Diffusion Approach to Long Distance Charge Migration in DNA: Time-Dependent and Steady-State Analytical Solutions for the Product Yields

In this study we report analytical solutions for both time-dependent and steady-state problems of unbiased charge transfer through a regular DNA sequence via a hopping mechanism. The phenomenon is treated as a diffusion of charge in a one-dimensional array of equally spaced and energetically equivalent temporary trapping sites. The solutions take into account the rates of charge hopping (k), side reactions (k(r)), and charge transfer to a terminal charge acceptor (k(t)). A detailed analysis of the time-dependent problem is performed for the diffusion-controlled regime, i.e., under the assumption that k(t) > k, which is also equivalent to the fast relaxation limit of charge trapping. The analysis shows that the kinetics of charge hopping through DNA is always multiexponential, but under certain circumstances it can be asymptotically approximated by a single-exponential term. In that case, the efficiency of charge transfer can be characterized by a single rate constant k(CT) = 1.23kN(-2) + k(r), where N is the DNA length expressed in terms of the number of equidistant trapping sites and k(r) is the rate of competing chemical processes. The absolute yield of charge transfer under steady-state conditions in general is obtained as Y(infinity) = omega [alpha sinh(alphaN) + omega cosh(alphaN)](-1), where alpha = (2k(r)/k)(1/2) and omega = 2k(t)/k. For the diffusion-controlled regime and small N, in particular, it turns into the known "algebraic" dependence Y(infinity) = [1 + (k(r)/k)N(2)](-1). At large N the solution is asymptotically exponential with the parameter alpha mimicking the tunneling parameter beta in agreement with earlier predictions. Similar equations and distance dependencies have also been obtained for the damage ratios at the intermediate and terminal trapping sites in DNA. The nonlinear least-squares fit of one of these equations to experimental yields of guanine oxidation available from the literature returns kinetic parameters that are in reasonable agreement with those obtained by Bixon et al. [Proc. Natl. Acad. Sci. U.S.A.1999, 96, 11713-11716] by numerical simulations, suggesting that these two approaches are physically equivalent.     

Influence of the 6th and 10th spatial harmonics on the peak shape of a quadrupole mass filter with round rods

The influence of the ratio of the rod radius, r, to field radius, r(0), on the peak shape for a linear quadrupole mass filter constructed with round rods has been investigated. The expansion of the potential in multipoles, phi(N),Phi(x, y) = sum(infinity)(N=0)A(N)phi(N)/r(N)(0) has been considered, and the peak shape and resolution have been determined by numerical calculation of ion trajectories in quadrupoles with different ratios, r/r(0). Geometries that make the dodecapole term (A(6)) zero (r/r(0) = 1.14511) do not give the best performance because the contribution of the 20-pole term, A(10), must be considered. The optimum ratio is r/r(0) approximately 1.13. With this ratio the dodecapole term (A(6)) is ca. 1 x 10(-3), but its effects are partially compensated by the A(10) term which has similar magnitude, but opposite sign.     

Effective multipoles and Yukawa electrostatics in dressed molecule theory

In this paper we derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvent. The solute and solvent molecules can have arbitrary sizes, shapes, and internal charge distributions. We use the exact statistical mechanical definition of renormalized charge distributions coming from "dressed molecule theory" to determine the effective multipoles of a molecule immersed in an electrolyte. The effects of many-body correlations are fully included in our formally exact theory. We restrict ourselves to sufficiently dilute solutions so the screened Coulomb potential decays for large distances like a Yukawa function, exp(-kappa r)/r, where r is the distance and 1/kappa is the decay length (it is normally different from the Debye length). The resulting "Yukawa electrostatics" differ in many respects from ordinary, unscreened electrostatics. The "Yukawa charge" of a molecule (the lowest order moment in the multipolar expansion) is in general not equal to its Coulombic charge and it is not the integral of the renormalized charge distribution of the molecule. Moreover, as shown in this paper, the multipolar expansion of the Yukawa potential does not correspond, contrary to the case of the Coulomb potential, to its asymptotic expansion for large r. As a consequence, the charge term in the multipolar expansion is not the leading term in the asymptotic expansion. Instead, for large r values, multipoles of all orders contribute to the leading asymptotic term. Thus, the electrostatic potential from, for example, an electroneutral solvent molecule in an electrolyte solution has generally the same range as that from an ion. The proper asymptotic expansion for electrostatic interactions in electrolytes is derived. It is briefly shown how the multipole expansion formalism can also be applied in the Poisson-Boltzmann approximation for primitive model electrolytes.     

