Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates

Simultaneous prediction of the molecular response properties,
such
as polarizability and the NMR shielding constant, at a low computational
cost is an unresolved issue. We propose to combine a linear-scaling
generalized energy-based fragmentation (GEBF) method and deep learning
(DL) with both molecular and atomic information-theoretic approach
(ITA) quantities as effective descriptors. In GEBF, the total molecular
polarizability can be assembled as a linear combination of the corresponding
quantities calculated from a set of small embedded subsystems in GEBF.
In the new GEBF-DL­(ITA) protocol, one can predict subsystem polarizabilities
based on the corresponding molecular wave function (thus electron
density and ITA quantities) and DL model rather than calculate them
from the computationally intensive coupled-perturbed Hartree–Fock
or Kohn–Sham equations and finally obtain the total molecular
polarizability via a linear combination equation. As a proof-of-concept
application, we predict the molecular polarizabilities of large proteins
and protein aggregates. GEBF-DL­(ITA) is shown to be as accurate enough
as GEBF, with mean absolute percentage error <1%. For the largest
protein aggregate (>4000 atoms), GEBF-DL­(ITA) gains a speedup ratio
of 3 compared with GEBF. It is anticipated that when more advanced
electronic structure methods are used, this advantage will be more
appealing. Moreover, one can also predict the NMR chemical shieldings
of proteins with reasonably good accuracy. Overall, the cost-efficient
GEBF-DL­(ITA) protocol should be a robust theoretical tool for simultaneously
predicting polarizabilities and NMR shieldings of large systems.