Time-dependent self-consistent-field TDSCF

For the case of intramolecular energy transfer from excited vibrational states, a mixed quantum-classical treatment was given by Gerber et al. already in 1982 [101]. These authors used a time-dependent self-consistent field (TDSCF) approximation. In the classical limit of TDSCF averages over wave functions are replaced by averages over bundles of trajectories, each obtained by SCF methods. 

Inserting the separation ansatz, i.e., U , results in two nonlinearly coupled single particle Schrodinger equations, the so-called time dependent self-consistent field (TDSCF) equations ... 

Another, purely quantum mechanical approximation is the so-called time-dependent self-consistent field (TDSCF) method. For general reviews see Kerman and Koonin (1976), Goeke and Reinhard (1982), and Negele (1982). For applications to molecular systems see, for example, Gerber and Ratner (1988a,b). In the TDSCF method the wavepacket is separated according to... 

Makri, N. and Miller, W.H. (1987). Time-dependent self-consistent field (TDSCF) approximation for a reaction coordinate coupled to a harmonic bath Single and multiple configuration treatments, J. Chem. Phys. 87, 5781-5787. 

The time-dependent self consistent field (TDSCF) approximation... 

The separation in Eqs. (4.7-4.S) and the use of the averaged potential in Eq. (4.8) follow from the general time-dependent self-consistent field (TDSCF) approach (Gerber et al. 1982 Gerber 1987 Makri and Miller 1987b). In this theory, a full wavefunction for two sets of coordinates, X and T, is approximated via... 

The second part of the chapter (Section III) deals with the time-dependent self-consistent-field (TDSCF) method for studying intramolecular vibrational energy transfer in time. The focus is both on methodological aspects and on the application to models of van der Waals cluster systems, which exhibit non-RRKM type of behavior. Both Sections II and III review recent results. However, some of the examples and the theoretical aspects are presented here for the first time. 

The SCF, or mean-field, approximation does not include the effect of energy transfer processes between the modes. The Cl approach incorporates such effects in a time-independent framework, but as was noted in the previous section this method loses much of the simplicity and insight provided by the SCF model. The most natural extension of the SCF approximation that also describes energy transfer among the coupled modes in the system, and treats this effect by a mean-field approach, is the time-dependent self-consistent-field (TDSCF), or time-dependent mean-field, approximation. 

R. Alimi, R. B. Gerber, A. D. Hammerich, R. Kosloff, and M. A. Ratner,/. Chem. Phys., 93, 6484 (1990). Validity of Time-Dependent Self-Consistent-Field (TDSCF) Approximations for Unimolecular Dynamics A Test for Photodissociation of the Xe-HI Cluster. 

However, if the correction terms are introduced as demonstrated above, it is just a way of approaching the limit in which the trial function is expressed as ff(r, t)X(R, t) with no restriction on the form of X(R, f), i.e., it is not for instance a GWP at all times We shall denote this limit the self-consistent field limit (SCF) or rather the time-dependent SCF limit (TDSCF). The reason for this designation is that the equations for the two wavefunctions are solved self-consistently, i.e., the TDSE for one mode involves the average interaction with the other and vice versa. Thus, if we insert a product type wavefunction r r, t)X R, t) in the TDSE, equation (7), using the expansion (1), multiply fi om the left with X(R, t) and integrate over R we get... 

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