Dynamics non-adiabatic

The basis of the BOA for bond making/breaking at metal surfaces is the neglect of the coupling terms in eq. (2.3). These terms are small if (1) nuclear velocities are 

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The simplest approach to simulating non-adiabatic dynamics is by surface hopping [175. 176]. In its simplest fomi, the approach is as follows. One carries out classical simulations of the nuclear motion on a specific adiabatic electronic state (ground or excited) and at any given instant checks whether the diabatic potential associated with that electronic state is mtersectmg the diabatic potential on another electronic state. If it is, then a decision is made as to whedier a jump to the other adiabatic electronic state should be perfomied. 

Finally, semi-classical approaches to non-adiabatic dynamics have also been fomuilated and siiccessfLilly applied [167. 181]. In an especially transparent version of these approaches [167], one employs a mathematical trick which converts the non-adiabatic surfaces to a set of coupled oscillators the number of oscillators is the same as the number of electronic states. This mediod is also quite accurate, except drat the number of required trajectories grows with time, as in any semi-classical approach. 

In this chapter, we look at the techniques known as direct, or on-the-fly, molecular dynamics and their application to non-adiabatic processes in photochemistry. In contrast to standard techniques that require a predefined potential energy surface (PES) over which the nuclei move, the PES is provided here by explicit evaluation of the electronic wave function for the states of interest. This makes the method very general and powerful, particularly for the study of polyatomic systems where the calculation of a multidimensional potential function is an impossible task. For a recent review of standard non-adiabatic dynamics methods using analytical PES functions see [1]. 

The standard semiclassical methods are surface hopping and Ehrenfest dynamics (also known as the classical path (CP) method [197]), and they will be outlined below. More details and comparisons can be found in [30-32]. The multiple spawning method, based on Gaussian wavepacket propagation, is also outlined below. See [1] for further infomiation on both quantum and semiclassical non-adiabatic dynamics methods. 

The first study in which a full CASSCE treatment was used for the non-adiabatic dynamics of a polyatomic system was a study on a model of the retinal chromophore [86]. The cis-trans photoisomerization of retinal is the primary event in vision, but despite much study the mechanism for this process is still unclear. The minimal model for retinal is l-cis-CjH NHj, which had been studied in an earlier quantum chemisti7 study [230]. There, it had been established that a conical intersection exists between the Si and So states with the cis-trans defining torsion angle at approximately a = 80° (cis is at 0°). Two... 

Including 7]xx and Fx in Langevin-type classical dynamics has been termed molecular dynamics with electronic frictions (MDEF) [70], and has now been used in several simulations of non-adiabatic dynamics. Of course, the key unknown is the magnitude of the electronic frictions (since they also determine Fx). 

Fortunately, the same limiting conditions that validate the friction approximation can also be used with time-dependent density functional theory to give a theoretical description of rjxx. This expression was originally derived to describe vibrational damping of molecules adsorbed on surfaces [71]. It was later shown to also be applicable to any molecular or external coordinate and at any location on the PES, and thus more generally applicable to non-adiabatic dynamics at surfaces [68,72]. The expression is... 

Figure 3.25. Probability of a given energy loss into e-h pairs of magnitude eh vs. A/icM occurring in associative desorption of a diatomic from a metal surface from 3D non-adiabatic dynamics, (a) is for H2 associative desorption from Cu(lll), with ( ) 0.02 eV and (b) is N2 associative desorption from Ru(0001), with (A/i ch) 0.5 eV. From Ref. [68].

A significant limitation in both the adiabatic and non-adiabatic dynamics discussed above is that they are only 3D. Recently quasi-classical adiabatic dynamics calculations of S on a 6D DFT PES have shown that the predominant reason that 5 <<1... 

S. Mahapatra, Quantum non-adiabatic dynamics through conical intersections Spectroscopy to reactive scattering, Int. Rev. Phys. Chem. 23 (2006) 483. 

S. Bonella and D.F. Coker. A semi-classical limit for the mapping Hamiltonian approach to electronically non-adiabatic dynamics. J. Chem. Phys., 114 7778, 2001. 

Bonella, S., Coker, D.F. LAND-map, a linearized approach to non-adiabatic dynamics using the mapping formalism. J. Chem. Phys. 122 194102 (2005). 

We consider next the so-called Landau-Zener model that provides insight into non-adiabatic dynamics. The Landau-Zener model concerns the transition probability between two one-dimensional linear intersecting diabatic potentials... 

NON-ADIABATIC DYNAMICS IN THE O-I-H2 REACTION A TIME-INDEPENDENT QUANTUM MECHANICAL STUDY... 

The generation of active coordinates for non-adiabatic dynamics is related with our interest in laser-driven control. The optimal control of photochemical reactions is based on shaped laser pulses designed to generate photoproducts selectively. 

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