Preliminary Assessment of the First-Order Density Matrix in Quantum Monte Carlo from Density Matrix Theory

• Published in: Journal of chemical theory and computation Vol. 19; no. 13; pp. 3861 - 3867
• Main Authors: Angelotti, Wagner F. D., Politi, José R. S., Custodio, Rogério
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 11-07-2023
• Subjects: Antisymmetry; Density; Electron spin; Electrons; Excitation; Matrix theory; Monte Carlo simulation; Quantum Electronic Structure; Wave functions
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.2c01174

The trial wave function commonly used in the quantum Monte Carlo method consists of the product of up-spin and down-spin Slater determinants, allowing accurate calculations of multielectronic properties, although it is not antisymmetric under the exchange of electrons with opposite spins. An alternative description that overcomes these limitations using the Nth-order density matrix was already presented. This study introduces two new strategies based on the Dirac–Fock density matrix for QMC that still fully preserve antisymmetry and electron indistinguishability. Simulations are performed for the ground and excited states of He, Li, and Be showing that the present formulation and the conventional separation of spins are appropriate for a correct description of these systems, except for singlet excited states of the He and Be atoms, and that a part of the antisymmetry (antiparallel spins) can be neglected.