Essentials of Computational Chemistry

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162 5 SEMIEMPIRICAL IMPLEMENTATIONS OF MO THEORY TS structures leading to different enantiomers, a %ee of 0 would result from equal TS energies, a %ee of 82 from relative energies of 1.4 kcal mol −1 , and a %ee of 98 from relative energies of 2.8 kcal mol −1 . Given this analysis, the near quantitative agreement between PM3 and those experimental cases showing %ee values below 90 reflects startlingly good accuracy for a semiempirical level of theory. Armed with such solid agreement between theory and experiment, Goldfuss and Houk go on to analyze the geometries of the various TS structures to identify exactly which interactions lead to unfavorably high energies and can be used to enhance chiral discrimination. They infer in particular that the optimal situation requires that the alkoxide carbon atom be substituted by two groups of significantly different size, e.g., a hydrogen atom and a bulky alkyl or aryl group. This work thus provides a nice example of how preliminary experimental work can be used to validate an economical theoretical model that can then be used to suggest future directions for further experimental optimization. However, it must not be forgotten that the success of the model must derive in part from favorable cancellation of errors – the theoretical model, after all, fails to account for solvent, thermal contributions to free energies, and various other possibly important experimental conditions. As such, application of the model in a predictive mode should be kept within reasonable limits, e.g., results for new β-amino alcohol structures would be expected to be more secure than results obtained for systems designed to use a substituted 1,2-diaminoethane ligand in place of the β-amino alcohol. Bibliography and Suggested Additional Reading Clark, T. 2000. ‘Quo Vadis Semiempirical MO-theory?’ J. Mol. Struct. (Theochem), 530, 1. Dewar, M. J. S. 1975. The PMO Theory of Organic Chemistry, Plenum: New York. Famini, G. R. and Wilson, L. Y. 2002. ‘Linear Free Energy Relationships Using Quantum Mechanical Descriptors’, in Reviews in Computational Chemistry, Vol. 18, Lipkowitz, K. B. and Boyd, D. B., Eds., Wiley-VCH: New York, 211. Hall, M. B. 2000. ‘Perspective on “The Spectra and Electronic Structure of the Tetrahedral Ions MnO4 − ,CrO4 2− ,andClO4 − ”’ Theor. Chem. Acc., 103, 221. Hehre, W. J. 1995. Practical Strategies for Electronic Structure Calculations, Wavefunction: Irvine, CA. Jensen, F. 1999. Introduction to Computational Chemistry, Wiley: Chichester. Levine, I. N. 2000. Quantum Chemistry, 5th Edn., Prentice Hall: New York. Pople, J. A. and Beveridge, D. A. 1970. Approximate Molecular Orbital Theory, McGraw-Hill: New York. Repasky, M. P., Chandrasekhar, J., and Jorgensen, W. L. 2002. ‘PDDG/PM3 and PDDG/MNDO: Improved Semiempirical Methods’, J. Comput. Chem., 23, 1601. Stewart, J. J. P. 1990. ‘Semiempirical Molecular Orbital Methods’ in Reviews in Computational Chemistry, Vol. 1, Lipkowitz, K. B. and Boyd, D. B., Eds., VCH: New York, 45. Thiel, W. 1998. ‘Thermochemistry from Semiempirical Molecular Orbital Theory’ in Computational Thermochemistry, ACS Symposium Series, Vol. 677, Irikura, K. K. and Frurip, D. J., Eds., American Chemical Society: Washington, DC, 142. Thiel, W. 2000. ‘Semiempirical Methods’ in Modern Methods and Algorithms of Quantum Chemistry, Proceedings, 2nd Edn., Grotendorst, J., Ed., NIC Series, Vol. 3, John von Neumann Institute for Computing: Jülich, 261. Whangbo, M.-H. 2000. “Perspective on ‘An extended Hückel theory. I. Hydrocarbons”’ Theor. Chem. Acc., 103, 252.
