Adiabatic Approximation and Its Accuracy

Abstract

In this chapter, the adiabatic theory for non-degenerate electronic states of diatomic molecules is reviewed and its possible refinements are discussed. Recent numerical results obtained for one- and two-electron molecules are used to discuss the accuracy of the adiabatic approximation by comparing the adiabatic results with the non-adiabatic or experimental ones, and also with those which result in the Born-Oppenheimer (clamped nuclei) approximation. The one- and two-electron molecules are the only real systems for which adiabatic calculations have been carried out. Results of these calculations may be exploited to get insight into the adiabatic approximation and its accuracy. For the dihydrogen cation accurate non-adiabatic calculations have been performed, and by comparing these results with those obtained in the adiabatic approach, one gets directly the magnitude of the non-adiabatic effects. For the H 2 molecule, the non-adiabatic calculations are significantly more difficult, and at present, no accurate results are available. However, in this case, accurate experimental data exist. Since the relativistic corrections, which are usually neglected, are known to be very small, one may get insight into the magnitude of the non-adiabatic effects by comparing the adiabatic results with the experimental ones. The adiabatic results can also be discussed from a different point of view. Since most molecular computations are carried out in the Born-Oppenheimer approximation, it is important to know how accurately it describes the vibronic states of molecules, and how different are the results obtained in the Born-Oppenheimer approximation from those resulting from the more consistent adiabatic theory.