Effect of the damping function in dispersion corrected density functional theory

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.     

Quantification of Noncovalent Interactions in Azide–Pnictogen, –Chalcogen,and –Halogen Contacts

The noncovalent interactions between azides and oxygen-containing moieties are investigated through a computational study based on experimental findings. The targeted synthesis of organic compounds with close intramolecular azide–oxygen contacts yielded six new representatives, for which X-ray structures were determined. Two of those compounds were investigated with respect to their potential conformations in the gas phase and a possible significantly shorter azide–oxygen contact. Furthermore, a set of 44 high-quality, gas-phase computational model systems with intermolecular azide–pnictogen (N, P, As, Sb), –chalcogen (O, S, Se, Te), and –halogen (F, Cl, Br, I) contacts are compiled and investigated through semiempirical quantum mechanical methods, density functional approximations, and wave function theory. A local energy decomposition (LED) analysis is applied to study the nature of the noncovalent interaction. The special role of electrostatic and London dispersion interactions is discussed in detail. London dispersion is identified as a dominant factor of the azide–donor interaction with mean London dispersion energy-interaction energy ratios of 1.3. Electrostatic contributions enhance the azide–donor coordination motif. The association energies range from −1.00 to −5.5 kcal mol⁻¹.     

Understanding the Fundamental Role of π/π, σ/σ, and σ/π Dispersion Interactions in Shaping Carbon‐Based Materials

Noncovalent interactions involving aromatic rings, such as π‐stacking and CH/π interactions, are central to many areas of modern chemistry. However, recent studies proved that aromaticity is not required for stacking interactions, since similar interaction energies were computed for several aromatic and aliphatic dimers. Herein, the nature and origin of π/π, σ/σ, and σ/π dispersion interactions has been investigated by using dispersion‐corrected density functional theory, energy decomposition analysis, and the recently developed noncovalent interaction (NCI) method. Our analysis shows that π/π and σ/σ stacking interactions are equally important for the benzene and cyclohexane dimers, explaining why both compounds have similar boiling points. Also, similar dispersion forces are found in the benzene???methane and cyclohexane???methane complexes. However, for systems larger than naphthalene, there are enhanced stacking interactions in the aromatic dimers adopting a parallel‐displaced configuration compared to the analogous saturated systems. Although dispersion plays a decisive role in stabilizing all the complexes, the origin of the π/π, σ/σ, and σ/π interactions is different. The NCI method reveals that the dispersion interactions between the hydrogen atoms are responsible for the surprisingly strong aliphatic interactions. Moreover, whereas σ/σ and σ/π interactions are local, the π/π stacking are inherently delocalized, which give rise to a non‐additive effect. These new types of dispersion interactions between saturated groups can be exploited in the rational design of novel carbon materials.     

Computational study of ground-state properties of μ2-bridged group 14 porphyrinic sandwich complexes

The structural properties of μ₂-bridged porphyrinic double-decker complexes are investigated and the influence of various ligands, metals, substituents, and bridging atoms on the dominant structural motif is elucidated. A variety of quantum chemical methods including semiempirical (SQM) methods and density functional theory (DFT) is assessed for the calculation of ecliptic and staggered conformational energies. Local coupled cluster (DLPNO-CCSD(T1)) data are generated for reference. The r²SCAN-3c composite scheme as well as the B2PLYP-D4/def2-QZVPP approach are identified as reliable methods. Energy decomposition analyses (EDA) and localized molecular orbital analyses (LMO) are used to investigate the bonding situation and the nature of the inter-ligand interaction energy underlining the crucial role of attractive London dispersion interactions. Targeted modification of the bridging atom, e.g., by replacing O²⁻ by S²⁻ is shown to drastically change the major structural features of the investigated complexes. Further, the influence of different substituents of varying size at the phthalocyanine ligand regarding the dominant conformation is described.     

二氯亚甲基锗烯与乙烯环加成反应机理的理论研究

The mechanism of a cycloaddition reaction between singlet dichloromethylene germylene and ethylene has been investigated with B3LYP/6-31G＊ method, including geometry optimization and vibrational analysis for the involved stationary points on the potential energy surface. Energies for the involved conformations were calculated by CCSD（T）//B3LYP/6-31G＊ method. On the basis of the surface energy profile obtained with CCSD（T）// B3LYP/6-31G＊ method for the cycloaddition reaction between singlet dichloromethylene germylene and ethylene, it can be predicted that the dominant reaction pathway is that an intermediate INT1 is firstly formed between the two reactants through a barrier-free exothermic reaction of 61.7 kJ/mol, and the intermediate INT1 then isomerizes to an active four-membered ring product P2.1 via a transition state TS2, an intermediate INT2 and a transition state TS2.1, in which energy barriers are 57.7 and 42.2 kJ/mol, respectively.     

Two-Metal Binding Motifs in Protein Crystal Structures

The binding of two metal ions that are in close proximity in proteins is examined using a combination of (1) crystallographic structural database analyses and (2) density functional theory calculations on model complexes. Divalent magnesium and manganese ions are the focus of the present study. It is found that in all proteins in the Protein Databank that have two closely positioned magnesium or manganese ions, these metal ions are generally bridged by at least one negatively charged oxygen-containing group—carboxylate, phosphate, or sulfate. This group transfers (negative) electron density to the metal ions and this helps to reduce electrostatic repulsion in the region. The geometry of the two-metal complex appears to depend on the nature of the negatively charged group between them. When a single oxygen atom is also in a bridging position, the two metal ions are found to be closer together than when only a carboxylate group binds them together. This suggests that this bridging oxygen atom may be negatively charged, e.g., a hydroxide ion rather than a water molecule. Details of the geometry of such bridges and the relevant motifs that are found in crystal structures are described.     

Study of H2O and HOCH2CH2OH Adsorption on the Relaxation Surface of β-Si3N4(0001) by Density Functional Theory

Density functional theory (DFT) B3LYP method is used to theoretically investigate the adsorption conformations of H2O and glycol on the relaxation surface of β-Si3N4(0001) with cluster models. For H2O, the most stable structure is that adsorbed through the H atom lying above a N(3) site of the relaxation surface of β-Si3N4(0001); while for glycol, it is the one adsorbed via the H atom lying above the center of Si(2) and N(3) of the same relaxation surface. The adsorption energy, adsorption bond and transfer electrons of the two adsorbed substances prove that glycol is easy to be adsorbed on the relaxation surface of β-Si3N4(0001).