Electron density topological properties are useful to assess the difference between hydrogen and dihydrogen complexes

A combined QTAIM/IRI topological analysis of the effect of axial/equatorial positions of NH2 and CN substituents in the [(PY5Me2)MoO]+ complex

By means of the Interaction Region Indicator (IRI) and Quantum Theory of Atoms in Molecules (QTAIM), the influence exerted by NH₂ (amino) and CN (cyano) as electron donor and electron acceptor substituent groups, respectively, located at para-positions of axial and equatorial pyridine rings of derivatized complexes coming from the [(PY₅Me₂)MoO]⁺ complex during the hydrogen molecular release in the gas phase was analyzed. In any case, a H-H covalent bond is forming at the transition state, with a strengthening of the electron density of 5.5% when the substituent group involved is NH₂ at the para-position of the axial pyridine ring. However, there was no difference between NH₂ and CN when these substituent groups are located at the para-positions of the equatorial pyridine rings. The topological properties of electron densities from the QTAIM are not perturbed by the electron donor and electron acceptor nature of the substituents, even when these substituent groups are located at the axial or equatorial pyridine rings of the Mo-based complex.

Strength of the [Z-I···Hal]- and [Z-Hal···I]- Halogen Bonds: Electron Density Properties and Halogen Bond Length as Estimators of Interaction Energy

Bond energy is the main characteristic of chemical bonds in general and of non-covalent interactions in particular. Simple methods of express estimates of the interaction energy, Eint, using relationships between Eint and a property which is easily accessible from experiment is of great importance for the characterization of non-covalent interactions. In this work, practically important relationships between Eint and electron density, its Laplacian, curvature, potential, kinetic, and total energy densities at the bond critical point as well as bond length were derived for the structures of the [Z-I···Hal]- and [Z-Hal···I]- types bearing halogen bonds and involving iodine as interacting atom(s) (totally 412 structures). The mean absolute deviations for the correlations found were 2.06-4.76 kcal/mol.

A Computational Study of Metallacycles Formed by Pyrazolate Ligands and the Coinage Metals M = Cu(I), Ag(I) and Au(I): (pzM)n for n = 2, 3, 4, 5 and 6. Comparison with Structures Reported in the Cambridge Crystallographic Data Center (CCDC)

The structures reported in the Cambridge Structural Database (CSD) for neutral metallacycles formed by coinage metals in their valence (I) (cations) and pyrazolate anions were examined. Depending on the metal, dimers and trimers are the most common but some larger rings have also been reported, although some of the larger structures are not devoid of ambiguity. M06-2x calculations were carried out on simplified structures (without C-substituents on the pyrazolate rings) in order to facilitate a comparison with the reported X-ray structures (geometries and energies). The problems of stability of the different ring sizes were also analyzed.

Relationships between Interaction Energy and Electron Density Properties for Homo Halogen Bonds of the [(A)nY-X···X-Z(B)m] Type (X = Cl, Br, I)

Relationships between interaction energy (Eint) and electron density properties at the X···X bond critical point or the d(X···X) distance were established for the large set of structures [(A)nY-X···X-Z(B)m] bearing the halogen bonds Cl···Cl, Br···Br, and I···I (640 structures in total). The best estimator of Eint is the kinetic energy density (Gb), which reasonably approximates the whole set of the structures as -Eint = 0.128Gb2 - 0.82Gb + 1.66 (R2 = 0.91, mean absolute deviation 0.39 kcal/mol) and demonstrates low dispersion. The potential and kinetic energy densities, electron density, and the d(X···X) distance behave similarly as estimators of Eint for the individual series Cl···Cl, Br···Br, and I···I. A number of the Eint(property) correlations are recommended for the practical application in the express estimates of the strength of the homo-halogen bonds.

Wave Function and Density Functional Theory Studies of Dihydrogen Complexes

We performed a benchmark study on a series of dihydrogen bond complexes and constructed a set of reference bond distances and interaction energies. The test set was employed to assess the performance of several wave function correlated and density functional theory methods. We found that second-order correlation methods describe relatively well the dihydrogen complexes. However, for high accuracy inclusion of triple contributions is important. On the other hand, none of the considered density functional methods can simultaneously yield accurate bond lengths and interaction energies. However, we found that improved results can be obtained by the inclusion of nonlocal exchange contributions.

