Related papers: Prediction of many-electron wavefunctions using at…
First principles calculations based on density functional theory are having an incerasing impact on our understanding of molecule-surface interactions. For example, calculations of the multi-dimensional potential energy surface have…
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…
The problem of construction of the Wannier functions (WFs) in a restricted Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming the so-called low-energy part of the spectrum) can be formulated in several different…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…
Methods for correcting residual energy errors of configuration interaction (CI) calculations of molecules and other electronic systems are discussed based on the assumption that the energy defect can be mapped onto atomic regions. The…
The expectation value of the Hamiltonian using a model wave function is widely used to estimate the eigenvalues of electronic Hamiltonians. We explore here a modified formula for models based on long-range interaction. It scales differently…
The projection of the eigenfunctions obtained in standard plane-wave first-principle electronic-structure calculations into atomic-orbital basis sets is proposed as a formal and practical link between the methods based on plane waves and…
Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…
Density functional theory with plane-wave basis sets is widely employed in computational materials science, including applications to isolated molecular systems. However, the inadequate description of electron correlation remains a…
In this paper I propose a new model for representing the formation energies of multicomponent crystalline alloys as a function of atom types. In the cases when displacements of atoms from their equilibrium positions are not large, the…
Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous works focuses on generating predictions for…
We demonstrate how to determine numerically nearly exact orthonormal orbitals that are optimal for evaluation of the energy of arbitrary (correlated) states of atoms and molecules by minimization of the energy Lagrangian. Orbitals are…
We consider the Friedrichs-Faddeev model in the case where the kernel of the potential operator is holomorphic in both arguments on a certain domain of $\mathbb{C}$. For this model we, first, study the structure of the $T$- and $S$-matrices…
We study the properties of the Hooke's law correlation energy ($\Ec$), defined as the correlation energy when two electrons interact {\em via} a harmonic potential in a $D$-dimensional space. More precisely, we investigate the $^1S$ ground…
We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies…
In this work, we refine the Bohr model of the hydrogen atom by describing the motion of the electron through a single real-valued stochastic process, effectively realizing Brownian motion under the Born rule. Our approach derives the…
The interaction between electrons and lattice vibrations determines key physical properties of materials, including their electrical and heat transport, excited electron dynamics, phase transitions, and superconductivity. We present a new…
Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…
We test a set of multiconfigurational wavefunction approaches for calculating the ground state electron population for a two-site Anderson model representing a molecule on a metal surface. In particular, we compare (i) a Hartree Fock like…
A new approach to chemical bonding is introduced in order to provide an improved understanding of the connection between basic quantum mechanics and the covalent pair bond. It's focus is on the fact that the energy of the bond is largely…