expression for the reduced matrix elements in terms of OPCC, IPCC (inner-product coupling coefficient) and the corresponding one- and two-electron integrals. Detail illustrative treatments include the discussion for one- and two-electron operators between many-electron states, the standard orthogonal state as well as the valence bond-type bonded tableau (BT) state.'

References 1. Q.Zhang and X.Li, J.Phys. A: Math.Gen.2O, 6185(1987). 2. I.L.Cooper and J.I.Musher, J.Chem.Phys.57, 1333(1972).

52 B-8

+ A SECOND-ORDER HEITLER-LONDON THEORY OF THE CHEMICAL BOND: H2 K.T. TANG AND J.P. TOENNIES MAX-PLANCK-INSTITUT FOR STRUMUNGSFORSCHUNG D-3400 GUTTINGEN

One of the fundamental problems of quantum chemistry is to acquire a physical understanding of the nature of the chemical bond. The one electron + bond in H2 is an ideal system for testing models since the results can be compared directly with exact calculations. Recently Chajasinski and Jeziors- ki1) have derived rather complicated analytical expressions for the second -order energy from the Murrell-Shaw and Musher-Amos theory and get agreement to within better than 3% with the exact results for R > 2 a.u.. In our ap- proach we show that it is possible to carry out a second-order Heitler-lon- don theory calculation by introducing one approximate identity, which is exact in perturbation theory without exchange. The result which is very simple, agrees with that of Chajasinski and Jeziorski except for "a factor 2 in the smallest term, which has only a 1?i-effect on the energy at the va- lence minimum. To further simplify the formulas, we use a simple electrostatic model to calculate the damped induction terms. The expression for the damping function agrees exactly with our previous analytical expression^' and devi- ates only very slightly from exact calculations.-'' The same model enables us tc obtain a simple expression for the spherical induction term, which is in excellent agreement with the exact result. ' Furthermore it is shown that .".he exchange polarization and second-order overlap terms can be appro- ximated ty their asymptotic values with the former being damped by the di- pole induction damping term. With this model we are able to get agreement with the exact results to within 2% down to R = 1 a.u. . The advantage of the present approach is that the potential energy is given by a series of terms, each of which has o simple physical interpretation. An analogous model has recently been 3 l shown to predict the Z and Z potential of H2 and Li2. '

!) G. Chajasinski and B. Jeziorski, Int.J. Quantum Chem. VII. 63 (1973) 2) K.T. Tang and J.P. Toennies, J.Chem.Phys. 80, 3726 (1984) 3) H. Kreek and W.J. Meath, J.Chem.Phys. 50, 2?89 (1969) 4) K.T. Tang, to be published 5) K.T. Tang and J.P. Toennies, to be published.

53 B-9 CALCULATIONS OF RELIABLE STATIC POLARIZABILITIES FOR SMALL POLYATOMIC MOLECULES AND THEIR APPLICATION TO POLYMER PHYSICS

Richard L. Jaffe and Kenneth Yao NASA Ames Research Center Moffett Field, California 94035, U. S. A.

Delano P. Chong Department of Chemistry University of British Columbia Vancouver, B. C. V6T 1W5, Canada

Andrew Komornicki Polyatomics Research Institute Mountain View, California 94043, U; S. A. An efficient prescription for computing the second-order static polarizability tensor for polyatomic molecules is described. The polarizability is computed as the second derivative, with respect to external electric field parameters, of the ab initio SCF energy. If the calculations employ minimal Gaussian atomic orbital basis sets augmented with field-induced polarization functions(l), the resulting average polarizabilities are generally within 10-15% of experiment and in excellent agreement with larger basis set Hartree Fock calculations. These basis sets are small enough to permit calculations of molecules containing up to 6-8 first and second row elements. In the present study, the average polarizability and polarizability anisotropy have been computed for more than 35 small polyatomic molecules including the series of fluoro- and chloro-methanes and silanes. The computed ': polarizability anisotropies for n-alkanes have been used to ;, parameterize model calculations for polyethylene. Similar calculations for simple methyl esters have been used to > interpret stress- and strain-birefringence measurements for / polymethyl methacrylate (PMMA). [i; i. CD G. D. Zeiss, V. R. Scott, N. Suzuki, D. P. Chong and I S. R. Langhoff, Mol. Phys. 37 (1979), 1543. i 54 B-10 Abstract for ICQC6 - A. Atomic and Molecular Quantum Mechanics TRANSITION FROM CLASSICAL MECHANICS TO QUANTUM MECHANICS: PERTURBED MULTIDIMENSIONAL HARMONIC OSCILATORS*

GABRIEL ALVAREZ,t SANDRO GRAFFL* AND HARRIS J. SILVERSTONE DEPARTMENT OF CHEMISTRY, THE JOHNS HOPKINS UNIVERSITY,

BALTIMORE, MARYLAND 21218

It is known from previous work1 that the detailed transition from classical mechanics to quantum mechanics, particularly in regard to the question of quantum corrections to the semiclassical quantization, can be completely understood for the one- dimensional x4 perturbed harmonic oscillator. This is a consequence of five facts: (i) The quantum perturbation series for the energy can be solved order-by-order in closed form, (ii) The quantum series rearranges directly into the classical canonical perturbation series plus quantum corrections proportional to successively higher powers of h2. (iii) The classical series2 and the subseries for the quantum corrections converge (subseries-by- subseries) to the terms of the "JWKB" expansion for the energy (to all orders of ft), (iv) The (all-order) JWKB expansion, conversely, yields the quantum perturbation series and consequentiy uniquely determines the exact eigenvalue, (v) The ratio of the quantum energy to the classical energy at action (n+l/2)fi differs from 1 asymptotically by ; l/[9Tc(n+l/2)2], independent of both h and the perturbation coupling constant, as the »' harmonic oscillator quantum number n approaches «>. An interesting additional feature of P the one-dimensional problem is the mechanism by which the convergence of the classical h. perturbation series and of the series for the quantum corrections gets turned into the '£ divergence of the quantum perturbation series. For multidimensional perturbed coupled |; oscillators, the situation is much more complicated by degeneracy in the quantum case and ,, resonance in the classical case. The quantum case can be formulated3 within the framework % of classical canonical perturbation theory with a classical potential modified by "quantum jf corrections." This, along with the order-by-order solvability of the quantum perturbation £ theory, permits discussion of the detailed transition from classical to quantum mechanics in f: the multidimensional case. f: *., •Supported in part by NSF Grant No. PHY-8502383. tFulbright Fellow. ^Permanent address: Dipartimento di Matematica, Universita di Bologna, 40127 Bologna, Italy 1G. Alvarez, S. Graffi, and H. J. Silverstone, [submitted to Phys. Rev. A, (1988)]. 2G. Turchetti, Nuovo Cim. 82B, 203 (1984). 3S. Graffi and T. Paul, Commun. Math. Phys. 108, 25 (1987).

55 B-ll

VAT.ENCE BOWD THEORY.

J. GERRATT1, H. RAIKONDI2 and D.L. COOPER3.

'Department of Theoretical Chemistry University of Bristol, Bristol BS8 ITS, United Kingdom. 2Dipartimento di Chlmlca Fisica ed Elettrochimica, Universita di Nilano, 20133 Milano, Italy. 3Department of Inorganic, Physical and Industrial Chemistry, University of Liverpool, PO Box 147, Liverpool L69 3BX, United Kingdom.

The spin-coupled valence bond theory provides very high quality electron- ic wave functions for both ground and excited states of molecular systems with- out losing essential physical and chemical insight. The 'zero order' wave function is the spin-coupled function. For an N-electron system this consists of a single configuration of N non-orthogonal orbitals. The orbitals are expanded in extensive multi-centre basis sets, whose coefficients are fully optimised simultaneously with the coefficients of all the allowed N-electron spin funct- ions. This is achieved by "'. use of an efficient second-order 'stabilized Newton-Raphson' method. This wave function by Itself incorporates a substantial degree of electron correlation and provides the correct topology of the ground state potential surfaces: Potential wells are given to 90-95% accuracy, equil- o ibrium positions of the nuclei to ca. 0.01A. The position and heights of potent- ial barriers are given to a similar precision. The spin-coupled wave function is further refined by a 'non-orthogonal CI', using virtual orbitals generated in the spin-coupled calculation. The final wave function is exceedingly compact and provides total energies, excitation energies, nuclear geometries, and other molecular properties of the same quality as current 'state-of-the-art' large-CI codes.

However it should be emphasised that the spin-coupled wave function alone incorporates the essential physics of the ground electronic state, and remains dominant over the whole potential surface. It has provided a series of essential insights into electronic structure. We have for the first time a simple picture of the motion of correlated electrons in molecules.

A survey will be presented of a number of systems where the spin-coupled theory has provided striking results. This includes benzene, other aromatic and non-aromatic systems, 1,3-dipolar systems such as diazoroethane and nitrone (CH2NHO), cycloaddition reactions, degenerate systems such as C3H3, and excited states of several radicals and ions. Finally, if time permits, recent extensions * of the theory in providing a second-quantised 'non-orthogonal many-body perturb- ation' theory - with applications to spin alignments in crystalline materials - will be outlined.

General References.

'Modern Valence Bond Theory'. D.L. Cooper, J. Gerratt and M. Raimondi, Adv. \ Chem. Phys. (1987) LXIX 319-397. J' 'Modern Valence Bond Theory: Was Kekule Right?'. J. Gerratt, 'Chemistry in Brit- ain', April 1987 327. '•

56 B-12

AB INITIO TEST OF THE PAIRWISE ADDITIVnY ASSUMPTION OF SEMIEMPIRICAL ELECTRONIC STRUCTURE METHODS Karl F. Freed and Xiao-Chuan Wang James Franck Institute and Department of Chemistry, The University of Chicago. Chicago, Illinois 60637 The ab initio, correlated effective valence shell Hamiltonian ( rtf v) method is applied to the CH2 molecule in order to test the underlying assumption of a pairwise additive parametrization that is common to all semiempirical electronic structure methods. As a preliminary step, we verify that the 9{v method is of suitable ab initio quality by comparing results of both second and third order six valence orbital •H v calculations with full configuration interaction (CI) calculations for CH2 that employ the same basis set of 25 Gaussian type orbitals. Good agreement is found for the rather sensitive lowest singlet-triplet adiabatic separation as well as the excitation energies to lowest singlet excited states and to a variety of ion states for which full CI data are available. The third order M v corrections are generally rather small and generally tend to improve agreement with full CI computations. The H v calculations again display the remarkable property of accurately representing the energies of all valence states of methylene and Its positive ions by use of a single calculation with a common set of valence orbitals. The comparisons with the model Hamiltonians of semiempirical methods employ M v calculations in which the methylene valence orbitals are taken as linear combinations of the 2s and 2p carbon atom orbitals and the hydrogen atom Is orbitals in order that the computed M v matrix elements may be transformed into ones within this atomic valence basis set. Because these starting methylene valence orbitals are poorer in quality than the molecular SCF valence orbitals used to test against full CI calculations, third order corrections are required for CH bond lengths less than 3au. However, the resulting energies are then close to those obtained from third order H v calculations with molecular SCF orbitals. Thus, our computations correspond to an accurate correlated ab initio treatment that has the unique feature of being representable in terms of the effective valence shell Hamiltonian in an atomic orbital basis. In addition to a substantial dependence of the one-center, two-electron carbon atom repuslion integral on CH bond length, we find a considerable variation with bond angle. The bond length and angle dependences arise from changes in the correlation energy with bonding. Both effects are not explicitly included in semiempirical methods, where these one-center integrals are taken to be constants, independent of molecular environment. The angle dependence represents a departure from pairwise additivity of parameters, i.e., of the matrix elements of M v. A similar analysis has been made of other one and two electron integrals in methylene using Cartesian and hybrid orbitals in order to investigate such features as the lack of rotational invariance of the m~ be elements of oi v and the choice of hybrids giving the weakest departure from ^airwise additivity.

57 B-13 CONSISTENT GENERALIZATION OF THE M0LLER-PLESSET PARTITIONING TO ARBITRARY REFERENCE STATES K. WOLINSKI and P. PULAY DEPARTMENT OF CHEMISTRY, UNIVERSITY OF ARKANSAS FAYETTEVILLE, ARKANSAS 72701

Many-body perturbation theory is the most efficient method for treating dynamical correlation. Among its variants, the Mtfller-Plesset (MP) partitioning is used almost exclusively for closed shells. Its generalization to open-shell and MC-SCF reference functions has been notoriously difficult, with the exception of UHF wave functions. UHF-based MP theory may, however, exhibit serious artifacts, due to spin contamination. In a recent paper [1], we have suggested a consistent generalization of the MP partitioning to arbitrary reference states, based on our non-canonical MP partitioning [2]. The present method is not analogous to quasi-degenerate perturbation theory: we have a single reference state. It is more similar to the partitionings proposed by Davidson and Bender, Hubac and Carsky, and Roos et al put it is free of some or their shortcomings. In particular, our definition is independent of the particular orbital representation of the reference wave function, unlike methods which require that the orbitals be eigenfunctions of H— Moreover, our definition includes the important semi-internal substitutions. We define a Fock operator f=h+j(D)-k(D) where D is the first-order density matrix of the reference wave function, and j, k are Coulomb and exchange operators. Our Ho is

Ho =p oFPo + PSFPS + PDFPD +- where F = f(l)+..f(N), and Pg, Pr>" are projectors to the reference wave function, and to the singles space, and to the doubles space, resp. The exact definition of the excited subspaces is given in Ref. 1. This definition leads to

'.' function is size-consistent. % In Ref. 1, we have shown that the method functions very well for effective y two-electron systems: the dissociation of H2, LiH, Li?, Heg* etc. Here we \ present second and third-order results for two-configuration, doublet, and i excited-state singlet systems. Our examples include the dissociation of fluorine, f hydrogen fluoride and CH3...H, the dipole moment and geometry of ozone, twisted I ethylene, the dissociation reaction HCN-*H+CN, and excited singlet states of formaldehyde. The results, even at second order, compare favorably with MC-CI results. 1. K. Wolinski, H. L. Sellers and P. Pulay, Chem. Phys. Lett. 140,225 (1987). 2. S. Saebo and P. Pulay, Theor. Chim. Acta 69,357 (1986). 3. W. Meyer in Methods of Electronic Structure Theory, edited by H. F. Schaefer, Plenum, New York, 1977, p. 413; H.-J. Werner and E. A. Reinsch, J. Chem. Phys. 76, i 3144(1982). I 58 B-14 Correlation potential for molecular systems from the single particle Green's function

L.J. Holleboom, J.G. Snijders, E J. Baerends and M.A. Buijse Dept. of Theoretical Chemistry Vrije Universiteit DeBoelelaanl083 1081HV Amsterdam The Netherlands

Abstract The Green's function (GF) formalism [1] is a viable method to study the electronic structure of atomic and molecular systems. One of the major advantages of the method is that measurable quantities such as the total ground state energy and the ionization potentials can be directly obtained without prior calculation of a wavefunn'on. The single particle GF can be considered as a time-dependent generalization of the one-density matrix. As such the expectation value of one-electron operators can be calculated. Though the fact that the total ground state energy can be obtained suggests that the two-elctron density is also contained in the single particle GF this is not the case. However it is possible to derive a local potential [2] describing the correlation effects from the single particle Green's function which is actually identical to the Slater-Lowdin correlation potential [3,4] r p(x ,x x x ) i 1 f 3 V v l h co^>h frr*2> \ } -T^. ^—Tj- l^- <

This potential could be put into the Hamiltonian H to obtain a hopefully accurate zero order Hamiltonian and small interaction Hamiltonian. Here we study the potential in itself and use it to judge the quality of an approximate single particle GF. The latter function is obtained by solving the Dyson equation G = GQ + GQXG where the self-energy Z is expanded to second order in the fluctuation operator H - F with F the sum of Fock operators. We now have two locally meaningful quantities i.e. the electron density p(Xj) and the correlation potential VcorT(x1) that can be derived from the single particle GF. Both can also be calculated from the two density matrix which in turn follows from a CI or otherwise obtained approximate wavefunction which allows one to compare and judge the results. We present results for some simple model systems namely He, Be and H2. For the Helium I atom we obtain a very accurate second order energy which can be understood from the local agreement between density and correlation potential obtained from a GF calculation on ) the one hand and a full CI calculation on the other hand. For the Beryllium atom one I expects that the Hartree-Fock solution is a bad starting point. Surprisingly the GF method : provides an accurate correlation energy though a closer look at the density and correlation ; potential reveals that this is due to fortuitous cancellation. The failure of a perturbative f approach, which the GF method is, when the zero order starting point is bad is clearly \ illustrated by plots of p(xj) and Veon(.X\) for the H2 molecule at various intemuclear : distances. References [1] W. von Niessen, J. Schirmer and L.S. Cederbaum Comp. Phys. Rep. 1 (1984) 57 [2] L.J. Holleboom et al submitted to J. Chem. Phys. [3] J.C. Slater Phys. Rev. 81 (1951) 385 [4] P.O. Lowdin Phys. Rev. 97 (1955) 1474

59 B-15 APPLICATIONS OF OPEN-SHELL COUPLED-CLUSTER THEORY WITH INCOMPLETE MODEL SPACE USING AN EIGENVALUE-INDEPENDENT PARTITIONING TECHNIQUE R.CHOUDHURY, D.SINHA AND P.MUKHERJEE THEORY GROUP. DEPARTMENT OF PHYSICAL CHEMISTEY. INDIAN ASSOCIATION FOR THE CULTIVATION OF SCIENCE, CALCUTTA 700-032, We shall report in this paper some illustrative numerical applications of our recently developed coupled-cluster (CC) theory with incomplete model space that produces connected effective hamiltonian H

MODEL SPACE AND EFFECTIVE HAMILTONIAN

CONGHAO DENG, ZEXIN WANG, DACHENG FENG AND ZHENGTING CAI DEPARTMENT OF CHEMISTRY, SHANDONG UNIVERSITY. JINAN, CHINA

A The effective hamiltonian H^[l] .A AA A ** H^rt = PH-rt. (1) in model space is not hermitian. SvrSek and Hubac[2] have tried to hermi- trze it by unitary transformation. But the transformed wavefunction is no longer in original model space. We have shown that it can be hermitrzed simply by written as

/» f /"A A » A» H«ff = j(PHJt+iCHP) J*A* . AAA A.AA = FHP +1(PVT+T*VP) (2) where we have defined T = |«fc| (3) A- P+T (4) and | ^^ is the normalized ket in model space. is the ket in complementary space. and the eigenket of H is l~l + ! (7) we have expressed H#« to third order perturbation. The eigenvalue Ei of H is

Et =• Hnun + Vmc (8) Vmc is defined as the (visidual) correlation energy, and we also have ex- pressed it to third order perturbation. We tried to seek a function f so that Vmc is expressed in terms of £ and model space only. By variation of the functional Vmc (f) with respect to f, we can get the best Vmc. The absolute value of Vmc is much smaller than of Ei, using variation method to calculate a small quantity would be better.

