Sixty-nine points of the Born–Oppenheimer (BO) potential energy surface (PES) for the ground state of H3+ have been computed using explicitly correlated Gaussian wave functions with optimized nonlinear parameters. The calculated points have an absolute error of about 0.02 cm−1 (0.1 microhartree), i.e., they are by at least one order of magnitude more accurate than ever reported. Similarly accurate adiabatic and relativistic corrections have also been evaluated by means of the Born–Handy formula and by direct perturbation theory (DPT), respectively.

The Gaussian functions containing correlation factors of the type exp(−βrij2), 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.

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