arXiv subjects

James J. Shepherd

Publications and source records attributed to James J. Shepherd.

At least 19 recordsLinked to original sources

arXiv2026

A Single Twist-Angle Selection Method for the Electronic Structure of Bilayer Materials

Structure factor twist averaging (sfTA) is a newer method that has been shown to reproduce twist-averaged (TA) CCSD energies for bulk systems at a low computational cost. In this work, we extend this method for the treatment of low-dimensional materials in the form of two variants: paired sfTA and binding sfTA. These variants affect which twist angles are used in the sfTA protocol, as well as how the special twist angle is selected, namely by using the binding structure factor. These changes are meant to incorporate the binding interaction into the twist-angle selection algorithm within sfTA. Both variants are tested on a variety of bilayer systems, and the resulting binding correlation energies are compared to original sfTA results. We show that the variants are able to produce results approaching TA, with binding sfTA producing the most accurate energies. We also use contour plots of the test systems to show that these improvements are most likely caused by a cancellation of errors.

cond-mat.mtrl-sci↗

arXiv2026

Van-der-Waals exchange-correlation functionals and their high pressure and warm dense matter applications

We investigate basic hydrogen quantities like the molecular bond length, the molecular dissociation energy and the van-der-Waals interaction in idealized situations in an effort to discern a suitable exchange-correlation functional for the molecular to metal transition in warm dense hydrogen. The best reproduction of bond length and dissociation energy is given by the r2SCAN functional, several vdW functionals and also HSE06 fair qualitatively and quantitatively no better than PBE or worse. In addition we investigate quantities like the static and dynamic ion structure factor, and the electronic DOS to determine differences between exchange-correlation functionals with and without van-der-Waals corrections in the transition region from the molecular to the metallic regime of hydrogen.

physics.chem-ph↗

arXiv2023

Sampling the reciprocal Coulomb potential in finite and anisotropic cells

We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born-von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb integrals under periodic boundary conditions, the treatment of the singularity at the Brillouin-zone center, as well as quadrature errors, which can cause severe convergence problems in anisotropic cells, necessary for the calculation of low-dimensional systems. We apply our strategy to the Hartree-Fock (HF) and coupled cluster (CC) theory and discuss the consequences of different sampling strategies on the different theories. We show that sampling the Coulomb potential via the widely used probe-charge Ewald method is unsuitable for CC calculations in anisotropic cells. To demonstrate the applicability of our developed approach, we study two representative, low-dimensional use cases: the infinite carbon chain, for which we report the first periodic CCSD(T) potential energy surface, as well as a surface slab of lithium hydride, for which we demonstrate the impact of different sampling strategies for calculating surface energies. We find that our Coulomb sampling strategy serves as a vital solution, addressing the critical need for improved accuracy in plane-wave based CC calculations for low-dimensional systems.

physics.comp-ph↗

arXiv2023

Electronic specific heat capacities and entropies from density matrix quantum Monte Carlo using Gaussian process regression to find gradients of noisy data

We present a machine learning approach to calculating electronic specific heat capacities for a variety of benchmark molecular systems. Our models are based on data from density matrix quantum Monte Carlo, which is a stochastic method that can calculate the electronic energy at finite temperature. As these energies typically have noise, numerical derivatives of the energy can be challenging to find reliably. In order to circumvent this problem, we use Gaussian process regression to model the energy and use analytical derivatives to produce the specific heat capacity. From there, we also calculate the entropy by numerical integration. We compare our results to cubic splines and finite differences in a variety of molecules whose Hamiltonians can be diagonalized exactly with full configuration interaction. We finally apply this method to look at larger molecules where exact diagonalization is not possible and make comparisons with more approximate ways to calculate the specific heat capacity and entropy.

physics.comp-ph↗

arXiv2023

How the exchange energy can affect the power laws used to extrapolate the coupled cluster correlation energy to the thermodynamic limit

