arXiv subjects

Tyler A. Anderson

Publications and source records attributed to Tyler A. Anderson.

6 recordsLinked to original sources

arXiv2025

Reproducibility of fixed-node diffusion Monte Carlo across diverse community codes: The case of water-methane dimer

Fixed-node diffusion quantum Monte Carlo (FN-DMC) is a widely-trusted many-body method for solving the Schrödinger equation, known for its reliable predictions of material and molecular properties. Furthermore, its excellent scalability with system complexity and near-perfect utilization of computational power makes FN-DMC ideally positioned to leverage new advances in computing to address increasingly complex scientific problems. Even though the method is widely used as a computational gold standard, reproducibility across the numerous FN-DMC code implementations has yet to be demonstrated. This difficulty stems from the diverse array of DMC algorithms and trial wave functions, compounded by the method's inherent stochastic nature. This study represents a community-wide effort to assess the reproducibility of the method, affirming that: Yes, FN-DMC is reproducible (when handled with care). Using the water-methane dimer as the canonical test case, we compare results from eleven different FN-DMC codes and show that the approximations to treat the non-locality of pseudopotentials are the primary source of the discrepancies between them. In particular, we demonstrate that, for the same choice of determinantal component in the trial wave function, reliable and reproducible predictions can be achieved by employing the T-move (TM), the determinant locality approximation (DLA), or the determinant T-move (DTM) schemes, while the older locality approximation (LA) leads to considerable variability in results. These findings demonstrate that, with appropriate choices of algorithmic details, fixed-node DMC is reproducible across diverse community codes-highlighting the maturity and robustness of the method as a tool for open and reliable computational science.

physics.comp-ph↗

arXiv2025

Energy needed to propel a tiny spacecraft to Proxima Centauri,and, an unstated assumption in Einstein's 1905 paper

The Breakthrough Starshot project aims to send a tiny 2 gram spacecraft to Proxima Centauri propelled by a light sail and powerful Earth-based lasers. We provide two derivations of the laser energy required to propel the spacecraft and give the reader the opportunity to decide which one is correct before providing the answer. In the second part of this paper we point out that one of the formulae in Einstein's amazing 1905 paper is correct only in certain limits, but Einstein fails to mention that. This has caused some confusion in the Breakthrough Starshot literature.

physics.class-ph↗

arXiv2024

Reducing the time-step errors in diffusion Monte Carlo

We modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error of the total energy. Further, we present a reweighting scheme that has the desirable feature that it is exactly size-consistent, i.e, the energy of a system containing widely separated fragments is the same as the sum of the energies of the individual fragments. The practical utility of the latter improvement is that it reduces the time-step error of the binding energies of some weakly interacting systems.

physics.chem-ph↗

arXiv2021

Accurate energies of transition metal atoms, ions, and monoxides using selected configuration interaction and density-based basis-set corrections

The semistochastic heat-bath configuration interaction (SHCI) method is a selected configuration interaction plus perturbation theory method that has provided near-full configuration interaction (FCI) levels of accuracy for many systems with both single- and multi-reference character. However, obtaining accurate energies in the complete basis set limit is hindered by the slow convergence of the FCI energy with respect to basis size. Here we show that the recently developed basis-set correction method based on range-separated density-functional theory can be used to significantly speed up basis-set convergence in SHCI calculations. In particular, we study two such schemes that differ in the functional used, and apply them to transition metal atoms and monoxides to obtain total, ionization, and dissociation energies well converged to the complete-basis-set limit within chemical accuracy.

physics.chem-ph↗

arXiv2021

Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo

We present a version of the T-moves approach for treating nonlocal pseudopotentials in diffusion Monte Carlo which has much smaller time-step errors than the existing T-moves approaches, while at the same time preserving desirable features such as the upper-bound property for the energy. In addition, we modify the reweighting factor of the projector used in diffusion Monte Carlo to reduce the time-step error. The latter is applicable not only to pseudopotential calculations but to all-electron calculations as well.

physics.chem-ph↗

arXiv2020

The Ground State Electronic Energy of Benzene

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$ζ$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

physics.chem-ph↗