Physical understanding through variational reasoning: electron sharing and covalent bonding

Insights into the variations of kinetic and potential energies in a multi-bond reaction: the reaction electronic flux perspective

CONTEXT

The debate over whether kinetic energy (KE) or potential energy (PE) are the fundamental energy components that contribute to forming covalent bonds has been enduring and stimulating over time. However, the supremacy of these energy components in reactions where multiple bonds are simultaneously formed or broken has yet to be explored. In this study, we use the reaction electronic flux (REF), an effective tool for investigating changes in driving electronic activity when bond formation or dissociation occurs in a chemical reaction, to examine the fluctuations in the KE and PE in a multi-bond reaction. To that end, the activation of CO2 by low-valent group 14 catalysts through a concerted σ -bond metathesis mechanism is analyzed. The findings of this preliminary study suggest that the REF can be utilized as a tool to rationalize alterations in the KE and PE in a multi-bond reaction. Specifically, analyses across the reaction coordinate reveal that changes in the KE and PE precede activation in the REF, stimulating the electronic activity where bond formation or dissociation processes dominate.

METHODS

The activation of CO2 by the low-valent LEH catalysts (L = N,N'-bis(2,6-diisopropyl phenyl)- β -diketiminate; E = Si, Ge, Sn, and Pb) was studied along the reaction coordinate at the M06-2X/6-31 G(d,p)-LANL2DZ(E) level of theory. The respective minimum energy path calculations were obtained using the intrinsic reaction coordinate (IRC) procedure. The reaction electronic flux (REF) was calculated through the computation of the electronic chemical potential using the frontier molecular orbital approximation. Mayer bond orders along the reaction coordinate have been determined using the NBO 3.1 program in Gaussian16. Most of the reaction coordinate quantities reported in this study (REF, KE, PE, among others) have been determined using the Kudi program and custom Python scripts.

Chemical Aristocracy: He3 Dication and Analogous Noble-Gas-Exclusive Covalent Compounds

Herein, we predict the first set of covalently bonded triatomic molecular compounds composed exclusively of noble gases. Using a combination of double-hybrid DFT, CCSD(T), and MRCI+Q calculations and a range of bonding analyses, we explored a set of 270 doubly charged triatomics, which included various combinations of noble gases and main group elements. This extensive exploration uncovered nine noble-gas-exclusive covalent compounds incorporating helium, neon, argon, or combinations thereof, exemplified by cases such as He32+ and related systems. This work brings to light a previously uncharted domain of noble gas chemistry, demonstrating the potential of noble gases in forming covalent molecular clusters.

Revisiting the bonding evolution theory: a fresh perspective on the ammonia pyramidal inversion and bond dissociations in ethane and borazane

This work offers a comprehensive and fresh perspective on the bonding evolution theory (BET) framework, originally proposed by Silvi and collaborators [X. Krokidis, S. Noury and B. Silvi, Characterization of elementary chemical processes by catastrophe theory, J. Phys. Chem. A, 1997, 101, 7277-7282]. By underscoring Thom's foundational work, we identify the parametric function characterizing bonding events along a reaction pathway through a three-step sequence to establish such association rigorously, namely: (a) computing the determinant of the Hessian matrix at all potentially degenerate critical points, (b) computing the relative distance between these points, and (c) assigning the unfolding based on these computations and considering the maximum number of critical points for each unfolding. In-depth examination of the ammonia inversion and the dissociation of ethane and ammonia borane molecules yields a striking discovery: no elliptic umbilic flag is detected along the reactive coordinate for any of the systems, contradicting previous reports. Our findings indicate that the core mechanisms of these chemical reactions can be understood using only two folds, the simplest polynomial of Thom's theory, leading to considerable simplification. In contrast to previous reports, no signatures of the elliptic umbilic unfolding were detected in any of the systems examined. This finding dramatically simplifies the topological rationalization of electron rearrangements within the BET framework, opening new approaches for investigating complex reactions.