REFERENCES [1] C. Blcch, Nucl. Phys. 6, 329 (1958) (2] M. Svrcek and I. Hubac, Int, J. Quan. Chem. S12, 33 (1978) 61 B-17

LOW FREQUENCY OL'NDINft VIBRATIONS R.D. AMOS AND J.C. RICE

University Chemical Laboratory, l.ensfield Road Cambridge CB2 1EW U.K.

I he compounds C,0«, C.0_, C,S_, C_S_, C,SO and C..SO have unusually low frequency bending motions - that for C,0_ is known to be 10cin~ . We have calculated structures and frequencies for this series of molecules, using SCF and MP2 methods with a variety of basis sets. The smaller members in the sequence have also been unincj the coupled-pai r lunet ional approach.

62 B-18

RENNER-TELLER ROVIBRONIC SPECTRUM OF THE HCS RADICAL

AND THE ROVIBRATIONAL SPECTRUM OF HCS"

P.Rosmus, J.Senekowitsch, S.Carter, H.-J.Werner and N.C.Handy

Using highly correlated electronic wavefunctions, the three-dimensional potential energy, electric dipole and electronic transition moment functions have been calculated for the first two electronic states of the HCS radical. Both states form a Renner-Teller pair, the lower has a bent equilibrium structure, the upper is linear. The results of the electronic structure calculations have been used in solutions of the nuclear motion problem. The standard perturbation theory results for the rovibrational levels will be compared with the variational rovibrational and rovibronic Renner-Teller results. In the calculation of the radiative transition probabilities between the rovibronic states contributions from the electric dipole moment functions of both electronic states as well as the elctronic transition moment function have been considered. The rovibronic spectrum of the hitherto unkown HCS radical will be predicted. For the HCS" ion the rovibrational terms and radiative transition probabilities will be predicted. In these calculations the rotationai-vibrational coupling has been fully accounted for.

P. Rosmus and N.C.Handy, University Chemical Laboratory, University of Cambridge, U.K. J. Senekowitsch, S. Carter, Department of Chemistry, University of Frankfurt, Frankfurt, Germany. H.-J. Werner, Department of Chemistry, University of Bielefeld, Bielefeld, Germany.

63 B-19

ON THE ASSIGNMENT OF THE EXCITED SINGLET STATES

IN THE CO2 MOLECULE

P. J. Knowles, P. Rosmus and H. J. Werner

High accuracy electronic structure calculations ( contracted MRCI wavefunctions with the quality of several 107 uncontracted configurations ) for the energies of CO2 in the low- 1 est states in each of 'S+, IIff, ' Att and *E~ symmetries, as a function of the symmetric stretching coordinate, will be reported. The positions of the electronically excited states have been determined with an expected accuracy of about 0.05 eV. The geometries and the harmonic force constants for the symmetric stretch modes at the barriers to linearity X for ths *£", AU and 'IIj states have been calculated. The results show that the electron- ically excited states l E~ and l A,, of linear CO2 cross in the Franck-Condon region of the l l absorption spectrum with the Ug state. It has been found that the Austate is separated by a barrier from the lowest dissociation asymptote and has a double minimum potential energy function. Implications for the interpretation of the absorption spectrum and the dynamics of the COj photodissociation will be discussed.

P.J.Knowles and P.Rosmus: University Chemical Laboratory, University of Cambridge, Cambridge, U.K. H.J.Werner: Department of Chemistry, University of Bielefeld, Bielefeld, Germany.

64 B-20

APPLICATION Of PROJEC7ED UNRESTRICTED MjliLLLR-PLESSET SECOND-ORDER ENERGY METHOD

by

J.E. RICE AND N.C. HANDY University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW

the formula for the second-order unrestricted M

I

A I 65 B-21 AB-INITIO MRD-CI CALCULATIONS FOR BREAKING A CHEMICAL BOND IN A MOLECULE IN A CRYSTAL OR OTHER SOLID ENVIRONMENT. JOYCE J. KAUFMAN, SZCZEPAN ROSZAK*, P. C. HARIHARAN AND PHILLIP B. KEEGSTRA. DEPARTMENT OF CHEMISTRY, THE JOHNS HOPKINS UNIVERSITY, BALTIMORE, MARYLAND, 21218 U.S.A.

Ab-initio MRD-CI calculations are necessary to describe bond- breaking processes in the ground and, especially, in electronically excited states. We have extended our approach based on localized orbital/"effective" CI Hamiltonian to MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. The ab-initio SCF is solved for the system of all the molecules in a unit reference cell (or even larger set of molecules) in the multipole environment of even farther out neighboring molecules. The resultant SCF wave function is localized. The localized occupied and virtual molecular orbitals in the region where the bond-breaking takes place are included explicitly in the MRD-CI (by the method of Buenker and Peyerimhoff) and the remainder of the localized occupied molecular orbitals are folded into an "effective" CI Hamiltonian. We had earlier verified the validity of this approach for the potential energy surfaces for bond-breaking in large molecules. The method is completely general and MRD-CI results will be presented for the H-X-NO^dissociation as a function of the number of molecules treated in the SCF and the number of surrounding molecules represented by multipoles. This research was supported by ONR Contract N00014-80-C-0003. The authors appreciate the CRAY XMP supercomputer time from the NSF San Diego Supercomputer Center. The authors thank Professor Robert Buenker, University of Wuppertal, Wuppertal, Federal Republic of Germany, for his collaboration in adapting his MRD-CI program at the Johns Hopkins University. •Visiting Scientist, the Johns Hopkins University; Permanent address: Institute of Organic and Physical Chemistry, Wroclaw, Poland.

66 B-22 A THEORETICAL STUDY OF PROTONATION OF TRIATOMIC SILICON-CARBON COMPOUNDS. A. LARGO-CABRERIZO AND J.R. FLORES, DEPARTAMENTO DE QUIMICA FISICA, FACULTAD DE CIENCIAS, 47005 VALLADOLID, SPAIN.

Recently, there has been a growing interest in the study of small silicon-carbon compounds. Proton affinity (PA) is an important property in gas-phase chemistry, since it is a measure of the molecule basicity. In this communication we present a comparative ab initio study of pro- tonation of C3, SiC2, Si2C, and Si3- Structures of protonated SiC2 and Si2C have been presented else- + + where (1,2). Therefore, we shall focus on the Si3H and C3H structures. + 1 + 1 3 The geometries of five Si3H states, £ , A1(1), ^(2), B2, and 1A1, were optimized at HF/6-31G** level. Vibrational analysis shows the 1C+ and l&i(2) species being transition states rather than true minima. Correlation calculations at MP4 level showed the *A' state, which comes from protonation of the Si3 ground state (3) at a terminal silicon atom, to lie the lowest in energy, although the energy differ- ence between *A' and ^B2 is just 2 kcal/mol. + 1 Two C3H states have been previously studied (4): ^ and Ai(l), ^£+ being the predicted ground state. We have also considered three 1 1 other states: A1(2), ^B2 and ^Fl . A1(2) was found to be a transition state and, although B2 lies the lowest in energy at HF level, *5I+ is found to be the ground state at correlated levels. The theoretical estimates for the proton affinities (at 298 K) are: PA(Si3)=200 kcal/mol; PA(C3)=184 kcal/raol; PA(SiC2)=232 kcal/mol; PA(Si2C)--210 kcal/mol. For SiC2 and Si2C protonation at carbon is thermochemically favoured. These values show that C3 comparatively has a very low PA. On the other hand, Si3 has a relatively high PA compared to the values of protonation at silicon for both SiC2 and Si2C. These facts can be explained on the basis of electronic structure arguments.

(1) J.R. Flores, A. Largo-Cabrerizo and J. Largo-Cabrerizo, J. Mol. '-% Struct. (Theochem) 120 (1986) 33. • (2) A. Largo-Cabrerizo and J.R. Flores, Chem. Phys. Lett., in press. 3 (3) K. Raghavachari, J. Chem. P.hys. 83 (1985) 3520; R.S. Grev and i H.F. Schaefer, Chem. Phys. Lett. 119 (1985) 111. J (4) K. Raghavachari, R.A. Whiteside, J.A. Pople and P.v.R. Schleyer, J. Am. Chem. Soc. 103 (1981) 5649. ; 67 B-23 ON POSSIBLE REACTION SCHEMES FOR PRODUCING THE SiNH MOLECULE IN INTER- + STELLAR SPACE: AN AB INITIO STUDY OF THE (SiH3N) SYSTEM. J.R. FLORES AND A. LARGO-CABRERIZO, DEPARTAMENTO DE QUIMICA FISICA, FACULTAD DE CIENCIAS, 47005 VALLADOLID, SPAIN.

Many molecules have been detected in interstellar space. Most of them are simple molecules containing first row atoms and hydrogen, but there are several molecules in which a second row atom "replaces" its + first row counterpart, such as SiO, SiS, CS, NS, H2CS, HCS , etc. It is quite possible that HSiN/SiNH isomers be present in interstellar space since they are the counterparts of the HCN/CNH isomers, which are abundant in interstellar space. In fact, an unidentified line was tentatively assigned by Lovas to HSiN (1). The most stable isomer, SiNH, has a very small dipole moment, so its rotational spectrum should not be easily observed. The following steps were first proposed by Turner and Dalgarno (2) to be responsible for the production of HSiN/SiNH

+ + Si + NH3 * (SiH2N) + H (a)

+ (SiH2N) + e" » (SiNH) + H (b)

but neither experimental nor theoretical information exists concerning these reactions. Since reaction (a) should be the rate-controlling step, we have carried out a complete study of the (SiH-jN)+ potential surface, which is then compared with the (CH3N)"1" one. + + The energy ordering of the (SiH2N) isomers is H2SiN {C2v) > + HSii»H (Cs) > SiNH2(C2v)- Only the most stable isomer can be produced in reaction (a), since, otherwise, it should be an endothermic + process. Other products, such as SiNH + H2 are not thermochemically favoured. Previous work (3) has shown that the existence of activation barrier for this reaction depends on the energy cf two transition states. These have been calculated at the MP4/MC-311Gxx//MP2/6-31Gx £ level. The results make clear that there is at least one mechanism .••' for reaction (a) involving no energy barrier. Another mechanism may $ be proposed which has a very small barrier. .'; In conclusion, reaction (a) is exothermic and barrier-free, so ?• it can take place in interstellar space conditions.

(1) F.J. Lovas, Astrophys. J. 193 (1974) 265. \ (2) J.L. Turner and A. Dalgarno, Astrophys. J. 213 (1977) 3f. :\ \\ (3) J.R. Flores, F. Gomez and J. Largo-Cabrerizo, Chem. Phys. Lett., #^ i.'i press.

68 B-24 Application of the Singles and Doubles Coupled Cluster - Model to Electron-rich Compounds: Cis and Trans FNNF, and the FNO and FON Isomers

Timothy J. Lee Department of Theoretical Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW United Kingdom

Abstract

Electron-:ich co-npounds have plagued ab initio theoretical chemists for the sim- ple reason tha* the commonly used methods such as configuration interaction (CI) theory and Moller Plesset (MP) perturbation theory yield unusally poor results. Many of these systems are characterized by numerous configurations which contribute a rea- sonably small fraction to the exact wavefunction. However, their combined effect is quite significant. Ozone would be a counterexample in this case since it is well doc-

umented that a second configuration is very important for Q-iv geometries. However, many electron-rich molecules are not really considered multireference problems by the standard definition. Therefore, we expect that the singles and doubles coupled cluster (CCSD) model should perform significantly better for these systems than singles and • doubles CI (CISD) or second order MP perturbation theory (MP2). We investigate I this hypothesis by rigorously locating the minimum energy geometries at each level of i theory.

;|! We present and compare MP2, CISD and CCSD equilibrium structures for the titled compounds using a double zeta plus polarization (DZP) basis set and also compare these to experiment where possible. We have also investigated the importance of a large one-particle basis set and fchus, present MP2 and CISD results using a triple zeta plus double polarization (TZ2P) basis set.

69 B-25 SEMIEMPIRICAL STUDY OF POLYATOMIC RARE GAS HALIDES IN GAS PHASE

AND SOLIDS

ISIDORE LAST, SOREQ NUCLEAR RESEARCH CENTER, YAVNE 70600, ISRAEL

THOMAS F. GEORGE, DEPARTMENT OF CHEMISTRY AND OF PHYSICS AND

ASTRONOMY, 239 FRONCHAK HALL, STATE UNIVERSITY OF NEW YORK AT

BUFFALO, BUFFALO, NEW YORK 14260

Systems formed by rare gas atoms and halogen atoms or molecules attract much attention, *irst of all due to their spectroscopic properties in ionic states formed by charge transfer. These systems were considered by the semiempirical diatomics-in-ionic- systeins (DIIS) method which takes into account the charge (hole) delocalization in ionic states and the coupling between the neutral and ionic states. In the DIIS method the Hamiltonian matrix elements are expressed in terms of diatomic potentials, except for those which are responsible for coupling between the ionic and neutral states. The coupling matrix elements are determined by fitting the diatomic transition moments. Calculations were performed for van der Waals complexes and clusters Xe Cl, Xe HC1 and ionic molecules (Xe )+Cl~ and (HXe )+Cl~, as well as for systems formed in Xe solids by Cl atom and HC1 molecule. The calculations give the structure of the systems, dissociation energies energies of electronic transitions, and transition moments. The calculations performed with the HC1 molecule show, in particular, the existence of ground state ionic molecule (HXe)+Cl~, the decrease of the KC1 electronic excitation energy in clusters and solids and the increase of the emission photon energy of ionic (HXe )+Cl~ systems as compared to XeijCl" molecule. The calculation performed with Cl atom into Xe solids shows, in particular, that the Cl atom has motional freedom in substitutional trapping sites. Due to this freedom the energy spectrum of the excitation to ionic activated complexes is broadened and has two wide maxima which were also found in recent experiments. % References: I.Last, T.F.George, J.Chem.Phys. 87, 1183 (1987), I.Last, T. T.F.George, M.E.Fajardo, and V.A.Apkarian, J.Chem.Phys. 87_, 5917 (1987), I.Last and T.F.George (sent for publication)

70 B-26

MULTIPLE-CONFIGTJRATION VERSUS SINGLE-CONFIGURATION STRUC- TURE-DEPENDENT PROPERTIES OF CLUSTERS ZdenSk SLANINA The J.Heyrovsky Institute of Physical Chemistry and Elec- trochemistry, Czechoslovak Academy of Sciences, CS-121 38 Prague 2, Czechoslovakia

Recentlyt existence o£ isomerism in molecular clusters was observed several times. Thus,the phenomenon originally predicted and demonstrated by sole analysis of potential hypersurfaces-'-can be now well postulated as a general clus- ter feature. The phenomenon is particularly singled out in the stationary—point hypersurface representation though in whole hypersurface approaches should manifest,too.With the cluster isomerism any structure-dependent quantity can be treated at two levels - either as partial or overall one composed of contributions of just one or all structures,re- spectively. The interplay can be shown with two (CO2)3\e) isomers^ of Dgd and Cs symmetry.Relative stability of both structures (mole fractions WJ.) changes with temperature con- siderably (below left). Above 469.1 K the Dad structure is less important though it is lower in potential energy by about 30 kJ/mol. Consequences are exemplified below right on the standard heat capacity at constant pressure (in J/ K/mol). The overall term is enhanced considerably and ex- hibits extremum course. 1. Z. Slaninai Contemporary Theory of Chemical Isomerism, D.Reidel,Dordrecht 1986. 2. S. H. Fleischman, K.D. Jordan! J. Phys. Chem. 91 (1987) 1300.

200-

a 150- '3

100-

504 200 400 600 T.K 200 400 600 71 B-27

ANISOTROPIC ATOM^ATOM POTENTIALS AND THE STRUCTURES OF THE LIQUID AND SOLID HALOGENS

P. MARK RODGER AND ANTHONY J. STONE (UNIVERSITY OF CAMBRIDGE) DOMINIC J. TILDESLEY (UNIVERSITY OF SOUTHAMPTON)

For many years, model intermolecular potentials have been based on isotropic atorn-atom-atom interactions, usually of the Lennard-Jones or exp-6 type, often sup- plemented by point-charge or central-multipole models of the electrostatic interactions. Such models are inadequate to account accurately for the detaiied properties of many molecular solids and fluids[l]. We describe a new type of potential model in which the constituent atoms are explicitly treated as non-spherical, so that the repulsive and dispersive atom-atom potentials are anisotropic. The electrostatic interactions are de- scribed by assigning point multipoles to the individual atoms. This approach yields a very flexible type of model, and contrary to general belief, it can be computationally very efficient. We have developed potentials of this type for CI2, Br2 and I2 that give a good description of (i) the crystal structure, (ii) the frequencies of the normal modes in the crystal, (iii) the liquid structure factor and (iv) several thermodynamic properties of the Iiquid[2]. This is the first time that a single model potential has succeeded in describing such a wide range of properties; moreover these systems have proved particularly difficult to model with conventional potentials.

