density functional theory – Optimization Online

An Orthogonalization-free Parallelizable Framework for All-electron Calculations in Density Functional Theory

Published: 2020/07/29

Applications - Science and Engineering, Nonlinear Optimization all-electron calculations, density functional theory, orthogonalization-free, parallel algorithm

All-electron calculations play an important role in density functional theory, in which improving computational efficiency is one of the most needed and challenging tasks. In the model formulations, both nonlinear eigenvalue problem and total energy minimization problem pursue orthogonal solutions. Most existing algorithms for solving these two models invoke orthogonalization process either explicitly or implicitly … Read more

Adaptive Regularized Self-Consistent Field Iteration with Exact Hessian for Electronic Structure Calculation

Published: 2012/10/08

Nonlinear Optimization density functional theory, kohn-sham total energy minimization, orthogonality constraints, regularized scf, trust-region methods

The self-consistent field (SCF) iteration has been used ubiquitously for solving the Kohn-Sham (KS) equation or the minimization of the KS total energy functional with respect to orthogonality constraints in electronic structure calculations. Although SCF with heuristics such as charge mixing often works remarkably well on many problems, it is well known that its convergence … Read more

Density-based Globally Convergent Trust-Region Methods for Self-Consistent Field Electronic Structure Calculations

Published: 2005/07/10, Updated: 2006/02/18

Juliano B. Francisco

Leandro Martínez

José Mario Martínez

Basic Sciences Applications, Constrained Nonlinear Optimization, Nonlinear Optimization convergence analysis, density functional theory, hartree-fock, kohn-sham, levenberg-marquardt, trust-region methods

A theory of globally convergent trust-region methods for self-consistent field electronic structure calculations that use the density matrices as variables is developed. The optimization is performed by means of sequential global minimizations of a quadratic model of the true energy. The global minimization of this quadratic model, subject to the idempotency of the density matrix … Read more