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arXiv:1811.11679 · Journal of Chemical Theory and Computation

The HANDE-QMC Project: Open-Source Stochastic Quantum Chemistry from the Ground State Up

James S. Spencer, Nick S. Blunt, Seonghoon Choi, Jiří Etrych, Maria-Andreea Filip, W. M. C. Foulkes, R. S. T. Franklin, Will J. Handley, Fionn D. Malone, Verena A. Neufeld, Roberto Di Remigio, Thomas W. Rogers, Charles J. C. Scott, James J. Shepherd, W. A. Vigor, Joseph Weston, Ruqing Xu, Alex J. W. Thom

Published Jan 25, 2019• 43 citations
arXivHTMLPDF

Abstract

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

DOI
10.1021/acs.jctc.8b01217

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•Jun 1, 2015•1 citation
Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.
In the last decade, stochastic versions of quantum chemistry methods such as coupled cluster Monte Carlo (CCMC) or full configuration interaction quantum Monte Carlo (FCIQMC) have made highly accurate energy calculations possible that are not accessible to the corresponding deterministic methods (full configuration interaction and coupled cluster) at the same accuracy. CCMC and FCIQMC parallelize well and exploit the sparsity in the wavefunction which decreases memory costs and makes calculations in larger systems tractable. With CCMC it is straightforward to set up high order coupled cluster calculations, such as CCSDTQ5, which includes quintuple excitations explicitly. In this thesis, the convergence of the energy accuracy with the coupled cluster levels up to CCSDTQ5 was tested on the uniform electron gas, a model solid system, for various degrees of electron correlation. This gave information on what coupled cluster level is needed to reach sufficient accuracy when modelling a solid system. Before large solid systems can be modelled, the CCMC and FCIQMC algorithms need to be optimised. The efficiency in one of the crucial steps in these algorithms, the spawnspawnspawn step, was improved, keeping computational and memory costs as low as possible. Furthermore, the convergence of CCMC and FCIQMC was accelerated by employing a quasi-Newton propagation. Using the model system information of what coupled cluster level is needed and having made great progress towards accelerating these methods, the computation of highly accurate energies in solid or large molecular systems should be more feasible in the future.
Two distinct types of Quantum Monte Carlo (QMC) calculations are applied to electronic structure problems such as calculating potential energy curves and producing benchmark values for reaction barriers. First, Variational and Diffusion Monte Carlo (VMC and DMC) methods using a trial wavefunction subject to the fixed node approximation were tested using the CASINO code.[1] Next, Full Configuration Interaction Quantum Monte Carlo (FCIQMC), along with its initiator extension (i-FCIQMC) were tested using the NECI code.[2] FCIQMC seeks the FCI energy for a specific basis set. At a reduced cost, the efficient i-FCIQMC method can be applied to systems in which the standard FCIQMC approach proves to be too costly. Since all of these methods are statistical approaches, uncertainties (error-bars) are introduced for each calculated energy. This study tests the performance of the methods relative to traditional quantum chemistry for some benchmark systems. References: [1] R. J. Needs et al., J. Phys.: Condensed Matter 22, 023201 (2010). [2] G. H. Booth et al., J. Chem. Phys. 131, 054106 (2009).
We expand upon the recent semi-stochastic adaptation to full configuration interaction quantum Monte Carlo (FCIQMC). We present an alternate method for generating the deterministic space without a priori knowledge of the wave function and present stochastic efficiencies for a variety of both molecular and lattice systems. The algorithmic details of an efficient semi-stochastic implementation are presented, with particular consideration given to the effect that the adaptation has on parallel performance in FCIQMC. We further demonstrate the benefit for calculation of reduced density matrices in FCIQMC through replica sampling, where the semi-stochastic adaptation seems to have even larger efficiency gains. We then combine these ideas to produce explicitly correlated corrected FCIQMC energies for the beryllium dimer, for which stochastic errors on the order of wavenumber accuracy are achievable.
We here apply the recently developed initiator density matrix quantum Monte Carlo (i-DMQMC) to a variety of atoms and molecules in vacuum. i-DMQMC samples the exact density matrix of a Hamiltonian at finite temperature and combines the accuracy of full configuration interaction quantum Monte Carlo (FCIQMC)—full configuration interaction (FCI) or exact energies in a finite basis set—with finite temperature. In order to explore the applicability of i-DMQMC for molecular systems, we choose to study a recently developed test set by Rubenstein and co-workers: Be, H 2 O, and H 10 at near-equilibrium and stretched geometries. We find that, for Be and H 2 O, i-DMQMC delivers energies with submillihartree accuracy when compared with finite temperature FCI. For H 2 O and both geometries of H 10, we examine the difference between FT-AFQMC and i-DMQMC, which, in turn, estimates the difference in canonical versus grand canonical energies. We close with two discussions: one of simulation settings (initiator error, the interaction picture, and different basis sets), and another of energy difference calculations in the form of specific heat capacity and ionization potential calculations.
Full configuration interaction quantum Monte Carlo for accurate ab initio\textit{ab initio}ab initio nuclear structure calculations: algorithms and calculation details
Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic many-body solver that has been widely applied to electronic, molecular, and condensed-matter systems. In this work we apply FCIQMC to ab initio\textit{ab initio}ab initio nuclear structure calculations using interactions derived from chiral effective field theory. We describe the algorithm in detail, including imaginary-time propagation, excitation generation, estimator choices, the initiator approximation with adaptive shift correction, and reduced-density-matrix (RDM) sampling. Benchmark calculations in small model spaces, where deterministic full configuration interaction (FCI) results are available, validate the stochastic calculation of energies, radii, and RDM-based pure estimators. For large model spaces, we analyze the residual finite-walker bias through systematic walker-number convergence and infinite-walker extrapolations. We also demonstrate that FCIQMC can be extended beyond ground-state calculations by computing the low-lying spectrum of 6^66Li.
In this thesis we investigate the recently developed Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method. This method, unlike the traditional methods in Quantum Monte Carlo (QMC), doesn’t require the use of the uncontrolled fixed node approximation and so potentially it can yield far more accurate results. This means that it can be thought of as a hybrid between the methods used by quantum chemists and QMC, and thus has spawned a new field of stochastic quantum chemistry. The work described in this thesis can be split into three distinct but interrelated parts. We begin with an investigation of the underlying FCIQMC stochastic process. We show that FCIQMC is an example of Markov Chain Monte Carlo. This means we can compute a stochastic matrix from which all details about the Monte-Carlo simulation can be obtained. Unfortunately the size of the space scales unfavourably as a function of system size meaning that we have only managed to compute the matrix for the smallest interesting two determinant system. We then use these results to quantify population control bias in FCIQMC for a two determinant system supplementing these analytical results with empirical results to investigate more realistic systems. We then attempt to quantify the efficiency of the FCIQMC algorithms, defining a measure of efficiency. After this we investigate the dependence of our measure on the system size. The error bar of the most efficient FCIQMC algorithm will decay fastest as a function of computer time. We then draw conclusions about the applicability of the FCIQMC method. Finally we describe an implementation of FCIQMC on a novel data flow computer architecture. In our implementation we made a modification to the FCIQMC algorithm to fit the data flow paradigm. We investigate the efficiency of the modified FCIQMC algorithm.