Self-diffusion coefficient of the hard-sphere fluid: system size dependence and empirical correlations

Molecular dynamics simulations have been used to calculate the self-diffusion coefficient, D, of the hard sphere fluid over a wide density range and for different numbers of particles, N, between 32 and 10 976. These data are fitted to the relationship D = D(infinity) - AN(-alpha) where the parameters D(infinity), A, and alpha are all density-dependent (the temperature dependence of D can be trivially scaled out in all cases). The value alpha = 1/3 has been predicted on the basis of hydrodynamic arguments. In the studied system size range, the best value of alpha is approximately 1/3 at intermediate packing fractions of approximately 0.35, but increases in the low- and high-density extremes. At high density, the scaling follows more closely that of the thermodynamic properties, that is, with an exponent of order unity. At low packing fractions (less than approximately 0.1), the exponent increases again, appearing to approach a limiting value of unity in the zero-density limit. The origin of this strong N dependence at low density probably lies in the divergence in the mean path between collisions, as compared with the dimensions of the simulation cell. A new simple analytical fit formula based on fitting to previous simulation data is proposed for the density dependence of the shear viscosity. The Stokes-Einstein relationship and the dependence of D on the excess entropy were also explored. The product Deta(s)p with p = 0.975 was found to be approximately constant, with a value of 0.15 in the packing fraction range between 0.2 and 0.5.     

Multiscale simulation of irreversible deposition in presence of double layer interactions

Sequential lattice Monte Carlo simulations, in which the transition probabilities are derived from the discrete form of the continuum-level mass conservation law, are used to predict the morphology of colloidal deposits. The simulations account for particle-surface (P-S) and particle-particle (P-P) electrostatic and van der Waals interactions. Simulation results for maximum coverage for monolayer deposition are in quantitative agreement with the hard-sphere RSA jamming limit. Moreover, as reported in earlier studies, monolayer simulations in the absence of P-S interactions qualitatively predict the monotonic increases in fractional coverage with increasing ionic strength, characterized by the Debye screening length (kappa a). Monolayer simulations with P-S interactions show that the dependence of fractional coverage on kappa a is strongly influenced by the ratio of particle to surface potentials (Psi(p)/Psi(s)). P-S and P-P forces achieve their respective maximum at different values of kappa a leading to a nonmonotonic trend in surface coverage as a function of kappa a. These results indicate that the incorporation of P-S interactions into colloidal deposition studies allows more accurate interpretation of the experimental data. In multilayer deposition simulations, balance between long-ranged weak interactions and short-ranged strong interactions between P-P and P-S, coupled with physical screening effects, resulted in widely varying coverages with height of the deposit, ionic strength, and Psi(p)/Psi(s). Moreover, fractal dimension of the deposit ranged from approximately 1 (kappa a < 1) to 1.7 (kappa a > 1). Qualitative kinetic analysis showed widely varying deposition rates in different layers depending on Psi(p)/Psi(s) and ionic strength. The multilayer system approached the monolayer system in the limit kappa a--> infinity and Psi(p)/Psi(s)--> infinity.     

Computer investigations on the asymptotic behavior of the rate coefficient for the annihilation reaction A + A → product and the trapping reaction in three dimensions

We have performed intensive computer simulations of the irreversible annihilation reaction: A + A → C + C and of the trapping reaction: A + B → C + B for a variety of three-dimensional fluids composed of identical spherical particles. We have found a significant difference in the asymptotic behavior of the rate coefficients for these reactions. Both the rate coefficients converge to the same value with time t going to infinity but the convergence rate is different: the O(t(-1/2)) term for the annihilation reaction is higher than the corresponding term for the trapping reaction. The simulation results suggest that ratio of the terms is a universal quantity with the value equal to 2 or slightly above. A model for the annihilation reaction based on the superposition approximation predicts the difference in the O(t(-1/2)) terms, but overestimates the value for the annihilation reaction by about 30%. We have also performed simulations for the dimerization process: A + A → E, where E stands for a dimer. The dimerization decreases the reaction rate due to the decrease in the diffusion constant for A. The effect is successfully predicted by a simple model.     

