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An alternative methodology to evaluate two-electron-repulsion integrals based on numerical approximation is proposed. Computational chemistry has branched into two major fields with methodologies based on quantum mechanics and classical…
Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by…
The stochastic resolution of identity (sRI) approximation significantly reduces the computational scaling of CC2 from O(N^5) to O(N^3), where N is a measure of system size. However, the inherent stochastic noise, while controllable, can…
Quantum computation offers significant potential for accelerating the simulation of molecules and materials through algorithms such as quantum phase estimation (QPE). However, the expected speedup in ground-state energy estimation depends…
The high computational scaling with the number of correlated electrons and the size of the basis set is a bottleneck which limits applications of coupled cluster (CC) algorithms. This is particularly so for calculations based on 2- or…
Quantum chemical methods dealing with challenging systems while retaining low computational costs have attracted attention. In particular, many efforts have been devoted to developing new methods based on the second-order perturbation that…
Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…
We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maximizing the (work) energy of a membrane governed by the…
We present a second-order formulation of multi-reference algebraic diagrammatic construction theory [Sokolov, A. Yu. J. Chem. Phys. 2018, 149, 204113] for simulating photoelectron spectra of strongly correlated systems (MR-ADC(2)). The…
We give two algorithms for output-sparse matrix multiplication (OSMM), the problem of multiplying two $n \times n$ matrices $A, B$ when their product $AB$ is promised to have at most $O(n^{\delta})$ many non-zero entries for a given value…
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…
This work presents a dynamic parallel distribution scheme for the Hartree-Fock exchange~(HFX) calculations based on the real-space NAO2GTO framework. The most time-consuming electron repulsion integrals~(ERIs) calculation is perfectly…
While the treatment of chemically relevant systems containing hundreds or even thousands of electrons remains beyond the reach of quantum devices, the development of quantum-classical hybrid algorithms to resolve electronic correlation…
The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to…
In the present article, we introduce the relativistic Cholesky-decomposed density (CDD) matrix second-order M{\o}ller-Plesset perturbation theory (MP2) energies. The working equations are formulated in terms of the usual intermediates of…
The electron pair approximation offers a resource efficient variational quantum eigensolver (VQE) approach for quantum chemistry simulations on quantum computers. With the number of entangling gates scaling quadratically with system size…
One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of…
In Paper I, the effective one-electron potentials (OEP) method was introduced and demonstrated as an efficient approach to reduce the computational cost of evaluation of the charge-transfer interaction energy within the effective fragment…
We propose HAMSI (Hessian Approximated Multiple Subsets Iteration), which is a provably convergent, second order incremental algorithm for solving large-scale partially separable optimization problems. The algorithm is based on a local…