Improved quantum Monte Carlo calculation of the ground-state energy of the hydrogen molecule

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Abstract
We report an improved Green’s function quantum Monte Carlo calculation of the nonrelativistic ground‐state energy of the hydrogen molecule, without the use of the Born–Oppenheimer or any other adiabatic approximations. A more accurate trial function for importance sampling and the use of the exact cancellation method combine to yield an energy which is a factor of 10 more accurate than that of previous quantum Monte Carlo calculations. The energy is less accurate than that of recently improved analytic variational calculations. The calculated energy is −1.164 0239 ±0.000 0009 hartree. Expressed as the dissociation energy and corrected for relativistic and radiative effects, the result is 36 117.84±0.20 cm−1, a value in agreement with the most recent experimental value 36 118.11±0.08 cm−1 obtained by Balakrishnan et al.