Pauling Bond Order Research Articles

On the π-Electron Content of Bonds and Rings in Benzenoid Hydrocarbons

The Pauling bond order can be viewed as a measure of the π-electron content of the respective carbon-carbon bond. In benzenoid hydrocarbons its values lie between 0 (in the case of essential single bonds) and 1 (in the case of essential double bonds). If the benzenoid molecule does not possess essential single and double bonds, then the Pauling bond orders are greater than 0 and less than 1, but may assume values arbitrarily close to 0 and 1. The π-electron content of a ring is equal to the sum of the π-electron contents of the carbon-carbon bonds forming this ring. We show that in benzenoid hydrocarbons the π-electron content of any (six-membered) ring lies between 0 and 5.5. If the molecule does not possess essential single and double bonds, then the π-electron content of any ring is greater than 0 and less than 5.5, but may assume values arbitrarily close to 0 and 5.5.

HEXAGONOIDAL PARTITIONING AND QUASI-SINGLE BONDS IN BENZENOID HYDROCARBONS

The concept of fully benzenoid hydrocarbons (molecular graphs; FBHs) is generalized. Each full-hexagon unit (aromatic sextet) in a FBH is replaced with a larger “hexagon-shaped” unit (subgraph; e.g., naphthalene, pyrene, coronene, or ovalene units). Such a molecular species may be called a “fully hexagonoid” hydrocarbon (FHHs). The Pauling bond order calculation suggests that a bond (edge) which interlinks one hexagon-shaped unit with another in the bottom of bays of FHH is quasi-single, if the two units are connected by more than two bonds. As a consequence, the hexagon-shaped units are delocalized locally in the hexagonoidal (graph-theoretical) partitioning.

Synthesis, Structure and Bonding of Gd6MTe2 (M: Co, Ni), Er6RuTe2.

AbstractFor Abstract see ChemInform Abstract in Full Text.

Synthesis, structure and bonding of Gd 6MTe 2 (M=Co, Ni), Er 6RuTe 2

Three new rare earth metal-rich compounds, Gd 6MTe 2 (M=Co, Ni) and Er 6RuTe 2, were synthesized in direct reactions between the R, R 3M, and R 2Te 3 (R=Gd, Er, M=Co, Ni, Ru). These materials all adopt the same Zr 6CoAl 2 structure type with space group P 62m (No. 189, Z=1). Single crystal structures of Gd 6CoTe 2 and Er 6RuTe 2 were determined and lattice parameters are a= b=8.3799(5), c=3.9801(4) Å, and a= b=8.1473(5) Å, c=3.9962(4) Å, respectively. Gd 6NiTe 2 was characterized by X-ray powder diffraction; lattice parameters are a= b=8.412(2), c=3.9577(9) Å. Metal–metal bonding correlations were analyzed using the empirical Pauling bond order concept.

Periodic n-dependence in the lowest excitation energies of the tube-like fullerenes C 60 + 10 n

A periodic n-dependence has been found in the lowest excitation energies of the tube-like fullerenes C 60 + 10 n ( n=1,2,…), each consisting of a pair of the bisected caps of C 60 and a single-wall cylinder. By inspection of the periodicity, the tube-like fullerenes are classified into three series of C 70 + 30 m , C 80 + 30 m and C 90 + 30 m ( m=0,1,2,…). The analysis with the Pauling bond order indicates the formation of a pseudo π-conjugation on each layer of the cyclo-pentaphenylene structure with 30 C-atoms in the central cylindrical parts of the tube-like fullerenes.

Description of covalent bond orders using the charge density topology

AbstractHybrid density functional calculations are employed to explore the relationships between covalent bond order, as defined using the atomic overlap matrix (AOM) formalisms developed by Cioslowski, Ángyán and others, and the parameters derived from a topological analysis of the electron density. Relationships are obtained for the specific cases of C—C, C—N, C—O, C—P and C—S bonds. The simple Pauling bond order–bond length relationship describes the data reasonably well in most cases, but the correlations show considerable scatter. Although no single parameter acts as a unified descriptor of bond order for all types of bond, in each case it is possible to find a model which describes the bond order data significantly better than the Pauling model based on bond length. The relationships presented can therefore be utilized to estimate rapidly the covalent part of the bond order from a topological analysis of the charge distribution for very large systems where the AOM‐based methods can become impractical to apply, and for charge density distributions which have been obtained from experiment (e.g. elastic x‐ray scattering). Copyright © 2003 John Wiley & Sons, Ltd.

