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

The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.

A new model, termed D4, for the efficient computation of molecular dipole-dipole dispersion coefficients is presented. As in the related, well established D3 scheme, these are obtained as a sum of atom-in-molecule dispersion coefficients over atom pairs. Both models make use of dynamic polarizabilities obtained from first-principles time-dependent density functional theory calculations for atoms in different chemical environments employing fractional atomic coordination numbers for interpolation. Different from the D3 model, the coefficients are obtained on-the-fly by numerical Casimir-Polder integration of the dynamic, atomic polarizabilities α(iω). Most importantly, electronic density information is now incorporated via atomic partial charges computed at a semi-empirical quantum mechanical tight-binding level, which is used to scale the polarizabilities. Extended statistical measures show that errors for dispersion coefficients with the proposed D4 method are significantly lower than with D3 and other, computationally more involved schemes. Alongside, accurate isotropic charge and hybridization dependent, atom-in-molecule static polarizabilities are obtained with an unprecedented efficiency. Damping function parameters are provided for three standard density functionals, i.e., TPSS, PBE0, and B3LYP, allowing evaluation of the new DFT-D4 model for common non-covalent interaction energy benchmark sets.

We present an extension of the DFT-D4 model [J. Chem. Phys., 2019, 150, 154122] for periodic systems.

Conspectus Quantum chemical methods are nowadays able to determine properties of larger chemical systems with high accuracy and Kohn–Sham density functional theory (DFT) in particular has proven to be robust and suitable for everyday applications of electronic structure theory. A clear disadvantage of many established standard density functional approximations like B3LYP is their inability to describe long-range electron correlation effects. The inclusion of such effects, also termed London dispersion, into DFT has been extensively researched in recent years, resulting in some efficient and routinely used correction schemes. The well-established D3 method has demonstrated its efficiency and accuracy in numerous applications since 2010. Recently, it was improved by developing the successor (termed D4) which additionally includes atomic partial charge information for the generation of pairwise dispersion coefficients. These coefficients determine the leading-order (two-body) and higher-order (three- or many-body) terms of the D4 dispersion energy which is simply added to a standard DFT energy. With its excellent accuracy-to-cost ratio, the DFT-D4 method is well suited for the determination of structures and chemical properties for molecules of most kinds. While dispersion effects in organic molecules are nowadays well studied, much less is known for organometallic complexes. For such systems, there has been a growing interest in designing dispersion-controlled reactions especially in the field of homogeneous catalysis. Here, efficient electronic structure methods are necessary for screening of promising model complexes and quantifying dispersion effects. In this Account, we describe the quality of calculated structural and thermodynamic properties in gas-phase obtained with DFT-D4 corrected methods, specifically for organometallic complexes. The physical effects leading to London dispersion interactions are briefly discussed in the picture of second-order perturbation theory. Subsequently, basic theoretical aspects of the D4 method are introduced followed by selected case studies. Several chemical examples are presented starting with the analysis of transition metal thermochemistry and noncovalent interactions for small, heavy element containing main group compounds. Computed reaction energies can only match highly accurate reference values when all energy contributions are included in the DFT treatment, thus highlighting the major role of dispersion interactions for the accurate description of thermochemistry in gas-phase. Furthermore, the correlation between structural and catalytic properties is emphasized where the accessibility of high quality structures is essential for reaction planning and catalyst design. We present calculations for aggregates of organometallic systems with intrinsically large repulsive electrostatic interactions which can be stabilized by London dispersion effects. The newly introduced inclusion of atomic charge information in the DFT-D4 model robustly leads to quantitatively improved dis...

Neutron diffraction of tri(3,5-tert-butylphenyl)methane at 20 K reveals an intermolecular C-H···H-C distance of only 1.566(5) Å, which is the shortest reported to date. The compound crystallizes as a C-symmetric dimer in an unusual head-to-head fashion. Quantum chemical computations of the solid state at the HSE-3c level of theory reproduce the structure and the close contact well (1.555 Å at 0 K) and emphasize the significance of packing effects; the gas-phase dimer structure at the same level shows a 1.634 Å C-H···H-C distance. Intermolecular London dispersion interactions between contacting tert-butyl substituents surrounding the central contact deliver the decisive energetic contributions to enable this remarkable bonding situation.

