Theory and Technique
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More Insight in Multiple Bonding with Valence Bond Theory K
More insight in multiple bonding with valence bond theory K. Hendrickx, B. Braida, P. Bultinck, P.C. Hiberty To cite this version: K. Hendrickx, B. Braida, P. Bultinck, P.C. Hiberty. More insight in multiple bonding with va- lence bond theory. Computational and Theoretical Chemistry, Elsevier, 2015, 1053, pp.180–188. 10.1016/j.comptc.2014.09.007. hal-01627698 HAL Id: hal-01627698 https://hal.archives-ouvertes.fr/hal-01627698 Submitted on 21 Nov 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. More insight in multiple bonding with valence bond theory ⇑ ⇑ K. Hendrickx a,b,c, B. Braida a,b, , P. Bultinck c, P.C. Hiberty d, a Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, LCT, F-75005 Paris, France b CNRS, UMR 7616, LCT, F-75005 Paris, France c Department of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium d Laboratoire de Chimie Physique, UMR CNRS 8000, Groupe de Chimie Théorique, Université de Paris-Sud, 91405 Orsay Cédex, France abstract An original procedure is proposed, based on valence bond theory, to calculate accurate dissociation ener- gies for multiply bonded molecules, while always dealing with extremely compact wave functions involving three valence bond structures at most. -
Theoretical Methods That Help Understanding the Structure and Reactivity of Gas Phase Ions
International Journal of Mass Spectrometry 240 (2005) 37–99 Review Theoretical methods that help understanding the structure and reactivity of gas phase ions J.M. Merceroa, J.M. Matxaina, X. Lopeza, D.M. Yorkb, A. Largoc, L.A. Erikssond,e, J.M. Ugaldea,∗ a Kimika Fakultatea, Euskal Herriko Unibertsitatea, P.K. 1072, 20080 Donostia, Euskadi, Spain b Department of Chemistry, University of Minnesota, 207 Pleasant St. SE, Minneapolis, MN 55455-0431, USA c Departamento de Qu´ımica-F´ısica, Universidad de Valladolid, Prado de la Magdalena, 47005 Valladolid, Spain d Department of Cell and Molecular Biology, Box 596, Uppsala University, 751 24 Uppsala, Sweden e Department of Natural Sciences, Orebro¨ University, 701 82 Orebro,¨ Sweden Received 27 May 2004; accepted 14 September 2004 Available online 25 November 2004 Abstract The methods of the quantum electronic structure theory are reviewed and their implementation for the gas phase chemistry emphasized. Ab initio molecular orbital theory, density functional theory, quantum Monte Carlo theory and the methods to calculate the rate of complex chemical reactions in the gas phase are considered. Relativistic effects, other than the spin–orbit coupling effects, have not been considered. Rather than write down the main equations without further comments on how they were obtained, we provide the reader with essentials of the background on which the theory has been developed and the equations derived. We committed ourselves to place equations in their own proper perspective, so that the reader can appreciate more profoundly the subtleties of the theory underlying the equations themselves. Finally, a number of examples that illustrate the application of the theory are presented and discussed. -
An Introduction to Hartree-Fock Molecular Orbital Theory
An Introduction to Hartree-Fock Molecular Orbital Theory C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology June 2000 1 Introduction Hartree-Fock theory is fundamental to much of electronic structure theory. It is the basis of molecular orbital (MO) theory, which posits that each electron's motion can be described by a single-particle function (orbital) which does not depend explicitly on the instantaneous motions of the other electrons. Many of you have probably learned about (and maybe even solved prob- lems with) HucÄ kel MO theory, which takes Hartree-Fock MO theory as an implicit foundation and throws away most of the terms to make it tractable for simple calculations. The ubiquity of orbital concepts in chemistry is a testimony to the predictive power and intuitive appeal of Hartree-Fock MO theory. However, it is important to remember that these orbitals are mathematical constructs which only approximate reality. Only for the hydrogen atom (or other one-electron systems, like He+) are orbitals exact eigenfunctions of the full electronic Hamiltonian. As long as we are content to consider molecules near their equilibrium geometry, Hartree-Fock theory often provides a good starting point for more elaborate theoretical methods which are better approximations to the elec- tronic SchrÄodinger equation (e.g., many-body perturbation theory, single-reference con¯guration interaction). So...how do we calculate molecular orbitals using Hartree-Fock theory? That is the subject of these notes; we will explain Hartree-Fock theory at an introductory level. 2 What Problem Are We Solving? It is always important to remember the context of a theory. -
