The Chemical Bond in C2

Quantum chemical calculations using the complete active space of the valence orbitals have been carried out for H_nCCH_n (n=0–3) and N₂. The quadratic force constants and the stretching potentials of H_nCCH_n have been calculated at the CASSCF/cc‐pVTZ level. The bond dissociation energies of the C?C bonds of C₂ and HC≡CH were computed using explicitly correlated CASPT2‐F12/cc‐pVTZ‐F12 wave functions. The bond dissociation energies and the force constants suggest that C₂ has a weaker C?C bond than acetylene. The analysis of the CASSCF wavefunctions in conjunction with the effective bond orders of the multiple bonds shows that there are four bonding components in C₂, while there are only three in acetylene and in N₂. The bonding components in C₂ consist of two weakly bonding σ bonds and two electron‐sharing π bonds. The bonding situation in C₂ can be described with the σ bonds in Be₂ that are enforced by two π bonds. There is no single Lewis structure that adequately depicts the bonding situation in C₂. The assignment of quadruple bonding in C₂ is misleading, because the bond is weaker than the triple bond in HC≡CH.     

Quantitative characterization of the P?C bonds in ylides of phosphorus

The nature of the carbon–phosphorus bond in trivalent and pentavalent carbon phosphorus compounds is currently a matter of some dispute. These compounds contain unusual bonds, unusual in the sense that the behavior of electrons in the compounds does not conform to that expected solely on the basis of carbon–carbon and carbon–hydrogen bonds. Quantitative measures of how a single electron, as a wave, is shared between any two spatial points are given by means of the sharing amplitude and the sharing index. 1 These quantities are orbital independent, rooted in the single particle density matrix, and do not depend on arbitrary localization procedures. The quantitative characterization of the P? C bonds in molecules such as PHCH₂, PH₃CH₂, PF₃CH₂, and PH₃CHF was carried out by means of the sharing indices. On the basis of interbasin sharing indices, the P? C bonds are: (mostly) double in PHCH₂, and single in PH₃CH₂, PF₃CH₂, and PH₃CHF. On the basis of the group basin charges and intergroup sharing indices between the CH₂ (or CHF) groups and the PH_1,3 (or PF₃) groups, the molecules are ionic with double bonds between the groups (in line with an ylene form). The sharing indices between atoms, which are not directly linked (secondary sharing indices), indicate that the electrons are quite delocalized over the basins of the following groups: CPH in PHCH₂, CPH₃ in PH₃CH₂, CPF₃ in PF₃CH₂, and CPH₃ in PH₃CHF. The sharing indices and the sharing amplitude offer the needed tools to put our understanding of the chemistry of a large number of compounds on a rigorous basis by elucidating the behavior of a single electron in a many electron system. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1387–1395, 2001     

The nature of the N?O bond in amine oxides

Despite the ubiquitous presence of amine oxides in chemistry, there is no consensus about the nature of the N O bond in these compounds. In this work, we have used electron density analysis to investigate the nature of this bond in substituted amine oxides, R₃NO, and have compared it with the nature of the N O bond in hydroxylamines, R₂NOR, and model molecules that have well-established chemical bond character. The results showed that the N O bond length and relative stability are proportional to the inductive effect of the substituents. Quantum chemical topology, natural bond orbitals (NBO), and natural resonance theory (NRT) analyses indicated that the N O bond is polar covalent in all the studied amine oxides, but the ionic contribution is different. NBO and NRT analyses revealed that molecules with more electronegative substituents have strongly delocalized N O and N R bonds, whereas molecules with electropositive substituents have localized bonds.     

Comparison of the Ability of N-Bases to Engage in Noncovalent Bonds

The lone pair of the N atom is a common electron donor in noncovalent bonds. Quantum calculations examine how various aspects of the base on which the N is located affect the strength and other properties of complexes formed with Lewis acids FH, FBr, F₂Se, and F₃As that respectively encompass hydrogen, halogen, chalcogen, and pnicogen bonds. In most cases the halogen bond is the strongest, followed in order by chalcogen, hydrogen, and pnicogen. The noncovalent bond strength increases in the sp<sp²<sp³ order of hybridization of N. Replacement of H substituents on the base by a methyl group or substituting N by C atom to which the base N is attached, strengthens the bond. The strongest bonds occur for trimethylamine and the weakest for N₂.     

