Transient instability in case II diffusion

A well-known model of one-dimensional Case II diffusion is reformulated in two dimensions. This 2-D model is used to study the stability of 1-D planar Case II diffusion to small spatial perturbations. An asymptotic solution based on the assumption of small perturbations and a small driving force is developed. This analysis reveals that while 1-D planar diffusion is indeed asymptotically stable to small spatial perturbations, it may exhibit a transient instability. That is, although any small perturbation is damped out over sufficiently long times, the amplitude of any perturbation initially grows with time. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 2941–2947, 1998     

Diffusion of condensable vapors in single adsorbent particles measured via concentration-swing frequency response

A concentration-swing frequency response method is extended to examine mass transfer mechanisms and the concentration dependence of mass transfer rates for adsorption of condensable vapors in single adsorbent particles. The adsorption kinetics of water and hexane in BPL activated carbon and the adsorption of water in silica gel are determined at several different concentrations. The mechanism that best describes the adsorption of water in BPL activated carbon is nanopore diffusion. The diffusivity of water in BPL activated carbon has a clear minimum at approximately P/Po = 0.5, and the concentration dependence of the diffusion data are not described well by the Darken relationship. Both nanopore diffusion and the Glueckauf linear driving force models can be used to describe the diffusion of hexane in BPL activated carbon for the pressure range studied, and the dependence of the diffusivity on concentration can be described approximately using the Darken relationship. However, the diffusion of water in silica gel cannot be described by the nanopore diffusion model and is best characterized by the Glueckauf linear driving force model. The results illustrate the ability of concentration-swing frequency response to accurately determine adsorption rate mechanisms and quantify the complex adsorption kinetics of condensable vapors using small quantities of adsorbent.     

低浓度三分子模型差速流动引起的化学不稳定性

建立了低浓度三分子反应模型反应-流动-扩散方程,理论分析了出现差速流动化学不稳定的条件,得到了临界流动速率c和扰动波包的群速度vg,讨论了扰动增长率与流速的关系,并理论研究了出现不稳定时系统的时、空结构.研究结果表明,化学反应在低浓度条件下也可能出现差速流动引起的化学不稳定.     

Comparative evaluation of MMPBSA and XSCORE to compute binding free energy in XIAP-peptide complexes

Evaluation of binding free energy in receptor-ligand complexes is one of the most important challenges in theoretical drug design. Free energy is directly correlated to the thermodynamic affinity constant, and, as a first step in druglikeness, a lead compound must have this constant in the range of micro- to nanomolar activity. Many efforts have been made to calculate it by rigorous computational approaches, such as free energy perturbation or linear response approximation. However, these methods are still computationally expensive. We focus our work on XIAP, an antiapoptotic protein whose inhibition can lead to new drugs against cancer disease. We report here a comparative evaluation of two completely different methodologies to estimate binding free energy, MMPBSA (a force field based function) and XSCORE (an empirical scoring function), in seven XIAP-peptide complexes using a representative set of structures generated by previous molecular dynamics simulations. Both methods are able to predict the experimental binding free energy with acceptable errors, but if one needs to identify slight differences upon binding, MMPBSA performs better, although XSCORE is not a bad choice taking into account the low computational cost of this method.     

Distant-dipole field in liquids and diffusion: a perturbative approach

A perturbative approach is employed to solve the Bloch-Torrey equations in the presence of distant-dipole fields in nuclear magnetic resonance. The procedure, although only carried out to first order in the perturbation parameter a=1/k2Dtaud, could, in principle, be generalized to higher orders. Here D is the diffusivity, taud the dipolar demagnetization time, and k is the wave vector of the spatial modulation of magnetization produced by the magnetic field gradient. The results are especially interesting for dilute binary mixtures consisting of molecular species with different diffusivities. In this case the calculated two-dimensional correlation spectroscopy revamped by asymmetric Z-gradient echo detection spectra are shown to be free from some inadequacies resulting from a simplistic application of standard approximations.     

Defect controlled dynamics of nematic liquids

The long time dynamical response of a nematic liquid exhibiting banded textures (inversion walls) during the twist Freedericksz transition is presented. A dynamical model of approach to equilibrium through defect interaction and the resulting dissolution of the banded textures is presented. A linear stability analysis shows that splay-bend inversion wall defects are unstable to two dimensional infinitesimal perturbations. A model of inversion wall segment collapse with production of a disclination line pair is given. The energy-momentum tensor gives the force of interaction between inversion walls and disclination lines. A perturbation analysis gives the evolution of the director field in closed form. Entropy production gives the velocity of each line. The growth law governing the wall dissolution is given.     

