Charge distribution in homonuclear bonds: A semiempirical modeling

Atoms characterized by nonequivalent electronegativities form chemical bonds by exchanging electrical charge. The fraction of charge exchanged is dictated by the electronegativity differences among the system atoms. In the electronegativity equalization method, the charge distribution is estimated by forcing the system to relax to a common chemical potential, which corresponds to its configuration of energy minimum. By definition, this method cannot be applied to homonuclear bonds. A model is proposed to estimate the charge shared in molecular orbitals of homonuclear molecules. The model expands upon the electronegativity equalization method by adding formalism to describe the spin coupling characteristic of homonuclear bonds. Results are in excellent agreement with other quantum mechanical estimations of the charge distributions. © 2013 Wiley Periodicals, Inc.     

An Exchange Charge Model for Covalent Bonds in Simple Homonuclear Diatomic Molecules

The point charge in Parr's simple bond charge model is replaced by the exchange charge, which can be evaluated according to a simple ab initio method. The calculated exchange charge correlate well with the experimental values of force constants and dissociation energies for homonuclear diatomic molecules H₂, Li₂, F₂, Na₂ and Cl₂.     

Toward a semiempirical density functional theory of chemical binding

The new ideas ofbond electronegativity andbond hardness are introduced, and a semiempirical density functional approach to the theory of molecular electronic structure and chemical binding is outlined. There result effective electronegativity equalization procedures that permit calculation of binding energies as well as partial charges. By a modelling of the bond electronegativity and bond hardness, a density functional interpretation of earlier bond charge models is established. Some numerical results are given for diatomic molecules.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Non-Equivalent Hybrid Atomic Orbitals and Covalent Bonds in a2 Molecules

In addition to having a noninteger value of λ for non-equivalent hybrid atomic orbitals sp ^λ the introduction of a noninteger occupation number to a valence configuration for atoms in a molecule renders a precise account of the covalent bond in homonuclear diatomic molecules. For instance, the following bond orders 0.05, 1.42 and 2.62 are obtained for the molecules Be², B² and C² according to the proposed method.     

Interesting periodic variations in physical and chemical properties of homonuclear diatomic molecules

We carry out a systematic study of various ground state and response properties of homonuclear diatomic molecules (from hydrogen to rubidium, including transition metals) as a function of atomic number of constituent atoms. We perform the ground state and response property calculations by using state of the art density functional theory/time dependent density functional theory. We observe that several properties of homonuclear diatomic molecules show periodic variations along rows and columns of the periodic table. The periodic variations in the ground state properties of diatomic molecules may be explained by the nature and type of the bond that exists between the constituent atoms. Similarly, the periodic variations in the response properties such as static dipole polarizability and strength of the van der Waals interaction between diatomic molecules have been correlated with the variations in metallic/nonmetallic character of the elements along the periodic table. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Molecular dipole moments and electronegativity

As suggested by acharge-transfer model based on Mulliken's definition of electronegativity, the dipole moments of various diatomic molecules and certain photoemission chemical shifts are shown to depend on the normalized electronegativity differences, [(x_B ? x_A)/$\text{x}$], and not simply on (x_B ? x_A).     

Orbital electronegativity and interaction of atoms in chemical compounds

A formula is suggested for the orbital electronegativity (OE) [1] in the calculation of the effective charges on atoms. This formula differs from that found in the literature [2] in that it takes electrostatic interaction into account. It is used with the self-consistent field method to calculate the effective charges on the atoms in a molecule XBeY, which are obtained for all the atoms of a molecule of the type ClBeX (X is F, Cl, Br, or I). It is shown that the effective negative charge on the Cl increases as the effective charge on X decreases (i.e., as the B-X bond becomes more covalent). Increased ionicity in this bond is generally due to the increased covalency in the opposite bond.     

