The Nature of the Chemical Bond Revisited: An Energy-Partitioning Analysis of Nonpolar Bonds

Correlation between Hammett substituent constants and directly calculated pi-conjugation strength

The results of an energy decomposition analysis of ortho-, meta-, and para-substituted benzylic cations and para-substituted benzylic anions H2C-C6H4Rq (R = H, F, CN, Me, OH, NH2, NO2, CHO, CO2H; q = +, -) are presented and discussed. The calculated values for the pi bonding between CH2(q) and C6H4R show for substituents which have pi orbitals a linear correlation with the Hammett sigma(p), sigma(+)(p), and sigma(m) constants.

Unicorns in the world of chemical bonding models

The appearance and the significance of heuristically developed bonding models are compared with the phenomenon of unicorns in mythical saga. It is argued that classical bonding models played an essential role for the development of the chemical science providing the language which is spoken in the territory of chemistry. The advent and the further development of quantum chemistry demands some restrictions and boundary conditions for classical chemical bonding models, which will continue to be integral parts of chemistry.

The Lewis legacy: the chemical bond--a territory and heartland of chemistry

Is chemistry a science without a territory? I argue that "chemical bonding" has been a traditional chemical territory ever since the chemical community amalgamated in the seventeenth century, and even before. The modern charter of this territory is Gilbert Newton Lewis, who started the "electronic structure revolution in chemistry." As a tribute to Lewis, I describe here three of his key papers from the years 1913, 1916, and 1923, and analyze them. Lewis has defined the quantum unit, the "electron pair bond," for construction of a chemical universe, and in so doing he charted a vast chemical territory and affected most profoundly the mental map of chemistry for generations ahead. Nevertheless, not all is known about the chemical bond" the chemical territory is still teaming with new and exciting problems of in new materials, nanoparticles, quantum dots, metalloenzymes, bonding at surface-vapor interfaces, and so on and so forth.

Why does electron sharing lead to covalent bonding? A variational analysis

Ground state energy differences between related systems can be elucidated by a comparative variational analysis of the energy functional, in which the concepts of variational kinetic pressure and variational electrostatic potential pull are found useful. This approach is applied to the formation of the bond in the hydrogen molecule ion. A highly accurate wavefunction is shown to be the superposition of two quasiatomic orbitals, each of which consists to 94% of the respective atomic 1s orbital, the remaining 6% deformation being 73% spherical and 27% nonspherical in character. The spherical deformation can be recovered to 99.9% by scaling the 1s orbital. These results quantify the conceptual metamorphosis of the free-atom wavefunction into the molecular wavefunction by orbital sharing, orbital contraction, and orbital polarization. Starting with the 1s orbital on one atom as the initial trial function, the value of the energy functional of the molecule at the equilibrium distance is stepwise lowered along several sequences of wavefunction modifications, whose energies monotonically decrease to the ground state energy of H2+. The contributions of sharing, contraction and polarization to the overall lowering of the energy functional and their kinetic and potential components exhibit a consistent pattern that can be related to the wavefunction changes on the basis of physical reasoning, including the virial theorem. It is found that orbital sharing lowers the variational kinetic energy pressure and that this is the essential cause of covalent bonding in this molecule.

Atom-atom partitioning of total (super)molecular energy: The hidden terms of classical force fields

Classical force fields describe the interaction between atoms that are bonded or nonbonded via simple potential energy expressions. Their parameters are often determined by fitting to ab initio energies and electrostatic potentials. A direct quantum chemical guide to constructing a force field would be the atom-atom partitioning of the energy of molecules and van der Waals complexes relevant to the force field. The authors used the theory of quantum chemical topology to partition the energy of five systems [H2, CO, H2O, (H2O)2, and (HF)2] in terms of kinetic, Coulomb, and exchange intra-atomic and interatomic contributions. The authors monitored the variation of these contributions with changing bond length or angle. Current force fields focus only on interatomic interaction energies and assume that these purely potential energy terms are the only ones that govern structure and dynamics in atomistic simulations. Here the authors highlight the importance of self-energy terms (kinetic and intra-atomic Coulomb and exchange).