Using free energy perturbation to predict effects of changing force field parameters on computed conformational equilibriums of peptides

We propose a method that may allow data about the conformational equilibriums of peptides to enter the parameter calibration phase in force field developments. The method combines free energy perturbation with techniques for extensive sampling in the conformational space. It predicts shifts in computed conformational equilibriums in response to separate or combined perturbations of force field parameters. As an example we considered a force field associated with an implicit solvent model. We considered two different approaches to define conformational states of four peptides. One is based on reaction coordinates and two-dimensional free energy surfaces. The other is based on the clustering analysis of sampled conformations. Effects of perturbing various model parameters on the equilibriums between nativelike states with other conformational states were considered. For one type of perturbation predicted to have consistent effects on different peptides, the predictions have been verified by actual simulations using a perturbed model.     

Further Validation of the Quartic Concentration Profile Approximation for Describing Intraparticle Transport in Cyclic Adsorption Processes

Models developed previously by the authors that describe nonlinear adsorption, and simultaneous pore and surface diffusion in a single particle, that are based on intraparticle quartic and parabolic concentration profile approximations, and that utilize the summation of the gas and adsorbed phases approach in the material balance formulations, were further validated under more diverse, yet more realistic, cycling conditions. Periodic square, sinusoidal and triangular wave functions were used to more accurately represent the periodic boundary conditions that the external surface of an adsorbent particle may be exposed to during repeated adsorption and desorption cycles in a fixed bed adsorber. Analytical solutions that describe the periodic uptake and release of the adsorbate by the adsorbent were obtained for all three periodic wave functions, and for both the quartic and parabolic profile approximations. By comparing the predictions obtained from both models with the exact numerical solution, the superiority of the quartic model over the parabolic model was clearly demonstrated for all wave functions, and for a wide range of adsorbate-adsorbent systems and bulk concentrations. Excellent agreement between the quartic and exact models was obtained in most cases. In general, the predictions improved as the wave function changed more gradually with time (triangular more gradual than sinusoidal and sinusoidal more gradual than square), as the degree of mathematical linearity of the adsorbate-adsorbent system increased, and as the maximum external surface concentration decreased (an isotherm nonlinearity effect). Subtle differences in the predictive ability of the new approximate models, stemming from the use of the different wave functions, were exposed. Overall, these results exemplify the importance of comparing the predictive ability of new approximate models that describe intraparticle transport under more diverse cycling conditions than are typically utilized in the literature, which has been dominated by the square wave function.     

Using one‐step perturbation to predict the effect of changing force‐field parameters on the simulated folding equilibrium of a β‐peptide in solution

Computer simulation using molecular dynamics is increasingly used to simulate the folding equilibria of peptides and small proteins. Yet, the quality of the obtained results depends largely on the quality of the force field used. This comprises the solute as well as the solvent model and their energetic and entropic compatibility. It is, however, computational very expensive to perform test simulations for each combination of force‐field parameters. Here, we use the one‐step perturbation technique to predict the change of the free enthalpy of folding of a β‐peptide in methanol solution due to changing a variety of force‐field parameters. The results show that changing the solute backbone partial charges affects the folding equilibrium, whereas this is relatively insensitive to changes in the force constants of the torsional energy terms of the force field. Extending the cut‐off distance for nonbonded interactions beyond 1.4 nm does not affect the folding equilibrium. The same result is found for a change of the reaction‐field permittivity for methanol from 17.7 to 30. The results are not sensitive to the criterion, e.g., atom‐positional RMSD or number of hydrogen bonds, that is used to distinguish folded and unfolded conformations. Control simulations with perturbed Hamiltonians followed by backward one‐step perturbation indicated that quite large perturbations still yield reliable results. Yet, perturbing all solvent molecules showed where the limitations of the one‐step perturbation technique are met. The evaluated methodology constitutes an efficient tool in force‐field development for molecular simulation by reducing the number of required separate simulations by orders of magnitude. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Study of pair correlation in three-electron atoms

Pair correlation in the ground state of the Li isoelectronic sequence is studied through four approximate wave functions which incorporate inter- and intrashell pair correlation. Of these functions, two possess symmetry appropriate to a three-electron system, while two do not. The functions are not variational functions in the usual sense. They are instead fixed linear combinations of products of orbitals and pair functions for the appropriate states of two-electron atoms. They are considered here as zero-order approximations to the exact wave functions, and the corresponding zero-order Hamiltonians are obtained. The simplest of these functions is improved by the introduction of a screening parameter for the “outer” electron. This latter function is found to be a satisfactory compromise between accuracy and simplicity and is proposed for study via higher-order perturbation theory.     

