J. Chem. Theory Comput.  19, 13 (2023)

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.

Phys. Rev. Materials 7, 063802 (2023)

Screened range-separated hybrid (SRSH) functionals within generalized Kohn-Sham density functional theory (GKS-DFT) have been shown to restore a general 1/(rɛ) asymptotic decay of the electrostatic interaction in dielectric environments. Major achievements of SRSH include an improved description of optical properties of solids and correct prediction of polarization-induced fundamental gap renormalization in molecular crystals. The density functional tight-binding method (DFTB) is an approximate DFT that bridges the gap between first-principles methods and empirical electronic structure schemes. While purely long-range corrected RSH are already accessible within DFTB for molecular systems, this work generalizes the theoretical foundation to also include screened range-separated hybrids, with conventional pure hybrid functionals as a special case. The presented formulation and implementation is also valid for periodic boundary conditions (PBC) beyond the Γ point. To treat periodic Fock exchange and its integrable singularity in reciprocal space, we resort to techniques successfully employed by DFT, in particular a truncated Coulomb operator and the minimum image convention. Starting from the first-principles Hartree-Fock operator, we derive suitable expressions for the DFTB method, using standard integral approximations and their efficient implementation in the dftb+ software package. Convergence behavior is investigated and demonstrated for the polyacene series as well as two- and three-dimensional materials. Benzene and pentacene molecular and crystalline systems show the correct polarization-induced gap renormalization by SRSH-DFTB at heavily reduced computational cost compared to first-principles methods.

Phys. Rev. Lett.  130, 026701 (2023)

Controlling edge states of topological magnon insulators is a promising route to stable spintronics devices. However, to experimentally ascertain the topology of magnon bands is a challenging task. Here we derive a fundamental relation between the light-matter coupling and the quantum geometry of magnon states. This allows us to establish the two-magnon Raman circular dichroism as an optical probe of magnon topology in honeycomb magnets, in particular of the Chern number and the topological gap. Our results pave the way for interfacing light and topological magnons in functional quantum devices.