A Reusable Library for Second-Order Orbital Optimization Using the Trust Region Method

TL;DR

A reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library is presented and a review of the theory behind trust region-based methods alongside various extensions are presented.

Abstract

We present a reusable, open-source software implementation of the second-order trust region algorithm in the new OpenTrustRegion library. We apply the implementation to the general-purpose optimization of molecular orbitals in various contexts within electronic-structure theory. Our permissibly licensed implementation can be included in any software package, be it free and open-source, academically licensed closed-source, or commercial. Detailing the implementation in OpenTrustRegion, we present a review of the theory behind trust region-based methods alongside various extensions. We demonstrate the robustness and efficiency of our optimization library with extensive benchmarks for self-consistent field calculations, orbital localization, as well as orbital symmetrization tasks, featuring challenging and pathological systems.

Figures (7)

• Figure 1: Interface between a given host program and the OpenTrustRegion library.
• Figure 2: Convergence of second-order orbital optimization of singlet (RHF) and triplet (UHF) states of selected pathological systems. Results are reported for the various implementations in OpenTrustRegion (present work), PySCF, and Orca.
• Figure 3: Timings for DIIS (in PySCF) followed by an internal stability check and second-order orbital optimization (in OpenTrustRegion) for HF calculations on the homologous series of the alkanes with different C--C bond lengths (ranging from $1.5$ to $5.0$ Å).
• Figure 4: Convergence of gPM and FB MO localization for buckminsterfullerene (green), circumcoronene (orange), and circumcircumcoronene (blue) in an aug-cc-pVDZ basis set.
• Figure 5: Convergence of the symmetrization of gPM and FB MOs for the same systems as in Fig. \ref{['fig:convergence_loc']}, albeit in a cc-pVDZ basis set: C$_{60}$ (green), C$_{54}$H$_{18}$ (orange), and C$_{96}$H$_{24}$ (blue).