Machine learning electronic structure methods based on the one-electron reduced density matrix.

The theorems of density functional theory (DFT) establish bijective maps between the local external potential of a many-body system and its electron density, wavefunction and, therefore, one-particle reduced density matrix. Building on this foundation, we show that machine learning models based on the one-electron reduced density matrix can be used to generate surrogate electronic structure methods. We generate surrogates of local and hybrid DFT, Hartree-Fock and full configuration interaction theories for systems ranging from small molecules such as water to more complex compounds like benzene and propanol. The surrogate models use the one-electron reduced density matrix as the central quantity to be learned. From the predicted density matrices, we show that either standard quantum chemistry or a second machine-learning model can be used to compute molecular observables, energies, and atomic forces. The surrogate models can generate essentially anything that a standard electronic structure method can, ranging from band gaps and Kohn-Sham orbitals to energy-conserving ab-initio molecular dynamics simulations and infrared spectra, which account for anharmonicity and thermal effects, without the need to employ computationally expensive algorithms such as self-consistent field theory. The algorithms are packaged in an efficient and easy to use Python code, QMLearn, accessible on popular platforms.

Which Physical Phenomena Determine the Ionization Potential of Liquid Water?

Understanding and predicting the properties of molecular liquids from the corresponding properties of the individual molecules is notoriously difficult because there is cooperative behavior among the molecules in the liquid. This is particularly relevant for water, where even the most fundamental molecular properties, such as the dipole moment, are radically different in the liquid compared to the gas phase. In this work, we focus on the ionization potential (IP) of liquid water by dissecting its individual contributions from the individual molecules making up the liquid. This is achieved by using periodic subsystem DFT, a state-of-the-art electronic structure method based on density embedding. We identify and evaluate four important electronic contributions to the IP of water: (1) mean-field, evaluated at the Hartree-Fock level; (2) electronic correlation, incorporated via DFT and wave function-based methods; (3) interaction with and (4) polarization of the environment, both evaluated ab initio with density embedding. Furthermore, we analyze their impact on the IP relative to the structural fluctuation of liquid water, revealing unexpected, hidden correlations, confirming that the broadening of the photoelectron spectra is mostly caused by intermolecular interactions confined in the first solvation shell.