Virial series for fluids of hard hyperspheres in odd dimensions

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of the Percus-Yevick equation for a fluid of hard spheres in (odd) d dimensions is used to investigate the convergence properties of the resulting virial series. This is done both for the virial and compressibility routes, in which the virial coefficients B(j) are expressed in terms of the solution of a set of (d-1)/2 coupled algebraic equations which become nonlinear for d>/=5. Results have been derived up to d=13. A confirmation of the alternating character of the series for d>/=5, due to the existence of a branch point on the negative real axis, is found and the radius of convergence is explicitly determined for each dimension. The resulting scaled density per dimension 2eta(1/d), where eta is the packing fraction, is wholly consistent with the limiting value of 1 for d-->infinity. Finally, the values for B(j) predicted by the virial and compressibility routes in the Percus-Yevick approximation are compared with the known exact values [N. Clisby and B. M. McCoy, J. Stat. Phys. 122, 15 (2006)].     

Toward a less costly but accurate calculation of the CCSD(T)/CBS noncovalent interaction energy

The popular method of calculating the noncovalent interaction energies at the coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] theory level in the complete basis set (CBS) limit was to add a CCSD(T) correction term to the CBS second-order Møller-Plesset perturbation theory (MP2). The CCSD(T) correction term is the difference between the CCSD(T) and MP2 interaction energies evaluated in a medium basis set. However, the CCSD(T) calculations with the medium basis sets are still very expensive for systems with more than 30 atoms. Comparatively, the domain-based local pair natural orbital coupled-cluster method [DLPNO-CCSD(T)] can be applied to large systems with over 1,000 atoms. Considering both the computational accuracy and efficiency, in this work, we propose a new scheme to calculate the CCSD(T)/CBS interaction energies. In this scheme, the MP2/CBS term keeps intact and the CCSD(T) correction term is replaced by a DLPNO-CCSD(T) correction term which is the difference between the DLPNO-CCSD(T) and DLPNO-MP2 interaction energies evaluated in a medium basis set. The interaction energies of the noncovalent systems in the S22, HSG, HBC6, NBC10, and S66 databases were recalculated employing this new scheme. The consistent and tight settings of the truncation parameters for DLPNO-CCSD(T) and DLPNO-MP2 in this noncanonical CCSD(T)/CBS calculations lead to the maximum absolute deviation and root-mean-square deviation from the canonical CCSD(T)/CBS interaction energies of less than or equal to 0.28 kcal/mol and 0.09 kcal/mol, respectively. The high accuracy and low cost of this new computational scheme make it an excellent candidate for the study of large noncovalent systems.     

Crystal structures of two polymorphs of Ca3[Al2N4

Green transparent single crystals of alpha-Ca3[Al2N4] (monoclinic, P2(1)/c, No. 14, a = 957.2(3) pm, b = 580.2(3) pm, c = 956.3(5) pm, beta = 111.62(3) degrees; Z = 4) were obtained from reactions of mixtures of the representative metals with nitrogen above temperatures of 1000 degrees C. beta-Ca3[Al2N4] (monoclinic, C2/c, No. 15, a = 1060.6(2) pm, b = 826.0(2) pm, c = 551.7(1) pm, beta = 92.1(1) degrees; Z = 4) was formed as a byproduct of a reaction of calcium with alumina under nitrogen at T = 930 degrees C in form of colorless crystals. The crystal structures of the two polymorphs contain edge- and corner-sharing AlN4 tetrahedra, leading to different layered anionic partial structures: infinity 2[AlN2/2N2/3)2(AlNN2/2N1/3)6/3(12-)] in the alpha-phase and infinity 2[Al2N2N4/2(6-)] in the beta-polymorph.     

