Reference-Density Hartree Screening for Gausslet Hamiltonians
Abstract
Gausslets are among the few electronic-structure bases that permit the four-index electron--electron interaction to be replaced by an accurate two-index integral diagonal approximation (IDA). Near a many-electron nucleus, however, the nuclear attraction and core-electron Hartree field are individually large and substantially cancel. Treating the first as a full finite-basis matrix while treating the second with IDA leaves an avoidable imbalance. We introduce reference-density Hartree screening: the Hartree field of a chosen reference density is represented accurately, and IDA is applied only to density fluctuations about it. Tests on He, Ne, atomic F, F2, and Cr2 show large reductions in direct Hartree errors, including transfer of fitted neutral-atom fields to molecules. For Cr2, atomic-core screening prevents the spurious HF collapse found with the unscreened q=5 and q=7 Hamiltonians, whereas finite-reference matching without screening does not. Screening leaves exchange and residual correlation unchanged. We therefore also introduce a low-rank one-particle correction that uses an accurate conventional Gaussian-basis Hartree--Fock calculation to match either occupied-space exchange information or the complete occupied Fock vectors. In F2 and Cr2, XHF reproduces the finite-reference energy and occupied Fock vectors to numerical precision and the selected states return after orbital perturbations. For Cr2, the corrected q=5 basis uses one quarter as many functions as the q=7 control while retaining sub-mHa mean-field accuracy. Screening provides the physical improvement to the direct field; the state-specific correction then restores the remaining accuracy of the Gaussian-basis mean-field reference.
Related
- Hartree-Fock Density-Matrix Renormalization Group for Very Long Chains
- The Evolution of Electronic Structure in Conjugated Molecules Revealed by Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory and Density-Based Analyses: II. Polyacenes
- Analytic Energy Gradients for Unrestricted Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory
- A basis-set-free reference for the exact exchange-energy density and functional development
- Computing electron overlap integrals for Gausslet orbitals on cubic lattices
BibTeX
@misc{white2026referencedensity,
title = {{Reference-Density Hartree Screening for Gausslet Hamiltonians}},
author = {Steven R. White},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01459},
eprint = {2609.01459},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01459},
}
RIS
TY - UNPB
TI - Reference-Density Hartree Screening for Gausslet Hamiltonians
AU - Steven R. White
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01459
UR - https://arxiv.org/abs/2609.01459
AB - Gausslets are among the few electronic-structure bases that permit the four-index electron--electron interaction to be replaced by an accurate two-index integral diagonal approximation (IDA). Near a many-electron nucleus, however, the nuclear attraction and core-electron Hartree field are individually large and substantially cancel. Treating the first as a full finite-basis matrix while treating the second with IDA leaves an avoidable imbalance. We introduce reference-density Hartree screening: the Hartree field of a chosen reference density is represented accurately, and IDA is applied only to density fluctuations about it. Tests on He, Ne, atomic F, F_2, and Cr_2 show large reductions in direct Hartree errors, including transfer of fitted neutral-atom fields to molecules. For Cr_2, atomic-core screening prevents the spurious HF collapse found with the unscreened q=5 and q=7 Hamiltonians, whereas finite-reference matching without screening does not. Screening leaves exchange and residual correlation unchanged. We therefore also introduce a low-rank one-particle correction that uses an accurate conventional Gaussian-basis Hartree--Fock calculation to match either occupied-space exchange information or the complete occupied Fock vectors. In F_2 and Cr_2, X_HF reproduces the finite-reference energy and occupied Fock vectors to numerical precision and the selected states return after orbital perturbations. For Cr_2, the corrected q=5 basis uses one quarter as many functions as the q=7 control while retaining sub-mHa mean-field accuracy. Screening provides the physical improvement to the direct field; the state-specific correction then restores the remaining accuracy of the Gaussian-basis mean-field reference.
ER -