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Register a new userA Phaseless Auxiliary-Field Quantum Monte Carlo Perspective on the Uniform Electron Gas at Finite Temperatures: Issues, Observations, and Benchmark Study
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We investigate the viability of the phaseless finite temperature auxiliary field quantum Monte Carlo (ph-FT-AFQMC) method for ab initio systems using the uniform electron gas as a model. Through comparisons with exact results and finite temperature coupled cluster theory, we find that ph-FT-AFQMC is sufficiently accurate at high to intermediate electronic densities. We show both analytically and numerically that the phaseless constraint at finite temperature is fundamentally different from its zero temperature counterpart (i.e., ph-ZT-AFQMC) and generally one should not expect ph-FT-AFQMC to agree with ph-ZT-AFQMC in the low temperature limit. With an efficient implementation, we are able to compare exchange-correlation energies to existing results in the thermodynamic limit and find that existing parameterizations are highly accurate. In particular, we found that ph-FT-AFQMC exchange-correlation energies are in a better agreement with a known parametrization than is restricted path-integral Monte Carlo in the regime of $Thetale0.5$ and $r_s le 2$, which highlights the strength of ph-FT-AFQMC.
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We assess the utility of Hartree-Fock (HF) trial wavefunctions in performing phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) on the uniform electron gas (UEG) model. The combination of ph-AFQMC with spin-restricted HF (RHF+ph-AFQMC), was found to be highly accurate and efficient for systems containing up to 114 electrons in 2109 orbitals, particularly for $r_s$ $le$ 2.0. Compared to spin-restricted coupled-cluster (RCC) methods, we found that RHF+ph-AFQMC performs better than CC with singles, doubles, and triples (RCCSDT) and similarly to or slightly worse than CC with singles, doubles, triples, and quadruples (RCCSDTQ) for $r_s$ $le$ 3.0 in the 14-electron UEG model. With the 54-electron, we found RHF+ph-AFQMC to be nearly exact for $r_s$ $le$ 2.0 and pointed out potential biases in existing benchmarks. Encouraged by these, we performed RHF+ph-AFQMC on the 114-electron UEG model for $r_s$ $le$ 2.0 and provided new benchmark data for future method development. We found that the UEG models with $r_s$ = 5.0 remain to be challenging for RHF+ph-AFQMC. Employing non-orthogonal configuration expansions or unrestricted HF states as trial wavefunctions was also found to be ineffective in the case of the 14-electron UEG model with $r_s$ = 5.0. We emphasize the need for a better trial wavefunction for ph-AFQMC in simulating strongly correlated systems. With the 54-electron and 114-electron UEG models, we stress the potential utility of RHF+ph-AFQMC for simulating dense solids.
Transition metal complexes are ubiquitous in biology and chemical catalysis, yet they remain difficult to accurately describe with ab initio methods due to the presence of a large degree of dynamic electron correlation, and, in some cases, strong static correlation which results from a manifold of low-lying states. Progress has been hindered by a scarcity of high quality gas-phase experimental data, while exact ab initio predictions are usually computationally unaffordable due to the large size of the systems. In this work, we present a data set of 34 3d metal-containing complexes with gas-phase ligand-dissociation energies that have reported uncertainties of $leq$ 2 kcal/mol. We perform all-electron phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) utilizing multi-determinant trial wavefunctions selected by a blackbox procedure. We compare the results with those from DFT with various functionals, and DLPNO-CCSD(T). We find MAE of 1.09 $pm$ 0.28 kcal/mol for our best ph-AFQMC method, vs 2.89 kcal/mol for DLPNO-CCSD(T) and 1.57 - 3.87 kcal/mol for DFT. We find maximum errors of 2.96 $pm$ 1.71 kcal/mol for our best ph-AFQMC method, vs 9.15 kcal/mol for DLPNO-CCSD(T) and 5.98 - 13.69 kcal/mol for DFT. The reasonable performance of several functionals is in stark contrast to the much poorer accuracy previously demonstrated for diatomics, suggesting a moderation in electron correlation due to ligand coordination. However, the unpredictably large errors for a small subset of cases with both DFT and DLPNO-CCSD(T) leave cause for concern, especially due to the unreliability of common multi-reference indicators. In contrast, the robust and, in principle, systematically improvable results of ph-AFQMC for these realistic complexes establish it as a useful tool for elucidating the electronic structure of transition metal-containing complexes and predicting their gas-phase properties.
Quantum Monte Carlo (QMC) methods are some of the most accurate methods for simulating correlated electronic systems. We investigate the compatibility, strengths and weaknesses of two such methods, namely, diffusion Monte Carlo (DMC) and auxiliary-field quantum Monte Carlo (AFQMC). The multi-determinant trial wave functions employed in both approaches are generated using the configuration interaction using a perturbative selection made iteratively (CIPSI) technique. Complete basis set full configuration interaction (CBS-FCI) energies estimated with CIPSI are used as a reference in this comparative study between DMC and AFQMC. By focusing on a set of canonical finite size solid state systems, we show that both QMC methods can be made to systematically converge towards the same energy once basis set effects and systematic biases have been removed. AFQMC shows a much smaller dependence on the trial wavefunction than DMC while simultaneously exhibiting a much larger basis set dependence. We outline some of the remaining challenges and opportunities for improving these approaches.
We outline how auxiliary-field quantum Monte Carlo (AFQMC) can leverage graphical processing units (GPUs) to accelerate the simulation of solid state sytems. By exploiting conservation of crystal momentum in the one- and two-electron integrals we show how to efficiently formulate the algorithm to best utilize current GPU architectures. We provide a detailed description of different optimization strategies and profile our implementation relative to standard approaches, demonstrating a factor of 40 speed up over a CPU implementation. With this increase in computational power we demonstrate the ability of AFQMC to systematically converge solid state calculations with respect to basis set and system size by computing the cohesive energy of Carbon in the diamond structure to within 0.02 eV of the experimental result.
The uniform electron gas (UEG) at finite temperature has recently attracted substantial interest due to the epxerimental progress in the field of warm dense matter. To explain the experimental data accurate theoretical models for high density plasmas are needed which crucially depend on the quality of the thermodynamic properties of the quantum degenerate correlated electrons. Recent fixed node path integral Monte Carlo (RPIMC) data are the most accurate for the UEG at finite temperature, but they become questionable at high degeneracy when the Brueckner parameter $r_s$ becomes smaller than $1$. Here we present new improved direct fermionic PIMC simulations that are exptected to be more accurate than RPIMC at high densities.
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