Reviews in Computational Chemistry Volume 18

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124 Polarizability in Computer Simulations used for the short-range repulsion, as well as from the use of point charges or dipoles rather than diffuse charge distributions. Evidence exists showing that diffuse charge distributions are necessary to ensure transferability, in both polarizable and nonpolarizable models. 35,53,205 Predicting phase coexistence behavior near the critical point seems to be a particularly difficult task, even for the best polarizable models. Almost no existing model that works well at ambient conditions has been demonstrated to predict the critical temperature and density to better than 10% accuracy. 61,206 And those that are specifically designed to work well near the critical point seem to do a poor job of reproducing the liquid structure at lower temperatures. 61 Part of the problem is that the simulations required to measure phase coexistence properties are computationally expensive due to the extensive sampling required. Because of this expense, phase coexistence properties have not typically been included in the list of target properties when parameterizing new water models. Thus, it is only now becoming clear how to construct a model that is transferable across hundreds of degrees, from supercooled liquid to supercritical fluid. It is not yet clear whether one particular type of polarizable model is better able to capture the variation of water properties under varying temperatures and densities than another. However, the current situation clearly underscores the considerable flexibility and ambiguities involved in parameterizing polarizable potentials. Transferability from the solid state to the liquid state is equally problematic. A truly transferable potential in this region of the phase diagram must reproduce not only the freezing point, but also the temperature of maximum density and the relative stability of the various phases of ice. This goal remains out of reach at present, and few existing models demonstrate acceptable transferability from solid to liquid phases. 33,52,207 One feature of water that has been demonstrated by both an EE model study 207 and an ab initio study 200 is that the dipole moments of the liquid and the solid are different, so polarization is likely to be important for an accurate reproduction of both phases. In addition, while many nonpolarizable water models exhibit a computed temperature of maximum density for the liquid, the temperature is not near the experimental value of 277 K. 53,62,208–215 For example, TIP4P 192 and SPC/E 4 models have a temperature of maximum density, TMD, near 248 K. 211,213,215 Several EE models 53,147,207 and one EE–PPD hybrid model 166 yield a TMD right at 277 K, suggesting that polarizability may be an important factor for this property as well. However, PPD models do not reproduce the T MD maximum density very well; one model does not even have a T MD 212 and another has a temperature dependence on the density that is much too strong. 62 One nonpolarizable model, the TIP5P model, which includes lonepair interaction sites, has been successfully constructed to have the correct TMD. 216 The successful transferability of water models from the bulk phases to more heterogeneous conditions is another important goal for scientists
developing polarizable models. A vast literature exists in this area, with applications ranging from the solvation of simple ions 27,82,202,217,218 and biomolecules 10 to hydrophobic hydration and the structure of water at interfaces 104,219,220 and in external electric fields. 206,220 Due to the wide variation in electrostatic environments encountered, it is not surprising to find that polarizable models generally (but not always) provide significant improvements over nonpolarizable models. Proteins and Nucleic Acids For both proteins and nucleic acids, there exist significant structuredetermining, hydrogen-bonding interactions between groups with p electrons: the peptide group for proteins and bases for nucleic acids. The extensive network of peptide hydrogen bonds in a-helices and b-sheets in proteins and the base-pair stacking in the double helix of nucleic acids are stablized by polarization of electrons with some p character. This stabilization has been labeled p-bond cooperativity or resonance-assisted hydrogen bonding. 221,222 The polarization of the p electrons in amides can be represented by the usual two dominant resonance structures H C N O H C N −O and in the nucleic acid bases (shown here for uracil), N O C N H H C C C H O N O C N H C C C O− H H Applications 125 Resonance structures like these are commonly cited as leading to the planar geometry of the peptide bond and nucleic acid bases. A number of quantum mechanical studies on the molecules N-methylactamide (NMA) and N-methylformamide (NMF), have addressed the importance of cooperative, or nonadditive, effects on hydrogen-bond formation. 223–225 Aggregates of NMA or NMF may be considered prototypes of the protein backbone. For these systems, the cooperative effects were found to add about 12–20% to the stabilization energy. Most of that energy can be decomposed into the polarization energy, with charge transfer making only a modest contribution, although the size of each component depends on the method of decomposition. 225 Experimental studies on NMA aggregates also
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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
Page 127 and 128: two to three orders of magnitude sl
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: Applications 123 classical and rigi
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 and 162: noteworthy in this regard because t
Page 163 and 164: References 135 9. P. Cieplak and P.
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
Page 187 and 188: In Eqs. [18] and [19], F0i is the e
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Table 1 Main Features of the Two-Pa
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and Hss ¼ U rep ss 1 2 X j;k ðmj
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λ i /eV 4 3 2 1 0 0 10 20 30 40 Bo
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the width/Stokes shift relation (Eq
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Table 3 Mapping of the Q Model on S
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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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Reviews in Computational Chemistry Volume 18

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