The relative strengths of ionic,covalent and multiple-bonding in diatomic molecules

Values of the ratio [D₀ : e²/r_e] are examined for diatomic molecules in which the bonding is essentially ionic, covalent, or multiple in character (D₀ is the dissociation energy, and e²/r_e the coulombic energy of attraction of point-changes at the internuclear bondlength, r_e). The ratio values in single-bonded diatomic molecules range from (0.75±0.17) in the essentially ionic alkali-metal halides, to (0.16±0.03) in the covalent alkali-metal dimers. For multiple-bonded covalent M₂ molecules, the ratio reaches 0.74 in triple-bonded N₂ and 0.56 in sextuple-bonded Mo₂; but in many first-row transition dimetals, multiple bonding does not lead to high ratio values. Higher ratios do occur in MO molecules. In relative terms, ionic character-in particular when associated with multiple bonding-is more effective than multiplicity per se in bond-strengthening.     

pi bonding in second and third row molecules: testing the strength of Linus's blanket

The flexibility of valence bond (VB) theory provides a new method of calculating pi-bond energies in the double-bonded species H(m)A=BH(n), where A, B = C, N, O, Si, P, S. This new method circumvents the problems usually associated with obtaining pi-bond strengths by targeting only the pi bond, while all other factors remain constant. In this manner, a clean separation between sigma- and pi effects can be achieved which highlights some expected trends in bond strength upon moving from left to right and up and down the Periodic Table. Intra-row pi bonds conform to the classic statement by Pauling [L. Pauling, The Natiure of the Chemical Bond, Cornell University Press, Ithaca, 1960, 3rd edition] regarding the relationship of heteronuclear bond strengths to their homonuclear constituents whereas inter-row pi bonds do not. This variance with Pauling's statement is shown to be due to the constraining effect of the underlying sigma bonds which prevents optimal p(pi)-p(pi) overlap. While Pauling's statement was based on the assumption that the resonance energy (RE) would be large for heteronuclear and small for homonuclear bonds, we have found large REs for all bonds studied herein; this leads to the conclusion that REs are dependent not only on the electronegativity difference but also the electronegativity sum of the constituent atoms. This situation where the bond is neither covalent nor ionic but originates in the covalent-ionic mixing has been termed charge shift (CS) bonding [S. Shaik, P. Maitre, G. Sini, P. C. Hiberty, J. Am. Chem. Soc. 1992, 114, 7861]. We have shown that CS bonding extends beyond single sigma bonds in first row molecules, thus supporting the idea that CS-bonding is a ubiquitous bonding form.     

Sizes of atoms and ions and covalency of bonding in molecules and crystals

A new system of atomic radii for the elements up to barium inclusive is constructed. Values of the radii are chosen so as the dependence between the dissociation energy of diatomic homonuclear molecules and a depth of atom overlapping is monotonous, and the scatter of data is minimal. The depth of overlapping is calculated as a difference between the sum of atomic radii and an experimental interatomic distance. Conclusions are made that: the radii of free atoms and ions are determined by the value of the electron density equal to 0.01 au; they considerably change in molecules and crystals only as a result of the charge transfer from cation to anion; covalent bonding is well described by the overlapping of free atoms (ions), confined by the surface of the given radius, and its energy depends upon the depth of overlapping of valence electron densities of atoms. A method of overlapping atoms is proposed for the approximate estimation of ionic sizes and charges in bound systems.     

Electronegativities of elements in covalent crystals

A new electronegativity table of elements in covalent crystals with different bonding electrons and the most common coordination numbers is suggested on the basis of covalent potentials of atoms in crystals. For a given element, the electronegativity increases with increasing number of bonding electrons and decreases with increasing coordination number. Particularly, the ionicity of a covalent bond in different environments can be well-reflected by current electronegativity values; that is, the ionicity of chemical bonds increases as the coordination number of the bonded atoms increases. We show that this electronegativity scale can be successfully applied to predict the hardness of covalent and polar covalent crystals, which will be very useful for studying various chemical and physical properties of covalent materials.     

Ionicity,atomic radii,and structure in the layered dichalcogenides of group IVb,Vb, and VIb transition metals

Pauling's electronegativities are introduced in considerations of bond lengths, lattice constants, atomic radii, charge densities, structures, and heats of formation of the layered dichalcogenides of Groups IVb, Vb, and VIb transition metals. Strong correlations are found between these and the fractional ionic character of the metal-chalcogen bonds as defined by Pauling. A critical effective radius ratio is defined that separates trigonal prismatic and octahedral compounds.     

Molecular electronegativity in density functional theory (VI)

Based on the density functional theory and partitioning the molecular electron density ρ (r) into atomic electronic densities and bond electronic densities, the expressions of the total molecular energy and the “effective electronegativity” of an atom or a bond in a molecule are obtained. The atom-bond electronegativity equalization model is then proposed for the direct calculation of the total molecular energy and the charge distribution of large molecules. Practical calculations show that the atom-bond electronegativity equalization model can reproduce the correspondingab initio values of the total molecular energies and charge distributions for a series of large molecules with a very satisfactory accuracy.     

