arXiv subjects

Nick S. Blunt

Publications and source records attributed to Nick S. Blunt.

27 records · Page 2Linked to original sources

arXiv2019

A hybrid approach to extending selected configuration interaction and full configuration interaction quantum Monte Carlo

We present an approach to combining selected configuration interaction (SCI) and initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In the current i-FCIQMC scheme, the space of initiators is chosen dynamically by a population threshold. Here, we instead choose initiators as the selected space (V) from a prior SCI calculation, allowing substantially larger initiator spaces for a given walker population. While SCI+PT2 adds a perturbative correction in the first-order interacting space (FOIS) beyond V, the approach presented here allows a variational calculation in the same space, and a perturbative correction in the second-order interacting space. The use of a fixed initiator space reintroduces population plateaus into FCIQMC, but it is shown that the plateau height is typically only a small multiple of the size of V. Thus, for a comparable fundamental memory cost to SCI+PT2, a substantially larger space can be sampled. The resulting method can be seen as a complementary approach to SCI+PT2, which is more accurate but slower for a common selected/initiator space. More generally, our results show that approaches exist to significantly improve initiator energies in i-FCIQMC, while still ameliorating the fermion sign problem relative to the original FCIQMC method.

physics.chem-ph↗

arXiv2019

Preconditioning and perturbative estimators in full configuration interaction quantum Monte Carlo

We propose the use of preconditioning in FCIQMC which, in combination with perturbative estimators, greatly increases the efficiency of the algorithm. The use of preconditioning allows a time step close to unity to be used (without time-step errors), provided that multiple spawning attempts are made per walker. We show that this approach substantially reduces statistical noise on perturbative corrections to initiator error, which improve the accuracy of FCIQMC but which can suffer from significant noise in the original scheme. Therefore, the use of preconditioning and perturbatively-corrected estimators in combination leads to a significantly more efficient algorithm. In addition, a simpler approach to sampling variational and perturbative estimators in FCIQMC is presented, which also allows the variance of the energy to be calculated. These developments are investigated and applied to benzene (30e,108o), an example where accurate treatment is not possible with the original method.

physics.chem-ph↗

arXiv2018

Excited-state diffusion Monte Carlo calculations: a simple and efficient two-determinant ansatz

We perform excited-state variational Monte Carlo and diffusion Monte Carlo calculations using a simple and efficient wave function ansatz. This ansatz follows the recent variation-after-response formalism, accurately approximating a configuration interaction singles wave function as a sum of only two non-orthogonal Slater determinants, and further including important orbital relaxation. The ansatz is used to perform diffusion Monte Carlo calculations with large augmented basis sets, comparing to benchmarks from near-exact quantum chemical methods. The significance of orbital optimization in excited-state diffusion Monte Carlo is demonstrated, and the excited-state optimization procedure is discussed in detail. Diffuse excited states in water and formaldehyde are studied, in addition to the formaldimine and benzonitrile molecules.

cond-mat.str-el↗

arXiv2018

The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up

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 last 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 semi-stochastic 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.

physics.comp-ph↗

arXiv2018

Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods

In this article we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of non-linear expectation values, and approaches by which these errors can be corrected. We begin with a study of the Krylov-projected FCIQMC (KP-FCIQMC) approach, which was recently introduced to allow efficient, stochastic calculation of dynamical properties. This requires the solution of a sampled effective Hamiltonian, resulting in a non-linear operation on these stochastic variables. We investigate the probability distribution of this eigenvalue problem to study both stochastic errors and systematic biases in the approach, and demonstrate that such errors can be significantly corrected by moving to a more appropriate basis. This is lastly expanded to include consideration of the correlation function QMC approach of Ceperley and Bernu, showing how such an approach can be taken in the FCIQMC framework.

cond-mat.str-el↗

arXiv2018

Response Formalism within Full Configuration Interaction Quantum Monte Carlo: Static Properties and Electrical Response

We formulate a general, arbitrary-order stochastic response formalism within the Full Configuration Interaction Quantum Monte Carlo framework. This modified stochastic dynamic allows for the exact response properties of correlated multireference electronic systems to be systematically converged upon for systems far out of reach of traditional exact treatments. This requires a simultaneous coupled evolution of a response state alongside the zeroth-order state, which is shown to be stable, non-transient and unbiased. We demonstrate this with application to the static dipole polarizability of molecular systems, and in doing so, resolve a discrepancy between restricted and unrestricted high-level coupled-cluster linear response results which were the high-accuracy benchmark in the literature.

cond-mat.str-el↗

arXiv2018

An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo

We present a perturbative correction within initiator full configuration interaction quantum Monte Carlo (i-FCIQMC). In the existing i-FCIQMC algorithm, a significant number of spawned walkers are discarded due to the initiator criteria. Here we show that these discarded walkers have a form that allows calculation of a second-order Epstein-Nesbet correction, that may be accumulated in a trivial and inexpensive manner, yet substantially improves i-FCIQMC results. The correction is applied to the Hubbard model, the uniform electron gas and molecular systems.

physics.chem-ph↗

arXiv2018

QMCPACK : An open source ab initio Quantum Monte Carlo package for the electronic structure of atoms, molecules, and solids

QMCPACK is an open source quantum Monte Carlo package for ab-initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wave functions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit (CPU) and graphical processing unit (GPU) systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://www.qmcpack.org .

physics.comp-ph↗

arXiv2017

The Python-based Simulations of Chemistry Framework (PySCF)

PySCF is a general-purpose electronic structure platform designed from the ground up to emphasize code simplicity, both to aid new method development, as well as for flexibility in computational workflow. The package provides a wide range of tools to support simulations of finite size systems, extended systems with periodic boundary conditions, low dimensional periodic systems, and custom Hamiltonians, using mean-field and post-mean-field methods with standard Gaussian basis functions. To ensure easy of extensibility, PySCF uses the Python language to implement almost all its features, while computationally critical paths are implemented with heavily optimized C routines. Using this combined Python/C implementation, the package is as efficient as the best existing C or Fortran based quantum chemistry programs. In this paper we document the capabilities and design philosophy of the current version of the PySCF package.

physics.chem-ph↗