Charge-shift bonding--a class of electron-pair bonds that emerges from valence bond theory and is supported by the electron localization function approach

This paper deals with a central paradigm of chemistry, the electron-pair bond. Valence bond (VB) theory and electron-localization function (ELF) calculations of 21 single bonds demonstrate that along the two classical bond families of covalent and ionic bonds, there exists a class of charge-shift bonds (CS bonds) in which the fluctuation of the electron pair density plays a dominant role. In VB theory, CS bonding manifests by way of a large covalent-ionic resonance energy, RE(CS), and in ELF by a depleted basin population with large variances (fluctuations). CS bonding is shown to be a fundamental mechanism that is necessary to satisfy the equilibrium condition, namely the virial ratio of the kinetic and potential energy contributions to the bond energy. The paper defines the atomic propensity and territory for CS bonding: Atoms (fragments) that are prone to CS bonding are compact electronegative and/or lone-pair-rich species. As such, the territory of CS bonding transcends considerations of static charge distribution, and involves: a) homopolar bonds of heteroatoms with zero static ionicity, b) heteropolar sigma and pi bonds of the electronegative and/or electron-pair-rich elements among themselves and to other atoms (e.g., the higher metalloids, Si, Ge, Sn, etc), c) all hypercoordinate molecules. Several experimental manifestations of charge-shift bonding are discussed, such as depleted bonding density, the rarity of ionic chemistry of silicon in condensed phases, and the high barriers of halogen-transfer reactions as compared to hydrogen-transfers.

The nature of the hydrogen bond: A synthesis from the interacting quantum atoms picture

The interacting quantum atoms approach [IQA, as presented by Blanco et al., J. Chem. Theory Comput. 1, 1096 (2005)] is applied to standard hydrogen bonded dimers. IQA is an interpretation tool based on a real space energy decomposition scheme fully consistent with the quantum theory of atoms in molecules. It provides a partition of every physical term present in the Hamiltonian into atomic and interatomic contributions. The procedure is orbital-free and self-contained, needing neither external references nor artificial intermediate states. Binding is the result of a competition between the destabilizing deformations suffered by the interacting fragments upon interaction and the stabilizing interaction energy itself. According to IQA, there is no incompatibility between the prevalent electrostatic image of hydrogen bonded systems and that favoring important covalent contributions. Depending on how we gather the different energetic terms, we may recover electrostatic or covalent pictures from the same underlying quantum mechanical description. Our results show that the nonclassical contributions to hydrogen bonding are spatially localized, involving only the H atom and its two nearest neighbors. IQA is well suited as a comparative tool. Its thin energetic decomposition allows us to recover exactly (or to a very good approximation) the quantities of the most widely used energy decomposition schemes. Such a comparison sheds light on the virtues and faults of the different methods and on the origin of the 50 years old debate regarding the covalent/electrostatic nature of the hydrogen bond.

Chemical Bonding in Phosphane and Amine Complexes of Main Group Elements and Transition Metals

The geometries and bond dissociation energies of the main group complexes X3B-NX3, X3B-PX3, X3Al-NX3, and X3Al-PX3 (X = H, Me, Cl) and the transition metal complexes (CO)5M-NX3 and (CO)5M-PX3 (M = Cr, Mo, W) have been calculated using gradient-corrected density functional theory at the BP86/TZ2P level. The nature of the donor-acceptor bonds was investigated with an energy decomposition analysis. It is found that the bond dissociation energy is not a good measure for the intrinsic strength of Lewis acidity and basicity because the preparation energies of the fragments may significantly change the trend of the bond strength. The interaction energies between the frozen fragments of the borane complexes are in most cases larger than the interaction energies of the alane complexes. The bond dissociation energy of the alane complexes is sometimes higher than that of the borane analogues because the energy for distorting the planar equilibrium geometry of BX3 to the pyramidal from in the complexes is higher than for AlX3. Inspection of the three energy terms, DeltaE(Pauli), DeltaE(orb), and DeltaE(elstat), shows that all three of them must be considered to understand the trends of the Lewis acid and base strength. The orbital term of the donor-acceptor bonds with the Lewis bases NCl3 and PCl3 have a higher pi character than the bonds of EH3 and EMe3, but NCl3 and PCl3 are weaker Lewis bases because the lone-pair orbital at the donor atoms N and P has a high percent s character. The calculated DeltaE(int) values suggest that the trends of the intrinsic Lewis bases' strengths in the main-group complexes with BX3 and AlX3 are NMe3 > NH3 > NCl3 and PMe3 > PH3 > PCl3. The transition metal complexes exhibit a somewhat different order with NH3 > NMe3 > NCl3 and PMe3 > PH3 > PCl3. The slightly weaker bonding of NMe3 than that of NH3 comes from stronger Pauli repulsion. The bond length does not always correlate with the bond dissociation energy, nor does it always correlate with the intrinsic interaction energy.

