Breakdown of the Born-Oppenheimer Approximation in the Calculation of Electric Hyperpolarizabilities

For the first time a nonadiabatic (all-particle) calculation has been carried out for the electric polarizabilities and hyperpolarizabilities of H₂⁺, HD⁺, and D₂⁺ in their lowest rovibronic states. The value of the hyperpolarizability γ is dramatically different from that which would be assumed from calculations based on the Born-Oppenheimer approximation unless account is taken of a vibrational contribution which (unlike its counterpart for the α polarizability) is nonzero even for a homonuclear diatomic molecule. For H₂⁺ we find that αzz=5.827 a.u. and γzzz=2.2×10³ a.u.