Approaching Exactness in Mean-Field Theory through Non-local Fragment-density-based Quantum Machine Learning

B. Huang

Due to the outstanding trade-off between efficiency and accuracy of density functional theory (DFT)

its combination with modern quantum mechanics based machine learning (QML) enables the accurate prediction of quantum properties of many-electron systems with high efficiency. The general scalability of such machine learning approaches

i.e.

predicting electronic structure details of large query compounds after training on small reference compounds

is still amiss. More importantly

the ever-growing quest for exactness in DFT is a mission impossible due to the enigmatic nature of the exchange-correlation potential. To overcome these limitations we introduce the Density Mediated Generalized Fock matrix machine learning (DMGF) model. DMGF

inspired by the linearity of quantum operators

essentially builds a linear map from the local density based non-local features to the generalized Fock matrix (from which quantum properties can be directly computed) for any electronic system

disregarding the nature of the reference method

i.e.

being either Hartree Fock (HF)

DFT or correlated post-HF. The density and knowledge necessary for the mapping is inferred from the reference data of atom-in-molecule-based fragments (also known as AMONs). We present numerical evidence that DMGF simultaneously achieves high efficiency

accuracy

scalability and transferability (EAST) for electronic structure details of novel test compounds. Systems studied include molecules of varying size spanning the typical organic chemical subspace

polymers

non-covalently interacting systems

as well as a solid. Our findings indicate that DMGF paves the way for computationally feasible

data-driven

numerically exact solutions to electronic structure problems for arbitrarily sized system

meanwhile bridging gaps between mean-field and correlated methods as well as between molecular and solid-state domains.