Oxidative Addition of Hydrogen Halides and Dihalogens to Pd. Trends in Reactivity and Relativistic Effects

We have theoretically studied the oxidative addition of HX and X(2) to palladium for X = F, Cl, Br, I and At, using both nonrelativistic and ZORA-relativistic density functional theory at BLYP/QZ4P. The purpose is 3-fold: (i) to obtain a set of consistent potential energy surfaces (PESs) to infer accurate trends in reactivity for simple, archetypal oxidative addition reactions; (ii) to assess how relativistic effects modify these trends along X = F, Cl, Br, I and At; and (iii) to rationalize the trends in reactivity in terms of the reactants' molecular-orbital (MO) electronic structure and the H-X and X-X bond strengths. For the latter, we provide full Dirac-Coulomb CCSD(T) benchmarks. All oxidative additions to Pd are exothermic and have a negative overall barrier, except that of HF which is approximately thermoneutral and has a positive overall barrier. The activation barriers of the HX oxidative additions decrease systematically as X descends in group 17 of the periodic table; those of X(2) first increase, from F to Cl, but then also decrease further down group 17. On the other hand, HX and X(2) show clearly opposite trends regarding the heat of reaction: that of HX becomes more exothermic and that of X(2) less exothermic as X descends in group 17. Relativistic effects can be as large as 15-20 kcal/mol but they do not change the qualitative trends. Interestingly, the influence of relativistic effects on activation barriers and heats of reaction decreases for the heavier halogens due to counteracting relativistic effects in palladium and the halogens.

Direct Estimate of the Strength of Conjugation and Hyperconjugation by the Energy Decomposition Analysis Method

The intrinsic strength of pi interactions in conjugated and hyperconjugated molecules has been calculated using density functional theory by energy decomposition analysis (EDA) of the interaction energy between the conjugating fragments. The results of the EDA of the trans-polyenes H2C=CH-(HC=CH)n-CH=CH2 (n = 1-3) show that the strength of pi conjugation for each C=C moiety is higher than in trans-1,3-butadiene. The absolute values for the conjugation between Si=Si pi bonds are around two-thirds of the conjugation between C=C bonds but the relative contributions of DeltaE pi to DeltaE orb in the all-silicon systems are higher than in the carbon compounds. The pi conjugation between C=C and C=O or C=NH bonds in H2C=CH--C(H)=O and H2C=CH-C(H)=NH is comparable to the strength of the conjugation between C=C bonds. The pi conjugation in H2C=CH-C(R)=O decreases when R = Me, OH, and NH2 while it increases when R = halogen. The hyperconjugation in ethane is around a quarter as strong as the pi conjugation in ethyne. Very strong hyperconjugation is found in the central C-C bonds in cubylcubane and tetrahedranyltetrahedrane. The hyperconjugation in substituted ethanes X3C-CY3 (X,Y = Me, SiH3, F, Cl) is stronger than in the parent compound particularly when X,Y = SiH3 and Cl. The hyperconjugation in donor-acceptor-substituted ethanes may be very strong; the largest DeltaE pi value was calculated for (SiH3)3C-CCl3 in which the hyperconjugation is stronger than the conjugation in ethene. The breakdown of the hyperconjugation in X3C-CY3 shows that donation of the donor-substituted moiety to the acceptor group is as expected the most important contribution but the reverse interaction is not negligible. The relative strengths of the pi interactions between two C=C double bonds, one C=C double bond and CH3 or CMe3 substituents, and between two CH3 or CMe3 groups, which are separated by one C-C single bond, are in a ratio of 4:2:1. Very strong hyperconjugation is found in HC[triple bond]C-C(SiH3)3 and HC[triple bond]C-CCl3. The extra stabilization of alkenes and alkynes with central multiple bonds over their terminal isomers coming from hyperconjugation is bigger than the total energy difference between the isomeric species. The hyperconjugation in Me-C(R)=O is half as strong as the conjugation in H2C=CH-C(R)=O and shows the same trend for different substituents R. Bond energies and lengths should not be used as indicators of the strength of hyperconjugation because the effect of sigma interactions and electrostatic forces may compensate for the hyperconjugative effect.

