  A Monte Carlo method for evaluating multi-center two-electron-repulsion
integrals over any type of orbitals (Slater, Sturmian, finite-range, numerical,
etc.) is presented. The approach is based on a simple and universal
(orbital-independent) gaussian sampling of the two-electron configuration space
and on the use of efficient zero-variance Monte Carlo estimators. Quite
remarkably, it is shown that the high level of accuracy required on
two-electron integrals to make Hartree-Fock (HF) and configuration interaction
(CI) calculations feasible can be achieved. A first zero-variance estimator is
built by introducing a gaussian approximation of the orbitals and by evaluating
the two-electron integrals using a correlated sampling scheme for the
difference between exact and approximate orbitals. A second one is based on the
introduction of a general coordinate transformation. The price to pay for this
simple and general Monte Carlo scheme is the high computational cost required.
However, we argue that the great simplicity of the algorithm, its
embarrassingly parallel nature, its ideal adaptation to modern computational
platforms and, most importantly, the possibility of using more compact and
physically meaningful basis sets make nevertheless the method attractive. HF
and near full CI (FCI) calculations using Slater-type orbitals (STO) are
reported for Be, CH4 and [H2N(CH)NH2]^+ (a simple model of cyanine). To the
best of our knowledge, our largest FCI calculation involving 18 active
electrons distributed among 90 orbitals for the cyanine molecule, is the most
extensive molecular calculation performed so far using pure STO orbitals (no
gaussian approximation, even for the challenging four-center two-electron
integrals).