Bond Bundle Analysis of Ketosteroid Isomerase

Bond bundle analysis is used to investigate enzymatic catalysis in the ketosteroid isomerase (KSI) active site. We identify the unique bonding regions in five KSI systems, including those exposed to applied oriented electric fields and those with amino acid mutations, and calculate the precise redistribution of electron density and other regional properties that accompanies either enhancement or inhibition of KSI catalytic activity. We find that catalytic enhancement results from promoting both inter- and intra-molecular electron density redistribution, between bond bundles and bond wedges within the KSI-docked substrate molecule, in the forward direction of the catalyzed reaction. Though the redistribution applies to both types of perturbed systems and is thus suggestive of a general catalytic role, we observe that bond properties (e.g., volume vs energy vs electron count) can respond independently and disproportionately depending on the type of perturbation. We conclude that the resulting catalytic enhancement/inhibition proceeds via different mechanisms, where some bond properties are utilized more by one type of perturbation than the other. Additionally, we find that the correlations between bond wedge properties and catalyzed reaction barrier energies are additive to predict those of bond bundles and atomic basins, providing a rigorous grounding for connecting changes in local charge density to resulting shifts in reaction barrier energy.

Analysis of chemical bonding of the ground and low-lying states of Mo2 and of Mo2Clx complexes, x = 2 - 10

In the present study, we perform accurate calculations via multireference configuration interaction and coupled cluster methodologies on the dimolybdenum molecule in conjunction with complete series of correlation and weighted core correlation consistent basis sets up to quintuple size. The bonding, dissociation energies, and spectroscopic parameters of the seven states that correlate to the ground state products are calculated. The ground state has a sextuple chemical bond and each of the calculated excited state has one less bond than the previous one. The calculated values for the ground(X1Σg+ ) state of Mo2 have been extrapolated to the complete basis set limits. Our final values, re=1.9324 Å and De(D0)=4.502{plus minus}0.007(4.471{plus minus}0.009) eV, are in excellent agreement with the experimental values of re=1.929, 1.938(9) Å and D0=4.476(10) eV. The Mo2 in 13Σg+ state is a weakly bound dimer, forming 5s...5pz bonds, with De=0.120 eV at re=3.53 Å. All calculated excited states (except 13Σg+) have a highly multireference character (C0=0.25-0.55). The ordering of the molecular bonding orbitals changes as the spin is increased from quintet to septet state. The quite low bond dissociation energy of the ground state is due to the splitting of the molecular bonding orbitals in two groups differing in energy by ~3 eV. Finally, the bond breaking of Mo2, as the multiplicity of spin is increased, is analyzed in parallel with the Mo-Mo bond breaking in a series of Mo2Clx complexes when x is increased. Physical insight into the nature of the sextuple bond and its low dissociation energy is provided.

The role of references and the elusive nature of the chemical bond

Chemical bonding theory is of utmost importance to chemistry, and a standard paradigm in which quantum mechanical interference drives the kinetic energy lowering of two approaching fragments has emerged. Here we report that both internal and external reference biases remain in this model, leaving plenty of unexplored territory. We show how the former biases affect the notion of wavefunction interference, which is purportedly recognized as the most basic bonding mechanism. The latter influence how bonding models are chosen. We demonstrate that the use of real space analyses are as reference-less as possible, advocating for their use. Delocalisation emerges as the reference-less equivalent to interference and the ultimate root of bonding. Atoms (or fragments) in molecules should be understood as a statistical mixture of components differing in electron number, spin, etc.

The theory of chemical bonding relies on arbitrary references. Here the authors report a fundamental study on the chemical bond showing that considering the binding fragments as objects in real space enables to eliminate inherent biases.

Orbital contraction and covalent bonding

According to Ruedenberg's classic treatise on the theory of chemical bonding [K. Ruedenberg, Rev. Mod. Phys. 34, 326-376 (1962)], orbital contraction is an integral consequence of covalent bonding. While the concept is clear, its quantification by quantum chemical calculations is not straightforward, except for the simplest of molecules, such as H₂ ⁺ and H₂. This paper proposes a new, yet simple, approach to the problem, utilizing the modified atomic orbital (MAO) method of Ehrhardt and Ahlrichs [Theor. Chim. Acta 68, 231 (1985)]. Through the use of MAOs, which are an atom-centered minimal basis formed from the molecular and atomic density operators, the wave functions of the species of interest are re-expanded, allowing the computation of the kinetic energy (and any other expectation value) of free and bonded fragments. Thus, it is possible to quantify the intra- and interfragment changes in kinetic energy, i.e., the effects of contraction. Computations are reported for a number of diatomic molecules H₂, Li₂, B₂, C₂, N₂, O₂, F₂, CO, P₂, and Cl₂ and the polyatomics CH₃-CH₃, CH₃-SiH₃, CH₃-OH, and C₂H₅-C₂H₅ (where the single bonds between the heavy atoms are studied) as well as dimers of He, Ne, Ar, and the archetypal ionic molecule NaCl. In all cases, it is found that the formation of a covalent bond is accompanied by an increase in the intra-fragment kinetic energy, an indication of orbital contraction and/or deformation.