Hydrogen–Hydrogen Bonding in Planar Biphenyl, Predicted by Atoms-In-Molecules Theory, Does Not Exist

Based on an Atoms-in-Molecules (AIM) analysis, Matta et al. recently claimed evidence for the existence of hydrogen-hydrogen bonding between ortho-hydrogen atoms, pointing towards each other from adjacent phenyl groups in planar biphenyl. This AIM result is opposed to the classical view that nonbonded steric repulsion between the ortho-hydrogen atoms is responsible for the higher energy of the planar as compared to the twisted geometry of biphenyl. In the present work, we address the question if hydrogen-hydrogen bonding in biphenyl exists, as suggested by AIM, or not. To this end, we have analyzed the potential energy surface for internal rotation of biphenyl in terms of two interacting phenyl radicals using density functional theory (DFT) at BP86/TZ2P. A detailed analysis of the bonding mechanism and a quantitative bond energy decomposition in the framework of Kohn-Sham DFT show that Pauli (or overlap) repulsion, mainly between C(ortho)--H(ortho) phenyl MOs, prevents biphenyl from being planar and forces it to adopt a twisted equilibrium geometry. Furthermore, a derivative of biphenyl in which all four ortho-hydrogen atoms have been removed does adopt a planar equilibrium geometry. Thus, our results confirm the classical view of steric repulsion between ortho-hydrogen atoms in biphenyl and they falsify the hypothesis of hydrogen-hydrogen bonding.

Toward a physical understanding of electron-sharing two-center bonds. I. General aspects

In 1916, Lewis and Kossel laid the empirical ground for the electronic theory of valence, whose quantum theoretical foundation was uncovered only slowly. We can now base the classification of the various traditional chemical bond types in a threefold manner on the one- and two-electron terms of the quantum-physical Hamiltonian (kinetic, atomic core attraction, electron repulsion). Bond formation is explained by splitting up the real process into two physical steps: (i) interaction of undeformed atoms and (ii) relaxation of this nonstationary system. We aim at a flexible bond energy partitioning scheme that can avoid cancellation of large terms of opposite sign. The driving force of covalent bonding is a lowering of the quantum kinetic energy density by sharing. The driving force of heteropolar bonding is a lowering of potential energy density by charge rearrangement in the valence shell. Although both mechanisms are quantum mechanical in nature, we can easily visualize them, since they are of one-electron type. They are however tempered by two-electron correlations. The richness of chemistry, owing to the diversity of atomic cores and valence shells, becomes intuitively understandable with the help of effective core pseudopotentials for the valence shells. Common conceptual difficulties in understanding chemical bonds arise from quantum kinematic aspects as well as from paradoxical though classical relaxation phenomena. On this conceptual basis, a dozen different bond types in diatomic molecules will be analyzed in the following article. We can therefore examine common features as well as specific differences of various bonding mechanisms.

Electronic structure of CO—An exercise in modern chemical bonding theory

This paper discusses recent progress that has been made in the understanding of the electronic structure and bonding situation of carbon monoxide which was analyzed using modern quantum chemical methods. The new results are compared with standard models of chemical bonding. The electronic charge distribution and the dipole moment, the nature of the HOMO and the bond dissociation energy are discussed in detail.

Why Do the Heavy-Atom Analogues of Acetylene E2H2(E = Si−Pb) Exhibit Unusual Structures?

DFT calculations at BP86/QZ4P have been carried out for different structures of E(2)H(2) (E = C, Si, Ge, Sn, Pb) with the goal to explain the unusual equilibrium geometries of the heavier group 14 homologues where E = Si-Pb. The global energy minima of the latter molecules have a nonplanar doubly bridged structure A followed by the singly bridged planar form B, the vinylidene-type structure C, and the trans-bent isomer D1. The energetically high-lying trans-bent structure D2 possessing an electron sextet at E and the linear form HEEH, which are not minima on the PES, have also been studied. The unusual structures of E(2)H(2) (E = Si-Pb) are explained with the interactions between the EH moieties in the (X(2)Pi) electronic ground state which differ from C(2)H(2), which is bound through interactions between CH in the a(4)Sigma(-) excited state. Bonding between two (X(2)Pi) fragments of the heavier EH hydrides is favored over the bonding in the a(4)Sigma(-) excited state because the X(2)Pi --> a(4)Sigma(-) excitation energy of EH (E = Si-Pb) is significantly higher than for CH. The doubly bridged structure A of E(2)H(2) has three bonding orbital contributions: one sigma bond and two E-H donor-acceptor bonds. The singly bridged isomer B also has three bonding orbital contributions: one pi bond, one E-H donor-acceptor bond, and one lone-pair donor-acceptor bond. The trans-bent form D1 has one pi bond and two lone-pair donor-acceptor bonds, while D2 has only one sigma bond. The strength of the stabilizing orbital contributions has been estimated with an energy decomposition analysis, which also gives the bonding contributions of the quasi-classical electrostatic interactions.