The need for accurate calculations on atoms and diatomic molecules is motivated by the
opportunities and challenges of such studies. The most commonly used approach for all …

A uniform derivation of the self-consistent field equations in a finite basis set is presented.
Both restricted and unrestricted Hartree–Fock (HF) theory as well as various density …

Augmented Lagrangian methods with general lower-level constraints are considered in the
present research. These methods are useful when efficient algorithms exist for solving …

A new framework is presented for evaluating the performance of self-consistent field
methods in Kohn–Sham density functional theory (DFT). The aims of this work are two-fold …

This article is concerned with the numerical solution of subspace optimization problems,
consisting of minimizing a smooth functional over the set of orthogonal projectors of fixed …

We give the formulation of a Riemannian Newton algorithm for solving a class of nonlinear
eigenvalue problems by minimizing a total energy function subject to the orthogonality …

As a proof of principle, self-consistent Kohn-Sham calculations are performed with the exact
exchange-correlation functional. Finding the exact functional for even one trial density …

In two recent papers regularization methods based on Taylor polynomial models for
minimization were proposed that only rely on Hölder conditions on the higher-order …

We present an efficient quasi-Newton orbital solver optimized to reduce the number of
gradient evaluations and other computational steps of comparable cost. The solver …

The density functional theory (DFT) in electronic structure calculations can be formulated as
either a nonlinear eigenvalue or a direct minimization problem. The most widely used …