Essentials of Computational Chemistry

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248 7 INCLUDING ELECTRON CORRELATION IN MO THEORY He, Y. and Cremer, D. 2000a. Mol. Phys., 98, 1415. He, Y. and Cremer, D. 2000b. Theor. Chem. Acc., 105, 110. He, Y. and Cremer, D. 2000c. J. Phys. Chem. A, 104, 7679. Head-Gordon, M., Rico, R. J., Oumi, M., and Lee, T. J. 1994. Chem. Phys. Lett., 219, 21. Helgaker, T., Klopper, W., Halkier, A., Bak, K. L., Jørgensen, P., and Olsen, J. 2001. in Quantum Mechanical Prediction of Thermodynamic Data, Cioslowski, J., Ed., Kluwer: Dordrecht, 1. Henry, D. J., Sullivan, M. B., and Radom, L. 2003. J. Chem. Phys., 118, 4849. Hylleraas, E. A. 1929. Z. Phys., 54, 347. Kallay, M. and Gauss, J. 2004. J. Chem. Phys., 120, 6841. Klopper, W. and Kutzelnigg, W. 1987. Chem. Phys. Lett., 134, 17. Krylov, A. I. 2001. Chem. Phys. Lett., 350, 522. Krylov, A. I. and Sherrill, C. D. 2002. J. Chem. Phys., 116, 3194. Langhoff, S. R. and Davidson, E. R. 1974. Int. J. Quantum Chem., 8, 61. Lee, T. J. and Taylor, P. R. 1989. Int. J. Quantum Chem., S23, 199. Levchenko, S. V. and Krylov, A. I. 2004. J. Chem. Phys., 120, 175. Li, S. H., Ma, J., and Jiang, Y. S. 2002. J. Comput. Chem., 23, 237. Martin, J. M. L. and de Oliveira, G. 1999. J. Chem. Phys., 111, 1843. McLean, A. D. and Chandler, G. S. 1980. J. Chem. Phys.,72, 5639. Møller, C. and Plesset, M. S. 1934. Phys. Rev., 46, 359. Page, C. S. and Olivucci, M. 2003. J. Comput. Chem., 24, 298. Parthiban, S. and Martin, J. M. L. 2001. J. Chem. Phys., 114, 6014. Petersson, G. A. and Frisch, M. J. 2000. J. Phys. Chem. A, 104, 2183. Pitarch-Ruiz, J., Sanchez-Marin, J., and Maynau, D. 2002. J. Comput. Chem., 23, 1157. Pople, J. A., Head-Gordon, M., and Raghavachari, K. 1987. J. Chem. Phys., 87, 5968. Pulay, P. 1983. Chem. Phys. Lett., 100, 151. Raghavachari, K., Trucks, G. W., Pople, J. A., and Head-Gordon, M. 1989. Chem. Phys. Lett., 157, 479. Saebø, S. and Pulay, P. 1987. J. Chem. Phys., 86, 914. Scheiner, A. C., Baker, J., and Andzelm, J. W. 1997. J. Comput. Chem., 18, 775. Schütz, M. 2002. Phys. Chem. Chem. Phys., 4, 3941. Schwartz, C. 1962. Phys. Rev., 126, 1015. Siegbahn, P. E. M., Blomberg, M. R., and Svensson, M. 1994. Chem. Phys. Lett., 223, 35. Slipchenko, L. V. and Krylov, A. I. 2002. J. Chem. Phys., 117, 4694. Thomas, J. R., DeLeeuw, B. J., O’Leary, P., Schaefer, H. F., III, Duke, B. J., and O’Leary, B. 1995. J. Chem. Phys., 102, 652. Wenthold, P. G., Squires, R. R., and Lineberger, W. C. 1998. J. Am. Chem. Soc., 120, 5279. Woon, D. E. and Dunning, T. H., Jr., 1995 J. Chem. Phys., 103, 4572. Zachariah, M. R., Westmoreland, P. R., Burgess, D. R., Jr., Tsang, W., and Melius, C. F. 1996. J. Phys. Chem., 100, 8737.
