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0346245246
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-
note
-
The tapering function was employed only for the actual molecular dynamics, and was not used in the computation of ΔE in the solvation dynamics calculations.
-
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35
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0001484477
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37
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0346245245
-
-
note
-
We picked starting configurations for the nonequilibrium trajectories from the ground-state (anion) equilibrium trajectory. The starting configurations had an average separation of ∼1 ps, with a minimum separation of 0.5 ps.
-
-
-
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38
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85086951362
-
-
note
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t1(0)〉.
-
-
-
-
39
-
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85086949060
-
-
note
-
spin = 1.7
-
-
-
-
41
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0001661973
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(a) Anderson, J.; Ullo, J.; Yip, S. J. Chem. Phys. 1987, 86 (7), 4078.
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(b) Chelli, R.; Cardini, G.; Procacci, P.; Righini, R.; Califano, S.; Albrecht, A. J. Chem. Phys. 2000, 113 (16), 6851.
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0035878496
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(c) Chelli, R.; Cardini, Ricci, M.; Bartolini, P.; Righini, R.; Califano, S. Phys. Chem. Chem. Phys. 2001, 3, 2803.
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44
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0348136170
-
-
note
-
Error bars shown are 2 standard deviations. For both of the autocorrelation functions, we calculated the error bars by breaking up the 200 ps equilibrium simulations into 127 separate 10 ps blocks with each starting point separated by 1.5 ps. These blocks were then correlated as per eq 2 and averaged.
-
-
-
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47
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0348136173
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note
-
On the basis of the solute-solvent center-of-mass RDFs in Figure 4a, we defined the first solvent shell for the neutral and anionic solutes as all THF molecules residing within 6.5 and 7.5 Å, respectively, the values of the minima after the first peak in the RDF. For Figure 5, we defined the first-shell molecules as those within 7.5 Å, regardless of the nature of the solute. This means that the two angular distributions each contain ∼12 solvent molecules, even though the first shell around the neutral (using the 6. 5 ̊ definition) only contains 8-9 molecules.
-
-
-
-
48
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0346875662
-
-
note
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αβ(t).
-
-
-
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49
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85086951364
-
-
note
-
15 it is also advantageous to integrate to obtain information about the magnitude of the coupling for a particular degree of freedom.
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-
-
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50
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0000456245
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Larsen, R. E.; David, E. F.; Goodyear, G.; Stratt, R. M. J. Chem. Phys. 1997, 107 (2), 524.
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Larsen, R.E.1
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52
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0347506139
-
-
note
-
This separation can be done directly using eqs 9a and 9b, whereas the use of eqs 10a and 10b would result in solute-solvent cross terms.
-
-
-
-
53
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0346245242
-
-
note
-
15Our choice to use the solvation velocity response function, J(t), is based on high noise levels in the acceleration response function, B(t); the second derivative function B(t) varies too rapidly and our 400 nonequilibrium trajectories did not provide sufficient statistics to accurately integrate B(t) twice (as in eq 10b).
-
-
-
-
55
-
-
85086949225
-
-
note
-
LJ directly into eq 1.
-
-
-
-
56
-
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0346245241
-
-
note
-
Admittedly, this projection of the solute and solvent coordinates onto the stationary lab frame is arbitrary because only relative separations matter for solvation dynamics. We could have just as easily chosen to project the solvation dynamics in a reference frame that moves along with the solute particle.
-
-
-
-
57
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0348136172
-
-
note
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We note that calculating the projection directly and integrating would have given the exact same curve, because the analysis using eqs 9a and 9b does not contain cross terms.
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-
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58
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0000958857
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Ladanyi, B. M.; Stratt, R. M. J. Phys. Chem. 1995, 99, (9), 2502.
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36549104961
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Kuharski, R. A.; Bader, J. S.; Chandler, D.; Sprik, M.; Klein, M. L.; Impey, R. W. J. Chem. Phys. 1988, 89, 3248; Bader, J. S.; Chandler, D. J. Phys. Chem. 1992, 96, 6423.
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Impey, R.W.6
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62
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0000476256
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Kuharski, R. A.; Bader, J. S.; Chandler, D.; Sprik, M.; Klein, M. L.; Impey, R. W. J. Chem. Phys. 1988, 89, 3248; Bader, J. S.; Chandler, D. J. Phys. Chem. 1992, 96, 6423.
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Bader, J.S.1
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63
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0348136169
-
-
note
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These projections onto the first-shell and nearest neighbor molecules are not integrated. They were computed directly by selecting the appropriate subset of molecules in the nonequilibrium average for S(t), eq 1.
-
-
-
-
64
-
-
0348136168
-
-
note
-
Figure 4a shows that the first solvent shell around the anion is both farther away (7.5 Å) than the neutral (6.5 Å) and contains more solvent molecules (12-13) than the neutral (8-9). We performed the nonequilibrium solute first-shell projections both for molecules within 6.5 and for molecules within 7.5 Å; this change of the first-shell definition only changed its contribution by ∼1 or 2%.
-
-
-
-
65
-
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0346245239
-
-
note
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In fact, due to packing constraints, some of the anion's first-shell solvent molecules need to translate out to become part of the second solvent shell around the neutral.
-
-
-
-
67
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0001272565
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However, solvation for this system occurs in the opposite manner to Onsager's famous "inverse snowball" (ref 51). See, for example: (a) ref 45. (b) Papazyan, A.; Maroncelli, M. J. Chem. Phys. 1993, 98 (8), 6431. (c) Fonseca, T.; Ladanyi, B. M. J. Phys. Chem. 1991, 95, (6) 2116.
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Papazyan, A.1
Maroncelli, M.2
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68
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10244274821
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However, solvation for this system occurs in the opposite manner to Onsager's famous "inverse snowball" (ref 51). See, for example: (a) ref 45. (b) Papazyan, A.; Maroncelli, M. J. Chem. Phys. 1993, 98 (8), 6431. (c) Fonseca, T.; Ladanyi, B. M. J. Phys. Chem. 1991, 95, (6) 2116.
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, Issue.6
, pp. 2116
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Fonseca, T.1
Ladanyi, B.M.2
-
69
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0346875659
-
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note
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Even though we will examine only the unoccupied anion state to describe the nonequilibrium solvation dynamics, the dynamics are driven only by the neutral solvent-solvent interactions. That is, modulation of the anion energy by solute or solvent motions is motivated not by the anion but by the new interactions with the now-occupied neutral state.
-
-
-
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70
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-
85086950971
-
-
note
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anion (not shown).
-
-
-
-
71
-
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0346245238
-
-
note
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The translational projections onto the anion solvation energy (not shown) are nearly identical to the translational projections of the total solvation energy gap shown in Figure 6a.
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-
-
-
72
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85086951805
-
-
note
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anion dash-dot curve, Figure 8) results solely from first-shell solvent rotations because the LJ potential is so short-ranged.
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73
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0347503504
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Smallwood, C. J. Bosma, W.; Larsen, R. E.; Schwartz, B. J. J. Chem. Phys. 2003, 119, 11263.
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