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.