References [1] A. J. Stone k S. L. Price, J. Phys. Chem (1988), in press. [2] P. M. Rodger, A. J. Stone & D. J. Tildesley, Mbiec. Phys. 63 (1988) 173; Chem. Phys. Lett. 145 (1988) 365.

72 B-28 NONSPHERICAL ATOMIC GROUNDSTATES AND CHEMICAL DEFORMATION DENSITY. K. RUEDENBERG, L. MILLER, R. A. JACOBSON CHEMISTRY DEPARTMENT AND AMES LABORATORY*, IOWA STATE UNIVERSITY, AMES, IOWA, USA AND W. H. E. SCHWARZ, CHEMISTRY DEPARTMENT, UNIVERSITY OF SIEGEN, SIEGEN, WEST GERMANY X-ray diffraction measurements determine total electron densities in crystals. Standard structure determinations are limited to locating the density peaks that occur where nuclear potentials have their singulari- ties. Modern diffraction techniques are sufficiently accurate to measure also finer density features which pertain to the valence electrons and are expected to embody information relevant to chemical bonding. The deduction of chemical inferences from the experimental data has however been troubled by ambiguities because it is based on the formation of difference densities. They are obtained by the subtraction of the superposition of all atomic densities and there exists uncertainty as regards the most appropriate choice of the latter. The common choice of spherically averaged atomic densities neglects the isoenergetic nonsphericity which can easily occur in atoms with degenerate ground states such as carbon, oxygen or fluorine. The extraction of non- spherical atomic densities from the experimental data on the other hand is not self-evident because of the apparent arbitrariness in separating density changes due to atomic orientations and, possibly, slight deformations from those due to chemical interactions between atoms. New constraints have been formulated by which nonspherical atomic densities are defined in terms of the experimental diffraction data. They essentially correspond to oriented p^oundstates and satisfy the N-repre- sentability conditions. These definitions yield a method for deriving nonspherical atomic densities from the experimental information. It has been implemented by a computer program and it has been applied to crystals of several organic molecules containing up to three benzene rings for which high accuracy measurements are available. The results obtained for the atomic densities and the derived difference densities contain instructive information. We thank Professors C. Kriiger and J. Dunitz for supplying the X-ray data.

•Operated for the U. S. Department of Energy by Iowa State University under Contract No. W-74O5-ENG-82. This work was supported by the Office of Basic Energy Sciences.

73 B-29

DYNAMICS OF MOLECULAR REACTIONS IN SOLIDS: PHOTODISSOCIATION OF HI

IN CRYSTALLINE XE.

R. ALIMI AND R.B. GERBER

DEPARTMENT OF PHYSICAL CHEMISTRY, AND

THE FRITZ HABER MOLECULAR DYNAMICS RESEARCH CENTER.

THE HEBREW UNIVERSITY, JERUSALEM, 91904 ISRAEL.

V.A.APKARIAN

DEPARTMENT OF CHEMISTRY

UNIVERSITY OF CALIFORNIA, IRVINE

CALIFORNIA 92717, USA.

Investigation of molecular reaction dynamics in crystalline solids promises unique advantages for first-principles understanding to reaction dynamics in condensed matter. This is primarily due to the pies- ence of local order that offers major simplifications compared to the situation in liquids. The photodissociation of HI impurities in a host Xe crystal is studied by molecular dynamics simu- l lations, using realistic potentials. From the calculated trajectories we analyze the motion of the fragments following photon absorption, and the sites and vibrations dynamics of the H atoms long after the reaction event is over, when the system has reached equilibrium. The main findings are as follows: (i) H exit from the reaction site is never direct upon photodissoci- ation, but follows as a jump after many collisions with the cage "walls". Phase and energy relaxation of the H atom precede exit from the reaction site. This suggests that a statistical approach can be formulated to describe the reaction rate, (ii) The photodissociation yield varies in a non-monotonic way with the tem- perature. It increases from 0 at C ° K to 0.2 at 17 ° K and then decreases when T is increased to 37 ° K. It •; seems that Ihe lattice vibrations first open pathways for the H atom exit, but at higher T, collisions with Xe atoms surrounding the cage enhance the return of H into the cage, (iii) The nascent H fragment exhibits .:'i transient but well defined high frequencies vibrations in the cage for a timescale of the order of 0.5 psec. v;j (iv) After the exit, the H atoms reach well defined octahedral sites in the lattice. j* Extensive quantum mechanical simulations are in progress, in which H is treated quantum mechani- I '•' cally, while the heavy atoms are treated classically. The main purpose of these simulations is to investi- \ gate the role of tunnelling in the photodissociation process.

74 B-30

COMPLEX SCALING IN STATISTICAL MECHANICS OF CONDENSED MATTER - THEORY AND

EXPERIMENTAL CONSEQUENCES

C. A. DREISMANN

I.N. STRANSKI-INSTITUTE FOR PHYSICAL AND THEORETICAL CHEMISTBY, TECHNICAL

UNIVERSITY OF BERLIN, D-1000 BERLIN 12, F.R. GERMANY

The Complex Scaling Method (CSM), in connection with the ensemble forma- lism of statistical mechanics, predicts the spontaneous emergence of short lived, large coherent-dissipative structures in amorphous condensed systems, e.g. in liquids at standard conditions /I/. These structures are formally represented by a large Jordan block - in the CSM-transformed second order density matrix /2/ - having a Segre characteristic equal to the number of the degrees of freedom of the emerged structures. The connection with Yang's concept of Off-Diagonal Long-Range Order /3/ is discussed. The appearance of coherent-dissipative structures is due to the thermal motion. A specific quantization condition for the "lifetimes" of the quantum states (after complex scaling) characterizes the creation of these structures. The minimum size of a coherent-dissipative structure obeys the equation s . = T .•(Uirk_T/ft), where T , represents the molecular relaxation time mm rel B rel of the process under consideration (that can be determined by a suitable spectroscopic experiment), cf. /1/. These structures are different from (i) the BCS states of superconductivity and (ii) the dissipative structures of phenomenological irreversible thermo- dynamics of Glansdorff and Prigogine. The conceptual differences as well as similarities are shortly discussed. Application to far-infrared absorption spectroscopy in liquids is made /I/. The above formula allows for an interpretation of the anomalous temperature dependence of the absorption bands of acetonitrile (and other molecules) from "first principles". The theoretical framework is also applied to the H -conductivity in water. : Different spectroscopic - and, thus far, unsuccessful - experiments for the detection of the assumed fast H+-motion A/ are interpreted in the light of ,; the CSM. It appears that the well known excess H+ conductance is due to mass interference. A novel relation between this conductance and the proton trans- :•; fer reaction rate constants /5/ is revealed and compared with well known ex- rj perimental results:. ;?, C.A.Ch.-Dreismann and E.J.Brandas, I + II, Ber.Bunsenges.Phys.Chem.f , April 1988. in press; E.J.Brandas and C.A.Ch.-Dreismann, in: "Resonances", Lecture Notes in Physics, Springer 1988, in press. /2/ A.J.Coleman, Rev.Mod.Phys. 35, 668 (1963); J.Math.Phys. _£, 1U25 (1965). /3/ C.N.Yang, Rev.Mod.Phys. 2k, 69U (1962). /h/ H.G.Hertz, Chem. Scripts 22, U?9 (1987). hi S.Meiboom, J.Chem.Phys. 3U, 375 (1961); R.E.Glick and K.C.Tewari, J.Chem. Phys. ik, 5**6 (1966); H.G.Hertz, H.Versmold and C.Yoon, Ber.Bunsenges. Phys.Chem. &, 577 (1983). 75 B-31

POLYMORPHISM AND MOLECULAR DISPLACEMENTS IN ORGANIC SOLID STATE.

CLAUDE DECORET, LABORATOIRE DE CHIMIE INDUSTRIELLE, UA805 DU C.N.R.S., BAT 305, UNIVERSITE CLAUDE BERNARD, 43 BOULEVARD DU 11 NOVEMBRE 1918, 69622 VILLEURBANNE CEDEX, FRANCE

Organic molecules often display several crystalline varieties. The polymor- phism is called conformational when it corresponds to different conforma- tions of the molecule. The relative stability of such arrangements and their mutual transformation have been the object of numerous static and dynamic models. Almost all studies are based on atom-atom potential methods. Lattice and molecular dynamics methods have been applied to plastic phase and to the corresponding ordereddisordered transition of small molecules or rigid molecules, such as benzene or naphthalene. Relative stability calculations have been often carried out for testing the efficiencies of atom-atom potential methods. Differencies, often of the order of few Kcal/mole, are generally well reproduced, even if absolute values depend of the choice of parameters. Concerning the transition between phases, it is to be said that experimen- tal studies show a great variety of parameter dependancy, feeding contro- versies. Single crystal-single crystal second order transformations sometimes are claimed to not exist. Nevertheless, such transformations would be of interest from both theoretical and experimental physic point of view, since they are conceived as cooperative displacements of molecules. Studies of relative stabilities and mutual transformaations of phases are of special interest for pharmaceutical and industries of explosives. It seems to us convenient to differentiate studies on molecular motion which imply a thermodynamic point of view, and molecular displacement studies, more linked with geometry and crystallographic symmetry point of view. Polymorphism is a very usefull support for modelizing molecular motion in space.

76 B-32 IMPROVED SCF THEORY OF INTERMOLECULAR INTERACTIONS WITHOUT BSSE

I. MAYER and P.R. SURJAN+

CENTRAL RESEARCH INSTITUTE FOR CHEMISTRY OF THE HUNGARIAN ACADEMY OF SCIENCES, H-1525 BUDAPEST, P.O.BOX 17, HUNGARY

Some further developments are made in the recent BSSE-free SCF theory of intermolecular interactions tl] based on the "Chemical Hamiltonian Approach" (CHA) £23. It is concluded that the most consistent results can be obtained by calculating the conventional energy expectation value for the orbitals obtained by solving the special CHA-SCF equations tl] , instead of using the previous non-symmetric CHA-SCF energy formula. The problem is tackled both by performing a further study of the simple analytical model discussed in C 3 "5 and by actual numerical applications for several simple systems. The potential curves predicted by the improved CHA-SCF method are close to those given by the Boys-Bernardi a posteriori correc- tion scheme and usually (but not always) go slightly beyond the latter.

References 1. I. Mayer and A. Vibtik, Chem. Phys. Letters V56_, 115 (1987), 140, 558 (1987); A\ Vibdk and I. Mayer, THEOCHEM, in press. 2. I. Mayer, Int. J. Quantum Chem. 23., 341 (1983); I. Mayer, p. 145 in "Modelling of Structure and Properties of Mole- cules" (ed. Z.B. Maksic), Ellis Horwood, Chichester 1987. 3. I. Mayer, Theor. Chim. Acta T2, 207 (1987)

+Permanent address: Chinoin Research Centre, H-1325 Budapest, P.O. Box 110, Hungary

77 B-33 Am Aaalysis of BASB-9F Hydrogea Bomdiag Using

tko Theory of Atoas ia Moleeiles

Marshall T. Carroll, Cheng Chang and Richard F. W. Bader

Department of Chemistry, McKaster University

Hamilton, Ontario, Canada L8S 4M1

Abstract

The theory of atoms in molecule* [II is applied to an analysis of hydrogen bonding. The Laplacian of the charge density is used to predict the structures and geometries of hydrogen-bonded gas-phase complexes of the type BASE-HF [2]. The bases include N2, OC, SC. 0C0, SCO, HCN, N2O, HCP, H2O, H2S, H3N, H3P, 03, 0S0, H,CO, IFF, HC1, N2S and HjCS. Many of the weaker coaplezes have not been characterized experimentally, and so, results of full 6-31G** geometry optimizations are presented. The Laplacian of the charge density, 7p, determines where charge is locally concentrated and depleted. The point where V*p attains its maximum magnitude in a region of charge concentration in the base defines the site of electrophilic attack by the acidic H of HF. The angle of electrophilic attack predicted in this manner is compared with the ab initio equilibrium angle that the R of HF makes with the base. In general, the angles predicted using the Laplacian are in good agreement with the ab initio and experimental results. The present results are compared with those obtained froa electrostatic models. The nature, energetics and mechanism of BASE-HF hydrogen bonding are examined using the theory of atoms in molecules. Both the form of the charge distribution and average values of the atomic properties are used to describe hydrogen bonding. A hydrogen bond exists if there is a bond path between the interacting atoms. The Laplacian of the charge density is positive at the hydrogen bond critical point r. , and so, H-bonds are examples of closed-shell interactions. The value of p at rb increases while the value of p at the H-F bond critical point decreases with increasing dissociation energy DQ. Upon complex formation, the F of OF gains electrons, increases in volume and is stabilized. The hydrogen loses electrons, decreases in volume and is destabilized with the destabilization increasing linearly with Dg. In general, the base atom participating in the D-bond gains electrons, decreases in volume and is stabilized. The transfer of charge froa base to acid explains the effect of dipole moment enhancement [3].

Rc-fezeaces

[1] Bader, R. F. W., and Nguyen-Dang, T. T., 1981, Adv. Quant. Chen., 14, 63^ Bader, R. F. W., Nguyen-Dang, T. T., and Tal, T., 1981, Rep. Prog. Phys., 44, 8931 Bader, R. F. W., 1985, Acct. Chea. Res., f. 18. [2] Carroll, N. T.. Chang, C, and Bader, R. F. V., 1988. Molec. Phys., C3, in press. (3] Legon, A. C, and Milieu, D. J., 1986, Chea. Rev., 8C, 635.

78 B-34

CALCULATION OF INTERMOLECULAR POTENTIAL ENERGY SURFACES BY AB INT10 AND MOLECULAR MECHANICS METHODS

JAMES R. DAMEWOOD, JR.; ROBERT A. KUMPF and WOLFGANG C, F. MUHLBAUER DEPARTMENT OF CHEMISTRY AND BIOCHEMISTRY UNIVERISTY OF DELAWARE NEWARK, DELAWARE (USA) 19716 Research in our laboratories has demonstrated the need for nonprejudicial searches of the potential energy hypersurface for molecular hydration.' As part of this research program, we have recently investigated the utility of applying modified molecular mechanics (MM2) methods to the calculation of the structure and energy of intermolecular complexes. This presentation will focus on the results we have obtained in a study of the hydration of formaldehyde. Possible configurations for 1:1 complexes between formaldehyde and water were generated in a nonprejudicial manner using a SOLvent DRIver program (SOLDRI) written in our labora- tories.-^ Over 88,00 geometries were used as input structures for the mole- cular mechanics calculation of potential energy hypersurfaces. Intermolecular separations between 2.9 and 4.0 A were considered. The quality of the molecular mechanics calculations was assessed by comparison to similar potential energy surfaces generated using ab initio techniques at levels of theory as high as MP4SDQ/6-311+G**. Quantitative agreement between these surfaces is excellent in terms of both associtation energies (RMS deviation = 1.3 kcal/mol in the binding region) and structures. Detailed comparisions of molecular mechanics and ab initio results will be presented. (1) Damewood, J. R., Jr.; Kumpf, R. A. J. Phys. Chem. £1, (1987). ibid. J. Chem. Soc, Chem. Commun. accepted for publication 1988. (2) Damewood, J. R., Jr.; Anderson, W. P.; Urban, J. J. J. Computational Chem. 9, 111 (1988). Damewood, J. R., Jr.; Urban, J. J.; Williamson, T. C.; Rheingold, A. J. Org. Chem. 53, 167 (1988). (3) MUhlbauer, W. C. F.; Damewood, J. R., Jr. submitted for publication. I I

79 B-35 A HE»F»M- IXXTBaiOM FOB MOLECULAR RECOGNITION APPLIED TO THE ANALYSIS OF COMPUTATIONAL STUDIES OF MODELS FOR CHIRAL STATIONARY PHASE INTERACTIONS. S. TOPIOL, W. B. CALDWELL, M. SAB10 AND J. MOROZ. DEPARTMENT OF MEDICINAL CHEMISTRY, BERLEX LABORATORIES INC., 110 EAST HANOVER AVENUE, CEDAR KNOLLS, NJ 07927.

A recently propos«d1 general criterion for molecular recognition is discussed in terms of chiral interactions. This criterion establishes a formal equivalence of one, two, and three points-of-attachment mechanisms for the differentiation of enantiomers. This scheme also provides a definition for the general symmetry requirements for chiral resolving agents. The two complexes of (S)-N-(2-naphthyl)alaninate with both enantiomers of N-(3,5-dinitrobenzoyl)leucine n-propylamide were studied as models for the interactions responsible for the separation of enantiomers using the chiral stationary phase systems developed by Pirkle and coworkers . Based on molecular mechanical, semiempirical and ab-initio quantum mechanical calculations it is suggested that: (i) contrary to earlier models, the pi-pi interactions between the dinitrobenzoyl and naphthyl groups are not the primary components of the total stabilizing interaction and in fact may be destabilizing in nature. This is supported by experimental findings of Wainer and coworkers . (ii) All of the primary components of the interactions of the two complexes are identical in nature and very similar in magnitude, (iii) Only two 'points-of-attachment', which are nearly equivalent in the two complexes, provide for the primary intermolecular stabilization, (iv) Chiral differentiation is achieved via small through space effects. These results are analyzed in terms of the above general criterion. Experiments which have been designed and are underway to test these analyses will be described. Further analysis of and suggestions for the general design of potential new chiral resolving agents will be discussed.

