Proposed sets of critical exponents for randomly branched polymers,using a known string theory model

The critical exponent ν for randomly branched polymers with dimensionality d equal to 3, is known exactly as 1/2. Here, we invoke an already available string theory model to predict the remaining static critical exponents. Utilizing results of Hsu et al. (Comput Phys Commun. 2005;169:114–116), results are added for d = 8. Experiment plus simulation would now be important to confirm, or if necessary to refine, the proposed values.     

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.     

Fragmentation of 3-hydroxyflavone; a computational and mass spectrometric study

In a recent study of the collision-induced dissociation of protonated and deprotonated molecules of 3-, 5-, 6-, 7-, 2'-, 3'- and 4'-hydroxyflavone, it was observed that the ratio, gamma, of the propensities for cross-ring cleavage (CRC) to ring opening (RO) varied by a factor of 660, i.e., from 0.014:1 (for deprotonated 3-hydroxyflavone) to 9.27:1 (for deprotonated 5-hydroxyflavone). An explanation for the variation of gamma was presented in terms of experimental NMR (13)C and (1)H spectra modified by computation. Deprotonated 3-hydroxyflavone exhibited the highest ion signal intensity for fragmentation following RO relative to that for CRC in that gamma = 0.014:1. Because no chemical computations of the fragmentation of protonated and deprotonated monohydroxyflavone molecules have been carried out thus far, the basis on which fragmentation mechanisms for deprotonated 3-hydroxyflavone have been proposed is principally chemical intuition. The energy states of product ions formed in the fragmentation of deprotonated 3-hydroxyflavone molecules were computed by the CBS-4M method implemented in Gaussian 03. The overly demanding calculations needed to handle diradicals reliably and directly were circumvented by a process in which each of the bond-breaking reactions was approximated by a process that gave two monoradicals. Bond energies were calculated, with one exception, from the approximation reactions as the energy of products minus the energy of reactants.     

Legendre transform of the noninteracting kinetic energy: Especially from March–Murray perturbation theory based on plane waves

The Legendre transform of the noninteracting kinetic energy is derived from the March–Murray perturbation theory based on plane waves. Further useful relations are summarized, and it is shown that insight can be gained from simple model systems where nonperturbative equations can be derived. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 138–142, 2001     

Exact exchange—correlation potential from low-order density matrices

The local energy equation derived by Dawson and March (1984) following the study of Cohen and Frishberg (1976) involves the low-order density matrices. Using this equation, a formally exact route is laid down by means of which the exchange-correlation potential of density functional theory can be derived in terms of the third- and lower-order density matrices. An integral equation for an approximate exchange potential is obtained, which may be solved iteratively within the Slater-Kohn-Sham scheme. © 1997 John Wiley & Sons, Inc.     

Kinetic energy density in terms of electron density for closed-shell atoms in a bare Coulomb field

A long-term aim in density functional theory is to obtain the kinetic energy density t(r) in terms of the ground-state electron density ρ(r). Here, t(r) is written explicitly in terms of ρ(r) for an arbitrary number 𝒩 of closed shells in a bare Coulomb field. In the limit as 𝒩→∞, closed results for t(r) follow from the earlier analysis of ρ(r) by Heilmann and Lieb. [Phys. Rev. A 52 , 3628 (1995)]. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 281–283, 1998     

Features of electrical discharges in air triggered by laser

A numerical study of laser-triggered discharges in air at atmospheric pressure is presented for an ultraviolet laser in small gaps. Two models, one for the ionization of the air by the laser pulse and the second for the streamer evolution have been computed. From results of numerical simulations the influence of the laser parameters such as energy, pulse duration and beam radius is analyzed and electron distributions are obtained for different small gaps. Electric field, streamer velocity and evolution of the ionized volume are calculated by means of streamer simulations. This paper shows the main features of the laser-triggered discharges and also the importance of using numerical simulations in a laser-triggered experiment.