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A Monte Carlo method for evaluating multi-center two-electron-repulsionintegrals 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 spaceand on the use of efficient zero-variance Monte Carlo estimators. Quiteremarkably, it is shown that the high level of accuracy required ontwo-electron integrals to make Hartree-Fock (HF) and configuration interaction(CI) calculations feasible can be achieved. A first zero-variance estimator isbuilt by introducing a gaussian approximation of the orbitals and by evaluatingthe two-electron integrals using a correlated sampling scheme for thedifference between exact and approximate orbitals. A second one is based on theintroduction of a general coordinate transformation. The price to pay for thissimple and general Monte Carlo scheme is the high computational cost required.However, we argue that the great simplicity of the algorithm, itsembarrassingly parallel nature, its ideal adaptation to modern computationalplatforms and, most importantly, the possibility of using more compact andphysically meaningful basis sets make nevertheless the method attractive. HFand near full CI (FCI) calculations using Slater-type orbitals (STO) arereported for Be, CH4 and [H2N(CH)NH2]^+ (a simple model of cyanine). To thebest of our knowledge, our largest FCI calculation involving 18 activeelectrons distributed among 90 orbitals for the cyanine molecule, is the mostextensive molecular calculation performed so far using pure STO orbitals (nogaussian approximation, even for the challenging four-center two-electronintegrals).

journal of chemical physics online/the journal of chemical physics/journal of chemical physics

Evaluating two-electron-repulsion integrals over arbitrary orbitals  using Zero Variance Monte Carlo: Application to Full Configuration  Interaction calculations with Slater-type orbitals