1S. Topiol, submitted for publication. 2W. H. Pirkle and T. C. Pochapsky. J. Am. Chem. Soc. 1986,108,352-354;ibid. 5627-5628; and references therein. I. W. Wainer and M. C. Alembik. J. Cromatogr. 1986,367,59-68.

I.

80 B-36 FROBLICH'S BOSK CONDENSATION OF DIELECTRIC MODES IN A BIOLOGICAL MEMBRANE SEEN AS A DAVYDOV SOLITON H. Bolterauer Instltut fur Theoretische Physik Justus-Lleblg-Universitat Giessen 6300 Giessen, F.R. Germany and J.A. Tuszyfiski Department of Physics The University of Alberta Edmonton, Alberta, Canada, T6G 2J1.

In this paper we present a detailed formulation of the FrShlich model*' for metabolically-actlve biological membranes. We base the descrip- tion on both Frohlich's conjectures and the actual biophysical data con- cerning the structure, composition and functions of biological membranes. The model Hamiltonian involves interaction terms for lipid tails and heads and also accounts for the presence of dielectrically-active material, mainly water. Couplings between the various degrees of freedom are included and a hierarchy of relaxation times discussed. It is subsequently demonstrated that under specific threshold condi- tions Bose condensation in the frequency space of dipolar oscillations may take place as was argued before by Fr

1) H. FrShlich, IEEE Trans. MIT 26_, 613 (1978). 2) A.S. Davydov, Biology and Quantum Mechanics (Fergamon, Oxford, 1982).

81 B-37 AB INITIO STUDY OF THE ELECTRONIC STRUCTURE AND CONDUCTION PROPERTIES OF NITROGEN AND OXYGEN CONTAINING ANALOGUES OF POLYISOTHIANAPHTHENE AND THEIR COPOLYMERS A:K.BAKHSHI DEPARTMENT OF CHEMISTRY,ARSD COLLEGE UNIVERSITY OF DELHI,DHAULA KUAN,NEW-DELHI 110021 INDIA Results of ab initio band structure calculations of polyiso- thianaphthene(PITN)(1-2) and two of its analogues polyisobe- nzopyrrole(PIBP) and polyisobenzofuran(PIBF) are reported and compared with those of their parent compounds polythiophene, polypyrrole and polyfuran respectively(3-4). As a result of the fusion of a benzene ring, each compound is found to bec- ome less insulating and more dopantphilie.PITN is predicted to have the smallest band gap followed by PIBF andPIBP. Com- parison of their electronic properties such as ionization potential(I.P) and electron affinity(E.A) shows that both PITN and PIBP have nearly the same capacity for oxidative(p-) doping while the capacity for reductive(n-) doping is nearly same in the case of PITN and PIBF. From the analysis of the Bloch wavefunctions of these systems it is found that their E.A values depend more on the heterocyclic substitution whe- reas the values of I.P are more influenced by substitution on the backbone.The problem of the copolymerisation of these he- terocyclic compounds is also examined and the electronic den- sity of states(DOS) of various random and periodic copolymers have been determined using simple negative factor counting method in its tight binding approximation. Random copolymers, in general are found to have better prospects for both p- and n- doping than their periodic counterparts.

References: l.M,Kolayashi,N.Colaneri,M.Boysel,F.Wudl & A.J.Heeger,J.Chem. Phys.,82,5717(1985). 2.A.K.Bakhshi & J.Ladik,Solid State Commun.,61,71(1987). 3.A.K.Bakhshi,M.Seel & J.Ladik,Phys.Rev.B,35(2),704(1987). 4.A.K.Bakhshi & N.K.Ray,J.Chem.Phys.,88,386(1988).

82 B-38 CASSCF STUDY ON THE ELECTRONIC STRUCTURE OF OXYGEN AND DIOXYGEN COMPLEXES OF IRON-PORPHYRINS

SHIGEYOSHI YAMAMOTO AND HIROSHI KASHIWAGI INSTITUTE FOR MOLECULAR SCIENCE

We have developed a new program named JASON2 (1] in order to perform ab initio CASSCF calculations on biomolecules with large basis sets. By using it. we have elucidated the electronic sturucture of oxygen and dioxygen complexes of iron-porphyrins which are active parts of hemoproteins. One of the complexes we treated is ferryl iron-oxo-porphyrin. FeP(py)O. (P = porphyrin. py = pyridine) (23. It is a model compound for peroxidase compound II. Peroxidase is a heme-containing enzyme which catalizes the oxidation of organic molecules. Calculated equilibrium bond distance and stretching vibration frequency of Fe-0 are in good agreemnet with the experimental data of HRP-II (horseradish peroxidase compound II). Calculated values of the Mttssbauer spectrum parameters are also consistent with experiments. It was revealed that the electronic structure of the Fe-0 bond is equivalent to that of the 0-0 bond of an elongated Oz molecule. The second compound is a it cation radical of oxo-porphyrin. FeP+(py)O. which is a model compound for peroxidase compound I (3). We confirmed the similarity of the electronic structure of the Fe-0 bond between compounds I and II. The third is FeP(NH3>03, a model compound for oxymioglobin or oxyhemoglobin. It was found that the a donation from Oa moiety to Fe dz2 and the n back-donation from Fe d« to 02 p* play an important role in its Fe-Oa bond-

References 1. S. Yamamoto. U. Nagashima. T. Aoyama and H. Kashiwagi. J. Comp.ut. Chem. . in press. 2. S. Yamamoto. J. Teraoka and H- Kashiwagi, J. Chem. Phys. . 88. 303 (1988). 3. S- Yamamotd and H. Kashiwagi, Chem. Phys. Lett. . 145, 111 (1988).

83 B-39

AB INITIO Cl INVESTIGATION OF NEUTRAL AND CATIONIC Na CLUSTERS.

VLASTA BONACIC-KOUTECKY1, PIERCARLO FANTUCCI2,

IHSAN BOOSTANI1, AND JAROSLAV KOUTECKY1

1. INSTITUT FÜR PHYSIKALISCHE UND THEORETISCHE CHEMIE,

FREIE UNIVERSITÄT BERLIN, D-1OOO BERLIN 33.

2. DIPARTIHENTO DI CHIMICA IN0R6ANICA E METALLORGANICA,

UNIVERSITA DI MILANO, VIA VENEZIAN 21,

1-20133 MILANO.

The quantum chemical investigation of the electronic and geometrical structure of neutral Na and cationic Na clusters n n (n=3-9) has been carried out with all-electron HF procedure followed by the multireference double-excitation configuration interaction (MRD-CI) procedure. The effective core potential HF treatment gives completely parallel results for optimized clus- ter geometries and stabilities. The calculated properties of sodium clusters (e.g. shapes, stability, ionization potentials, fragmentation behaviour) are very similar to the properties of Li and Li clusters. Some minor deviations from this parallel n n behaviour are discussed. The systematic underestimation of ionization potentials and overestimation of interatomic di- stances of Na clusters is analyzed and preliminary results conceiving the effect of the core polarization in Na clusters n are presented. The comparison with the local spin density treatment as well as «ith the jellium model treatment of Na and Na clusters is carried out. The general rules determining the electronic properties of small alkali netal clusters are again confirmed.

•v'

84 B - 40

VALENCE-BOND CALCULATIONS ON LATER-SECOND ROW ELEMENT

FLUORIDES AND N2 AND ISOELECTRONIC MOLECULES

ROBERT G.A.R. MACLAGAN

DEPARTMENT OF CHEMISTRY,

UNIVERSITY OF CANTERBURY,

CHRISTCHURCH,

NEW ZEALAND.

Minimal basis set valence-bond calculations on CIF3, SFg, and PF5,* with, and without, the use of 3d orbitals will be described.

For CIF3, the most important structure is a spin-paired diradical structure. The covalent structure with three covalent Cl-F bonds has a sufficiently low importance that 3d orbitals are not essential tor describing the bonding in CIF3. Chlorine 3d orbitals do have a significant contribution to the calculated energy.

Valence-bond calculations are reported for the isoelectronic series of molecules N2, CO, BF, NO+ and CN\ Only two or three structures are required to obtain an energy lower than that obtained with the molecular orbital approximation. Structures in which the electronegative element loses a a-orbital or gains a re-orbital are favoured, n-bonds tend to be favoured over a-bonds. The bonding in NO+ resembles that in CO, whereas that in - resembles that in N2.

Collaborator: Dr. R.W. Simpson, Division of Chemistry, N.R.C., Ottawa, Canada. •-.•$

8S B-41

HYDROGEN-BONDED COMPLEXES INVOLVING BENZENE AS AN H-ACCEPTOR

B.V. CHENEY

LABORATORIES OF THE UPJOHN COMPANY

KALAMAZOO, Ml 49001 U.S.A.

Weak 1:1 complexes between benzene and the hydrogen halides, HF and HCI, have recently been characterized in the gas phase by means of the Fourier transform microwave molecular beam technique.1-3 in each case, the spectral results show that, on average, the structure is a symmetric top with the hydrogen lying between the ring center and the halogen. Large amplitude oscillations in both complexes made it difficult to determine equilibrium structures. Although the Ti-electron system of benzene may play the role of proton acceptor in associations with other electrophilic hydrides, no measurements on such complexes have been reported as yet.

Kollman and coworkders4 performed limited ab initio molecular orbital calculations on C6H6 HF using the minimal STO-3G basis set. No relaxation of the subunit geometry was allowed in the calculations. The vertical approaches of HF along the C6 axis of the ring and toward the center of a CC bond were found to be equally favorable.

In this study, ab initio molecular orbital theory has been used to investigate n hydrogen bonding in dimers involving benzene and the following H donors: NH3, H2O, HF, H2S. and HCI. Symmetry-restricted geometry optimization was carried out at the Hartree-Fock level using 3-21G(*) basis sets. Effects of electron correlation were assessed using second-order Moller-Plesset perturbation theory with 6-316* basis sets in single-point calculations at the final geometry. The structures feature weak association and a flat potential surface in the region where TT hydrogen bonding occurs. At all levels of theory employed in this study, the binding strength of the H-donors follows the order: HF > H2O, HCI > H2S, NH3. In every case, the dimer exhibits a substantially larger calculated dipole moment than the polar monomer, which suggests that complex formation is accompanied by significant redistribution of electronic charge.

1. Baiocchi, F.A.; Williams. J.H.; Klemperer, W. J. Phys. Chem, 1983,87, 2079. 2. Read. W.G.; Campbell, E.J.; Henderson, G.; Flygare, W.H. J. Am. Chem. Soc, 1981.103,7670. 3. Read, W.G.; Campbell, E.J.; Henderson, G. J. Chem. Phys., 1983,78,3501. 4. Kollman, P.; McKelvey, J.; Johansson, A.; Rothenberg, S. J. Am. Chem. Soc., 1975,97,955.

86 B-42

Three- and Four-Membered Rings Formed by Addition of CH2, SiH2,

GeH2, or SnH2 to C=P Triple Bonds Kerwin D. Dobbs, Alan H. Cowley, and James E. Boggs* Department of Chemistry, University of Texas, Austin, Texas 78712, U.SA.

It has recently been demonstrated experimentally that phosphaalkynes, RCsP, add carbene,1 silylene,2 and germylene3 moieties to form the first known examples of three- membered rings containing phosphorus-carbon double bonds. The corresponding tin chemistry, however, has been found to proceed in quite a different fashion. Two stannylene units add across the triple bond of a phosphaalkyne, forming a new four- membered ring.4 A comprehensive study of the structure, stability, and chemistry of these new heterocyclic molecules has been carried out with non-empirical molecular orbital methods. The structures of model ring systems - H£=P£H2 and HC=PEH2EE2 (E = C, Si, Ge, and Sn) - were optimized, using split-valence 3-21GW basis sets and analytical gradient techniques. Theoretical structural parameters are in very good agreement with the limited experimental data available in the form of x-ray structures of substituted derivatives. As expected, homodesmotic and isodesmic analyses of these three- and four- membered rings yield strain energies which are considerably smaller than the corresponding values for the similar hydrocarbon systems, cyclopropene and cyclobutene. These same analyses also indicate that the four-membered ring is more stable than the corresponding three-membered ring in every case, including the tin compounds. An examination of the valence molecular orbitals indicates that the HOMO for the three- and four-membcred rings in which E = C is the phosphorus-carbon n bond while the underlying orbital is best described as the phosphorus lone pair orbital. However, for E = Si, Ge, and Sn, the energetic ordering of these two molecular orbitals is reversed. Consideration of the possible mechanisms for interconversion of the three- and four-membered rings provides a plausible explanation for the experimental formation of a four-membered ring in the case of the tin compound while the three-membered rings are obtained from carbene, silylene, or germylene addition to the OP bond.

(1) O. Wagner, G. Maas, and M. Regitz, Angew. Chem. Int. Ed. Engl. 1987,26,1257. (2) A. Schafer, M. Weidenbruch, W. Saak, and S. Pohl, Angew. Chem. Int. Ed. Engl. 1987,26,116. (3) A. H. Cowley, S. W. Hall, C. M. Nunn, and J. M. Power, /. Chem. Soc, Chem. Commun., in press. (4) A. H. Cowley, S. W. Hall, C. M. Nunn, and J. M. Power, Angew. Chem. :*. Ed. Engl., in press.

87 B-43

CHARGE TRANSFER IN COPPER-COMPLEXES OF GLYOXAL AND DITIHENE. A. HENRIKSSON-ENFLO AND H. HOLMGREN INSTITUTE OF THEORETICAL PHYSICS, UNIVERSITY OF STOCKHOLM, VANADISVAGEN 9, S-113 46 STOCKHOLM, SWEDEN.

Metal complexes of glyoxal and dithiene has been used as model compounds for the role of metals in biological systems1. This special study presents quantum chemical calculations on the ab initio SCF level on the copper complexes of glyoxal and dithiene (see fig.) with total charge on the complex varying from +2 to -3.

Fig. 1. The complex studied. The total charge n is varied between n - +2, +1, 0, -1, -2, -3. The ligand binding atoms X are oxygen or sulfur.

In biological systems copper can be found in enzymes as amine oxidases, ceruloplasmin, cytochrome oxidase , superoxide dismutase and tyrosinase. Essential for enzymes is charge transfer. The model complex can also be used af- model system for organic superconductors. Mulliken population analysis has been performed for the complexes in the figure with the total charge on the complex varying from +2, +1, 0, -1, -2, and -3. In the complexes with X - oxygen both the gross and the net populations' on copper show a clear alternation between the two different oxidation states of copper when the total charge on the complex is varied from -t-2,+1, 0, -1, -2 to -3 so that for n even the copper atom occurs in a higher oxidation state than for n odd.

For the complexes with X - sulfur, on the other hand, the gross charges on copper is slowly growing from -0.1 in the n - +2 complex to +0.43 in the n - -3 complex. Due to the diffuse functions on sulfur values for the gross populations can be misleading because the contributing functions do not belong to the copper atom alone but rather to a larger part of the molecule. The net charges again, show the same behavior as in the oxygen complexes. The results will be discussed in terms of charge transfer.

1 Fischer-Hjalmars, I. and Henriksson-Enflo, A., Metals in Biology: an Attempt at Classification, Adv. Quant. Chem. 16, (1982), 1. 88 B-44

QUANTUM MECHANICAL CALCULATIONS ON VIBRONIC ACTIVITY IN THE MCD SPECTRA OF CAHEONYL COMPOUNDS

GIANCARLO MARCONI

ISTITUTO FRAE/CMR, Via Castagnoli 1, 40126 BOLOGNA, ITALY.

In the past, the Magnetic Circular Dichroism of a number of corbonyls in the region of the first nit * absorption band was detected* '. By examing the Constance of some spectral features, the authors were able to drawn some conclusion about the sign and , size of the vibronic components of the MCD signals in this region.

In particular they extrapolated that, for C2V ketones, in general the B term of b^ and a2 vibrational modes should be positive, whereas that of b2 modes should be negative. In order to verify this hypotesis we extended the method already used to elucidate the vibronic activity on the MCD spectra of benzene and formaldehyde' ',and calculated in detail the B terms arising from the vibrational modes of acetone, cyclobutanone and cyclopentanone. The method employed to calculated the vibronic integrals is the wellkncwn "orbital following" method* ' implemented using a semi- enpirical hamiltonian (INDO/S); the magnetic and electric dipole moments.were calculated within the complete angular momentum operator method. Despite the difficulty in calculating such a property, which is second order in vibronic perturbations, the results show an overall agreement with the experimental signs and .: sizes of the MCD terms in this carbonyl series and allow for a £ '•A straightforward analysis of the mechanisms governing the intensity .§ distribution in the MCD bands of vibronic origin. q 1) L. Seamans, A. Moscovitz, G. Barth, E. Bunnenberg, and C. Djeras- f si, J. Am. Chem. Sec. 94_ (1972) 6464. r 2) G. Marconi, Chem. Phys. Lett., in press. J 3) G. Orlandi, Chem. Phys. Lett., 44_ (1976) 277; G. Marconi, Chem. Ijj Phys. 57 (1981) 311 M,

89 B-45

THE VALENCE-BOND NATURE OF PLANAR AND TRANS-BENT DOUBLE BONDS

G. TRINQUIER and J.-P. MALRIEU

Laboratoire de Physique Quantique (C.N.R.S., U.A. 505) Universite Paul Sabatier, 31062 TOULOUSE CEDEX, FRANCE

The trans-bent distorsions of double bonds occuring in disilene, digermene or distannene (H2X=XH2), and in various other systems, can be understood from two different arguments.