8 Density Functional Theory 8.1 Theoretical Motivation 8.1.1 Philosophy What a strange and complicated beast a wave function is. This function, depending on one spin and three spatial coordinates for every electron (assuming fixed nuclear positions), is not, in and of itself, particularly intuitive for systems of more than one electron. Indeed, one might approach the HF approximation as not so much a mathematical tool but more a philosophical one. By allowing the wave function to be expressed as a Slater determinant of one-electron orbitals, one preserves for the chemist some semblance of clarity by permitting each electron still to be thought of as being loosely independent. It was noted in Section 7.6.1 that wave functions can be dramatically improved in quality by removing this rough independence and including in the wave functional form a dependence on interelectronic distances (R12 methods). The key disadvantage? The wave function itself is essentially uninterpretable – it is an inscrutable oracle that returns valuably accurate answers when questioned by quantum mechanical operators, but it offers little by way of sparking intuition. One may be forgiven for stepping back from the towering edifice of molecular orbital theory and asking, shouldn’t things be simpler? For instance, rather than having to work with a wave function, which has rather odd units of probability density to the one-half power, why can’t we work with some physical observable in determining the energy (and possibly other properties) of a molecule? That such a thing should be possible would probably not have surprised physicists before the discovery of quantum mechanics, insofar as such simple formalisms are widely available in classical systems. However, we may take advantage of our knowledge of quantum mechanics in asking about what particular physical observable might be useful. Having gone through the exercise of constructing the Hamiltonian operator and showing the utility of its eigenfunctions, it would be sufficient to our task simply to find a physical observable that permitted the apriori construction of the Hamiltonian operator. What then is needed? The Hamiltonian depends only on the positions and atomic numbers of the nuclei and the total number of electrons. The dependence on total number of electrons immediately suggests that a useful physical observable would be the electron density ρ, since, integrated over all space, it gives the total Essentials of Computational Chemistry, 2nd Edition Christopher J. Cramer © 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09181-9 (cased); 0-470-09182-7 (pbk)
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Essentials of Computational Chemist
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Essentials of Computational Chemist
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For Katherine
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viii CONTENTS 2.5 Menagerie of Mode
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x CONTENTS 7 Including Electron Cor
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xii CONTENTS 11.4 Strengths and Wea
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Preface to the First Edition Comput
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PREFACE TO THE FIRST EDITION xvii d
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xx PREFACE TO THE SECOND EDITION to
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Known Typographical and Other Error
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1 What are Theory, Computation, and
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Activation free energy (kcal mol
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1.3 COMPUTABLE QUANTITIES 5 etc.) f
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a a r 1 1.3 COMPUTABLE QUANTITIES 7
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1.3 COMPUTABLE QUANTITIES 9 path is
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1.4 COST AND EFFICIENCY 11 this is
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1.4 COST AND EFFICIENCY 13 kinds of
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Physical quantity (unit name) BIBLI
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2 Molecular Mechanics 2.1 History a
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2.2 POTENTIAL ENERGY FUNCTIONAL FOR
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2.3 FORCE-FIELD ENERGIES AND THERMO
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Heat of formation A E nb (A) 2.4 GE
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gradient vector, g, which is define
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Eq. (2.38) as 2.4 GEOMETRY OPTIMIZA
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2.4 GEOMETRY OPTIMIZATION 47 that t
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2.4 GEOMETRY OPTIMIZATION 49 is opp
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Table 2.1 Force fields Name (if any
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12 Davies, E. K. and Murrall, N. W.
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5 (MM2(85), MM2(91), Chem-3D) Compr
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2.5 MENAGERIE OF MODERN FORCE FIELD
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2.6 FORCE FIELDS AND DOCKING 63 Fig
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2.7 CASE STUDY: (2R ∗ ,4S ∗ )-1
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REFERENCES 67 Cramer, C. J. 1994.
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3 Simulations of Molecular Ensemble
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3.2 PHASE SPACE AND TRAJECTORIES 71
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m −b r eq −b 3.3 MOLECULAR DYNA
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and 3.3 MOLECULAR DYNAMICS 75 p(t +
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3.3 MOLECULAR DYNAMICS 77 step mean
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3.3 MOLECULAR DYNAMICS 79 of course
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3.4 MONTE CARLO 81 One way to reduc
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3.5 ENSEMBLE AND DYNAMICAL PROPERTY
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3.6 KEY DETAILS IN FORMALISM 89 Fig
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3.6 KEY DETAILS IN FORMALISM 91 alc
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3.6 KEY DETAILS IN FORMALISM 93 mor
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3.6 KEY DETAILS IN FORMALISM 95 der
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3.6 KEY DETAILS IN FORMALISM 97 to
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3.8 CASE STUDY: SILICA SODALITE 99
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BIBLIOGRAPHY AND SUGGESTED ADDITION
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REFERENCES 103 Jaqaman, K. and Orto
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106 4 FOUNDATIONS OF MOLECULAR ORBI
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132 5 SEMIEMPIRICAL IMPLEMENTATIONS
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166 6 AB INITIO HARTREE-FOCK MO THE
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298 8 DENSITY FUNCTIONAL THEORY Tab
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300 8 DENSITY FUNCTIONAL THEORY dou
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302 8 DENSITY FUNCTIONAL THEORY Cho
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9 Charge Distribution and Spectrosc
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9.1 PROPERTIES RELATED TO CHARGE DI
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H H P O H H H F Cl Cl P P F H F F P
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9.3 SPECTROSCOPY OF NUCLEAR MOTION
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Energy hn 0→1 9.3 SPECTROSCOPY OF
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9.4 NMR SPECTRAL PROPERTIES 345 The
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9.4 NMR SPECTRAL PROPERTIES 347 Tab
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9.5 CASE STUDY: MATRIX ISOLATION OF
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REFERENCES 351 The use of computed
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REFERENCES 353 Rablen, P. R., Pearl
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356 10 THERMODYNAMIC PROPERTIES of
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358 10 THERMODYNAMIC PROPERTIES whe
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360 10 THERMODYNAMIC PROPERTIES tha
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362 10 THERMODYNAMIC PROPERTIES (Th
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364 10 THERMODYNAMIC PROPERTIES the
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368 10 THERMODYNAMIC PROPERTIES Ene
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372 10 THERMODYNAMIC PROPERTIES 10.
