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WIREs Comput Mol Sci
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Extended tight‐binding quantum chemistry methods

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Abstract This review covers a family of atomistic, mostly quantum chemistry (QC) based semiempirical methods for the fast and reasonably accurate description of large molecules in gas and condensed phase. The theory is derived from a density functional (DFT) perturbation expansion of the electron density in fluctuation terms to various orders similar to the original density functional tight binding model. The term “eXtended” in their name (xTB) emphasizes the parameter availability for almost the entire periodic table of elements (Z ≤ 86) and improvements of the underlying theory regarding, for example, the atomic orbital basis set, the level of multipole approximation and the treatment of the important electrostatic and dispersion interactions. A common feature of most members is their consistent parameterization on accurate gas phase theoretical reference data for geometries, vibrational frequencies and noncovalent interactions, which are the primary properties of interest in typical applications to systems composed of up to a few thousand atoms. Further specialized versions were developed for the description of electronic spectra and corresponding response properties. Besides a provided common theoretical background with some important implementation details in the efficient and free xtb program, various benchmarks for structural and thermochemical properties including (transition‐)metal systems are discussed. The review is completed by recent extensions of the model to the force‐field (FF) level as well as its application to solids under periodic boundary conditions. The general applicability together with the excellent cost‐accuracy ratio and the high robustness make the xTB family of methods very attractive for various fields of computer‐aided chemical research. This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods Electronic Structure Theory > Semiempirical Electronic Structure Methods Software > Quantum Chemistry
This schematically depicts the proposed multilevel modeling scheme based on the GFN family of methods (first bubble), which are described in this review. These methods are generally used at the initial stages of the multilevel workflow, where a large number of calculations needs to be carried out. This typically includes screening over numerous potential candidate molecules (visualized by the diameter of the cone) or extensive structural sampling of different molecular conformations. In subsequent steps (second bubble), the theory level (accuracy) is increased (electronic structure as well as including thermostatistical [RRHO] and solvation [solv] free energies [G]) while the number of considered candidate structures is reduced. At the end of this workflow, only very few structures need to be treated by high‐level theory levels (third bubble) to accurately determine the thermodynamic state (at equilibrium) and the respective property. The latter is often a spectroscopic property and is usually obtained as a thermostatistical Boltzmann ensemble average over all remaining candidates, based on free energies computed at the high‐level of theory
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Comparison between GFN0‐xTB and DLS‐76 volumes for 222 experimentally known zeolite framework structures. The inset shows a structure overlay of the only significant outlier (see text)
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Cartoon representation of the GFN‐FF optimized (blue) structure of hemocyanin (PDB: 1JS8), including an explicit water solvent shell of 6 Å (red)
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Calculated ECD spectrum of cytochrome c (blue solid line). The individual transition strengths are broadened by Gaussian functions with a full width at 1/e maximum of 0.5 eV and the spectrum is red‐shifted by 0.5 eV. The experimental spectrum in water (gray solid line) is taken from Reference 166
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Structural overlay of experimental crystal (gray) and GFN2‐xTB/GBSA(H2O)‐optimized metallo‐protein structures (blue). 1NX2 and 1QJJ were computed as closed‐shell systems with charges equal to +1 and −11, respectively. 5FTZ was treated as a doublet with a net charge of +6 (see Reference 129 for details)
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Comparison of GFN2‐xTB thermostatistical data with corresponding B97‐3c DFT reference values for 39 organic molecules ranging from ethane (smallest) to n‐octane (largest). The solid line shows the one‐to‐one correspondence and the dashed ones indicate a common error range for chemical accuracy, that is, ±1 kcal/mol
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Automatic workflow for GFNn‐xTB based EI‐MS calculations (modified from Reference 152). The hexafluorobenzene molecule is taken as an example
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The (PCP)Ir(N2) pincer complex and its protomers: (a) Lewis structure of (PCP)Ir(N2) in the unprotonated state, (b–e) most stable protomers of [(PCP)Ir(N2)H]+. The proton position is highlighted for better visibility. Relative energies below the structures correspond to the GFN2‐xTB[GBSA(THF)] level
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Pd‐pincer metallomacrocycle: (a) Lewis structure of the metallomacrocycle, (b) overlay between the crystal structure (transparent blue) and the lowest conformer generated at the GFN2‐xTB[GBSA(acetonitrile)] level, (c) overlay of the 10 lowest energy conformers
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Structure overlays of the GFN2‐xTB optimized (transparent blue; the GBSA solvation model was applied) and X‐ray reference structures (color code; the respective CSD code is given) for three metal–organic polyhedra (carbon bound hydrogen atoms are omitted for better visibility). The heavy‐atom RMSDs (hRMSD) are given and the timings were obtained with normalopt settings on 14 CPU Intel® Xeon® E5‐2660 v4 2.00 GHz CPU cores