Puting aside the X-X sigma bond, a strongly correlated pi bond jnay be eventually associated with a diradicalar character. MCSCF calculations with two active electrons (pi active space) actually induce a planar to trans-bent distortion when the -XH2 radicalar center has intrinsic trend to pyramidalize (as the silyl radical SiH3 does for instance).

If the molecule is seen as two interacting fragments XH2, the problem is that of a two-bond set (sigma + pi). MCSCF wavefunctions with four active electrons (sigma + pi active space), have been decomposed into orthogonal valence-bond (VB) components. The contributions of these are followed as the molecule is progressively trans-bent distorted. The main contributions remain the products of the open-shell configurations (of BJL type) at each fragment together with the sigma singly-ionic forms. However, the product of the (n )2 closed-shell configurations (of A type) at each fragment plays a major part in the stabilization of trans-bent geometries. The larger the

2 A - BL singlet-triplet separation in XH2, the larger the weight of.that VB component, the more bent the geometry. I

90 B-46

AB INITIO CONFIGURATION INTERACTION INVESTIGATION OF THE

EXCITED STATES OF Li4 AND Na^ CLUSTERS.

VLASTA BONACIC-KOUTECKY, PIERCARLO FANTUCCI*

AND JAROSLAV KOUTECK/

INSTITUT FUR PHYSIKALISCHE UND THEORETISCHE CHEMIE,

FREIE UNIVERSITAT BERLIN, D-1OOO BERLIN 33.

Vertical spectrum for the low lying excited states of Li. and Na. clusters in its optimal rhombic geometry has been de- termined employing large scale direct configuration interaction procedure. The energy of the lowest triplet state has also been computed by allowing a full relaxation of the atomic nuclei. The optimum geometry is found to be a distorted tetrahedron. The atomization potential curves have been determined. The nature of the wave functions of the excited states is discus- sed. The importance of the p functions in the bonding of alkali metal clusters is illustrated by the correlation of lew lying o excited states of the Li, clusters which include a Li P state in their dissociation products. The possibilities of the pre- dissociative processes of alkali metal clusters are discussed.

'i

*) Permanent address: Dipartimento di Chimica Inorganica e t Metallorganica, Universita di Milano, Via Venezian 21, ',; 1-20133 Milano. *":•

91 B-47 CHIMISTE : Semi-empirical computation of vibrational spectra

M.T.C. Martins Costa, D. Rinaldi, J.L.Rivail Laboratoire de Chimie The"orique Unite" Associ6e au C. N. R. S. 510 University de Nancy I, B. P. 239 54506 Vandoeuvre-les-Nancy (FRANCE)

This is a general-purpose semi-empirical molecular-orbital package, using the sym- metry properties of the molecule in several calculation steps, in particular when com- puting frequencies of the vibrational spectra. The force constant matrix in cartesian coordinates is computed using an analytical approach. There is a gain in time compared with the usual numerical approach, although it remains relatively time consuming. The diagonalisation of this matrix, after elimination of the molecular translations and rotations, leads to the vibrational normal modes expressed in terms of cartesian dis- placements. These normal modes are subsequentely used in order to assign a symmetry to the vibrational spectral lines. This methodology has been applied to the complete analysis of the vibrational spec- tra of the 4-nitropyridine-N-oxyde.

References M.T.C. Martins Costa, D. Rinaldi, J.L. Rivail, J. Mol. Struct. (Theockem), 166, 125 (1988). M. Joyeux, M.T.C. Martins Costa, D. Rinaldi, N. Q. Dao, J. Ckem. Phys., submit- i ted. 1

92 B-48 AB-INITIO EFECTIVE CORE POTENTIAL DETERMINATION FOR THE Kr++ 0_ COLLISIONAL SYSTEMS. B. Ramiro and P. Wahndn Dept. Qulraica E.T.S.I. Telecomunicacidn Universidad Polit<5cnica de Madrid. 28040-MADRID- SPAIN Investigation of the dynamics of ion-molecule vibrational in- teraction at low collision energies, has recently received a great attention because of the measurements of vibrationally resolved charge transfer spectra for a number of different systems and over a wide range of scattering angle (1). The results contribute to - the field of the non-adiabatic charge transfer vibronic coupling phenomena. For a quantitative treatment, a well knowledge of the entire potential hypersurface for the ABC* system would be required. At this low energies (Eion<30 e.V.) only the two electronic ground state surfaces of the asymptotically differently charge system A + BC and A+BC need to be considered, since no experimental evidence involving another electronic states was found. In spite of that, the systematic ab-initio determinations of these only two potential energies hypersurfaces and coupling (neededs to carry out dynami- calculations) is a really tedious work (2), specially when the co- llisional system contains heavy atoms. In this case the heavy atom is treated by a pseudopotential method. In the present contribution, an ab-initio effective core po- tential angular momentum dependent, obtained from numerical Hartree-Fock wave functions is used to study Kr++ O collisional processes. This system was choosen because of the analogy of the Kr and H ionization potentials. Recently the H + O_ system has been lar- gely studied from the theoretical and experimental point of view (4) . The pseudopotential based on Kahan and Hay (3) fromalism has the following form:

1 = 0 m were L=L max. core +1 The electronic energy obtained for the Kr with this model.- is -17.8655 a.u. and for the 4p energy orbital is -0.5171 a.u.(very close to the experimental I.P. wich.is 0.5146 a.u.). Potential energy results on Kr++ O at several geometries - will be shown at the conference. REFERENCES: 1) M. Noll, J.P. Tonnies, J. Chem. Phys. 85. 6_, 3313 (1986) 2) V. Staemmler, F.A. Gianturco, Int. J. Quant. Chem.28,553(1985) 3) L. Kahan, P. Baybutt, D.G. Truhlar, J. Chem.Phys.65,3826(1976) P. J. Hay, W.R. Wadt, J. Chem. Phys. £1' 270> (1985) 4) D. Grimbert, B. Lassier, V. Sidis, XV ICPEAC Brighton 671(1987) 93 POSTER SESSION c

Ii C-l RIGOROUS ONE-PARTICLE DESCRIPTION OF MANY-ELECTRON EXCITATIONS

L.FRITSCHE AND J.CORDES

INSTITUT FUR THEORETISCHE PHYSIK DER TECHNISCHEN UNIVERSITXT CLAUSTHAL, D-3392 CLAUSTHAL-ZELLERFELD WEST GERMANY

We advance a new concept of mapping the N-electron problem on- to a one-particle problem that consists in self-consistently solving Kohn-Sham (KS-)type one-particle equations. The poten- tial in these equations turns out to be local and energy-inde- pendent as in the KS-theory. It contains the full many-body information via the coupling-strength averaged electronic pair 1 correlation function gs«s(r ,r) and its functional derivative with respect to the spin-dependent densities n and a rest 2 such that Ns(N-l)J^n| , integrated over N-l particle coordi- In nates, gives the exact density ^ns'£)* ' certain cases An may be a linear combination of a few determinants.) The total energy En can be expressed as in the Kohn-Sham theory. Results are presented for a series of free atoms obtained with a cer- tain universal approximation to fs's'l'l'- They agree well with experimental data. Excitation energies Ef-E^ in extended systems are shown to be expressible by £f-€"i+Afi where 6f and £i are the respective one-particle energies and 4fi denotes a correction that reflects the transition-induced relaxation of gs's<£''£)-

94 C-2 Solution of the Nuclear Schrodinger Equation by the Quantum Monte Carlo Approach

Timothy J. Lee and Nicholas C. Handy Department of Theoretical Chemistry, University Chemical Laboratory, Lensfield Road, Cambridge CB2 1EW United Kingdom

Abstract Highly accurate solutions of the nuclear Schrodinger equation for molecules are very difficult to obtain once there are more than three or four atoms. Currently, the most common method in use for small molecules is a variational approach coupled with very large basis sets. However, this technique becomes impractical for larger molecular systems for two reasons. Firstly, the basis set required to achieve accurate results grows rapidly with respect to the number of nuclear degrees of freedom, so as to make the numerical solution impossible, even on today's supercomputers. Secondly, since most of these variational methods use an internal coordinate representation of the kinetic energy operator, a new and non-trivial derivation (and program implementation) must be performed for each type (shape) of molecular structure.

Several workers have decided to use normal coordinate expansions of the kinetic and potential energy in conjunction with a variational method. However, a problem then occurs in treating the Coriolis part of the kinetic energy operator. Moreover, it has been known for sometime that the potential energy does not converge as quickly in a normal coordinate expansion and this is especially true for molecular systems of intense interest, such as weakly bound hydrogen bonded complexes. Thus, an interesting and promising alternative is to use a Quantum Monte Carlo (QMC) method to solve the nuclear Schrodinger equation.

One advantage of the QMC method is that the kinetic energy and potential energy operators may be conveniently expressed in different coordinate systems. We have chosen a center of mass cartesian coordinate representaion for the kinetic energy operator and an internal coordinate expansion for the potential energy. We present the detailed formulae and several applications of our method. 95 C-3

RECENT RESULTS WITH THE LOCAL CORRELATION TREATMENT S. SAEBO (DEPARTMENT OF CHEMISTRY, MISSISSIPPI STATE UNIVERSITY) P. PULAY (DEPARTMENT OF CHEMISTRY, UNIVERSITY OF ARKANSAS) The goal of the local correlation treatment [1-6] is the elimination of the steep (e.g. sixth-power) dependence of the computational effort on the molecular size, which characterizes conventional methods of dynamical correlation beyond the MP2 method. It is based on the notion that the ground-state orbitals of most molecules can be very well localized. Restricting our attention to pair correlation, localization of the internal orbitals can be used to achieve two kinds of savings: (1) The pair correlation energy betwen two distant orbitals is small, and can be either neglected or, preferably, treated at a low (second order) level with very little loss in accuracy. (2) The unphysical increase of the dimension of the external (virtual) space with increasing molecular size is eliminated by using a local correlation basis. The latter is different for every pair: it includes the valence atomic orbitals of the atoms on which the two internal orbitals are localized, projected against the internal (occupied]) orbitals. In effect, this is a configuration selection scheme, without the disadvantages of random configuration selection. A further advantage of the local correlation treatment is the elimination of basis set superposition errors at the correlated level. This is particularly important for the calculation of weak interactions. The local correlation treatment can be implemented with various many-body methods: variational CI, coupled cluster and coupled pair methods, and many-body perturbation theory. Because of the size of the molecules, we use mostly the latter. Note that the exact Mtfller-PIesset partitioning can be formulated with localized internal orbitals [4,5]. We shall present recent results using the local correlation treatment, with particular emphasis on supercomputer performance. We will present detailed timing data for very large calculations (over 200 basis functions at the MP4-SDQ level). We will also discuss the force constants of benzene. The latter have been the subject of some controversy lately [7-9]. The new results confirm the validity of our quantum mechanical-empirical force field [10]. We shall also discuss calculations of intermolecular forces, in particular the elimination of the basis set superposition error. 1. P. Pulay, Chem. Phys. Lett. 100,151 (1983). 2. S. Saebo and P. Pulay, Chem. Phys. Lett. 113 13 (1985). 3. P. Pulay and S. Saebo, in Geometrical Derivatives of Energy Surfaces and Molecular Properties, edited by P. J<6rgensen and J. Simon (Reidel, Dordrecht, 1986), p. 95. 4. P. Pulay and S. Saebo, Theor. Chim. Acta 69,357 (1986). 5. S. Saebo and P. Pulay, J. Chem. Phys. 86,914 (1987). 6. S. Saebo and P. Pulay, J. Chem. Phys. 88,1884 (1988). 7. A. G. Ozkabak, L. Goodman, S. N. Thakur, and K. Krogh-Jespersen, J. Chem. Phys. 83,6047 (1985). 8. P. Pulay, J. Chem. Phys. 85,1703 (1986). 9. A. G. Ozkabak and L. Goodman, J. Chem. Phys. 87,2564 (1987). 10. P. Pulay, G. Fogarasi, and J. E. Boggs, J. Chem. Phys. 74,3999 (1981).

96 C-4

A GENERAL FORMULATION OF THE MATRIX ELEMENTS OF THE

THIRD ORDER SPIN-ADAPTED REDUCED HAMILTONIAN

L. LAIN AND A. TORRE

DPTO. QUIMICA FISICA, UPV, APDO. 644, 48080 BILBAO, SPAIN

J. KARWOWSKI

INSTYTUT FIZYKI UMK, GRUDZIADZKA 5, PL-87-100, TURUN, POLAND

C. VALDEMORO

I. CIENCIA DE MATERIALES, CSIC, SERRANO 123, 28006 MADRID, SPAIN

The theory of spin-adapted reduced Hamiltonians (SRH), constructs a N-representable Hamiltonian matrix wich contains all the relevant information about the N-electronic states of a selected spin symmetry (C- Valdemoro. Phys. Rev. A31, 2114, (1985)). So, based in the eigenvalues of this SRH matrix of any order p (p

97 C-5

On the exactness of the first Extended Koopman's Ionisation Potential J.G. Snijders and B.T. Pickupt Department of Theoretical Chemistry Vrije Universiteit De Boelelaan 1083,1081HV Amsterdam the Netherlands Abstract The extended Koopman's (EK) [1] method was originally conceived as an approximate method to calculate ionisation potentials by approximating the ion-states as a linear combination of states arising from the (in principle) exact ground state by annihilating a complete set of orbitals. Subsequently it was claimed [2,3] that the first ionisation potential obtained by the EK method is exact. Numerical examples supporting this claim were given, especially for 2 electron systems. On the other hand one of us (BTP) seemed to have shown [4] that the exact and EK ionisation potentials already differ in second order, even for two-electron systems, leading to an apparent paradox. In this paper we show that in this analysis a term is missing in 2n<* order, such that in the case of a 2-electron system all EK ionisation potentials are indeed exact to 2n(* order (not only the lowest one), while for N-electron system they will in general be different. In fact it can easily be shown that in a 2-electron system all EK eigenvalues are exact in all orders, provided none of the natural orbital occupancies vanish. In the general case exactness of the first IP would imply unlikely conditions on the Dyson orbisils. It is also shown that in a simple 3-orbital model these conditions do not hold, and consequently all EK ionisation potentials are different from their exact counterparts.

References

[1] D.W. Smith and O.W. Day, J.Chem.Phys. 62 (1975) 113 O.W. Day, D.W. Smith and R.C. Morrison, J.Chem.Phys. 62 (1975) 115 [2] M. Morrell, P.C. Parr and M.Levy, J.Chem.Phys. 62 (1975) 549 [3] J. Katriel and E.R. Davidson, Proc.Nat.Acad.Sci. 77 (1980) 4403 [4] B.T. Pickup, Chem.Phys.Lctt. 33 (1975) 422

* Permanent Adress: Department of Chemistry The University Sheffield S3 7HF United Kingdom

98 C-6

AB-INITIO STUDY OF THE TWO-PHOTON BOUND-BOUND ELECTRONIC TRANSITIONS OF TRANS-BUTADIENE V. GALASSO DIPARTIMENTO DI SCIENZE CHIMICHE, UNIVERSITA' DI TRIESTE, 1-34127 TRIESTE (ITALY)

The two-photon absorption properties of trans-1,3-butadiene have been calculated at ab-initio level employing RPA vertical excitation energies and transition moments and taking the random molecular orientation into account. Use has been made of Dunning1 s GTO basis set [3s2pld|ls] augmented by adding to center of mass two sets of diffuse spd functions and the full manifold of valence and spd Rydberg (up to n=4) excitations have been considered. For single-beam two-photon absorption with every possible combination of photon polarisation the transition probability coefficients and polarisation ratios for the low-lying Ag and 1 Bg final states are reported. The Ag states exhibit larger two-photon absorptivity than the Bg states. The strongest two- photon absorptivity is predicted under excitation from linearly polarised (1Ag) and circularly polarised ( Bg) photons. The case of concerted absorption of two photons with various polarisations from two laser beams has been also investigated exhaustively as a function of the photon frequencies.

99 C-7

STUDIES OF RAMAN SCATTERING FROM PREDISSOCIATING MOLECULES USING TIME-INDEPENDENT MULTICHANNEL SCATTERING METHODS Karl F. Freed and Sungyul Lee James Franck Institute and Department of Chemistry, The University of Chicago. Chicago, Illinois 60637 Raman scattering from predissociating molecules is studied by computations for model Morse potential systems using a recently developed stable (quantum) algorithm for propagating the time-independent multichannel second order transition amplitudes*. Both resonance and near resonance Raman scattering are treated, with the former containing the weak emission from the molecule once it has crossed over from the bound intermediate state to the dissociative surface. As with time-dependent wave packet methods, it is possible to treat the predissociative Raman amplitudes with an analog of a "short time" approximation that only requires integration out to regions where the input Franck-Condon amplitudes are negligible and where the nonadiabatic dynamics may be ignored^, thereby obviating the need for the usually formidible problem of transforming to an asymptotic representation. It should be emphasized, moreover, that the long time nature of weak predissociations would make such systems unpleasant to treat with short time wave packet dynamics. Our one-dimensional example is based on potentials for the bromine molecule, where the excited states are composed of a bound Morse potential that is nonadlabatically coupled to a repulsive state. The ground state is also taken to be have a Morse potential whose anharmonicity introduces no extra difficulties as it does when applying wave packet propagation methods. Calculations are perrormed of the Raman spectrum when oscillator strength is present to one or both of the excited surfaces for several model situations in which the ground state equilibrium position is shifted relative to the position of the crossing point between the excited surfaces and in which the strength of the nonadiabatic coupling is varied. Situations are obtained in which there are considerable contributions due to a long emission progression from the molecule when it is on the repulsive surface. An analysis is presented of role of bound-continuum interferences and of the dissociative state contributions to the nonresonant Raman scattering. We are in the process of extending the computations to two-dimensional models of predissociation, and results of these calculations will also be described. lS. J. Singer. S. Lee, K. F. Freed, and Y. B. Band. J. Chem. Phys. 87, 4762, (1987) S. J. Singer, S. Lee, and K. F. Freed, to be published.

