All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe

We report all-electron variational and diffusion quantum Monte Carlo (VMC and DMC) calculations for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculations were performed using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number $Z$, but the DMC calculations are tractable and well behaved in all cases. We discuss the scaling of the computational cost of DMC calculations with $Z$.

Figure 1

The correlation energy $E_{\mathrm{c}}$ as a function of atomic number $Z$. Crosses: “exact” values. Diamonds: DMC values. The dotted line is a fit to the “exact” values giving $E_{\mathrm{c}}\propto Z^{1.33}$, while the dashed line is a fit to the DMC data giving $E_{\mathrm{c}}\propto Z^{1.26}$.

Figure 2

The logarithm of the CPU time required to obtain a fixed error bar in the energy versus $\ln \left(Z\right)$ for our DMC calculations. The dashed line shows the fitted scaling of $Z^{5.47}$. The CPU times are measured in seconds.