Automation of Active Space Selection for Multireference Methods via Machine Learning on Chemical Bond Dissociation

Abstract

Predicting and understanding the chemical bond is one of the major challenges of computational quantum chemistry. Kohn−Sham density functional theory (KS-DFT) is the most common method, but approximate density functionals may not be able to describe systems where multiple electronic configurations are equally important. Multiconfigurational wave functions, on the other hand, can provide a detailed understanding of the electronic structure and chemical bond of such systems. In the complete-active-space self-consistent field (CASSCF) method one performs a full configuration interaction calculation in an active space consisting of active electrons and active orbitals. However, CASSCF and its variants require the selection of these active spaces. This choice is not black-box; it requires significant experience and testing by the user, and thus active space methods are not considered particularly user-friendly and are employed only by a minority of quantum chemists. Our goal is to popularize these methods by making it easier to make good active space choices. We present a machine learning protocol that performs an automated selection of active spaces for chemical bond dissociation calculations of main group diatomic molecules. The protocol shows high prediction performance for a given target system as long as a properly correlated system is chosen for training. Good active spaces are correctly predicted with a considerably better success rate than random guess (larger than 80% precision for most systems studied). Our automated machine learning protocol shows that a "black-box" mode is possible for facilitating and accelerating the large-scale calculations on multireference systems where single-reference methods such as KS-DFT cannot be applied.

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

“… 11 − 17 Given that nitrobenzene is a strongly correlated system, the complete active space self-consistent field (CASSCF) method is one of the most adequate approaches for studying such a compound. 18 − 21 Unfortunately, due to exponential growth in the computational cost, 22 the application of exact CASSCF is limited to small size active spaces, whose limit is approximately 20 electrons distributed in 20 orbitals; only when massive parallelization was implemented, 23 it was possible to enlarge the active space to 22 electrons distributed in 22 orbitals. 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.…”

Multireference Methods are Realistic and Useful Tools for Modeling Catalysis

“…While selection of the active space has historically been considered a step requiring human intervention, it is encouraging that promising automated procedures have started to appear, particularly those exploiting powerful machine learning techniques. [92][93] This should lead to MR methods becoming more routine, particularly for single point calculations. Future studies should target enlarging the set of systems to which these approaches can be systematically applied.…”

“…Acquisition of "chemical knowledge" by machine learning algorithms has been demonstrated by Jablonka et al in a study designed to assign automatically the correct oxidation states of atoms. [91] More recently, Jeong et al [92] have reported a proof-of-concept study using machine learning for automated active space selection. Their results, although limited to small chemical spaces, demonstrate the feasibility of an automated procedure for active space selection that can in principle be enlarged by increasing the dimensions and variability of the training set.…”

Perspective on integrating machine learning into computational chemistry and materials science

“…By employing a probabilistic input space and a structured target space, one obtains a model that can, e.g., be used to generate novel molecular structures. The probability distribution over molecular space can be modeled explicitly, for example using variational autoencoders, 47 or implicitly, e.g., by generative adversarial networks 48 that provide access to the distribution only through sampling. In a supervised setting, generative models can facilitate inverse design by learning a probability distribution of chemical structures conditioned on a desired target range of one or multiple properties.…”

“…As a consequence, these methods (e.g., Complete Active Space Self Consistent Field (CASSCF)) have been hard to use by non-expert users in a black box manner in the past. Jeong et al 66 recently introduced a ML protocol based on decision trees for active space selection in bond dissociation studies. Their approach is able to predict active spaces able to reproduce the dissociation curves of diatomic molecules with a success rate of approximately 80 percent precision compared to random selection.…”