Fundamental relation between molecular geometry and real-space topology. Combined AIM, ELI-D, and ASF analysis of hapticities and intramolecular hydrogen-hydrogen bonds in zincocene-related compounds

Despite numerous advanced and widely distributed bonding theories such as MO, VB, NBO, AIM, and ELF/ELI-D, complex modes of bonding such as M-Cp*((R)) interactions (hapticities) in asymmetrical metallocenes or weak intramolecular interactions (e.g., hydrogen-hydrogen (H···H) bonds) still remain a challenge for these theories in terms of defining whether or not an atom-atom interaction line (a "chemical bond") should be drawn. In this work the intramolecular Zn-C(Cp*(R)) (R = Me, -(CH2)2NMe2, and -(CH2)3NMe2) and H···H connectivity of a systematic set of 12 zincocene-related compounds is analyzed in terms of AIM and ELI-D topology combined with the recently introduced aspherical stockholder fragment (ASF) surfaces. This computational analysis unravels a distinct dependency of the AIM and ELI-D topology against the molecular geometry for both types of interactions, which confirms and extends earlier findings on smaller sets of compounds. According to these results the complete real-space topology including strong, medium, and weak interactions of very large compounds such as proteins may be reliably predicted by sole inspection of accurately determined molecular geometries, which would on the one hand afford new applications (e.g., accurate estimation of numbers, types, and strengths of intra- and intermolecular interactions) and on the other hand have deep implications on the significance of the method.

A fuzzy-atom analysis of electron delocalization on hydrogen bonds

The extent of electron delocalization is quantified for set of cyclic complexes exhibiting two or more hydrogen bonds (HBs). In particular, the delocalization index (DI) between the atoms directly involved in the HB, and the ING (a normalized n-center delocalization index) have been evaluated using several fuzzy-atom schemes, namely Becke, Becke-ρ, Hirshfeld, and Hirshfeld-Iterative. The results have been compared with the widely used Quantum Theory of Atoms in Molecules (QTAIM) atomic definition. The DI values are found to correlate very well with geometrical or topological descriptors widely used in the literature to characterize HB systems. Among all fuzzy-atom methods, the ones that can better accommodate the different partial ionic character of the bonds perform particularly well. The best performing fuzzy-atom scheme for both pairwise and n-center electron delocalization is found to be the Becke-ρ method, for which similar results to QTAIM model are obtained with a much reduced computational cost. These results open up a wide range of applications of such electron delocalization descriptors based on fuzzy-atoms for noncovalent interactions in more complex and larger systems.

The hydrogen bond – practice and QTAIM theory

IR intensities in the spectra of H-complexes as a source of electron-density data ρ(r_c) (e a⁻³) = 10⁻²(ΔA^1/2) (A, 10⁻⁴ cm mmol^−1/2).

Modulating weak intramolecular interactions through the formation of beryllium bonds: complexes between squaric acid and BeH2

The electronic structure of the two most stable isomers of squaric acid and their complexes with BeH2 were investigated at the B3LYP/6-311 + G(3df,2p)// B3LYP/6-31 + G(d,p) level of theory. Squaric acid forms rather strong beryllium bonds with BeH2, with binding energies of the order of 60 kJ mol(-1). The preferential sites for BeH2 attachment are the carbonyl oxygen atoms, but the global minima of the potential energy surfaces of both EZ and ZZ isomers are extra-stabilized through the formation of a BeH···HO dihydrogen bond. More importantly, analysis of the electron density of these complexes shows the existence of significant cooperative effects between the beryllium bond and the dihydrogen bond, with both becoming significantly reinforced. The charge transfer involved in the formation of the beryllium bond induces a significant electron density redistribution within the squaric acid subunit, affecting not only the carbonyl group interacting with the BeH2 moiety but significantly increasing the electron delocalization within the four membered ring. Accordingly the intrinsic properties of squaric acid become perturbed, as reflected in its ability to self-associate.