A DFT-based study of the hydrogen-bonding interactions between epicatechin and methanol/water

Tea polyphenols are essential components that give tea its medicinal properties. Methanol and water are frequently used as solvents in the extraction of polyphenols. Hydrogen-bonding interactions are significant in the extraction reaction. Density functional theory (DFT) techniques were used to conduct a theoretical investigation on the hydrogen-bonding interactions between methanol or water and epicatechin, an abundant polyphenol found in tea. After first analyzing the epicatechin monomer's molecular geometry and charge characteristics, nine stable epicatechin (EC) H₂O/CH₂OH complex geometries were discovered. The presence of hydrogen bonding in these improved structures has been proven. The calculated hydrogen bond structures are very stable, among which the hydrogen bond bonded with a hydroxyl group has higher stability. The nine complex structures’ hydrogen bonds were thought to represent closed-shell-type interactions. The interaction energy with 30O-31H on the epicatechin benzene ring is the strongest in the hydrogen bond structure. While the other hydrogen bonds were weak in strength and mostly had an electrostatic nature, the hydrogen bonds between the oxygen atoms in H₂O or CH₂OH and the hydrogen atoms of the hydroxyl groups in epicatechin were of moderate strength and had a covalent character. Comparing the changes in the hydrogen bond structure vibration peak, the main change in concentration peak is the hydrogen bond vibration peak in the complex. Improved the study on the hydrogen bond properties of CH₂OH and H₂O of EC.     

The Na⋅⋅⋅B Bond in NaBH3−: A Different Type of Bond

A newly introduced Na−B bond in NaBH₃⁻ has been a challenge for the chemical bonding community. Here, a series of MBH₃⁻ (M=Li, Na, K) species and NaB(CN)₃⁻ are studied within the context of quantum chemical topology approaches. The analyses suggest that M–B interaction cannot be classified as an ordinary covalent, dative, or even simple ionic interaction. The interactions are controlled by coulombic forces between the metals and the substituents on boron, for example, H or CN, more than the direct M–B interaction. On the other hand, while the characteristics of the (3, −1) critical points of the bonds are comparable to weak hydrogen bonds, not covalent bonds, the metal and boron share a substantial sum of electrons. To the best of the author's knowledge, the characteristics of these bonds are unprecedented among known molecules. Considering all paradoxical properties of these bonds, they are herein described as ionic-enforced covalent bonds.     

Theoretical study on the interactions of halogen‐bonds and pnicogen‐bonds in phosphine derivatives with Br2, BrCl,and BrF

The MP2 ab initio quantum chemistry methods were utilized to study the halogen‐bond and pnicogen‐bond system formed between PH₂X (X = Br, CH₃, OH, CN, NO₂, CF₃) and BrY (Y = Br, Cl, F). Calculated results show that all substituent can form halogen‐bond complexes while part substituent can form pnicogen‐bond complexes. Traditional, chlorine‐shared and ion‐pair halogen‐bonds complexes have been found with the different substituent X and Y. The halogen‐bonds are stronger than the related pnicogen‐bonds. For halogen‐bonds, strongly electronegative substituents which are connected to the Lewis acid can strengthen the bonds and significantly influenced the structures and properties of the compounds. In contrast, the substituents which connected to the Lewis bases can produce opposite effects. The interaction energies of halogen‐bonds are 2.56 to 32.06 kcal·mol^?1; The strongest halogen‐bond was found in the complex of PH₂OH???BrF. The interaction energies of pnicogen‐bonds are in the range 1.20 to 2.28 kcal·mol^?1; the strongest pnicogen‐bond was found in PH₂Br???Br₂ complex. The charge transfer of lp(P) ? σ*(Br? Y), lp(F) ? σ*(Br? P), and lp(Br) ? σ*(X? P) play important roles in the formation of the halogen‐bonds and pnicogen‐bonds, which lead to polarization of the monomers. The polarization caused by the halogen‐bond is more obvious than that by the pnicogen‐bond, resulting in that some halogen‐bonds having little covalent character. The symmetry adapted perturbation theory (SAPT) energy decomposition analysis showes that the halogen‐bond and pnicogen‐bond interactions are predominantly electrostatic and dispersion, respectively.     

