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

ABSTRACT

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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Density functional theory
• quadrupole moment
• ethylene
• bifuran
• pure-sampling quantum monte carlo

Acknowledgments

The authors thank Compute Canada for giving us access to their high-performance computing facilities at SHARCNET. We gratefully acknowledge Ajhit Perera's sharing with us the results of his unpublished CCSD(T) calculations on ethylene. Valuable guidance for this work was provided by Ulrike Salzner. Stuart Rothstein acknowledges hospitality afforded to him when a visitor to Hebrew and Bilkent Universities and a participant at the 58th Sanibel Symposium. Roi Baer gratefully acknowledges the support from the US-Israel Binational Science Foundation [grant number BSF-2015687].

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Stuart M. Rothstein http://orcid.org/0000-0002-0583-8625

Roi Baer http://orcid.org/0000-0001-8432-1925