arXiv subjects

William Z. Van Benschoten

Publications and source records attributed to William Z. Van Benschoten.

6 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↗

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↗

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↗