An Experimental Chemist's Guide to Ab Initio Quantum Chemistry
J. Phys. Chem. 1991, 95, 1017-1029 1017 FEATURE ARTICLE An Experimental Chemist’s Guide to ab Initio Quantum Chemistry Jack Simons Chemistry Department, University of Utah, Salt Lake City, Utah 84112 (Received: October 5, 1990) This article is not intended to provide a cutting edge, state-of-the-art review of ab initio quantum chemistry. Nor does it offer a shopping list of estimates for the accuracies of its various approaches. Unfortunately, quantum chemistry is not mature or reliable enough to make such an evaluation generally possible. Rather, this article introduces the essential concepts of quantum chemistry and the computationalfeatures that differ among commonly used methods. It is intended as a guide for those who are not conversant with the jargon of ab initio quantum chemistry but who are interested in making use of these tools. In sections I-IV, readers are provided overviews of (i) the objectives and terminology of the field, (ii) the reasons underlying the often disappointing accuracy of present methods, (iii) and the meaning of orbitals, configurations, and electron correlation. The content of sections V and VI is intended to serve as reference material in which the computational tools of ab initio quantum chemistry are overviewed. In these sections, the Hartree-Fock (HF), configuration interaction (CI), multiconfigurational self-consistent field (MCSCF), Maller-Plesset perturbation theory (MPPT), coupled-cluster (CC), and density functional methods such as X, are introduced. The strengths and weaknesses of these methods as well as the computational steps involved in their implementation are briefly discussed. 1. What Does ab Initio Quantum Chemistry Try To Do? quantitative predictions to be made. -
Diagonalization, Eigenvalues Problem, Secular Equation
Diagonalization, eigenvalues problem, secular equation Diagonalization procedure of a matrix A with dimensionality n × n (e.g. the Hessian matrix) 2 3 a11 a12 : : : a1n 6 7 6 a21 a22 : : : a2n 7 6 7 A = 6 . 7 6 . 7 4 5 an1 an2 : : : ann consists in finding a matrix C such, that the matrix D=C−1AC is diagonal: 2 3 d1 0 ::: 0 6 7 6 0 d2 ::: 0 7 −1 6 7 C AC = D = 6 . 7 6 . 7 4 5 0 0 : : : dn Equation C−1AC=D can also be written as AC = CD Denoting the elements of matrix C by cij and using te fact that D is diagonal (i.e., its elements dij are of the form djδij, where δij denotes the Kronecker delta, δii=1 i δij=0 for i6=j) we obtain X X X (AC)ij = aik ckj (CD)ij = cik dkj = cik dj δkj = djcij k k k Diagonalization, eigenvalues problem, secular equation Employing the equation (AC)ij = (CD)ij we obtain X aik ckj = djcij k In matrix notation this equation takes the form ACj = dj Cj where Cj is the jth column of matrix C. This is equation for the eigenvalues (dj) and eigenvectors (Cj) of matrix A. Solving this equation, that is the solving the so called eigenproblem for matrix A, is equivalent to diagonalization of matrix A. This is because the matrix C is built from the (column) eigenvectors C1;C2;:::;Cn: C = [C1;C2;:::;Cn] The equation for eigenvectors can also be written as( A − dj E) Cj = 0, where E is the unit matrix with elements δij. -
A Comparison of Pariser-Parr-Pople Calculations on Furan with Nddo(+
University of New Hampshire University of New Hampshire Scholars' Repository Doctoral Dissertations Student Scholarship Fall 1975 A COMPARISON OF PARISER-PARR-POPLE CALCULATIONS ON FURAN WITH NDDO(+ NEGLECT OF DIATOMIC DIFFERENTIAL OVERLAP) CALCULATIONS ON FURAN AND PYRROLE INCLUDING A COMPARISON WITH AB INITIO AND OTHER SEMIEMPIRICAL METHODS DONALD RICHARD LAND University of New Hampshire, Durham Follow this and additional works at: https://scholars.unh.edu/dissertation Recommended Citation LAND, DONALD RICHARD, "A COMPARISON OF PARISER-PARR-POPLE CALCULATIONS ON FURAN WITH NDDO(+ NEGLECT OF DIATOMIC DIFFERENTIAL OVERLAP) CALCULATIONS ON FURAN AND PYRROLE INCLUDING A COMPARISON WITH AB INITIO AND OTHER SEMIEMPIRICAL METHODS" (1975). Doctoral Dissertations. 2349. https://scholars.unh.edu/dissertation/2349 This Dissertation is brought to you for free and open access by the Student Scholarship at University of New Hampshire Scholars' Repository. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of University of New Hampshire Scholars' Repository. For more information, please contact [email protected]. INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1.The sign or "target” for pages apparently lacking from the document photographed is "Missing Page(s)”. If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. -
B3.1 Quantum Structural Methods for Atoms and Molecules