Effect of the H-bonding on aromaticity of purine tautomers

Four tautomers of purine (1-H, 3-H, 7-H, and 9-H) and their equilibrium H-bonded complexes with F(-) and HF for acidic and basic centers, respectively, were optimized by means of the B3LYP/6-311++G(d,p) level of theory. Purine tautomer stability increases in the following series: 1-H < 3-H < 7-H < 9-H, consistent with increasing aromaticity. Furthermore, the presence of a hydrogen bond with HF does not change this order. For neutral H-bonded complexes, the strongest and the weakest intermolecular interactions occur (-14.12 and -10.49 kcal/mol) for less stable purine tautomers when the proton acceptor is located in the five- and six-membered rings, respectively. For 9-H and 7-H tautomers the order is reversed. The H-bond energy for the imidazole complex with HF amounts to -14.03 kcal/mol; hence, in the latter case, the fusion of imidazole to pyrimidine decreases its basicity. The ionic H-bonds of N(-)···HF type are stronger by ~10 kcal/mol than the neutral N···HF intermolecular interactions. The hydrogen bond N(-)···HF energies in pyrrole and imidazole are -32.28 and -30.03 kcal/mol, respectively, and are substantially stronger than those observed in purine complexes. The aromaticity of each individual ring and of the whole molecule for all tautomers in ionic complexes is very similar to that observed for the anion of purine. This is not the case for neutral complexes and purine as a reference. The N···HF bonds perturb much more the π-electron structure of five-membered rings than that of the six-membered ones. The H-bonding complexes for 7-H and 9-H tautomers are characterized by higher aromaticity and a much lower range of HOMA variability.

Cation-anion hydrogen bonds: a new class of hydrogen bonds that extends their strength beyond the covalent limit. A theoretical characterization

The existence of O-H···O hydrogen bonds having a strength within the -80 to -210 kcal/mol range, that is, in the range of strength of covalent bonds and well beyond the so-called covalent limit (-50 kcal/mol), is reported on complexes where the O-H proton donor and O acceptor groups are located in ions of opposite sign. A complete analysis of short distance O-H···O hydrogen bonds between charged fragments was performed for cases where the OH and O groups are both located on charged molecules. It shows that these interactions (a) are nonsymmetrical for the O-H and H···O distances, (b) have a noncovalent H···O bond critical point, and (c) have a strong and energetically stable electrostatic component when the OH and O groups are located in oppositely charged molecules. These cation-anion O-H···O interactions are energetically stable, satisfy the usual topology for hydrogen bonds, HBs, and also have the same directionality found in other HBs. Therefore, they should be considered as a new class of HBs, the cation-anion hydrogen bonds.

Dihydrogen bonding: donor-acceptor bonding (AH...HX) versus the H2 molecule (A-H2-X)

Dihydrogen bonds (DHBs) play a role in, among others, crystal packing, organometallic reaction mechanisms, and potential hydrogen-storage materials. In this work we have analyzed the central H-H bond in linear H(4), LiH...HX, BH(4)(-)...HX, and AlH(4)(-)...HX complexes with various X by using the quantitative molecular orbital model contained in Kohn-Sham density functional theory at the BP86/TZ2P level of theory. First, we address the questions of if and how one can distinguish, in principle, between a H...H donor-acceptor DHB and the formation of an H(2) molecule by using the simple H(4) model system. The results of these analyses have been used to gain an understanding of the bonding in more realistic model systems (some of which have been studied experimentally), and how this differs from the bonding in H(4).

Nucleophilic substitution at phosphorus centers (SN2@p)

We have studied the characteristics of archetypal model systems for bimolecular nucleophilic substitution at phosphorus (SN2@P) and, for comparison, at carbon (SN2@C) and silicon (SN2@Si) centers. In our studies, we applied the generalized gradient approximation (GGA) of density functional theory (DFT) at the OLYP/TZ2P level. Our model systems cover nucleophilic substitution at carbon in X(-)+CH3Y (SN2@C), at silicon in X(-)+SiH3Y (SN2@Si), at tricoordinate phosphorus in X(-)+PH2Y (SN2@P3), and at tetracoordinate phosphorus in X(-)+POH2Y (SN2@P4). The main feature of going from SN2@C to SN2@P is the loss of the characteristic double-well potential energy surface (PES) involving a transition state [X--CH3--Y]- and the occurrence of a single-well PES with a stable transition complex, namely, [X--PH2--Y]- or [X--POH2--Y](-). The differences between SN2@P3 and SN2@P4 are relatively small. We explored both the symmetric and asymmetric (i.e. X, Y=Cl, OH) SN2 reactions in our model systems, the competition between backside and frontside pathways, and the dependence of the reactions on the conformation of the reactants. Furthermore, we studied the effect, on the symmetric and asymmetric SN2@P3 and S(N)2@P4 reactions, of replacing hydrogen substituents at the phosphorus centers by chlorine and fluorine in the model systems X(-)+PR2Y and X(-)+POR2Y, with R=Cl, F. An interesting phenomenon is the occurrence of a triple-well PES not only in the symmetric, but also in the asymmetric SN2@P4 reactions of X(-)+POCl2--Y.