Related papers: Explicitly Correlated Gaussian Basis Approach to P…
We consider a specific form of explicitly correlated Gaussians -- with tensor pre-factors -- which appear naturally when dealing with certain few-body systems in nuclear and particle physics. We derive analytic matrix elements with these…
We demonstrate that basis sets suitable for electronic structure calculations can be obtained from simple accuracy considerations for the hydrogenic one-electron ions $Y^{(Y-1)+}$ for $Y\in[1,Z]$, necessitating no self-consistent field…
We formulate the calculation of the ground-state wavefunction and energy of a system of strongly correlated electrons in terms of scattering matrices. A hierarchy of approximations is introduced which results in an incremental expansion of…
Deformed correlated Gaussian basis functions are introduced and their matrix elements are calculated. These basis functions can be used to solve problems with nonspherical potentials. One example of such potential is the dipole…
Electronic structure methods for accurate calculation of molecular properties have a high cost that grows steeply with the problem size, therefore, it is helpful to have the underlying atomic basis functions that are less in number but of…
Ensemble Density Functional Theory (EDFT) is a generalization of ground-state Density Functional Theory (GS DFT), which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms…
We extend density matrix embedding theory to periodic systems, resulting in an electronic band structure method for solid-state materials. The electron correlation can be captured by means of a local impurity model using various choices of…
The theory of correlated electron systems is formulated in a form which allows to use as a reference point an ab initio band structure theory (AIBST). The theory is constructed in two steps. As a first step the total Hamiltonian is…
For more than 150 years the structure of the periodic system of the chemical elements has intensively motivated research in different areas of chemistry and physics. However, there is still no unified picture of what a periodic system is.…
Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
Our electronic structure theory for crystalline solids is commonly built on the periodic potential assumption $V(\mathbf r)=V(\mathbf r+\mathbf R)$ for every lattice translation $\mathbf R$, enabling Bloch eigenstates, crystal momentum as a…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…
We introduce highly local basis sets for electronic structure which are very efficient for correlation calculations near the complete basis set limit. Our approach is based on gausslets, recently introduced wavelet-like smooth orthogonal…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
We propose a system-oriented basis-set design based on even-tempered basis functions to variationally encode electronic ground-state information into molecular orbitals. First, we introduce a reduced formalism of concentric even-tempered…
We calculate the electrostatic potential of a periodic lattice of arbitrary extended charges by using the Cartesian multipole formalism. This method allows the separation of the long-range potential from the contact potential (potential on…
Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are calculated analytically. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics.
Various explicitly correlated Gaussian (ECG) basis sets are considered for the solution of the molecular Schr\"odinger equation with particular attention to the simplest polyatomic system, H$_3^+$. Shortcomings and advantages are discussed…