arXiv subjects

Alex J. W. Thom

Publications and source records attributed to Alex J. W. Thom.

43 records · Page 3Linked to original sources

arXiv2018

A study of the dense Uniform Electron Gas with high orders of Coupled Cluster

We investigate the accuracies of different coupled cluster levels in a finite model solid, the 14 electron spin-non-polarised uniform electron gas. For densities between $\mathrm{r}_\mathrm{s}$ = 0.5 $\mathrm{a}_\mathrm{0}$ and $\mathrm{r}_\mathrm{s}$ = 5 $\mathrm{a}_\mathrm{0}$, we calculate ground state correlation energies with stochastic coupled cluster ranging from coupled cluster singles and doubles (CCSD) to coupled cluster including all excitations up to quintuples (CCSDTQ5). We find the need to add triple excitations for an accuracy of 0.01eV/electron beyond $\mathrm{r}_\mathrm{s}$ = 0.5 $\mathrm{a}_\mathrm{0}$. Quadruple excitations start being significant past $\mathrm{r}_\mathrm{s}$ = 3 $\mathrm{a}_\mathrm{0}$ . At $\mathrm{r}_\mathrm{s}$ = 5 $\mathrm{a}_\mathrm{0}$, CCSD gives a correlation energy with a 16% error and CCSDT is in error by 2% compared to the CCSDTQ5 result. CCSDTQ5 gives an energy in agreement with full configuration interaction quantum Monte Carlo results.

physics.chem-ph↗

arXiv2018

Holomorphic Hartree-Fock Theory: The Nature of Two-Electron Problems

We explore the existence and behaviour of holomorphic restricted Hartree-Fock (h-RHF) solutions for two-electron problems. Through algebraic geometry, the exact number of solutions with $n$ basis functions is rigorously identified as $\frac{1}{2}(3^n - 1)$, proving that states must exist for all molecular geometries. A detailed study on the h-RHF states of HZ (STO-3G) then demonstrates both the conservation of holomorphic solutions as geometry or atomic charges are varied and the emergence of complex h-RHF solutions at coalescence points. Using catastrophe theory, the nature of these coalescence points is described, highlighting the influence of molecular symmetry. The h-RHF states of HHeH$^{2+}$ and HHeH (STO-3G) are then compared, illustrating the isomorphism between systems with two electrons and two electron holes. Finally, we explore the h-RHF states of ethene (STO-3G) by considering the $π$ electrons as a two-electron problem, and employ NOCI to identify a crossing of the lowest energy singlet and triplet states at the perpendicular geometry.

physics.chem-ph↗

arXiv2017

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 behaviour of a coupled cluster wavefunction representation we propose new approaches based upon 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 selection 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 at the level of CCSDT by 77% and at CCSDTQ56 by 98%.

physics.chem-ph↗

arXiv2016

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.

physics.chem-ph↗

arXiv2015

Holomorphic Hartree-Fock theory: an inherently multireference approach

We investigate the existence of holomorphic Hartree-Fock solutions using a revised SCF algorithm. We use this algorithm to study the Hartree-Fock solutions for H$_{2}$ and H$_{4}^{2+}$ and report the emergence of holomorphic solutions at points of symmetry breaking. Finally, we find these holomorphic solutions for H$_{4}$ and use them as a basis for Non-Orthogonal Configuration Interaction at a range of rectangular geometries and show them to produce energies in good agreement with Full Configuration Interaction.

physics.chem-ph↗

arXiv2015

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 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 CCSD and previously unattainable CCSDT correlation energies for up to rs = 2, showing a requirement to include triple excitations to accurately calculate energies at high densities.

physics.chem-ph↗

arXiv2014

Holomorphic Hartree-Fock Theory and Configuration Interaction

We investigate the Hartree-Fock solutions to H2 in a minimal basis. We note the properties of the solutions and their disappearance with geometry and propose a new method, Holomorphic Hartree-Fock theory, where we modify the SCF equations to avoid disappearance of the solutions. We use these solutions as a basis for a non-orthogonal Configuration Interaction to produce a smooth binding curve over a complete range of geometries.

physics.chem-ph↗