Finite size error is commonly removed from coupled cluster theory calculations by $N^{-1}$ extrapolations over correlation energy calculations of different system sizes ($N$), where the $N^{-1}$ scaling comes from the total energy. However, previous studies in the quantum Monte Carlo community suggest an exchange-energy-like power law of $N^{-2/3}$ is also be present in the correlation energy when using the conventional Coulomb interaction. The rationale for this is that the total energy goes as $N^{-1}$ and the exchange energy as $N^{-2/3}$; so, the correlation energy should be a combination of the two power laws. Further, in coupled cluster theory, these power laws are related to the low $G$ scaling of the transition structure factor, $S(G)$, which is a property of the coupled cluster wavefunction calculated from the amplitudes. We show that data from coupled cluster doubles calculations on the uniform electron gas(UEG) fit a function with a low $G$ behavior of $S(G)$~$G$. The pre-factor for this linear term is derived from the exchange energy to be consistent with an $N^{-2/3}$ power law at large $N$. Incorporating the exchange structure factor into the transition structure factor results in a combined structure factor of $S(G)$~$G^2$, consistent with an $N^{-1}$ scaling of the exchange-correlation energy. We then look for the presence of an $N^{-2/3}$ power law in the energy. First, we develop a plane-wave cutoff scheme with less noise than the traditional basis set used for the UEG. Then, we collect data from a wide range of electron numbers and densities to systematically test 5 methods using $N^{-1}$ scaling, $N^{-2/3}$ scaling, or combinations of both scaling behaviors. We find that power laws that incorporate both $N^{-1}$ and $N^{-2/3}$ scaling perform better than either alone, especially when the pre-factor for $N^{-2/3}$ scaling can be found from exchange energy calculations.

physics.comp-ph↗

arXiv2022

Piecewise Interaction Picture Density Matrix Quantum Monte Carlo

The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact $N$-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC method (IP-DMQMC) which overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.

physics.chem-ph↗

arXiv2022

Machine learning for a finite size correction in periodic coupled cluster theory calculations

We introduce a straightforward Gaussian process regression (GPR) model for the transition structure factor of metal periodic coupled cluster singles and doubles (CCSD) calculations. This is inspired by the method introduced by Liao and Grüneis for interpolating over the transition structure factor to obtain a finite size correction for CCSD [J. Chem. Phys. 145, 141102 (2016)], and by our own prior work using the transition structure factor to efficiently converge CCSD for metals to the thermodynamic limit [Nat. Comput. Sci. 1, 801 (2021)]. In our CCSD-FS-GPR method to correct for finite size errors, we fit the structure factor to a 1D function in the momentum transfer, $G$. We then integrate over this function by projecting it onto a k-point mesh to obtain comparisons with extrapolated results. Results are shown for lithium, sodium, and the uniform electron gas.

physics.comp-ph↗

arXiv2021

The sign problem in density matrix quantum Monte Carlo

Density matrix quantum Monte Carlo (DMQMC) is a recently-developed method for stochastically sampling the $N$-particle thermal density matrix to obtain exact-on-average energies for model and \emph{ab initio} systems. We report a systematic numerical study of the sign problem in DMQMC based on simulations of atomic and molecular systems. In DMQMC, the density matrix is written in an outer product basis of Slater determinants and has a size of space which is the square of the number of Slater determinants. In principle this means DMQMC needs to sample a space which scales in the system size, $N$, as $\mathcal{O}[(\exp(N))^2]$. In practice, there is a system-dependent critical walker population ($N_c$) which must be exceeded in order to remove the sign problem, and this imposes limitations by way of storage and computer time. We establish that $N_c$ for DMQMC is the square of $N_c$ for FCIQMC. By contrast, the minimum $N_c$ in the interaction picture modification of DMQMC (IP-DMQMC) only is directly proportionate to the $N_c$ for FCIQMC. We find that this comes from the asymmetric propagation of IP-DMQMC compared to the symmetric propagation of canonical DMQMC. An asymmetric mode of propagation is prohibitively expensive for DMQMC because it has a much greater stochastic error. Finally, we find that the equivalence between IP-DMQMC and FCIQMC seems to extend to the initiator approximation, which is often required to study larger basis sets and other systems. This suggests IP-DMQMC offers a way to ameliorate the cost of moving between a Slater determinant space and an outer product basis.

