Nuclear dynamics permutational symmetry

In this chapter, we discussed the permutational symmetry properties of the total molecular wave function and its various components under the exchange of identical particles. We started by noting that most nuclear dynamics treatments carried out so far neglect the interactions between the nuclear spin and the other nuclear and electronic degrees of freedom in the system Hamiltonian. Due to... 

Wigner rotation/adiabatic-to-diabatic transformation matrices, 92 Electronic structure theory, electron nuclear dynamics (END) structure and properties, 326-327 theoretical background, 324-325 time-dependent variational principle (TDVP), general nuclear dynamics, 334-337 Electronic wave function, permutational symmetry, 680-682 Electron nuclear dynamics (END) degenerate states chemistry, xii-xiii direct molecular dynamics, structure and properties, 327 molecular systems, 337-351 final-state analysis, 342-349 intramolecular electron transfer,... 

The quantum number v embodies the set of nuclear dynamic states with their labels (see below) and /c stands for the electronic quantum state. Thus, the nuclear wave function is always determined relatively to particular electronic states which, in turn, must be correlated to the (point) symmetries of the system. This stationary wave function may define, for particular cases, a class of geometric elements having an invariant center of mass. Actually, the (equivalence) class of configurations are those for which symmetry operations leave invariant this center of mass. This framework shares the discrete symmetries, such as permutation and space reflection invariances that are properties of the molecular eigenstates. There exists, then, a specific geometric framework pok- At this point, the expectation value ofH ,. taken with respect to the universal wave function is stationary to any geometric variation. 

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