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Bulletin of the American Physical Society

An accurate, compact and computationally efficient representation of orbitals for quantum Monte Carlo calculations

Ye Luo, K. Esler, Paul R. C. Kent, Luke Shulenburger

Published Mar 13, 2017• 0 citations
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Practical Aspects of Quantum Monte Carlo for the Electronic Structure of Molecules

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The scale and complexity of the quantum system to which real-space quantum Monte Carlo (QMC) can be applied in part depends on the representation and memory usage of the trial wavefunction. B-splines, the computationally most efficient basis set, can have memory requirements exceeding the capacity of a single computational node. This situation has traditionally forced a difficult choice of either using slow internode communication or a potentially less accurate but smaller basis set such as Gaussians. Here, we introduce a hybrid representation of the single particle orbitals that combine a localized atomic basis set around atomic cores and B-splines in the interstitial regions to reduce the memory usage while retaining the high speed of evaluation and either retaining or increasing overall accuracy. We present a benchmark calculation for NiO demonstrating a superior accuracy while using only one eighth of the memory required for conventional B-splines. The hybrid orbital representation therefore expands the overall range of systems that can be practically studied with QMC.
Model-independent compact representations of imaginary-time data are presented in terms of the intermediate representation (IR) of analytical continuation. We demonstrate the efficiency of the IR through continuous-time quantum Monte Carlo calculations of an Anderson impurity model. We find that the IR yields a significantly compact form of various types of correlation functions. This allows the direct quantum Monte Carlo measurement of Green's functions in a compressed form, which considerably reduces the computational cost and memory usage. Furthermore, the present framework will provide general ways to boost the power of cutting-edge diagrammatic/quantum Monte Carlo treatments of many-body systems.
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.