An Excursion from Normal to Inverted C?C Bonds Shows a Clear Demarcation between Covalent and Charge‐Shift C?C Bonds

What is the nature of the C? C bond? Valence bond and electron density computations of 16 C? C bonds show two families of bonds that flesh out as a phase diagram. One family, involving ethane, cyclopropane and so forth, is typified by covalent C? C bonding wherein covalent spin‐pairing accounts for most of the bond energy. The second family includes the inverted bridgehead bonds of small propellanes, where the bond is neither covalent nor ionic, but owes its existence to the resonance stabilization between the respective structures; hence a charge‐shift (CS) bond. The dual family also emerges from calculated and experimental electron density properties. Covalent C? C bonds are characterized by negative Laplacians of the density, whereas CS‐bonds display small or positive Laplacians. The positive Laplacian defines a region suffering from neighbouring repulsive interactions, which is precisely the case in the inverted bonding region. Such regions are rich in kinetic energy, and indeed the energy‐density analysis reveals that CS‐bonds are richer in kinetic energy than the covalent C? C bonds. The large covalent–ionic resonance energy is precisely the mechanism that lowers the kinetic energy in the bonding region and restores equilibrium bonding. Thus, different degrees of repulsive strain create two bonding families of the same chemical bond made from a single atomic constituent. It is further shown that the idea of repulsive strain is portable and can predict the properties of propellanes of various sizes and different wing substituents. Experimentally (M. Messerschmidt, S. Scheins, L. Bruberth, M. Patzel, G. Szeimies, C. Paulman, P. Luger, Angew. Chem. 2005 , 117, 3993–3997; Angew. Chem. Int. Ed. 2005 , 44, 3925–3928), the C? C bond families are beautifully represented in [1.1.1]propellane, where the inverted C? C is a CS‐bond, while the wings are made from covalent C? C bonds. What other manifestations can we expect from CS‐bonds? Answers from experiment have the potential of recharting the mental map of chemical bonding.     

Synergistic and Diminutive Effects between Regium and Aerogen Bonds

The aerogen bond is formed in complexes of HCN−XeF₂O and C₂H₄−XeF₂O. The lone pair on the N atom of HCN is a better electron donor in the aerogen bond than the π electron on the C=C bond of C₂H₄. The coinage substitution strengthens the aerogen bond in MCN−XeF₂O (M=Cu, Ag, and Au) and its enhancing effect becomes larger in the Au<Cu<Ag pattern. The aerogen bond is further enhanced by the regium bond in C₂H₂−MCN−XeF₂O and C₂H₄−MCN−XeF₂O, but is weakened by the regium bond in MCN−C₂H₄−XeF₂O and C₂(CN)₄−MCN−XeF₂O. Simultaneously, the regium bond is also strengthened or weakened in these triads. The synergistic and diminutive effects between regium and aerogen bonds have been explained by means of charge transfer and electrostatic potentials.     

Diboron Bonds Between BX3 (X=H,F, CH3) and BYZ2 (Y=H,F; Z=CO,N2, CNH)

The ability of B atoms on two different molecules to engage with one another in a noncovalent diboron bond is studied by ab initio calculations. Due to electron donation from its substituents, the trivalent B atom of BYZ₂ (Z=CO, N₂, and CNH; Y=H and F) has the ability to in turn donate charge to the B of a BX₃ molecule (X=H, F, and CH₃), thus forming a B⋅⋅⋅B diboron bond. These bonds are of two different strengths and character. BH(CO)₂ and BH(CNH)₂, and their fluorosubstituted analogues BF(CO)₂ and BF(CNH)₂, engage in a typical noncovalent bond with B(CH₃)₃ and BF₃, with interaction energies in the 3–8 kcal/mol range. Certain other combinations result in a much stronger diboron bond, in the 26–44 kcal/mol range, and with a high degree of covalent character. Bonds of this type occur when BH₃ is added to BH(CO)₂, BH(CNH)₂, BH(N₂)₂, and BF(CO)₂, or in the complexes of BH(N₂)₂ with B(CH₃)₃ and BF₃. The weaker noncovalent bonds are held together by roughly equal electrostatic and dispersion components, complemented by smaller polarization energy, while polarization is primarily responsible for the stronger ones.     

