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A graph-theoretical approach lead to a formulation of the necessary structural constraints on a conjugated hydrocarbon system which forms the repeating unit for an aromatic polymer to show conductivity. A procedure for an estimate of the energy gap associated with the conjugated monomer unit has been described. It allows evaluation of the associated determinants simply and without performing the actual lengthy expansions. It is based on corresponding graph decompositions. The approach is illustrated on several selected benzenoid hydrocarbons. General rules covering a wide range of polymers which are potentially conductive are given. They are based on the structure of the single repeating unit and the corresponding graph-theoretical characterizations. The approach may facilitate further search for organic potential semiconductors.

Algorithms for making Kekule-structure and algebraic-structure enumerations for unbranched catacondensed hydrocarbons with even-membered rings are described. A pictorial presentation of the algorithms is obtained and is shown to reduce to an earlier well-known recursion (of Gordon and Davison) applicable to polyhex chains.

Properties of molecular graphs having identical topological spectra are investigated in some detail. It has been established that whole families of isospectral graphs can be derived from a molecular skeleton of vinyl benzene. A pair of isospectral graphs are obtained by an exchange of two non-equivalent residuals attached to particular sites of the skeleton. Additional pairs of isospectral graphs can be derived from related skeletons in which ortho positions of vinyl benzene are occupied by substituents. No constraints have to be imposed on the nature and form of the residuals or the substituting groups. This allows construction of larger isospectral systems including polymeric species. The theoretical foundation for the construction of isospectral graphs described in this work rests on the factorization of the eigenvalue problem of the adjacency matrix associated with molecular graphs which is analogous to a fragmentation of a secular determinant of a Huckel MO problem as outlined some time ago by Heilbr...

The H + 2 ground state energy is calculated over the range of internuclear separation from R = 0.2 au to R = 8.0 au, using a Laplace transform-type wave function. The integral transform is made on Slater-type functions with the weighting function f (ν, p , α) = α (ν+3)/2 exp (− p α/2). The electronic energy E = −1.0833 au for the equilibrium internuclear distance ( R = 2.0 au) is obtained with incomplete optimization. Still lower energy is expected for larger values of the parameters v and p . The difference between the calculated and the exact energies is not excessive over the whole range of internuclear separations considered.

The hybridization in cyclopropane, spiropentane, nortricyclene and 1,1 -dimethyl cyclopropane is calculated applying the criterion of maximum overlap. The s-p content in the general hybrids is found to be sensitive to changes in the interorbital angle Θ ij. The results give information about the strain associated with bent bonds and its delocalization. The application also allows calculations of skeletal angles, such as ∢ C1 C2 C3 in nortricyclene, which determine the geometry of the molecule.

The hybridisation in cyclopropene, cyclobutene, 1-methylcyclobutene, and 3-methylcyclobutene, all containing a double bond in the ring, is considered by applying the method of maximum overlap. The results show a considerable increase in s-contribution for the hybrids forming the double bond. The participation of s-orbitals in the hybrids forming the double bond is larger in cyclobutene than in cyclopropene, an indication that the preference for s-character will be even more pronounced in strain-free systems. The calculated bond overlaps are compared with the experimental bond energies. Instead of assuming the simple proportionality when scaling an overlap, a general linear relationship E=kS–l must be used.

For some thirty hydrocarbons the s character of hybrids obtained by the application of the maximum overlap method have been correlated with C-H and C-C spin-spin coupling constants. The following relationships were obtained: $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}} = 1079a_{{\text{CH}}}^{\text{2}} /(1 + S_{{\text{CH}}}^{\text{2}} ) - 54.9$$ , $$J_{{\text{C}}_{\text{1}}^{{\text{13}}} - {\text{C}}_{\text{2}}^{{\text{13}}} } = 1020.5a_{{\text{C}}_{\text{1}} }^2 a_{{\text{C}}_{\text{2}} }^{\text{2}} /(1 + S_{{\text{CC}}}^{\text{2}} ) - 8.2$$ . Here the coupling constants are expressed in cps units. In the calculation of the maximum overlap hybrids either the experimental bond lengths or a standard bond lengths were used. For the $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}}$$ and $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}} $$ coupling constants the standard deviations are 0.9 cps and 1.9 cps respectively. It has been suggested that the large additive constant in the $$J_{{\text{C}}^{{\text{13}}} - {\text{H}}}$$ correlation may be attributed to the ionic character of C-H bonds. A good agreement with the experimental data strongly supports the idea that the Fermi contact term and the hybridization are dominant factors in determining carbon-hydrogen and carbon-carbon spin-spin coupling constants across one bond, at least in hydrocarbons.