physics.chem-ph↗

arXiv2021

Effective Hamiltonians for the study of real metals using quantum chemical theories

Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a central role in molecular quantum chemistry because of its systematic improvability and computational efficiency. In this hierarchy, coupled cluster singles and doubles (CCSD) is one of the most important steps in moving towards chemical accuracy and, in recent years, its scope has successfully been expanded to the study of insulating surfaces and solids. Here, we show that CCSD theory can also be applied to real metals. In so doing, we overcome the limitation of needing extremely large supercells to capture long range electronic correlation effects. An effective Hamiltonian can be found using the transition structure factor--a map of electronic excitations from the Hartree--Fock wavefunction--which has fewer finite size effects than conventional periodic boundary conditions. This not only paves the way of applying coupled cluster methods to real metals but also reduces the computational cost by two orders of magnitude compared to previous methods. Our applications to phases of lithium and silicon show a resounding success in reaching the thermodynamic limit, taking the first step towards a truly universal quantum chemical treatment of solids.

cond-mat.mtrl-sci↗

arXiv2021

Power laws used to extrapolate the coupled cluster correlation energy to the thermodynamic limit

Recent calculations using coupled cluster on solids have raised discussion of using a $N^{-1/3}$ power law to fit the correlation energy when extrapolating to the thermodynamic limit, an approach which differs from the more commonly used $N^{-1}$ power law which is (for example) often used by quantum Monte Carlo methods. In this paper, we present one way to reconcile these viewpoints. Coupled cluster doubles calculations were performed on uniform electron gases reaching system sizes of $922$ electrons for an extremely wide range of densities ($0.1<r_s<100.0$) to study how the correlation energy approaches the thermodynamic limit. The data were corrected for basis set incompleteness error and use a selected twist angle approach to mitigate finite size error from shell filling effects. Analyzing these data, we initially find that a power law of $N^{-1/3}$ appears to fit the data better than a $N^{-1}$ power law in the large system size limit. However, we provide an analysis of the transition structure factor showing that $N^{-1}$ still applies to large system sizes and that the apparent $N^{-1/3}$ power law occurs only at low $N$.

physics.comp-ph↗

arXiv2020

Accelerating convergence to the thermodynamic limit with twist angle selection applied to methods beyond many-body perturbation theory

We recently developed a scheme to use low-cost calculations to find a single twist angle where the couple cluster doubles energy of a single calculation matches the twist-averaged coupled cluster doubles energy in a finite unit cell. We used initiator full configuration interaction quantum Monte Carlo ($i$-FCIQMC) as an example of an exact method beyond coupled cluster doubles theory to show that this selected twist angle approach had comparable accuracy in methods beyond coupled cluster. Further, at least for small system sizes, we show that the same twist angle can also be found by comparing the energy directly (at the level of second-order Moller-Plesset theory) suggesting a route toward twist angle selection which requires minimal modification to existing codes which can perform twist averaging.

physics.chem-ph↗

arXiv2020

NECI: N-Electron Configuration Interaction with emphasis on state-of-the-art stochastic methods

We present NECI, a state-of-the-art implementation of the Full Configuration Interaction Quantum Monte Carlo algorithm, a method based on a stochastic application of the Hamiltonian matrix on a sparse sampling of the wave function. The program utilizes a very powerful parallelization and scales efficiently to more than 24000 CPU cores. In this paper, we describe the core functionalities of NECI and recent developments. This includes the capabilities to calculate ground and excited state energies, properties via the one- and two-body reduced density matrices, as well as spectral and Green's functions for ab initio and model systems. A number of enhancements of the bare FCIQMC algorithm are available within NECI, allowing to use a partially deterministic formulation of the algorithm, working in a spin-adapted basis or supporting transcorrelated Hamiltonians. NECI supports the FCIDUMP file format for integrals, supplying a convenient interface to numerous quantum chemistry programs and it is licensed under GPL-3.0.

physics.comp-ph↗

arXiv2019

Using density matrix quantum Monte Carlo for calculating exact-on-average energies for ab-initio Hamiltonians in a finite basis set