The effective nuclear charge model—IX. On the transferability of effective nuclear charges defined from homonuclear diatomic molecules

Effective nuclear charges of many triatomic molecules have been calculated inversely by the least squares method (Jacobian matrix method) from the experimental force constants which are determined by normal coordinate analyses using the observed vibrational data. The values of effective nuclear charges thus obtained are compared with those defined from homonuclear diatomic molecules. The results show that the transferability of effective nuclear charges from homonuclear diatomic molecules to triatomic molecules is moderately good. This gives support to the utility of the effective nuclear charge model.     

Vibrational spectra and structural considerations of compounds NaLnTiO4

The Raman and infrared spectra of compounds NaLnTiO₄ (Ln = lanthanide, including yttrium) are reported and discussed. Their most striking feature is a strong band in both spectra at about 900 cm^?1. This band is ascribed to a vibration localized in the TiO bond directed towards the NaO layers. The relevant oxygen anion is very poorly charge compensated, and the TiO bond is, therefore, very strong. Pauling's electrostatic valence rule appears to be of great use in these considerations. These compounds do not show ferroelectricity.     

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.     

Bond critical points in the electronic structures of the main group diatomic hydrides of lithium through bromine

The bond critical points and associated electronic properties of the diatomic hydrides of the twenty-one main group elements from lithium to bromine have been calculated with large basis sets. As part of a systematic study of the polarity of chemical bonds, the position of the bond critical point, the charge density at the bond critical point, the Laplacian of the charge density at the bond critical point, and the molecular dipole moment of each molecule have been calculated. Particular attention has been paid to the effect of bond length elongation and contraction on the electronic properties. Variation of the bond length reveals that with atoms of low electronegativity, the bond critical point of AH tends to follow atom A, whereas with atoms of high electronegativity, the bond critical point tends to follow the hydrogen atom as the bond lengthens. Furthermore, it is shown that some properties of the diatomic hydrides vary monotonically within each row of the periodic table, while others effect a classification according to the character of the bond.     

Classification of metal-oxide bonded interactions based on local potential- and kinetic-energy densities

A classification of the hydrogen fluoride H-F-bonded interactions comprising a large number of molecules has been proposed by Espinosa et al. [J. Chem. Phys. 117, 5529 (2002)] based on the ratio /Vr(c)/ / Gr(c) where /Vr(c)/ is the magnitude of the local potential-energy density and Gr(c) is the local kinetic-energy density, each evaluated at a bond critical point r(c). A calculation of the ratio for the M-O bonded interactions comprising a relatively large number of oxide molecules and earth materials, together with the constraints imposed by the values of inverted Delta2rho r(c) and the local electronic energy density, Hr(c) = Gr(c) + Vr(c), in the H-F study, yielded practically the same classification for the oxides. This is true despite the different trends that hold between the bond critical point and local energy density properties with the bond lengths displayed by the H-F and M-O bonded interactions. On the basis of the ratio, Li-O, Na-O, and Mg-O bonded interactions classify as closed-shell ionic bonds, Be-O, Al-O, Si-O, B-O, and P-O interactions classify as bonds of intermediate character with the covalent character increasing from Be-O to P-O. N-O interactions classify as shared covalent bonds. C-O and S-O bonded interactions classify as both intermediate and covalent bonded interactions. The C-O double- and triple-bonded interactions classify as intermediate-bonded interactions, each with a substantial component of covalent character and the C-O single-bonded interaction classifies as a covalent bond whereas their local electronic energy density values indicate that they are each covalent bonded interactions. The ratios for the Be-O, Al-O, and Si-O bonded interactions indicate that they have a substantial component of ionic character despite their classification as bonds of intermediate character. The trend between the ratio and the character of the bonded interactions is consistent with trends expected from electronegativity considerations. The ratio increases as the net charges and the coordination numbers for the atoms for several Ni-sulfides decrease. On the contrary, the ratio for the Si-O bonded interactions for the orthosilicate, forsterite, Mg2SiO4, and the high-pressure silica polymorph, stishovite, decreases as the observed net atomic charges and the coordination numbers of Si and O increase in value. The ratio for the Ni-Ni bonded interactions for the Ni-sulfides and bulk Ni metal indicate that the interactions are intermediate in character with a substantial component of ionic character.