Diabatic and adiabatic representation

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

In what follows we introduce the model Hamiltonian using both diabatic and adiabatic representations. Adopting diabatic electronic basis states /j ), the molecular model Hamiltonian can be written as [162, 163]... 

As long as no approximation is introduced, it is clear that the equations of motion are equivalent in the diabatic and adiabatic representations. This is no longer true, however, once the classical-path approximation is employed the resulting classical-path equations of motion in the adiabatic representation are... 

Smith, F. T. Diabatic and adiabatic representations for atomic collision problems, Phys.Rev., 179(1969)111-123. 

Symmetry properties of the nuclear wavefunction are different in the diabatic and adiabatic representations. The pair of adiabatic electronic states (see (1)) belong to the Al and A2 irreducible representations of the double group of S3. The diabatic states obtained from the adiabatic ones by applying the U matrix form a basis for the two dimensional irreducible representation E of S3. For quartet nuclear spin states, the electronuclear wavefunction, nuclear spin part excluded, must belong to the A2 irreducible representation. This requires the nuclear wavefunction (without nuclear spin) to be of the same E symmetry as the electronic one, because of the identity E x E = Ai + A2 + E. For doublet spin states, the E electronuclear wave-function (nuclear spin excluded) is obtained with an Ai or A2 nuclear wavefunction, combined with the E electronic ones. 

V. Aquilanti, G. Grossi, and A. Lagana, Hyperspherical diabatic and adiabatic representations for chemical reactions. Chem. Phys. Lett, 93 174-178,1982. 

Fig. 14.4 A schematic display of a curve crossing reaction in the diabatic and adiabatic representations. See Section 2.4 for further details. (Note This is same as Fig. 2.3).

The second term not considered in the Born-Oppenheimer approximation is the second derivative. It is often neglected in the calculation of nonradiative lifetimes. The knowledge of the diabatic and adiabatic representations, as well as the rotation matrix, readily gives estimates of the second derivative matrix elements. It was shown for LiH [28,29] that this second term is not negligible compared to the first... 

Delos, J.B. and Thorson, W.R. (1972) Studies of the potential-curve-crossing problem. II. General theory and a model for dose crossings. General theory and a model for dose crossings. Phys. Rev., A., 6, 728 Delos, J.B. and Thorson, W.R. (1975) Diabatic and adiabatic representations for atomic collision processes. J. Chem. Phys.,... 

TSH calculations were done using the fewest switches method 13). )etails are similar to work that was described earlier (77), except that here we have considered calculations in both the diabatic and adiabatic representations. A time step of 1 atomic unit was used for all calculations, and 2000 trajectories were used to determine the reaction probabilities at each energy. Variation of the results with respect to the numerical parameters was within statistical uncertainty. We found the diabatic results to be significantly less sensitive to time step dian the adiabatic results. 

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