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Register a new userAccelerating the Convergence of Auxiliary-Field Quantum Monte Carlo inSolids with Optimized Gaussian Basis Sets
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We investigate the use of optimized correlation consistent gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second order M{o}ller--Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely calculations in the Kohn--Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn--Sham basis, and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si and MgO, and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.
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We explore the extended Koopmans theorem (EKT) within the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method. The EKT allows for the direct calculation of electron addition and removal spectral functions using reduced density matrices of the $N$-particle system, and avoids the need for analytic continuation. The lowest level of EKT with AFQMC, called EKT1-AFQMC, is benchmarked using small molecules, 14-electron and 54-electron uniform electron gas supercells, and diamond at the $Gamma$-point. Via comparison with numerically exact results (when possible) and coupled-cluster methods, we find that EKT1-AFQMC can reproduce the qualitative features of spectral functions for Koopmans-like charge excitations with errors in peak locations of less than 0.25 eV in a finite basis. We also note the numerical difficulties that arise in the EKT1-AFQMC eigenvalue problem, especially when back-propagated quantities are very noisy. We show how a systematic higher order EKT approach can correct errors in EKT1-based theories with respect to the satellite region of the spectral function. Our work will be of use for the study of low-energy charge excitations and spectral functions in correlated molecules and solids where AFQMC can be reliably performed.
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.
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.
We investigate the use of interpolative separable density fitting (ISDF) as a means to reduce the memory bottleneck in auxiliary field quantum Monte Carlo (AFQMC) simulations of real materials in Gaussian basis sets. We find that ISDF can reduce the memory scaling of AFQMC simulations from $mathcal{O}(M^4)$ to $mathcal{O}(M^2)$. We test these developments by computing the structural properties of Carbon in the diamond phase, comparing to results from existing computational methods and experiment.
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