Nearly diabatic potential surfaces

B. Research on Nearly Diabatic Potential Energy Surfaces... 

The sudden changes in the adiabatic wavefunctions near avoided crossings make it more convenient to use diabatic potential energy surfaces when simulating photodissociation dynamics. The adiabatic potentials, usually constructed from electronic structure calculation data, should therefore be transformed to diabatic potentials. The adiabatic-diabatic transformation yields diabatic states for which the derivative couplings above approximately vanish. The diabatic potential energy surfaces are obtained from the adiabatic ones by a unitary orthogonal transformation [22,23]... 

This model can be commonly used to describe the Cl of tm and nn electronic states of the pyrazine molecule. Near the bottom of the two potential surfaces, the two electronic states in the diabatic approximation are described by j(njt ) and The adiabatic approximation and b wiU be employed to describe the electronic states in the Cl region. Thus,... 

Diabatic surfaces were obtained for the neutral according to the scheme outlined in Sec. 5.2.1.2. For (3 < 80°, the 2 A surface approaches very close to the 3 A (both in C iv notation) and the diabatization can no longer be described by a two-state scheme. Also near j3 = 160° the 2 A and 3 A surfaces cross and again the simple phenomenological two-state diabatization scheme fails. We employ Gaussian functions to damp the computed coupling potential surface VniR) in these regions to make the diabatic curves coincide with the adiabatic. 

Let a crossing of diabatic surfaces of potential energy occur in a certain point R0. Taking into account only the linear expansion term of the difference between the energies of the diabatic states near the crossing point (the Landau-Zener model)... 

In order to test our methods, we consider a model of two quantum states coupled to a quasiclassical variable, suitable for describing the near resonant electron transfer of an alkali atom such as Na as it approaches a metal surface M at thermal energies. The two asymptotic potential energies correspond to a ground state of neutral components Na + M (state 1) and an excited state for ionic components Na" " + M (state 2), which cross at a short distance. The model consists of two diabatic surfaces and a coupling term given by [21,22]... 

Through the iteration steps, wave packet evolution can be realized on multiple electronie states. This process is represented schematically in Figure 8.2, where part of the wave packet initially in state 1 occurs in state 2 when moving near the crossing area of the potential energy surfaces under the diabatic representation. Thus, the final analysis using the time-independent part of the propagated wave packet can be implemented on each individual electronic state involved to obtain dynamical quantities. 

Divergent couplings ai e a nuisance for the computational treatment of the nuclear dynamics. In cases of exact or near degeneracy of electronic potential-energy surfaces it is therefore preferable to introduce an alternative electronic representation, the so-called diabatic (or quasi-diabatic) representation, which avoids singular coupling elements. The basic concept of diabatic states has been introduced in early descriptions of atomic collision processes and vibronic-coupling phenomena in molecular spectroscopy. ... 

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