Bond length features of linear carbon chains of finite to infinite size: Visual interpretation from Pauling bond orders

AbstractSchemes for Kekulé structure counting of linear carbon chains are suggested. Mathematical formulas, which calculate the Pauling bond order P(k, N) of a chemical bond numbered by k, are given for the carbon chain with N carbon atoms. By use of the least‐squares fitting of a linearity, relationships between Pauling bond orders and bond lengths are obtained, and such correlation of the Pauling bond order–bond length can be qualitatively extended to the excited states. The relative magnitudes of Pauling bond orders in unsaturated carbon chains dominate C–C bond lengths a well as the bond length feature with the chain size increasing. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 144–149, 2003

Determination of Quasi-Single Bonds and Local Delocalization in Fully Arenoid Hydrocarbons

In fully benzenoid hydrocarbons (FBHs), a bond that interlinks one full-hexagon unit (aromatic sextet) with another was termed "quasi-single" by Clar and Zander (9); this local delocalization of aromatic sextets explains well the chemical properties of FBHs. The concept of FBH has been generalized by Nikoli ' et al. (1), Knop et al. (2), and Gutman and Cyvin (12); they partitioned a given benzenoid molecular graph graph-theoretically, and called it a fully arenoid hydrocarbon (FAH). This note shows that the Pauling bond order is a good index for judging whether each bond in FAHs is quasi-single or not, and that not all the full-arene units in the graph-theoretical partitioning are locally delocalized.

Classical Valence Similarity in Fullerene Derivatives

The generalized Pauling bond order was enumerated in the C60 fullerene cage molecule (truncated icosahedral symmetry). This index measures chemical similarity in fullerene derivatives such as dihydrofullerene (C60H2), anionized monohydrofullerene (C60H−), N-substituted monohydrofullerene (C59NH), the fullerene dimer ((C60)2), and the dianionic fullerene dimer ((C60)2 2−). It is also useful in judging the chemical stability of isomers.

Modeling the metal-semiconductor interaction: Analytical bond-order potential for platinum-carbon

We propose an analytical interatomic potential for modeling platinum, carbon, and the platinum-carbon interaction using a single functional form. The ansatz chosen for this potential makes use of the fact that chemical bonding in both covalent systems and d-transition metals can be described in terms of the Pauling bond order. By adopting Brenner's original bond-order potential for carbon [Phys. Rev. B 42, 9458 (1990)] we devise an analytical expression that has an equivalent form for describing the C-C/Pt-Pt/Pt-C interactions. It resembles, in the case of the pure metal interaction, an embedded-atom scheme, but includes angularity. The potential consequently provides an excellent description of the properties of Pt including the elastic anisotropy ratio. The parameters for both the Pt-Pt interaction and the Pt-C interaction are systematically adjusted using a combination of experimental and theoretical data, the latter being generated by total-energy calculations based on density-functional theory. This approach offers good chemical accuracy in describing all types of interactions, and has a wide applicability for modeling metal-semiconductor systems.

Location of the doped scandium ion Sc 2+ and π-electron delocalization in endohedral metallofullerene Sc@C 82

The Pauling bond order was calculated for each bond in all the pentagon-isolated nine isomers of the fullerene cage molecule C 82. The classical resonance theory then suggests the existence of π-electron conjugated regions, each of which is composed of 6-membered carbon sites, in the isomers; and at such a region the doped dication Sc 2+ in metallofullerene Sc@C 82 is located. This situation looks like π-complex formation between a benzene molecule and a silver cation Ag +, as proposed by R.S. Mulliken in 1952.

Linear relationship between the bond lengths and the Pauling bond orders in fullerene molecules

The Pauling bond orders are calculated for the fullerene molecules, C60 and C70, and are correlated to the bond lengths. It is concluded that there is a good linear relationship between them.

Study of chemically stable/unstable isomers of the fullerene hydrides, C60H2 and C60H4, by use of a generalized Pauling bond order method

A new index, defined as a generalization of the Pauling bond order, i.e. a ratio between the number of Kekulé structures in an isomer of the hydride derivatives C60H2 and C60H4 to that in the fullerene C60 molecule, is proposed. This index is shown to be useful for predicting the chemical stability/instability of the hydride isomers.

Graph-theoretical rules for predicting bond lengths in hexagon-shaped benzenoid hydrocarbons

A particular kind of chemical bond, hereafter called `gnomonic', is defined in hexagon-shaped benzenoid hydrocarbons, each (molecular graph) of which is similar to the remaining part of it after the assignment of a gnomonic bond to a double bond in Kekulé structure counting. Mathematical equations, which express Pauling bond orders for gnomonic bonds, are given. By use of such equations, four graph-theoretical rules in relation to intermolecular and/or intramolecular comparison of gnomonic bond lengths are stated. The rules, applied to eight benzenoid hydrocarbons, are in good agreement with the AM1-optimized calculation.

Bonding and Site Preferences in the New Quasi-Binary Zr2.7Hf11.3P9

The new quasi-binary Zr2.7Hf11.3P9was synthesized by arc-melting of Zr, Hf, Co, and HfP in a ratio corresponding to the initial composition “Zr2.25Hf6.75Co2P4”. Zr2.7Hf11.3P9crystallizes in the Zr14P9structure type, which is unknown in the binary Hf/P system. The ideal orthorhombic lattice dimensions (space groupPnnm(No. 58),Z=4) were refined toa=16.640(7) Å,b=27.40(2) Å,c=3.619(1) Å,V=1650(2) Å3. The structure consists of three-dimensional condensed one-, two-, and three-capped trigonal (Zr, Hf)6P prisms, occurring with numerous shortM–Mbonds (M=Zr, Hf). Each of the 15 metal sites is statistically occupied by a mixture of Zr and Hf, which varies significantly from site to site. The Hf/Zr ratio in a given site depends on theM–MandM–P interactions. The systematic increase of this ratio with increasing total bond order, as evaluated via Mulliken overlap populations and Pauling bond orders, can be understood based on the trend that Hf forms strongerM–MandM–P bonds than Zr. As expected for a metal-rich phosphide, band structure calculations for the hypothetical “Hf14P9” carried out with the extended Hückel approximation result in a significant density of states at the Fermi level.

