arXiv subjects

A. J. W. Thom

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

8 recordsLinked to original sources

arXiv2025

Application of Correlated-Wavefunction and Density-Functional Theories to Endofullerenes: A Cautionary Tale

A recent study by Panchagnula et al. [J. Chem. Phys. 161, 054308 (2024)] illustrated the non-concordance of a variety of electronic structure methods at describing the symmetric double-well potential expected along the anisotropic direction of the endofullerene Ne@C$_{70}$. In this article we present new correlated-wavefunction data from coupled cluster theory for this system, and scrutinise a variety of state-of-the-art density-functional approximations (DFAs) and dispersion corrections (DCs). We identify rigorous criteria for the double-well potential and compare the shapes, barrier heights, and minima positions obtained with the DFAs and DCs to the correlated wavefunction data. We show that many of the DFAs are extremely sensitive to the numerical integration grid used, the dispersion damping function, and the extent of exact-exchange mixing. We pose the Ne@C$_{70}$ system as a challenge to functional developers and as a diagnostic system for testing dispersion corrections, and reiterate the need for more experimental data for comparison.

physics.chem-ph↗

arXiv2024

Targeting spectroscopic accuracy for dispersion bound systems from ab initio techniques: translational eigenstates of Ne@C$_{70}$

We investigate the endofullerene system Ne@C$_{70}$, by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. We compare a plethora of electronic structure methods including: MP2, SCS-MP2, SOS-MP2, RPA@PBE, C(HF)-RPA, which were previously used for He@C$_{60}$ in J. Chem. Phys. 160, 104303 (2024), alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C$_{60}$ to C$_{70}$ introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the methods. Due to the large cost of these calculations, the PES is interpolated using Gaussian Process Regression due to its effectiveness with sparse training data. The nuclear Hamiltonian is diagonalised using a symmetrised double minimum basis set outlined in J. Chem. Phys. 159, 164308 (2023), with translational energies having error bars $\pm 1$ and $\pm 2$ cm$^{-1}$. We quantify the shape of the ground state wavefunction by considering its prolateness and kurtosis, and compare the eigenfunctions between electronic structure methods from their Hellinger distance. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well, and different translational eigenspectra which also differ from the Lennard-Jones (LJ) PES given in J. Chem. Phys. 101, 2126,2140 (1994). We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES, nor recreate the eigenstates and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C$_{60}$, due to the lack of concordance between all electronic structure methods we require more experimental data in order to properly validate the choice.

physics.chem-ph↗

arXiv2024

Translational eigenstates of He@C$_{60}$ from four-dimensional \textit{ab initio} Potential Energy Surfaces interpolated using Gaussian Process Regression

We investigate the endofullerene system $^3$He@C$_{60}$ with a four-dimensional Potential Energy Surface (PES) to include the three He translational degrees of freedom and C$_{60}$ cage radius. We compare MP2, SCS-MP2, SOS-MP2, RPA@PBE and C(HF)-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalised to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number $n$ is lifted due to the anharmonicity in the radial potential. The $(2l+1)$-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96cm$^{-1}$ and 110cm$^{-1}$ depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of approximately $\pm$ 1.5cm$^{-1}$. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two \textit{ab initio} methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

physics.chem-ph↗

arXiv2023

Exploring the parameter space of an endohedral atom in a cylindrical cavity

Endohedral fullerenes, or endofullerenes, are chemical systems of fullerene cages encapsulating single atoms or small molecules. These species provide an interesting challenge of Potential Energy Surface (PES) determination as examples of non-covalently bonded, bound systems. While the majority of studies focus on C$_{60}$ as the encapsulating cage, introducing some anisotropy by using a different fullerene, e.g., C$_{70}$ can unveil a double well potential along the unique axis. By approximating the potential as a pairwise Lennard-Jones (LJ) summation over the fixed C cage atoms, the parameter space of the Hamiltonian includes three tunable variables: $(M,\varepsilon,σ)$ representing the mass of the trapped species, the LJ energy, and length scales respectively. Fixing the mass and allowing the others to vary can imitate the potentials of endohedral species trapped in more elongated fullerenes. We choose to explore the LJ parameter space of an endohedral atom in C$_{70}$ with $\varepsilon\in$ [20cm$^{-1}$, 150cm$^{-1}$], and $σ\in$ [2.85Å , 3.05Å]. As the barrier height and positions of these wells vary between [1cm$^{-1}$, 264cm$^{-1}$] and [0.35Å, 0.85Å] respectively, using a 3D direct product basis of 1D harmonic oscillator (HO) wavefunctions centred at the origin where there is a local maximum is unphysical. Instead we propose the use of a non-orthogonal basis set, using 1D HO wavefunctions centred in each minimum and compare this to other choices. The ground state energy of the X@C$_{70}$ is tracked across the LJ parameter space, along with its corresponding nuclear translational wavefunctions. A classification of the wavefunction characteristics, namely the prolateness and ``peanut-likeness'' based on its statistical moments is also proposed.

physics.chem-ph↗

arXiv2022

The density and pressure of helium nano-bubbles encapsulated in silicon

The $1s^2->1s2p(^1P)$ excitation in confined and compressed helium atoms in either the bulk material or encapsulated in a bubble is shifted to energies higher than that in the free atom. For bulk helium, the energy shifts predicted from non-empirical electronic structure computations are in excellent agreement with the experimentally determined values. However, there are significant discrepancies both between the results of experiments on different bubbles and between these and the well established descriptions of the bulk. A critique is presented of previous attempts to determine the densities in bubbles by measuring the intensities of the electrons inelastically scattered in STEM experiments. The reported densities are untrustworthy because it was assumed that the cross section for inelastic electron scattering was the same as that of a free atom whilst it is now known that this property is greatly enhanced for atoms confined at significant pressures. It is shown how experimental measurements of bubbles can be combined with data on the bulk using a graphical method to determine whether the behavior of an encapsulated guest differs from that in the bulk material. Experimental electron energy loss data from an earlier study of helium encapsulated in silicon is reanalyzed using this new method to show that the properties of the helium in these bubbles do not differ significantly from those in the bulk thereby enabling the densities in the bubbles to be determined. These enable the bubble pressures to be deduced from a well established experimentally derived equation of state. It is shown that the errors of up to 80% in the incorrectly determined densities are greatly magnified in the predicted pressures which can be too large by factors of over seven. This has major practical implications for the study of radiation damage of materials exposed to $α$ particle bombardment.

physics.chem-ph↗

arXiv2016

Understanding and Improving the Efficiency of Full Configuration Interaction Quantum Monte Carlo

Within Full Configuration Interaction Quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per timestep and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree--Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem.

physics.chem-ph↗

arXiv2015

Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project

The HANDE quantum Monte Carlo project offers accessible stochastic algorithms for general use for scientists in the field of quantum chemistry. HANDE is an ambitious and general high-performance code developed by a geographically-dispersed team with a variety of backgrounds in computational science. In the course of preparing a public, open-source release, we have taken this opportunity to step back and look at what we have done and what we hope to do in the future. We pay particular attention to development processes, the approach taken to train students joining the project, and how a flat hierarchical structure aids communication

cs.SE↗

arXiv2015

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 reweighting scheme to remove the bias caused by population control commonly used in Diffusion Monte Carlo [J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step.

physics.chem-ph↗