Explicitly correlated Gaussian functions in variational calculations: the ground state of helium dimer

An explicitly correlated wave function is applied to variationally solve the Schrodinger equation within the Born-Oppenheimer approximation for the ground state of the helium dimer. The total electronic energy E as a function of the internuclear distance R is calculated for a wide range of R. An upper bound to the interaction energy curve is also presented. High accuracy of these calculations enables a derivative function d E/d R to be computed. At the equilibrium distance of 5·6 bohr the electronic energy is - 5·807 483 422 E h and the upper bound to the interaction energy equals - 10·95 K. To date, this is the most accurate variational total electronic energy curve of a four electron system.