d- and s-orbital populations in the d block: unbound atoms in physical vacuum versus chemical elements in condensed matter. A Dronskowski-population analysis

The electron configurations of Ca, Zn and the nine transition elements M in between (and their heavier homologs) are reviewed on the basis of density functional theory and experimental facts. The d-s orbital energy and population patterns are systematically diverse. (i) The dominant valence electron configuration of most free neutral atoms M0 of groups g = 2–12 is 3d g−2 4s 2 (textbook rule), or 3d g−14s 1. (ii) Formal M q+ cations in chemical compounds have the dominant configuration 3d g−q 4s 0 (basic concept of transition metal chemistry). (iii) M0 atoms in metallic phases [M∞] of hcp, ccp(fcc) and bcc structures have intermediate populations near 3d g−1 4s 1 (lower d populations for Ca (ca. ½) and Zn (ca. 10)). Including the 4p valence orbitals, the dominant metallic configuration is 3d g−δ 4(sp) δ with δ ≈ 1.4 (±0.2) throughout (except for Zn). (iv) The 3d,4s population of atomic clusters M m varies for increasing m smoothly from single-atomic 3d g−24s 2 toward metallic 3d g−14s 1. – The textbook rule for the one-electron energies, i.e., ns < (n−1)d, holds ‘in a broader sense’ for the s block, but in general not for the d block, and never for the p block. It is more important to teach realistic atomic orbital (AO) populations such as the ones given above.

Principles Determining the Structure of Transition Metals

For the better part of a century researchers across disciplines have sought to explain the crystallography of the elemental transition metals: hexagonal close packed, body centered cubic, and face centered cubic in a form similar to that used to rationalize the structure of organic molecules and inorganic complexes. Pauling himself tried with limited success to address the origins of transition metal stability. These early investigators were handicapped, however, by incomplete knowledge regarding the structure of metallic electron density. Here, we exploit modern approaches to electron density analysis to first comprehensively describe transition metal electron density. Then, we use topological partitioning and quantum mechanically rigorous treatments of kinetic energy to account for the structure of the density as arising from the interactions between metallic polyhedra. We argue that the crystallography of the early transition metals results from charge transfer from the so called "octahedral" to "tetrahedral cages" while the face centered cubic structure of the late transition metals is a consequence of anti-bonding interactions that increase octahedral hole kinetic energy.

Dual XH-π Interaction of Hexafluoroisopropanol with Arenes

The dual XH (OH and CH) hydrogen-bond-donating property of 1,1,1,3,3,3-hexafluoroisopropanol (HFIP) and the strong dual XH-π interaction with arenes were firstly disclosed by theoretical studies. Here, the high accuracy post-Hartree-Fock methods, CCSD(T)/CBS, reveal the interaction energy of HFIP/benzene complex (-7.22 kcal/mol) and the contribution of the electronic correlation energy in the total interaction energy. Strong orbital interaction between HFIP and benzene was found by using the DFT method in this work to disclose the dual XH-π intermolecular orbital interaction of HFIP with benzene-forming bonding and antibonding orbitals resulting from the orbital symmetry of HFIP. The density of states and charge decomposition analyses were used to investigate the orbital interactions. Isopropanol (IP), an analogue of HFIP, and chloroform (CHCl₃) were studied to compare them with the classical OH-π, and non-classical CH-π interactions. In addition, the influence of the aggregating effect of HFIP, and the numbers of substituted methyl groups in benzene rings were also studied. The interaction energies of HFIP with the selected 24 common organic compounds were calculated to understand the role of HFIP as solvent or additive in organic transformation in a more detailed manner. A single-crystal X-ray diffraction study of hexafluoroisopropyl benzoate further disclosed and confirmed that the CH of HFIP shows the non-classical hydrogen-bond-donating behavior.

Substituent Effects on the Quantum Interference of Two-Center One-Electron Bonds: [B2X6]- (X = H, F, Cl, CN, OH, CH3, and OCH3)

The interference energy analysis (IEA) provided by the generalized product function energy partitioning (GPF-EP) method was applied to investigate the influence of the neighboring atoms on the nature of the two-center one-electron (2c1e) bonds in the anion dimers of BX₃ species (X = H, F, Cl, CN, OH, CH₃, and OCH₃). The species were studied at the GVB-PP(6/12).SC(1,2)/6-31**G++ level of calculation. The IEA has revealed that there is a balance between two main factors determining the chemical stability of the species. Quantum interference acts as the sole stabilizing effect in the formation of the chemical bonds, particularly as the result of the drop in kinetic energy, and the electronegativity of the substituent has a direct influence on the magnitude of this effect. The quasi-classical energy is responsible for the destabilizing factors, mainly the group bulkiness, and the "electron-withdrawing" effect in the case of the cyano group.

