Reviews in Computational Chemistry Volume 18

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200 Charge-Transfer Reactions in Condensed Phases and get narrower than the absorption lines (Figure 17). The opposite trend holds for negatively solvatochromic dyes with higher major multipoles in their ground states. The lower free energy surface has two minima in the normal CT region (Figure 12). Two absorption transitions exist in this case, even for selfexchange reactions. The reason is the symmetry breaking induced by a nonzero adiabatic transition dipole leading to e < 1 (the standard MH picture, Figure 15, is recovered when m12 ¼ 0). The energy splitting between the two minima of the lower free energy surface gives rise to two transition frequencies and normalized intensity 6 4 2 0 0.7 em 0.8 abs 4 5 6 reduced frequency Figure 17 The normalized absorption (abs.) and emission (em.) intensities at e ¼ 0:7 (solid lines) and e ¼ 0:8 (long-dashed lines) versus the reduced frequency hn=l I . The dash–dotted lines indicate the lower boundary for the energy of the incident light nmin (Eq. [149]). hn ð1Þ abs ¼ lv þ l I þ F I s þ e E12 ½151Š hn ð2Þ abs ¼ lv þ l I F I s e E12 ½152Š The combination of Eq. [134] with Eq. [144] provides an effective formalism for the band shape analysis of CT spectra when a substantial degree of electronic delocalization is involved. Equation [134] is exact for a TS donor– acceptor complex and, therefore, can be used for an arbitrary degree of electronic delocalization as long as the assumption of decoupling of the vibrational and solvent modes holds. Figure 18 illustrates the application of the band shape em abs
ε/M −1 cm −1 4000 2000 0 analysis via Eqs. [134] and [144] to two CT complexes studied in Ref. 87 when the traditional band shape analysis 16,17 fails to fit the experimental spectra. The fitting procedure employs the simulated annealing technique in the space of four parameters: l I , lv, nv, and E12. Polarizable Chromophores The model of polarizable dipolar chromophores suggests that the 3D nuclear reaction field of the solvent serves as a driving force for electronic transitions. Even in the case of an isotropic solute polarizability, two projections of the reaction field should be included: the longitudinal (parallel to the difference solute dipole) component and the transverse (perpendicular to the difference dipole) component. The d function in Eq. [18] eliminates integration over only one of these two field component. The integral still can be taken analytically resulting in a closed-form solution for the Franck–Condon factor FCWD s iðnÞ ¼bAi 2 + 8 12 − ν /10 16 3 cm−1 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi lijaij 3 jhn X0j e bðjaijjhn X0jþlia 2 i Þ I1 2b q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jaij 3 lijhn X0j ½153Š where I1ðxÞ is the first-order modified Bessel function. The normalization factor 2 blia Ai ¼ð1 e i Þ 1 ½154Š 3 + Optical Band Shape 201 Figure 18 Fits of experimental spectra in acetonitrile (solid lines) 87 to Eqs. [134] and [144] (dash–dotted lines, almost indistinguishable from the experimental spectra on the graph scale). The labeling of the donor–acceptor complexes is according to Ref. 87.
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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
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negligible errors in such propertie
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ecome significant at field strength
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noteworthy in this regard because t
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References 135 9. P. Cieplak and P.
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References 137 48. E. L. Pollock an
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References 139 Computational Chemis
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References 141 139. J. Hinze and H.
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References 143 178. J. J. P. Stewar
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References 145 216. M. W. Mahoney a
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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 203 and 204: Table 1 Main Features of the Two-Pa
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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
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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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