Essentials of Computational Chemistry

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292 8 DENSITY FUNCTIONAL THEORY Table 8.5 Mean absolute errors in bond lengths for different methods over several different test sets ( ˚A) Level of theory Test sets a MO theoretical methods A B C HF 0.022 0.021 MP2 0.014 b 0.014 0.022 QCISD 0.013 b CCSD(T) 0.005 b LSDA functionals SVWN 0.017 0.016 0.013d GGA and MGGA functionals BLYP 0.014 0.021 0.048 0.019 c 0.022 d BP86 0.018 d BPW91 0.014 0.017 0.020 0.017 d HCTH 0.013 c 0.014 d OLYP 0.018 d PBE 0.012 0.016 d PKZB 0.027 d PWPW91 0.012 0.014 d mPWPW91 0.012 TPSS 0.014 d VSXC 0.013 d Hybrid functionals BH&HLYP 0.015 B1LYP 0.005 B1PW91 0.010 B97-1 0.008c mPW1PW91 0.010 PBE1PBE 0.012 0.010d TPSSh 0.010d B3LYP 0.004 0.008c 0.010 0.030 d
8.6 GENERAL PERFORMANCE OVERVIEW OF DFT 293 Table 8.5 (continued) Level of theory Test sets a A B C B3P86 0.008 d B3PW91 0.008 0.011 0.020 0.009 d mPW3PW91 0.008 a A: G2 subset (32 molecules containing only first-row atoms, see Johnson, Gill, and Pople 1993), 6-311G(d,p) basis set unless otherwise specified; B: (108 molecules including first- and second-row atoms, see Scheiner, Baker, and Andzelm 1997), 6-31G(d,p) basis set; C: (40 molecules containing third-row atoms Ga-Kr, see Redfern, Blaudeau, and Curtiss 1997). b 6-31G(d,p) basis set. c A 40-molecule subset with a polarized triple-ζ basis set, see Hamprecht et al. (1998). d A 96-molecule set with the 6-311++G(3df,3pd) basis set, see Staroverov et al. (2003). complexes of Ni, Pd, and Pt. Over the 10 unique metal–carbon bond lengths for which experimental data are available, they observed no error in excess of 0.01 ˚A except for W, where the error was 0.017 ˚A. At the HF and MP2 levels using equivalent basis sets, the corresponding average absolute errors are 0.086 and 0.028 ˚A, and the maximum deviations are 0.239 and 0.123 ˚A (Frenking et al. 1996). To the extent DFT shows systematic weaknesses in geometries, it is in those areas where it similarly does poorly for energetics. Thus, van der Waals complexes tend to have interfragment distances that are too large because the dispersion-induced attraction is not properly modeled (although it may accidentally be mimicked by BSSE). Hydrogen bonds are somewhat too short as a rule, and indeed, most charge transfer complexes have their polarities overestimated so that they are too tightly bound. Finally, the tendency noted above in Section 8.5.6 for DFT to overdelocalize structures can show up in geometrical predictions. Thus, for instance, in 1,3-butadiene DFT tends to predict the formal single bond to be a bit too short and the formal double bonds to be somewhat too long (and this extends to other conjugated π systems). As already noted above in Section 8.5.6, this can also lead to a tendency to favor higher symmetry structures over ones of lower symmetry since the former tend to have more highly delocalized frontier orbitals (see also Section 9.1.6). Finally, loose transition state structures can result from this phenomenon; for instance, the C–Cl bond lengths in the TS structure illustrated in Figure 6.12 are 2.45 and 2.39 ˚A attheBLYP/6- 31G(d) and B3LYP/6-31G(d) levels of theory, respectively. Of course, this is a significant improvement over HF theory, and insofar as TS structures tend to be fairly floppy, the remaining geometrical errors may have only small energetic consequences. Wiest, Montiel, and Houk (1997) have studied carefully a large number of TS structures for organic electrocyclic reactions and, based on comparison to experiment (particularly including kinetic isotope effect studies) and very high levels of electronic structure theory,
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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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204 7 INCLUDING ELECTRON CORRELATIO
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Page 324 and 325: 9 Charge Distribution and Spectrosc
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9.3 SPECTROSCOPY OF NUCLEAR MOTION
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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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