Molecular Structure Theory without the Born–Oppenheimer Approximation: Rotationless Vibrational States of LiH

Low-lying rotationless states of the lithium hydride
molecule are
studied in the framework of the variational method without assuming
the Born–Oppenheimer (BO) approximation. Highly accurate solutions
to the six-particle (two nuclei and four electrons) Schrödinger
equation are obtained by means of expanding the wave functions of
the considered states in terms of many thousands of all-particle explicitly
correlated Gausssians. The basis functions are optimized independently
for each state using the analytic energy gradient with respect to
the nonlinear parameters. The non-BO wave functions obtained in the
calculations are used to evaluate the leading-order relativistic and
quantum electrodynamics energy corrections in the framework of the
perturbation theory. The geometric structure of the molecule in the
ground and excited states is discussed based on the analysis of the
nucleus–nucleus correlation functions. The non-BO energies
and structural parameters obtained of this work are compared with
the most accurate BO results currently available.