Biomedical subjects
Publications and source records attributed to N H March.
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.
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.
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.
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).
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.
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.
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.
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.
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%.
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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.