Molecular Orbitals Support Energy-Stabilizing "Bonding" Nature of Bader's Bond Paths

Our MO-based findings proved a bonding nature of each density bridge (DB, or a bond path with an associated critical point, CP) on a Bader molecular graph. A DB pinpoints universal physical and net energy-lowering processes that might, but do not have to, lead to a chemical bond formation. Physical processes leading to electron density (ED) concentration in internuclear regions of three distinctively different homopolar H,H atom-pairs as well as classical C-C and C-H covalent bonds were found to be exactly the same. Notably, properties of individual MOs are internuclear-region specific as they (i) concentrate, deplete, or do not contribute to ED at a CP and (ii) delocalize electron-pairs through either in- (positive) or out-of-phase (negative) interference. Importantly, dominance of a net ED concentration and positive e^--pairs delocalization made by a number of σ-bonding MOs is a common feature at a CP. This feature was found for the covalently bonded atoms as well as homopolar H,H atom-pairs investigated. The latter refer to a DB-free H,H atom-pair of the bay in the twisted biphenyl (Bph) and DB-linked H,H atom-pairs (i) in cubic Li₄H₄, where each H atom is involved in three highly repulsive interactions (over +80 kcal/mol), and (ii) in a weak attractive interaction when sterically clashing in the planar Bph.

The Basics of Covalent Bonding in Terms of Energy and Dynamics

We address the paradoxical fact that the concept of a covalent bond, a cornerstone of chemistry which is well resolved computationally by the methods of quantum chemistry, is still the subject of debate, disagreement, and ignorance with respect to its physical origin. Our aim here is to unify two seemingly different explanations: one in terms of energy, the other dynamics. We summarize the mechanistic bonding models and the debate over the last 100 years, with specific applications to the simplest molecules: H2+ and H2. In particular, we focus on the bonding analysis of Hellmann (1933) that was brought into modern form by Ruedenberg (from 1962 on). We and many others have helped verify the validity of the Hellmann-Ruedenberg proposal that a decrease in kinetic energy associated with interatomic delocalization of electron motion is the key to covalent bonding but contrary views, confusion or lack of understanding still abound. In order to resolve this impasse we show that quantum mechanics affords us a complementary dynamical perspective on the bonding mechanism, which agrees with that of Hellmann and Ruedenberg, while providing a direct and unifying view of atomic reactivity, molecule formation and the basic role of the kinetic energy, as well as the important but secondary role of electrostatics, in covalent bonding.

Observing the 3D Chemical Bond and its Energy Distribution in a Projected Space

Our curiosity-driven desire to "see" chemical bonds dates back at least one-hundred years, perhaps to antiquity. Sweeping improvements in the accuracy of measured and predicted electron charge densities, alongside our largely bondcentric understanding of molecules and materials, heighten this desire with means and significance. Here we present a method for analyzing chemical bonds and their energy distributions in a two-dimensional projected space called the condensed charge density. Bond "silhouettes" in the condensed charge density can be reverse-projected to reveal precise three-dimensional bonding regions we call bond bundles. We show that delocalized metallic bonds and organic covalent bonds alike can be objectively analyzed, the formation of bonds observed, and that the crystallographic structure of simple metals can be rationalized in terms of bond bundle structure. Our method also reproduces the expected results of organic chemistry, enabling the recontextualization of existing bond models from a charge density perspective.

Quantifying individual (anti)bonding molecular orbitals' contributions to chemical bonding

The shapes of molecular orbitals (MOs) in polyatomic molecules are often difficult for meaningful chemical interpretations. We report protocols to quantify contributions made by individual orbitals (molecular canonical and natural) of classical bonding, non-bonding or anti-bonding nature to (i) electron density into the inter-nuclear region and (ii) diatomic electron delocalization, DI(A,B). In other words, these protocols universally explain orbital's inputs to two fundamental and energy-lowering mechanisms of chemical bonding (interactions) and ease the chemical interpretation of their character in polyatomic molecules. They reveal that the MO and real-space density descriptions of the interactions are equivalent and, importantly, equally apply to all atom-pairs regardless if they are involved in a highly attractive or repulsive interaction. Hence, they not only remove ambiguity in chemical bonding interpretations (based on either MO or electron density approaches) but also demonstrate complementarity between the two such seemingly different techniques. Finally, our approach challenges some classical assumptions about MOs, such as the role of core electrons, the degree of bonding in antibonding MOs and the relative importance of frontier orbitals. Just as an example, we show that orthodox antibonding orbitals can make a significant contribution of a bonding nature to a classical covalent bond or major contribution to DI(A,B) of an intramolecular and highly repulsive HH interaction.

