![]() Opposed to many older SQM approaches that try to approximate HF or DFT results rather “globally” for almost all chemical properties and systems, but in the spirit of the special purpose GFN methods, the approach proposed here aims primarily at reproducing a fully self-consistent field (SCF) converged ωB97X-3c one-particle density matrix P as efficiently as possible. It represents a fundamental ingredient for the here described method and is used in its unmodified form see Ref. This new vDZP basis set performs universally well for thermochemistry and non-covalent interactions and provides small basis set superposition and incompleteness errors with triple- ζ or even quadruple- ζ quality. ![]() This was achieved by (a) relatively deep contraction (a large number of Gaussian primitive functions per AO) and (b) full optimization of primitive exponents and contraction coefficients with respect to DFT ( ωB97X-D3 43) energies of representative neutral and charged atoms and molecules of the respective element. 42 The basic idea is to avoid the matrix diagonalization bottleneck that appears in many low-cost electronic structure methods (including DFT for system sizes of 5000–10000 atoms) by constructing a compact (medium-sized) but inherently accurate AO basis set. Very recently, we designed and optimized a completely new vDZP basis set for all elements of Z = 1–86, including the lanthanides, with the goal of using it also for an extended basis set TB method. However, the reasoning for a minimal AO representation in SQM is clearly twofold: first, it speeds up integral and, in particular, matrix diagonalization steps, and second, often overlooked, it avoids numerically large and complicated one-center matrix elements of the Hamiltonian between AOs of the same angular momentum in a vDZP basis. This is not fulfilled by any current SQM method. The current view is that reasonable mean-field calculations should employ at least properly polarized valence double- ζ (vDZP) type basis sets consisting of two valence shells for each occupied one in the atomic ground state. For good reasons, this somewhat non-physical description of electronic structure was already abandoned decades ago for HF and DFT treatments. Although third- and higher-row elements in the DFTB and GFN-xTB include d-functions, the most important “core” elements H, C, N, O, and F lack such polarization AOs and, in fact, the typically considered valence shells are minimally described. One of the fundamental reasons for the mentioned SQM problems (besides the typical integral approximations applied very differently in various methods) is, in our opinion, the use of mostly minimal, atom-centered atomic orbital (AO) basis functions. This method may be used out-of-the-box to generate molecular/atomic features for machine learning applications or as the basis for accurate high-speed DFT methods. As an example application, the vibrational Raman spectrum of an entire protein with 327 atoms with respect to the DFT reference calculation is shown. It performs robustly for difficult transition metal complexes, for highly charged or zwitterionic systems, and for chemically unusual bonding situations, indicating a generally robust approximation of the (self-consistent) Kohn–Sham potential. ![]() The method globally achieves a high accuracy for the target properties at a speedup compared to the ωB97X-V/vDZP reference of about 3–4 orders of magnitude. ![]() The key features of the method are as follows: (a) it is non-self-consistent with an overall fixed number of only three required matrix diagonalizations (b) only AO overlap integrals are needed to construct the effective Hamiltonian matrix (c) new P-dependent terms emulating non-local exchange are included and (d) only element-specific empirical parameters (about 50 per element) need to be determined. Additional properties considered are orbital energies, dipole polarizabilities and dipole moments, and dipole polarizability derivatives. The primary target of this so-called density matrix tight-binding method is to reproduce the one-particle density matrix P of a molecular ωB97X-V range-separated hybrid density functional theory (DFT) calculation in exactly the same basis set. The inner-shell electrons are accounted for by standard, large-core effective potentials and approximations to them. Here, a completely new and consistently parameterized tight-binding electronic structure Hamiltonian evaluated in a deeply contracted, properly polarized valence double-zeta basis set (vDZP) is described. Existing semiempirical molecular orbital methods suffer from the usually minimal atomic-orbital (AO) basis set used to simplify the calculations. ![]()
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