Many-electron explicitly correlated Gaussian functions. I. General theory and test results

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Abstract
The Gaussian functions containing correlation factors of the type exp(−βr ij 2), employed so far in variational calculations of two‐electron atoms and molecules are generalized for many‐electron systems. Explicit formulas for necessary one‐, two‐, three‐, and four‐electron integrals over s‐type correlated Gaussians are given. Preliminary computations for the H3 and LiH molecules yield significantly lower energy values than all previously published variational results.