Fixed-node diffusion Monte Carlo method for lithium systems

We study lithium systems over a range of a number of atoms, specifically atomic anion, dimer, metallic cluster, and body-centered-cubic crystal, using the fixed-node diffusion Monte Carlo method. The focus is on analysis of the fixed-node errors of each system, and for that purpose we test several orbital sets in order to provide the most accurate nodal hypersurfaces. The calculations include both core and valence electrons in order to avoid any possible impact by pseudopotentials. To quantify the fixed-node errors, we compare our results to other highly accurate calculations, and wherever available, to experimental observations. The results for these Li systems show that the fixed-node diffusion Monte Carlo method achieves accurate total energies, recovers $96–99\%$ of the correlation energy, and estimates binding energies with errors bounded by $0.1 \mathrm{eV}/\mathrm{at}$.

Figure 1

Schematic depiction of the $D_{2h} {\mathrm{Li}}_4$ parameters.

Figure 2

The DMC energy extrapolated to $\tau =0$ for a ${\mathrm{Li}}_4$ molecule. Both wave functions originate from the same configuration-interaction CI-SD calculation, but they have had the determinant weights and Jastrow coefficients reoptimized with different assumed cutoff distances in the Jastrow, as described in the text.

Figure 3

QMC results for $S\left(k\right)$ for several sizes of the simulation cell. Squares denote results from the 54-atom simulation; circles, 16-atom simulation; and triangles, eight-atom simulation. The curves shown are fit to the 54-atom data with the function $S\left(k\right)=exp\left\{-a{k}^b\right\}$. For small $k$, RPA predicts $b=2$. For the fits shown, the $b$ parameter for VMC is 1.45; DMC with the mixed estimator, 1.67; and the DMC extrapolated estimator, 1.99.

Figure 4

The total energy per atom for twist averaged FN-DMC with and without the finite-size error (FSE) corrections [56] plotted against the inverse of the number of atoms in the cell. The data are fit with an extrapolation to infinite bulk size. The infinite bulk total energy per atom of $-7.5371$ Ha for the FN-DMC and $-7.5369$ for the FN-DMC with FSE corrections. These values are within error bars of each other. The statistical error bars on the data are smaller than the size of the plot symbol, thus they are not visible.