Representation adiabatic

Single surface calculations with a vector potential in the adiabatic representation and two surface calculations in the diabatic representation with or without shifting the conical intersection from the origin are performed using Cartesian coordinates. As in the asymptotic region the two coordinates of the model represent a translational and a vibrational mode, respectively, the initial wave function for the ground state can be represented as. 

Single surface calculations with proper phase treatment in the adiabatic representation with shifted conical intersection has been performed in polai coordinates. For this calculation, the initial adiabatic wave function tad(9, 4 > o) is obtained by mapping t, to) ittlo polai space using the relations,... 

So far, we have treated the case n = /lo, which was termed the adiabatic representation. We will now consider the diabatic case where n is still a variable but o is constant as defined in Eq. (B.3). By multiplying Eq. (B.7) by j e I o) I arid integrating over the electronic coordinates, we get... 

II. n-ELECTRONIC STATE ADIABATIC REPRESENTATION A. Born-Huang Expansion... 

In the -electronic-state adiabatic representation involving real electronic wave functions, the skew-symmetiic first-derivative coupling vector mahix... 

Ignoring all nonadiabatic couplings to higher electronic states, the nuclear motion in a two-state elechonic manifold is described explicitly in the adiabatic representation by... 

In Chapter IV, Englman and Yahalom summarize studies of the last 15 years related to the Yang-Mills (YM) field that represents the interaction between a set of nuclear states in a molecular system as have been discussed in a series of articles and reviews by theoretical chemists and particle physicists. They then take as their starting point the theorem that when the electronic set is complete so that the Yang-Mills field intensity tensor vanishes and the field is a pure gauge, and extend it to obtain some new results. These studies throw light on the nature of the Yang-Mills fields in the molecular and other contexts, and on the interplay between diabatic and adiabatic representations. 

Adiabatic Representation.—Let w be any complete ortho-normal set of functions, variable in time, but not necessarily in accordance with Eq. (7-49). Substitute the expansion... 

If the hamiltonian is truly stationary, then the wx are the space-parts of the state function but if H is a function of t, the wx are not strictly state functions at all. Still, Eq. (7-65) defines a complete orthonormal set, each wx being time-dependent, and the quasi-eigenvalues Et will also be functions of t. It is clear on physical grounds, however, that to, will be an approximation to the true states if H varies sufficiently slowly. Hence the name, adiabatic representation. 

Having learned how states change in the adiabatic representation, we now turn briefly to examine the equation of motion of matrices. Clearly,... 

In this section we give the relations between the nonadiabatic coupling matrix elements in the quasi-diabatic and adiabatic representations. We do not obtain simple... 

Yarkony DR (2001) Nuclear dynamics near conical intersections in the adiabatic representation. I. The effects of local topography on interstate transition. J Chem Phys 114 2601... 

In collaboration with E.L. Sibert, we have learned to interpret these Franck-Con-don forbidden, pure torsional band intensities in S,-S0 absorption spectra quantitatively and thus place the key ml+ assignment on firm ground.27 The forbidden bands follow the selection rule Am = 3, so we need a perturbation of the form Vel cos 3a. Working in an adiabatic representation with the S0 and S, electronic states denoted by y0(g a) and /,( a) and the torsional states by m" and m, the electric dipole transition moment is,... 

---