REFERENCES 163 Zerner, M. 1991. ‘Semiempirical Molecular Orbital Methods’ in Reviews in Computational Chemistry, Vol. 2, Lipkowitz, K. B. and Boyd, D. B., Eds., VCH: New York, 313. References Barrows, S. E., Dulles, F. J., Cramer, C. J., French, A. D., and Truhlar, D. G. 1995. Carbohydr. Res., 276, 219. Beck, B., Horn, A., Carpenter, J. E., and Clark, T. 1998. J. Chem. Inf. Comput. Sci. 38, 1214. Bernal-Uruchurtu, M. I., Martins-Costa, M. T. C., Millot, C., and Ruiz-Lopez, M. F. 2000. J. Comput. Chem., 21, 572. Bingham, R. C., Dewar, M. J. S., and Lo, D. H. 1975. J. Am. Chem. Soc., 97, 1285, 1307. Bishop, D. M. 1966. J. Chem. Phys., 45, 1880 and references therein. Casadesus, R., Moreno, M., Gonzalez-Lafont, A., Lluch, J. M., and Repasky, M. P. 2004. J. Comput. Chem., 25, 99. Chuang, Y.-Y., Radhakrishnan, M. L., Fast, P. L., Cramer, C. J., and Truhlar, D. G. 1999. J. Phys. Chem., 103, 4893. Clementi, E. and Roetti, C. 1974. At. Data Nucl. Data Tables., 14, 177. Cramer, C. J., Famini, G. R., and Lowrey, A. H. 1993. Acc. Chem. Res., 26, 599. Csonka, G. I. 1993. J. Comput. Chem., 14, 895. Cusachs, L. C., Reynolds, J. W., and Barnard, D. 1966. J. Chem. Phys., 44, 835. Da Motta Neto, J. D. and Zerner, M. C. 2001. Int. J. Quant. Chem., 81, 187. Dannenberg, J. A. 1997. J. Mol. Struct. (Theochem), 401, 287. Dewar, M. J. S., Hashmall, J. A., and Venier, C. G. 1968. J. Am. Chem. Soc., 90, 1953. Dewar, M. J. S., Jie, C., and Yu, J. 1993. Tetrahedron, 49, 5003. Dewar, M. J. S., Zoebisch, E. G., Healy, E. F., and Stewart, J. J. P. 1985. J. Am. Chem. Soc., 107, 3902. Ferguson, D. M., Gould, W. A., Glauser, W. A., Schroeder, S., and Kollman, P. A. 1992. J. Comput. Chem., 13, 525. Genin, H. and Hoffmann, R. 1998. Macromolecules, 31, 444. Goh, S. K. and Marynick, D. S. 2001. J. Comput. Chem., 22, 1881. Goldfuss, B. and Houk, K. N. 1998. J. Org. Chem., 63, 8998. Hall, M. B. and Fenske, R. F. 1972. Inorg. Chem., 11, 768. Hinze, J. and Jaffé, H. H. 1962. J. Am. Chem. Soc., 84, 540. Hoffmann, R. 1963. J. Chem. Phys., 39, 1397. Holder, A., Dennington, R. D., and Jie, C. 1994. Tetrahedron, 50, 627. Jug, K. and Schulz, J. 1988. J. Comput. Chem., 9, 40. Khandogin, L, Hu, A. G., and York, D. M. 2000. J. Comput. Chem., 21, 1562. Koopmans, T. 1933. Physica (Utrecht), 1, 104. Kotzian, M., Rösch, N., and Zerner, M. C. 1992. Theor. Chim. Acta, 81, 201. Lopez, X. and York, D. M. 2003. Theor. Chem. Acc., 109, 149. Martin, B., Gedeck, P., and Clark, T. 2000. Int. J. Quant. Chem., 77, 473. Mataga, N. and Nishimoto, K. 1957. Z. Phys. Chem., 13, 140. Mulliken, R. S., Rieke, C. A., and Orloff, H. 1949. J. Chem. Phys., 17, 1248. Nanda, D. N. and Jug, K. 1980. Theor. Chim. Acta, 57, 95. Pachkovski, S. and Thiel, W. 1996. J. Am. Chem. Soc., 118, 7164. Pariser, R. and Parr, R. G. 1953. J. Chem. Phys., 21, 466, 767. Pekeris, C. L. 1959. Phys. Rev., 115, 1216. Pilcher, G. and Skinner, H. A. 1962. Inorg. Nucl. Chem., 24, 937. Pople, J. A. 1953. Trans. Faraday Soc., 49, 1375.
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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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212 7 INCLUDING ELECTRON CORRELATIO
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250 8 DENSITY FUNCTIONAL THEORY num
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252 8 DENSITY FUNCTIONAL THEORY for
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254 8 DENSITY FUNCTIONAL THEORY fun
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256 8 DENSITY FUNCTIONAL THEORY Not
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258 8 DENSITY FUNCTIONAL THEORY emp
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260 8 DENSITY FUNCTIONAL THEORY whe
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264 8 DENSITY FUNCTIONAL THEORY [As
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266 8 DENSITY FUNCTIONAL THEORY som
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268 8 DENSITY FUNCTIONAL THEORY for
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272 8 DENSITY FUNCTIONAL THEORY Ano
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274 8 DENSITY FUNCTIONAL THEORY Eve
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276 8 DENSITY FUNCTIONAL THEORY val
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278 8 DENSITY FUNCTIONAL THEORY acc
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280 8 DENSITY FUNCTIONAL THEORY als
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282 8 DENSITY FUNCTIONAL THEORY Tab
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294 8 DENSITY FUNCTIONAL THEORY con
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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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