Alex J. W. Thom

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space

We have developed a new quantum Monte Carlo method for the simulation of correlated many-electron systems in full configuration-interaction (Slater determinant) spaces. The new method is a population dynamics of a set of walkers, and is designed to simulate the underlying imaginary-time Schrödinger equation of the interacting Hamiltonian. The walkers (which carry a positive or negative sign) inhabit Slater determinant space, and evolve according to a simple set of rules which include spawning, death and annihilation processes. We show that this method is capable of converging onto the full configuration-interaction (FCI) energy and wave function of the problem, without any a priori information regarding the nodal structure of the wave function being provided. Walker annihilation is shown to play a key role. The pattern of walker growth exhibits a characteristic plateau once a critical (system-dependent) number of walkers has been reached. At this point, the correlation energy can be measured using two independent methods--a projection formula and a energy shift; agreement between these provides a strong measure of confidence in the accuracy of the computed correlation energies. We have verified the method by performing calculations on systems for which FCI calculations already exist. In addition, we report on a number of new systems, including CO, O(2), CH(4), and NaH--with FCI spaces ranging from 10(9) to 10(14), whose FCI energies we compute using modest computational resources.

LOBA: a localized orbital bonding analysis to calculate oxidation states, with application to a model water oxidation catalyst

We propose a method for calculation of oxidation states in transition metal complexes, utilizing a bonding analysis based on localized molecular orbitals in conjunction with traditional population analyses. The localized orbital bonding analysis (LOBA) is seen to accurately produce both the oxidation state and chemically intuitive views of bonding in the complexes studied. This is in contrast to simple population analyses where the oxidation states are not reproduced for even simple systems and more complex analyses which break down on problematic systems. We report the application to a manganese complex with potential activity as oxygen-evolving catalyst, determining the location of the oxidations.

Hartree-Fock solutions as a quasidiabatic basis for nonorthogonal configuration interaction.

Using the method of self-consistent field metadynamics, we locate some of the low-energy solutions to the Hartree-Fock (HF) equations on LiF and O(3). The located solutions qualitatively resemble the adiabatic electronic states in these systems. We formulate the method of nonorthogonal Configuration Interaction (CI) to interact these solutions with cubic scaling with system size and quadratic scaling with the number of solutions. The resultant solutions display the avoided crossings and, in O(3), a conical intersection expected of the adiabatic states. In LiF the relevant solutions coalesce and disappear from Unrestricted HF space indicating a more general HF theory is required.

Developments in stochastic coupled cluster theory: The initiator approximation and application to the uniform electron gas

We describe further details of the stochastic coupled cluster method and a diagnostic of such calculations, the shoulder height, akin to the plateau found in full configuration interaction quantum Monte Carlo. We describe an initiator modification to stochastic coupled cluster theory and show that initiator calculations can at times be extrapolated to the unbiased limit. We apply this method to the 3D 14-electron uniform electron gas and present complete basis set limit values of the coupled cluster singles and doubles (CCSD) and previously unattainable coupled cluster singles and doubles with perturbative triples (CCSDT) correlation energies for up to r(s) = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities.

A combinatorial approach to the electron correlation problem

Starting from a path-integral formulation of quantum statistical mechanics expressed in a space of Slater determinants, we develop a method for the Monte Carlo evaluation of the energy of a correlated electronic system. The path-integral expression for the partition function is written as a contracted sum over graphs. A graph is a set of distinct connected determinants on which paths can be represented. The weight of a graph is given by the sum over exponentially large numbers of paths which visit the vertices of the graph. We show that these weights are analytically computable using combinatorial techniques, and they turn out to be sufficiently well behaved to allow stable Monte Carlo simulations in which graphs are stochastically sampled according to a Metropolis algorithm. In the present formulation, graphs of up to four vertices have been included. In a Hartree-Fock basis, this allows for paths which include up to sixfold excitations relative to the Hartree-Fock determinant. As an illustration, we have studied the dissociation curve of the N(2) molecule in a VDZ basis, which allows comparison with full configuration-interaction calculations.

Linked coupled cluster Monte Carlo

We consider a new formulation of the stochastic coupled cluster method in terms of the similarity transformed Hamiltonian. We show that improvement in the granularity with which the wavefunction is represented results in a reduction in the critical population required to correctly sample the wavefunction for a range of systems and excitation levels and hence leads to a substantial reduction in the computational cost. This development has the potential to substantially extend the range of the method, enabling it to be used to treat larger systems with excitation levels not easily accessible with conventional deterministic methods.

Open-Source Development Experiences in Scientific Software: The HANDE Quantum Monte Carlo Project

J. S. Spencer, 2, ∗ N. S. Blunt, W. A. Vigor, F. D. Malone, W. M. C. Foulkes, James J. Shepherd, and A. J. W. Thom ∗ Department of Materials, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom Department of Physics, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom University Chemical Laboratory, Lensfield Road, Cambridge, CB2 1EW, United Kingdom Department of Chemistry, Imperial College London, Exhibition Road, London, SW7 2AZ, United Kingdom Department of Chemistry, Rice University, Houston, TX 77005-1892, USA (Dated: July 22, 2014)

Stochastic coupled cluster theory: Efficient sampling of the coupled cluster expansion

We consider the sampling of the coupled cluster expansion within stochastic coupled cluster theory. Observing the limitations of previous approaches due to the inherently non-linear behavior of a coupled cluster wavefunction representation, we propose new approaches based on an intuitive, well-defined condition for sampling weights and on sampling the expansion in cluster operators of different excitation levels. We term these modifications even and truncated selections, respectively. Utilising both approaches demonstrates dramatically improved calculation stability as well as reduced computational and memory costs. These modifications are particularly effective at higher truncation levels owing to the large number of terms within the cluster expansion that can be neglected, as demonstrated by the reduction of the number of terms to be sampled when truncating at triple excitations by 77% and hextuple excitations by 98%.

Minimising biases in full configuration interaction quantum Monte Carlo

We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to, in general, minimise the bias. We show a reweight ing scheme to remove the bias caused by population control commonly used in diffusion Monte Carlo [Umrigar et al., J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step.

EXTRA: Towards the exploitation of eXascale technology for reconfigurable architectures

To handle the stringent performance requirements of future exascale-class applications, High Performance Computing (HPC) systems need ultra-efficient heterogeneous compute nodes. To reduce power and increase performance, such compute nodes will require hardware accelerators with a high degree of specialization. Ideally, dynamic reconfiguration will be an intrinsic feature, so that specific HPC application features can be optimally accelerated, even if they regularly change over time. In the EXTRA project, we create a new and flexible exploration platform for developing reconfigurable architectures, design tools and HPC applications with run-time reconfiguration built-in as a core fundamental feature instead of an add-on. EXTRA covers the entire stack from architecture up to the application, focusing on the fundamental building blocks for run-time reconfigurable exascale HPC systems: new chip architectures with very low reconfiguration overhead, new tools that truly take reconfiguration as a central design concept, and applications that are tuned to maximally benefit from the proposed run-time reconfiguration techniques. Ultimately, this open platform will improve Europes competitive advantage and leadership in the field.