We review a recent development in high-accuracy non-Born-Oppenheimer calculations of atomic and molecular systems in a basis of explicitly correlated Gaussian functions. Much of the recent progress in this area is due to the derivation and implementation of analytical gradients of the energy functional with respect to variational linear and non-linear parameters of the basis functions. This method has been used to obtain atomic and molecular ground and excited state energies and the corresponding wave functions with accuracy that exceeds previous calculations. Further, we have performed the first calculations of non-linear electrical properties of molecules without the Born-Oppenheimer approximation for systems with more than one electron. The results for the dipole moments of such systems as HD and LiH agree very well with experiment. After reviewing our non-Born-Oppenheimer results we will discuss ways this method can be extended to deal with larger molecular systems with and without an external perturbation.

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We present very high-accuracy fully nonadiabatic calculated values for the dipole moments for the ground states of LiH and LiD. These results were calculated via numerical differentiation of the energy obtained at different electric field strengths. The values for the energy were obtained from variational optimization with analytical gradients of the wave function expanded in a basis of explicitly correlated floating s-type Gaussian functions. The values obtained for LiH and LiD, 2.3140 and 2.3088 a.u., are nearly identical to those obtained by experiment.

We present non-Born-Oppenheimer quantum-mechanical calculations of the behavior of isolated molecules of the H2 isotopomer series in static electric fields. Some conceptual aspects of such calculations are discussed. The values for polarizabilities and hyperpolarizabilities of the H2 isotopomers which we present are the first ever fully nonadiabatic calculated values of these properties.

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