A Ranked-Orbital Approach to Select Active Spaces for High-Throughput Multireference Computation

Abstract

The past decade has seen a great increase in the application of high-throughput computation to a variety of important problems in chemistry. However, one area which has been resistant to the highthroughput approach is multireference wave function methods, in large part due to the technicalities of setting up these calculations and in particular the not always intuitive challenge of active space selection. As we look toward a future of applying high-throughput computation to all areas of chemistry, it is important to prepare these methods for large-scale automation. Here, we propose a ranked-orbital approach to select active spaces with the goal of standardizing multireference methods for high-throughput computation. This method allows for the meaningful comparison of different active space selection schemes and orbital localizations, and we demonstrate the utility of this approach across 1120 multireference calculations for the excitation energies of small molecules. Our results reveal that it is helpful to distinguish the method used to generate orbitals from the method of ranking orbitals in terms of importance for the active space. Additionally, we propose our own orbital ranking scheme that estimates the importance of an orbital for the active space through a pair-interaction framework from orbital energies and features of the Hartree−Fock exchange matrix. We call this new scheme the "approximate pair coefficient" (APC) method and we show that it performs quite well for the test systems presented.

Electronic Structure of Nitrobenzene: A Benchmark Example of the Accuracy of the Multi-State CASPT2 Theory

“…To overcome this drawback, new approaches and methods are being developed with the objective of enlarging the treatable active spaces or select the optimal minimum of active orbitals. 18 − 25 On the other hand, until now, the general tendency was to select by hand the minimal active space in accordance with the chemical problem under study. However, this methodology has serious inconveniences when orbitals are strongly correlated and could lead to inexact results or erroneous conclusions.…”

“…26 − 32 In particular, nitrobenzene is at the limit of the CASSCF capabilities because it demands an active space of 20 electrons distributed in 17 orbitals. 25 − 31 For this reason, the application of the CASSCF method to this system with an active space of this size is a challenging task due to the huge number of electrons and orbitals that has to be included. However, the objective of this work is to treat nitrobenzene with such a large active space.…”

Large-Scale Benchmarking of Multireference Vertical-Excitation Calculations via Automated Active-Space Selection

“…67 The molecular point group was reduced to the highest available symmetry implemented for the PySCF SA-CASSCF solver: C 2h , C 2v , C s , or D 2h . The APC-rankedorbital active-space-selection scheme 36,59 starts with a set of candidate localized orbitals, ranks them by their approximated orbital entropies, and then eliminates orbitals starting from the lowest-entropy orbitals (those with the highest entropies are considered to be the most important) until the active space size reaches a predetermined maximum number of configuration state functions. We next describe the generation of candidate orbitals, then the ranking scheme, and finally the maximum-size criteria.…”

“…[39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58] Recently, we published the ranked-orbital approach to select active spaces and the approximate pair coefficient (APC) approximation for low-cost estimates of the orbital entropies used in the ranking. 59 This automated scheme, inspired by the entropy-driven approach of Stein and Reiher, 42 allows for the flexible selection of active space size with a hierarchy of levels (max (8,8), max (10,10), max (12,12)...) reminiscent of the CI level sequence (CISD, CISDT, CISDTQ, ...).…”

Machine-Learned Energy Functionals for Multiconfigurational Wave Functions

“…With the exception of benzene, all active spaces for CASSCF calculations were chosen automatically using the ranked-orbital approach. 68 The highest 23 doubly occupied orbitals and the lowest 23 virtual orbitals of a closed-shell RHF wave function were individually Boyslocalized, 69 and the approximate pair coefficient (APC) method 68 was employed on all doubly occupied orbitals and the localized virtual orbitals to approximate orbital entropies (the remaining virtual orbitals were not considered for the active space). These entropies were then used to rank the orbitals in terms of importance, and the final active space was selected by setting a maximum number of allowed CSFs in the wave function expansion (e.g., max(2,2), max(4,4), and max(6,7)) and dropping orbitals from the active space until the size of the active space satisfied the threshold.…”