The Molecular Hamiltonian
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We begin by considering the formulation of Hamiltonians for molecules both rigid and nonrigid. Although we are primarily concerned with molecular symmetry groups and their structure, an excursion into the theory of molecular dynamics is necessary for several reasons. First of all, while it is true that notions of molecular symmetry ultimately derive from the essential indistinguishability of identical micro-particles (nuclei), which is a non-dynamical concept, in practice our point of view is of necessity dynamics dependent. Thus, the feasibility of a particular transformation  — in other words, the extent to which a given symmetry is manifest in a given experiment — is obviously entirely contingent upon the forces acting within the molecule, for a finite experimental resolution/observation time. Conversely, since it is not possible at present to set up and solve nontrivial many-particle (nuclear or molecular) problems using a set of coordinates displaying all permutational symmetries in a simple fashion [2,3], the very way in which we approach the dynamics is directly determined by intuitive ideas concerning feasibility. One of the points we shall seek to emphasize throughout our work is the close relation between descriptions of symmetry and dynamics. Again, a knowledge of the transformation from cartesian to molecular (Born-Oppenheimer) coordinates used to rewrite the Hamiltonian is essential when we come to the important practical problem of determining the induced action of permutations of identical nuclei upon molecular wavefunctions.
KeywordsRigid Molecule Coriolis Coupling Nuclear Configuration Nonrigid Molecule Rotational Constraint
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