Quantum Monte Carlo methods have recently made it possible to calculate the electronic structure of relatively large molecular systems with very high accuracy. These large systems range from positron complexes [NH₂,Ps] with ∼10 electrons to C₂₀ isomers with 120 electrons, to silicon crystal structures of 250 atoms and 1000 valence electrons. The techniques for such calculations and a sampling of applications are reviewed.

Accurate ground state energies comparable to or better than the best previous ab initio results can be obtained using the fixed-node quantum Monte Carlo (FN-DQMC) method. The residual energy, the nodal error due to the error in the nodal structure of a trial wave function, is examined in this study using nodal surfaces given by near HF-limit wave functions. The study is aimed at better understanding of the nodal error and the cancellation of nodal errors in calculating energy differences. Calculations have been carried out for the first-row hydrides LiH to FH and the corresponding atoms. The FN-DQMC ground state energies are among the lowest to date. The dissociation energies De have been calculated with accuracies of 0.5 kcal mol−1 or better. For all hydrides, the dissociation energies are consistent with experimental values. The fixed-node quantum Monte Carlo method can therefore offer a very straight-forward way to calculate highly accurate dissociation energies.

The accuracy of the fixed-node diffusion quantum Monte Carlo (FN-DQMC) method is compared to the coupled cluster method CCSD(T). For a test set of 20 small molecules and 17 reactions the electronic contribution to the reaction enthalpy is calculated with the FN-DQMC method using the nodes of a Slater determinant calculated at the HF/cc-pVTZ level. By comparison with reference reaction enthalpies the FN-DQMC method is shown to be more accurate than the CCSD(T)/cc-pVDZ method and almost as accurate as CCSD(T)/cc-pVTZ. The deviation from the reference data is comparable to the CCSD(T)/cc-pVTZ deviation, but, with only two exceptions, of opposite sign.