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arXiv:2011.14715

Automatic selection of active spaces for strongly correlated systems using machine learning algorithms

Pavlo Golub, Andrej Antalík, Libor Veis, Jiří Brabec

Published Nov 30, 2020• 3 citations
arXivHTMLPDF

Abstract

The 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 non-trivial task. In this article, we present the neural network (NN) based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed from one transition metal and various ligands, on which we have performed DMRG and calculated 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 ML models could correctly predict the importance of orbitals with the high accuracy. Also, the ML models show a high degree of transferability on systems much larger than any complex used in training procedures.

DOI
10.48550/arxiv.2011.14715

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The 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 non-trivial task. In this article, we present the neural network (NN) based approach for automatic selection of active spaces, focused on transition metal systems. The training set has been formed from artificial systems composed from one transition metal and various ligands, on which we have performed DMRG and calculated 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 ML models could correctly predict the importance of orbitals with the high accuracy. Also, the ML models show a high degree of transferability on systems much larger than any complex used in training procedures.
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.
We introduce a new database SC1MC-2020 of artificial mono transition metal complexes involving reference data (HF energy, orbitals, and integrals), and one- and two-site entropies obtained from corresponding DMRG calculations. The purpose of this database is to include all important metal - ligand interactions of strongly correlated systems and obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information almost immediately for any similar systems with high degree of transferability.
Efficient and robust approximations to the full configuration interaction (full-CI) method such as the density matrix renormalization group (DMRG) and the full-CI quantum Monte Carlo (FCIQMC) algorithm allow for multiconfigurational self-consistent field (MC-SCF) calculations of molecules with many strongly correlated electrons. This opens up the possibility to treat large and complex systems that were previously untractable, but at the same time it calls for an efficient and reliable active space selection as the choice of how many electrons and orbitals enter the active space is critical for any multireference calculation. In this work we propose an Active Space Selection based on 1st order perturbation theory (ASS1ST) that follows a "bottom-up" strategy and utilizes a set of quasi-natural orbitals together with sensible thresholds for their occupation numbers. The required quasi-natural orbitals are generated by diagonalizing the virtual and internal part of the one-electron reduced density matrix that is obtained from strongly contracted n-electron valence perturbation theory (SC-NEVPT) on top of a minimal active space calculation. Self-consistent results can be obtained when the proposed selection scheme is applied iteratively. Initial applications on four chemically relevant benchmark systems indicate the capabilities of ASS1ST. Eventually, the strengths and limitations are critically discussed.
Accurate electronic structure calculations are essential in modern materials science, but strongly correlated systems pose a significant challenge due to their computational cost. Traditional methods, such as complete active space self-consistent field (CASSCF), scale exponentially with system size, while alternative methods like the density matrix renormalization group (DMRG) scale more favorably, yet remain limited for large systems. In this work, we demonstrate how a simple machine learning model can enhance quantum chemical DMRG calculations, improving their accuracy to chemical precision, even for systems that would otherwise require considerably higher computational resources. The systems under study are polycyclic aromatic hydrocarbons, which are typical candidates for DMRG calculations and are highly relevant for advanced technological applications.
We introduce a new version of the database SC1MC (SC1MC-2022), obtained by extension of the recent SC1MC-2020, which includes artificial mono transition metal complexes. The database involves reference data used as inputs for training of machine learning models, one- and two-site entropies, and mutual information obtained at the DMRG level for canonical and split-localised orbitals. The purpose of this database is to obtain as much as possible information about the electronic correlation structure, which could be exploited by machine learning models to estimate these important information without a significant computational cost for any similar type of systems with some degree of transferability.
The quality of multi-scale modelling techniques in molecular electronic structure calculations, such as embedding and subspace methods, relies upon the chosen active space. The automation of active space selection is vital for ensuring the accuracy, reproducibility, and scalability in such calculations. In this work, we introduce Tensor Network Active Space Selection using the Entanglement Feature. Through the isolation of strongly correlated electrons, this method provides a scalable foundation for embedding methods in multi-scale modelling. By representing the purities of all possible orbital partitions as a Matrix Product State, our method isolates regions of strong electron correlation without requiring manual preselection of target atoms or the calculation of expensive high-order density matrices. The results demonstrate that this approach leads to lower ground state energies and more accurate dipole moments than other fully automated selection schemes such as those based solely on single-orbital entropy or the selection of spatial orbitals around the HOMO/LUMO gap.