The general analytic expression for S4-symmetry-invariant potential functions of tetra-atomic homonuclear molecules

The potential energy of a homonuclear X₄ molecule is an invariant of the atom permutation group S₄ acting on the internal coordinates of X₄. It is shown by means of invariant theory that six algebraically independent invariants and five additional invariants are required to express the general invariant function for this group. Explicit expressions for these 11 invariants are given.     

Photoionization mass spectrometry of molecular clusters using synchrotron radiation

The photoionization and dissociative ionization of molecular aggregates using synchrotron radiation is reported. The main objective of the review is to consider the intracluster relaxation processes after ionization. For hydrogen-bonded systems proton transfer is dominant. For small clusters (n<4) appearance potentials, ionization potentials, absolute proton affinities, proton solvation energies and intermolecular bond energies in the ionic clusters are deduced. For van der Waals aggregates proton transfer can also be used to characterize the intermolecular bond in the ionic cluster. Aggregates of CH₄, SiH₄, CH₃F show proton transfer in contrast to simple aromatic compounds, which reveal no proton transfer. From the fragmentation pattern and appearance potentials relaxation by intracluster ion molecule reactions is discussed. In heterogeneous clusters intracluster Penning ionization is observed. The shift of the charge transfer resonances depends on the π-electron density in the aromatic system. The width and spectral position of these resonances are influenced by the cluster size.     

The evaluation of moments for polycyclic hydrocarbons

The evaluation of some moments of the energy in the Hückel theory of conjugated molecules is considered. It is shown that, for molecules consisting entirely of hexagons, the moments ₄ and ₆ can be expressed in terms of four graphical invariants. Partial results are given for other molecules. Since the total energy can be expressed as a series of moments the implications for the energy are discussed. In this discussion two other invariants play a major role. The conclusion is suggested that an analysis of moments in terms of graphical invariants should be of prime importance in understanding these molecules.     

Isomer combinatorics for acyclic conjugated polyenes: enumeration and beyond

A combinatorial approach to fully conjugated acyclic polyenes (C _N H _{N +2}) is considered with a view to the extension of standard enumeration techniques to treat a widened range of chemically interesting features. As a first step, enumerations are made respecting: placement of single and double bonds, the occurrence of cis/trans isomers, and the degree (and type) of “radicality” of such conjugated networks. As a further extension, several structural (graph-theoretic) invariants averaged over various types of isomer classes and sub-classes are made, and then these invariants are utilized to estimate several physicochemical properties averaged over these same classes or sub-classes. The properties currently so considered are heats of formation, indices of refraction, and magnetic susceptibilities. Finally, the asymptotic behaviors of isomer counts and isomer properties in the many-atom limit is elaborated. Received: 10 August 1998 / Accepted: 17 November 1998 / Published online: 16 March 1999     

Isotopic invariants of pyramidal symmetrical XY3 molecules and evaluation of molecular constants

The isotopic invariants of pyramidal symmetrical XY₃ molecules are calculated in terms of frequencies, Coriolis coupling constants, molecular geometry parameters and masses of the constituent atoms. These invariants are used to evaluate force constants, compliance constants and mean amplitudes of vibration of four sets of 12 isotopic molecules.     

Statistical thermodynamics in the framework of the lattice fluid model, 2. Binary mixture of polydisperse polymers of special distribution

In this paper, the Gibbs free energy, the equation of state and the chemical potentials of polydisperse multicomponent polymer mixtures are derived. For general binary mixtures of polydisperse polymers, we also give the Gibbs free energy, the equation of state and the chemical potentials and derive the stability criteria and spinodal. Furthermore, binary polydisperse polymer mixtures of special distribution, i.e., Flory distribution, uniform distribution and Schulz distribution, are discussed and the influence of polydispersity on the interaction energy parameter is considered. For these special-distribution systems, the spinodal curves are simulated and the influence of chain length and polydispersity on the spinodal curves is discussed. The results suggest that the spinodal temperature of the mixture with a given volume fraction of one component decreases with increasing polydispersity and the extent of the shift decreases with increasing degree of polymerization when η = M̄_w/M̄_n is given. In addition, the variations of the spinodal curves with polydispersity and chain length are shown and they are qualitatively compared with the experimental results.     

Permutation representations in molecular symmetry

The reducible representations of the point groups are generally studied because of their relevance to molecular orbital and vibration theory. Triple correlations within the polyhedra are described by group-theoretical invariants that are related to the permutation representations and termed polyhedral isoscalar factors. These invariants are applied in theorems on matrix elements referring to the symmetry-adapted bases at different centres. Further invariants or geometrical weight factors inter-relate different types of reduced matrix elements of irreducible tensors (generalization of the Wigner-Eckart theorem to the polycentric case). As a demonstration a complete tabulation is given for the point group C ₄.     