Pattern formation in excitable media with concentration-dependent diffusivities

We study a model of pattern formation in an excitable medium with concentration-dependent diffusivities. The reaction terms correspond to a two-variable Gray-Scott model in which the system has only one stable steady state. The diffusion coefficients of the two species are assumed to have a functional relationship with the concentration of the autocatalyst. A transition from self-replicating behavior to stationary spots is observed as the influence of the local autocatalyst concentration on the diffusion process increases. Notably, the transition occurs even though there is no change in the relative diffusivities of the activator and inhibitor. The observed time-independent patterns exhibit an unusual dependence on the size and geometry of an initial perturbation. Initial perturbations with a large spatial size, for example, sometimes revert to the homogeneous equilibrium state, whereas perturbations of smaller spatial extent develop into stable spots at the same parameter values.     

Contribution of concentration-dependent surface diffusion in ternary adsorption kinetics of ethane, propane and n-butane in activated carbon

The role of concentration-dependent surface diffusion in the adsorption kinetics of a multicomponent system is investigated in this paper. Ethane, propane and n-butane are selected as the model adsorbates and Ajax activated carbon as the model adsorbent. Adsorption equilibrium isotherm and dynamic parameters extracted from single-component systems are used to predict the ternary adsorption equilibria and kinetics. The effect of concentration-dependent surface diffusion on the adsorption kinetics predictions is studied by comparing the results of two mathematical models with the experimental data. Three diffusion mechanisms, macropore, surface and micropore diffusions are incorporated in both models. The distinction between these two models is the use of the chemical potential gradient as the driving force for the diffusion of the adsorbed species in one model and the concentration gradient in the other. It was found that the model using the chemical potential gradient provides a better prediction of the ternary adsorption kinetics data, suggesting the importance of the concentration dependency of the surface diffusion, which is implicitly reflected in the chemical potential gradient. The kinetic model predictions are also affected by the way how single-component adsorption equilibrium isotherm data are fitted.     

Perturbation theory for the radial distribution function for simple polar fluids

The radial distribution function for a fluid whose molecules interact according to the Stockmayer potential was calculated by means of thermodynamic perturbation theory using two different approximations for the perturbation term and was compared with computer simulation results. The approximation based on the Percus-Yevick equation was found to be in much better agreement with the simulations than was the “simplified superposition approximation” to the perturbation term.     

Sensitivity of PSA process performance to input variables

Mathematical models for pressure swing adsorption (PSA) processes essentially require the simultaneous solutions of mass, heat and momentum balance equations for each step of the process using appropriate boundary conditions for the steps. The key model input variables needed for estimating the separation performance of the process are the multicomponent adsorption equilibria, kinetics and heats of adsorption for the system of interest. A very detailed model of an adiabatic Skarstrom PSA cycle for production of high purity methane from a ethylene-methane bulk mixture is developed to study the sensitivity of the process performance to the input variables. The adsorption equilibria are described by the heterogeneous Toth model which accounts for variations of isosteric heats of adsorption of the components with adsorbate loading. A linear driving force model is used to describe the kinetics. The study shows that small errors in the heats of adsorption of the components can severely alter the overall performance of the process (methane recovery and productivity). The adsorptive mass transfer coefficients of the components also must be known fairly accurately in order to obtain precise separation performance.     

DIFFUSIVITY OF RARE EARTH ION IN POROUS ION EXCHANGE RESINS

TheporousionexchangeresinshavebecomeanimportantreactivepolarermaterialwhicharewidelyappliedinindustrialoperationsHowever,afewstudi..[l--3]reportedtheintraparticlediffusivityofporousionexchangers.Theionexchangedisplacementprocessonporousresinbedforseparationofrareearthsistheoneofthebestwaystoenhancetheeffectivityofthismethod.TounderstandthediffusionoftheionintheresinisveryavailablefolimproVingtheprocess.EXPERIMENTAL1.Pre--experimentsAllthereagentsusedareA.R.grade.152'154Euisusedasaradiot…     

How Do Metal Ions Modulate the Rate-Determining Electron-Transfer Step in Cytochrome P450 Reactions?