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374 10 THERMODYNAMIC PROPERTIES gen
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382 10 THERMODYNAMIC PROPERTIES Tab
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384 10 THERMODYNAMIC PROPERTIES Clo
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386 11 IMPLICIT MODELS FOR CONDENSE
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12 Explicit Models for Condensed Ph
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12.2 COMPUTING FREE-ENERGY DIFFEREN
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∆G 12.2 COMPUTING FREE-ENERGY DIF
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12.4 SOLVENT MODELS 445 In some cas
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12.4 SOLVENT MODELS 447 increases t
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12.5 RELATIVE MERITS OF EXPLICIT AN
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12.5 RELATIVE MERITS OF EXPLICIT AN
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12.6 CASE STUDY: BINDING OF BIOTIN
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REFERENCES 455 Levy, R. M. and Gall
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13 Hybrid Quantal/Classical Models
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13.2 BOUNDARIES THROUGH SPACE 459 a
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13.2 BOUNDARIES THROUGH SPACE 461 i
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13.2 BOUNDARIES THROUGH SPACE 463 T
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13.2 BOUNDARIES THROUGH SPACE 465 W
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13.3 BOUNDARIES THROUGH BONDS 467 t
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13.3 BOUNDARIES THROUGH BONDS 469 o
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180 180 4 10 15 15 20 150 6 8 150 8
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13.3 BOUNDARIES THROUGH BONDS 473 O
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13.3.3 Frozen Orbitals 13.3 BOUNDAR
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Link atom LSCF GHO 13.4 EMPIRICAL V
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13.4 EMPIRICAL VALENCE BOND METHODS
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13.4 EMPIRICAL VALENCE BOND METHODS
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13.5 CASE STUDY: CATALYTIC MECHANIS
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REFERENCES 485 Gao, J., Amara, P.,
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14 Excited Electronic States 14.1 D
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14.1 DETERMINANTAL/CONFIGURATIONAL
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14.1 DETERMINANTAL/CONFIGURATIONAL
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14.2 SINGLY EXCITED STATES 493 and
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14.2 SINGLY EXCITED STATES 495 Tabl
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14.2 SINGLY EXCITED STATES 497 wher
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14.3 GENERAL EXCITED STATE METHODS
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14.3 GENERAL EXCITED STATE METHODS
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14.4 SUM AND PROJECTION METHODS 503
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14.4 SUM AND PROJECTION METHODS 505
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14.5 TRANSITION PROBABILITIES 507 o
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14.5 TRANSITION PROBABILITIES 509 I
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14.6 SOLVATOCHROMISM 511 overlap) l
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14.7 CASE STUDY: ORGANIC LIGHT EMIT
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BIBLIOGRAPHY AND SUGGESTED ADDITION
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REFERENCES 517 Kim, K., Shavitt, I,
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520 15 ADIABATIC REACTION DYNAMICS
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Appendix A Acronym Glossary Note: B
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ACRONYM GLOSSARY 551 ECP Effective
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ACRONYM GLOSSARY 553 mPW1S mPW1PW91
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ACRONYM GLOSSARY 555 SF-CISD Spin-f
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558 APPENDIX B H 3 C CH 3 H H H a
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560 APPENDIX B Linear molecule? no
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562 APPENDIX B Table B.5 Product ru
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Appendix C Spin Algebra C.1 Spin Op
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function we have SPIN ALGEBRA 567
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SPIN ALGEBRA 569 + = 1 1 ( 2 2 α(
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C.3 UHF Wave Functions SPIN ALGEBRA
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SPIN ALGEBRA 573 = 〈cs s |H |cs s
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Appendix D Orbital Localization D.1
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ORBITAL LOCALIZATION 577 〈|H |〉
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E rel (kcal mol −1 ) 10 8 6 4 2 0
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582 INDEX B3PW91, 266-267, 284, 288
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584 INDEX Convergence (continued) f
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Global minimum, 23, 46, 97, 146, 38
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Matrix diagonalization, (see also S
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primitive, 168-173 Slater-type, 134
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Reductive dechlorination, 422-424 R
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SYBYL, 58 Symmetry, 182-188, 209, 2
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