Exponentially correlated Gaussian functions in variational calculations: Energy expectation values in the ground state helium dimer

Exponentially correlated Gaussian wave functions have been employed to compute expectation values of energy operators in the electronic ground state of the helium dimer. The expectation values are calculated for a wide range of internuclear distances, 0.0 less than or equal to R/a(0)less than or equal to 15.0, with particular regard to small R. The results include the total and the interaction energy, the energy derivative with respect to R, and components of the kinetic and the Coulomb energy. The variation of the expectation values of the kinetic and Coulomb energy yields information on the electron cloud dynamics upon the geometry change. The electronic energy and its derivative are analyzed with respect to rigorous theoretical constrains which they should fulfill. The Thirring upper bound is evaluated from an accurate electrostatic potential computed for the beryllium atom. This potential is also used to check the accuracy of the united atom perturbation theory. Smooth transition of all the expectation values to the limit of united atom verifies the validity of the Born-Oppenheimer approximation in large energies. As the wave function used is presently the most accurate variational wave function obtained for the He-2, the results reported may serve as benchmarks. (C) 1999 American Institute of Physics. [S0021-9606(99)30316-0].