100 C-8 QUANTUM CHEMICAL SIMULATION: SMALL SILICON CLUSTERS AND LOCAL STRUCTURE OF a-Si:H V.E. GUSAKOV, V.I. GOGOLINSKY, E.V. KURMISHEV Institute of Physics of Solids and Semiconductors, 220726 Minsk, USSR Byelorussian State University, 220080 Minsk, USSR Institute of General Physics, 117942, Moscow, USSR The goal of the investigation of the properties of clu- sters of atoms is to use clusters with increasing numbers of atoms to understand the transition from molecular behavior to the behavior of bulk condensed matter / 1-3 /« In the present work the ground-state geometries of free small silicon clus- ters and silicon clusters for wich the dangling bonds were saturated with hydrogen atoms, have been investigated in a systematic manner by means of SCF MO LCAO ( MNEO ) calculations. The clusters consisting of 2 to 17 Si atoms have been studied. Pair distribution functions, topological indexes, fragmentati- on energy, electronic properties of the clusters have been ana- lysed* The obtained ground-state geometries of S±2 - Sig clus- ters are in good agreement with those ealier obtained in / 1 /. The most stable structure for Sin corresponds to a pentogonal bipyramidal geometry and is significantly more stable than a tricapped tetrahedron wich was considered in / 1 /. The ground- state geometries of Sig - Si

( 2.34 - 2.37 ) A. a** ( 109.5 i 1 )°, r2« ( 3.84 - 3.86) A; a2== ( 109.5 ± 5^8 )• and Q* ( 35 - 45 )*. 1. K; Raghavacnari. J. Chem. Phys. 84 (1986 ), 5672. 2. K. Raghavachari, McM. Rohlfikg, Chem. Phys. Letters, 143 (-1988 ), 428. 3. E.V. Kurmyshev, V.E. Gusakov, I.N. Sisakian, Preprint N237, Moscow, 1987.

101 C-9

CONDUCTIVITY IN 3d TRANSITION METAL SALTS AND OXIDES AND LAYERS OF CuO TREATED BY A CLUSTER MODEL.

by Sve:- Larsson Chalmers University of Technology Department of Physical Chemistry S—412 96 Gothenburg, Sweden

The relationship between electronic structure and conductivity and other physical properties of 3d transition metal oxides has been discussed since the 1950's. Recently the occurence of superconductivity at high temperature in ceramic materials which contain layers of CuO has further stimulated this discussion. It was early pointed out that the band model can not explain the lack of conductivity for the oxides (1). A local model which takes screening and relaxation into account has a greater chance of success (2). Unfortunately, lack of reliable parameters which determine relaxation and screening have prevented a detailed explanation along these lines. Experimental results may not be decisive as to which model is the correct one. Thus an experimental activation energy may be interpreted either as affecting the :arrier concentration (band model) or the carrier mobility (local model). In this paper clusters of different sizes have been examined. An NDO type model is set up which includes correlation effects. Parameters which determine screening are obtained from local density calculations on atoms. The model adequately describes satellite intensities in ESCA spectra. The condition for conductivity is determined by the relative magnitudes of an intermetal effective coupling matrix element and a thermal barrier where the latter is due to dielectric relaxation (A ) and bond reorganization (A.). The results are consistent with the experimental results. Low conductivity results since the intermetallic coupling is small compared to the bond reorganization. Comments are offered regarding high temperature superconductivity.

1. D. Adler in 'Solid State Physics', Eds Seitz, Turnbull and Ehrenreich (Academic, 1968), volume 21 2. R.R. Heikes and W.D. Johnston, J. Chem Phys. 26. 582 (1957).

102 C-LO

SOLVENT CLUSTERS: STRUCTURES, ORDER-DISORDER TRANSITIONS AND

SPECTRA

SAMUEL LEUTWYLER and JURG B5SIGER

Institut fur Anorganische, Analytische und Physikalische Chemie,

Universitlt Bern, Freiestr.3, CH-3000 Bern 9.

Electronic spectra of carbazole«Arn clusters (n = 1 to 35) produced in supersonic beams were measured by size-specific resonant two-photon-ionization techniques. The spectral features such as spectral shifts, peak halfwidths, and peak shapes are extremely size-dependent, and both narrow and broad features are observed up to n=30. > Structures and order-disorder transitions of the rare-gas solvent clusters carbazole*Ar_ were studied both experimentally and by computer simulations for n=l to 32. Absolute and local minimum-energy structures were obtained by molecular-dynamics annealing techniques. Order-disorder transitions of these solvent clusters were studied by Monte Carlo simulations. Four quasi-2D order-disorder * transitions were found: the racemization and surface-decoupling ' transitions reflect the loss of cluster-substrate orientational correlation, while cluster rigid-fluxlonal and melting ' transitions derive from the loss of intracluster bond- orientational and bond-length order.The simulations indicate that the change from sharp to broad spectral structures is due to •• surface decoupling transitions. Second-layer promotion and side- crossing transitions are three-dimensional transitions which , occur in larger clusters (n z 8). For clusters with n=8 to 20 spectral shifts and peakwidths and -shapes are influenced by both ! 2-D and 3-D transition types. Closure of the first solvent shell *. takes place at nM30. ;*' Solvent cluster optical spectra were studied by both ^ classical and semiclassical simulation techniques and give i^f ,, fascinating and detailed information on the interplay of W f, structure and spectral broadening mechanisms. f

103 C-ll THE RELATIONSHIP BETWBEN OF THE GEOMETRY CONFIGURATION AND THE MC d-P 5t BOND OF TRANSITION METAL CLUSTERS LI JUN-QIAN DEPARTMENT OF CHEMISTRY, FUZHOU UNIVERSITY, FUZHOU FUJI AN, CHINA.

It was proved that there is the Multiple Centre d-PflBond in the tran- sition aetal clusters, and it has an obvious effect on the M-M bond, UV spectra and CVE of the clusters**»23. In this paper, it has been further shown that the bonding is an iaportant factor to decide the geoaetry confi- guration of the clusters. A series of the electronic structure of soae Mo clusters at various 0 0 B angle d and p ( II ^Bv jj /l+K B,B' = 0, S or Cl) have B t Mo , been calculated by using R. Hoffaann's SCCC-ERMO aethod. It is seen that the SUB of one-electron energies at the configuration of equilibrium is lo- west, and at <* , f >90°, which are according to noraal sp" hybrid theory, the energy is higher, in spite of the variation of the Mo-Mo bond length. Froa the component of the orbitals, it is found that the P(d) orbitals of bridge B(B') atoas aix only with the d orbitals of Mo atoas, and the S orbi- tals do not aix aarkedly with Mo atoaic orbitals. This should be natural reason that the *, B<90° in the clusters so far given. There is a directly proportional relation roughly between the ct(0) and h value (h is the nuaber of the MC d-P9lantibonding holes, the aore h value, the stronger is the d-Pfl bondCH) as follows:

JOB JUS JUOO h 4320 40 42 d

Jast so, a series of 2-6 nuclear Mo clusters can be stabilized at 60*< <90°, even though, in the light of the noraal structure role, it is dif- ficult. [1] Li Jun-Qian, J. Mol.Struc. (Theochea), in press. [2] Li Jun-Oian, Book of Abstracts (XXV ICCC) 44 (1987). 104 C-12

VIDRATIONAL DYNAMICS OF VAN DER WAALS CLUSTERS WITH THE SELF-CONSISTENT FIELD THEORY

R.B. GERBER and T.R. HORN

DEPARTMENT OF PHYSICAL CHEMISTRY and

THE FRITZ HABER RESEARCH CENTER FOR MOLECULAR DYNAMICS

THE HEBREW UNIVERSITY, JERUSALEM 91904, ISRAEL

M.A.RATNER

DEPARTMENT OF CHEMISTRY, NORTHWESTERN UNIVERSITY

EVANSTON, ILLINOIS 60201, USA

A study of the vibrational dynamics of Van der Waals clusters is presented via a Self-Consistent Field (SCF) analysis. Van der Waals clusters such as l2He,XeHe2 are characterized by high amplitude, anharntonic motion, and exhibit considerable delocalization in their bound states. Any meaningful analysis must therefore rely on the structural distribution given by the wavefunction rather than rigid geometry. SCF calculations are remarkably well suited to such a task. Furthermore, the simplicity of the single mode expressions that SCF involves is conducive to physical insight The first part of our investigation focuses on the efficacy of SCF in application to ^He and XeHe2- Through selection among an (albeit limited) set of curvelinear coordinate systems, SCF estimates can be significantly improved and compare favorably with exact methods. Spheroidal coordinates are found to be very suitable for the ^He cluster, while hyperspherical coordinate provide an excellent description of the XeHe2 system, particularly with regard to the delocalization of the He atoms. In both cases, the physical reasons for the choice of the optimal coordinates is given. In the case of the several atom clusters XeHen and l2Hen, an extended version of SCF can be implemented by combining a coordinate system which con- tains displacement modes for the individual He atoms and a correlation function to assure hard wall repul- sion between the He atoms. Of particular interest in this part of the study, are the spectroscopic and struc- tural implications of the additional He atoms and the influence of spin statistics when the differing nuclear spins of 3He (a fermion) and 4He (a boson) are taken into account We conclude with discussion of a sys- tematic approach to the general cluster problem, within the framework of Self-Consistent Field Theory.

References 1. R.B. Gerber and M.A. Rattier, Adv. Chem. Phys. 70,97 (1988). 2. G.C. Schatz, R.B. Gerber and MA. Rattier, J. Chem. Phys. (in Press).

105 ICQC 6, Jerusalem, August 21-25, 1988

C-13 RELATIVISTIC EXTENDED HUCKEL DESCRIPTION OF ACTINOID ORGANO- METALLICS: ON THE CHEMICAL DIFFERENCE OF Th AND U

Pekka Pyykko and Liisa J. Laakkonen

Department of Chemistry, University of Helsinki, Et. Hesperiankatu 4, 00100 Helsinki, Finland

Kazuyuki Tatsumi

Department of Macromolecular Science, Osaka University, Toyonaka, Osaka 560, Japan

A set of radial (single-zeta 7s7p6p, double-zeta 6d5f) and energy ("ABC") parameters is presented for the early actinoids (An = Th - Np). The criterion for chemical reasonableness have been the metal 6d and 5f characters in the bonding molecular orbitals of the compounds An(C0T)2 and AnCp* (COT = CgHg, 5 Cp = CcjHr), as compared to those, calculated by more fundamental methods (Quasirelativistic Multiple Scattering, Discrete Variational Method). Special attention has been paid to the ' chemical difference between thorium and uranium. Quasi- i relativistic averages of the parameters have already been used . i For a review on relativistic semiempirical methods, and a '• diskette with the ITEREX program, see ref.2. i The question "why is uranyl linear and the isoelectronic ThOo is bent" is further analysed within the present model. I 1 K. Tatsumi and A. Nakamura, J.Am.Chem.Soc. 109 (1987) 3195. ;| 2 P. Pyykko, Methods in Comp.Chem. (Ed. S. Wilson) 2 (1988) § Plenum, London and New York. % i

106 C-14 EXPERIMENTAL ASSIGNMENTS FOR THE ELECTRONIC EXCITED STATES OF SMALL, ACYCLIC MOLECULES RUTH MCDIARMID NIDDK, National Institutes of Health Bethesda, Md. 20892, USA There is an unfortunate bias on the part of both experimentalists and theorists to select from the universe of available data that subset of theoretical or experimental data that best corroborates their current experimental or theoretical results. This prejudice is believed to be unavoidable for small organic molecules -- acetone, ethylene, butadiene, etc. -- for which neither "exact" calculations nor rotationally resolved, hence traditionally assignable, spectroscopic measurements are possible. We will show that it is now possible to provide experimental symmetry assignments for some rotationally unresolved states in some molecules through the use of newer spectroscopic techniques, such as the exploitation of polarization properties in resonant multiphoton spectroscopy^- • * and the correlation of similar excited states through a series of related molecules.

These techniques have been applied to three molecules, butadiene, hexatriene/ and acetone.'1' The experimental determination of the assignments and transition energies of the lower energy spectroscopic bands of these molecules will be illustrated and the experimentally derived conclusions compared with the correctly correlated, theoretically calculated energies of the transitions that give rise to these bands.

References 1. W. M. McClain and R. A. Harris in "Excited States Vol 3", (ed. E. C. Lim, Academic, N.Y., 1977) Chap. 1. 2. D. M. Friedrich, J. Chem. Phys. 7JL 3258 (1981). 3. R. McDiarmid, in preparation. 4. R. McDiarmid and A. Sabljic, J. Chem. Phys., in press.

i. 107 C-15 THE FORCE METHOD IN QUANTUM CHEMISTRY AND ITS APPLICATION IN CHEMICAL BINDING RESEARCH PENG ZHOUREN LIU SHUBING CHEMISTRY DEPARTMENT, LANZHOU UNIVERSITY, CHINA

This paper gives the results of the first two parts of our series research on the force method in Quan- tum Chemistry* Based on the Molecular Orbital Multi Centre Electric Charge Distribution (MOMCECD)point, we have advised a new sub-force division program y and discussed their contributions » One of the sub- forces —— orbital overlap force (OOF) was used as the general binding criterion , in which Mean Orbital Force (MOF) model by us and Bader's binding, crite- rion are included • We defined a new concept called Forcescopy by using OOF values calculated for the purpose of proving the accordance of the force me- thod with the energy method . Various examples were calculated and conclusions have been confirmed .

REFERENCE •fi

'•: • OK Du,Q.S.,Peng,ZiPR.,AGTA CHMICA SIMCAr42,843( 1984)?42,1021(1984)

(2 K Dete),B»M. rRev»Mod-Phys, ,45,22 (1973)

(3). Bader,R,F,VT»,HennekerfW.H. and Cade,P,E, , J.

Chem.Phys.r46,3341(1967) (4). Tal,"2» and Katriel,J«, Theor^GhimJlcta, 46,173

0977) . 108 C-16 THE EFFECT OF CONSTRAINING THE SOLVENT MOLECULE DISPLACEMENTS ON ELECTRON TRANSFER REACTIONS A. GONZALEZ-LAFONT, J.M. LLUCH, A. OLIVA Y J. BERTRAN DEPARTAMENT OE QUIMICA, UNIVERSITAT AUTONOMA DE BARCELONA, 08193 BELLATERRA (BARCELONA), SPAIN.

Up to the present, most models (1,2) proposed to explain the outer sphere electron transfer reaction rates in solution imply a drastic reduction of the degrees of freedom of the solvent system. In this work we have tested the influence of these simplifications on the self-exchange reaction Fe+ + Fe + ) Fe + + Fe+ in water. Several simulations of water clusters around each ion have been done by using the Monte Carlo method. Different constraints to the movement of the water molecules have been imposed. It has been found that the probability of solvent fluctuations suitable for electron transfer to be produced tends to decrease as far as the number of degrees of freedom allowed to vary is increased. If all degrees of freedom are taken into account, these fluctuations have a very low probability and it is practically impossible to compute them starting from an equilibrium distribution of the solvent around the reactants. We have developed a strategy to circumvent this difficulty and to get solvent configurations that favour the electron transfer.

(1) R.A. Marcus, J. Chem. Phys. , _43, 679 (1965). (2) R.R. Dogonadze, A.M. Kuznetsov and V.G. Levich, Electrochim. Acta, 13, 1025 (1968).

109 C-17 THEORETICAL MODELS FOR SOLVENT INTERVENTION ON S 2 REACTIONS.

C. ALEMAN, F. MASERAS, A. LLEDOS, M. DURAN, AND J. BERTRAN.

DEPARTAMENT DE QUIHICA, UNIVERSITAT AUTONOMA DE BARCELONA, 08193 BELLATERRA,

CATALONIA, SPAIN.

The S2 fluoride exchange in the (FCH F)~ system (1) and the S 2 water exchange in the (H OCH.,OH2) + system (2) have been well studied theoretically in gas phase. The present work studies the intervention of solvent on these processes, using different models to represent it. In the first one, a reduced number of solvent molecules is taken into account, within the supermolecule model. In the second one, a continuum representation for the solvent is taken, within the model of the cavity (3). Finally, in the third model a discrete-continuum model is used, taking a small number of solvent molecules within a cavity model. Ab initio SCF calculations have been performed on these three models. The 3-21G basis set has been used for the (H20CH30H2)+ system, whereas the 3-21+G has been employed in the (FCH F) system to adequately represent anions. In the application of the discrete model, the main conclusion arising is that solvation parameters appear as main components of the transition vector at the transition state. Therefore, solvent parameters play an active role in the reaction coordinate. Application of both the continuum and discrete-continuum models shows that the well depth of the intermediate is decreased due to the electronic reorganization of the systems. These results are discussed and compared with the Monte Carlo calculations of Jorgensen (4)and the Molecular Dynamics results of Wilson (5).

REFERENCES: (1) M. Urban, I. Cernusak, V. Kello, Chem. Phys. Letters 105 (1984), 625. (2) K. Raghavachari, J. Chandrasekhar, R.C. Burnier, J. Am. Chem. Soc. 106 (1984), 3124. (3) S. Miertus, E. Scrocco, J. Tomasi, Chem. Phys. 55 (1981), 117. (4) J. Chandrasekhar, S.F. Smith, W.L. Jorgensen, J. Am. Chem. Soc. 107 (1985) 154. (5) J.P. Bergsma, B.J. Gertner, K.R.Wilson, J.T. Hynes, J. Chem. Phys. 86 (1987) 1356.

