Nonadiabatic effects methods

One can also ask about the relationship of the FMS method, as opposed to AIMS, with other wavepacket and semiclassical nonadiabatic dynamics methods. We first compare FMS to previous methods in cases where there is no spawning, and then proceed to compare with previous methods for nonadiabatic dynamics. We stress that we have always allowed for spawning in our applications of the method, and indeed the whole point of the FMS method is to address problems where localized nuclear quantum mechanical effects are important. Nevertheless, it is useful to place the method in context by asking how it relates to previous methods in the absence of its adaptive basis set character. There have been many attempts to use Gaussian basis functions in wavepacket dynamics, and we cannot mention all of these. Instead, we limit ourselves to those methods that we feel are most closely related to FMS, with apologies to those that are not included. A nice review that covers some of the... 

As mentioned, most calculations we have done so far have concerned molecular systems. However, prior to development of the non-BO method for the diatomic systems, we performed some very accurate non-BO calculations of the electron affinities of H, D, and T [43]. The difference in the electron affinities of the three systems is a purely nonadiabatic effect resulting from different reduce masses of the pseudoelectron. The pseudoelectrons are the heaviest in the T/T system and the lightest in the H/H system. The calculated results and their comparison with the experimental results of Lineberger and coworkers [44] are shown in Table 1. The calculated results include the relativistic, relativistic recoil. Lamb shift, and finite nuclear size corrections labeled AEcorr calculated by Drake [45]. The agreement with the experiment for H and D is excellent. The 3.7-cm increase of the electron affinity in going from H to D is very well reproduced by the calculations. No experimental EA value is available for T. 

If the Born-Oppenheimer approximation is not valid—for example, in the vicinity of surface crossings—nonadiabatic coupling effects (that couple nuclear and electronic motion) need to be taken in account to correctly describe the motion of the molecular system. This is done, for instance, when one needs to describe a jump between two different PESs. In this case, one uses semiclassi-cal theories and the surface-hopping method, which we discuss subsequently. We now discuss in some detail how the region in which nonadiabatic effects become important can be characterized topologically. 

Almost all the published PESs have been used to perform quasiclassical trajectory (QCT) [71,83] studies of the title reaction. Those calculations have been mainly focused in adiabatic studies in each PES. In addition, the trajectory surface hopping method [56], has been used to study the nonadiabatic effects between the X A and B M PESs. 

J. Chem. Phys., 103, 7277-7286 (1995) d) S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators,/. Chem. Phys., 104, 1394-1398 (1996) e) D. Antoniou, S. D. Schwartz, Nonadiabatic Effects in a Method that Combines Classical and Quantum Mechanics, /. Chem. Phys., 104, 3526-3530 (1996) f) S. D. Schwartz, The Interaction Representation and Non-Adiabatic Corrections to Adiabatic Evolution Operators II Nonlinear Quantum Systems, /. 

The interactions in the processes (1.1) and (1.2) are not of a long-range type. The excitation can be transferred only by exchange of electrons. As the incident energy of our interest is in the thermal range, the PSS method is applicable. We ignore the nonadiabatic effects for the determination of the phase shift. The potential energy curves are obtained by the Heitler-London... 

The following part of this section describes our recent advances in applying accurate quantum wave packet methods to compute rate constants and to understand nonadiabatic effects in tri-atomic and tetra-atomic molecular reactions. The quantum nonadiabatic approaches that we present here are based on solving the time-dependent Schrodinger equation formulated within an electronically diabatic representation. 

In this context, one of the most efficient approaches is based on mixed quantum-classical dynamics in which the nonadiabatic effects are simulated using Tully s surface hopping (TSH) method [13, 14]. It is applicable to a large variety of systems ranging from isolated molecules and clusters to complex nanostructures... 

It is getting more and more important to treat realistic large chemical and even biological systems theoretically by taking into account the quantum mechanical effects, such as nonadiabatic transition, tunneling, and intereference. The simplest method to treat nonadiabatic dynamics is the TSH method introduced... 

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