arXiv subjects

Peter R. Franke

Publications and source records attributed to Peter R. Franke.

2 recordsLinked to original sources

arXiv2026

On the performance of QTP functionals applied to second-order response properties II: Dynamic polarizability and long-range C$_6$ coefficients

This work is the second in the series "On the performance of QTP functionals applied to second-order response properties." In the first paper (J. Chem. Phys. 162, 054105, 2025), we demonstrated the good performance of Quantum Theory Project functionals in predicting static perturbed second-order properties, such as static polarizabilities, nuclear magnetic resonance (NMR) spin-spin coupling constants, and NMR chemical shifts. In the present study, we focus on frequency-dependent properties, namely dynamic polarizabilities and C$_6$ dispersion coefficients. For completeness, a total of 25 exchange-correlation (XC) functionals were investigated. Dynamic polarizabilities were evaluated at five different perturbation wavelengths: 632.99 nm, 594.10 nm, 543.52 nm, 514.50 nm, and 325.13 nm. This property was also computed using HF and EOM-CCSD. In general, EOM-CCSD results are very close to those obtained with linear-response CC3, except at the highest frequency. Among Kohn-Sham calculations, TPSS0 and QTP01 showed the best overall performance for dynamic polarizabilities. We also assessed how well QTP functionals reproduce the pole structure of the CO molecule. For the C$_6$ dispersion coefficients, calculations were performed using the Casimir-Polder equation. The best overall performance was obtained with O3LYP; however, the first eleven ranked functionals show very similar accuracy. Within the QTP family, QTP01 and LC-QTP provide the best results for C$_6$ coefficients.

physics.chem-ph↗

arXiv2025

Exploiting a Shortcoming of Coupled-Cluster Theory: The Extent of non-Hermiticity as a Diagnostic Indicator of Computational Accuracy

The fundamental non-Hermitian nature of the forms of coupled-cluster (CC) theory widely used in quantum chemistry has usually been viewed as a negative, but the present letter shows how this can be used to advantage. Specifically, the non-symmetric nature of the reduced one-particle density matrix (in the molecular orbital basis) is advocated as a diagnostic indicator of computational quality. In the limit of full coupled-cluster theory (which is equivalent to full configuration interaction (FCI)), the electronic wavefunction and correlation energy are exact within a given one-particle basis set and the symmetric character of the exact density matrix is recovered. The extent of the density matrix asymmetry is shown to provide a measure of ``how difficult the problem is'' (like the well-known T$_1$ diagnostic), but its variation with level of theory also gives information about ``how well this particular method works'', irrespective of the difficulty of the problem at hand. The proposed diagnostic is described and applied to a select group of small molecules, and an example of its overall utility for the practicing quantum chemist is illustrated through its application to the beryllium dimer (Be$_2$). Future applications of this idea to excited states, open-shell systems, symmetry-breaking problems and extension of the method to the two-particle density are then proposed.

physics.chem-ph↗