Polyatomic systems total wave function

The total wave function ij/(Q, q, t) of the polyatomic system in question satisfies the time-dependent Schrodinger equation ([Pg.248]

If the electronic wave function (j>(Q, q) remains stationary during the time evolution of the entire polyatomic system, the expansion [Eq. (5)] of the total wave function reduces to a single term, i.e., the nuclear and electronic motion is... 

In polyatomic systems, there is a serious problem with the adiabatic basis (this is why the diabatie functions are preferred). As we will see later, the adiabatic electronic wave function is multivalued, and the corresponding rovibrational wave function, having to compensate for this (because the total wave function must be single-valued), also has to be multivalued. 

Thus, a unitary approach linking the quantum mechanical formalisms at the chemical bonding level has been extensively researched. It was recently established that for an adequate treatment in quantum space of the polyatomic combinations, the electronic density p(r) and not the historical wave function v /(rj,...,r ) stays as the main variable for a system with N electrons. It is so because quite contrary to the wave function, the electronic density is an experimentally detectable quantity defined in the real three-dimensional space, and not within a 3N Hilbert abstract space. It is also directly related with the total number of electrons in the concerned system through the functional relation Jp(r)dT = N. Therefore, the electronic density receives the central role within the newest quantum paradigm of matter, the Density Functional Theory (Walter Kohn as its father, the Nobel laureate in Chemistry for this theory in 1998). 

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