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Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. Bell & Howell Information and Learning 300 North Zeeb Road. Ann Arbor. Ml 48106-1346 USA UIVQ800-521-0600 Spin-Orbit Configuration Interaction Calculations of Actinide and Lanthanide Systems DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Scott Raymond BrozeU, M. S. ***** The Ohio State University 1999 Dissertation Committee: Approved by Professor Russell M. Pitzer, Adviser Professor Eric Herbst Adviser Professor Emeritus Isaiah Shavitt Graduate Program in Chemical Physics UMI Number: 9951<^6 UMI MScroform 9951636 Copyright 2000 by Bell & Howell Wbrmadon and Learning Company. Ail rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. Bell & Howell Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, MI 48106-1346 ABSTRACT Spectroscopic properties of actinide and lanthanide systems were calculated via spin-orbit multireference configuration interaction (SOMRCI) methods using rela- tivistic efiective potentials (REPs) and correlation consistent (cc) basis sets. A program for generating electron configuration lists was written in C + + using the standard template library. Based on an earlier program, this rewrite has no restrictions on the number of basis functions or the number of electrons and has an improved user interface. Uranium REP core sizes were studied. A 78-electron core size, valence space of 6s~6p^5f^6d^7s^, leads to energy levels in mediocre agreement with experiment and to uranyl ion (UO 2 bond lengths that are a few picometers too short. Including the electrons in the valence space corrects these problems. Including, in addition, the electrons in the valence space yields worse results because relativistic effects are large for this subshell. cc-pVDZ and cc-pVTZ basis sets for actinides and lanthanides have been de­ veloped. In a study on trends in correlation and SO energies are similar to those found in Dunning’s original work on the correlation energy in the oxygen atom. Exponents of Gaussian functions optimized for both correlation and SO energy are u nearly identical to those optimized for correlation energy only. Contraction coeffi­ cients for Gaussian basis sets for use with REPs are best determined from atomic natural orbitals, as indicated by a study on the oxygen atom. The ground and excited states of AmOg AmOg and CmOg ^‘'"were calculated. The ground state of the americyl cation is ‘^^ 3 / 2 u- The first ligand to metal charge transfer (LMCT) state is The ground and first LMCT states of the isoelectronic dioxoamericum(V) and curyl cations are and ^Ilo+g. Agreement with experimental excitation energies is good. Other electronic / <— / transitions have been tentatively assigned. Electronic spectra of various cations of uranium, plutonium, americium, curium, praseodymium, and europium, were calculated. For and Pr^^, the agreement is within 20% of experiment for SOMRCI singles and doubles (SOh'IRCISD) using 78 electron core REPs for U and a 46 electron core REP for Pr and cc-pVDZ basis sets. For U, either using a cc-pVTZ basis set or using a 68 electron core REP improves the energy levels to within 10%. All of these cations have been more extensively studied experimentally as dopants in solid crystalline materials. A model of crystalline calcium fluoride was developed and electronic spectra of these cations as dopants in CaFg were calculated. Generally, the agreement is within 25% of experiment. However, the ground state crystal field splittings of the p ions Am^"^, Cm^"^, and Eu^'*' are about a factor of 20 smaller than the corresponding experimental values, which are less than 50 cm~^. ui DEDICATION Shall I compare thee to a summer’s day? Thou art more lovely and more temperate. Rough winds do shake the darling buds of May, And su m m er’s lease hath all too short a date. Sometime too hot the eye of heaven shines, And often is his gold complexion dimm’d; And every fair from fair sometime declines. By chance or nature’s changing course untrinun’d; But thy eternal summer shall not fade Nor lose possession of that fair thou ow’st: Nor shall Death brag thou wander’st in his shade. When in eternal lines to time thou grow’st: So long as men can breathe or eyes can see. So long lives this, and this gives life to thee. William Shakespeare IV ACKNOWLEDGMENTS I thank Dr. Russell M. Pitzer for his thoughtful guidance, boundless patience, and professional deportment. He is an exemplary scientist, a comprehensive scholar, and a quintessential advisor. I thank many colleagues for their Mendship and assistance, especially Lars Ojamae, Wolfgang Kiichle, Jo Ann Balozy, Phillip Christiansen, Clinton Nash, Michael Seth, Bert de Jong, Steve Parker, Gary Kedziora, and former and current Pitzer group students: Ke Zhao, Zhiyong Zhang, Jean-Phillipe Blaudeau, and Spiridoula Matsika. VITA 1989 ........................................................................B .S . — Case Western Reserve Univer­ sity, Cleveland, U.S.A. 1993 ........................................................................M. S. — John Carroll University, Cleveland, U.S.A. 1993-1999 .............................................................Graduate School Fellowship, Teach­ ing Associate and Research Associate, Ohio State University PUBLICATIONS “Atomic Orbital Basis Sets for Use with Efiective Core Potentials,” J.-P. Blaudeau, S. R. Brozell, S. Matsika, Z. Zhang, and R. M. Pitzer, Int. J. Quantum Chem. Submitted. FIELDS OF STUDY Major Field: Chemical Physics Studies in Theoretical Chemistry: Professor Russell M. Pitzer VI TABLE OF CONTENTS Page Abstract............................................................................................................................. ii Dedication......................................................................................................................... iv Acknowledgments ............................................................................................................ v V i t a ................................................................................................................................... vi List of Tables................................................................................................................... x List of Figures ................................................................................................................ xiv Chapters: 1. Introduction ............................................................................................................ 1 2. Configuration Generation Softw are .................................................................. 9 2.1 Introduction ................................................................................................ 9 2.2 Multireference Configuration E xp losion ............................................... 10 2.3 The Original CGDBG Program ............................................................ 15 2.4 Design of the New CGDBG Program ................................................... 19 2.4.1 First Implementation................................................................... 19 2.4.2 Final Implementation ................................................................ 21 2.4.3 User In terface................................................................................ 24 2.4.4 Program Notes ............................................................................. 24 2.5 Profiles of CGDBG Programs ................................................................ 25 2.6 Conclusions ................................................................................................ 27 vu 3. Relativistic Effective Potential Development.................................................. 28 3.1 Introduction ............................................................................................... 28 3.2 B ackground................................................................................................ 29 3.2.1 Relativistic Quantum Physics ................................................. 29 3.2.1-1 Special Relativity ............................................................ 30 3.2.1.2 The Klein-Gordon Equation ......................................