We here apply the recently developed initiator density matrix quantum Monte Carlo (i-DMQMC) to a wide range of chemical environments using 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. By way of exploring the applicability of i-DMQMC for molecular systems, we choose to study a recently developed test set by Rubenstein and coworkers: Be, H2O, and H10 at near-equilibrium and stretched geometries. We find that, for Be and H2O, i-DMQMC delivers energies which are sub-millihartree accuracy when compared with finite temperature FCI. For H2O and both geometries of H10 we examine the difference between FT-AFQMC and i-DMQMC which in turn is an estimate of the difference in canonical versus grand canonical energies. We close with a discussion of simulation parameters (initiator error and different basis sets) and by showing energy difference calculations in the form of specific heat capacity and ionization potential calculations.

physics.chem-ph↗

arXiv2019

Fully quantum embedding with density functional theory for full configuration interaction quantum Monte Carlo

In common with many high-accuracy electronic structure methods, the initiator adaptation of full configuration interaction quantum Monte Carlo (i-FCIQMC) has difficulty treating realistic systems with large numbers of electrons. This barrier has prevented the application of i-FCIQMC to questions of catalysis that, even for the simplest of models, require high-accuracy modeling of several features of the electronic structure, such as strong and dynamic correlation, and localized vs. delocalized bonding. We here present a fully-quantum embedded version of i-FCIQMC , which we apply to calculate the bond dissociation energy of an ionic bond (LiH) and a covalent bond (HF) physisorbed to a benzene molecule. The embedding is performed using a recently-developed Huzinaga projection operator approach, which affords good synergy with i-FCIQMC by minimizing the number of orbitals in the calculation. We find that, without embedding, i-FCIQMC struggles to converge these calculations due to their substantial system sizes and a lack of error cancellation between reactants and products. With embedding, the i-FCIQMC calculation converges straightforwardly to CCSD(T) benchmarks. Our results suggest that embedded i-FCIQMC will be able treat system sizes well beyond our current reach (even though embedding introduces an error). We discuss how embedding might be improved (and thus the introduced error reduced) using i-FCIQMC energies as benchmarks.

physics.chem-ph↗

arXiv2019

An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas

We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the non-zero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, and which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over $N_\mathrm{s}$ twist angles from $N_s$ CCD calculations to $N_s$ MP2 calculations plus one CCD calculation.

physics.chem-ph↗

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↗

arXiv2017

Morphology of passivating organic ligands around a nanocrystal

Semiconductor nanocrystals are a promising class of materials for a variety of novel optoelectronic devices, since many of their properties, such as the electronic gap and conductivity, can be controlled. Much of this control is achieved via the organic ligand shell, through control of the size of the nanocrystal and the distance to other objects. We here simulate ligand-coated CdSe nanocrystals using atomistic molecular dynamics, allowing for the resolution of novel structural details about the ligand shell. We show that the ligands on the surface can lie flat to form a highly anisotropic 'wet hair' layer as opposed to the 'spiky ball' appearance typically considered. We discuss how this can give rise to a dot-to-dot packing distance of one ligand length since the thickness of the ligand shell is reduced to approximately one-half of the ligand length for the system sizes considered here; these distances imply that energy and charge transfer rates between dots and nearby objects will be enhanced due to the thinner than expected ligand shell. Our model predicts a non-linear scaling of ligand shell thickness as the ligands transition from 'spiky' to 'wet hair'. We verify this scaling using TEM on a PbS nanoarray, confirming that this theory gives a qualitatively correct picture of the ligand shell thickness of colloidal quantum dots.

physics.chem-ph↗

arXiv2016

Accurate exchange-correlation energies for the warm dense electron gas

Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average $N$-body density matrices for uniform electron gas systems of up to 10$^{124}$ matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the $k$-space configuration path-integral formalism disagree by up to $\sim$$10$\% at certain reduced temperatures $T/T_F \le 0.5$ and densities $r_s \le 1$. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that DMQMC can calculate free energies directly and present exact free energies for $T/T_F \ge 1$ and $r_s \le 2$.

cond-mat.str-el↗