Reviews in Computational Chemistry Volume 18

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204 Charge-Transfer Reactions in Condensed Phases polarizability of the solute, a0i, treated as input available from experiment or independent calculations, is thus split into the polarizability from the 1 $ 2 transition and the component a0i from all other transitions. The solvent effect on the transition between the states 1 and 2 then includes three components: (1) solvation of the fixed charges (dipole moments) of the chromophore, (2) self-polarization of the solute’s electronic cloud due to polarizability, and (3) change in the electronic occupation numbers induced by the off-diagonal coupling of the transition dipole to the solvent field. Figure 20 compares the solvent-induced FCWD calculated in the TSM (dash–dotted lines, Eq. [144]), the polarizable model (dashed line, Eq. [153]), and the hybrid model (solid lines). The latter incorporates the effects of both the electronic delocalization between the ground and excited states and polarizability due to the coupling of these two states to all other excited states of the chromophore. The latter model was called the adiabatic polarizable model (APM). 100 The APM thus includes the linear and all nonlinear polarizabilities arising from transitions between the ground and excited states and only linear polarizability for all other states. The emission line is broader than the absorption line due to a higher excited state polarizability when electron delocalization is neglected (Figure 20, dashed lines). The inclusion of electronic delocalization through the transition dipole narrows the emission line and reduces the maxima separation (APM, solid lines). Finally, the neglect of polarizability from higher lying electronic states in the TSM (dash–dotted lines) generates an even narrower emission band. The line shape is therefore a result of a compensation between the polarizability effect tending to increase both the emission width and the Stokes shift for a0 > 0 and the opposite effect of electronic delocalization. Intensity 10 5 0 em abs 18 20 22 24 − ν /10 3 cm −1 Figure 20 Absorption (abs.) and emission (em.) solvent-induced FCWD of C153 in acetonitrile calculated according to the APM model (solid lines), the TSM (dash–dotted lines), and the polarizable model (Eq. [153], dashed lines).
0.2 0.1 0 12 16 20 24 28 32 The application of the APM model to the absorption and emission spectra of C153 gives good agreement with experimentally observed spectra in a broad range of solvent polarities. 100 The quality of the calculations is illustrated in Figure 21 where the experimental (dashed lines) and calculated (solid lines) absorption and emission spectra are compared for acetonitrile and acetone as the solvent. The distinction between the optical band shapes calculated on various levels of the theory shown in Figure 20 and the excellent agreement with the experimental results shown in Figure 21 indicate that transitions to higher excited states (polarizability) and solvent-induced mixing between the adiabatic states (transition dipole) are both crucial for reproducing the optical band shape of C153. For this chromophore, the electronic mixing effect is significant due to its high transition dipole moment, m12 ¼ 5:78 D, close in magnitude to the difference in the excited- and ground-state dipole moments, m0 7:5 D. Depending on the relative magnitudes of the polarizability change, a0, and the transition dipole, m12, polarizability and electronic mixing effects may become more or less important for other optical dyes. For all such cases, the APM provides a general framework for analyzing the FCWD of activated and optical transitions by lifting the two restrictions of the MH theory: the TSM and the neglect of electronic overlap in the FCWD (assumptions 1 and 2 in the Introduction). In fact, the APM also provides a general framework for analyzing the effects of coupling between the vibrational solute modes and the solvent fluctuations (assumption 3), 100 but this problem still requires further studies, both experimental and theoretical. SUMMARY acn em abs em abs − ν /10 3 cm −1 0 12 16 20 24 28 32 The concept of free energy surfaces has proven its vitality over many years of fruitful applications to electron transfer kinetics. The direct connection 0.2 0.1 Summary 205 − ν /10 3 cm −1 Figure 21 Normalized experimental (dashed lines) and calculated (solid lines) absorption (abs.) and emission (em.) spectra of C153 in acetonitrile (acn) and acetone (acet). acet
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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
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Introduction 149 applications). For
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FCWD(∆E ) FCWD(0) ∆E = 0 ∆E
Page 181 and 182: Introduction 153 Equations [6]-[12]
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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 207 and 208: λ i /eV 4 3 2 1 0 0 10 20 30 40 Bo
Page 209 and 210: the width/Stokes shift relation (Eq
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: βσ 2 /10 3 cm −1 14 12 10 8 Opt
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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