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

Xuecheng Shao, Lukas Paetow, Mark E. Tuckerman, Michele Pavanello

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number6281
JournalNature communications
Issue number1
StatePublished - Dec 2023

ASJC Scopus subject areas

  • General Chemistry
  • General Biochemistry, Genetics and Molecular Biology
  • General Physics and Astronomy


Dive into the research topics of 'Machine learning electronic structure methods based on the one-electron reduced density matrix'. Together they form a unique fingerprint.

Cite this