Accurate Atomic Correlation Energies and Virial Trends for Correlation-Consistent Effective Core Potentials III: Quantitative Separation of Fixed-Node Biases and Localization Errors in Cs-Rn
Abstract
Atomic benchmarks for sixth-period elements (Cs-Rn) are established to sub-millihartree precision under correlation-consistent effective core potentials (ccECPs) using coupled-cluster [up to CCSDT(Q)] and full configuration interaction methods. These references systematically characterize electron correlation, potential-to-kinetic energy partitioning, and combined fixed-node and locality biases (η) in fixed-node diffusion Monte Carlo (FNDMC). The valence kinetic-to-total energy ratio (ξ) departs from the non-relativistic all-electron Coulombic virial limit (ξ=100%), remaining confined between 25.8% and 37.6%. The Un-pseudizing of semi-core shells decreases ξ as the attractive potential energy deepens faster than the accompanying kinetic energy escalates. Periodic trends in ξ reveal a 5d plateau near 34%, with a lanthanide-contraction-driven maximum in Hf, followed by a sharp decline across the 6p block. In FNDMC, η escalates rapidly at the onset of group-1/2 and toward the 6p closed-shell limit, peaking at 5.42% in Rn. Although fixed-node errors dominate η in most sixth-period elements, a locality error inversion occurs in Bi, with Pb exhibiting comparable error magnitudes. Furthermore, core-valence partitioning alters trial wavefunction nodal topology: in Tl, three-dimensional nodal cross-sections reveal isolated toroidal domains that confine walkers. This work completes the periodic-table-wide ccECP database from H to Rn, revealing how pseudopotential choices govern energy partitioning, nodal topology, and the balance between fixed-node and localization errors.
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BibTeX
@misc{madany2026accurate,
title = {{Accurate Atomic Correlation Energies and Virial Trends for Correlation-Consistent Effective Core Potentials III: Quantitative Separation of Fixed-Node Biases and Localization Errors in Cs-Rn}},
author = {Omar Madany and Lubos Mitas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24450},
eprint = {2610.24450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24450},
}
RIS
TY - UNPB
TI - Accurate Atomic Correlation Energies and Virial Trends for Correlation-Consistent Effective Core Potentials III: Quantitative Separation of Fixed-Node Biases and Localization Errors in Cs-Rn
AU - Omar Madany
AU - Lubos Mitas
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24450
UR - https://arxiv.org/abs/2610.24450
AB - Atomic benchmarks for sixth-period elements (Cs-Rn) are established to sub-millihartree precision under correlation-consistent effective core potentials (ccECPs) using coupled-cluster [up to CCSDT(Q)] and full configuration interaction methods. These references systematically characterize electron correlation, potential-to-kinetic energy partitioning, and combined fixed-node and locality biases (η) in fixed-node diffusion Monte Carlo (FNDMC). The valence kinetic-to-total energy ratio (ξ) departs from the non-relativistic all-electron Coulombic virial limit (ξ=100%), remaining confined between 25.8% and 37.6%. The Un-pseudizing of semi-core shells decreases ξ as the attractive potential energy deepens faster than the accompanying kinetic energy escalates. Periodic trends in ξ reveal a 5d plateau near 34%, with a lanthanide-contraction-driven maximum in Hf, followed by a sharp decline across the 6p block. In FNDMC, η escalates rapidly at the onset of group-1/2 and toward the 6p closed-shell limit, peaking at 5.42% in Rn. Although fixed-node errors dominate η in most sixth-period elements, a locality error inversion occurs in Bi, with Pb exhibiting comparable error magnitudes. Furthermore, core-valence partitioning alters trial wavefunction nodal topology: in Tl, three-dimensional nodal cross-sections reveal isolated toroidal domains that confine walkers. This work completes the periodic-table-wide ccECP database from H to Rn, revealing how pseudopotential choices govern energy partitioning, nodal topology, and the balance between fixed-node and localization errors.
ER -