Reviews in Computational Chemistry Volume 18
Reviews in Computational Chemistry Volume 18
Reviews in Computational Chemistry Volume 18
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176 Charge-Transfer Reactions <strong>in</strong> Condensed Phases<br />
Optical excitations quite often generate considerable changes <strong>in</strong> fixed<br />
partial charges, usually described <strong>in</strong> terms of the difference solute dipole<br />
m0 (‘‘0’’ refers here to the solute). Chromophores with high magnitudes of<br />
the ratio m0=R 3 0 , where R0 is the effective solute radius, are often used as<br />
optical probes of the local solvent structure and solvation power. 68 High<br />
polarizability changes are also quite common for optical chromophores, 69 as<br />
is illustrated <strong>in</strong> Table 2. Naturally, the theory of ET reactions and optical transitions<br />
needs extension for the case when the dipole moment and polarizability<br />
both vary with electronic transition:<br />
m01 ! m02 a01 ! a02 ½85Š<br />
To derive the <strong>in</strong>stantaneous free energies Ei, one needs an explicit model<br />
for a dipolar polarizable solute <strong>in</strong> a dipolar polarizable solvent. This need is<br />
addressed by the Drude model for <strong>in</strong>duced solute and solvent dipole<br />
moments. 70 The Drude model represents the <strong>in</strong>duced dipoles as fluctuat<strong>in</strong>g<br />
vectors: p j for the solvent molecules and p 0 for the solute. The potential energy<br />
of creat<strong>in</strong>g a fluctuat<strong>in</strong>g <strong>in</strong>duced dipole p is given by that of a harmonic oscillator,<br />
p 2 =2a, with the polarizability a appear<strong>in</strong>g as the oscillator mass. The<br />
system Hamiltonian Hi is the sum of the solvent–solvent, Hss, and solute–<br />
solvent, H ðiÞ<br />
0s , parts, giv<strong>in</strong>g<br />
Hi ¼ H ðiÞ<br />
0s þ Hss<br />
½86Š<br />
In Hi, the permanent and <strong>in</strong>duced dipoles add up result<strong>in</strong>g <strong>in</strong> the solute–<br />
solvent and solvent–solvent Hamiltonians <strong>in</strong> the form<br />
H ðiÞ<br />
0s ¼ Ii þ U rep<br />
0s<br />
X<br />
j<br />
ðm0i þ p0Þ T0j ðmj þ pjÞþð1=2a0iÞ½o 2<br />
0 _p2 0 þ p20 Š ½87Š<br />
Table 2 Ground-State Polarizability (a1) and Trace of the Tensor of Polarizability<br />
Variation (1/3)Tr[ a] for Several Optical Dyes and Charge Transfer Complexes<br />
Chromophore a1/A˚ 3<br />
(1/3)Tr[ a]/A˚ 3<br />
Anthracene 25 17<br />
2,20-Bipyrid<strong>in</strong>e-3,30diol 21 11<br />
Bis(adamantylidene) 42 29<br />
1-Dimethylam<strong>in</strong>o-2,6-dicyano-4-methylbenzene 22 35<br />
Tetraphenylethylene 50 38<br />
[(NC)5Fe II CNOs III (NH3)5]<br />
[(NC)5Os<br />
57<br />
II CNRu III (NH3)5] (190) 317 a<br />
a<br />
For two different CT transitions.