Spectroscopy and Selection Rules
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There are several incentives for determining conditions under which quantities of the form (Φ1, OΨ2) are equal to zero. Here Ψ1 and Ψ2 are wave functions and O is an operator. In the LCAO (linear combination of atomic orbitals) approximation to molecular orbitals, two basis functions Ψ1 and Ψ2 do not “mix,” if (Ψ1, HΨ2) = (Ψ1, Ψ2) = 0. Thus a criterion for the vanishing of the matrix elements H12 and S12 can simplify the interpretation and calculation of molecular orbitals.
KeywordsMatrix Element Direct Product Selection Rule Vibrational Energy Magnetic Dipole Moment
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