The nonsinglet instabilities of the hartree-fock solutions for nonalternant hydrocarbons

The nonsinglet instabilities of the restricted Hartree-Fock (RHF) solutions for the nonalternant hydrocarbons, propalene, pentalene, heptalene and nonalene, that have been known to show the lattice instabilities (bond-length alternations) when treated within a semiempirical RHF approximation are examined. By examining the energy lowerings due to the appearance of the spin-density-wave (SDW) solutions, or better, of the singlet projected SDW solutions, we show that the treatment of the lattice instability based on the RHF theory is valid at least in these molecules. On the basis of the energy lowerings E(E _RHF-E _SDW), we discuss-the dependence of the electron correlation energies on the number of -electrons.     

Exchange polarization effects in the interaction of closed-shell systems

Explicit formulae for the calculation of the exchange polarization energy in the interaction of closed-shell atoms or molecules have been derived by assuming neglect of the electron correlation within the noninteracting systems. The dispersion part of the exchange polarization energy has been represented as a sum of contributions arising from the interaction of two, three or four orbitals at a time. Each of these contributions is given by an integral involving the orbitals engaged in the interaction and the pair functions describing the dispersion interaction between these orbitals. The numerical calculations for the interaction of two ground-state beryllium atoms show that the exchange dispersion energy is positive and quenches about 5 to 10 per cent of the dispersion term. This results in a decrease of the interaction energy, computed as a sum of the SCF and dispersion components, by 6 to 30 per cent for interatomic distances ranging from 10 to 7 bohrs.Simplified formulae for estimating the exchange dispersion energy in the interaction of larger systems are also proposed and their accuracy is discussed.     

Many-orbital cluster expansion for the exchange-repulsion energy in the interaction of closed-shell systems

The energy of exchange repulsion between two closed-shell systems described by determinantal wave functions has been represented as a sum of contributions arising from the interaction of two, three and four orbitals at a time. These contributions have been calculated for the interaction of two neon atoms. It has been found that in the van der Waals minimum region the two-orbital components are of secondary importance and that about 90% of the total exchange energy originates from the three-orbital interactions ofL-shell electrons. The four-orbital as well as the double-exchange terms have been found negligible. The approximate algorithms for evaluation of the exchange repulsion energy have been tested and discussed.This work was partly supported by the Polish Academy of Sciences within the project MR-I.9.     

Instability of closed-shell Hartree-Fock solutions within the framework of the geminal approach

The universal instability of the closed-shell Hartree-Fock solution within the framework of the approach in which the wave function is approximated by an antisymmetrized product of geminals was proved. It was shown that these results are applicable to the Goddard Gl-function method, the generalized valence bonds method, and also the Smeyers gamma-function method.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 22, No. 4, pp. 394–400, July–August, 1986.     

Sedimentation equilibrium in nonideal heterogeneous systems. I. Fundamental equations for heterogeneous solute systems and some preliminary results

The sedimentation-equilibrium method is extended to treat nonideal solutions of heterogeneous macromolecules. The solute is assumed to be heterogeneous not only in molecular weight but also in other quantities such as partial specific volume, second virial coefficient and specific refractive increment. General expressions for various observable molecular weights, especially for weight-average, z-average, and number-average molecular weights, are derived. Their dependences on sedimentation parameter and solute concentration are discussed in detail. For the extrapolation of observable molecular weights, giving a type of weight-average, and z-average, to infinite dilution to estimate the molecular weight and the second virial coefficient, average concentration is superior as a concentration variable to original concentration. The plots of observable molecular weight versus average concentration are usually less influenced by the choice of the sedimentation parameter, especially of rotor speed. The general expressions are applied to a few special cases; monodisperse polymer, polydisperse homologous polymer, and polymer blend. The results are compared with experiments on a monodisperse, polystyrene, a polydisperse poly(methyl methacrylate), and a mixture of the two polymers, all in 2-butanone at 25°C. The agreement between the theory and experiments is satisfactory.     

New method for the direct calculation of electron density in many-electron systems. I. Application to closed-shell atoms

Analytical properties of hydrogen-like atomic orbitals (HAO ) that are used in the MOLCAO approach to the quantum theory of molecules have been studied. Addition and expansion theorems for HAO have been proved, both in coordinate and momentum representations. A close relation has been established between HAO and the reduced Bessel functions of half-integer indices. New methods are suggested to calculate integrals for atomic and molecular form factors, and multicenter integrals, for the HAO basis in the MO LCAO theory.     

Approximate solutions of the Bloch-McConnell equations for two-site chemical exchange.

Approximate formulas for the transverse-relaxation rate constant and resonance frequency have been derived for nuclear spins subject to two-site chemical exchange. The new results are more accurate than previous approximations when chemical exchange does not approach the fast-exchange limit or when site populations are not highly asymmetric. Results are derived from an effective average evolution operator that contains contributions from both exact eigenvalues of the Bloch-McConnell equations. These expressions are useful for interpretation of chemical exchange processes in NMR spectroscopy.     

A note on the orbital energy-splitting of closed-shell systems in the DODS scheme

Investigating the lowering of the total energy and the orbital energy-splittings of electrons with spins α and β, respectively, in the DODS scheme, ab initio calculations have been performed for the formaldehyde molecule. The results obtained by changing the CO distance and the orbital exponents of the C and O atoms indicate that the decrease of the electron density in the CO bond region causes larger orbital energy-splittings and lowering of the energy.     