Cytochrome P450 (CYP450) enzymes play important roles in maintaining human health and their reaction rates are dependent on the first electron transfer from the reduction partner. Interestingly, experimental work has shown that this step is highly influenced by the addition of metal ions. To understand the effect of external perturbations on the CYP450 first reduction step, we have performed a computational study with model complexes in the presence of metal and organic ions, solvent molecules, and an electric field. The results show that these medium-range interactions affect the driving force as well as electron-transfer rates dramatically. Based on the location, distance, and direction of the ions/electric field, the catalytic reaction rates are enhanced or impaired. Calculations on a large crystal structure with bonded alkali metal ions indicated inhibition patterns of the ions. Therefore, we predict that the active forms of the natural CYP450 isozymes will not have more than one alkali metal ion bound in the second-coordination sphere. As such, this study provides an insight into the activity of CYP450 enzymes and the effects of ions and electric field perturbations on their activity.     

Localized impurity states in the Hartree-Fock,LCAO approximation II. The F Center in KCI

We apply the techniques of a previous paper (I) to the F center in KCl. Our purpose is to place the application of Hartree-Fock methods to the F center on a firm theoretical basis by calculating in a consistent manner the magnitude and effect of approximations commonly made in less complete treatments. It is shown that the familiar point-ion approximations and crystal-field approximations with partial consideration of exchange effects are special cases of our results. We compute wave functions and energies step by step for each of the various levels of approximation possible with our model. It is found that the functions resulting from the point-ion model are not good approximations to the final wave functions. Our results show that exchange effects with at least the first two shells of nearest neighbors should be considered since they are of the same order of magnitude as terms in the point-ion model. Overlaps of the F-center function with ion functions out to sixth neighbors are considered. The absorption energy for the F center is calculated to be 0.1619 Ry as compared with the experimentally observed energy of 0.170 Ry. The magnetic hyperfine structure contact terms are calculated for the first two shells of nearest neighbor ions, using approximate orthogonalized functions, and found to be 29.7 Mc/h for the nearest neighbor K⁺ ions and 10.9 Mc/h for the next nearest neighbor Cl^? ions. The experimentally observed values are 21.6 and 7.0, respectively. Given these differences and the excessively low values of the one-electron energies, it is concluded that electronic and ionic polarization effects in the ionized crystal states must be considered to calculate accurate F-center wave functions and absolute energy levels.     

A new strategy for the evaluation of force parameters from quantum mechanical computations

A new strategy for the determination of force parameters is presented. The equilibrium values appearing in the force field equations representing the “stretching” and “bending” of bonds are directly determined from quantum mechanical calculations without geometrical restrictions. The determination of the force parameters is carried out by means of a rigorous fitting between the quantum mechanic and the molecular mechanical energy variations arising from the perturbation of the geometric variables. The strategy presented here has been incorporated into a computer program named PAPQMD, which was developed in order to provide nonquantum mechanical experts with a powerful tool for the determination of approximate force parameters. The program was developed upon the assumption that force parameters are not universal, but they strongly depend on the molecular environment. This implies that the parametrization procedure should be done in a molecular model close to the molecule or molecules to be studied by means of molecular mechanical or dynamic methods, and consequently, it is no longer supposed that the variation of one geometrical parameter does not affect the rest of the molecular geometry. PAPQMD performs the fitting between molecular mechanics and quantum mechanical energies considering all the perturbations that the modification in one geometric variable causes in all the others, enabling the parametrization even of large molecules. The ability of our method to reproduce experimentally derived force parameters is discussed and compared with the widely used Hopfinger's strategy. The study of the behavior of PAPQMD and Hopfinger's strategies for reproducing the force parameters of two complex molecules demonstrates the superiority of the methodology presented here.     

Multiconfiguration Pair-Density Functional Theory for Transition Metal Silicide Bond Dissociation Energies,Bond Lengths,and State Orderings

Transition metal silicides are promising materials for improved electronic devices, and this motivates achieving a better understanding of transition metal bonds to silicon. Here we model the ground and excited state bond dissociations of VSi, NbSi, and TaSi using a complete active space (CAS) wave function and a separated-pair (SP) wave function combined with two post-self-consistent field techniques: complete active space with perturbation theory at second order and multiconfiguration pair-density functional theory. The SP approximation is a multiconfiguration self-consistent field method with a selection of configurations based on generalized valence bond theory without the perfect pairing approximation. For both CAS and SP, the active-space composition corresponds to the nominal correlated-participating-orbital scheme. The ground state and low-lying excited states are explored to predict the state ordering for each molecule, and potential energy curves are calculated for the ground state to compare to experiment. The experimental bond dissociation energies of the three diatomic molecules are predicted with eight on-top pair-density functionals with a typical error of 0.2 eV for a CAS wave function and a typical error of 0.3 eV for the SP approximation. We also provide a survey of the accuracy achieved by the SP and extended separated-pair approximations for a broader set of 25 transition metal–ligand bond dissociation energies.