Accurate atomic correlation and total energies for correlation consistent effective core potentials II: Rb-Xe elements

Abstract

We employ correlation-consistent effective core potentials (ccECPs) to perform exact or nearly exact correlation and total energy calculations for the fifth-row elements (Rb-Xe). Total energies are calculated using various correlated methods: configuration interaction (CI), coupled-cluster (CC) up to perturbative quadruple excitations whenever feasible, and stochastic quantum Monte Carlo (QMC) approaches. In order to estimate the energy at the complete basis set (CBS) limit, the basis sets are constructed systematically through aug-cc-p(C)VnZ for each ccECP and further extrapolated to the CBS limit within the corresponding methods. Kinetic energies are evaluated at the FCI/CISD level to provide insights into the electron density and localization of the ccECPs. We also provide data sets for widely used diffusion Monte Carlo (DMC) to quantify fixed-node biases with single-reference trial wavefunctions. These comprehensive benchmarks validate the accuracy of ccECPs within the CC, CI, and QMC methodologies, thus providing accurate and tested valence-only Hamiltonians for many-body electronic structure calculations.

Figures (7)

• Figure 1: Fixed-node DMC errors ($\epsilon$) for ccECPs, as a percentage of the correlation energy using single-reference trial functions: $100\epsilon/|E_{corr}|$. Labels indicate the core sizes employed for each element set in the current study. T-moves were used in all the calculations.
• Figure 2: Fixed-node DMC errors ($\epsilon$) for ccECPs, as a percentage of the correlation energy using single-reference trial functions: $100\epsilon/|E_{corr}|$. Comparison is shown between $3d$ and $4d$ transition metals. Data for $3d$-TM are from our previous work acc_engI
• Figure 3: Fixed-node DMC errors ($\epsilon$) for ccECPs, as a percentage of the correlation energy using single-reference trial functions: $100\epsilon/|E_{corr}|$. This graph compares FN errors for different rows of p-block main group elements. For B and C atoms we include results with two-reference trial functions that eliminate the pronounced near-degeneracy effects. Data for $5p$ elements is from current work, the rest is shown for comparison using our previous work acc_engI.
• Figure 4: Fixed-node DMC errors ($\epsilon$) for ccECPs, as a percentage of the correlation energy using single-reference trial functions: $100\epsilon/|E_{corr}|$. All the elements belong to isovalent $np^2$ and $np^3$ configurations.
• Figure 5: Estimated kinetic energy of ccECPs as a percentage of the total energy, $100E_{kin}/|E_{total}|$.