Low-Lying Isomers of Free-Space Halogen Clusters with Tetrahedral and Octahedral Symmetry in Relation to Stable Molecules Such as SF6.

Motivated by previous work involving one of us (N.H.M.) on some 20 stable tetrahedral (t) and octahedral (o) molecules, including XF(4) (X = C, Si, Ge), the natural orbital functional PNOF6 is here used to study the free-space halogen cluster t-F(4). We consider an extended functional PNOF6(Nc) by coupling Nc orbitals (Nc > 1) to each orbital below the Fermi level, which improves the description of the electron pairs. Similar studies are presented for t-Cl(4). The successful calculation on the stable molecule BrF(5) (Theor. Chem. Acc. 2013, 132, 1298) has prompted a study of the clusters o-F(6) and o-Cl(6) too. The size relation with calculated known stable molecules and the experimental data are finally considered. In the case of the o-SF(6), the geometry optimization with fixed octahedral symmetry has also been performed at the PNOF6(3) level of theory, leading to an equilibrium distance of 2.95 au in perfect agreement with the experiment. Our results confirm the multireferential character of Z(4) and Z(6) compounds (Z = H, F, Cl), in contrast with the single-reference character of the XZ(4) (X = C, Si, Ge) and YZ(6) (Y = S, Se, U) compounds; therefore, despite the clear patterns within a group, it is not possible to extrapolate the results to the case when the atomic number, X or Y, becomes zero.

Second-order Møller-Plesset calculations of total ground-state energies of tetrahedral and octahedral molecules at equilibrium, confronted with some model-dependent scaling properties.

Using second-order Møller-Plesset (MP2) optimized geometries, calculations of total energies of some 20 tetrahedral and octahedral molecules have been carried out. We have then confronted these first-principles results, which of course include a fraction of the electronic correlation energy, with some model-dependent scaling properties. In particular, one scaling relation emerging from the semiclassical Thomas-Fermi electron density method relates the known nuclear-nuclear potential energy, V(nn), at equilibrium to the electron-nuclear term, V(en), and the total kinetic energy.

Exact integral constraint requiring only the ground-state electron density as input on the exchange-correlation force - partial differential(V)(xc)(r)/partial differential(r) for spherical atoms.

Following some studies of integral(n)(r)inverted DeltaV(r)dr by earlier workers for the density functional theory (DFT) one-body potential V(r) generating the exact ground-state density, we consider here the special case of spherical atoms. The starting point is the differential virial theorem, which is used, as well as the Hiller-Sucher-Feinberg [Phys. Rev. A 18, 2399 (1978)] identity to show that the scalar quantity paralleling the above vector integral, namely, integral(n)(r) partial differential(V)(r)/partial differential(r)dr, is determined solely by the electron density n(0) at the nucleus for the s-like atoms He and Be. The force - partial differential(V)/ partial differential(r) is then related to the derivative of the exchange-correlation potential V(xc)(r) by terms involving only the external potential in addition to n(r). The resulting integral constraint should allow some test of the quality of currently used forms of V(xc)(r). The article concludes with results from the differential virial theorem and the Hiller-Sucher-Feinberg identity for the exact many-electron theory of spherical atoms, as well as for the DFT for atoms such as Ne with a closed p shell.

Statistical correlations in an ideal gas of particles obeying fractional exclusion statistics.

After a brief discussion of the concepts of fractional exchange and fractional exclusion statistics, we report partly analytical and partly numerical results on thermodynamic properties of assemblies of particles obeying fractional exclusion statistics. The effect of dimensionality is one focal point, the ratio mu/k_(B)T of chemical potential to thermal energy being obtained numerically as a function of a scaled particle density. Pair correlation functions are also presented as a function of the statistical parameter, with Friedel oscillations developing close to the fermion limit, for sufficiently large density.

Structural corrections to Stokes-Einstein relation for liquid metals near freezing.

Using recent progress relating the self-diffusion coefficient to excess entropy, structural corrections to the Stokes-Einstein relation are proposed for liquid metals near the melting temperature.

Optimized geometry of the cluster Gd2O3 and proposed antiferromagnetic alignment of f-electron magnetic moment.

