Reviews in Computational Chemistry Volume 18

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180 Charge-Transfer Reactions in Condensed Phases In many practical cases, the factors fei are very close to unity and can be omitted. The parameters ~a0i and ~m0i are then equal to their gas-phase values a0i and m0i. Equation [100] then gives the polarizability change in terms of spectroscopic moments and gas-phase solute dipoles. Experimental measurement and theoretical calculation of a0 ¼ a02 a01 is still challenging. Perhaps the most accurate way to measure a0 presently available is that by Stark spectroscopy, 74–76 which also gives m0. Equation [100] can therefore be used as an independent source of a0, provided all other parameters are available, or as a consistency test for the band shape analysis. One of the consequences of a nonzero a0 is that the relation between the solvent-induced Stokes shift and the corresponding spectral width (lv ¼ 0) h nst ¼ bs 2 ½101Š which is valid for linear solvation response and a0 ¼ 0, does not hold any more. In Figure 9, the widths bs2 i are plotted versus the Stokes shift obtained by varying the static dielectric constant of the solvent in the range Es ¼ 3 – 65. The aborption width deviates downward from the unity slope line predicted by Eq. [101], and the emission width goes upward. The opposite behavior follows from nonlinear solvation effects: 77 the absorption width deviates upward from Eq. [101], and the emission width goes downward. This situation arises because nonlinear solvation results in narrowing of emission lines in contrast to the broadening effect of a0 > 0. The two effects, therefore, tend to compensate each other for a0 > 0 and to enforce each other for a0 < 0. Both the inequality of the charge separation (CS) and charge recombination (CR) reorganization energies (l1 6¼ l2, Figure 8) and the deviation from βσ 2 i /eV 10 8 6 4 2 em abs 1 2 3 4 5 h ∆ν st /eV Figure 9 Absorption (abs.) and emission (em.) widths obtained by changing the static solvent dielectric constant in the range Es ¼ 3 65 versus the Stokes shift; E1 ¼ 2:0. The dash–dotted line indicates the equality h nst ¼ bs 2 is valid for a0 ¼ 0.
the width/Stokes shift relation (Eq. [101], Figure 9) are indicators of a nonparabolic form of the CS and CR free energy surfaces. Another indication of this effect is the energy gap law. The energy gap law refers to the dependence of the activation energy of a reaction on the difference in the Gibbs energy between the products and reactants. 34,38,50 The Marcus equation, Eq. [9], is an example of the energy gap law. Experimentally, the energy gap law is monitored by changing the gas-phase component of F0 through chemical substitution of the donor and/or acceptor units. 48 The solvent component of Fi is usually assumed to be reasonably constant. Figure 10 shows the activation energy of the forward (charge separation, CS) reaction plotted against FCS ¼ F0 and backward (charge recombination, CR) reaction plotted against FCR ¼ F0 for the transition m01 ¼ 0 ! m02 ¼ 15 D and a01 ¼ 20 A ˚ 3 ! a02 ¼ 40 A ˚ 3 . Two important effects of nonzero a0 manifest themselves in Figure 10. First, in contrast to the case of zero a0, the maxima of the CS and CR curves do not coincide, as is suggested by Eq. [9]. Second, the CR curve is broader and shallower from the side of negative energy gaps compared to the CS curve. The energy gap law for thermally activated ET reactions is often obtained by superimposing CS and CR data on a common scale of F0. 78 For such a procedure, depending on the energy range studied, two outcomes can be predicted. For a narrow range of FCS and FCR values close to zero, act −βF i 0 −1 −2 −3 −4 CR α 02 = 2α 01 Beyond the Parabolas 181 −5 −5 −4 −3 ∆FCS , ∆FCR /eV −2 −1 Figure 10 ET energy gap law for the charge separation (CS, m01 ! m02, FCS ¼ F0) and charge recombination (CR, m02 ! m01, FCR ¼ F0) reactions at a01 ¼ 20 A˚ 3 and a02 ¼ 40 A˚ 3 . Parameters are as in Figure 8. The points and dashed line are drawn to illustrate two possible outcomes of combining CS and CR experimental data in one plot with a common energy gap scale (see the text). The open circles correspond to crossing curves, whereas the solid squares correspond to a single curve bridged by the dashed line. CS
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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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CHAPTER 3 Potentials and Algorithms
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Vn (1 + cos(nω + γ)) 2 K θ (θ
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are modified by their environment w
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Table 1 Polarizability Parameters f
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The polarizable point dipole models
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two to three orders of magnitude sl
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M i z i + q i d i k i and shell cha
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Shell Models 103 on estimates of sh
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minimization can be replaced by mor
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The energy required to create a cha
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for all i ði:e:; 8 iÞ: @U @qi l
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where we have used q Cl ¼ qNa. The
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Electronegativity Equalization Mode
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Electronegativity Equalization Mode
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of N molecules is taken as a Hartre
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is treated using variable charges.
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water have been developed, includin
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Applications 123 classical and rigi
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developing polarizable models. A va
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Comparison of the Polarization Mode
Page 157 and 158: negligible errors in such propertie
Page 159 and 160: ecome significant at field strength
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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
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Page 187 and 188: In Eqs. [18] and [19], F0i is the e
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Page 197 and 198: energy surfaces of ET. 33,50-56 It
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Page 203 and 204: Table 1 Main Features of the Two-Pa
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Page 207: λ i /eV 4 3 2 1 0 0 10 20 30 40 Bo
Page 211 and 212: Table 3 Mapping of the Q Model on S
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Page 215 and 216: F ± (Y ad )/λ I 0.8 0.4 0 −0.4
Page 217 and 218: it by choosing the GMH basis set 7
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Page 225 and 226: m 12 /D 6 5.5 5 4.5 4 3.5 17 18 19
Page 227 and 228: In Eq. [144], the coordinates Y km
Page 229 and 230: ε/M −1 cm −1 4000 2000 0 analy
Page 231 and 232: βσ 2 /10 3 cm −1 14 12 10 8 Opt
Page 233 and 234: 0.2 0.1 0 12 16 20 24 28 32 The app
Page 235 and 236: References 207 7. M. D. Newton, Adv
Page 237 and 238: References 209 59. R. Kubo and Y. T
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