Structures,vibrational frequencies,topologies, and energies of hydrogen bonds in cysteine‐formaldehyde complexes

The hydrogen bonding interactions between cysteine (Cys) and formaldehyde (FA) were studied with density functional theory regarding their geometries, energies, vibrational frequencies, and topological features of the electron density. The quantum theory of atoms in molecules and natural bond orbital analyses were employed to elucidate the interaction characteristics in the Cys‐FA complexes. The intramolecular hydrogen bonds (H‐bonds) formed between the hydroxyl and the N atom of cysteine moiety in some Cys‐FA complexes were strengthened because of the cooperativity. Most of intermolecular H‐bonds involve the O atom of cysteine/FA moiety as proton acceptors, while the strongest H‐bond involves the O atom of FA moiety as proton acceptor, which indicates that FA would rather accept proton than providing one. The H‐bonds formed between the CH group of FA and the S atom of cysteine in some complexes are so weak that no hydrogen bonding interactions exist among them. In most of complexes, the orbital interaction of H‐bond is predominant during the formation of complex. The electron density (ρ_b) and its Laplace (?²ρ_b) at the bond critical point significantly correlate with the H‐bond parameter δR, while a linearly relationship between the second‐perturbation energy E(2) and ρ_b has been found as well. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

A 3-D bonding perspective of the factors influencing the relative stability of the S1/S0 conical intersections of the penta-2,4-dieniminium cation (PSB3)

A balanced treatment of the covalent and ionic contributions to the ground and excited states originating from torsion about double bonds is known to be strongly dependent on the presence of dynamic electron correlation. We undertake an analysis of the minimum energy pathways corresponding to deactivation of the first excited singlet state of PSB3. In doing so we consider torsion about the three double bonds including other intramolecular degrees of freedom, such as the bond length alternation. The 3-D bond-path analysis provides a new ‘bond-localized orbital-like’ directional interpretation of bonding. Therefore, we present a more sophisticated method of determination of the degree of covalent and ionic contributions known to be responsible for altering the relative stability of the S₁/S₀ conical intersections. The results presented suggest that the commonly used simplified multi-reference methodologies that often result in incorrect predictions for the excited state deactivation reaction mechanism.     

A simple model of hydrogen bonding with particular application to trends in hydrogen‐bonded dimers

A simple model has been proposed to explain trends in the computed interaction energy, bond length changes, frequency shifts and infrared intensities for the chlorofluoromethanes CF_nCl_mH, FH and FArH on complexation with the isoelectronic diatomics BF, CO, N₂ and the rare gas atoms Kr, Ar, Ne to form a series of linear or nearly linear hydrogen‐bonded complexes. The dipole moment derivative of the proton donor (with respect to the stretching coordinate) and the chemical hardness of the hydrogen‐bonded atom of the proton acceptor are identified as two useful parameters for rationalizing the changes in some of the molecular properties of the proton donor when the hydrogen bond is formed. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Comment on “Realization of Lewis Basic Sodium Anion in the NaBH3− Cluster”

We challenge the interpretation of the chemical bond in NaBH₃^? proposed by Liu et al. We argue that NaBH₃^? has an electron‐sharing Na?BH₃^? covalent bond rather than a dative bond Na^?→BH₃.     

Covalent versus Dative Bonds to Main Group Metals,a Useful Distinction

Textbooks of inorganic chemistry describe the formation of adducts by coordination of an electron donor to an electron acceptor, often using the amine-boranes, X₃N → BY₃, as examples. In the Lewis (electron dot) formulas of the compounds, the dative bond in H 3 N → BH₃ and the covalent bond in H₃C?CH₃ are both represented by a shared electron pair. In the simple molecular orbital or valence bond models the wave functions of both electron pairs would be constructed in the same manner from the appropriate sp³ type atomic orbitals on the bonded atoms; the difference between the covalent and the dative bond becomes apparent only after the orbital coefficients have been analyzed. This may be the reason why many structural chemists seem reluctant to distinguish between the two types of bonds. The object of this article is to remind the reader that the physiocochemical properties of covalent and dative bonds may be – and often are – quite different, and to show that a distinction between the two provides a basis for understanding the structures of a wide range of main group metal compounds.     

The Nature of the Fourth Bond in the Ground State of C2: The Quadruple Bond Conundrum

Does, or doesn’t C₂ break the glass ceiling of triple bonding? This work provides an overview on the bonding conundrum in C₂ and on the recent discussions regarding our proposal that it possesses a quadruple bond. As such, we focus herein on the main point of contention, the 4th bond of C₂, and discuss the main views. We present new data and an overview of the nature of the 4th bond—its proposed antiferromagnetically coupled nature, its strength, and a derivation of its bond energy from experimentally based thermochemical data. We address the bond‐order conundrum of C₂ arising from generalized VB (GVB) calculations by comparing it to HC?CH, and showing that the two molecules behave very similarly, and C₂ is in no way an exception. We analyse the root cause of the deviation of C₂ from the Badger Rule, and demonstrate that the reason for the smaller force constant (FC) of C₂ relative to HC?CH has nothing to do with the bond energies, or with the number of bonds in the two molecules. The FC is determined primarily by the bond length, which is set by the balance between the bond length preferences of the σ‐ versus π‐bonds in the two molecules. This interplay in the case of C₂ clearly shows the fingerprints of the 4th bond. Our discussion resolves the points of contention and shows that the arguments used to dismiss the quadruple bond nature of C₂ are not well founded.     

