This article was published online on 30 August 2012. An error was subsequently identified. This notice is included in the online and print version to indicate that both have been corrected on 7 September 2012.
Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo†
Article first published online: 30 AUG 2012
Copyright © 2012 Wiley Periodicals, Inc.
International Journal of Quantum Chemistry
Volume 113, Issue 2, pages 155–160, 15 January 2013
How to Cite
Delle Site, L., Ghiringhelli, L. M. and Ceperley, D. M. (2013), Electronic energy functionals: Levy–Lieb principle within the ground state path integral quantum Monte Carlo. Int. J. Quantum Chem., 113: 155–160. doi: 10.1002/qua.24321
- Issue published online: 4 DEC 2012
- Article first published online: 30 AUG 2012
- Manuscript Accepted: 3 AUG 2012
- Manuscript Received: 2 AUG 2012
- Manuscript Revised: 2 AUG 2012
- Heisenberg Stipendium of the Deutsche Forschungsgemeinschaft (DFG). Grant Number: DE 1140/5-1
- density functional theory;
- ground state path integral quantum Monte Carlo;
- kinetic energy functional;
- Levy–Lieb constrained search;
- advanced Monte Carlo
We propose a theoretical/computational protocol based on the use of the Ground State Path Integral Quantum Monte Carlo for the calculation of the kinetic and Coulomb energy density for a system of N interacting electrons in an external potential. The idea is based on the derivation of the energy densities via the (N − 1)-conditional probability density within the framework of the Levy–Lieb constrained search principle. The consequences for the development of energy functionals within the context of density functional theory are discussed. We propose also the possibility of going beyond the energy densities and extend this idea to a computational procedure where the (N − 1)-conditional probability is an implicit functional of the electron density, independently from the external potential. In principle, such a procedure paves the way for an on-the-fly determination of the energy functional for any system. © 2012 Wiley Periodicals, Inc.