Travelling waves in an open cubic autocatalytic system

A continuous-flow, unstirred reactor (CFUR) is considered in which the reaction is purely cubic autocatalysis and in which the exchange of reactants between the reactor and its reservoir is modelled by linear diffusive interchange terms. The system is capable of supporting two, stable, spatially uniform stationary states. The possibilities of initiating travelling waves of permanent form (front waves), in which the concentrations vary monotonically between these two stationary states is, investigated. It is seen that the formation of front waves requires the dimensionless parameter D _A /D _B (D _A ,D _B being the diffusion coefficients of reactant and autocatalyst, respectively) to be such that 4, a result confirmed by numerical integrations of an initial-value problem. For values of larger than this, permanent-form waves are not initiated with a more complex structure evolving in the initial-value problem. Here the forward-propagating front leaves behind a region in which oscillations in the concentrations of both species are observed. These individual oscillations are spatially fixed with the region where this oscillatory response is observed propagating backwards into the region of spatially uniform concentration.     

Density scaling and exchange-correlation energy

The exchange-correlation energy is studied using the density scaling proposed by Chan and Handy [G. K.-L. Chan and N. C. Handy, Phys. Rev. A 59, 2670 (1999)]. It is shown that there exists a value of the scaling factor for which the correlation energy disappears. The optimized potential method and the Krieger-Li-Iafrate approach are generalized to incorporate correlation.     

Regular Liesegang patterns and precipitation waves in an open system

We investigate the regular and moving Liesegang pattern formation phenomena in an open system. First, simulations have been performed at fixed coupling between the reactive medium and the reservoir, later this control parameter was varied during the simulations resulting in various phenomena. We predicted and monitored for the first time various--dynamically changing--precipitation structures and a spatial hysteresis phenomenon, which is beyond the scope of the Turing instability. The dynamics of the reaction is well detectable using specific quantities: the total amount of precipitate and its center of gravity.     

Density matrix in the open shell theory

All the second-order density matrix spin components for the spin-projected Slater determinant are presented as expansions in direct products of powers of unprojected spin- and residual electron density matrices. Spin components of the second-order transition density matrices between spin-projected Slater determinants built of orthogonal orbitals are also obtained.     

Density scaling and relaxation of the Pauli principle

The relaxation of the Pauli principle associated with density scaling is examined. Scaling the density has been investigated in the development of density functional computational methods with higher accuracy. Scaling the density by rho(r)(zeta)=rho(r)zeta reduces the number of electrons to M=Nzeta when zeta>1. The minimum kinetic energy of the scaled density, T(s)[rhozeta], can be scaled back to the N-electron system by multiplying the M-electron Kohn-Sham-type occupation numbers by zeta to produce T(zeta)[rho]. This relaxes the Pauli principle when the orbital occupation numbers are greater than 1 in the N-electron system. The effects of antisymmetry on solutions to the Kohn-Sham equations are examined for Ne and the Be isoelectronic series. The changes in T(zeta)[rho] and the exchange energy E(xzeta)[rho] when zeta is varied show that these two quantities are inextricably linked.     

The energy mismatch in multiphonon relaxation

Modifications are presented for zero temperature to the energy gap law which take into account the energy mismatch (the difference between the energy gap and the nearest excited level of the effective vibrator). The results for the decay rate of rare earth ions in f → f excitation show a sub-linear dependence on the square width of the spectrum of the electron—phonon interaction for small width.     

Travelling waves in an open quadratic autocatalytic chemical system

The travelling waves that are initiated in an autocatalytic reaction–diffusion system with quadratic rate law are considered. The system is modelled on the basis of a continuous-flow, unstirred reactor. The model is used to determine whether any of the complex structures reported for cubic autocatalytic reaction–diffusion systems can also be observed in the quadratic model. This is found not to be the case. The range of behaviour of the quadratic model is much less complex, with only front waves being initiated under the necessary conditions, which are established. There are, however, some unusual transient features to be found after the initial passage of the wave front. This revised version was published online in July 2006 with corrections to the Cover Date.     