The simple electrostatic point charge model of the ligand field theory is extended by representing each ligand by N fractional point charges. The special cases N=6,18, and 62 are considered. A spherical charge distribution gives results similar to those of the point charge model. The splittings for non-spherical charge distributions are found to depend strongly on the orientation of the ligand charge.

The hybridization in methylenecyolopropane, dimethylenecyclopropane, bisethanoallene, and related molecules containing double bonds externally attached to a cyclopropane ring is considered by applying the method of maximum overlap. The results show that the bond overlap of an exocyclic double bond is larger than the bond overlap of a normal C=C bond, and double bonds in allenes have even larger overlap than an exocyclic C=C bond. The results of the calculations are correlated with some available experimental data.

The splittings ofd-orbitals for seven coordinated complexes of the type NbF7 2− is calculated using a point charge model. The perturbed energies are expressed as a function of λ =G 2/G 4. The results are very sensitive on assumed geometrical angles of the molecule.

The hybridization in cyclobutane, bicyclobutane, 1,3-dimethylcyclobutane, 1,3-dimethylbioyclobutane, bicyclo(1.1.1)pentane, tricyclo(1.1.0.02,4)butane, cubane and tetracyclo-(3.3.1.02,804,6)nonane is considered applying the method of maximum overlap (Tab. 1). Overlap seems to be a good index of a CC bond: overlaps below 0.6000 are characteristic for molecules containing C3-ring (δ ∼ 20‡), between 0.6000 and 0.6300 for four membered ring (δ ∼ 10‡), and above 0.6300 for normal or very slightly bent bonds (δ

The splitting and the order of 3d- and 4d-orbital energies for some complexes of the first- and second-transition series having dodecahedral geometry is calculated by the simple crystal-field model. The relative order of energy levels depends on the nature of the ligands and their distances from the metal. The energy behaviour is further examined as a function of the ratio G2 : G4 by assuming first all ligands equal and at the same distance from central metal, and then for cases when all ligands are equal but at different distances from the central metal. The discussion is extended to cases when different ligands are present in the complex. The results suggest that there is no representative energy diagram valid for all MX8 dodecahedral complexes. The calculations are applied to some complexes of Zr, Mo, Ti, Cr, and Co in order to illustrate the variations met in actual cases. It is found that dxy is the most stable for 4d and dz2 for 3d complexes examined.

The infra-red and Raman spectra of CH3HgBr and CD3HgBr are reported. Force constants have been calculated on the basis of an almost complete force field which was arrived at by systematic modifications of an approximate field using the Jacobian matrix. All the constants which significantly affect the calculated frequencies have been taken into account; the calculated force field is consistent with the hybrid orbital force field, which has not been assumed, although further refinements are necessary if a more detailed comparision is expected.

The first three cycloalkanes have been studied by the method of maximum overlap using orbitals suggested by Clementi. The angles describing the bent bonds are compared with the results obtained from similar calculations based on Slater orbitals. Clementi orbitals give results which are in better agreement with the experimental data.

Hybridisation in valence isomers of benzene: ‘ Dewar ’ benzene, benzvalene, and prismane, is considered by the method of maximum overlap. All these molecules are highly strained as evidenced by a larger p-content of the hybrids involved in C–C bonds. The calculated exponents n of spn-hybrids for C–H bonds correlate with n.m.r. chemical shifts of the protons. A linear relationship τ= 5(n– 1) represents the experimental data quite well. An exception is found in molecules containing three-membered rings, which show a considerable deviation from the above relationship. Other factors beyond the nearest carbon atom influence are responsible for these deviations.

Hybridisation in norbornane, camphenilane, isocamphane, and camphane, all of which contain a bicyclo[2,2,1]-heptane skeleton, is considered by applying the method of maximum overlap. Hybrids describing the methylene bridge have a much higher p-content, which is characteristic for strained bonds in cyclic systems. The calculated amounts of s-character for C–H bonds at carbon atoms 1 and 7 are consistent with experimental values for the spin–spin coupling constant J(13C–H).