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.     

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 solution chemistry on the surface charge of polymeric reverse osmosis and nanofiltration membranes

A streaming potential analyzer has been used to investigate the effect of solution chemistry on the surface charge of four commercial reverse osmosis and nanofiltration membranes. Zeta potentials of these membranes were analyzed for aqueous solutions of various chemical compositions over a pH range of 2 to 9. In the presence of an indifferent electrolyte (NaCl), the isoelectric points of these membranes range from 3.0 to 5.2. The curves of zeta potential versus solution pH for all membranes display a shape characteristic of amphoteric surfaces with acidic and basic functional groups. Results with salts containing divalent ions (CaCl₂, Na₂SO₄, and MgSO₄) indicate that divalent cations more readily adsorb to the membrane surface than divalent anions, especially in the higher pH range. Three sources of humic acid, Suwannee River humic acid, peat humic acid, and Aldrich humic acid, were used to investigate the effect of dissolved natural organic matter on membrane surface charge. Other solution chemistries involved in this investigation include an anionic surfactant (sodium dodecyl sulfate) and a cationic surfactant (dodecyltrimethylammonium bromide). Results show that humic substances and surfactants readily adsorb to the membrane surface and markedly influence the membrane surface charge.     

A study of peralkylated derivatives of bis(η6-benzene)chromium by gas-phase electronic absorption spectroscopy

The gas-phase electronic absorption spectra of (⁶-C₆R₆)₂Cr (R = Me (1) and Et (2)) reveal Rydberg structures, which disappear on going to the condensed phase. Each spectrum shows a Rydberg series converging to the ionization threshold. The first ionization potential determined as the series convergence limit is 4.662±0.008 eV for 1 and 4.667±0.019 eV for 2. The Rydberg bands are due to the transitions from the non-bonding MO 3d_z2 to the R4s and Rnp (n = 4—10) levels. The influence of methyl and ethyl substituents on the term values of the Rydberg transitions depends on the principal quantum number of the Rydberg MO.     

Potential distribution around a charged spherical colloidal particle in a medium containing its counterions and a small amount of added salts

A theory is developed for the potential distribution around a charged spherical colloidal particle carrying ionized groups on the particle surface in a medium containing its counterions (i.e., counterions produced from dissociation of the particle surface groups) and a small amount of added salts on the basis of the theory of Imai and Oosawa. Numerical solutions to the Poisson–Boltzmann equation for the potential distribution are obtained for the case of dilute (but not infinitely dilute) particle suspensions of volume fraction 1 for a1 (where is the Debye–Hückel parameter and a is the particle radius). Here we have taken into account the effects of (i) counterions from the particle surface groups, and (ii) the finite particle volume fraction. These effects, which are usually neglected in the conventional Poisson–Boltzmann equation, are found to be important. It is found that, as in the case of completely salt-free media, there is a certain critical value of the particle charge (which is the same as that for the completely salt-free case). When the particle charge is lower than the critical value, the potential is given by a Coulomb potential. If the particle charge is higher than the critical value, then counterions are accumulated in the vicinity of the particle surface (counterion condensation) and the potential becomes less dependent on the particle charge. The above behaviors can be observed even for the case where the electrolyte concentration is higher than the concentration of counterions from the particle surface groups, if the conditions 1 and a1are both satisfied.     

SSCH3光解离的多参考理论计算

摘要运用多参考微扰理论(Multireference MΦller-Plesset theory)计算了SSCH3垂直激发能及其S-C与S-S两种断键方式的绝热(Adiabatic)与非绝热(Diabatic)的基态和激发态势能曲线, 研究了在193nm激光作用下SSCH3的光解离过程, 理论计算值与实验值相符.     

The electrostatic field of B-DNA

The electrostatic field associated with one complete turn of B-DNA is presented. Two base sequences poly (dG) · poly (dC) and poly (dA) · poly (dT) are studied and the effects of sodium counterions bound to the nucleic acid are investigated. The contrasts between the electrostatic potential and the electrostatic field of the macromolecules are discussed and the possible applications of the field are considered.     

Electrochemistry of capillary systems with narrow pores. IV. Dialysis potentials

The dialysis potentials of different collodion membranes with graded pore sizes and electrochemical activities have been measured in dilute aqueous KCl solutions as functions of concentration. It is possible to predict the value of the diffusion potential within a few millivolts on the basis of electrical conductivity data obtained with the same membranes. In general, the measured values are lower than those calculated. It is assumed that this difference is caused by the membranes having a distribution of pore sizes.     

二氧化碳和氧气的快速电化学方法联合测定

根据Ｏ２和ＣＯ２在二甲亚砜（ＤＭＳＯ）介质中Ｐｔ电极上的伏安特性，采用微电极并结构计算机控制的电位调制技术，建立了快速联合测定ＣＯ２和Ｏ２的调制电位脉冲库仑法和调制电位脉冲电流法，取得了满意的结果。一次测量时间快达４０ｍｓ。ＣＯ２检测范围０￣１０％（体积百分比）；Ｏ２检测范围不受限制。通过编程设计特定的调制电位－时间波形，可保持连续检测的长期稳定性。