Essentials of Computational Chemistry

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Physical quantity (unit name) BIBLIOGRAPHY AND SUGGESTED ADDITIONAL READING 15 Table 1.1 Useful quantities in atomic and other units Symbol Value in a.u. Value in SI units Value(s) in other units Angular momentum ¯h 1 1.055 × 10 −34 J s 2.521 × 10 −35 cal s Mass me 1 9.109 × 10 −31 kg Charge e 1 1.602 × 10 −19 C 1.519 × 10 −14 statC Vacuum permittivity 4πε0 1 1.113 × 10 −10 C 2 J −1 m −1 2.660 × 10 −21 C 2 cal −1 ˚A −1 Length (bohr) a0 1 5.292 × 10 −11 m 0.529 ˚A 52.9 pm Energy (hartree) Eh 1 4.360 × 10 −18 J 627.51 kcal mol −1 2.626 × 10 3 kJ mol −1 27.211 eV 2.195 × 10 5 cm −1 Electric dipole moment ea0 1 8.478 × 10 −30 C m 2.542 D Electric polarizability e 2 a 2 0 E−1 h 1 1.649 × 10 −41 C 2 m 2 J −1 Planck’s constant h 2π 6.626 × 10 −34 J s Speed of light c 1.370 × 10 2 2.998 × 10 8 ms −1 Bohr magneton µB 0.5 9.274 × 10 −24 J T −1 Nuclear magneton µN 2.723 × 10 −4 5.051 × 10 −27 J T −1 to arise. To be safe, scientific publishing that includes computational results should always state what code or codes were used, to include version numbers, in obtaining particular model results (clearly version control of computer codes is thus just as critical as it is for models). 1.5 Note on Units In describing a computational model, a clear equation can be worth 1000 words. One way to render equations more clear is to work in atomic (or theorist’s) units. In a.u., the charge on the proton, e, the mass of the electron, me, and¯h (i.e., Planck’s constant divided by 2π) areall defined to have magnitude 1. When converting equations expressed in SI units (as opposed to Gaussian units), 4πε0, whereε0 is the permittivity of the vacuum, is also defined to have magnitude 1. As the magnitude of these quantities is unity, they are dropped from relevant equations, thereby simplifying the notation. Other atomic units having magnitudes of unity can be derived from these three by dimensional analysis. For instance, ¯h 2 /mee 2 has units of distance and is defined as 1 a.u.; this atomic unit of distance is also called the ‘bohr’ and symbolized by a0. Similarly, e 2 /a0 has units of energy, and defines 1 a.u. for this quantity, also called 1 hartree and symbolized by Eh. Table 1.1 provides notation and values for several useful quantities in a.u. and also equivalent values in other commonly used units. Greater precision and additional data are available at http://www.physics.nist.gov/PhysRefData/. Bibliography and Suggested Additional Reading Cramer, C. J., Famini, G. R., and Lowrey, A. 1993. ‘Use of Quantum Chemical Properties as Analogs for Solvatochromic Parameters in Structure–Activity Relationships’, Acc. Chem. Res., 26, 599.
16 1 WHAT ARE THEORY, COMPUTATION, AND MODELING? Irikura, K. K., Frurip, D. J., Eds. 1998. Computational Thermochemistry, American Chemical Society Symposium Series, Vol. 677, American Chemical Society: Washington, DC. Jensen, F. 1999. Introduction to Computational Chemistry, Wiley: Chichester. Jorgensen, W. L. 2004. ‘The Many Roles of Computation in Drug Discovery’, Science, 303, 1813. Leach, A. R. 2001. Molecular Modelling, 2nd Edn., Prentice Hall: London. Levine, I. N. 2000. Quantum Chemistry, 5th Edn., Prentice Hall: New York. Truhlar, D. G. 2000. ‘Perspective on “Principles for a direct SCF approach to LCAO-MO ab initio calculations”’ Theor. Chem. Acc., 103, 349. References Almlöf, J., Faegri, K., Jr., and Korsell, K. 1982. J. Comput. Chem., 3, 385. Cramer, C. J., Denmark, S. E., Miller, P. C., Dorow, R. L., Swiss, K. A., and Wilson, S. R. 1994. J. Am. Chem. Soc., 116, 2437. Ghosh, A. 2003. Curr. Opin. Chem. Biol., 7, 110.
Page 2 and 3: Essentials of Computational Chemist
Page 4 and 5: Essentials of Computational Chemist
Page 6 and 7: For Katherine
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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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204 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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