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We present a pedagogical derivation of the Hartree--Fock equations using the second-quantization atomic-orbital density-matrix formalism developed by Kj{\ae}rgaard, J{\o}rgensen, Olsen, Coriani, and Helgaker for AO-based response theory.…
The general procedure underlying Hartree-Fock and Kohn-Sham density functional theory calculations consists in optimizing orbitals for a self-consistent solution of the Roothaan-Hall equations in an iterative process. It is often ignored…
The treatment of atomic anions with Kohn-Sham density functional theory (DFT) has long been controversial since the highest occupied molecular orbital (HOMO) energy, $E_{HOMO}$, is often calculated to be positive with most approximate…
The nuclear-electronic orbital (NEO) method is a well-established approach for treating nuclei quantum mechanically in molecular systems beyond the usual Born-Oppenheimer approximation. In this work, we present a strategy to implement the…
The exchange-correlation energy in Kohn-Sham density functional theory is expressed as a functional of the electronic density and the Kohn-Sham orbitals. An alternative to Kohn-Sham theory is to express the energy as a functional of the…
We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
Orbital-free density functional theory (OFDFT) offers a challenging way of electronic-structure calculations scaled as $\mathcal{O}(N)$ computation for system size $N$. We here develop a scheme of the OFDFT calculations based on the…
In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic ($B$ field)…
The current investigation focuses on detailed analysis of the anchor based optimization approach (ABOA), its comparison with alternative global fitting protocols and on the global analysis of the truncation of basis effects in the…
Converged approximate density functional calculations usually do not bind anions, due to large self-interaction error. But Hartree-Fock calculations have no such prob- lem, producing negative HOMO energies. A recently proposed scheme for…
We present a fully numerical framework for the optimization of molecule-specific quantum chemical basis functions within the quantics tensor train format using a finite-difference scheme. The optimization is driven by solving the…
Atomic basis sets are widely employed within quantum mechanics based simulations of matter. We introduce a machine learning model that adapts the basis set to the local chemical environment of each atom, prior to the start of self…
We present a simple way to describe the lowest unoccupied diffuse states in carbon nanostructures in density functional theory (DFT) calculations using a minimal LCAO (linear combination of atomic orbitals) basis set. By comparing plane…
The evaluation of exact (Hartree--Fock, HF) exchange operator is a crucial ingredient for the accurate description of electronic structure in periodic systems through ab initio and hybrid density functional approaches. An efficient…
We present a method to perform fully selfconsistent density-functional calculations, which scales linearly with the system size and which is well suited for very large systems. It uses strictly localized pseudoatomic orbitals as basis…
The Fock exchange operator plays a central role in modern quantum chemistry. The large computational cost associated with the Fock exchange operator hinders Hartree-Fock calculations and Kohn-Sham density functional theory calculations with…
We present model-assisted density fitting (MADF) basis set generator, an algorithm for generating primitive atomic Gaussian density fitting (DF) basis sets (DFBSs) from a contracted Gaussian orbital basis set (OBS). The MADF algorithm…
Simplified Hartree-Fock computations are carried out on the atoms He through Ne, using orthonormalized basis functions for the 1s, 2s and 2p orbitals dependent on three parameters. Using Mathematica with the new Apple M1 chip, computations…
We have developed a reduced-cost non-Dyson third-order algebraic diagrammatic construction theory for the electron-attachment problem based on state-specific frozen natural orbitals. Density fitting and truncated natural auxiliary functions…