arXiv subjects

Yorick Leonard Adrian Schmerwitz

Publications and source records attributed to Yorick Leonard Adrian Schmerwitz.

3 recordsLinked to original sources

arXiv2026

Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations I: Dipole Moments of Rydberg States

Rydberg excited states are challenging to describe due to their highly diffuse character. Orbital-optimized density functional calculations typically provide more accurate values of the excitation energy of Rydberg states than time-dependent density functional theory approaches, but their performance with respect to excited-state properties such as the dipole moment remains largely unexplored as existing benchmarks are limited to the lowest excited state. Here, orbital-optimized density functional calculations with a plane-wave basis set are used to compute the dipole moment of several Rydberg states of a set of small molecules. Plane waves provide a flexible representation of diffuse Rydberg orbitals, whereas commonly used atomic orbitals basis sets are found to yield significant discrepancies in the magnitude and orientation of the dipole moment, even when diffuse functions are included and the excitation energy agrees well with the plane-wave results. The generalized gradient approximation functional PBE used in combination with the plane-wave representation of the orbitals gives good agreement with higher-level coupled-cluster calculations performed with sufficiently diffuse basis sets, when the latter are available. The hybrid functional PBE0 further improves the results, while PBE with globally scaled explicit Perdew-Zunger self-interaction correction generally leads to larger errors and an overestimation of the dipole moment, despite restoring the correct asymptotic $-1/r$ dependence of the effective Kohn--Sham potential.

physics.chem-ph↗

arXiv2026

Excited-state Properties Beyond the Excitation Energy from Orbital-Optimized Density Functional Calculations II: Absorption Spectra

Previous benchmarks of orbital-optimized density functional calculations of transition intensities in molecules have primarily been restricted to the lowest electronic excitation. Here, the performance of this variational approach is assessed across several valence and Rydberg excited states of small molecules, calculating the absorption spectra up to 10~eV. A plane-wave basis set is employed to accurately describe diffuse Rydberg excitations, while the transition dipole moment is evaluated from nonorthogonal Kohn--Sham determinants within the projector augmented wave formalism. Comparison with higher-level coupled-cluster results shows that orbital-optimized calculations provide a good description of oscillator strengths for states with predominantly single-configurational character, even with the generalized gradient approximation functional PBE. The inclusion of exact exchange and self-interaction correction further improves the results, with the latter yielding the smallest errors (mean absolute relative error of $\sim$25%). In contrast, large errors for all functionals are found for multi-configurational states, due to an inability of the approach to describe the multi-configurational character. Nonorthogonality between independently optimized states has previously been raised as a possible source of error in transition properties. In the present benchmark, no correlation of the nonorthogonality between the ground and excited states with the error on the transition intensity is found. These results establish the performance of orbital-optimized density functional calculations for absorption spectra of small molecules and highlight the need for extensions that combine state-specific orbital relaxation with a multi-configurational treatment.

physics.chem-ph↗

arXiv2024

Saddle Point Search Algorithms for Variational Density Functional Calculations of Excited Electronic States with Self-Interaction Correction

Excited electronic states of molecules and solids play a fundamental role in fields such as catalysis and electronics. In electronic structure calculations, excited states typically correspond to saddle points on the surface described by the variation of the energy as a function of the electronic degrees of freedom. A direct optimization algorithm based on generalized mode following is presented for density functional calculations of excited states. While conventional direct optimization methods based on quasi-Newton algorithms usually converge to the stationary point closest to the initial guess, even minima, the generalized mode following approach systematically targets a saddle point of a specific order l by following the l lowest eigenvectors of the electronic Hessian up in energy. This approach thereby recasts the challenging saddle point search as a minimization, enabling the use of efficient and robust minimization algorithms. The initial guess orbitals and the saddle point order of the target excited state solution are evaluated by performing an initial step of constrained optimization freezing the electronic degrees of freedom involved in the excitation. In the context of Kohn-Sham density functional calculations, typical approximations to the exchange-and-correlation functional suffer from a self-interaction error. The Perdew and Zunger self-interaction correction can alleviate this problem, but makes the energy variant to unitary transformations in the occupied orbital space, introducing a large amount of unphysical solutions that do not fully minimize the self-interaction error. An extension of the generalized mode following method is proposed that ensures convergence to the solution minimizing the self-interaction error.

physics.chem-ph↗