One-electron bonds are not "half-bonds"

Despite the success of the molecular orbital (MO) and valence-bond (VB) models to describe the electronic structure and properties of molecules, neither MO nor VB provides an explanation for the nature of the chemical bond. The first to address this problem was Ruedenberg, who showed that chemical bonds result from quantum interference. He developed a method to calculate the interference contribution to the total electronic energy and density and applied it to molecules containing typical two-centre two-electron (2c-2e) covalent bonds. To test the generality of Ruedenberg's hypothesis, we developed a powerful Interference Energy Analysis (IEA) method to calculate the interference contributions of individual chemical bonds to the total energy of diatomic and polyatomic molecules, and showed that any two-electron bond, despite its polarity, results from quantum interference. Nevertheless, many stable molecules are experimentally known whose chemical structures clearly indicate the existence of two-centre one-electron bonds (2c-1e). Therefore, the question remains if quantum interference will be the dominant effect for these systems. This work describes the extension of the IEA for treating two-centre one-electron bonds, making use of a Generalised Product Function (GPF) built from spin coupled wave functions of N electrons in M orbitals, SC(N,M). Several diatomic and polyatomic molecules were analysed and whenever possible the results were compared with the analogous case of a two-electron bond. The results indicate that interference is the dominant effect for the one-electron bonds, which reinforces the role of quantum interference as the central element in chemical bonding theory.

Adhesion, forces and the stability of interfaces

Weak molecular interactions (WMI) are responsible for processes such as physisorption; they are essential for the structure and stability of interfaces, and for bulk properties of liquids and molecular crystals. The dispersion interaction is one of the four basic interactions types – electrostatics, induction, dispersion and exchange repulsion – of which all WMIs are composed. The fact that each class of basic interactions covers a wide range explains the large variety of WMIs. To some of them, special names are assigned, such as hydrogen bonding or hydrophobic interactions. In chemistry, these WMIs are frequently used as if they were basic interaction types. For a long time, dispersion was largely ignored in chemistry, attractive intermolecular interactions were nearly exclusively attributed to electrostatic interactions. We discuss the importance of dispersion interactions for the stabilization in systems that are traditionally explained in terms of the “special interactions” mentioned above. System stabilization can be explained by using interaction energies, or by attractive forces between the interacting subsystems; in the case of stabilizing WMIs, one frequently speaks of adhesion energies and adhesive forces. We show that the description of system stability using maximum adhesive forces and the description using adhesion energies are not equivalent. The systems discussed are polyaromatic molecules adsorbed to graphene and carbon nanotubes; dimers of alcohols and amines; cellulose crystals; and alcohols adsorbed onto cellulose surfaces.

Bond orders of the diatomic molecules

Bond order quantifies the number of electrons dressed-exchanged between two atoms in a material and is important for understanding many chemical properties. Diatomic molecules are the smallest molecules possessing chemical bonds and play key roles in atmospheric chemistry, biochemistry, lab chemistry, and chemical manufacturing. Here we quantum-mechanically calculate bond orders for 288 diatomic molecules and ions. For homodiatomics, we show bond orders correlate to bond energies for elements within the same chemical group. We quantify and discuss how semicore electrons weaken bond orders for elements having diffuse semicore electrons. Lots of chemistry is effected by this. We introduce a first-principles method to represent orbital-independent bond order as a sum of orbital-dependent bond order components. This bond order component analysis (BOCA) applies to any spin-orbitals that are unitary transformations of the natural spin-orbitals, with or without periodic boundary conditions, and to non-magnetic and (collinear or non-collinear) magnetic materials. We use this BOCA to study all period 2 homodiatomics plus Mo₂, Cr₂, ClO, ClO⁻, and Mo₂(acetate)₄. Using Manz's bond order equation with DDEC6 partitioning, the Mo–Mo bond order was 4.12 in Mo₂ and 1.46 in Mo₂(acetate)₄ with a sum of bond orders for each Mo atom of ∼4. Our study informs both chemistry research and education. As a learning aid, we introduce an analogy between bond orders in materials and message transmission in computer networks. We also introduce the first working quantitative heuristic model for all period 2 homodiatomic bond orders. This heuristic model incorporates s–p mixing to give heuristic bond orders of ¾ (Be₂), 1¾ (B₂), 2¾ (C₂), and whole number bond orders for the remaining period 2 homodiatomics.