Model calculations of the spontaneous curvature, mean and Gaussian bending constants for a thermodynamically open surfactant film

The spontaneous curvature (H(0)), mean and Gaussian bending constants (k(c) and k (c)), as defined in the well-known Helfrich expression, have been calculated from a detailed model for a thermodynamically open surfactant layer. The effect of head group cross-section area, surfactant tail length and electrolyte concentration for monovalent ionic surfactants have been investigated. Geometrical packing constraints subjected to the aggregated hydrocarbon tails and electrostatics are found to be the dominant contributions to H(0), k(c) and k (c). In addition, the transition from spherocylindrical micelles to vesicles were investigated in terms of the three parameters and the following simple expressions were derived as criteria for coexistence between micelles and vesicles H(0)=1/4 xi and N(ves)/N(mic)=exp[4 pi(k(c)+k (c))/kT], where xi is the thickness of the hydrocarbon part of the film and N(mic) and N(ves) the average aggregation numbers of micelles and vesicles, respectively. However, it is found that the ratio N(ves)/N(mic) is order of magnitudes too large for vesicles to form at all in charged single-surfactant systems where the surfactant head is of moderate size.     

First stretching overtone of BiH3: an extreme local-mode case for XH3-type molecule?

The first stretching overtone region of short-lived, formerly inaccessible BiH3 near 3405 cm(-1) has been measured by Fourier-transform infrared spectroscopy with a resolution of 0.0066 cm(-1). Only the 2nu1(A1)/nu1+nu3(E) band system has been observed. Rotational analysis, with transitions reaching J'max=14, has revealed almost perfect local-mode behavior for the upper states denoted as (200A1/E) in the local-mode notation. Ratios of vibration-rotation interaction parameters q(eff)/alpha(eff)(BB) and r(eff)/alpha(eff)(BC), and the appropriate rotational constant differences, are in good agreement with theoretical local-mode limit values. A simple stretching vibrational model reproduces the observed vibrational term values well, and the potential parameters obtained are close to true values.     

Improved configuration space sampling: Langevin dynamics with alternative mobility

We present a new and efficient method for determining optimal configurations of a large number (N) of interacting particles. We use a coarse-grained stochastic Langevin equation in the overdamped limit to describe the dynamics of this system and replace the standard mobility by an effective space dependent inverse Hessian correlation matrix. Due to the analogy of the drift term in the Langevin equation and the update scheme in Newton's method, we expect accelerated dynamics or improved convergence in the convex part of the potential energy surface Phi. The stochastic noise term, however, is not only essential for proper thermodynamic sampling but also allows the system to access transition states in the concave parts of Phi. We employ a Broyden-Fletcher-Goldfarb-Shannon method for updating the local mobility matrix. Quantitative analysis for one and two dimensional systems shows that the new method is indeed more efficient than standard methods with constant effective friction. Due to the construction, our effective mobility adapts high values/low friction in configurations which are less optimal and low values/high friction in configurations that are more optimal.     

Properties of Coulomb crystals: rigorous results

Rigorous equalities and bounds for several properties of Coulomb crystals are presented. The energy e(N) per particle pair is shown to be a nondecreasing function of the particle number N for all clusters described by double-power-law pairwise-additive potentials epsilon(r) that are unbound at both r-->0 and r-->infinity. A lower bound for the ratio of the mean reciprocal crystal radius and e(N) is derived. The leading term in the asymptotic expression for the shell capacity that appears in the recently introduced approximate model of Coulomb crystals is obtained, providing in turn explicit large-N asymptotics for e(N) and the mean crystal radius. In addition, properties of the harmonic vibrational spectra are investigated, producing an upper bound for the zero-point energy.     