There is currently experimental interest in assemblies of Gd2O3 clusters. This has motivated the present study in which a single such cluster in free space is examined quantitatively by spin-density functional theory, with appropriate relativistic corrections incorporated for Gd. First, the nuclear geometry of the cluster is optimized, and it is found to be such that the two Gd atoms lie in a symmetry axis perpendicular to the isosceles triangle formed by the O atoms. Then, a careful study is made of the magnetic arrangement of the localized f-electron moments on the two Gd atoms. The prediction of the present treatment is that the localized spins are aligned antiferromagnetically. An alternative picture using superexchange ideas leads to the same conclusion.

Differential virial theorem in relation to a sum rule for the exchange-correlation force in density-functional theory.

Holas and March [Phys. Rev. A. 51, 2040 (1995)] gave a formally exact theory for the exchange-correlation (xc) force F(xc)(r)= -inverted Deltaupsilon(xc)(r) associated with the xc potential upsilon(xc)(r) of the density-functional theory in terms of low-order density matrices. This is shown in the present study to lead, rather directly, to the determination of a sum rule nF(xc)=0 relating the xc force with the ground-state density n(r). Some connection is also made with an earlier result relating to the external potential by Levy and Perdew [Phys. Rev. A. 32, 2010 (1985)] and with the quite recent study of Joubert [J. Chem. Phys. 119, 1916 (2003)] relating to the separation of the exchange and correlation contributions.

Compressibility and specific heats of heavier condensed rare gases near the liquid-vapor critical point.

This study concerns the way to describe some physical properties of simple liquids by using the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. It constructively analyzes the recent contribution of Sarkisov [G. N. Sarkisov, J. Chem. Phys. 119, 373 (2003)] on the structural behavior of a simple fluid near the liquid-vapor critical point. His work, already compared with computer simulation studies, is here brought into direct contact for the heavier condensed rare gases Ar, Kr, and Xe with (a) experiment and (b) earlier theoretical investigations. Directions for future studies then emerge.

Chemical potential, Teller's theorem, and the scaling of atomic and molecular energies.

FOR ATOMS AND HOMONUCLEAR DIATOMIC MOLECULES, IT IS ARGUED THAT THE ELECTRONIC ENERGIES HAVE THE FORMS [FORMULA: see text] and [Formula: see text] [Formula: see text], respectively,where Z is the atomic number, N is the number of electrons, and R is the internuclear distance. By using the Lieb-Simon theorem that the Thomas-Fermi theory is exact in the limit of large atomic number and the Teller theorem that molecules are not bound in the Thomas-Fermi theory, it is then shown, among other results, that the electron-electron repulsion energy for neutral systems has no term in Z(2) and that the nucleus-nucleus repulsion energy for neutral molecules is probably [unk](Z(5/3)). For neutral atoms, it is predicted and verified that the chemical potential (electronegativity) is [unk](Z(-1/3)) for large Z. Tetrahedral and octahedral molecules are briefly discussed.

Generalized Stokes-Einstein relation for liquid metals near freezing.

Deviations from a Stokes-Einstein relation between the self-diffusion coefficient D and shear viscosity eta for liquid metals near freezing are shown to correlate with a net transit parameter xi introduced recently by Wallace [Phys. Rev. E 58, 538 (1998)] in a two-parameter model of D. Brief comments are made on the single exception of In, for the seven liquid metals for which suitable experimental data are available.

Relation between transport and thermodynamic properties in liquid sp-electron metals near freezing.

Classical statistical mechanics based on assumed pair potentials leads, for liquid metals, to an approximate relation between shear viscosity eta, surface tension sigma, and thermal velocity vT defined as (kBT/M)(1/2), with M the ionic mass. Theory predicts for the dimensionless grouping sigma/etav(T) evaluated at the melting temperature Tm a single value 15 / 16; liquid sp-electron metals exhibit, however, a scatter from around 0.7 to 2.3. Therefore, an alternative grouping sigma/etav(s), with v(s) the velocity of sound, is considered here in detail, first using experimental data and second using both theoretical and semiempirical arguments. The scatter of sigma/etav(s) at Tm is less than for the earlier grouping, and also insight can be gained as to various physical factors determining sigma/etav(s). In essence, this quantity is proportional to the product of two factors, both dimensionless, namely, the surface thickness L measured in units of the mean interionic separation, and the square root of the energy Mv(2)s, measured in units of the thermal energy kBTm. Theoretical estimates are made of both of these factors, in fair accord with the experimental data.

