Generalized classical theory of magnetism

We consider an Ising model with Kac potential ^dK(¦x¦) which may have arbitrary sign, and show, following Gates and Penrose, that the free energy in the classical limit0+ can be obtained from a variational principle. When the Fourier transform of the potential has its maximum atp=0 one recovers the usual mean-field theory of magnetism. When the maximum occurs forp ₀0, however, one obtains an oscillatory or helicoidal phase in which the magnetization near the critical point oscillates with period 2/¦p ₀¦. An example with a potential possessing parameter-dependent oscillations is shown to exhibit crossover phenomena and a multicritical Lifshitz point in the classical limit.     

Melnikov's criterion for nondifferentiable weak-noise potentials

The stationary probability density of Fokker-Planck models with weak noise is asymptotically of the form exp[–1 /(q)]. If is smooth, it satisfies a Hamilton-Jacobi equation at zero energy and can be interpreted as the action of an associated Hamiltonian system. Under this assumption, has the properties of a Liapounov function, and can be used, e.g., as a thermodynamic potential in nonequilibrium steady states. We consider systems having several attractors and show, by applying Melnikov's method to the associated Hamiltonian, that in general is not differentiable. A small perturbation of a model with differentiable leads to a nondifferentiable . The method is illustrated on a model used in the treatment of the unstable mode in a laser.     

XANES Determination of Intraatomic Potentials

A new scheme has been developed for determining the parameters of the local one-electron potential in molecules and solids. The scheme is based on interpretation of the experimental X-ray absorption near edge struucture. The scheme is an extension of the method for solving the inverse problem of XANES theory suggested by one of the authors. In this scheme, oscillator strengths and maximum heights are considered along with the energy and half-width of spectral maxima. The scheme is used for determining the intraatomic potential in the nitrogen molecule.Original Russian Text Copyright © 2004 by Yu. F. Migal and O. M. Kholodova__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 986–989, November–December, 2004.     

Theoretical studies of mechanisms of cycloaddition reaction between difluoromethylene carbene and acetone

Mechanisms of the cycloaddition reaction between singlet difluoromethylene carbene and acetone have been investigated with the second‐order Møller–Plesset (MP2)/6‐31G* method, including geometry optimization and vibrational analysis. Energies for the involved stationary points on the potential energy surface (PES) are corrected by zero‐point energy (ZPE) and CCSD(T)/6‐31G* single‐point calculations. From the PES obtained with the CCSD(T)//MP2/6‐31G* method for the cycloaddition reaction between singlet difluoromethylene carbene and acetone, it can be predicted that path B of reactions 2 and 3 should be two competitive leading channels of the cycloaddition reaction between difluoromethylene carbene and acetone. The former consists of two steps: (i) the two reactants first form a four‐membered ring intermediate, INT2, which is a barrier‐free exothermic reaction of 97.8 kJ/mol; (ii) the intermediate INT2 isomerizes to a four‐membered product P_2b via a transition state TS2b with an energy barrier of 24.9 kJ/mol, which results from the methyl group transfer. The latter proceeds in three steps: (i) the two reactants first form an intermediate, INT1c, through a barrier‐free exothermic reaction of 199.4 kJ/mol; (ii) the intermediate INT1c further reacts with acetone to form a polycyclic intermediate, INT3, which is also a barrier‐free exothermic reaction of 27.4 kJ/mol; and (iii) INT3 isomerizes to a polycyclic product P₃ via a transition state TS3 with an energy barrier of 25.8 kJ/mol. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Effect of ionic strength on the formal potential of the glass electrode in various saline media

We examined the variation with ionic strength (I, adjusted with KCl, KNO₃, KBr, NaCl or NaClO₄) of the formal potential (E_const) for glass electrodes exhibiting a Nernstian response (i.e. E_cell=E_const−s log [H⁺]). For this purpose, we investigated the different factors included in the formal potential, so we obtained reported values for the liquid junction potential as a function of ionic strength and determined the logarithm of the activity coefficient for the proton in various saline media, using Pitzer equations.     

Crystallization of binary carboxylic acids characterized with streaming potential measurement

The streaming potential of supersaturated solution of binary carboxylic acids, which have even carbon atoms, was determined to characterize crystallization under different temperatures. The value of the streaming potential was related to the type and solubility of the acids and the starting temperature of crystallization, and was easily influenced by the pressure difference of the liquid or the rate of temperature decline. When the temperature was declined to the point where a crystal nucleus appeared, the streaming potential reached the minimum. Thereafter, as the temperature was sequentially lowered, some minicrystals grew, and the streaming potential presented an ascendant tendency. The higher the starting temperature of the acids saturated solution, the higher is the temperature corresponding to the streaming potential minimum. The less the carbon atoms in the acids and the greater the solubility of the acids are, the higher is the temperature of the streaming potential minimum. Copyright © 2007 John Wiley & Sons, Ltd.     

Automatic sequential determination of the hydrogen peroxide scavenging activity and evaluation of the antioxidant potential by the 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) radical cation assay in wines by sequential injection analysis

An automatic system that performs two analytical procedures, allowing the evaluation of the relative antioxidant capacity of wine samples, was developed. Automation was carried out using a sequential injection analysis (SIA) system that allowed, thanks to its versatility, the development of two methodologies. One is based on the decolorization assay of the 2,2′-azinobis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS) radical, using a spectrophotometric detector. A second methodology allowed the evaluation of the hydrogen peroxide scavenging activity by measuring the oxidation of homovanylic acid (HVA) to its fluorescent dimer, using a fluorescent detector.The developed automatic methodologies were evaluated using trolox as standard and subsequently using other antioxidant substances as gallic acid, caffeic acid, ascorbic acid, catechin and taxifolin which are abundant in wine and whose antioxidant activities were compared to that shown by trolox. The spectrophotometric and fluorimetric assays showed linearity intervals between 0.001 and 0.01 mM, and 0.001 and 0.008 mM of trolox, respectively.The evaluation of the antioxidant power of 20 white and red wine samples, from different Portuguese wine producing regions, was carried out sequentially, in the automatic system. The results were expressed in trolox equivalent antioxidant capacity (TEAC) and presented, for the ABTS and hydrogen peroxide scavenging activity methodologies, detection limits of 8.4 × 10⁻⁷ and 1.4 × 10⁻⁴ mM and relative standard deviation (R.S.D. (%)) in the range 0.6-2.4 and 1-1.8, respectively.     

Computer modelling of the conformational equilibrium of 2-and 2,5,5-substituted 1,3,2-dioxaborinanes

Empirical, semiempirical, and nonempirical quantum-chemical methods were used to study the conformational equilibrium of 2,5,5-substituted 1,3,2-dioxaborinanes. The sofa invertomers were found to correspond to the local and global minima on the potential energy surface. The position of the equilibrium between these forms is a function of the substituents at C₍₅₎ of the heterocycle. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1860–1865, December, 2007.     

Principal component analysis of the effects of wavefunction modification on the electrostatic potential of indole

The molecular electrostatic potential (MEP) of the indole molecule was calculated in a three‐dimensional grid in which the molecule was centered at the origin. To evaluate the dependence of MEP on the type of calculation, semiempirical, ab initio, and density functional theory methods with different basis sets were employed. The data matrix generated by these calculations was analyzed by principal component analysis (PCA). The appearance of outliers and the effect of wavefunction modifications such as the introduction of electron correlations and diffuse functions were highlighted by the use of PCA. The spatial localization of such effects around the molecule was possible from the loadings values associated with the graphical analysis of the grid points. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005