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

Creyon Bio, 3210 Merryfield Row San Diego, CA 92121 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. Specifically, we show that all desired 1-and 2-theory (DFT) and coupled-clusters methods, are electron correlations can be predicted at any level of theory key to ab initio understanding of molecular properties. However, these methods are slow. Specifically, currently considered to be the gold standard of quantum the sequence of n-electron reduced density matrices (n-chemistry it still involves major approximations which RDMs) forms a hierarchy of complexity that encodes preclude it from describing strongly correlated systems correlations between more and more electrons as n increase. Nevertheless, For example the 2RDM, which is obtained by making use of the fact that quantum correlations are essentially tracing the full electronic reduced density matrix over local, i.e. the quantum nearsightedness principle all electron coordinates but 2, encodes correlations between [2, 3], the latest generation of quantum chemistry 2 electrons.