Machine learning the electronic structure of molecules via the one-body reduced density matrix

Computing electronic structures is one of the most important yet computationally expensive tasks of the computational chemist and material scientist.  Machine learning methods can be employed to learn the electronic structure of molecules and materials for example by learning the electron density[1,2]. In this talk, we present a new paradigm. We show that models that learn the map linking the external potential to the one-body reduced density matrix can reproduce the results of local and hybrid density functional theory, Hartree-Fock and full configuration interaction theories for small to mid-sized molecules such as benzene and propanol. We also show that standard quantum chemistry or an additional machine learning model can be used to evaluate molecular observables, energies and forces from the predicted density matrices. The resulting surrogate electronic structure methods perform essentially any of the tasks typically assigned to standard electronic structure methods, such as computing band gaps and Kohn-Sham orbitals, running energy-conserving ab-initio molecular dynamics simulations, and generating infrared spectra that include anharmonicity and thermal effects, without using costly algorithms. We have developed a user-friendly and efficient Python code, QMLearn, that implements the machine learning models developed in this work[3,4].

[1] F. Brockherde, L. Vogt, L. Li, M. E. Tuckerman, K. Burke, and K.-R. Müller, Nat. Commun. 8, 1 (2017).

[2] Y. Bai, L. Vogt-Maranto, M. E. Tuckerman, and W. J. Glover, Nat. Commun. 13, 7044 (2022).

[3] “QMLearn: A quantum machine learning electronic structure method,” Available at https://gitlab.com/pavanello-research-group/qmlearn (2023).

[4] X. Shao, L. Paetow, M. E. Tuckerman, and M. Pavanello, Nat. Commun. 14, 6281 (2023).