We propose a semiempirical quantum chemical method, designed for the fast calculation of molecular Geometries, vibrational Frequencies and Non-covalent interaction energies (GFN) of systems with up to a few thousand atoms. Like its predecessors GFN-xTB and GFN2-xTB, the new method termed GFN0-xTB is parameterized for all elements up to radon (Z = 86) and mostly shares well-known density functional tight-binding approximations as well as basis set and integral approximations. The main new feature is the avoidance of the self-consistent charge iterations leading to speed-ups of a factor of 2-20 depending on the size and electronic complexity of the system. This is achieved by including only quantum mechanical contributions up to first-order which are incorporated similar to the previous versions without any pair-specific parameterization. The essential electrostatic electronic interaction is treated by a classical electronegativity equilibration charge model yielding atomic partial charges that enter the electronic Hamiltonian indirectly. Furthermore, the atomic charge-dependent D4 dispersion correction is included to account for long range London correlation effects. Formulas for analytical total energy gradients with respect to nuclear displacements are derived and implemented in the xtb code allowing numerically very precise structure optimizations. The neglect of self-consistent energy terms not only leads to a large gain in computational speed but also can increase robustness in electronically difficult situations because ill-convergence or artificial charge-transfer (CT) is avoided. The comparison of GFN0-xTB and GFN/GFN2-xTB allows dissection of quantum electronic polarization and CT effects thereby improving our understanding of chemical bonding. Compared the the most sophisticated multipole-based GFN2-xTB model (which approaches DFT accuracy for the target properties closely), GFN0-xTB performs slightly worse for non-covalent interactions and molecular structures, while very good results are observed for conformational energies. Vibrational frequencies are obtained less accurately than with GFN/GFN2-xTB but they may still be useful for various purposes like estimating relative thermostatistical reaction energies. Most exceptional is the fact that even relatively complicated transition metal complex structures can be accurately optimized with a non-self-consistent quantum approach. The new method bridges the gap between force-fields and traditional semiempirical methods with its excellent computational cost to accuracy ratio and is intended to explore the chemical space of large molecular systems and solids.

We propose a semiempirical quantum chemical method, designed for the fast calculation of molecular Geometries, vibrational Frequencies and Non-covalent interaction energies (GFN) of systems with up to a few thousand atoms. Like its predecessors GFN-xTB and GFN2-xTB, the new method termed GFN0-xTB is parameterized for all elements up to radon (Z = 86) and mostly shares well-known density functional tight-binding approximations as well as basis set and integral approximations. The main new feature is the avoidance of the self-consistent charge iterations leading to speed-ups of a factor of 2-20 depending on the size and electronic complexity of the system. This is achieved by including only quantum mechanical contributions up to first-order which are incorporated similar to the previous versions without any pair-specific parameterization. The essential electrostatic electronic interaction is treated by a classical electronegativity equilibration charge model yielding atomic partial charges that enter the electronic Hamiltonian indirectly. Furthermore, the atomic charge-dependent D4 dispersion correction is included to account for long range London correlation effects. Formulas for analytical total energy gradients with respect to nuclear displacements are derived and implemented in the <i>xtb </i>code allowing numerically very precise structure optimizations. The neglect of self-consistent energy terms not only leads to a large gain in computational speed but also can increase robustness in electronically difficult situations because ill-convergence or artificial charge-transfer (CT) is avoided. The comparison of GFN0-xTB and GFN/GFN2-xTB allows dissection of quantum electronic polarization and CT effects thereby improving our understanding of chemical bonding. Compared to the most sophisticated multipole-based GFN2-xTB model (which approaches DFT accuracy for the target properties closely), GFN0-xTB performs slightly worse for non-covalent interactions and molecular structures, while very good results are observed for conformational energies. Vibrational frequencies are obtained less accurately than with GFN/GFN2-xTB but they may still be useful for various purposes like estimating relative thermostatistical reaction energies. Most exceptional is the fact that even relatively complicated transition metal complex structures can be accurately optimized with a non-self-consistent quantum approach. The new method bridges the gap between force-fields and traditional semiempirical methods with its excellent computational cost to accuracy ratio and is intended to explore the chemical space of large molecular systems and solids.<br>