Benchmark study of popular density functionals for calculating binding energies of three-center two-electron bonds

Benchmark Study of Density Functional Theory Methods in Geometry Optimization of Transition Metal-Dinitrogen Complexes

The current benchmark study is focused on determining the most precise theoretical method for optimizing the geometry of transition metal-dinitrogen complexes. To accomplish this goal, seven density functional (DF) methods from five distinct classes of density functional theory (DFT) have been selected, including B3LYP-D3(BJ), BP86-D3(BJ), PBE0-D3(BJ), ωB97X-D, M06, M06-L, and TPSSh-D3(BJ). These DFs will be utilized with the Karlsruhe basis set (def2-SVP). To carry out this benchmark study, a total of forty-two structurally diverse transition metal-dinitrogen compounds with experimentally known X-ray data have been selected from the Cambridge Crystallographic Data Centre (CCDC). Based on a comparison of the theoretical data with experimental values (X-ray) of the selected transition metal-dinitrogen compounds, statistical parameters such as root-mean-square deviation (RMSD) and N-N and M-N bond lengths are obtained to evaluate the performance of the seven chosen DFs. According to the obtained results, among all DFT methods used in the study, Minnesota functionals (M06 and M06-L) and TPSSh-D3(BJ) show good performance, with lower RMSD values. This suggests that these three methods are the most reliable for optimizing the geometry of transition metal-dinitrogen complexes. Based on the absolute errors of the N-N and M-N bond lengths relative to the X-ray data, further analysis is conducted, and it is determined that M06-L is the best functional for optimizing the geometry of transition metal-dinitrogen compounds. Additionally, the influence of using a high-level basis set (def2-TZVP) compared to def2-SVP on the calculated RMSD among the seven chosen methods is found to be negligible.

Testing of Exchange-Correlation Functionals of DFT for a Reliable Description of the Electron Density Distribution in Organic Molecules

Researchers carrying out calculations using the DFT method face the problem of the correct choice of the exchange-correlation functional to describe the quantities they are interested in. This article deals with benchmark calculations aimed at testing various exchange-correlation functionals in terms of a reliable description of the electron density distribution in molecules. For this purpose, 30 functionals representing all rungs of Jacob's Ladder are selected and then the values of some QTAIM-based parameters are compared with their reference equivalents obtained at the CCSD/aug-cc-pVTZ level of theory. The presented results show that the DFT method undoubtedly has the greatest problems with a reliable description of the electron density distribution in multiple strongly polar bonds, such as C=O, and bonds associated with large electron charge delocalization. The performance of the tested functionals turned out to be unsystematic. Nevertheless, in terms of a reliable general description of QTAIM-based parameters, the M11, SVWN, BHHLYP, M06-HF, and, to a slightly lesser extent, also BLYP, B3LYP, and X3LYP functionals turned out to be the worst. It is alarming to find the most popular B3LYP functional in this group. On the other hand, in the case of the electron density at the bond critical point, being the most important QTAIM-based parameter, the M06-HF functional is especially discouraged due to the very poor description of the C=O bond. On the contrary, the VSXC, M06-L, SOGGA11-X, M06-2X, MN12-SX, and, to a slightly lesser extent, also TPSS, TPSSh, and B1B95 perform well in this respect. Particularly noteworthy is the overwhelming performance of double hybrids in terms of reliable values of bond delocalization indices. The results show that there is no clear improvement in the reliability of describing the electron density distribution with climbing Jacob's Ladder, as top-ranked double hybrids are also, in some cases, able to produce poor values compared to CCSD.

Dependence of the substituent energy on the level of theory

Most often, the substituent effects are described using rather troublesome Hammett constants. Quite recently, it has been proposed to use the so-called substituent energy, which is based on total energies of the X-substituted polycyclic aromatic hydrocarbon and phenyl. This article concerns the influence of the applied level of theory (i.e., both the basis set and the method) on the determined values of the substituent energies. For this purpose, the energies of the NH₂ and NO₂ groups in 16 unique positions of naphthalene, anthracene, tetracene, phenanthrene, and pyrene were calculated using 10 different basis sets and 23 various exchange-correlation functionals representing the entire Jacob's Ladder, from local, through gradient- and meta-gradient-corrected, to hybrid and double-hybrid ones. Additionally, using even larger 6-311++G(2df,2p) basis set, the energies of NH₂ , NO₂ , CN, and Cl were also computed. Both the basis set and the method used have little effect on the substituent energy if the substituent is in the benzene-like position. On the contrary, the effect of the level of theory is pronounced especially in the case of the most spatially crowded 4-substituted phenanthrene. Substituent energies have been shown to be very useful theoretical parameters describing the proximity effect in the substituted derivatives of polycyclic aromatic hydrocarbons.

Lewis acid-catalyzed domino generation/[2,3]-sigmatropic rearrangement of ammonium ylides to access chiral azabicycles

[2,3]-Sigmatropic rearrangement of ammonium ylides represents a fundamental reaction for stereoselective synthesis of nitrogenous compounds. However, its applicability is limited by the scarcity of efficient, catalytic, and mild methods for generating ammonium ylides. Here, we report silver-catalyzed domino generation/[2,3]-sigmatropic rearrangement of ammonium ylides, furnishing chiral azabicycles with bridgehead quaternary stereogenic centers in high enantiomeric purity (up to 99% ee). A combination of density functional theory calculations and experimental studies revealed that residual water in the reaction system is crucial for the mild reaction conditions by functioning as a proton shuttle to assist carbon-silver bond protonation and C2─H deprotonation to generate the ammonium ylide. This reaction has a broad application scope. Besides the diverse substituents, N-fused azabicycles of various ring sizes are also easily accessed. In addition to silver salts, this strategy has also been successfully implemented by using a stoichiometric amount of nonmetallic I2.

Role of Alkaline-Earth Metal-Catalyst: A Theoretical Study of Pyridines Hydroboration

Density functional theory (DFT) calculations have been performed to investigate the mechanism of alkaline-earth-metal-catalyzed hydroboration of pyridines with borane. In this reaction, the active catalytic species is considered to be an alkaline earth metal hydride complex when the corresponding alkaline earth metal is used as the catalyst. The theoretical results reveal that initiation of the catalytic cycle is hydride transfer to generate a magnesium hydride complex when β-diimine alkylmagnesium is used as a pre-catalyst. The magnesium hydride complex can undergo coordination of the pyridine reactant followed by hydride transfer to form a dearomatized magnesium pyridine intermediate. Coordination of borane and hydride transfer from borohydride to magnesium then give the hydroboration product and regenerate the active magnesium hydride catalyst. The rate-determining step of the catalytic cycle is hydride transfer to pyridine with a free energy barrier of 29.7 kcal/mol. Other alkaline earth metal complexes, including calcium and strontium complexes, were also considered. The DFT calculations show that the corresponding activation free energies for the rate-determining step of this reaction with calcium and strontium catalysts are much lower than with the magnesium catalyst. Therefore, calcium and strontium complexes can be used as the catalyst for the reaction, which could allow mild reaction conditions.