Rovibronic/vibronic wave functions

IT. Total Molecular Wave Functdon TIT. Group Theoretical Considerations TV. Permutational Symmetry of Total Wave Function V. Permutational Symmetry of Nuclear Spin Function VT. Permutational Symmetry of Electronic Wave Function VIT. Permutational Symmetry of Rovibronic and Vibronic Wave Functions VIIT. Permutational Symmetry of Rotational Wave Function IX. Permutational Symmetry of Vibrational Wave Function X. Case Studies Lis and Other Systems... 

VII. PERMUTATIONAL SYMMETRY OF ROVIBRONIC AND VIBRONIC WAVE FUNCTIONS... 

VII. Permutational Symmetry of Rovibronic and Vibronic Wave Functions... 

The complete wave function of a molecule is called the rovibronic wave function. In the simplest approximation, the rovibronic function is a product of rotational, vibrational, and electronic functions. For certain applications, the rotational motion is first neglected, and the vibrational and electronic motions are treated together. The rotational motion is then taken into account. The wave function for electronic and vibrational motion is called the vibronic wave function. Just as we separately classified the electronic and vibrational wave functions according to their symmetries, we can do the same for the vibronic functions. In the simplest approximation, the vibronic wave function is a product of electronic and vibrational wave functions, and we can thus readily determine its symmetry. For example, if the electronic state is an e2 state and the vibrational state is a state, then the vibronic wave function is... 

As discussed in preceding sections, FI and have nuclear spin 5, which may have drastic consequences on the vibrational spectra of the corresponding trimeric species. In fact, the nuclear spin functions can only have A, (quartet state) and E (doublet) symmetries. Since the total wave function must be antisymmetric, Ai rovibronic states are therefore not allowed. Thus, for 7 = 0, only resonance states of A2 and E symmetries exist, with calculated states of Ai symmetry being purely mathematical states. Similarly, only -symmetric pseudobound states are allowed for 7 = 0. Indeed, even when vibronic coupling is taken into account, only A and E vibronic states have physical significance. Table XVII-XIX summarize the symmetry properties of the wave functions for H3 and its isotopomers. 

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