Form of spinless first- and second-order density matrices in atoms and molecules, derived from eigenfunctions of S2 and Sz

Many-electron theory of atoms and molecules starts out from a spin-independent Hamiltonian H. In principle, therefore, one can solve for simultaneous eigenfunctions Ψ of Hand the spin operators S² and S_z. The fullest possible factorization into space and spin parts is here exploited to construct the spinless second-order density matrix Γ, and hence also the first-order density matrix. After invoking orthonormality of spin functions, and independently of the total number of electrons, the factorized form of Ψ is shown to lead to Γ as a sum of only two terms for S = 0, a maximum of three terms for S = 1/2 and four terms for S ≥ 1. These individual terms are characterized by their permutational symmetry. As an example, theground state of the Be atom is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Studies on technetium and some carboxylic and hydroxamic acids

Interactions between technetium and salicylic acid, oxalic acid, gentisic acid, dipicolinic acid, pyridine-2,5-dicarboxylic acid, salicylhydroxamic acid, dipicolindihydroxamic acid and 5-methoxycarbonyl-2-pyridinehydroxamic acid are described. The complexation reactions have been investigated (pH, , stability, stoichiometry) and the results obtained have been comparatively evaluated.     

Liquid Madelung energy and Schottky defect energy related to liquid structure and melting temperature for alkali halides

Motivated by the work of Reiss et al in which the melting temperature T_m of alkali halides is correlated with Coulomb energy, we consider the cohesive energy W of ionic melts and Schottky defect energy E_s in the hot crystal, relative to the thermal energy k_BT_m It is shown here that W is accurately approximated by the liquid Madelung energy and hence that Wk_BT_m relates to the charge-charge direct correlation function c_QQ(r) at r = 0 The existence of a “Madelung constant” for the liquid at T_m is thereby demonstrated through the alkali halide series An estimate of the ratio E_s/k_BT_m then considered, the basic additional ingredient being argued to be the static dielectric constant of the solid The BarrDawson-Lidiard empirical correlation between E_s, and k_BT_m can be understood in this way.     

Remarks on scaling a model of Witten-Sander type

We try to prove rigorously that the perimeter of the large Witten-Sander cluster does not scale as the square root of its area, by making a forced comparison with the ill-posed Hele-Shaw problem of fluid dynamics. The attempt is not completely successful; nevertheless some interesting consequences of the comparison are derived.     

Origin and information content of the compensation effect

An attempt is made to assess: (i) The conditions under which a compensation effect should be observable, (ii) The associated physical properties affected by such compensation. (iii) The nature of the information which can be gleaned from studies of compensation. Specific attention is given to simple desorption processes and the main conclusion is that the compensation law in adsorption indicates a phenomenon involving many molecules. However the Meyer-Neldel rule in semiconductors is also embraced, as well as observations of the compensation effect in liquids.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

Many-body effects in polymers: especially polyacetylene

Many-electron effects in polymers are considered, with emphasis on the way electron-electron interactions are reflected in ground-state properties. After a survey of results on graph theory, built up from valence-bond structures, in which the importance of size consistency again emerges, some specific results of ground-state electron pair correlations in polyacetylene and polydiacetylene are considered, motivated by the linear dispersion of the π-electron plasmon, as measured in the optical experiments of Ritsko et al. The way in which such collective excitations can affect ground-state pair correlations is discussed as is the influence of low dimensionality. A brief summary is given of the way in which the energy gap in polyacetylene and polydiacetylene depends on electron-electron repulsion although unlike the plasmon problem where the long-range Coulomb repulsion e²/r_ij is essential, this problem is usefully tackled using the on-site Hubbard repulsion. Again, there can be no doubt that correlation is important in the ground states of polyacetylene and polydiacetylene. However, recent work on bond-charge repulsion shows that whether correlation enhances or suppresses dimerization depends strongly on the particular thermodynamic state in question: this is illustrated by specific examples relating to the metal-insulator transition in low-dimensional solids. A quite different aspect of many-body phenomena will then be considered, pertaining especially to AC electrical transport in biopolymers. Here, the importance of disorder in the experimental results currently available is stressed. A power law behaviour of the frequency-dependent conductivity, i.e. σ(ω) proportional to ω^s, is a characteristic feature at suitably high frequencies. This focusses attention on the power, s, and a brief discussion of simple models shows that, for those considered to date s< 1, with possible values of 1/4 and 1/2 being exhibited. A possible influence of a compensation effect on the high-frequency conductivity is suggested. It is argued, following Kreuzer and March, that this is a many-particle phenomenon ANDS = 1-(T/T_c) for T < T_c, where T_c is the compensation temperature; a result apparently due to Dyre. The possibility of further experimental and theoretical studies related to the many-body phenomena is referred to.