110 C-18 POTENTIAL ENERGY CHARACTERISTICS FOR THE REARRANGEMENT REACTION OF HON TO HNO BT MCSCF METHOD

LIU RUOZHUANG(B.Z.LIU) AND IU JIANGUO(J.G.TU) (DEPT. OF CHEMISTRT, BEIJING NORMAL UNIVERSITY, BEIJING 100009, PEOPLE'S REPUBLIC OF CHINA)

ABSTRACT In this paper, the optimized geometries of HON, HNO, the transition rtate and the reaction path( intrinsic reaction coordinate ) of their rearrangement reaction are presented based on MCSCF ab initio calculation with 3-21G basis set. The vibrational analysis and currature data show that the N=0 stretching ribrational mode is adiabatic, while the OH + NH stretching mode is a dynamic degree of freedom and the currature of the IRC mainly consists of the latter normal mode. On the reaction path, there are two narrow peaks of the curvature, which shows the dy- namic effect will take place at these regions.

REFERENCES (1) H.W.Brown and G.C.Pimental, J.Chem.Phys., 2£, 883(1958) (2) W.H.Miller, N.C.Handy, J.E.Adams, J.Chem.Phys., 21* 99(1980) (3) S.Kato, K.Morokuma, J.Chem.Phys., 21» 3900(1980)

m C-19

ELECTRONIC INDICES FROM LOWDIN'S POPULATION SCHEME

L.S. YADAV, 3.S. YADAV+ AND D.K. RAI DEPARTMENT OF PHYSICS, BANARAS HINDU UNIVERSITY VARANASI - INDIA - 221005

Classical chemical parameters e.g. orbital and atomic charges, multipli- city of bonds (bond orders), atomic and molecular valencies and oxidation numbers for a set of hydrocarbons and their respective monofluoroderivatives have been computed using STO-3G, 4-31G, 3-21G, 6-31G and 6-31G* basis sets in ab initio formaJism via Muiliken's and Lowdin's population schemes. A comparative survey of the indices so obtained reveals that L'dwdin's popula- tion scheme performs better for almost all parameters and 6-31G* basis set is observed to be most appropriate than .rest of the basis set considered. The effect of fluorosubstitutions on single, double and triple bond between C-C atoms has also been brought out. The basic effect of non-bonded interactions on valence index and oxidation number is observed to be playing vital role in molecular framework. A number of definitions proposed by pioneer workers have also been put under test in the present study. Multiplicity of bonds and oxidation numbers have been found useful in elucidating the structural aspects of the molecular geometries while valence index looks as a measure of chemi- cal reactivity for further covalent bond formation.

+Present address: Department of Chemistry, New Jersey Institute of Technology NEWARK, NJ. 07102, U.S.A.

112 C-20 THE MCCONNELL RELATION OF NEWLY MODIFIED INDO MO METHOD

CHENG CHEN INSTITUTE OF APPLIED CHEMISTRY CHUNG CHENG INSTITUTE OF TECHNOLOGY TASIII, TAOYUAN, TAIWAN, R. 0. C.

McConnrll relation' 'is a siiap^e and reliabe linear formula for interpretation of the ESH spectra or pi type free radie«*ls( the radical molecules v,it!i pi type singly (2—3) occupied MO ) by using HMO and Hartree Fock methods . Tlie"INDO-MO model with s-p sCiiiaMtion" has been successfully il >y us Tor botii o^iea ..mi closed shell proble.as ~ . In order to testify ttie importance of IT-TT interaction between 2p of carbon anu Is of iiydrogen in our: UQ wethoci, we apply McConnell relation to proceed a linear correlation study for 122 data points of pi free radicals. The calculated McConnell- consti-at, Q, is equal *to 24.6 gauss. In this statistical treatment, the calculated standard deviation and correlation coefficient of H hyperfine coupling constants are l*-01 ^auss and 0,980. The iiiost results of our calculation are reasonably good.

1. II. M. McConnell, J. Chain. Phys., 2A, 764 (1956). 2. L. C. Snyder and A. T. Amos, J. Cheiu. Phys., _42, 3670 (1965). 3. J. E. Bloor, a. H. Giosou, and P. N. Daylcin, J. Phys. Cliem., 20, 1457 (19G6). 4. C. Chen, F. 0. Ellison, M. Cnsoig, and J. CJiou, J. Chin., Cheio. Soc., ,32, 385 (1985). 5. C. Chen and X. C. Sun, J. Chin..Chem. Soc., jUj 169(1987). 6. C. Chen ami K. C. Sun, " s-p Separation Model INDO-MO Method and the Theoretic*l Study of fl Hyperfine Coupling Constant ", h*s been iiccepted by J. Mol. Stru., 7 TflEOCMBM lor publication recently. 113 C-21 THE ROLE OF J>D ORBITALS IN THE BONDING OF PHOSPHORUS COMPOUNDS

LEMIN LI LI XIAO DEPARTMENT OF CHEMISTRY, PEKING UNIVERSITY, BEIJING, CHINA ZHENGXUAN LIANG COMPUTER CENTER,THE ACADEMY OF SCIENCES OF CHINA,BEIJING,CHINA The question of 3d orbital participation in the bonding of phosphorus compounds is still an open controversy although many studies on it have been done. We realized that it is necessary to define precisely the atomic orbitals in the molecular envi- ronment in order to put the discussion on sounder foundation and get less arbitrary conclusion. It has been proposed that the orbitals of an atom in molecular environment can be defined as the wave functions of an electron moving in an effective central potential field which is the spherical average of the molecular potential field with the center on the related atomic nucleus. We have performed ab initio LCAO-MO-SCF calculations of PHj ,PFj ?P%F*,PF3-,0PF3 and (CHa)sPCH^, and obtained the atomic orbitals and their energy levels of the atoms in these molecules as well as the electron population over these orbit- als. The following conclusion can be drawn. (1) Under the in- fluence of highly electronegative ligands the 3d orbitals con- tract considerably, their radial distribution maxima may lie in the bonding area and their energy levels may drop to a value which is only several eV higher than that of the 3p orbitals. The crystal field split is large and some split levels of 3d orbitals are even lower than those of 3p orbitals. (2) When the phosphorus atom combines with highly electronegative ligands, although there is not any occupied MO which mainly consists of 3d orbitals, the electron population on the 3d orbitals is com- parable to that on the 3s or 3p orbitals. The 3d orbitals in- deed are chemically active components and play important role in determining the properties of phosphorus compounds. (3) The formal positive charge on phosphorus atom is not large, which seems not enough to cause the 3d orbitals contracting and drop- ping their energy levels to that extent. Two other factors must be taken into account, that is, the superposition of the ligand potentials can contribute to the spherical average potential field with center on phosphorus atom and the concerted forma- tion of «" bonds and p-d JC bonds in fact transfers the electrons ; from 3s and 3p to 3d, which would not apparently increase the ;] positive charge of phosphorus atom but would make the 3d orbit- | al electrons feel larger effective nuclear charge. (4) When the % 3d orbitals are only minor components of the occupied MOs, the < 3-center-if-electron bond model seems acceptable. However, the : appearance of 3-center-V-electron bond requires the existence ~: of highly electronegative ligands, which would also makes the 3d orb'itals actively participate in bonding, the perfect 3-cen- 1 ter-Zf-electron bond can only exist in special circumstances. J (1) H.Kwart, K.G.King, "d-Orbitals in the Chemistry of Silicon, |l Phosphorus and Sulfur", Spring-verlag, Berlin, 1977. ; (2) M.O'Keeffe, B.Domenges, G.V.Gibbs,J.Phys.Chem.,1985,89,23Oif. 1

114 C-22

ORBITAL IMAGING OF "LONE PAIR" ELECTRONS IN NH2CH3, NH(CH3)3, N(CH3)3, NH3,

NF3 and (CH3)2O BY ELECTRON MOMENTUM SPECTROSCOPY. C. E. Brion. A.O. Bawagan, and S.A.J. Clark, Department of Chemistry, The University of British Columbia, Vancouver, BC, Canada, V6T 1Y6

Electron Momentum Spectroscopy (EMS) provides a direct experimental route [1] to the laboratory imaging of individual orbitals within the Target Hartree-Fock Approximation (THFA). A direct oscilloscope picture of an Ar 3p orbital in momentum space is shown in figure 1. This capability of EMS is providing stringent tests for molecular wavefunctions in the chemically sensitive low p (large r) region [2]. In addition EMS is a powerful means of

Figure 1. Ar 3p orbital as observed by EMS

investigating bonding [3] and reactivity [4,5] at the fundamental electronic level. In particular the electron density of each of the outermost molecular orbitals of NH3CH3, NH(CH3)a, N(CH3)3 and NF3, is found to exhibit a very much higher degree of s-character than the corresponding orbital in NH3 [4]. Increasing methyl substitution in NH3 results in increasing amounts of s-character in the experimental momentum profiles. This trend is qualitatively predicted by MO calculations which indicate appreciable delocalization of electron density away from the nitrogen in the methyl amines and NF3. The relevance of the present results to current under- standing of the methyl inductive effect is discussed. Similar results are presented for (CH3)20 [7] in comparison with earlier work on H20 [2] and 'CHjOH [8].

[1] C.E. Brion, Intern. J. Quantum Chem. 29 (1986) 1397. [2] A.O. Bawagan, C.E. Brion, E.R. Davidson and D. Feller, Chem. Phys. _U3 (1987) 19. [3] K.T. Leung and C.E. Brion, J.A.C.S. JiO6 (1984) 5859. [4] A.O. Bawagan and C.E. Brion, Chem. Phys. Letters 137 (1987) 573. [5] A.O. Bawagan an C.E. Brion, Chem. Phys., in press (1988). [6] A.O. Bawagan, R. Miiller-Fiedler, C.E. Brion, E.R. Davidson and C. Boyle, Chem. Phys. in press (1988). [7] S.A.J. Clark, A.O. Bawagan and C.E. Brion, to be published. [8] A. Minchinton, C.E. Brion and E. Weigold, Chem. Phys. 62 (1981) 369. 115 C-23

THE VALENCE ORBITAL MOMENTUM DISTRIBUTIONS OF CO AND H,CO: QUANTITATIVE COMPARISONS USING HARTREE FOCK AND CORRELATED WAVE FUNCTIONS. C.E. Brion. C.L. French, and A.O. Bawagan, Dept. of Chemistry, The University of British Columbia, Vancouver, BC, Canada, V6T 1Y6, E.R. Davidson and C. Boyle, Dept. of Chemistry, Indiana University, Bloomington, Indiana 47405, USA and P. Bagus, IBM Almaden Research Centre, 650 Harry Road, San Jose, California 95120-6099. USA.

The binding energies and momentum profiles (XMPs) of the four valence orbitals of CO have been investigated [1] by high resolution electron momentum spectroscopy [2]. Experimental momentum profiles are compared on a quantitative basis to theoretical calculations using SCF wavefunctions ranging in quality from minimal basis to a recently published 136-GTO wavefunction which is essentially at the Hartree-Fock limit. Calculated momentum distributions for the So orbital are very basis set dependent while calculations of DZ or better quality give very similar momentum distributions for the 3o, 4o and lit orbitals. The In experimental momentum profile is not well described in the low momentum region even at the Hartree-Fock limit with basis set saturation including polarization and diffuse functions. Binding energy spectra and momentum profiles in the satellite region beyond 22 eV binding energy of CO are studied in detail. Measurements in the binding energy spectrum of 24 and 28 eV have experimental momentum profiles which are assigned to the 4a and In main lines respectively. The structure above 30 eV is shown to be predominantly due to satellites of the (3o) orbital process.

Similar results are also presented for H,CO [3]. Good quantitative agreement is obtained between the measured XMPs and the momentum distributions of H,CO calculated from a near Hartree-Fock wavef unction except for the outermost 2b, orbital. A preliminary configuration interaction study suggests that the discrepancy observed for the outermost 2bt orbital cannot be accounted for by inclusion of electron correlation and electronic relaxation effects. The measured 5aa and lb, XMPs confirm earlier orbital assignments made by Hood et al [4]. Extensive many-body structures are observed in the inner valence binding energy region and these are assigned predominantly to the (3at) process. [1] C.L. French, C.E. Brion, A.O. Bawagsin. P.S. Bagus and E.R. Davidson, Chem. Fhys. in press (1988). [2] C.E. Brion, Intern. J. Quantum Chem. 29 (1986) 1397. [3] A.O. Bawagan, C.E. Brion, E.R. Davidson and C. Boyle, to be published. [4] S.T. Hood, A. Hamnett, and C.E. Brion, Chem. Phys. Letters 39 (1976) 252.

116 C-24

ELECTRON MOMENTUM SPECTROSCOPY OF THE VALENCE ORBITALS OF H,O, H,S, NH3 AND PH,: QUANTITATIVE COMPARISONS USING HARTREE-FOCK LIMIT AND CORRELATED WAVE FUNCTIONS. C.E. Brion. A.O. Bawagan, C.L. French, R. Muller-Fiedler, and S.A.J. Clark, Department of Chemistry, The University of British Columbia, Vancouver, BC, Canada, V6T 1Y6 and E.R. Davidson, D. Feller and C. Boyle, Department of Chemistry, Indiana University. Bloomington, Indiana 47405, USA.

Electron Momentum Spectroscopy (EMS) is an emerging new technique in experimental quantum mechanics for investigating the momentum of electrons in valence orbitals [1]. The large discrepancies found earlier between experimental measurements at low momentum resolution and calculations based on near Hartree-Focx wavefunctions for the valence orbital electron momentum distributions of H.O and NH, are investigated. New and improved high-resolution [2] EMS measurements for the valence orbitals of H20 and NH, [3] have been placed on a common intensity scale using the binding energy spectra. Investigation of possible vibrational effects by means of new measurements of the momentum distributions of D20 indicates no detectable differences with the H20 results, within experimental error. A quantitative comparison of these experimental results with both the shapes and magnitudes of momentum distributions calculated in the PWIA and THFA approximations using new, very precise Hartree-Fock (single-configuration) wavefunctions is made. These wavefunctions, which include considerable polarization and very diffuse functions are effectively converged at the HF limit for total energy, dipole moment and momentum distribution. Use of these wavefunctions permits establishment of basis set independence. The significant discrepancies between theory and experiment which still remain for the momentum distributions of the lblf 3at and 2a} orbitals of H20 at the THFA level are largely removed by CI calculations of the full ion-neutral overlap amplitude (OVD). These wavefunctions for the final ion and neutral ground states, generated from the accurate HF limit basis sets, recover up to 88% of the correlation energy in H20. The present work clearly shows the need for adequate consideration of electron correlation effects in describing the low-momentum parts of the lblt 3a,, and 2aa electron distributions of H20, a region which is of crucial importance in problems related to chemical bonding and reactivity. Similar behaviour is found in the case of NH, [3]. In contrast inclusion of correlation is found to have little effect on the calculated distributions for HaS [A] and PH, [5] where good agreement between experiment and theory is already obtained at the Hartree-Fock Limit. In addition experimental and theoretical investigations of electron correlation effects in the ionization of the inner-valence orbitals are presented.

[1] C.E. Brion, Intern. J. Quantum Chem. 29 (1986) 1397. , [2] A.O. Bawagan, C.E. Brion, E.R. Davidson and D. Feller, Chem. Phys. 113 (1987) 19. [3] A.O. Bawagan, R. Muller-Fiedler, C.E. Brion, E.R. Davidson and C. Boyle, Chen. Phys., in press 1988. [4] C.L. French, C.E. Brion and E.R. Davidson, Chem. Phys., in press 1988. [5] S.A.J. Clark, C.E. Brion and E.R. Davidson, to be published.

117 C-25

CORRELATION IN THE GROUNDSTATE OF MnO4-

MARTENA.BUYSE. EVERT-JAN BAERENDS, PETER UCHTENVELDT DEP.THEOR.CHEM., FREE UNIVERSITY, DEBOELELN1083. 1081HV AMSTERDAM, THE NETHERLANDS

If a hole is created in the non-bonding oxygen 2p shell of the groundstate of MnO4% either by ionisation or by a charge transfer type excitation, we introduce an extra correlation error, not present in the groundstate, caused by neglect of hole-localisation effects [1]. On an energy scale the magnitude of this error is roughly 3 eV. We would therefore expect the ASCF excitation energy for the first excited state, which is It1-»2e, to be too high by a few eV. In reality however the ASCF excitation energy is too low by more then 1 eV [2,3], which leads to the conclusion that the correlation energy is much larger in the groundstate then in the first excited state. Although the permangate ion has been a subject for extensive study (see eg [3] and references therein), until now no detailed analysis of correlation in the groundstate of MnO4~ has been published. In this work therefore we will study this groundstate on SCF and CI level and we will present an explanation for the cause and consequences of the large correlation error.

