Machine Learning Enhanced DFTB Method for Periodic Systems: Learning from Electronic Density of States

Density functional tight binding (DFTB) is an approximate
density
functional based quantum chemical simulation method with low computational
cost. In order to increase its accuracy, we have introduced a machine
learning algorithm to optimize several parameters of the DFTB method,
concentrating on solids with defects. The backpropagation algorithm
was used to reduce the error between DFTB and DFT results with respect
to the training data set and to obtain adjusted DFTB Hamiltonian and
overlap matrix elements. Afterward, the generalization capability
of the trained model was tested for geometries not being part of the
training set. In the current work, we have focused on defective periodic
silicon and silicon carbide systems as target materials and the density
of states (DOS) as target property to demonstrate the feasibility
of our approach. The trained model was able to reduce the differences
between the DFTB and DFT DOS significantly, while other derived properties
(for example, Mulliken population distribution, projected DOS) remained
physically sound. Also, the transferability of the obtained model
could be verified. Our method allows to carry out relatively fast
simulations with high accuracy and only moderate training efforts,
and represents a good compromise for cases, where long-range effects
make direct machine learning predictions difficult.