The nature of the chemical bond revisited: an energy-partitioning analysis of nonpolar bonds

The nature of the chemical bond in nonpolar molecules has been investigated by energy-partitioning analysis (EPA) of the ADF program using DFT calculations. The EPA divides the bonding interactions into three major components, that is, the repulsive Pauli term, quasiclassical electrostatic interactions, and orbital interactions. The electrostatic and orbital terms are used to define the nature of the chemical bond. It is shown that nonpolar bonds between main-group elements of the first and higher octal rows of the periodic system, which are prototypical covalent bonds, have large attractive contributions from classical electrostatic interactions, which may even be stronger than the attractive orbital interactions. Fragments of molecules with totally symmetrical electron-density distributions, like the nitrogen atoms in N(2), may strongly attract each other through classical electrostatic forces, which constitute 30.0 % of the total attractive interactions. The electrostatic attraction can be enhanced by anisotropic charge distribution of the valence electrons of the atoms that have local areas of (negative) charge concentration. It is shown that the use of atomic partial charges in the analysis of the nature of the interatomic interactions may be misleading because they do not reveal the topography of the electronic charge distribution. Besides dinitrogen, four groups of molecules have been studied. The attractive binding interactions in H(n)E-EH(n) (E=Li to F; n=0-3) have between 20.7 (E=F) and 58.4 % (E=Be) electrostatic character. The substitution of hydrogen by fluorine does not lead to significant changes in the nature of the binding interactions in F(n)E-EF(n) (E=Be to O). The electrostatic contributions to the attractive interactions in F(n)E-EF(n) are between 29.8 (E=O) and 55.3 % (E=Be). The fluorine substituents have a significant effect on the Pauli repulsion in the nitrogen and oxygen compounds. This explains why F(2)N-NF(2) has a much weaker bond than H(2)N-NH(2), whereas the interaction energy in FO-OF is much stronger than in HO-OH. The orbital interactions make larger contributions to the double bonds in HB=BH, H(2)C=CH(2), and HN=NH (between 59.9 % in B(2)H(2) and 65.4 % in N(2)H(2)) than to the corresponding single bonds in H(n)E-EH(n). The orbital term Delta E(orb) (72.4 %) makes an even greater contribution to the HC triple bond CH triple bond. The contribution of Delta E(orb) to the H(n)E=EH(n) bond increases and the relative contribution of the pi bonding decreases as E becomes more electronegative. The pi-bonding interactions in HC triple bond CH amount to 44.4 % of the total orbital interactions. The interaction energy in H(3)E-EH(3) (E=C to Pb) decreases monotonically as the element E becomes heavier. The electrostatic contributions to the E-E bond increases from E=C (41.4 %) to E=Sn (55.1 %) but then decreases when E=Pb (51.7 %). A true understanding of the strength and trends of the chemical bonds can only be achieved when the Pauli repulsion is considered. In an absolute sense the repulsive Delta E(Pauli) term is in most cases the largest term in the EPA.     

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

We reply to the comment by S. Pan and G. Frenking who challenged our interpretation of the Na^?:→BH₃ dative bond in the recently synthesized NaBH₃^? cluster. Our conclusion remains the same as that in our original paper ( https://doi.org/10.1002/anie.201907089 and https://doi.org/10.1002/ange.201907089 ). This conclusion is additionally supported by the energetic pathways and NBO charges calculated at UCCSD and CASMP2(4,4) levels of theory. We also discussed the suitability of the Laplacian of electron density (QTAIM) and Adaptive Natural Density Partitioning (AdNDP) method for bond type assignment. It seems that AdNDP yields more sensible results. This discussion reveals that the complex realm of bonding is full of semantic inconsistencies, and we invite experimentalists and theoreticians to elaborate this topic and find solutions incorporating different views on the dative bond.     

Comment on “density and physical current density functional theory” by Xiao‐Yin Pan and Viraht Sahni

A recent paper by Xiao‐Yin Pan and Viraht Sahni [Int. J. Quant. Chem. 110, 2833 (2010)] claims that current density functional theory should be based on the physical current density rather than the paramagnetic current density, as in the standard Vignale‐Rasolt formulation. In this comment we show that the claims in the paper by Pan and Sahni are erroneous. © 2012 Wiley Periodicals, Inc.     

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.     

Reply to ‘comment on “extending Hirshfeld‐I to bulk and periodic materials”’

The issues raised in the comment by Manz are addressed through the presentation of calculated atomic charges for NaF, NaCl, MgO, SrTiO $$_3$$ , and La $$_2$$ Ce $$_2$$ O $$_7$$ , using our previously presented method for calculating Hirshfeld‐I charges in solids (Vanpoucke et al., J. Comput. Chem. doi: 10.1002/jcc.23088). It is shown that the use of pseudovalence charges is sufficient to retrieve the full all‐electron Hirshfeld‐I charges to good accuracy. Furthermore, we present timing results of different systems, containing up to over 200 atoms, underlining the relatively low cost for large systems. A number of theoretical issues are formulated, pointing out mainly that care must be taken when deriving new atoms in molecules methods based on “expectations” for atomic charges. © 2012 Wiley Periodicals, Inc.     

