This work investigates the accuracy of real-space quantum Monte Carlo (QMC) methods for calculating molecular geometries. We present the equilibrium bond lengths of a test set of 30 diatomic molecules calculated using variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) methods. The effect of different trial wavefunctions is investigated using single determinants constructed from Hartree-Fock (HF) and Density Functional Theory (DFT) orbitals with LDA, PBE, and B3LYP functionals, as well as small multi-configurational self-consistent field (MCSCF) multi-determinant expansions. When compared to experimental geometries, all DMC methods exhibit smaller mean-absolute deviations (MADs) than those given by HF, DFT, and MCSCF. The most accurate MAD of 3 ± 2 × 10(-3) Å is achieved using DMC with a small multi-determinant expansion. However, the more computationally efficient multi-determinant VMC method has a similar MAD of only 4.0 ± 0.9 × 10(-3) Å, suggesting that QMC forces calculated from the relatively simple VMC algorithm may often be sufficient for accurate molecular geometries.
We present an efficient scheme for representing many-body wave functions in quantum Monte Carlo (QMC) calculations. The scheme is based on
B splines (blip functions), which consist of localized cubic splines centered on the points of a regular grid. We show that blip functions are unbiased, systematically improvable, and conveniently obtained from any standard plane-wave density functional theory (PW-DFT) code, and therefore provide a convenient and natural interface between PW-DFT and QMC calculations. We present tests on a 16-atom system of
Si in the $\ensuremath{\beta}$-tin structure, and on 2- and 8-atom systems of
MgO in the
NaCl structure. We show that already with such small systems the speed-up of blip functions with respect to plane waves is between one and two order of magnitudes, without compromising the accuracy.
Abstract It is difficult to imagine that density functional theory (DFT) could be useful in improving quantum Monte Carlo methods, but it is easy to imagine that QMC could be useful in improving density functional methods. Since QMC can produce accurate wavefunctions and since wavefunctions lead to all other properties one should be able, in principle, to use QMC to predict the exchangecorrelation energy functional Exc[n(r)], the key (unknown) quantity required in DFT. In practice, that is not so easy, but this paper shows how QMC can take steps in that direction by providing insights gained from comparisons of results from QMC and DFT. The authors considered the case of the strongly inhomogeneous electron gas using variational Q:tvIC to obtain wavefunctions 1/J>. and energies E[7/J>.] for the ground state of the Hamiltonian iI>- = T +AVee+V >. associated with the coupling constant A in the range 0 to 1. Optimization of a Slater-Jastrow many-body wavefunction was made by minimizing a penalty function given by a weighted sum of the variance in local energies and a sum of squares of electron density differences. The variational parameters in 7/J>. and v>. were repeatedly varied to reach convergence followed by additional calculations to obtain the local values of the exchange-correlation energies e c and the exchange-correlation holes n c from which Exe and nxc could be determined.