Integrity basis approach to the elastic free energy functional of liquid crystals

Using the method integrity basis, the most general SO(3)-invariant free energy density up to all powers in _xβ and up to second order in Q_xβ,y is established. The method provides all analytically independent elastic modes for nematics and cholesterics in the form of 33 so-called, irreducible invariants. Interestingly, among the irreducible invariants there are only three chiral terms (i.e. linear in Q_δ,β,y ). They give rise locally to three independent helix modes in chiral, biaxial liquid crystals. This conclusion generalizes results of Trebin and Govers and Vertogen and contradicts a statement of Pleiner and Brandt, according to which only one twist term is supposed to exist. The most general free energy expansion can be written as sum of 39 additive invariants, which are multiplied by arbitrary polynomials in TrQ² and TrQ³.     

Verres du systeme La2S3La2O3Ga2O3Ga2S3

The extent of the glass forming region is described as a function of the composition and of the cooling speed. The shape of this region is explained from the previously described La₂S₃La₂O₃Ga₂O₃Ga₂S₃ phase diagram. Glasses are obtained after relatively slow cooling (5°/min), in a definite region of compositions, which coincides with a relatively large concentration of ternary invariants. The thermal properties (transition temperatures and crystallization temperatures) were measured by DTA. For a relatively large region of compositions, glasses return to the equilibrium conditions with intermediate formation of the La_3.33Ga₆S₁₂O₂ metastable crystalline phase. An approach to the structure of the glasses is made by comparison with the crystal structures of the numerous ternary and quaternary crystalline compounds observed in the system, and by the comparison of the Raman spectra. It appears that these gallium oxysulfide glasses have many structural analogies with germanium sulfide glasses.     

Nonempirical parameters of the nonlocal core pseudopotential for the second and third row elements

For the core pseudopotential (CP) model constructed in terms of Bonifacic-Huzinaga nonlocal CP theory, parameters of the local component of CP are calculated for the second-and third-row elements. The resulting CP are associated with the Coulomb, exchange, and correlation potentials created by the nuclear charge and electron density of the core electrons. The electronic structure and potential energy surface are calculated for the hydrides of the second-row elements (LiH, CH₄, NH₃, H₂O, HF); the calculations are performed by the nonempirical nonlocal CP method. The results of these calculations agree well with those of SCF MO LCAO ab initio calculations and with experimental data.     

Theoretical studies of organometallic compounds. I. All electron and pseudopotential calculations of Ti(CH3)nCl4 − n (n = 0–4)

The performance of effective core potentials (ECP) and model potentials (MP) has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules Ti(CH₃)_nCl_{4 ? n} (n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G basis set from Hehre and a (53321/521/41) basis set from Huzinaga. For the ECP calculations the potentials developed by Hay and Wadt, and for the MP calculations, the model potentials developed by Sakai and Huzinaga, are employed. © 1992 by John Wiley & Sons, Inc.     

Highly discriminating distance-based topological index

A new topological indexJ (based on distance sumss_i as graph invariants) is proposed. For unsaturated or aromatic compounds, fractional bond orders are used in calculatings_i. The degeneracy ofJ is lowest among all single topological indices described so far. The asymptotic behaviour ofJ is discussed, e.g. whenn → ∞ in C_nH_{2n = 2},Jar π for linear alkanes, andJ → ∞ for highly branched ones.     

Theoretical study of chemisorption on niobium clusters: carbon monoxide and oxygen

We have studied chemisorption on niobium clusters based on the local spin density approximation in a scheme which uses pseudopotentials and a plane wave expansion of the electronic wave functions. Results are presented for geometries and the electronic structure of Nb₄ and Nb₈, and compared with experimental data of ionization potentials. Key issues concerning atomic and molecular adsorption on metal clusters are the nature of the binding, the preferred configurations, and the changes induced on the cluster properties. We have examined these questions in the case of carbon monoxide and oxygen. For carbon monoxide, we calculate a significant reduction of the stretch vibration frequency and, in the case of oxygen, shifts of the ionization potentials were obtained. Our results for oxygen are in agreement with experimental data, indicating only a minor shift of the ionization potential due to oxidation, also as a function of coverage.     

Mean-square torque of CO2 mixed with argon. interpretation in terms of intermolecular potentials

Spectral moments of CO₂ mixed with argon are measured for the v₃ vibration in the 5–300 bar range. The experimental values of the second moment are in excellent agreement with theory. The resulting mean-square torques are compared with those derived from potentials obtained with the electron gas model. One of these potentials is in satisfactory agreement with experiment.     