气液色谱法研究聚合物/溶剂体系气液平衡

 用气液色谱法测定了聚二甲基硅氧烷（PDMS）／溶剂、聚甲基丙烯酸甲酯（PMMA）／溶剂体系在不同温度下以质量分数表示的无限稀溶剂活度系数和Flory－Huggins相互作用参数。应用UNIFAC和UNIFAC－FV模型对PDMS／溶剂、PMMA／溶剂体系中以质量分数表示的无限稀溶剂活度系数进行了估算。结果表明,用这两个模型预测PDMS／溶剂、PMMA／溶剂体系中的无限稀溶剂活度系数有待修正或采用其它模型进行估算。     

Anisotropic local motions and location of amide protons in proteins

A new method has been developed to obtain dynamic and structural information about peptide planes in proteins by a combination of measurements of weak short-range cross-correlation rates R(H(N)N/NC') that are due to concerted fluctuations of the H(N)-N and N-C' dipole-dipole interactions and stronger long-range cross-correlation rates R(C'H(N)/H(N)N) and R(NH(N)/H(N)C(alpha)). The rates were interpreted using the axially symmetric Gaussian axial fluctuation model (GAF). The oscillation amplitudes as well as the positions of H(N) atoms with respect to peptide planes in ubiquitin were determined. Most N-H(N) bonds were found not to lie exactly along the bisector of the N-C' and N-C(alpha) bonds but to be slightly tilted toward the carbon-terminal side of the peptide.     

Extrapolation of electron correlation energies to finite and complete basis set targets

The electron correlation energy of two-electron atoms is known to converge asymptotically as approximately (L+1)(-3) to the complete basis set limit, where L is the maximum angular momentum quantum number included in the basis set. Numerical evidence has established a similar asymptotic convergence approximately X(-3) with the cardinal number X of correlation-consistent basis sets cc-pVXZ for coupled cluster singles and doubles (CCSD) and second order perturbation theory (MP2) calculations of molecules. The main focus of this article is to probe for deviations from asymptotic convergence behavior for practical values of X by defining a trial function X(-beta) that for an effective exponent beta=beta(eff)(X,X+1,X+N) provides the correct energy E(X+N), when extrapolating from results for two smaller basis sets, E(X) and E(X+1). This analysis is first applied to "model" expansions available from analytical theory, and then to a large body of finite basis set results (X=D,T,Q,5,6) for 105 molecules containing H, C, N, O, and F, complemented by a smaller set of 14 molecules for which accurate complete basis set limits are available from MP2-R12 and CCSD-R12 calculations. beta(eff) is generally found to vary monotonically with the target of extrapolation, X+N, making results for large but finite basis sets a useful addition to the limited number of cases where complete basis set limits are available. Significant differences in effective convergence behavior are observed between MP2 and CCSD (valence) correlation energies, between hydrogen-rich and hydrogen-free molecules, and, for He, between partial-wave expansions and correlation-consistent basis sets. Deviations from asymptotic convergence behavior tend to get smaller as X increases, but not always monotonically, and are still quite noticeable even for X=5. Finally, correlation contributions to atomization energies (rather than total energies) exhibit a much larger variation of effective convergence behavior, and extrapolations from small basis sets are found to be particularly erratic for molecules containing several electronegative atoms. Observed effects are discussed in the light of results known from analytical theory. A carefully calibrated protocol for extrapolations to the complete basis set limit is presented, based on a single "optimal" exponent beta(opt)(X,X+1,infinity) for the entire set of molecules, and compared to similar approaches reported in the literature.     

Rapid gas analyses for the investigation of spontaneous combustion using capillary gas chromatography

A simple and fast but sensitive and precise gas chromatographic method is described for the quantitative determination of O(2), N(2), CO, CO(2), C1 and C2-hydrocarbons for coal research. Gas analyses are necessary to obtain parameters for modelling spontaneous combustion and to predict long term coal behaviour. The method is based on a single PLOT-type capillary column in a single channel gas chromatograph. Using a micro-volume TCD coupled in series with a FID detector containing a capillary methanizer it is possible to determine high and trace level gases simultaneously. Trace quantities of CO and CO(2) can be determined with a single analysis and the detection limits are improved significantly using the capillary methanizer. The detection limit of the described method is approximately ten parts per million CO(2) and one part per million CO. Using the same instrument configuration the O(2)/N(2) ratios (major components), as parameter for coal reactivity, are also determined. The proposed approach is restricted to the determination of gases evolved during coal studies and the application to other gas mixtures is not considered.     

