Machine Learning 1- and 2-electron reduced density matrices of polymeric molecules

TL;DR

This paper demonstrates a machine learning approach to predict 1- and 2-electron reduced density matrices of polymeric molecules, enabling accurate energy calculations and addressing the N-representability problem.

Contribution

It introduces a novel ML method for directly predicting valid reduced density matrices of polymers, bypassing traditional N-representability challenges.

Findings

ML models accurately predict 1- and 2-electron RDMs

Predicted RDMs enable precise molecular energy calculations

Method generalizes to new conformations and molecules

Abstract

Encoding the electronic structure of molecules using 2-electron reduced density matrices (2RDMs) as opposed to many-body wave functions has been a decades-long quest as the 2RDM contains sufficient information to compute the exact molecular energy but requires only polynomial storage. We focus on linear polymers with varying conformations and numbers of monomers and show that we can use machine learning to predict both the 1-electron and the 2-electron reduced density matrices. Moreover, by applying the Hamiltonian operator to the predicted reduced density matrices we show that we can recover the molecular energy. Thus, we demonstrate the feasibility of a machine learning approach to predicting electronic structure that is generalizable both to new conformations as well as new molecules. At the same time our work circumvents the N-representability problem that has stymied the adaption of 2RDM methods, by directly machine-learning valid Reduced Density Matrices.