Bond orders were computed for 288 diatomics, and a new bond order component analysis (BOCA) was applied to selected diatomics.

The Virial Theorem and Covalent Bonding

A long-held view of the origin of covalent binding is based on the notion that electrostatic forces determine the stability of a system of charged particles and that, therefore, potential energy changes drive the stabilization of molecules. A key argument advanced for this conjecture is the rigorous validity of the virial theorem. Rigorous in-depth analyses have however shown that the energy lowering of covalent bonding is due to the wave mechanical drive of electrons to lower their kinetic energy through expansion. Since the virial theorem applies only to systems with Coulombic interaction potentials, its relevance as a foundation of the electrostatic view is tested here by calculations on analogues of the molecules H₂⁺ and H₂, where all 1/ r interaction potentials are replaced by Gaussian-type potentials that yield one-electron "atoms" with realistic stability ranges. The virial theorem does not hold in these systems, but covalent bonds are found to form nonetheless, and the wave mechanical bonding analysis yields analogous results as in the case of the Coulombic potentials. Notably, the key driving feature is again the electron delocalization that lowers the interatomic kinetic energy component. A detailed discussion of the role of the virial theorem in the context of covalent binding is given.

Covalent Bonding in the Hydrogen Molecule

This work addresses the continuing disagreement between two schools of thought concerning the mechanism of covalent bonding. According to Hellmann, Ruedenberg, and Kutzelnigg, covalent bonding is a quantum mechanical phenomenon whereby lowering of the kinetic energy associated with electron sharing, i.e., delocalization, is the key stabilization mechanism. The opposing view of Slater, Feynman, and Bader has maintained that the source of stabilization is electrostatic potential energy lowering due to electron density redistribution to binding regions between nuclei. Following our study of H₂⁺ we present an analogous detailed study of H₂ where bonding involves an electron pair with repulsion and correlation playing a significant role in its properties. We use a range of different computational approaches to study and reveal the relevant contributions to bonding as seen in the electron density and corresponding kinetic and potential energy distributions. The energetics associated with the more complex electronic structure of H₂, when examined in detail, clearly agrees with the analysis of Ruedenberg; i.e., covalent bonding is due to a decrease in the interatomic kinetic energy resulting from electronic delocalization. Our results support the view that covalent bonding is a quantum dynamical phenomenon requiring a properly quantized kinetic energy to be used in its description.

Quantifying the Role of Orbital Contraction in Chemical Bonding

This work reports an approach to variationally quantify orbital contraction in chemical bonds by an extension of an energy decomposition analysis (EDA). The orbital contraction energy is defined as the energy lowering due to optimization of the isolated fragments (that combine to form the bond) with a specially constructed virtual set of contraction/expansion functions. This set contains one function per occupied orbital, obtained as the linear response to scaling the nuclear charges. EDA results for a variety of single bonds show substantial changes in the importance of orbital contraction; it plays a critical role for bonds to H but only a very minor role in the bonds between heavier elements. Additionally, energetic stabilization due to rehybridization is separated from inductive polarization by the fact that no mixing with virtual orbitals is involved and is shown to be significant in fragments such as NH₂, OH, and F.

Description of Polar Chemical Bonds from the Quantum Mechanical Interference Perspective

The Generalized Product Function Energy Partitioning (GPF-EP) method has been applied to a set of molecules, AH (A = Li, Be, B, C, N, O, F), CO and LiF with quite different dipole moments, in order to investigate the role played by the quantum interference effect in the formation of polar chemical bonds. The calculations were carried out with GPF wave functions treating all the core electrons as a single Hartree-Fock group and the bonding electrons at the Generalized Valence Bond Perfect-Pairing (GVB-PP) level, with the cc-pVTZ basis set. The results of the energy partitioning into interference and quasi-classical contributions along the respective Potential Energy Surfaces (PES) show that the main contribution to the depth of the potential wells comes from the interference term, which is an indication that all the molecules mentioned above form typical covalent bonds. In all cases, the stabilization promoted by the interference term comes from the kinetic contribution, in agreement with previous results. The analysis of the effect of quantum interference on the electron density reveals that while polarization effects (quasi-classical) tend to displace electronic density from the most polarizable atom toward the less polarizable one, interference (quantum effects) counteracts by displacing electronic density to the bond region, giving rise to the right electronic density and dipole moment.