Ground-state properties of benzenoid hydrocarbons by simple bond orbital resonance theory approach

π-electron energies and bond orders of benzenoid hydrocarbons with up to five fused hexagons have been considered by the simple Bond Orbital Resonance Theory (BORT) approach. The corresponding ground states were determined according to four BORT models. In the first three models a diagonalisation of the Huckel-type Hamiltonian was performed in the bases of Kekule, of Kekule and mono-Claus and of Kekule and Claus resonance structures, respectively. In the fourth model a simple BORT ansatz was used. According to this ansatz, the ground state is a linear combination of the positive Kekule structures, all with equal coefficients. It was shown that π-electron energies and bond orders obtained by these models correlate much better with the PPP energies and bond orders than with the Huckel energies and bond orders. This indicates that a simple BORT approach is quite reliable in predicting the more sophisticated PPP results. Concerning the relative performance of the four BORT models, the best results were obtained with the BORT ansatz. The performance deteriorates with the expansion of the basis set. This is attributed to the fact that in these models the improvement of the basis set is not accompanied with the corresponding improvement of the Hamiltonian. Comparing the BORT-ansatz bond orders with the Pauling bond orders, it was shown that BORT-ansatz bond orders correlate much better with the PPP bond orders.

Notizen: Polysulfonylamine, LXXVIII [1] 1-Mesyl-4 -dimethylaminopyridinium - dimesylamid: Darstellung und Festkörperstruktur / Polysulfonylamines, LXXVIII [1] 1-Mesyl-4-dimethylaminopyridinium Dimesylamide: Synthesis and Solid State Structure

Treating (MeSO2)3N with 4-dimethylaminopyridine in MeCN afforded the ionic title compound (monoclinic, space group P21/c). The bond lengths of the 4-dimethylaminopyridinium moiety suggest a semiquinoid resonance form with a double bond to the exocyclic nitrogen and two localized carbon-carbon double bonds in the ring. The ring and the exocyclic N and S atoms of the cation are essentially coplanar. The S -N bond distances in the cation (173.4 pm) and the anion (159.1 and 159.6 pm) correlate with Pauling bond orders of 1.0 and 1.7, respectively. The anion displays a staggered conformation with approximate C2 symmetry ( S - N -S 120.4°).

Cut invariant d and bond orders of Kekuléan benzenoids

In this paper, for benzenoids, the concepts of a Δ cut circuit and a V cut segment are proposed; and for Kekuléan benzenoids a cut invariant d corresponding to a Δ cut circuit or a V cut segment is given. The quantity d has a close relation with Pauling bond orders of the cut edges.

Hf5.08Mo0.92P3, a New Mixed Transition-Metal Phosphide: Structure, Bonding, and Site Preferences

A new structure type which is similar to that of many known binary early transition-metal phosphides, sulfides, and selenides has been found in the ternary Hf–Mo–P system. The compound Hf5.08Mo0.92P3has been synthesized by high-temperature techniques and characterized by single-crystal X-ray diffraction. The space group isPnma(no. 62) with lattice parametersa= 18.231(7),b= 3.537(1),c= 9.695(5),Z= 4. The strength of the metal–metal and metal–phosphorus bonding in different metal sites in Hf2P and Hf5.08Mo0.92P3has been determined by both Pauling bond orders (PBO) and Mulliken overlap populations (MOP) from extended Hückel tight-band calculations. Site preferences of the two metals in Hf5.08Mo0.92P3are evaluated by MOP analysis.

Nb(x)()Ru(6)(-)(x)()Te(8), New Chevrel-Type Clusters Containing Niobium and Ruthenium(,).

Phases of composition Nb(x)()Ru(6)(-)(x)()Te(8) were prepared by reacting stoichiometric mixtures of the elements at high temperature in evacuated silica ampules. The structure of Nb(3.33)Ru(2.67)Te(8) was refined from X-ray powder data using the Rietveld method. Nb(3.33)Ru(2.67)Te(8) crystallizes isotypic with Mo(6)Q(8) (Q = S, Se, Te) in the rhombohedral space group R&thremacr; with the hexagonal lattice parameters a = 10.34106(5) Å, c = 11.47953(7) Å, and Z = 3. Its structure consists of M(6)Te(8) mixed-metal clusters (M = Nb, Ru) which are connected by intercluster M-Te bonds to form a three-dimensional network. Metal-metal bonding in these phases is analyzed in terms of Pauling bond orders and found to be weaker compared to that in related cluster compounds. Nb(x)()Ru(6)(-)(x)()Te(8) are the first representatives of Chevrel-type cluster phases with complete substitution of Mo by other metals. The chemical perspectives arising from this substitution are discussed.