Reviews in Computational Chemistry Volume 18

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134 Polarizability in Computer Simulations packages, thereby making these methods much more accessible to the nonspecialist. In particular, we expect polarizable models, and especially polarizable water models, to become more prevalent in biomolecular simulations involving heterogeneous solvent environments. Inclusion of polarizability in the potentials for proteins and other macromolecular systems is also likely to become more common, and hence a careful assessment of the importance of polarizability to these systems is needed. Until the importance of polarizability has been clearly demonstrated, the added computational cost of modeling the polarization makes it is unlikely that polarizable models will displace more traditional models for the bulk of routine simulation, particularly when applied to large systems. Future directions in the development of polarizable models and simulation algorithms are sure to include the combination of classical or semiempirical polarizable models with fully quantum mechanical simulations, and with empirical reactive potentials. The increasingly frequent application of Car– Parrinello ab initio simulations methods 156 may also influence the development of potential models by providing additional data for the validation of models, perhaps most importantly in terms of the importance of various interactions (e.g., polarizability, charge transfer, partially covalent hydrogen bonds, lone-pair-type interactions). It is also likely that we will see continued work toward better coupling of charge-transfer models (i.e., EE and semiempirical models) with purely local models of polarization (polarizable dipole and shell models). REFERENCES 1. J. A. McCammon and S. C. Harvey, Dynamics of Proteins and Nucleic Acids, Cambridge University Press, Cambridge, UK, 1987. 2. M. Rigby, E. B. Smith, W. A. Wakeham, and G. C. Maitland, The Forces Between Molecules, Oxford Science Publications, Oxford, UK, 1986. 3. T. A. Halgren, J. Am. Chem. Soc., 114, 7827–7843 (1992). Representation of van der Waals (vdW) Interactions in Molecular Mechanics Force Fields: Potential Form, Combination Rules, and vdW Parameters. 4. H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem., 91, 6269–6271 (1987). The Missing Term in Effective Pair Potentials. 5. K. Watanabe and M. L. Klein, Chem. Phys., 131, 157–167 (1989). Effective Pair Potentials and the Properties of Water. 6. L. Kuyper, D. Ashton, K. M. Merz Jr., and P. A. Kollman, J. Phys. Chem., 95, 6661–6666 (1991). Free Energy Calculations on the Relative Solvation Free Energies of Benzene, Anisole, and 1,2,3-Trimethoxybenzene: Theoretical and Experimental Analysis of Aromatic Methoxy Solvation. 7. W. L. Jorgensen and J. Gao, J. Am. Chem. Soc., 110, 4212–4216 (1988). Cis–Trans Energy Difference for the Peptide Bond in the Gas Phase and in Aqueous Solution. 8. D. E. Williams, Biopolymers, 29, 1367–1386 (1990). Alanyl Dipeptide Potential-Derived Net Atomic Charges and Bond Dipoles, and Their Variation with Molecular Conformation.
References 135 9. P. Cieplak and P. Kollman, J. Comput. Chem., 12, 1232–1236 (1991). On the Use of Electrostatic Potential Derived Charges in Molecular Mechanics Force Field. The Relative Solvation Free Energy of Cis- and Trans-N-Methyl-Acetamide. 10. S. W. Rick and B. J. Berne, J. Am. Chem. Soc., 118, 672–679 (1996). Dynamical Fluctuating Charge Force Fields: The Aqueous Solvation of Amides. 11. J. J. Urban and G. R. Famini, J. Comput. Chem., 14, 353–362 (1993). Conformational Dependence of the Electrostatic Potential-Derived Charges of Dopamine: Ramifications in Molecular Mechanics Force Field Calculation in the Gas Phase and Aqueous Solution. 12. U. Dinur and A. T. Hagler, J. Comput. Chem., 16, 154–170 (1995). Geometry-Dependent Atomic Charges—Methodology andApplication to Alkanes, Aldehydes, Ketones, and Amides. 13. U. Koch, P. L. A. Popelier, and A. J. Stone, Chem. Phys. Lett., 238, 253–260 (1995). Conformational Dependence of Atomic Multipole Moments. 14. C. J. F. Böttcher, Theory of Electric Polarization, 2nd ed., Elsevier, New York, 1973. 15. T. P. Lybrand and P. A. Kollman, J. Chem. Phys., 83, 2923–2933 (1985). Water–Water and Water–Ion Potential Functions Including Terms for Many Body Effects. 16. P. Cieplak, T. P. Lybrand, and P. A. Kollman, J. Chem. Phys., 86, 6393–6403 (1987). Calculations of Free Energy Changes in Ion–Water Clusters Using Nonadditive Potentials and the Monte Carlo Method. 17. B. J. Berne and A. Wallqvist, J. Chem. Phys., 88, 8016–8017 (1988). Comment on: ‘‘Water– Water and Water–Ion Potential Functions Including Terms for Many-Body Effects,’’ T. P. Lybrand and P. Kollman, J. Chem. Phys. 83, 2923 (1985), and on ‘‘Calculation of Free Energy Changes in Ion–Water Clusters Using Nonadditive Potentials and the Monte Carlo Method,’’ P. Cieplak, T. P. Lybrand, and P. Kollman, J. Chem. Phys. 86, 6393 (1987). 18. P. Kollman, T. Lybrand, and P. Cieplak, J. Chem. Phys., 88, 8017 (1988). Reply to ‘‘Comment on ‘‘Water–Water and Water–Ion Potential Functions Including Terms for Many-Body Effects,’’ T. P. Lybrand and P. Kollman, J. Chem. Phys. 83, 2923 (1985), and on ‘‘Calculation of Free Energy Changes in Ion–Water Clusters Using Nonadditive Potentials and the Monte Carlo Method,’’ P. Cieplak, T. P. Lybrand, and P. Kollman, J. Chem. Phys. 86, 6393 (1987)’’. 19. J. A. C. Rullman and P. T. van Duijnen, Mol. Phys., 63, 451–475 (1988). A Polarizable Water Model for Calculation of Hydration Energies. 20. F. H. Stillinger and C. W. David, J. Chem. Phys., 69, 1473–1484 (1978). Polarization Model for Water and Its Ionic Dissociation Products. 21. P. Barnes, J. L. Finney, J. D. Nicholas, and J. E. Quinn, Nature (London), 282, 459–464 (1979). Cooperative Effects in Simulated Water. 