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

Abstract

<div>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.</div>

How will quantum computers provide an industrially relevant computational advantage in quantum chemistry?

“…53 They include: (i) a calculation involving a complete active space (CAS) with 20 electrons in 20 spatial orbitals, realized within the framework of the MCSCF method on a chromium trimer (corresponding to approximately 4.2•10 9 single determinants (SDs)); (ii) a single point CASSCF calculation on a pentacene molecule with 22 electrons in 22 spatial orbitals (corresponding to approximately 5.0 • 10 11 SDs); (iii) a single iteration of the iterative CI algorithm for a chromium tetramer with 24 electrons in 24 spatial orbitals (∼ 7.3 • 10 12 SDs). 54 All these CI calculations utilized the 6-31G* basis set. To put the number of the SDs in chemical context, a FCI calculation on the propene molecule in the minimal STO-3G and the larger but still very small 6-31G basis set would correspond to 24 electrons in 21 and 39 spatial orbitals, respectively.…”

“…In year 2017 Reiher and co-workers 4 estimated that a CAS of the size (54,54), which is far larger than what CASCI or CASSCF can address on a classical computer, should be within our computational means to treat on a quantum computer. Would such a CAS be sufficient for an accurate, converged description of non-dynamic correlation in the FeMo-co system?…”

The Ranked-Orbital Approach to Selecting Active Spaces

“…The past five years have seen a large amount of research on the topic of automatically selecting the active space. 25,[29][30][31][32][33][34][35][36][37][38][39][40] A new approach for selecting active spaces that has gathered a lot of attention in recent years goes by the name of AutoCAS, 25,30 and is centered around the idea of choosing orbitals that vary in occupation (0, ↑, ↓, 2) within a low-cost or even partially converged DMRG calculation. This variance is measured through the single-orbital entropy, given for an orbital i as 41…”

$\mathbb{i}$CAS: Imposed Automatic Selection and Localization of Complete Active Spaces

“…While the combinatorial complexity can be alleviated to a large extent by imposing certain restrictions on the occupation patterns so as to a priori reduce the space size [15][16][17][18][19][20][21][22][23][24][25][26][27] or by using some highly efficient posteriori selection schemes as the CI solver, [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44] the first three issues pertinent to orbital selection and optimization are more delicate. Although the selection of active orbitals can be automated by using, e.g, occupation numbers of NOs, [1][2][3][4]45,46 information entropies, [47][48][49] machine learning, 50 subspace projection, [51][52][53] stepwise testing, 54 etc., the so-constructed CAS cannot be guaranteed to be the same for all geometries of complex systems due to the underlying cutoff thresholds or varying parameters. Herewith, we propose an automated approach for constructing a CAS that is guaranteed to be the s...…”