Á. Nagy

Fisher information in density functional theory

The Euler equation of the density functional theory is derived from the principle of minimum Fisher information. Both time-independent and time-dependent cases are analyzed. It is shown that Fisher information is a measure of the quality of the approximate density.

Adenosine Triphosphatase Activity at the External Surface of Chicken Brain Synaptosomes

Abstract: An ATP‐hydrolysing activity on the external surface of intact synaptosomes from chicken forebrain has been investigated. The observed ATPase activity was not due to leakage of the intracellular ATPase activities, to artefacts resulting from breakage of the nerve endings during the incubation and isolation periods, or to possible contamination by other subcellular particles. Disruption of the synaptosomes resulted in an approximately 2.5‐fold increase of the basal, Mg2+‐dependent ATPase activity, suggesting that the plasma membrane was acting as a permeability barrier to the substrate. ATP hydrolysis was maximal (0.8 μumol Pi/min/mg protein) at pH 8.2 in a medium containing either Mg2+ or Ca2+ ions. Ouabain (0.2 mM) and oligomycin (2 μg/mg protein) had no appreciable effect on this ATPase activity. Kinetic studies of the enzyme revealed an apparent Km value for ATP of approximately 4 ± 10−5M. These data are consistent with the view that the observed ATP hydrolysis was being catalysed by an ectoenzyme, i.e., an enzyme in the plasma membrane of the nerve endings with its active site facing the external medium. The rapid hydrolysis of the released ATP is a suspected function for this ecto‐ATPase.

A generalized statistical complexity measure: Applications to quantum systems

A two-parameter family of complexity measures C(α,β) based on the Renyi entropies is introduced and characterized by a detailed study of its mathematical properties. This family is the generalization of a continuous version of the Lopez-Ruiz–Mancini–Calbet complexity, which is recovered for α=1 and β=2. These complexity measures are obtained by multiplying two quantities bringing global information on the probability distribution defining the system. When one of the parameters, α or β, goes to infinity, one of the global factors becomes a local factor. For this special case, the complexity is calculated on different quantum systems: H-atom, harmonic oscillator, and square well.

Ground- and excited-state cusp conditions for the electron density

Higher-order cusp relations are derived for the wave function and the electron density of the ground and the excited states of atoms, ions or molecules. The total energy is expressed in terms of the electronic potential and density terms defined at the nucleus. It is proved that the linear term of the spherical part in the expansion of the Kohn–Sham potential, the classical Coulomb and the exchange correlation potentials around a nucleus are all equal to zero. A relationship involving the values of the density and its second and third derivatives at the nucleus is derived.

Effective potential in density matrix functional theory

In the previous paper it was shown that in the ground state the diagonal of the spin independent second-order density matrix n can be determined by solving a single auxiliary equation of a two-particle problem. Thus the problem of an arbitrary system with even electrons can be reduced to a two-particle problem. The effective potential of the two-particle equation contains a term v(p) of completely kinetic origin. Virial theorem and hierarchy of equations are derived for v(p) and simple approximations are proposed. A relationship between the effective potential u(p) of the shape function equation and the potential v(p) is established.

Mössbauer study of bridged ferrocene derivatives

Abstract The molecular geometry of a series of trimethylene bridged ferrocene derivatives has been studied by means of Mossbauer techniques. The differences in quadrupole splitting and isomer shift among the various derivatives can best be explained as being due to differences in the planarity of the cyclopentadienyl rings.

Cyclic voltammetry of arylferrocenes and ferrocene analogues of chalcones. Substituent effects on the electron density distribution in ferrocene derivatives

Abstract Cyclic voltammetry studies of arylferrocenes and two series of ferrocene analogues of chalcone are presented. Good correlations of the oxidation potentials (E 1 2 ) with the σ Hammett constants as well as with the 13C chemical shifts for carbon atoms with different positions in the ferrocenyl moiety have been found. The different sensitivities of these series to the substituent effects is discussed. The variation of the electron density distribution at the carbon atoms of the cyclopentadienyl rings is given numerically as a function of the electron-donating or electron-withdrawing strengths of the substituents.

Alternatives to the electron density for describing Coulomb systems

Stimulated by the difficulty of deriving effective kinetic energy functionals of the electron density, the authors consider using the local kinetic energy as the fundamental descriptor for molecular systems. In this ansatz, the electron density must be expressed as a functional of the local kinetic energy. There are similar results for other quantities, including the local temperature and the Kohn-Sham potential. One potential advantage of these approaches--and especially the approach based on the local temperature--is the chemical relevance of the fundamental descriptor.

Correlation energy density from ab initio first- and second-order density matrices: A benchmark for approximate functionals

A procedure has been proposed to construct numerically the exchange‐correlation exc(r) and correlation ec(r) energy densities of density functional theory using the correlated first‐ and second‐order density matrices from ab initio calculations. ec(r) as well as its kinetic and potential components have been obtained for the two‐electron He atom and H2 molecule. The way various correlation effects manifest themselves in the form of ec(r) has been studied. The ec(r) have been compared with some density functional local and gradient‐corrected models ecmod(r). The investigation of the shape of the model energy densities ecmod(r) has been extended to the Be2 and F2 molecules and the corresponding correlation energies Ec have been calculated and discussed for a number of atomic and molecular systems. The results show the importance of a proper modeling of ec(r) in the molecular bond midpoint region.

Differential equation for the ground-state electron density in a Hookean atom with two electrons repelling coulombically

Abstract A homogeneous linear third-order differential equation is constructed which is satisfied by the exact ground-state electron density in the Hookean atom with two electrons interacting via their full Coulombic repulsion.