New insight into the electronic structure of iron(IV)‐oxo porphyrin compound I. A quantum chemical topological analysis

The electronic structure of iron‐oxo porphyrin π‐cation radical complex Por^·+Fe^IV?O (S? H) has been studied for doublet and quartet electronic states by means of two methods of the quantum chemical topology analysis: electron localization function (ELF) η(r) and electron density ρ(r). The formation of this complex leads to essential perturbation of the topological structure of the carbon–carbon bonds in porphyrin moiety. The double C?C bonds in the pyrrole anion subunits, represented by pair of bonding disynaptic basins V_i=1,2(C,C) in isolated porphyrin, are replaced by single attractor V(C,C)_i=1–20 after complexation with the Fe cation. The iron–nitrogen bonds are covalent dative bonds, N→Fe, described by the disynaptic bonding basins V(Fe,N)_i=1–4, where electron density is almost formed by the lone pairs of the N atoms. The nature of the iron–oxygen bond predicted by the ELF topological analysis, shows a main contribution of the electrostatic interaction, Fe^δ+···O^δ?, as long as no attractors between the C(Fe) and C(O) core basins were found, although there are common surfaces between the iron and oxygen basines and coupling between iron and oxygen lone pairs, that could be interpreted as a charge‐shift bond. The Fe? S bond, characterized by the disynaptic bonding basin V(Fe,S), is partially a dative bond with the lone pair donated from sulfur atom. The change of electronic state from the doublet (M = 2) to quartet (M = 4) leads to reorganization of spin polarization, which is observed only for the porphyrin skeleton (?0.43e to 0.50e) and S? H bond (?0.55e to 0.52e). © 2012 Wiley Periodicals, Inc.     

Intramolecular Natural Energy Decomposition Analysis: Applications to the Rational Design of Foldamers

We describe an intramolecular version of the natural energy decomposition analysis (NEDA), with the aim of evaluating interactions between molecular fragments across covalent bonds. The electronic energy in intramolecular natural energy decomposition analysis (INEDA) is divided into electrical, core, and charge transfer components. The INEDA method describes the fragments using the nonfragmented electronic density, and, therefore, there are no limitations in how to choose the boundary orbital. We used INEDA to evaluate the interaction energies that give origin to barriers of rotation around C_amide C_aromatic (C_am C_ar) and N_amide C_aromtaic (N_am C_ar) bonds in arylamide‐foldamer building blocks. We found that differences of barrier height between models with different ortho‐aryl substituents stem from charge transfer and core interactions. In three‐center hydrogen‐bond (H‐bond) models with an NH proton donor H‐bound to two electronegative ortho‐aryl substituents, the interaction energy of the three‐center system is larger than in either of the two‐center H‐bond subsystem alone, indicating an increase of overall rigidity. The combination of INEDA and NEDA allows the evaluation of intermolecular and intramolecular interactions using a consistent theoretical framework. © 2018 Wiley Periodicals, Inc.     

Strongly Bound π-Hole Tetrel Bonded Complexes between H2SiO and Substituted Pyridines. Influence of Substituents

Ab initio calculation at the MP2/aug-cc-pVTZ level has been performed on the π-hole based N^…Si tetrel bonded complexes between substituted pyridines and H₂SiO. The primary aim of the study is to find out the effect of substitution on the strength and nature of this tetrel bond, and its similarity/difference with the N^…C tetrel bond. Correlation between the strength of the N^…Si bond and several molecular properties of the Lewis acid (H₂SiO) and base (pyridines) are explored. The properties of the tetrel bond are analyzed using AIM, NBO, and symmetry-adapted perturbation theory calculations. The complexes are characterized with short N^…Si intermolecular distances and high binding energies ranging between −142.72 and −115.37 kJ/mol. The high value of deformation energy indicates significant geometrical distortion of the monomer units. The AIM and NBO analysis reveal significant coordinate covalent bond character of the N⋅⋅⋅Si π-hole bond. Sharp differences are also noticed in the orbital interactions present in the N⋅⋅⋅Si and N⋅⋅⋅C tetrel bonds.