Shell model of assemblies of equicharged particles subject to radial confining potentials

A shell model of an assembly of N equicharged particles subject to an arbitrary radial confining potential N W(r), where W(r) is parameterized in terms of an auxiliary function Λ(t), is presented. The validity of the model requires that Λ(t) is strictly increasing and concave for any t ∈ (0, 1), Λ'(0) is infinite, and Λ(t) = -t(-1) Λ'(t)/Λ'(t) is finite at t = 0. At the bulk limit of N → ∞, the model is found to correctly reproduce the energy per particle pair and the mean crystal radius R(N), which are given by simple functionals of Λ(t) and Λ'(t), respectively. Explicit expressions for an upper bound to the cohesive energy and the large-N asymptotics of R(N) are obtained for the first time. In addition, variational formulation of the cohesive energy functional leads to a closed-form asymptotic expression for the shell occupancies. All these formulae involve the constant ξ that enters the expression -(ξ/2) n(3/2) for the leading angular-correlation correction to the minimum energy of n electrons on the surface of a sphere with a unit radius (the solution of the Thomson problem). The approximate energies, which constitute rigorous upper bounds to their exact counterparts for any value of N, include the cohesive term that is not accounted for by the mean-field (fluidlike) theory and its simple extensions but completely neglect the surface-energy correction proportional to N.     

Electrophoretic mobility of a highly charged colloidal particle in a solution of general electrolytes.

For a highly charged particle in an electrolyte solution, counterions are condensed very near the particle surface. The electrochemical potential of counterions accumulated near the particle surface is thus not affected by the applied electric field, so that the condensed counterions do not contribute to the particle electrophoretic mobility. In the present paper we derive an expression for the electrophoretic mobility mu(infinity) of a highly charged spherical particle of radius a and zeta potential zeta in the limit of very high zeta in a solution of general electrolytes with large ka (where k is the Debye-Hückel parameter) on the basis of our previous theory for the case of symmetrical electrolytes (H. Ohshima, J. Colloid Interface Sci. 263 (2003) 337). It is shown that zeta can formally be expressed as the sum of two components: the co-ion component, zetaco-ion, and the counterion component, zetacounterion (where zeta = zetaco-ion + zetacounterion) and that the limiting electrophoretic mobility mu(infinity) is given by mu(infinity) = epsilonr epsilon0 zetaco-ion(infinity)/eta + 0(1/ka), where zetaco-ion(infinity) is the high zeta-limiting form of zetaco-ion, epsilonr and eta are, respectively, the relative permittivity and viscosity of the solution, and epsilon0 is the permittivity of a vacuum. That is, the particle behaves as if its zeta potential were zetaco-ion(infinity), independent of zeta. For the case of a positively charged particle in an aqueous electrolyte solution at 25 degrees C, the value of zetaco-ion(infinity) is 35.6 mV for 1-1 electrolytes, 46.0 mV for 2-1 electrolytes, and 12.2 mV for 1-2 electrolytes. It is also found that the magnitude of mu(infinity) increases as the valence of co-ions increases, whereas the magnitude of mu(infinity) decreases as the valence of counterions increases.     

Synthesis, characterization, and structural and theoretical analysis of Gd4B3C4: a novel rare earth metal borocarbide containing two different boron-carbon arrangements

The synthesis by arc-melting techniques, the single-crystal X-ray structure, and the theoretical analysis of Gd4B3C4 are reported. It crystallizes in the triclinic space group P1 with a = 3.637(2) A, b = 3.674(2) A, c = 11.859(5) A, alpha = 93.34(5) degrees, beta = 96.77(5) degrees, gamma = 90.24(5) degrees, and Z = 1. In this structure, the boron and carbon atoms form two different types of nonmetal arrangements: 1-D (BC)infinity branched chains and finite (0-D) linear CBC "molecular" units. Gd4B3C4 is the first characterized member of the rare earth metal borocarbide series in which both 1-D and "molecular" 0-D nonmetal atom systems coexist. From the structural and theoretical analysis, the following formal charge distribution can be proposed within the ionic limit: (Gd3+)4(BC2(5-)(BC3-)2.e-. Tight-binding calculations suggest that the excess electron in the ionic limit is mainly localized on the Gd atoms (at the bottom of the 5d band), while LAPW calculations favor its localization on the (BC)infinity chain. The bonding within this compound is fully analyzed and compared to other members of the rare earth metal borocarbide series.