Deductive Molecular Mechanics: Bridging Quantum and Classical Models of Molecular Structure

Abstract

In the previous chapter we used the general scheme of electron variable separation to analyze current hybrid methods and suggest improvements to them. The situation in which we find ourselves is that the variable separation technique proposed in Chapter 1 can and should be used to sequentially construct hybrid methods by applying the GF form of the trial wave function for the complex molecular system. The prerequisite, for such an enterprise is that the orbitals of the system can be divided into complementary orthogonal carrier subspaces for the quantally and classically treated subsystems of the complex system. This prerequisite is, however, not taken for granted unless for some reason the required subspaces can be defined on symmetry grounds (as in the case of π-systems in the Hückel and other similar methods), and that is what we shall provide in this chapter. The way it is done here may seem too indirect. It is, however, necessary to follow this route. The key relation to be established is that between the geometry of the classically treated part of the complex system and the orbitals spanning the carrier space for its quantally treated part. Clearly the orbitals located on the frontier atoms are most sensitive to the geometry variations occurring in the classically treated subsystem right next to the frontier. However, to get this dependence we need a general theory relating forms of the orbitals to the geometries of the molecules. The required theory has to be constructed in terms of local quantities, i.e. hybrid orbitals rather than molecular orbitals, which is what we provide in this chapter.