Chemical bonding: the orthogonal valence-bond view

Chemical bonding is the stabilization of a molecular system by charge- and spin-reorganization processes in chemical reactions. These processes are said to be local, because the number of atoms involved is very small. With multi-configurational self-consistent field (MCSCF) wave functions, these processes can be calculated, but the local information is hidden by the delocalized molecular orbitals (MO) used to construct the wave functions. The transformation of such wave functions into valence bond (VB) wave functions, which are based on localized orbitals, reveals the hidden information; this transformation is called a VB reading of MCSCF wave functions. The two-electron VB wave functions describing the Lewis electron pair that connects two atoms are frequently called covalent or neutral, suggesting that these wave functions describe an electronic situation where two electrons are never located at the same atom; such electronic situations and the wave functions describing them are called ionic. When the distance between two atoms decreases, however, every covalent VB wave function composed of non-orthogonal atomic orbitals changes its character from neutral to ionic. However, this change in the character of conventional VB wave functions is hidden by its mathematical form. Orthogonal VB wave functions composed of orthonormalized orbitals never change their character. When localized fragment orbitals are used instead of atomic orbitals, one can decide which local information is revealed and which remains hidden. In this paper, we analyze four chemical reactions by transforming the MCSCF wave functions into orthogonal VB wave functions; we show how the reactions are influenced by changing the atoms involved or by changing their local symmetry. Using orthogonal instead of non-orthogonal orbitals is not just a technical issue; it also changes the interpretation, revealing the properties of wave functions that remain otherwise undetected.

Covalent bonds are created by the drive of electron waves to lower their kinetic energy through expansion

An analysis based on the variation principle shows that in the molecules H2 (+), H2, B2, C2, N2, O2, F2, covalent bonding is driven by the attenuation of the kinetic energy that results from the delocalization of the electronic wave function. For molecular geometries around the equilibrium distance, two features of the wave function contribute to this delocalization: (i) Superposition of atomic orbitals extends the electronic wave function from one atom to two or more atoms; (ii) intra-atomic contraction of the atomic orbitals further increases the inter-atomic delocalization. The inter-atomic kinetic energy lowering that (perhaps counter-intuitively) is a consequence of the intra-atomic contractions drives these contractions (which per se would increase the energy). Since the contractions necessarily encompass both, the intra-atomic kinetic and potential energy changes (which add to a positive total), the fact that the intra-atomic potential energy change renders the total potential binding energy negative does not alter the fact that it is the kinetic delocalization energy that drives the bond formation.

The source of chemical bonding

Developments in the application of quantum mechanics to the understanding of the chemical bond are traced with a view to examining the evolving conception of the covalent bond. Beginning with the first quantum mechanical resolution of the apparent paradox in Lewis's conception of a shared electron pair bond by Heitler and London, the ensuing account takes up the challenge molecular orbital theory seemed to pose to the classical conception of the bond. We will see that the threat of delocalisation can be overstated, although it is questionable whether this should be seen as reinstating the issue of the existence of the chemical bond. More salient are some recent developments in a longstanding discussion of how to understand the causal aspects of the bonding interaction--the nature of the force involved in the covalent link--which are taken up in the latter part of the paper.

100th anniversary of Bohr's model of the atom

In the fall of 1913 Niels Bohr formulated his atomic models at the age of 27. This Essay traces Bohr's fundamental reasoning regarding atomic structure and spectra, the periodic table of the elements, and chemical bonding. His enduring insights and superseded suppositions are also discussed.

Interference energy in C-H and C-C bonds of saturated hydrocarbons: dependence on the type of chain and relationship to bond dissociation energy

Interference energy for C-H and C-C bonds of a set of saturated hydrocarbons is calculated by the generalized product function energy partitioning (GPF-EP) method in order to investigate its sensitivity to the type of chain and also its contribution to the bond dissociation energy. All GPF groups corresponding to chemical bonds are calculated by use of GVB-PP wave functions to ensure the correct description of bond dissociation. The results show that the interference energies are practically the same for all the C-H bonds, presenting only small variations (0.5 kcal.mol(-1)) due to the structural changes in going from linear to branched and cyclic chains. A similar trend is verified for the C-C bonds, the sole exception being the cyclopropane molecule, for which only the C-C bond exhibits a more significant variation. On the other hand, although the interference energy is quantitatively the most important contribution to the bond dissociation energy (DE), one cannot predict DE only from the bond interference energy. Differences in the dissociation energies of C-C and C-H bonds due to structural changes in the saturated hydrocarbons can be mainly attributed to quasi-classical effects.

