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Chernyak, V.5
Mukamel, S.6
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22
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33748624844
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The connections between these inherent-structure ideas and instantaneous normal modes (and, in particular, with imaginary instantaneous normal modes) were first explored by
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The connections between these inherent-structure ideas and instantaneous normal modes (and, in particular, with imaginary instantaneous normal modes) were first explored by R. A. LaViolette and F. H. Stillinger, 83, 4079 (1985).
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Laviolette, R.A.1
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M. Cho, G. R. Fleming, S. Saito, I. Ohmine, and R. M. Stratt, 100, 6672 (1994).
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32
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The first quantitative attempts to use imaginary modes to understand diffusion were those of the Keyes group:
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The first quantitative attempts to use imaginary modes to understand diffusion were those of the Keyes group: B. Madan, T. Keyes, and G. Seeley, J. Chem. Phys. 92, 7565 (1990);
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Keyes, T.2
Seeley, G.3
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35
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Some of their more recent work on the applications and implications of imaginary modes includes
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Some of their more recent work on the applications and implications of imaginary modes includes P. Moore and T. Keyes, J. Chem. Phys. 100, 6709 (1994);
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J. Chem. Phys.
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Moore, P.1
Keyes, T.2
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47
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0001418512
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There have also been a number of less heuristic attempts to see how imaginary modes might enter the INM expressions for spectroscopically observable dynamics. See, for example
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There have also been a number of less heuristic attempts to see how imaginary modes might enter the INM expressions for spectroscopically observable dynamics. See, for example, J. T. Kindt and C. A. Schmuttenmaer, J. Chem. Phys. 106, 4389 (1997).
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0000456245
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R. E. Larsen, E. F. David, G. Goodyear, and R. M. Stratt, J. Chem. Phys. 107, 524 (1997).
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Larsen, R.E.1
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Stratt, R.M.4
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50
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22244468995
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note
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So far, the only quantitative binary-mode theories that have been developed have been for dynamics in atomic liquids (Refs. 19, 25, and 26). However, there is evidence that aspects of solvation and vibrational population relaxation in molecular liquids are analogously governed by the motion of the solute and a single solvent. See Ref. 8.
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As we shall discuss further, papers have already begun to appear discussing the time evolution of instantaneous normal modes. See, in particular, Refs. 29 and 30
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As we shall discuss further, papers have already begun to appear discussing the time evolution of instantaneous normal modes. See, in particular, Refs. 29 and 30.
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note
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We have formulated the INM theory here as it would apply to neat atomic fluids, the subject of this paper. The generalizations to molecular fluids and to both dilute-solute/solvent systems and to other kinds of mixtures have been discussed previously by ourselves and others. See, for example, Refs. 5 6 7 8, 16, and 18.
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55
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22244457333
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in edited by W. H. Miller Plenum, New York
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J. Tully, in Dynamics of Molecular Collisions, edited by W. H. Miller (Plenum, New York, 1976), Part B.
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(1976)
Dynamics of Molecular Collisions
, Issue.PART B
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Tully, J.1
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58
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22244477053
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This result was first observed numerically by (unpublished)
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This result was first observed numerically by M. Buchner (unpublished).
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Buchner, M.1
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note
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α(t)〉 will decay simply because the true (microscopic) modes are constantly changing their ordering. For the modes we consider, adiabatic lifetimes computed from correlation functions of this sort, such as those in Ref. 30, will turn out to be far smaller than the true mode-mixing times.
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Cambridge University Press, Cambridge Chap. 2
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W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C (Cambridge University Press, Cambridge, 1988), Chap. 2.
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(1988)
Numerical Recipes in C
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Press, W.H.1
Flannery, B.P.2
Teukolsky, S.A.3
Vetterling, W.T.4
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note
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1. We note that this distinction has no effect on any of the calculations performed in Ref. 25.
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That is, the atom projections of the modes differ from the ideal, isolated binary-mode values of 0.5 by about as much after the event as they did before the event
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That is, the atom projections of the modes differ from the ideal, isolated binary-mode values of 0.5 by about as much after the event as they did before the event.
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α(t) in Eq. (4.17), rather than the "bare" 0th-order eigenvalues of Eq. (4.5). See, for example Electron Correlation in Molecules Clarendon, Oxford Chap. 4. We have two main reasons for taking this step. For one thing, there is a shift in the time evolution of the bare eigenvalues from that the exact dynamics (altering the timing of the scattering event). More importantly, since the bare eigenvalues actually cross one another, using them in Eq. (4.17) would lead to an unphysical divergence. Note that in order to remove the divergence one has to renormalize by using 2nd or higher order formulas for the eigenvalues
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α(t) in Eq. (4.17), rather than the "bare" 0th-order eigenvalues of Eq. (4.5). See, for example, S. Wilson, Electron Correlation in Molecules (Clarendon, Oxford, 1984), Chap. 4. We have two main reasons for taking this step. For one thing, there is a shift in the time evolution of the bare eigenvalues from that the exact dynamics (altering the timing of the scattering event). More importantly, since the bare eigenvalues actually cross one another, using them in Eq. (4.17) would lead to an unphysical divergence. Note that in order to remove the divergence one has to renormalize by using 2nd or higher order formulas for the eigenvalues.
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(1984)
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Wilson, S.1
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P. Moore, A. Tokmakoff, T. Keyes, and M. D. Fayer, J. Chem. Phys. 103, 3325 (1995).
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Moore, P.1
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Fayer, M.D.4
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Of course, it is this intramode anharmonicity that makes the eigenvalues change in time and eventually become resonant with other modes - which is an important source of anharmonicity
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Of course, it is this intramode anharmonicity that makes the eigenvalues change in time and eventually become resonant with other modes - which is an important source of anharmonicity.
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See, for example
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See, for example, S. Palese, S. Mukamel, R. J. Dwayne Miller, and W. T. Lotshaw, J. Phys. Chem. 100, 10380 (1996).
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Palese, S.1
Mukamel, S.2
Dwayne Miller, R.J.3
Lotshaw, W.T.4
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