Electronic state adiabatic representation

In coordinate representation, there exists alternative base representations, adiabatic and diabatic. Both representations are equivalent if the basis are complete. For a thorough discussion on adiabatic-diabatic electronic state transformations the reader is referred to the work by Baer [49, 50], see also the work by Chapuisat et al. [51] In this... 

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... 

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... 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

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. 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

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. 

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,... 

In the previous section, we discussed the calculation of the PESs needed in Eq. (2.16a) as well as the nonadiabatic coupling terms of Eqs. (2.16b) and (2.16c). We have noted that in the diabatic representation the off-diagonal elements of Eq. (2.16a) are responsible for the coupling between electronic states while Dp and Gp vanish. In the adiabatic representation the opposite is true The off-diagonal elements of Eq. (2.16a) vanish while Du and Gp do not. In this representation, our calculation of the nonadiabatic coupling is approximate because we assume that Gp is negligible and we make an approximation in the calculation of Dp. (See end of Section n.A for more details.)... 

Coupling matrices, electronic state adiabatic representation ... 

Single-valued potential, adiabatic-to-diabatic transformation matrix, non-adiabatic coupling, 49-50 topological matrix, 50-53 Skew symmetric matrix, electronic states adiabatic representation, 290-291 adiabatic-to-diabatic transformation, two-state system, 302-309 Slater determinants ... 

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