Intramolecular energy transfer in a one-dimensional europium tetracyanoplatinate

The one-dimensional, polymeric compound (C15H11N3)Eu(H2O)2(NO3)(Pt(CN)4).CH3CN (1) has been shown to display an efficient donor-acceptor intramolecular energy-transfer (IET) process where ligand donors transfer energy to the Eu (III) acceptor. Single-crystal X-ray diffraction has been used to investigate the structural features of this compound in order to help understand the observed IET process. Crystallographic data: 1, monoclinic, space group P2(1)/c, a = 12.835(1) A, b = 15.239(1) A, c = 13.751(2) A, beta = 105.594(9) degrees , V = 2590.8(5) A(3), and Z = 4 (T = 290 K).     

Directing energy transfer in discrete one-dimensional oligonucleotide-templated assemblies

Monodisperse DNA-templated one dimensional dye assemblies have been constructed in which the energy transfer can be directed. Fluorescence experiments suggest an optimum transfer efficiency for stacks of 30 bases long.     

Recent advances in one-dimensional nanostructures for energy electrocatalysis

Catalysts play decisive roles in determining the energy conversion efficiencies of energy devices. Up to now, various types of nanostructured materials have been studied as advanced electrocatalysts. This review highlights the application of one-dimensional (1D) metal electrocatalysts in energy conversion, focusing on two important reaction systems—direct methanol fuel cells and water splitting. In this review, we first give a broad introduction of electrochemical energy conversion. In the second section, we summarize the recent significant advances in the area of 1D metal nanostructured electrocatalysts for the electrochemical reactions involved in fuel cells and water splitting systems, including the oxygen reduction reaction, methanol oxidation reaction, hydrogen evolution reaction, and oxygen evolution reaction. Finally, based on the current studies on 1D nanostructures for energy electrocatalysis, we present a brief outlook on the research trend in 1D nanoelectrocatalysts for the two clean electrochemical energy conversion systems mentioned above.     

Core-electron relaxation energy in small metallic particles

A general calculation method for screening in a finite electron gas proposed by Cini, is applied to study of core-hole relaxation energy in small metallic particles. In order to obtain quantitative results, a pseudopotential theory is developed for the core-hole perturbation which provides excellent agreement with the generally accepted excited-atom model in the bulk limit. The transition and noble metals treated by means of a semi-empirical extension of the method. The present calculation method of extra-atomic relaxation energies, involving an electron gas approximation for the conduction electrons allows straightforward applications of the method of Cini in the case of a finite-spherical metal particle. The relaxation energy is found to give an important contribution to core-hole binding energy shifts in small particles.     

Markovian approximation in the relaxation of open quantum systems

In this paper, we examine the validity of the Markovian approximation and the slippage scheme used to incorporate short time transient memory effects in the Markovian master equations (Redfield equations). We argue that for a bath described by a spectral function, J(omega), that is dense and smoothly spread out over the range omega(d), a time scale of tau(b) approximately 1/omega(d) exists; for times of t > tau(b), the Markovian approximation is applicable. In addition, if J(omega) decays to zero reasonably fast in both the omega --> 0 and omega --> infinity limits, then the bath relaxation time, tau(b), is determined by the width of the spectral function and is weakly dependent on the temperature of the bath. On the basis of this criterion of tau(b), a scheme to incorporate transient memory effects in the Markovian master equation is suggested. Instead of using slipped initial conditions, we propose a concatenation scheme that uses the second-order perturbation theory for short time dynamics and the Markovian master equation at long times. Application of this concatenation scheme to the spin-boson model shows that it reproduces the reduced dynamics obtained from the non-Markovian master equation for all parameters studied, while the simple slippage scheme breaks down at high temperatures.     

Free energy of an inhomogeneous polymer-polymer-solvent system

The free energy of an inhomogeneous polymer-polymer-solvent system has been obtained by extending Debye's approach for a polymer-solvent system. Our ternary result reduces to Debye's result for a binary polymer-solvent system and to McMaster's result for a binary polymer-polymer system at the appropriate limits. Like Debye's work, we neglect the entropic gradient contribution to free energy. Based on the ternary result we suggest a generalized expression for the free energy of multiple polymers dissolved in a common solvent. This expression is used to find the free energy of an inhomogeneous polydispersed polymer-solvent system.     

