This generalized Wilson loop method avoids the above cumbersome challenges and allows for easy implementation and efficient calculations.
Here, using shift vector and shift current conductivity tensor as an example, we present a gauge-invariant generalized approach for efficient and direct calculations of nonlinear optical responses by representing interband Berry curvature, quantum metric, and shift vector in a generalized Wilson loop. However, this indirect method often suffers from the divergence at band degeneracy and optical zeros as well as convergence issues and high computation costs when summing over the states. Nonlinear light-matter interaction, as the core of ultrafast optics, bulk photovoltaics, nonlinear optical sensing and imaging, and efficient generation of entangled photons, has been traditionally studied by first-principles theoretical methods with the sum-over-states approach. We distribute the materials database and tools developed in this work publicly. To ensure predictive power, we adopt a learning framework where we repeatedly test the model on new low energy crystal structures and then add them to the fitting dataset, iterating until predictions improve.
#Ranking the screening efficacy of atomic orbitals plus#
We include both two-body and three-body effective interaction terms in our model, plus self-consistent charge transfer, enabling our model to work for metallic, covalent, and ionic bonds with the same parameter set. To tackle these challenges, we develop a density functional theory database of nearly one million materials, which we use to fit a universal set of tight-binding parameters for 65 elements and their binary combinations. Furthermore, most previous models consider only simple two-body interactions, which limits accuracy. However, well-tested parameter sets are generally only available for a limited number of atom combinations, making routine use of this method difficult. Parameterized tight-binding models fit to first principles calculations can provide an efficient and accurate quantum mechanical method for predicting properties of molecules and solids. The present work validates the general applicability of Slater and Koster’s scheme of linear combinations of atomic orbitals and points to future ab initio tight-binding parametrizations and linear-scaling DFT development. The Mulliken charge and bond order analyses are performed under QO basis set, which satisfy sum rules. Band structure, density of states, and the Fermi surface are calculated from this real-space tight-binding representation for various extended systems (Si, SiC, Fe, and Mo) and compared with plane-wave DFT results. We demonstrate that these minimal-basis orbitals can exactly reproduce all the electronic structure information below an energy threshold represented in the form of environment-dependent tight-binding Hamiltonian and overlap matrices. Wave functions obtained from plane-wave density-functional theory (DFT) calculations using norm-conserving pseudopotential, ultrasoft pseudopotential, or projector augmented-wave method are efficiently and robustly transformed into a set of spatially localized nonorthogonal quasiatomic orbitals (QOs) with pseudoangular momentum quantum numbers.
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