Abstract

All widely used semi-empirical quantum chemical methods like PM6 , DFTB, or GFN -xTB are formulated in a (almost) minimal basis set of atomic orbitals, which limits the achievable accuracy for many important chemical properties. Recently, we proposed a new special purpose tight-binding (TB) electronic Hamiltonian termed PTB [1] which is expressed in an accurate polarized valence double-zeta AO basis set (vDZP). The basis has been specially optimized in molecular DFT calculations using standard ECPs for all elements up to radon². The PTB method aims primarily at reproducing the one-particle density matrix of a DFT reference calculation with the accurate wB97X-V³ range-separated hybrid (RSH) density functional in exactly the same AO basis. The combination of wB97X(-V) with vDZP/ECP and an adjusted D4 dispersion correction defines a new member in our hierarchy of efficient composite electronic structure methods, termed wB97X-3c². The basis set optimization concept is furthermore applied to a minimal set of AOs which – as a totally new ingredient – is made adaptive, i.e., radially different for symmetry distinct atoms in a molecule. This q-vSZP set⁴ forms the basis of our third-generation tight-binding model GP3 -xTB which includes non-local Fock-exchange as well as other new many-center Hamiltonian terms (e.g., atomic correction potentials, ACP ). It aims at general purpose (GP) applicability in chemistry and more closely approaches DFT accuracy than previous semi-empirical methods at only slightly increased computational cost. When the number of primitive Gaussians in q-vSZP is somewhat reduced, and this basis is coupled with wB97M-D4⁵ and ACPs, an extremely efficient new 3c-composite method dubbed wB97M-3c is obtained.

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