Water between plates in the presence of an electric field in an open system

Molecular dynamics simulations of water at 298 K and 1 atm of pressure are used to investigate the electric-field dependence of the density and polarization density of water between two graphite-like plates of different sizes (9.8 x 9.2 and 17.7 x 17.2 A) in an open system for plate separations of 8.0, 9.5, and 16.4 A. The interactions with water were tuned to "hard-wall-like" and "normal" C-O hydrophobic potentials. Water between the larger plates at 16.4 A separation is layered but is metastable with respect to capillary evaporation at zero field (Bratko, D.; Curtis, R. A.; Blanch, H. W.; Prausnitz, J. M. J. Chem. Phys. 2001, 115, 3873). Applying a field decreases the density of the water between the plates, in apparent contradiction to thermodynamic and integral equation theories of bulk fluid electrostriction that ignore surface effects, rendering them inapplicable to finite-sized films of water between hydrophobic plates. This suggests that the free energy barrier for evaporation is lowered by the applied field. Water, between "hard-wall-like" plates at narrower separations of 9.5 A and less, shows a spontaneous but incomplete evaporation at zero field within the time scale of our simulation. Evaporation is further enhanced by an electric field. No such evaporation occurs, on these time scales, for the smaller plates with the "hard-wall-like" potential at a separation of 8.0 A at zero field, signaling a crossover in behavior as the plate dimension decreases, but the water density still diminishes with increasing field strength. These observations could have implications for the behavior of thin films of water between surfaces in real physical and biological systems.     

Vibrational energy relaxation of large-amplitude vibrations in liquids

Given the limited intermolecular spaces available in dense liquids, the large amplitudes of highly excited, low frequency vibrational modes pose an interesting dilemma for large molecules in solution. We carry out molecular dynamics calculations of the lowest frequency ("warping") mode of perylene dissolved in liquid argon, and demonstrate that vibrational excitation of this mode should cause identifiable changes in local solvation shell structure. But while the same kinds of solvent structural rearrangements can cause the non-equilibrium relaxation dynamics of highly excited diatomic rotors in liquids to differ substantially from equilibrium dynamics, our simulations also indicate that the non-equilibrium vibrational energy relaxation of large-amplitude vibrational overtones in liquids should show no such deviations from linear response. This observation seems to be a generic feature of large-moment-arm vibrational degrees of freedom and is therefore probably not specific to our choice of model system: The lowest frequency (largest amplitude) cases probably dissipate energy too quickly and the higher frequency (more slowly relaxing) cases most likely have solvent displacements too small to generate significant nonlinearities in simple nonpolar solvents. Vibrational kinetic energy relaxation, in particular, seems to be especially and surprisingly linear.     

Vibrational energy relaxation of small molecules and ions in liquids

A theoretical/computational framework for determining vibrational energy relaxation rates, pathways, and mechanisms, for small molecules and ions in liquids, is presented. The framework is based on the system—bath coupling approach, Fermi’s golden rule, classical time-correlation functions, and quantum correction factors. We provide results for three specific problems: relaxation of the oxygen stretch in neat liquid oxygen at 77 K, relaxation of the water bend in chloroform at room temperature, and relaxation of the azide ion anti-symmetric stretch in water at room temperature. In each case, our calculated lifetimes are in reasonable agreement with experiment. In the latter two cases, theory for the observed solvent isotope effects illuminates the relaxation pathways and mechanisms. Our results suggest several propensity rules for both pathways and mechanisms.     

Photodissociation of diphenyldiazomethane and energy relaxation in the diphenylcarbene fragment

The dynamics of photodissociation of diphenyldiazomethane and energy relaxation in the diphenylcarbene fragment are investigated using picosecond laser methods. The equilibrium constant, free energy difference, and energy separation between the low-lying singlet and ground triplet states of the carbene are obtained.     

Vibrational energy relaxation of isotopically labeled amide I modes in cytochrome c: theoretical investigation of vibrational energy relaxation rates and pathways

With use of a time-dependent perturbation theory, vibrational energy relaxation (VER) of isotopically labeled amide I modes in cytochrome c solvated with water is investigated. Contributions to the VER are decomposed into two contributions from the protein and water. The VER pathways are visualized by using radial and angular excitation functions for resonant normal modes. Key differences of VER among different amide I modes are demonstrated, leading to a detailed picture of the spatial anisotropy of the VER. The results support the experimental observation that amide I modes in proteins relax with subpicosecond time scales, while the relaxation mechanism turns out to be sensitive to the environment of the amide I mode.