Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.39176

Computing electron overlap integrals for Gausslet orbitals on cubic lattices

Xianrui Yin·Fereshteh Ghasempour·Christian B. Mendl
View original source ↗Read source document ↗Export metadata ↓

Abstract

Gausslet orbitals on a cubic lattice, introduced in [Steven R. White, J. Chem. Phys. 147, 244102 (2017)], represent a localized, smooth, and systematically refineable basis set featuring a "diagonal" approximability of the electron repulsion integral tensor. The present work develops efficient algorithms for evaluating overlap integrals required for electronic-structure simulations using these Gausslets, specifically the kinetic, nuclear, and electron repulsion integrals (both with and without the diagonal approximation). Computational efficiency improvements rest on the exploitation of translation, permutation, and octahedral symmetries, a reordering and precomputation of nested sums, as well as an early truncation of small coefficients. Our algorithms reduce the number of electron repulsion integrals on a $5 \times 5 \times 5$ grid from $125^4 = 244140625$ to $138187$ due to symmetries, and achieve a wall-clock runtime for evaluating the remaining integrals with a truncation tolerance of $10^{-5}$ in under 1 second on a laptop computer. We apply the developed methodology to compute the ground state of the hydrogen atom and molecule as a demonstration.

Explore related subjects

physics.chem-phphysics.comp-phquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Xianrui Yin, Fereshteh Ghasempour, Christian B. Mendl. 2026-10-05. Computing electron overlap integrals for Gausslet orbitals on cubic lattices. https://arxiv.org/abs/2609.39176

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Systematically Improvable Numerical Atomic Orbital Basis Using Contracted Truncated Spherical Waves

To solve the Kohn-Sham equation within the framework of density functional theory, we develop a scheme to construct numerical atomic orbital (NAO) basis sets by contracting truncated spherical waves (TSWs). The contraction minimizes the trace of the kinetic operator in the residual space, generalizing the spillage minimizing scheme [M. Chen et al., J. Phys. Condens. Matter 22, 445501 (2010); P. Lin et al., Phys. Rev. B 103, 235131 (2021)]. In addition to the systematic improvability inherited from previous schemes, the use of TSW instead of plane waves as the expansion basis bridges reference states and NAOs more effectively, and eliminates spurious interactions between periodic images, thereby enabling better transferability through the inclusion of extensive reference states. Benchmarks demonstrate that the constructed NAO achieves satisfactory precision for various properties of both molecules and bulk systems, including total energy, bond length, atomization energy, lattice constant, cohesive energy, band gap, and energy-level alignment. By incorporating unoccupied states, the improved transferability in describing the conduction band is demonstrated to be effective and substantial.

physics.chem-ph↗
arXiv2026

Augmented Roothaan-Hall Hessian Applied to Spin-Restricted Open-Shell Density-Functional Theory

We generalize the augmented Roothaan-Hall (ARH) Hessian formalism to the self-consistent field (SCF) optimization of spin-restricted open-shell (RO) wavefunctions, encompassing high-spin, low-spin, and two-determinant electronic states. A detailed ARH formulation is presented. We demonstrate that ARH is a highly efficient optimization algorithm for rapidly identifying accurate SCF solutions, primarily owing to its systematic construction of an effective Hessian, particularly in the case of Euclidean quadratic energy functions. The ARH is built upon a universal energy formulation, including grid-based integration, for spin-restricted closed-shell, spin-unrestricted and RO density functional theory (DFT), thereby unifying and simplifying their numerical implementation. The performance of the present method is evaluated using two benchmarking studies. First, for a series of iron-sulfur clusters exhibiting different spin states, which represent notoriously challenging SCF problems, the ARH algorithm demonstrates superior convergence efficiency relative to L-BFGS and truncated Newton methods, requiring much fewer RO-SCF iterations to achieve convergence. Second, the ARH approach tends to avoid convergence to higher-energy stationary points in two-determinant RO-SCF calculations for singlet excited states of selected photoactive compounds. Finally, an application of the ARH-based RO-SCF is illustrated by an investigation of the mechanistic origin of the spin-crossover phenomenon in Ni(II)-porphyrin complex utilized as a contrast agent.

physics.chem-ph↗
arXiv2026

From $\langle n \rangle$ to $n$: Separating multi-particle dynamics by intensity cycling

We address the interpretation of transient spectroscopy signals proportional to average excitation number in terms of discrete number of excitations. Building on our recent intensity cycling approach, we derive a general scheme to isolate multi-particle dynamics from any transient signal under minimal assumptions. The key result is a general formula expressing the extracted nonlinear signal terms by multi-excitation propagators. We demonstrate the approach on exciton transport and annihilation in organic nanoparticles, and carrier recombination in silicon nanocrystals.

physics.chem-ph↗