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18
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0039160150
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T. D. Sewell, C. C. Chambers, D. L. Thompson, and R. D. Levine, Chem. Phys. Lett. 208, 125 (1993).
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(1993)
Chem. Phys. Lett.
, vol.208
, pp. 125
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Sewell, T.D.1
Chambers, C.C.2
Thompson, D.L.3
Levine, R.D.4
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21
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85033042052
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note
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Specifically, for a Hamiltonian with self anharmonicity terms one cannot use a harmonic approximation. We emphasized this in our original paper (Ref. 10) and reiterate this point below. Guo et al. (Ref. 15) have not followed our procedure and so the results they report do not constitute a test of our method.
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26
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0001293858
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And this is used in the computations of spectra for harmonic potentials. See, for example D. Tannor and E. J. Heller, J. Chem. Phys. 77, 202 (1982).
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(1982)
J. Chem. Phys.
, vol.77
, pp. 202
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Tannor, D.1
Heller, E.J.2
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29
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85033059764
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note
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Within our approximation that f(x) is sufficiently slowly varying that its derivative is constant, Eq. (11), this pair of variables is, in fact, canonical {f(x),p} = 1. where the curly brackets are the Poisson brackets. Of course, this is not exactly consistent with Eq. (13). The factorization method (Ref. 27) has identified all the potentials for which the factorization (7)-(9) is exact.
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30
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85033069083
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note
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Nor is it reasonable to use x for f(x) as was apparently done in Ref. 15. As noted therein, the harmonic approximation can introduce spurious resonances which are not evident in the exact dynamics and this is the reason for the unphysical oscillations reported there. The (self) anharmonicities need to be realistically handled.
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31
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85033061490
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The question of "partial remedy" has also been discussed by McCormack and Lim (Ref. 14) in their reply to Schlier (Ref. 13)
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The question of "partial remedy" has also been discussed by McCormack and Lim (Ref. 14) in their reply to Schlier (Ref. 13).
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32
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85033059006
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note
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Note that Guo et al. have incorrectly stated [Eqs. (2) and (3) of Ref. 15] that the correspondence principle implies that the classical and quantum results are in agreement. Textbooks that discuss the quantal-classical correspondence assume that the quantum numbers are large so that the difference of 1/2 (in units of ℏω) can be neglected. If the system has a high energy content this is the right classical limit of the quantum case. At very low energies, which are the subject of their paper, this statement is incorrect.
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36
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36549091743
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One can argue that quantum mechanically dissociation is still possible by tunneling. That is in principle correct but the required time scale is not what one would estimate by allowing the molecule to move classically using its zpe to overcome the barrier, except if there are partial barriers to the energy transfer [M. J. Davis and S. K. Gray, J. Chem. Phys. 84, 5389 (1986).
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(1986)
J. Chem. Phys.
, vol.84
, pp. 5389
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Davis, M.J.1
Gray, S.K.2
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44
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36449000765
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G. Ashkenazi, R. Kosloff, S. Ruhman, and H. Tal-Ezer, J. Chem. Phys. 103, 10005 (1995).
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(1995)
J. Chem. Phys.
, vol.103
, pp. 10005
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Ashkenazi, G.1
Kosloff, R.2
Ruhman, S.3
Tal-Ezer, H.4
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