Statistical mechanical theory for steady state systems. VII. Nonlinear theory

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics.     

On the role of symmetry in the ab initio hartree-fock linear-combination-of-atomic-orbitals treatment of periodic systems

The symmetry properties of the mono- and bielectronic terms contributing to the Fock matrix in the ab initio Hartree–Fock treatment of periodic systems are discussed. A computational scheme which takes full advantage of the point symmetry is presented; in this respect, it represents a generalization of the scheme proposed in Int. J. Quantum Chem. 17 , 501 (1980). Computational details and numerical examples are reported; it is shown that with respect to two of the bottlenecks of this kind of calculation, namely, computer time and backing storage required for the bielectronic integrals, it is possible to obtain saving factors as large as h and h², respectively, where h is the order of the point group. Preliminary tests are reported which indicate that the study of relatively complicated systems, like quartz or corundum (9 and 10 atoms in the unit cell, respectively) at an ab initio Hartree–Fock level is now within reach.     

Examination of the Hund rule in closed-shell systems: Investigation of spin correlation effects

The validity of the Hund rule in atomic orbitals (AO s) of the carbon atoms inside closed-shell molecules, such as acetylene, ethylene, and ethane, is examined. Electron-pair populations and contributions of the two-electron covalent structures with parallel (?) and antiparallel (↑↓) spins are calculated by multielectron population analysis of MO + CI wave functions. Such an analysis, which allows the visualization of various cooperative electronic effects in some target AO s, is extended on the basis of (strictly orthogonal) hybrid orbitals. Although the HF level shows, incorrectly, that the Hund rule is not satisfied, the CI clearly shows a preference for (?) spins to those of (↑↓): This holds for both the electron-pair populations [those of (↑↓) spins diminish with the CI more drastically than those of (?) spins], as well as for contributions of the two-electron covalent structures [those of (?) spins increase with the CI more drastically than do those of (?) spins]. The calculation of the correlation functions (or dependent functions) in AO space allows the comparison of repulsive or “attractive” behaviour of (?) and (↑↓) spins in various AO couples. Mutual dependence of the two electrons inside the sigma system increases in the series ethane < ethylene < acetylene. Also found is that parallel spins in (pure) AO s of sigma systems are preferred to the antiparallel spins when going from ethane to acetylene. The preference parallel–antiparallel spins in AO s belonging to two different atoms, including hydrogens, is also examined. © 1993 John Wiley & Sons, Inc.     

New possibilities of Möller-Plesset perturbation theory for calculating correlation energies of closed-shell systems

A new scheme for generating and selecting configurational wave functions (CWF) including the correlation effects is suggested. Standard Möller-Plesset perturbation theory (SMP) is modified in such a way that the newly constructed CWF and the Hartree-Fock reference determinant are the eigenfunctions of a zero-order Hamiltonian. Possessing all advantages of SMP, the calculation scheme allows for more than 80% of the empirical correlation energy in the second order. The results for diatomic hydrides are comparable in accuracy to those obtained by the configuration interaction method.     

Study of cryostructurization of polymer systems VII. Structure formation under freezing of poly(vinyl alcohol) aqueous solutions

Rheological properties of the cryogels produced by freezing of concentrated aqueous solutions of poly(vinyl alcohol) have been studied. These properties were shown to depend on the polymer concentration in the initial solution, on PVA molecular weight, cryostructurization duration and temperature. Electron microscopy demonstrates the heterogeneous porous structure of these cryogels and the dependence of the observed pattern on the conditions of formation of the studied objects.     

Cyclization of ylidenemalononitriles. VII. Studies on sulfur-containing heterocyclic systems

Ring closure of ylidenemalononitrile adducts has been extended to the syntheses of isomeric sulfur heterocycles. The malononitrile derivatives of thiochromanone, thiochromone and iso-thiochromanone have been synthesized, and results of the acidic ring closure experiments on these compounds are reported. The thiochromanone adducts gave an interesting disproportionation reaction, and experiments designed to support the proposed route are presented.     

Corresponding state relations for the Newtonian viscosity of polymer solutions. II. Further systems and concentrated solutions

In earlier work we have indicated a superposition principle for moderately concentrated mixtures (c ? 2/[η]) in good and poor solvents. By an examination of data on a number of vinyl polymers and cellulose derivatives in good as well as poor solvents, the validity of this principle is extended to concentrated solutions (c ? 50%). The characteristic concentration factor γ is proportional to M over the whole concentration range, with 0.47 ≤ a₁ ≤ 1.10 being larger for good than for poor solvents, the result obtained earlier. Significant deviations from this relationship are noted in good solvents for those low molecular weights at which deviations from the usual intrinsic viscosity relationship occur. This may be related to the expansion factor of the polymer coil. On the basis of these results, the concentration and molecular weight dependence of the viscosity in the concentrated solution can be related to each other in terms of the parameter a₁ and thus to thermodynamic characteristics. In this manner a bridge between the relatively dilute and concentrated regions is established. Currently used semiempirical expressions are analyzed in terms of these results. For the polystyrene–cyclohexane systems and θ ? 9 ≦ T ≦ θ + 3, γ can be identified with the critical concentration for phase separation. Provided an “entanglement” concentration c_e exists, in the neighbourhood of which the concentration dependence of the viscosity changes reapidly, γ can alternatively be shown to be proportional to c_e, or c_e ∝ M. The temperature reduction scheme suggested earlier remains to be investigated.