Quantum structural methods for atoms and molecules 1907 B3.1 Quantum structural methods for atoms and molecules Jack Simons B3.1.1 What does quantum chemistry try to do? Electronic structure theory describes the motions of the electrons and produces energy surfaces and wave- functions. The shapes and geometries of molecules, their electronic, vibrational and rotational energy levels, as well as the interactions of these states with electromagnetic fields lie within the realm of quantum structure theory. B3.1.1.1 The underlying theoretical basis—the Born–Oppenheimer model In the Born–Oppenheimer [1] model, it is assumed that the electrons move so quickly that they can adjust their motions essentially instantaneously with respect to any movements of the heavier and slower atomic nuclei. In typical molecules, the valence electrons orbit about the nuclei about once every 10−15 s (the inner-shell electrons move even faster), while the bonds vibrate every 10−14 s, and the molecule rotates approximately every 10−12 s. So, for typical molecules, the fundamental assumption of the Born–Oppenheimer model is valid, but for loosely held (e.g. Rydberg) electrons and in cases where nuclear motion is strongly coupled to electronic motions (e.g. when Jahn–Teller effects are present) it is expected to break down. This separation-of-time-scales assumption allows the electrons to be described by electronic wavefunc- tions that smoothly ‘ride’ the molecule’s atomic framework. These electronic functions are found by solving ˆ a Schrodinger¨ equation whose Hamiltonian He contains the kinetic energy Te of the electrons, the Coulomb repulsions among all the molecule’s electrons Vee, the Coulomb attractions Ven among the electrons and all of the molecule’s nuclei, treated with these nuclei held clamped, and the Coulomb repulsions Vnn among all of these nuclei, but it does not contain the kinetic energy TN of all the nuclei. -
AM65 746.Pdf
American Mineralogist, Volume 65, pages 746-755, 1980 Stereochemistry and energies of single two-repeat silicate chains E. P. Mnacsrn Department of Geological Sciences University of British Columbia Vancouver,Brilish Columbia, Canada V6T 284 Abstract The wide variety of hypothetically possibletwo-repeat chains is discussedand results of cNDo/2 MO calculationson isolatedHsSi3Oro clusters modeling thesechains are presented. Calculations indicate that within the wide spectrum of possiblechains a rather restricted rangeof conformationsis energeticallyfavored. Despite the neglectof M-cationsbetween the chains,calculated conformations of minimum energycompare favorably with observedcon- formations.The chain of lowestcalculated energy is similar to that found in NarSiOr. Chains with conformationsintermediate to NazSiO, and a straight pyroxenechain are predicted to be favored over other conformations.This is in agreementwith observedtwo-repeat chain structures. Introduction sion of the chain in over fifty different structures.His study revealsthat even-periodicchains becomeless The single-chain silicates comprise an important stretched with higher mean electronegativity and classof mineralsbecause of their great abundancein higher mean valence of the M-cations. In odd-peri- crustal and upper mantle rocks. Members of this odic chains the degree of chain shrinkage is strongly classpossess continuous chains of silicate tetrahedra correlatedwith the meanelectronegativity and lessso linked such that each tetrahedron possessestwo with the mean radius -
Acronyms Used in Theoretical Chemistry
Pure & Appl. Chem., Vol. 68, No. 2, pp. 387-456, 1996. Printed in Great Britain. INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY PHYSICAL CHEMISTRY DIVISION WORKING PARTY ON THEORETICAL AND COMPUTATIONAL CHEMISTRY ACRONYMS USED IN THEORETICAL CHEMISTRY Prepared for publication by the Working Party consisting of R. D. BROWN* (Australia, Chiman);J. E. BOWS (USA); R. HILDERBRANDT (USA); K. LIM (Australia); I. M. MILLS (UK); E. NIKITIN (Russia); M. H. PALMER (UK). The focal point to which to send comments and suggestions is the coordinator of the project: RONALD D. BROWN Chemistry Department, Monash University, Clayton, Victoria 3 168, Australia. Responses by e-mail would be particularly appreciated, the number being: rdbrown @ vaxc.cc .monash.edu.au another alternative is fax at: +61 3 9905 4597 Acronyms used in theoretical chemistry synogsis An alphabetic list of acronyms used in theoretical chemistry is presented. Some explanatory references have been added to make acronyms better understandable but still more are needed. Critical comments, additional references, etc. are requested. INTRODUC'IION The IUPAC Working Party on Theoretical Chemistry was persuaded, by discussion with colleagues, that the compilation of a list of acronyms used in theoretical chemistry would be a useful contribution. Initial lists of acronyms drawn up by several members of the working party have been augmented by the provision of a substantial list by Chemical Abstract Service (see footnote below). The working party is particularly grateful to CAS for this generous help. It soon became apparent that many of the acron ms needed more than mere spelling out to make them understandable and so we have added expr anatory references to many of them. -
