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(b) Keirstead, W.; Wilson, K. R.; Hynes, J. T. J. Chem. Phys. 1991, 95, 5256. See also ref 25.
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85033065393
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Bursulaya, B. D.; Zichi, D. A.; Kim, H. J. To be submitted.
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Bursulaya, B. D.; Zichi, D. A.; Kim, H. J. To be submitted.
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51
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85033065612
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For simplicity, a point dipolar solute will be assumed throughout for our theoretical analysis, even though extended charge distributions were used in the actual simulations.
-
For simplicity, a point dipolar solute will be assumed throughout for our theoretical analysis, even though extended charge distributions were used in the actual simulations.
-
-
-
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52
-
-
85033063827
-
-
If one is interested in, e.g., solute rotational dynamics, then the nuclear coordinates associated with rotational motions, i.e., the solid angle variable for the solute orientation, should not be averaged out. This will increase the dimensionality of G.
-
If one is interested in, e.g., solute rotational dynamics, then the nuclear coordinates associated with rotational motions, i.e., the solid angle variable for the solute orientation, should not be averaged out. This will increase the dimensionality of G.
-
-
-
-
53
-
-
85033061063
-
-
note
-
The number of solvent coordinates needed for Gdepends on the multipole character variation of the solute charge distribution during the charge shift processes under consideration. Thus if the solute electronic structure variation involves the Mh pole moment, 21 + 1 independent coordinates are needed in general.
-
-
-
-
54
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0001203249
-
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This approximation and its variants are widely used to analyze charge shift and transfer processes in solution. However, for important exceptions requiring multiple solvent coordinates, see: Kim, H. J.; Hynes, J. T. y. Chem. Phys. 1990, 93, 5211.
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Jortner, J., Pullman, B., Eds.; Kluwer: Dordrecht
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Hynes, J. T.; Carter, E. A.; Ciccotti, G.; Kim, H. J.; Zichi, D. A.; Ferrario, M.; Kapral, R. In Perspectives in Photosynthesis; Jortner, J., Pullman, B., Eds.; Kluwer: Dordrecht, 1990.
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Berendsen, H. J. C.; Gigera, J. R.; Straatsma, T. P. J. Phys. Chem. 1987, 97, 6269.
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67
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85033061766
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-
note
-
In order for a certain electronic state ipl to be isotropically polarizable, one needs at least three independent transition dipole vectors, : e.g., along the x, y, and z molecular axes, to describe a., a, and ou. i Thus a minimum of three additional VB states that are higher in energy than y° are required.
-
-
-
-
72
-
-
85033061316
-
-
note
-
A self-consistency condition between the central and image solute charges to satisfy the system periodicity was handled numerically by an iterative step inserted into the Ewald summation algorithm. The convergence was usually attained with a couple of iterations except near the beginning of the equilibration period. Essentially no CPU overhead was found for this, and the quantum simulations were as efficient as the classical ones.
-
-
-
-
73
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85033066176
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However, if the transition dipole moment is sufficiently large, solvation can induce a considerable solute electronic structure change. This could also be accompanied by a significant polarizability change.
-
However, if the transition dipole moment is sufficiently large, solvation can induce a considerable solute electronic structure change. This could also be accompanied by a significant polarizability change.
-
-
-
-
75
-
-
0000971326
-
-
The statistical error E in the radial distribution functions was calculated for several different r values according to Fincham et al. [J. Chem. Phys. 1986, 84, 4535] with proper account of the statistical inefficiency s.50 The latter factor is due to the fact that the MD configurations are correlated, especially at short times. We have found that both s and E vary with r, but neither of them shows a strong dependence. For instance, in the case of g-n(r) for the QP2 solute, the respective £and s values are 0.011 and 4 for r = 2.5 A, 0.016 and 10 for r = 3.5 A, and 0.011 and 6 for r = 4.5 A. Thus the standard error for g(r) is in the range 0.01-0.015.
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J. Chem. Phys.
, vol.84
, pp. 4535
-
-
Fincham1
-
76
-
-
85033064211
-
-
note
-
In the actual numerical calculations, we employed Fourier-Laplace integral transforms rather than Laplace transforms; thus, the z variable is complex-valued. This makes the inversion procedure much more efficient. The details are as follows. Due to numerical inaccuracies, £= C' -z usually diverges for large z. To avoid this, we approximate the asymptotic behavior of Ças a Fourier-Laplace transform of a gaussian function A exp[- '/j22] with two undetermined parameters A and B. For small z, the actual Cl -z values obtained from the simulations are used. These two functions are smoothly connected at a patching point zp. Since the Fourier-Laplace transform is complex-valued, both the real and imaginary parts need to be continuous at Zp. These two conditions completely determine the two parameters A and B for a given patching point. By varying zp, we have found the optimal £that yields the best C. A similar method has been employed in refs 25 and 8b.
-
-
-
-
77
-
-
85033045759
-
-
This also indicates that the time-dependent friction results determined via the C, inversion are quite reliable, (b) The poor agreement for QPO is probably due to the breakdown of the point dipole approximation in eq 4.9 and the neglect of the cross correlation between the short-range and long-range interactions.
-
(a) This also indicates that the time-dependent friction results determined via the C, inversion are quite reliable, (b) The poor agreement for QPO is probably due to the breakdown of the point dipole approximation in eq 4.9 and the neglect of the cross correlation between the short-range and long-range interactions.
-
-
-
-
78
-
-
85033069370
-
-
Considering the approximate nature of eq 4.15, moderate agreement in the dynamic behavior is not so surprising.
-
Considering the approximate nature of eq 4.15, moderate agreement in the dynamic behavior is not so surprising.
-
-
-
-
81
-
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85033056912
-
-
By contrast, F± is little affected by the solute polarizability along the molecular axis. The MD results show that the Fj. values for both QP2 and CN2 are nearly the same as F for the CN2 solute.
-
By contrast, F± is little affected by the solute polarizability along the molecular axis. The MD results show that the Fj. values for both QP2 and CN2 are nearly the same as F for the CN2 solute.
-
-
-
-
84
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0041477605
-
-
Maroncelli, M.; Kumar, V. P.; Papazyan, A. J. Phys. Chem. 1993, 97, 13.
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J. Phys. Chem.
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, pp. 13
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Maroncelli, M.1
Kumar, V.P.2
Papazyan, A.3
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88
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0012607756
-
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J. Chem. Plm. 1992, 96, 5354.
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(1992)
J. Chem. Plm.
, vol.96
, pp. 5354
-
-
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90
-
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85033057316
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-
Private communication.
-
Fleming, G. R. Private communication.
-
-
-
Fleming, G.R.1
-
92
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36049058132
-
-
The statistical errors for the TCP's are estimated according to: Zwanzig, R.; Ailawadi, N. K. Phys. Rev. 1969, 182, 280.
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(1969)
Phys. Rev.
, vol.182
, pp. 280
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Zwanzig, R.1
Ailawadi, N.K.2
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