We will show that in the groundstate of MnO4" the distance between oxygen and manganese is too large for effective Mn3d-O2p overlap. Naively one maybe would expect that it is the repulsion between the oxygen atoms that prevents the Mn-O distance becoming small enough for efficient overlap, but it is shown that this is not the case. The real cause of the trouble is the limited spatial extension of the 3d-orbital. In first row transition metals the 3d-orbital is of about equal size as the 3s/3p shell, although the 3d is much higher in energy. Orbitals that overlap with the 3d to form a bond will at the same time overlap with the 3s/3p orbitals. This leads to considerable exchange (Pauli-) repulsion of ligand shells with the 3s/3p shell when the metal-ligand distance is short enough for strong 3d- ligand 2p bonding. As a consequence, the Mn-0 equilibrium distance is too long for effective 3d-2p overlap. The small 3d-2p overlap leads to a SCF wavefunction with too much weight on ionic terms. (Compare with the SCF error in H2 at larger internuclear distances.) In singly bonded systems (like H2) we can correct this error by mixing in configurations that involve double excitations from the bonding to the antibonding orbital. In multiply bonded systems like MnO4~, the situation can be more complex because too large weights on ionic contributions can be avoided already at the SCF level by (partial) localisation of the bonding orbitals [4]. In MnO4" the le bonding orbital is localised strongly towards the oxygen (72% O2p character) while the 5h bonding orbital is localised slightly towards manganese (55% Mn3d character) and this leads to a loss of covalent character. To correct the SCF error and to restore the covalency in a CI calculation, we must not only mix in double excitations from bonding to antibonding orbitals like Iele-»2e2e and 5t25t2-»7t27t2, but now also doubles like Ie5t2-»2e7t2 and singles like 5t2—»7t2 and le->2e are Decoming important References [1] H.B. Broer-Braam, thesis 1981 [2] R Hsu, C. Peterson, R.M. Pitzer, J. Chem. Phys. 64(2) 791 (1976) [3J H. Johansen, S. Rettrup, Chem. Phys. 74 77 (1983) [4] R.F. Fenske, J.R. Jensen, J. Chem. Phys. 71(8), 3374 (1979) 118 C-26

SIMULATION OF WATER SOLUTIONS OF CU(I) AT INFINITE DILUTION

M. Natalia D. S. Cordeiro and Jose A. N. F. Gomes Departamento de Quimica, Faculdade de Ciencias, Universidade do Porto, 4000 Porto, Portugal. A. Gonzaiez-Lafont, J. M. Lluch, A. Oliva and J. Bertran Departament de Quimica, Facuitat de Ciencies, Universitat Autdnoma de Barcelona, Bellaterra, Spain.

Abstract: + Results of Monte Carlo simulations of the Cu (H20)|00 system are reported for the N.V.T. ensemble at 298K. A cubic distribution of the water molecules around the copper ion with a density of ca. Igcrn"' and periodic boundary conditions was considered, adopting the minimal image technique. The interaction energies of the system were computed in the + pairwise approach, using an ab initio pair potential for the Cu - H20 interactions(i); for the H20 - H20 interactions, the ab initio MCY potential of Matsuoka et al. (2) and the empirical TIP4P potential of Jorgensen et at. have been used. The interaction energies, the radial distribution functions and the running coordination numbers are presented for each of the two H20 - H20 potential functions. In this work, a coordination number of 6 was found with the TIP4P potential, while the MCY potential predicts a coordination number of 7. Empirical potentials like TIP4P tend to be simpler functions leading to faster computer simulations.

The finantial suport of INIC (Lisboa) is gratefully acknowledged.

[1] - M. N. D. S. Cordeiro, J. A N. F. Gomes, A. G. Lafont, J. M. Lluch, A. Oliva and J. Bertran, J. Chem. Soc. Faradav Trans. 2. in press. 12] - 0. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys.. 6A 1351 (1976). ..-• 119 C-27 Applications of Quasibosons to Electron Pair Correlation.

P.E.Hoggan. present address: Laboratoiie de Chimie The'orique, U.A. C.N.R.S 510, Universite de Nancyl, B.P. 239, 54506 Vandoeuvre - les - Nancy, Prance. Presented at The Sixth International Conference on Quantum Chemistry, VIQC Jerusalem, Israel 1988. July 19, 1988

Abstract The many bodied ferraion pioblem is expiessed in the Hubbaid approxima- tion in terms of quasibosons (reft: 1,2) foi a clean semi - infinite solid containing Gee elections. The nse of closed shell RHF calculations is thus justified for a closed shell adsorbed molecular structure on a surface described by a teio order spectrum of Bloch eigenfunctions. (xef: 3) The Green's matrix perturbation series is evaluated using the algebra of adapted Liouvillian supeiopetatots foi & carrier space of reduced density ma- trices. In this way, the finite perturbation series is established fot the Green's matrix rather than the perturbed Hamiltonian of the system. A recuxsive pro- cedure is derived, which is equivalent to polarising the whole - system wave- function under the influence of the potential induced by the adsordate. The Hartree-Fock Green's matrix which has already been shown to be con- vergent (re£ 4) is then applied for a Perfect Periodic Solid substrate. This approximation has been validated by appealing to the integral formalism foi the case of ccp as well as simple cubic solids and is here applied to such a metal over an spd basis at the MNDO level (ret: 5). The present method is preferred because of its analytical convenience and resulting highly vectorisable algorithm in the light of current developments in array processor technology. 1

1 Bibliography;

(1) H Buentsen, Phys. Rev B 2& p4l43 (1983) (2) M. Girardeau, J. Math. Phys. 4 plO96 (1963); li p681 (1970); 12 p!799 (1971) } (3) J.C.Inkson, Many - Body Theory of Solids, Plenum N.Y.2e (1986) esp. Ch2 : (4) R.S.Ciien et al. Chem. Phyt. 12ft p!77 (1988) ' I. (5) P.E.Hoggan Cantab. Fellow. Diss. Galloway, Cambridge (1987) (limited ed.)

120 C-29

THEORY OF HUON CATAL72ED FUSION

KRZYSZTOF SZALEBICZ Department of Physics, University of Delaware, Newark, DE 19716

In the last decade muon catalyzed fusion has been a subject of intensive research efforts worldwide. Already in 1940s Sakharov and Frank independently pointed oat that such a process is possible thanks to the basic laws of quantum mechanics. If in the Hz ion one replaces the electron by a muon - a particle with the sane charge as an electron but 207 tines nore nassive - the resulting tdjt ion is about two hundred tines smaller than the electronic ion. In muonic ions the nuclei are so close together that the fusion takes place in 10~12 second, without need for high temperature and pressure. After the fusion, muon is usually free and nay form the next molecule. However, muons live only two microseconds and are expensive to produce. In the early 1960s nuon catalyzed fusion research was abandoned since it was believed that, on the average, one muon may form only one molecule in its lifetime. Recent experiments, however, have shown that one muon can catalyze almost 200 fusions, renewing hopes for a new energy source. Despite the nuclear reaction being the central point of the process, the major parameters of the muon cycle depend on Coulombic forces. We have been performing accurate quantum mechanical calculations for muonic molecular ions. Such calculations are critical for understanding the phenomenon of muon catalyzed fusion, fie expand the wave functions in basis sets containing several thousands of terns which give solutions of the Schrodinger equation with accuracy of 15 decimal figures. Our calculations provided the most accurate energy levels to date for molecular muonic ions. These results will allow theoretical prediction of the formation rates for these ions. At present, the major bottleneck of the muon catalyzed cycle seems to be sticking of the muons to the alpha particles synthesized in the nuclear reactions. Stuck muons are lost for further fusions, ffe are theoretically investigating the probability of this sticking. We have obtained the Coulombic sticking fractions accurate to about four digits, a substantial improvement over the previous literature results, but the disagreement ; between theory and experiment has still not been resolved. There have been ' several speculations that strong nuclear forces are responsible for this 1 disagreement. We include effects of these forces in our calculations by •$• imposing boundary conditions on the wave functions at the nuclear radius. -f To add flexibility in this region our basis sets contain irregular terms, < i.e. negative powers of the nuclear distance. Alternatives to the classical ; expression for the sticking amplitude are being derived. Other topics of our work include calculations of the finite size corrections to energy levels of muonic molecules, improved determination of the molecular formation rates and investigation of the role of the internal resonances in i | this formation. *||

121 C-3 0 "Calculations of Reliable Static Polarizabilities for Small Polyatomic Molecules and their Application to Polymer Physics"

Richard L. Jaffe and Kenneth Yao NASA Ames Research Center Computational Chemistry Branch Moffett Field, CA 94035, U.S.A.

Delano P. Chong Department of Chemistry University of British Columbia Vancouver, B.C. V6T 1W5, Canada

and 'Andrew Komornicki Polyatomics Research Institute Mountain View, CA 94043, U.S.A.

ABSTRACT An efficient prescription for computing the second-order static polarizability tensor for polyatomic molecules is described. The polarizability is computed as the second derivative, with respect to external electric field parameters, of the ab initio SCF energy. If the calculations employ minimal Gaussian atomic orbital basis sets augmented with field-induced polarization functions(l), the resulting average polarizabilities are generally within 10-15% of experiment and in excellent agreement with larger basis set Hartree Fock calculations. These basis sets are small enough to permit calculations of molecules containing up to 6-8 first and second row elements. In the present study, the average polarizability and polarizability anisotropy have been computed for more than 35 small polyatomic molecules including the series of fluoro- and chloro-methanes and silanes. The computed polarizability anisotropies for n-alkanes have been used to parameterize model calculations for polyethylene. Similar calculations for simple methyl esters have been used to interpret stress- and strain-birefringence measurements for polymethyl methacrylate (PMMA).

122 INDEX

Abbott P.C. B-3 49 Cadet J. A-46 45 B-4 50 Cal Z. B-16 61 Aleman C. C-17 110 Calais J.L. A-8 8 Alimi R. B-29 74 Caldwell W.B. B-3 5 80 Alvarez 6. B-10 55 Campos-Martinez J. A-16 16 Amos R.D. B-17 62 A-17 17 Andre J.M. A-8 8 Cao Y. A-32 32 Anguiano J A-45 44 Carrol M.T. B-33 78 Apkarian V.A. B-29 74 Carter S. B-18 63 Castro E.A. A-4 4 B Chandler G.S. B-4 50 Charro E. A-6 6 Bader R.F.W. B-3 3 78 Cheng Chang B-33 78 Baerends E.-J. C-25 118 Cheng Chen C-20 113 Baerends E.-J. B-14 59 Chen J.-Q. A-l 1 Bakhshi K. B-37 82 Cheney B.V. B-41 86 Balint-Kurti G. A-27 27 Chojnacki H. A-19 19 Barone V. A-46 45 Chong D.F. B-9 54 Barientos R.C. A-6 6 C-20 122 Barzaghi H. A-32 32 Christov S.G. A-23 23 Basch H. A-36 36 Clark S.A.J. C-22 115 Bawagan A.O. C-22 115 C-24 117 C-23 116 Colle R. A-22 22 C-24 117 Cooper D.L. B-ll 56 Bellido M.N. A-18 18 Cordes J. C-l 94 Bertran J. C-16 109 Cordeiro M.N.D.S. C-26 119 C-17 110 Cortina A.M. A-16 16 A-24 24 A-29 29 Billing G.D. A-13 13 Courbin C. A-12 12 Bliznyuk A.A. A-35 35 Cowley A.H. B-42 87 Boisiger J. C-10 103 Bofill J.M. A-25 25 D Boggs J.A. B-42 87 Bolterauer H. B-36 81 Dacheng F. B-16 61 Bonacic-Koutecky V. A-39 39 Damewood Jr.J.R. B-34 79 A-41 41 Decoret C. B-31 76 I B-39 84 Delchev Y.I. A-38 38 B-46 91 Delgado-Barrio G. A-16 16 Boustany I. B-39 84 A-17 17 Brion C. C-22 115 A-29 29 C-23 116 A-30 30 C-24 117 Delhalle J. A-8 8 Bucur M. A-14 14 Deng D. B-16 61 Buyse H.A. B-14 59 Derecskei-Kovacs A. A-7 7 C-25 118 Dobbs K.D. B-42 87

123 Dreismann CA. B-30 75 Grein F. B-5 51 Duch W. B-2 46 Gusakov V.E- C-8 101 Duran M. C-17 110 u E n A-15 15 Enflo A. B-43 88 Hall S.G. Handy N.C. B-18 63 F B-20 65 C-2 95 Fantucci P- A-41 41 Harlharan P.C. B-21 66 B-39 84 Hernandez M. A-30 30 B-46 91 Hoggan P.E. C-27 120 Feng D. B-16 61 Holleboom L.J. B-14 59 Fernandez F.M. A-4 4 Holmgren H. B-43 88 Fernandez-Sanz J. A-21 21 Horn T.R. C-12 105 A-44 43 A-4 5 44 Flores J.R. B-22 67 IJ B-2 3 68 Fortunelll A. A-22 22 Ishida K. A-5 5 Freed K.F. B-12 57 Jacobson R.A. B-28 73 C-7 100 Jaffe R.L. B-9 54 French C.L. C-23 116 C-30 122 C-24 117 Jiang Y. A-4 3 42 Fripiat J.G. A-8 8 Fritsche L. C-l 94

6 K

Galasso V. C-6 99 Kama S.P. B-5 51 A-10 10 Karwowski J. C-4 97 Gatti C. A-32 32 Kashiwagi H. B-38 83 George T.F. B-25 70 Katriel J. A-l 1 Georgiev M. A-20 20 A-2 2 Gerber R.B. A-31 31 A-3 3 B-29 74 Kaufman J.J. B-21 66 C-12 105 Keegstra P.B. B-21 66 Gerratt J. B-ll 56 Kim C.K. A-40 40 l Gilmore R. A-l 1 Kirtman B. A-9 9 ••• A-2 2 Knowles P.J. B-19 64 A-3 3 Komornicki A. C-30 122 Gogolinsky V.l. C-8 101 B-9 54 Gomes G.A.N.F. C-26 119 Kosloff R. A-31 31 Gonzales-Lafont A. C-16 109 Koutecky J. A-41 41 !i Graffi S. B-10 55 Krusic P.J. A-47 46 § Grand A. A-46 45 Kumpf R.A. B-34 79 -\ A-47 46 Kurmyshev E.V. C-8 101 •;,

124 L Mukherjee D. B-15 60 Muckerman J.T. A-13 13 Laakkonen L.J. C-13 106 Muehlerbauer W.C.F. B-34 79 Lain L. C-4 97 Mueller-Fiedler R. C-24 117 Largo-Cabrerizo A. B-22 67 B-23 68 N Larsson S. C-9 102 Last I. B-25 70 Nino A. A-18 18 Lavrik 0.1. A-35 35 Novoselsky A. A-l 1 Lee. B.C. A-40 40 A-2 2 Lee I. A-40 40 A-3 3 Lee S. C-7 100 Lee T.J. C-2 95 O B-24 69 Leutwyler S. C-10 103 Oliva A. C-16 109 Li J.Q. C-ll 104 Oltean M. A-14 14 Li L. C-21 114 Osman R. A-36 36 Li X. A-43 42 C-21 114 P B-6 52 Liang J.Y. A-26 26 Pavlov R.L. A-38 38 Lichtenveldt P. C-25 118 Pewestroff W. A-41 41 Lipscomb W.N. A-26 26 Pickup B.T. C-5 98 Liu R.Z. C-18 111 Pouchan C. A-21 21 Lledos A. C-17 110 Pulay P. A-25 25 Lluch J.M. C-16 109 C-3 96 B-13 58 H Pyka M. A-19 19 Pyykkoe P. C-13 106 Maclagan R.J.A.R. B-40 85 Macovei V. A-14 14 R Malrieu J.P. B-45 90 Marconi G. B-44 89 Rai D.K. C-19 112 Marquez Cruz A. A-44 43 Raimondi M. B-ll 56 A-45 44 Rami.ro B. B-48 93 Martin I. A-6 6 Ratner M.A. C-12 105 Martins-Costa M.T.C. B-47 92 Rice J.E. B-20 65 Maseras F. C-17 110 B-17 62 Mayer I.P. B-32 77 Rinaldi D. B-47 92 McDiarmid R. C-14 107 Rivail J.L. B-47 92 Michl J. A-39 39 Rodger P.M. B-27 72 Miller L. B-28 73 Rohmer M.M. A-28 28 Miret-Artes S. A-17 17 Roncero 0. A-16 16 A-29 29 A-30 30 •3 A-30 30 Rosmus P. B-18 63 Misiak P. A-19 19 B-19 64 Moiseyev N. A-29 29 Roszak S. B-21 66 I Moroz J. B-35 80 Ruedenberg K. B-28 73

125 s Velev V.G. A-38 38 Villareal H.P. A-16 16 Sabio M. B-35 80 A-17 17 Saebo S. C-3 96 A-2 9 29 Salto N. A-15 15 A-30 30 Salas P. A-12 12 Voisin C. A-46 45 Sanchez Marcos E. A-24 24 Voituriez L. A-46 45 Schoeffel K. A-39 39 Voityuk A.A. A-35 35 Schwarz W.H.E. B-28 73 Senekowitsch J. B-18 63 W Shubing L. C-15 108 Silverstone H.J. B-10 55 Wahnon P. B-48 93 Simonucci S. Ä-22 22 A-12 12 Slanina Z. B-26 71 Wang X.C. B-12 57 Smeyers Y.G. A-18 18 Wang Y.-L. A-32 32 Snijders J.6. C-5 98 Wang Z. B-16 61 B-14 59 Weatherford C.W. A-ll 11 Srivastava V. A-33 33 Werner H.J. B-18 63 A-34 34 B-19 64 Stevens W.J. A-36 36 Wolinski K. B-13 58 Stone A.J. B-27 72 Surjan P.R. B-32 77 Y Szalewicz K. C-29 121 Yadav J.S. C-19 112 T C-19 112 Yamamoto S. B-38 83 Tamassy-Lentei I. A-7 7 Yao K. B-9 54 Tang K.T. B-8 53 Yeager D.L. B-l 47 Tatsumi K. C-13 106 Yinnon A.T. A-31 31 Temkin Ä. A-ll 11 Yu J.G. C-18 111 Toennies J.P. B-8 53 Yu W. A-43 42 Topiol S. B-35 80 Torre A. C-4 97 Z Trinquier G. B-45 90 Tuszynski J.A. B-36 81 Zexin W. B-16 61 Zhang H. A-43 42 V Zhang Q. B-6 52 Zhengtlng C. B-16 61 Valdemoro C. C-4 97 Zhengxuan L. C-21 114 Vallleres M. A-l 1 Zhouren P. C-15 108 A-2 2

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