New Basis Set for Molecular Calculations. II. a CNDO Study of Electric Dipole Moments and Electronic Valence Population on AH An
Home Search Collections Journals About Contact us My IOPscience New basis set for molecular calculations. II. A CNDO study of electric dipole moments and electronic valence population on AH and AB systems using the modified Slater orbitals This content has been downloaded from IOPscience. Please scroll down to see the full text. 1980 J. Phys. B: At. Mol. Phys. 13 211 (http://iopscience.iop.org/0022-3700/13/2/010) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 200.130.19.138 This content was downloaded on 26/09/2013 at 19:29 Please note that terms and conditions apply. J. Phys. B: Atom. Molec. Phys. 13 (1980) 211-216. Printed in Great Britain New basis set for molecular calculations 11. A CNDO study of electric dipole moments and electronic valence population on AH and AB systems using the modified Slater orbitals. B J Costa Cabral t and J D M Vianna$ f Instituto de Fisica, Universidade Federal da Bahia, Campus FederacBo, 40 000 Salvador Ba, Brazil f Departamento de Fisica, Instituto de Cibncias Exatas, Universidade de Brasilia, 70 910 Brasilia DF, Brazil Received 10 January 1979, in final form 4 June 1979 Abstract. The modified Slater orbitals (MSO) basis set is utilised in calculation of the electronic valence population and the electric dipole moments in AH and AB systems, A and B being a second-row elements (from B to F). The Hartree-Fock-Roothaan equations are solved using the CNDO/BW method. The resonance integrals are evaluated with and without the inclusion of valence state ionisation potentials. -
Symmetry-Adapted Perturbation Theory Based on Multiconfigurational
Symmetry-adapted perturbation theory based on multiconfigurational wave function description of monomers Michał Hapka,∗,y,z Michał Przybytek,z and Katarzyna Pernaly yInstitute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland zFaculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland E-mail: [email protected] Abstract We present a formulation of the multiconfigurational (MC) wave function symmetry- adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA) equations. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H2 ··· H2 dimer in out-of-equilibrium geome- tries and interaction between the argon atom and excited state of ethylene. In both cases SAPT(MC) closely reproduces benchmark results. Using the C2H4*··· Ar complex as an ex- ample, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and de- velop a procedure allowing for their computation. -
Valence Bond Theory, Its History, Fundamentals, and Applications. A
1 Valence Bond Theory, its History, Fundamentals, and Applications. A Primer† Sason Shaik1 and Philippe C. Hiberty2 1Department of Organic Chemistry and Lise Meitner-Minerva Center for Computational Chemistry, Hebrew University 91904 Jerusalem, Israel 2Laboratoire de Chimie Physique, Groupe de Chimie Théorique, Université de Paris-Sud, 91405 Orsay Cedex, France † This review is dedicated to Roald Hoffmann – A great teacher and a friend. 2 INTRODUCTION The new quantum mechanics of Heisenberg and Schrödinger had provided chemistry with two general theories, one called valence bond (VB) theory and the other molecular orbital (MO) theory. The two theories were developed at about the same time, but have quickly diverged into rival schools that have competed, sometimes fervently, on charting the mental map and epistemology of chemistry. In a nutshell, until the mid 1950s VB theory had dominated chemistry, then MO theory took over while VB theory fell into disrepute and almost completely abandoned. The 1980s and onwards marked a strong comeback of VB theory, which has been ever since enjoying a Renaissance both in the qualitative application of the theory and in the development of new methods for its computer implementation.1 One of the great merits of VB theory is its pictorially institutive wave function that is expressed as a linear combination of chemically meaningful structures. It is this feature that has made VB theory so popular in the 1930s-1950s, and it is the same feature that underlies its temporary demise and ultimate resurgence. As such, the comeback of this theory is an important development, and it seems timely to review VB theory, to highlight its insight into chemical problems, and some of its state-of-the-art methodologies.