Adiabatic electronic states

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, in brief, we demonstrate the influence of the upper adiabatic electronic state(s) on the ground state due to the presence of a Cl between two or more than two adiabatic potential energy surfaces. Considering the HLH phase, we present the extended BO equations for a quasi-JT model and for an A -1- B2 type reactive system, that is, the geometric phase (GP) effect has been inhoduced either by including a vector potential in the system Hamiltonian or... 

Here, the integrand is the off-diagonal gradient mahix element between adiabatic electronic states,... 

V is the derivative with respect to R.) We stress that in this formalism, I and J denote the complete adiabatic electronic state, and not a component thereof. Both /) and y) contain the nuclear coordinates, designated by R, as parameters. The above line integral was used and elaborated in calculations of nuclear dynamics on potential surfaces by several authors [273,283,288-301]. (For an extended discussion of this and related matters the reviews of Sidis [48] and Pacher et al. [49] are especially infonnative.)... 

This choice of elements for the u, (qx,) matrix will diabatize the adiabatic electronic states i andj while leaving the remaining states unaltered. 

By using the fact that for a finite number of adiabatic electronic states n, we choose a U(qx) that satisfies Eq. (47) [rather than Eq. (42) that has no solution], Eq. (35) now reduces to... 

In the two-adiabatic-electronic-state Bom-Huang description of the total orbital wave function, we wish to solve the corresponding nuclear motion Schrodinger equation in the diabatic representation... 

The matrix of vectors F is thus the defining quantity, and is called the non-adiabatic coupling matrix. It gives the strength (and direction) of the coupling between the nuclear functions associated with the adiabatic electronic states. 

The remaining combinations vanish for symmetry reasons [the operator transforms according to B (A") hreducible representation]. The nonvanishing of the off-diagonal matrix element fl+ is responsible for the coupling of the adiabatic electronic states. 

Now, we discuss briefly the situation when one or both of the adiabatic electronic states has/have nonlinear equilibrium geometry. In Figures 6 and 7 we show two characteristic examples, the state of BH2 and NH2, respectively. The BH2 potential curves are the result of ab initio calculations of the present authors [33,34], and those for NH2 are taken from [25]. 

As mentioned at the end of Section II.C, the presence of the W ad(Rx) Vr. xad(R 0 term in the w-adiabatic-electronic-state Schrodinger equation (15) introduces numerical inefficiencies in its solution, even if none of the elements... 

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