Machine Learning-Assisted Selection of Active Spaces for Strongly Correlated Transition Metal Systems

Abstract

Active space quantum chemical methods could provide very accurate description of strongly correlated electronic systems, which is of tremendous value for natural sciences. The proper choice of the active space is crucial but a nontrivial task. In this article, we present a neural network-based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed of one transition metal and various ligands, on which we have performed the density matrix renormalization group and calculated the single-site entropy. On the selected set of systems, ranging from small benchmark molecules up to larger challenging systems involving two metallic centers, we demonstrate that our machine learning models could predict the active space orbitals with reasonable accuracy. We also tested the transferability on out-of-the-model systems, including bimetallic complexes and complexes with ligands, which were not involved in the training set. Also, we tested the correctness of the automatically selected active spaces on a Fe­(II)–porphyrin model, where we studied the lowest states at the DMRG level and compared the energy difference between spin states or the energy difference between conformations of ferrocene with recent studies.

Ab Initio Methods in First‐Row Transition Metal Chemistry

“…This "tedious" strategy can be eased by performing preliminary calculations with a modest basis set, such as double-ζ for the metal and minimal for the ligand atoms. One can also utilize some recently proposed "black-box" techniques [96][97][98][99][100][101][102][103][104] based on DMRG, [96] NEVPT2, [97] or even machine learning [98,99] to choose active spaces. Still, at the moment, it is the users' responsibility to check their chosen active spaces or experiment on several choices of active space.…”

“…Furthermore, experienced knowledge is needed to use multireference methods, since finding balanced active spaces for TM com- plexes is not trivial. Even though numerous automated procedures for the active space selection are available, [96][97][98][99][100][101][102][103][104] they might not always produce uniform active spaces for different spin states or along the reaction pathway. In addition, the accuracy of these methods, especially of multireference perturbation theory and local coupled cluster approaches, for TM complexes is an important topic that requires further investigations.…”

Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet–Triplet Gaps of Biradicals

“…Here, we take a different approach and identify the most appropriate CASs by means of single-orbital entropies and two-orbital mutual information. 49 − 51 …”

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

“…Although CASSCF has been used since the 1980s, 25 the prospect of automated active space selection has only received significant attention within the last decade or so. [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, ...).…”