Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran

We perform all-electron, pure-sampling quantum Monte Carlo (QMC) calculations on ethylene and bifuran molecules. The orbitals used for importance sampling with a single Slater determinant are generated from Hartree-Fock and density functional theory (DFT). Their fixed-node energy provides an upper bound to the exact energy. The best performing density functionals for ethylene are BP86 and M06, which account for 99% of the electron correlation energy. Sampling from the π-electron distribution with these orbitals yields a quadrupole moment comparable to coupled cluster CCSD(T) calculations. However, these, and all other density functionals, fail to agree with CCSD(T) while sampling from electron density in the plane of the molecule. For bifuran, as well as ethylene, a correlation is seen between the fixed-node energy and deviance of the QMC quadrupole moment estimates from those calculated by DFT. This suggests that proximity of DFT and QMC densities correlates with the quality of the exchange nodes of the DFT wave function for both systems.