Functional assessment of “in vivo” and “in silico” mutations in the guanine binding site of RNase T1: A DFT study

Experimentally, the functional assessment of amino acid side chains in proteins is carried out by comparing parameters such as binding constants for the wild‐type protein and a mutant protein in which the considered side chain is deleted. In the present study, we apply a density functional theory (DFT) methodology to obtain changes in binding energy upon mutations in the enzyme ribonuclease T₁. Mutant structures were either taken directly from crystallographic data (“in vivo”) allowing for conformational changes upon mutation, or derived from the wild‐type (“in silico”). Excluding entropic contributions, the computed interaction energy changes upon mutation in vivo correlate qualitatively well with experimental binding free energy changes. In contrast, the in silico approach does not perform as well, especially for residues that contribute largely to binding. Subsequently, we assessed the applicability of the in vivo approach by analyzing the functional cooperativity between pairs of side chains. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Knots “Choke Off” Polymers upon Stretching

Long polymer chains inevitably get tangled into knots. Like macroscopic ropes, polymer chains are substantially weakened by knots and the rupture point is always located at the “entry” or “exit” of the knot. However, these phenomena are only poorly understood at a molecular level. Here we show that when a knotted polyethylene chain is tightened, most of the stress energy is stored in torsions around the curved part of the chain. The torsions act as “work funnels” that effectively localize mechanical stress in the immediate vicinity of the knot. As a result, the knot “chokes” the chain at its entry or exit, thus leading to bond rupture at much lower forces than those needed to break a linear, unknotted chain. Our work not only explains the weakening of the polymer chain and the position of the rupture point, but more generally demonstrates that chemical bonds do not have to be extensively stretched to be broken.     

Pentagermapyramidane: Crystallizing the “Transition‐State” Structure

The first example of the homonuclear pyramidanes, pentagermapyramidane, was synthesized, fully characterized, and computationally studied to reveal its peculiar structural features and the nature of its apex‐to‐base bonding interactions. Both solid‐state and solution structures of pentagermapyramidane are discussed based on the computed stabilities of its square‐pyramidal and distorted forms.     

A New Approach to the Design of Neutral 10‐C‐5 Trigonal‐Bipyramidal Carbon Compounds: A “π‐Electron Cap” Effect

DFT (B3LYP, M06‐2X) and MP2 methods are applied to the design of a wide series of the potentially 10‐C‐5 neutral compounds based on 6‐azabicyclotetradecanes: XC¹(YCH₂CH₂CH₂)₃N 1 – 3 , XC¹(YC₆H₄CH₂)₃N 4 – 6 , XC¹[Y(tBuC₆H₃)CH₂]₃N 7 – 9 and carbatranophanes 10 – 25 (X=Me, F, Cl; Y=O, NH, CH₂, SiH₂; Z=O, CH₂, (CH₂)₂, (CH₂)₃). Carbatranophanes 10 – 25 are characterized by a sterical compression of their axial 3c–4e XC¹←N fragment with respect to that in the parent molecules 4 – 6 . A magnitude of the revealed effect depends on a valence surrounding of the central carbon atom C¹, the size and the nature of the side chains (Z) that link the “π‐electron cap” with a tetradecane backbone. This circumstance allowed us to obtain 10‐C‐5 structures with the configuration of the bonds around the C¹ atom, which corresponds to practically an ideal trigonal bipyramid. In these compounds, the values of the covalence ratio χ of approximately 0.6 for the coordination C¹←N contacts with a covalent contribution (atoms in molecules (AIM) and natural bond orbital (NBO)) are record in magnitude. These values lie close to a low limit of the interval of the χ_Si←D change (0.6–0.9) being characteristic of the dative and ionic‐covalent (by nature) Si←D bond (D=N, O) in the known 10‐Si‐5 silicon compounds.     

“Hummingbird” Behaviour of N‐Heterocyclic Carbenes Stabilises Out‐of‐Plane Bonding of AuCl and CuCl Units

An N‐heterocyclic carbene substituted by two expanded 9‐ethyl‐9‐fluorenyl groups was shown to bind an AuCl unit in an unusual manner, namely with the Au?X rod sitting out of the plane defined by the heterocyclic carbene unit. As shown by X‐ray studies and DFT calculations, the observed large pitch angle (21°) arises from an easy displacement of the gold(I) atom away from the carbene lone‐pair axis, combined with the stabilisation provided by weak CH???Au interactions involving aliphatic and aromatic H atoms of the NHC wingtips. Weak, intermolecular Cl???H bonds are likely to cooperate with the H???Au interactions to stabilise the out‐of‐plane conformation. A general belief until now was that tilt angles in NHC complexes arise mainly from steric effects within the first coordination sphere.     

Comment on “Extending Hirshfeld‐I to bulk and periodic materials”

In recent years, several methods have been developed that partition the electron density among atoms using spherically symmetric atomic weights. D. E. P. Vanpoucke, P. Bultinck, and I. Van Driessche (J. Comput. Chem. 2012, doi: 10.1002/jcc.23088) recently reported a periodic implementation of the Hirshfeld‐I method that uses a combination of Becke‐style and uniform integration grids and modified atomic reference densities to compute net atomic charges in periodic materials. Herein, this method is discussed in the context of earlier periodic implementations of the Hirshfeld‐I method, the Iterated Stockholder Atoms method, and the density derived electrostatic and chemical method.