Adiabatic approach eigenstates

The semi-classical equations of motion obtained above involve only the transverse adiabatic vector potential which is, by definition, independent of the choice of gauge functions/(q) and g(q). The (Aj -f A2)/2M term in the potential is also independent of those two arbitrary functions. The locally quadratic approach to Gaussian dynamics therefore gives physically equivalent results for any choice of /(q) and g(q). The finding that the locally quadratic Hamiltonian approach developed here is strictly invariant with respect to choice of phases of the adiabatic electronic eigenstates supersedes the approximate discussion of gauge invariance given earlier by Romero-Rochin and Cina [25] (see also [40]). 

The double adiabatic approach provides a convenient starting point for a detpt theory (2i). The principle modification is the treatment of the FC factors for the overlap of the proton initial and final eigenstates, when the final proton state is characterized by a repulsive surface. The sum over final proton states becomes an integration over a continuum of states, and bound-unbound FC factors need to be evaluated. An approach can be formulated with methods that have been used to discuss bond-breaking electron-transfer reactions (22). If the motion along the repulsive surface for the dissociation can treated classically. 

Within the quasiclassical approach the nuclei are considered to be subject to a classical motion in the field of force, the potential of which is given by the energy pertinent to one of the eigenstates of the electronic subsystem. In the case of electronically adiabatic processes, the field of force for the nuclear motion is determined by a single potential energy surface (pertinent to a single electronic state). 

Presumably the most straightforward approach to chemical dynamics in intense laser fields is to use the time-independent or time-dependent adiabatic states [352], which are the eigenstates of field-free or field-dependent Hamiltonian at given time points respectively, and solve the Schrodinger equation in a stepwise manner. However, when the laser field is approximately periodic, one can also use a set of field-dressed periodic states as an expansion basis. The set of quasi-static states in a periodic Hamiltonian is derived by a Floquet type analysis and is often referred to as the Floquet states [370]. Provided that the laser field is approximately periodic, advantages of using the latter basis set include (1) analysis and interpretation of the electron dynamics is clearer since the Floquet state population often vary slowly with the timescale of the pulse envelope and each Floquet state is characterized as a field-dressed quasi-stationary state, (2) under some moderate conditions, the nuclear dynamics can be approximated by mixed quantum-classical (MQC) nonadiabatic dynamics on the field-dressed PES. The latter point not only provides a powerful clue for interpretation of nuclear dynamics but also implies possible MQC formulation of intense field molecular dynamics. 

Another important statistical approach to this same problem is the statistical adiabatic channel model (SACM) of Quack and Troe, - which adiabatically correlates the eigenstates of the orthogonal modes along the reaction coordinate, thereby generating rovibrational adiabatic channels. The adiabatic approximation reduces the multidimensional dynamical problem to essentially a one-dimensional barrier-crossing problem. The catch, of course, is that it is extremely difficult to compute the requisite adiabatic channels, though no more difficult than a rigorous quantum mechanical implementation of VTST would be. An authoritative account of adiabatic channel methods is to be found in Statistical Adiabatic Channel Models. 

MEG. MEG can raise the photovoltaic efficiency to 44o/ 3,5,6,i5,s4 TDDFT-NAMD method described in Section 2.6.1 was used to simulate Auger dynamics in nanoscale systems. To simulate Auger dynamics, electron correlation is taken into account in the adiabatic basis in which all Coulomb interactions are described in the Hamiltonian for fixed nuclear coordinates. The eigenstates are coupled through NAC which arise from nuclear motion during molecular dynamics. This approach allows us to include phonon assisted Auger dynamics. This picture is complimentary to the traditional Auger model which employs diabatic initial and final states and is independent of nuclear coordinates. ... 

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