Numerical coupled Hartree-Fock study of the total (electronic and nuclear) parallel polarizability and hyperpolarizability for the FH, H₂ ⁺, HD⁺, and D₂⁺ molecules

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 β_zzz exceed the electronic component and change the sign of the total hyperpolarizability. γ_zzzz is similarly increased by an order of magnitude. It is also shown that a Born-Oppenheimer treatment of H₂⁺ for Y_zzzz is in perfect agreement with a recent fully nonadiabatic three particle solution.