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Quantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order M{{\o}}ller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been…
The adopted level densities (LD) for the nuclei produced through different reaction mechanisms significantly impact the calculation of cross sections for the many reaction channels. Common LD models make simplified assumptions regarding the…
Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles,…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
The precise tuning required to observe critical phenomena in gravitational collapse poses a challenge for most numerical codes. First, threshold estimation searches may be obstructed by the appearance of coordinate singularities, indicating…
Computationally efficient and accurate quantum mechanical approximations to solve the many-electron Schr\"odinger equation are at the heart of computational materials science. In that respect the coupled cluster hierarchy of methods plays a…
The sensitivity of computed DFT (Density Functional Theory) molecular properties (including energetics, geometries, vibrational frequencies, and infrared intensities) to the radial and angular numerical integration grid meshes, as well as…
A uniform derivation is presented of the self-consistent field equations in a finite basis set. Both restricted and unrestricted Hartree-Fock (HF) theory as well as various density functional (DF) approximations are considered. The unitary…
A representation of polymer self-consistent field theory equivalent to quantum density functional theory is given in terms of non-orthogonal basis sets. Molecular integrals and self-consistent equations for spherically symmetric systems…
In an era where scientific experimentation is often costly, multi-fidelity emulation provides a powerful tool for predictive scientific computing. While there has been notable work on multi-fidelity modeling, existing models do not…
Quantum-chemical calculations aimed at deriving magnetic coupling constants in exchange-coupled spin clusters commonly utilize a broken-symmetry (BS) approach. This involves calculating several distinct collinear spin configurations,…
Accurate wave-function descriptions of pristine and defected solids remain challenging due to the simultaneous presence of finite-size, basis-set, and correlation errors. While embedding techniques alleviate finite-size effects and…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
Among many current data processing systems, the objectives are often not the reproduction of data, but to compute some answers based on the data resulting from queries. The similarity identification task is to identify the items in a…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting)…
We present a comparison of methods for treating the electrostatic interactions of finite, isolated systems within periodic boundary conditions (PBCs), within Density Functional Theory (DFT), with particular emphasis on linear-scaling (LS)…
Quantum-field-theoretic descriptions of interacting condensed bosons have suffered from the lack of self-consistent approximation schemes satisfying Goldstone's theorem and dynamical conservation laws simultaneously. We present a procedure…
We derive a formalism, the separation method, for the efficient and accurate calculation of two-body matrix elements for a Gaussian potential in the cylindrical harmonic-oscillator basis. This formalism is of critical importance for…
Classical simulation of many-body quantum systems remains economical only when wavefunction amplitudes stay localized in the working basis. Fixed-basis sparse-state simulators scale memory as $\mathcal{O}(k)$ by keeping the largest…