Related papers: Analytic gradients for natural orbital functional …
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
We use an effective field theory (EFT) approach to calculate the next to leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex…
We report the development of the theory and computer program for analytical nuclear energy gradients for (extended) multi-state complete active space perturbation theory (CASPT2) with full internal contraction. The vertical shifts are also…
Despite recent advances, systematic quantitative treatment of the electron correlation problem in extended systems remains a formidable task. Systematically improvable Green's function methods capable of quantitatively describing weak and…
This study presents an evaluation of derivative-free optimization algorithms for the direct minimization of Hartree-Fock-Roothaan energy functionals involving nonlinear orbital parameters and quantum numbers with noninteger order. The…
A recently developed finite element approach for fully numerical atomic structure calculations [S. Lehtola, Int. J. Quantum Chem. 119, e25945 (2019)] is extended to the description of atoms with spherically symmetric densities via…
The possibility to use functionals of occupation numbers and natural orbitals for interacting fermions is discussed as an alternative to multi-reference energy density functional method. An illustration based on the two-level Lipkin model…
Ab initio no-core configuration interaction (NCCI) calculations for the nuclear many-body problem have traditionally relied upon an antisymmetrized product (Slater determinant) basis built from harmonic oscillator orbitals. The accuracy of…
This work presents the formalism and implementation of excited state nuclear forces within density functional linear response theory (TDDFT) using a plane wave basis set. An implicit differentiation technique is developed for computing…
Fractional gradient descent has been studied extensively, with a focus on its ability to extend traditional gradient descent methods by incorporating fractional-order derivatives. This approach allows for more flexibility in navigating…
Existing algorithms to solve alternating-current optimal power flow (AC-OPF) often exploit linear approximations to simplify system models and accelerate computations. In this paper, we improve a recent hierarchical OPF algorithm, which…
We demonstrate in the present study that self-consistent calculations based on the self-energy functional theory (SFT) are possible for the electronic structure of realistic systems in the context of quantum chemistry. We describe the…
We introduce a unified framework -- Quantum Neural Ordinary and Partial Differential Equations (QNODEs and QNPDEs) -- which extends the continuous-time formalism of classical neural ordinary and partial differential equations into quantum…
Machine learning is employed to build an energy density functional for self-bound nuclear systems for the first time. By learning the kinetic energy as a functional of the nucleon density alone, a robust and accurate orbital-free density…
We develop a unified framework for nonparametric functional estimation based on kernel transport along orbits of discrete group actions, which we term \emph{Twin Spaces}. Given a base kernel $K$ and a group $G = \langle\varphi\rangle$…
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…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
We introduce Effective Atom Theory (EAT), a framework that transforms combinatorial materials design into a smooth, gradient-driven optimization within density functional theory (DFT). Atoms are represented as probabilistic mixtures of…
In the present article, we show how to formulate the partially contracted n-electron valence second order perturbation theory (NEVPT2) energies in the atomic and active molecular orbital basis by employing the Laplace transformation of…
A new method for implementing the kinetic energy operator for real-space, grid-based electronic structure codes is developed. It is based on multi-order Adaptive Finite Differencing (AFD) and uses atomic pseudo orbitals produced by the…