A Robust Non-Self-Consistent Tight-Binding Quantum Chemistry Method for large Molecules

Abstract

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.

Assessing conformer energies using electronic structure and machine learning methods

“…Calculations were performed using Open Babel version 3.0 [25] for all force field calculations (MMFF94 [26][27][28][29][30] and UFF [31,32] ); OpenMOPAC for PM7 [33] ; xtb version 6.2 [34] for GFN0, [35] GFN1, [36] and GFN2 calculations [37] ; and Orca 4.0.1 [38] for all density functional and ab initio calculations, unless otherwise indicated. For density functional methods, the D3(BJ) [39][40][41][42] dispersion correction scheme was used as indicated, except for ωB97X-D3, [43] which uses a similar approach.…”

Robust Atomistic Modeling of Materials, Organometallic, and Biochemical Systems

“…Theidea of ageneral GFN-type FF is inspired by the latest developments in the field of SQM methods,n amely the evolution of GFN1-, GFN2, and especially GNF0-xTB [25] methods,where the latest key ingredient was the introduction of ac lassical electronegativity-equilibrium (EEQ) atomiccharge model [26,27] for the description of pairwise interatomic electrostatic interactions.T his allowed to truncate the fundamental expansion of the DFT energy E [1]i nt erms of electron-density fluctuations d1 after the first-order term, leading to an on-self-consistent method which employs classical atomic charges.GFN-FF introduces approximations to the remaining quantum-mechanical terms in GFN0-xTB by replacing most of the extended-Hückel-type theory (EHT) for covalent bonding by classical bond, angle,a nd torsion terms.T oh ighlight the ancestry from the xTB methods,t he similarities and differences between FF and QM methods are illustrated in Figure 2.…”

Van Der Waals Potential: An Important Complement to Molecular Electrostatic Potential in Studying Intermolecular Interactions

“…Geometries of all involved monomer structures except for cyclo [18]carbon have been optimized by Gaussian 16 A.03 program [17] at B3LYP/6-31G* level. [18,19] The molecular dynamics (MD) simulation was realized by xtb 6.3 preview 2 code [20] based on GFN0-xTB [21] or GFN1-xTB [22] theory. The GFN-xTB series of theory can be regarded as a semi-empirical variant of density functional theory, [21] since it is quite efficient, we were able to conduct the MD simulation for a long time to ensure adequate sampling.…”

“…[18,19] The molecular dynamics (MD) simulation was realized by xtb 6.3 preview 2 code [20] based on GFN0-xTB [21] or GFN1-xTB [22] theory. The GFN-xTB series of theory can be regarded as a semi-empirical variant of density functional theory, [21] since it is quite efficient, we were able to conduct the MD simulation for a long time to ensure adequate sampling. GFN0-xTB is the cheapest and crudest version of GFN-xTB theory, the GFN1-xTB is evidently more accurate and robust than GFN0-xTB while the cost is increased by about one order of magnitude.…”