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

Abstract

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.

Computational Chemistry as Applied in Environmental Research: Opportunities and Challenges

“…344 In the area of materials science with implications in environmental fields, ML algorithms have great potential and have been applied to reduce the computational cost of simulating extended systems (biomolecules, organic, organic−inorganic hybrid materials, metals, among others) and in the understanding of different phenomena (electron transport, magnetic and optical properties) with acceptable accuracy. 93,345…”

“…ML-based quantum chemical methods have been recently used in environmental problems to give insights into radical chemical reactions, new particle formation, heterogeneous (photo)­catalysis, and photochemical transformations . In the area of materials science with implications in environmental fields, ML algorithms have great potential and have been applied to reduce the computational cost of simulating extended systems (biomolecules, organic, organic–inorganic hybrid materials, metals, among others) and in the understanding of different phenomena (electron transport, magnetic and optical properties) with acceptable accuracy. , …”

Obtaining Robust Density Functional Tight-Binding Parameters for Solids across the Periodic Table

“…Unlike empirical interatomic potentials, it can thus be applied to systems where charge transfer, excitations, and/or chemical reactions are of interest, e.g., in catalysis. − In this context, the development of extensions such as self-consistent charge (SCC) DFTB (also known as DFTB2) and DFTB3 , has been highly influential. Recently, the development of hybrid functionals and machine learning (ML) approaches in DFTB have further expanded its domain of applicability. , However, being a semiempirical method, the lacking availability of general parametrizations remains a bottleneck toward more widespread adoption.…”

Efficient Parameterization of Density Functional Tight-Binding for 5f-Elements: A Th–O Case Study

“…In conventional DFTB parametrizations, the parameters that determine the Hamiltonian of the system, including the two-center bond and overlap integrals, are fixed to the values computed from DFT, while the empirical pairwise repulsive potentials are optimized to minimize the energy and force errors with respect to DFT reference calculations. − The accuracy and transferability of the DFTB model obtained in the conventional approach can be limited because the central force pairwise repulsive potential cannot accurately describe the angularly dependent forces inherent to interatomic bonding . One of the most straightforward ways to overcome this limitation is to extend the pairwise repulsive potential to include many-body effects using either alternative functional forms or neural networks. ,− Recent work by our team showed that it is also possible to improve the accuracy of angularly dependent forces by optimizing the radial dependencies of Slater–Koster bond integrals alongside with the two-center repulsive pair potentials. ,− Compared to the challenge of adopting many-body repulsive potentials, optimizing the Slater–Koster bond integrals does not increase either the complexity or computational expense of the final DFTB model, which can be implemented in any of the standard DFTB codes. However, when the radial dependencies of the Slater–Koster bond integrals are treated as adjustable terms to be optimized, the number of parameters in the model tends to increase precipitously with the number of elements and with a prefactor that is more daunting when heavy elements with d and f orbitals are included.…”