Synthesis and electrochemistry of cis-dioxomolybdenum(VI) complexes with tridentate Schiff base ligands containing O,N and S donor atoms

The synthesis and characterization of a number of cis-dioxomolybdenum(VI) coordination complexes involving tridentate (ONS) ligands is described. The Schiff base ligands were obtained by condensation of 5-substituted salicylaldehydes with o-aminobenzenethiol or 2-aminoethanethiol. The chemical properties of these molybdenum complexes are compared with those having tridentate ligands with the ONO donor atom set. Cyclic voltammetry was used to obtain cathodic reduction potentials (E_pc) for the irreversible reduction of the Mo(VI) complexes. Although the reductions are irreversible, trends are observed in E_pc both within each series and when different series are compared. Cathodic reduction potentials for the four series examined span the range from ?1.53 to ?1.05 V versus NHE. There are three ligand features whose effect systematically alters the Mo(VI) cathodic reduction potentials. These include (1) the X-substituent on the salicylaldehyde portion of each ligand; (2) the degree of ligand delocalization; and (3) the substitution of a sulphur donor atom for an oxygen donor atom. Each of these effects is considered separately with regard to the Mo(VI) cathodic reduction potentials and then their cumulative effect is described.     

Mathematics of Periodic Tables for Benzenoid Hydrocarbons

The upper and lower bounds for invariants of polyhex systems based on the Harary and Harborth inequalities are studied. It is shown that these invariants are uniquely correlated by the Periodic Table for Benzenoid Hydrocarbons. A modified periodic table for total resonant sextet (TRS) benzenoids based on the invariants of Ds and r(empty) is presented; Ds is the number of disconnections among the empty rings for fused TRS benzenoid hydrocarbons. This work represents a contribution toward deciphering the topological information content of benzenoid formulas.     

Two-photon properties of the La and Lb bands of substituted benzenes computed from CNDO/S

Two-photon tensor invariants proportional to two-photon absorptivities are calculated from CNDO/S CI wavefunctions for a variety of substituted benzenes for transitions to the two lowest singlet states, L_b^? (B_2u^?) and L₃⁺ (B_1u⁺). Providing hexagonal geometry is used, the results demonstrate considerable effectiveness by this method for predicting the relative sensitivity of these bands to vibronic, inductive and conjugative effects, including the intensity ratios for multiple substitutions by aza, methyl and amino. The method fails for fluorobenzene.     

An accurate analytical formula for the van der Waals potentials of homonuclear rare-gas dimers with one adjustable parameter

In the present article, the Tang–Toennies–Yiu (TTY) potential model is modified by introducing one adjustable parameter. Then, the van der Waals potentials of He₂, Ne₂, Ar₂, Kr₂, and Xe₂ are calculated by this model with the adjustable parameter being determined by the well determined well depth D_e of these systems. Based on the derived potentials, the vibrational energy spacings of these systems are also calculated. It is shown that the present derived potentials and vibrational energy spacings agree well with experiment and other theoretical calculations. Finally, the normalization constant A in the asymptotic wave function of rare-gas atoms is estimated. The present derived normalization constant A is very close to the one by calculating the ratio between the Hartree–Fock function and the asymptotic wave function. The results confirm that absorbing the first-order polarization energy into the exchange energy expression is a well approximation for the present systems.     

Molecular electrostatic potentials-II: Mechanistic aspects of electrophilic interactions of some five-membered heterocycles

The interactions of furan, pyrrole and N-methyl pyrrole with electrophiles have been investigated by means of the calculated molecular electrostatic potentials, obtained from INDO wave functions, which indicate the most attractive sites and pathways of attack for an approaching electrophile. The very distinct preference of these heterocycles for α-substitution can be interpreted quite satisfactorily in the case of furan if it is assumed that the α-hydrogen moves out of the plane of the molecule, forming a quasi-tetrahedral carbon, as an initial step in the reaction. For pyrrole and N-methyl pyrrole it is found to be necessary to invoke out-of-plane “bending” of the N-H, N-CH₃ and C_α-H_α bonds to explain both the preference for α-substitution, and also the relative selectivities of furan, pyrrole and N-methyl pyrrole. The energies, atomic charges and bond orders of various forms of these heterocycles are also discussed.     

Unimolecular dissociation of trivalent metal cluster ions (Al n + , Ga n + , In n + ): evidence for a transition from covalent to metallic bonding

Unimolecular dissociation of aluminum, gallium and indium clusters is investigated. Small sizes dissociate into two channels: either the evaporation of a neutral or a charged monomer. Above a given size n _c, only dissociation of a neutral atom subsists. The evaporation of a charged monomer is characteristic of trivalent metal clusters and is consistent with the size evolution of the ionization potential towards the atomic value. The experiments are interpreted in the framework of the statistical R.R.K. model. For smaller sizes (n < n _c), as two evaporation processes are in competition, we have evaluated cluster relative dissociation energies and ionization potentials. The competition between the two evaporation channels is well mirrored by the evolution of the ionization potentials independently measured by near-threshold photoionization experiments. For gallium, our measurements have revealed that the covalent to metal transition occurs for larger sizes (n = 30–50 atoms) than for aluminum clusters.