22. M. Sprik and M. L. Klein, J. Chem. Phys., 89, 7556–7560 (1988). A Polarizable Model for Water Using Distributed Charge Sites. 23. P. Ahlström, A. Wallqvist, S. Engström, and B. Jönsson, Mol. Phys., 68, 563–581 (1989). A Molecular Dynamics Study of Polarizable Water. 24. P. Cieplak, P. A. Kollman, and T. P. Lybrand, J. Chem. Phys., 92, 6755–6760 (1990). A New Water Potential Including Polarization: Application to Gas-Phase, Liquid, and Crystal Properties of Water. 25. U. Niesar, G. Corongiu, E. Clementi, G. R. Kneller, and D. K. Bhattacharya, J. Phys. Chem., 94, 7949–7956 (1990). Molecular Dynamics Simulations of Liquid Water Using the NCC Ab Initio Potential. 26. S. Kuwajima and A. Warshel, J. Phys. Chem., 94, 460–466 (1990). Incorporating Electric Polarizabilities in Water–Water Interaction Potentials. 27. J. Caldwell, L. X. Dang, and P. A. Kollman, J. Am. Chem. Soc., 112, 9144–9147 (1990). Implementation of Nonadditive Intermolecular Potentials by Use of Molecular Dynamics: Development of a Water–Water Potential and Water–Ion Cluster Interactions. 28. L. X. Dang, J. Chem. Phys., 97, 2659–2660 (1992). The Nonadditive Intermolecular Potential for Water Revised.
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Reviews in Computational Chemistry
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Kenny B. Lipkowitz Department of Ch
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vi Preface three-dimensional struct
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viii Preface some descriptors and i
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Epilogue and Dedication My associat
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Contents 1. Clustering Methods and
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Contents xv Electron Transfer in Po
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Contributors John M. Barnard, Barna
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Contributors to Previous Volumes *
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Volume 3 (1992) Tamar Schlick, Opti
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Volume 7 (1996) Geoffrey M. Downs a
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Volume 11 (1997) Mark A. Murcko, Re
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T. Daniel Crawford* and Henry F. Sc
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Topics Covered in Volumes 1-18 * Ab
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Reviews in Computational Chemistry
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2 Clustering Methods and Their Uses
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10 Clustering Methods and Their Use
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42 The Use of Scoring Functions in
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Table 1 Reference List for the Most
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Page 117 and 118: CHAPTER 3 Potentials and Algorithms
Page 119 and 120: Vn (1 + cos(nω + γ)) 2 K θ (θ
Page 121 and 122: are modified by their environment w
Page 123 and 124: Table 1 Polarizability Parameters f
Page 125 and 126: The polarizable point dipole models
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Page 129 and 130: M i z i + q i d i k i and shell cha
Page 131 and 132: Shell Models 103 on estimates of sh
Page 133 and 134: minimization can be replaced by mor
Page 135 and 136: The energy required to create a cha
Page 137 and 138: for all i ði:e:; 8 iÞ: @U @qi l
Page 139 and 140: where we have used q Cl ¼ qNa. The
Page 141 and 142: Electronegativity Equalization Mode
Page 143 and 144: Electronegativity Equalization Mode
Page 145 and 146: of N molecules is taken as a Hartre
Page 147 and 148: is treated using variable charges.
Page 149 and 150: water have been developed, includin
Page 151 and 152: Applications 123 classical and rigi
Page 153 and 154: developing polarizable models. A va
Page 155 and 156: Comparison of the Polarization Mode
Page 157 and 158: negligible errors in such propertie
Page 159 and 160: ecome significant at field strength
Page 161: noteworthy in this regard because t
Page 165 and 166: References 137 48. E. L. Pollock an
Page 167 and 168: References 139 Computational Chemis
Page 169 and 170: References 141 139. J. Hinze and H.
Page 171 and 172: References 143 178. J. J. P. Stewar
Page 173 and 174: References 145 216. M. W. Mahoney a
Page 175 and 176: CHAPTER 4 New Developments in the T
Page 177 and 178: Introduction 149 applications). For
Page 179 and 180: FCWD(∆E ) FCWD(0) ∆E = 0 ∆E
Page 181 and 182: Introduction 153 Equations [6]-[12]
Page 183 and 184: Paradigm of Free Energy Surfaces 15
Page 185 and 186: Paradigm of Free Energy Surfaces 15
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This situation is of course not sat
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F ± (Y ad )/λ I 0.8 0.4 0 −0.4
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it by choosing the GMH basis set 7
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Anharmonic higher order terms gain
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of the radiation is the perturbatio
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individual vibrational excitations
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m 12 /D 6 5.5 5 4.5 4 3.5 17 18 19
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In Eq. [144], the coordinates Y km
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ε/M −1 cm −1 4000 2000 0 analy
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βσ 2 /10 3 cm −1 14 12 10 8 Opt
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0.2 0.1 0 12 16 20 24 28 32 The app
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References 207 7. M. D. Newton, Adv
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References 209 59. R. Kubo and Y. T
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