Ground-state wave function nonlinear molecules

Qualitative information about molecular wave functions and properties can often be obtained from the symmetry of the molecule. By the symmetry of a molecule, we mean the symmetry of the framework formed by the nuclei held fixed in their equilibrium positions. (Our starting point for molecular quantum mechanics will be the Born-Oppenheimer approximation, which regards the nuclei as fixed when solving for the electronic wave function see Section 13.1.) The symmetry of a molecule can differ in different electronic states. For example, HCN is linear in its ground electronic state, but nonlinear in certain excited states. Unless otherwise specified, we shall be considering the symmetry of the ground electronic state. 

For diatomics and other linear molecules, only (4.1. IS) is satisfied, whereas, for nonlinear molecules, the wave function is an eigenfunction of the discrete symmetry operations R of the (finite) molecular point group. It should be emphasized that the enforcement of spin and point-group symmetries on approximate wave functions constitutes a restriction on the wave fuiKtion, which in variational ground-state calculations may raise the electronic energy above what would be obtained in an unrestricted treatmenL Symmetry restrictions are discussed in Section 4.4. 

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