Electronic structure molecular potential energy surfaces

Molecular applications have thus far involved the calculation of the electronic structure and potential energy surfaces of negative ion "compound states" and of "diabatic states" in the continuous spectrum of polyelectronic diatomics and triatomics and of energies and partial widths with interchannel coupling of vibrational shape and predissociating resonances of diatomics. The same principles and methodologies can be applied to many more such cases. 

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

E. Kracka, T. H. Dunning, Jr., Advances in Molecular Electronic Structure Theory Calculation and Characterization of Molecular Potential Energy Surfaces T. H. Dunning, Jr. Ed., 129, JAI, Greenwich (1990). 

During the last decades, a large body of structural information has been derived from gas-electron diffraction studies. The corresponding results are nearly exclusively reported in the literature in terms of r distances, or the equivalent thermal average intemuclear distances, which are denoted r. The r distances are defined by the relation, r = r — If. Alternative methods for interpreting gas-electron diffraction data are possible, for example, in terms of -geometries5, but they are currently too complex to apply in routine stmctural analyses, because they require detailed information on the molecular potential energy surface which is not usually available. 

This expansion of the total electronic wavefunction is very compact, and provides a great deal of physical and chemical visuality. The spin-coupled structure (18) by itself reproduces with very reasonable accuracy all the features of a ground-state molecular potential energy surface. For example the spin-coupled function typically yields 85% of the observed binding energy, and equilibrium internuclear separations are accurate to 0.01 A. This function consequently dominates expansion (17) for all nuclear geometries. The various excited structures provide angular and other types of correlation as an extra quantitative refinement but do not alter the qualitative picture. 

At present, reaction path methods represent the best approach for utilizing ab initio electronic structure theory directly in chemical reaction dynamics. To study reaction dynamics we need to evaluate accurately the Born-Oppenheimer molecular potential energy surface. Our experience suggests that chemical reaction may take place within in a restricted range of molecular configurations (i.e., there is a defined mechanism for the reaction). Hence we may not need to know the PES everywhere. Reaction path methods provide a means of evaluating the PES for the most relevant molecular geometries and in a form that we can use directly in dynamical calculations. 

Fig. 2 The molecular structure of I—III and the representation of the potential energy surfaces for adiabatic to nonadiabatic electron transfer reactions...

---