Topology, connectivity, and electronic structure of C and B cages and the corresponding nanotubes.

After a brief discussion of the structural trends which appear with an increasing number of atoms in B cages, a one-to one correspondence between the connectivity of B cages and C cage structures will be proposed. The electronic level spectra of both systems from Hartree-Fock calculations is given and discussed. The relation of curvature introduced into an originally planar graphitic fragment to pentagonal "defects" such as are present in buckminsterfullerene is also briefly treated. A study of the structure and electronic properties of B nanotubes will then be introduced. We start by presenting a solution of the free-electron network approach for a "model boron" planar lattice with local coordination number 6. In particular the dispersion relation E(k) for the pi-electron bands, together with the corresponding electronic Density Of States (DOS), will be exhibited. This is then used within the zone-folding scheme to obtain information about the electronic DOS of different nanotubes obtained by folding this model boron sheet. To obtain the self-consistent potential in which the valence electrons move in a nanotube, "the March model" in its original form was invoked, and the results are reported for a carbon nanotube. Finally, heterostructures, such as BN cages and fluorinated buckminsterfullerene, will be briefly treated, the new feature here being electronegativity difference.

The kinetic energy change on covalent bond formation.

Stimulated by an analysis of the classical molecular orbital and valence bond descriptions of the two-electron normal covalent bond (both faulty), the argument is made that there exist good representations of the kinetic energy change DeltaT, on nonpolar covalent bond formation in a diatomic molecule, of the form DeltaT(R) = integralF(R - r')S(r')dr'. Here F is a nonlinear response function which itself involves the overlap S. The kinetic change is known to satisfy the sum rule integral(0) (infinity)DeltaT(R)dR = Z(alpha)Z(beta) exactly; it is shown how this can be built into the treatment by the use of Fourier transform methods. Also considered is integral(0) (infinity)DeltaT(R)R(2)dR, which is an important additional property of the kinetic energy change. Representation of DeltaT(R) as a Morse function, already known to be highly accurate, is shown to exactly conform to the proposed form.

The effect of temperature on canine papillary muscle.

Measurements of the total duration, tA, of the action potential for canine papillary muscle in the temperature range 25-45 degrees C are shown to follow the law ta = tau exp (Q/kBT), with tau and the activation energy Q independent of temperature, T, and kB equal to Boltzmann's constant. The value obtained for Q = 0.65 +/- 0.10 eV. Results are also presented for the temperature dependence of points V(x) on the action potential curve, where x is the percentage of repolarisation within the range 30% less than x less than 100%.

Equilibrium geometries of low-lying isomers of some Li clusters, within Hartree-Fock theory plus bond order or MP2 correlation corrections.

In a recent study by Kornath et al. [J. Chem. Phys. 118, 6957 (2003)], the Li(n) clusters with n=2, 4, and 8 have been isolated in argon matrices at 15 K and characterized by Raman spectroscopy. This has prompted us to carry out a theoretical study on such clusters up to n=10, using Hartree-Fock theory, plus low-order Møller-Plesset perturbation corrections. To check against the above study of Kornath et al., as a by-product we have made the same approximations for n=6 and 8 as we have for n=10. This has led us to emphasize trends with n through the Li(n) clusters for (i) ground-state energy, (ii) HOMO-LUMO energy gap, (iii) dissociation energy, and (iv) Hartree-Fock eigenvalue sum. The role of electron correlation in distinguishing between low-lying isomers is plainly crucial, and will need a combination of experiment and theory to obtain decisive results such as that of Kornath et al. for Li(8). In particular, it is shown that Hartree-Fock theory plus bond order correlations does account for the experimentally observed symmetry T(d) symmetry for Li(8).