Revealing charge-transfer effects in gas-phase water chemistry

An understanding of the interactions involving water and other small hydrogenated molecules such as H(2)S and NH(3) at the molecular level is an important and elusive scientific goal with potential implications for fields ranging from biochemistry to astrochemistry. One longstanding question about water's intermolecular interactions, and notably hydrogen bonding, is the extent and importance of charge transfer (CT) , which can have important implications for the development of reliable model potentials for water chemistry, among other applications. The weakly bound adducts, commonly regarded as pure van der Waals systems, formed by H(2)O, H(2)S, and NH(3) with noble gases or simple molecules such as H(2), provide an interesting case study for these interactions. Their binding energies are approximately 1 or 2 kJ/mol at most, and CT effects in these systems are thought to be negligible. Our laboratory has performed high-resolution molecular-beam scattering experiments that probe the (absolute scale) intermolecular potential of various types of these gas-phase binary complexes with extreme sensitivity. These experiments have yielded surprising and intriguing quantitative results. The key experimental measurable is the "glory" quantum interference shift that shows a systematic, anomalous energy stabilization for the water complexes and clearly points to a significant role for CT effects. To investigate these findings, we have performed very accurate theoretical calculations and devised a simple approach to study the electron displacement that accompanies gas-phase binary intermolecular interactions in extreme detail. These calculations are based on a partial progressive integration of the electron density changes. The results unambiguously show that water's intermolecular interactions are not typical van der Waals complexes. Instead, these interactions possess a definite, strongly stereospecific CT component, even when very weak, where a water molecule may act as electron donor or acceptor depending on its orientation. CT is mediated by an asymmetric role played by the two hydrogen atoms, which causes strong orientation effects. The careful comparison of these calculations with the experimental results shows that the stabilization energy associated to CT is approximately 2-3 eV per electron transferred and may make up for a large portion of the total interaction energy. A simple electron delocalization model helps to validate and explain these findings.

Natural bond orbital analysis: a critical overview of relationships to alternative bonding perspectives

We sketch the basic principles of natural bond orbital (NBO) theory, including critical discussion of its relationship to alternative bonding concepts and selected illustrations of its application to a broad spectrum of chemical bonding motifs. Particular emphasis is placed on the close NBO connections to prequantal bonding, and electromerism concepts, as well as the deep roots in quantal eigenvalue, superposition, and Pauli exclusion concepts that are manifested in many aspects of NBO donor-acceptor analysis. With respect to leading alternative perspectives, we identify similarities and differences that distinguish NBO theory from the corresponding precepts of valence bond theory, molecular orbital theory, and Bader's quantum theory of atoms in molecules, with critical discussion of the assumptions underlying characteristic differences in each case.

Worlds apart in chemistry: a personal tribute to J. C. Slater

A reading of the book of Dirac's life entitled The Strangest Man is a most stirring experience, bringing one back to the beginnings of quantum mechanics where every attempt was made "to establish a basis for theoretical quantum mechanics founded exclusively on relationships between quantities which are in principle observable." The prime movers in this quest were Heisenberg and Dirac. One of Dirac's most important contributions in the passage from classical to quantum mechanics, a passage that consumed much of his early efforts, was unfortunately published in an obscure Russian journal where it remained largely unread until it was found by Feynman while a graduate student at Princeton. The paper posed the question, "what corresponds in the quantum theory to the Lagrangian method of classical mechanics?", a method that, as Dirac pointed out, is clearly superior in the simplicity of its structure to that of the classical Hamiltonian approach. Dirac's partial answer to this question provided the key to solving the problem of introducing the action integral into quantum mechanics that occupied Feynman's mind, leading to his formulation of the path integral technique. His contribution was followed two years later by Schwinger's independently derived statement of the quantum action principle, each contribution providing a complete formulation of quantum mechanics stated in terms of single principle. The present paper points out that the successful introduction of the action principle into quantum mechanics made possible by Dirac, enables one to proceed still further by extending Schwinger's quantum action principle to an open system, to an atom in a molecule. Thus the quantum theory of an atom in a molecule has its roots in the question posed by Dirac in 1933. The paper proposes a return to a greater use of the theorems of quantum mechanics in interpretive chemistry from that begun by Slater in 1933, a staunch advocate of theory following in the footsteps of observation.