Systematic reduction of sign errors in many-body calculations of atoms and molecules

M. Bajdich,1 M. L. Tiago,1 R. Q. Hood,2 P. R. C. Kent,3 F. A. Reboredo1

1Materials Science and Technology Division, Oak Ridge National Laboratory
Condensed Matter and Materials Division, Lawrence Livermore National Laboratory
Center for Nanophase Materials Sciences, Oak Ridge National Laboratory


We have developed a new systematically convergeable algorithm – Self-Healing Diffusion Quantum Monte Carlo - for predicting the electronic structure of atoms and molecules. In the first demonstration of this algorithm we have shown that it can readily treat systems as large as a carbon fullerene molecule with 20 atoms and modest computational effort. This result suggests that the new method will be fully capable of obtaining previously unavailable benchmark accuracy results for nanoscale systems. These results will guide cheaper but less accurate computational methods, such as density functional theory, significantly improving the robustness of theoretical predictions.


Our new method is a significant extension of the well-established Diffusion Quantum Monte Carlo method. In this quantum mechanical and wavefunction-based approach, the energy and other properties of a molecule or solid-state system are obtained to a very high accuracy. However, in the traditional approach, a variational error is introduced: in order to make the computation scale non-exponentially, the locations where the wavefunction are zero are approximated and chosen in advance. This is the so-called “fixed node” approximation and a manifestation of the famous Fermion sign problem in quantum mechanics. In the new method, the Fermion sign error is systematically reduced via a new optimization process and a robust theory of Fermion nodes. This optimization process, called “self-healing” because information from an initially poor wavefunction is used to obtain information about the more optimal solution, is the first time that the Fermion sign problem has been systematically reduced entirely within Diffusion Monte Carlo. We were able to obtain converged solutions starting from random initial wavefunctions, indicating that the method is very robust and likely to be applicable where other electronic structure methods fail. The Self-Healing Diffusion Monte Carlo (SHDMC) approach potentially removes the most significant source of error in, e.g., calculations of many materials and reactions involved in catalysis, energy conversion, and energy storage. Popular methods such as density functional theory introduce uncontrolled errors; SHDMC can provide benchmark results, aiding in method development and improving the overall robustness of electronic structure calculations.


Computations were performed at NERSC (DE-AC02- 05CH11231) and NCCS (DE-AC05-00OR22725). Research was supported by U.S. DOE BES Division of Materials Sciences & Engineering (FAR, MLT) and ORNL LDRD program (MB). The Center for Nanophase Materials Sciences research was sponsored by the U. S. DOE Division of Scientific User Facilities (PRCK). Research at LLNL was performed under U.S. DOE contract DE-AC52-07NA27344 (RQH).


“Systematic reduction of sign errors in many-body calculations of atoms and molecules,” M. Bajdich, M. L.Tiago, R. Q. Hood, P. R. C. Kent, and F.A. Reboredo. Phys. Rev. Lett. 104, 193001 (2010), doi: 10.1103/PhysRevLett.104.193001