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The Ac‐Ala19‐Lys‐H+ molecule. (a) Most stable α‐helical and folded conformations of Ac‐Ala19‐Lys‐H+ in the gas phase at GFN2‐xTB level. As indicated by the arrow, both forms can interchange depending on the protonation site (Ac‐H+ vs. Lys‐H+). (b) Comparison of corresponding conformational energies at the GFN2‐xTB and PBE0‐D4/def2‐TZVPD//PBEh‐3c levels in the gas phase
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The ibuprofen molecule: (a) most populated conformers of ibuprofen in the gas phase obtained at the GFN2‐xTB level, (b) Lewis structure of the molecule including highlighted dihedral angles, (c) highest lying conformer of ibuprofen in the gas phase obtained at the GFN2‐xTB level. Relative energies below the structures correspond to the GFN2‐xTB level, energies in parenthesis refer to PBE0‐D3/def2‐TZVPP results obtained for the fully optimized DFT structures
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Exemplary transition state (TS) localization with GFN2‐xTB driven mGSM for reaction 15 (the Lewis structures are given) of the MOBH35141,142 test set. The mGSM reaction path along the reaction coordinate (RC) is depicted in blue whereas the relevant TS, whose structure is shown as inset, is marked with a red circle. The respective reaction energies ΔER and reaction barriers ΔE predicted by GFN2‐xTB (blue) and TPSS‐D3(BJ)/SVP (green) as well as the corresponding coupled‐cluster reference values (gray) are also shown
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Mean absolute deviations (MADs) in kcal/mol of GFNn‐xTB methods, GFN‐FF, PM6‐D3H4, and PM7 for various benchmarks sets comprising non‐covalent interaction energies (a) and conformational energies (b). The respective inset shows the average MAD over all tested sets compared to the low‐cost composite QM methods HF‐3c and B97‐3c as well as a few large basis DFT results taken from Reference 132. (c) The association energies for 30 large supramolecular complexes (S30L133 test set) computed with GFN2‐xTB, GFN‐FF, and PM6‐D3H4 together with the respective DLPNO‐CCSD(T)134,135/CBS*136 reference values. The inset depicts the MADs for the GFNn‐xTB methods and GFN‐FF as well as further SQM, low‐cost composite, and large basis set DFT methods. (d) MADs in kcal/mol of GFN1‐xTB, GFN2‐xTB, PM6‐D3H4, and DFTB3‐D3(BJ) for five reaction barrier height test sets. Except for the S30L and MALT205137 sets, the geometries and reference values are taken from the GMTKN55132 database
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Performance of GFN‐FF in comparison to the universal (UFF) and highly specialized FFs (OPLS2005 and AMBER*) for a set of 70 protein structures.129 Average hRMSD, Cα RSMD, and average deviations of four distinctive dihedral angles w.r.t. the corresponding crystal structure given in Å and degree, respectively
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Comparison of (a) VTB and PBE0/TZVP73,74 CM572 reference atomic charges and (b) sTDA‐xTB and SCS‐CC2/TD‐DFT75 reference excitation energies. The black line denotes a one to one correspondence of the two data sets
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(a) Normal distribution plots of deviations in calculated equilibrium rotational constants Be for the ROT34 set108,109 (see inset for the respective structures) are shown. (b) Structure overlays and corresponding heavy‐atom RMSDs (hRMSD) in Å w.r.t. the crystal structure or DFT reference structures of four exemplary complexes from the lanthanide set106 are depicted (GFN2‐xTB‐optimized structures are shown in transparent blue, carbon bound hydrogen atoms are omitted for better visibility). (c) Correlation plots for bond lengths and angles in pm and degree, respectively, calculated with GFN1‐ and GFN2‐xTB for the subset of the TMG145 set.107 (d) Structure overlays and hRMSD in Å w.r.t. DFT reference structures of four exemplary complexes from the TMG145 set107 are shown. The respective Cambridge Structural Database (CSD) codes are placed below each structure: Crabtree catalyst (JAFFOL), Brintzinger‐Kaminsky catalyst (QAJGOY), Grubbs‐Hoveyda I catalyst (CEBHEW), and Karstedt's catalyst variant (YECXUA)
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Schematic representation of the fragmented Hessian algorithm. A complex molecular structure with Nc atoms is divided into several chemically reasonable fragments (of size Nfrag) and the Hessian of each fragment Hfrag is diagonalized individually. The diagonalized Hessian Hdiag is constructed from the fragments, instead of diagonalizing the Hessian of the entire system Hc, thus reducing the overall computational costs
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CPU times (given in seconds on a logarithmic scale) for single point energy plus gradient calculations of 14 proteins. Computations were performed using a quad‐core desktop machine with 4.20 GHz Intel i7‐7700K CPUs. The PDB identifiers are given on the abscissa, the corresponding number of atoms is given on top
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Computational workflow of the sTDA‐xTB method. The VTB (valence tight‐binding) part uses geometry‐dependent electronegativity difference‐based charges as input and generates Mulliken charge‐based CM5 charges72 in a trunctated SCC procedure. The XTB (extended tight‐binding) step then uses these charges as input and generates orbitals in a minimal+diffuse basis set for a subsequent excited state calculation at the simplified Tamm‐Dancoff approximated TD‐DFT (sTDA) level
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Overview of the GFN family of methods with main components and classification of the most important terms. Dark gray shaded areas denote a quantum mechanical description while light gray parts indicate a classical or semi‐classical description. The parts surrounded by the arrows are treated in an iterative, self‐consistent fashion. For a more detailed discussion including the definition of the acronyms see text
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