SQM methods approximate single-reference Hartree–Fock (HF) or first-principles DFT theory and have been investigated extensively in the 1980s and 1990s. Semiempirical quantum mechanical (SQM) methods (7-9) provide a well-known alternative route because they are at least 2 orders of magnitude faster than conventional DFT treatments. (4-6) The disadvantages of the FF treatment are numerous, including difficulties with metals, proton transfer and protonation states, polarization and chemical reactions, and can only be circumvented by a quantum mechanical (QM) treatment of the electrons. For instance, many interesting proteins with 2000–5000 atoms are out of reach for routine DFT optimizations, and such investigations are conducted at the force-field (FF) level. For fairly large systems with 1000 or more atoms, however, even simplified schemes such as the PBEh-3c hybrid DFT (1, 2) and Hartree–Fock/minimal basis set (HF-3c) (3) composite methods, which we have proposed in the past few years, become computationally unfeasible. These computations serve as a starting point for investigations of various spectroscopic and/or thermochemical properties, possibly with higher-level wave function theory (WFT) methods. In quantum chemistry, geometry optimizations, vibrational frequency calculations, and molecular dynamics simulations are currently dominated by Kohn–Sham density functional theory (DFT) for system sizes up to a few hundred atoms. The accuracy of the method, called Geometry, Frequency, Noncovalent, eXtended TB (GFN-xTB), is extensively benchmarked for various systems in comparison with existing semiempirical approaches, and the method is applied to a few representative structural problems in chemistry. Key features of the Hamiltonian are the use of partially polarized Gaussian-type orbitals, a double-ζ orbital basis for hydrogen, atomic-shell charges, diagonal third-order charge fluctuations, coordination number-dependent energy levels, a noncovalent halogen-bond potential, and the well-established D3 dispersion correction.
The parametrization covers all spd-block elements and the lanthanides up to Z = 86 using reference data at the hybrid density functional theory level. The functional form of the method is related to the self-consistent density functional TB scheme and mostly avoids element-pair-specific parameters. We propose a novel, special purpose semiempirical tight binding (TB) method for the calculation of structures, vibrational frequencies, and noncovalent interactions of large molecular systems with 1000 or more atoms.
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