Numerical coupled Hartree–Fock study of the total (electronic and nuclear) parallel polarizability and hyperpolarizability for the FH, H+2, HD+, and D+2 molecules

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Abstract
Polarizabilities and hyperpolarizabilities of molecules have both electronic and vibrational contributions. The latter can be important in experimental determinations involving static electric fields, as in the Kerr effect. This paper reports purely numerical coupled Hartree–Fock calculations for the electronic states of FH. Electronic energy surfaces obtained for different electric field strengths are then used to solve, numerically, the nuclear equation for several vibrational states. The vibrational contributions to βzzz exceed the electronic component and change the sign of the total hyperpolarizability. γzzzz is similarly increased by an order of magnitude. It is also shown that a Born–Oppenheimer treatment of H+2 for γzzzz is in perfect agreement with a recent fully nonadiabatic three particle solution.