Quantum Monte Carlo calculation of the singlet-triplet splitting in methylene

The fixed-node quantum Monte Carlo (QMC) method is used to calculate the total energy of CH₂ in the ³B₁ and ¹A₁ states. For both states, the best QMC variationally bounded energies lie more than 15 kcal/mol (0.024 h) below the best previous variational calculations. Subtracting these energies to obtain the singlet-triplet splitting yields T_e=9.4±2.2 kcal/mol. Adjusting for zero-point energies and relativistic effects, we obtain T ₀=8.9±2.2 kcal/mol. This result is in excellent agreement with the recent direct measurements of McKellar et al. of T₀=9. 05±0.06 kcal/mol, and of Leopold et al. of ∼9 kcal/mol, as well as with recent threoretical investigations which indicate an energy gap of 9-11 kcal/mol. We summarize the QMC method, discuss a possible scheme for iteratively correcting the procedure, and note that the present results were obtained using only single determinant functions for both states, in contrast to conventional ab initio approaches which must use at least two configurations to properly describe the singlet state.