Cold and ultracold chemical reactions of F+HCl and F+DCl

We report quantum dynamics calculations of F((2)P)+HCl(v,j)-->HF(v('),j('))+Cl((2)P) and F+DCl(v,j)-->DF(v('),j('))+Cl reactions at cold and ultracold temperatures. The effect of rotational and vibrational excitations of the HCl molecule on the reactivity is investigated. It is found that, in the ultracold regime, vibrational excitation of the HCl molecule from v=0 to v=2 enhances the reactivity by four orders of magnitude. The rotational excitation from j=0 to j=1 decreases the reactivity while the rotational excitation from j=0 to j=2 increases the reactivity. The overall effect of rotational excitation was found to be much smaller than vibrational excitation. The reactivity of the F+DCl system is significantly lower than that of the F+HCl case indicating the importance of quantum tunneling at low energies. For both reactions, Feshbach resonances corresponding to Fcdots, three dots, centered HCl or Fcdots, three dots, centeredDCl triatomic states occur at low energies. We also explored the validity of the coupled-states approximation for cold collisions taking the F+HCl(v=0,j=0) reaction as an illustrative example. It is found that the coupled-states approximation is generally valid for the background scattering even at low energies but it is inadequate to accurately describe the rich resonances in the energy dependence of the cross section resulting from the decay of van der Waals complexes. It is further shown that the coupled-states approximation cannot be used for scattering in the Wigner threshold regime when the molecule is initially in a rotationally excited level.     

球型胶体颗粒的表面电位和表面电荷密度的关系

胶体颗粒的表面电荷密度和表面电位之间的关系是颗粒表面的基本性质之一．要确定这个关系,需要解Poisson-Boltzmann(PB)方程,求出颗粒外的电位分布．然而对于球形颗粒,PB方程却没有解析解．Loeb等,求出了数值解,近似解析表达式虽然很多,也比较复杂,     

How "sticky" are short-range square-well fluids?

The aim of this work is to investigate to what extent the structural properties of a short-range square-well (SW) fluid of range lambda at a given packing fraction eta and reduced temperature T* = kBT/epsilon can be represented by those of a sticky-hard-sphere (SHS) fluid at the same packing fraction and an effective stickiness parameter tau(T*,lambda). Such an equivalence cannot hold for the radial distribution function g(r) since this function has a delta singularity at contact (r = sigma) in the SHS case, while it has a jump discontinuity at r = lambda sigma in the SW case. Therefore, the equivalence is explored with the cavity function y(r), i.e., we assume that [formula: see text]. Optimization of the agreement between y(SW) and y(SHS) to first order in density suggests the choice tau(T*,lambda) = [12(e(1/T* - 1)(lambda - 1)](-1). We have performed Monte Carlo (MC) simulations of the SW fluid for lambda = 1.05, 1.02, and 1.01 at several densities and temperatures T* such that tau(T*,lambda) = 0.13, 0.2, and 0.5. The resulting cavity functions have been compared with MC data of SHS fluids obtained by Miller and Frenkel[J. Phys.: Condens. Matter 16, S4901 (2004)]. Although, at given values of eta and tau, some local discrepancies between y(SW) and y(SHS) exist (especially for lambda = 1.05), the SW data converge smoothly toward the SHS values as lambda-1 decreases. In fact, precursors of the singularities of y(SHS) at certain distances due to geometrical arrangements are clearly observed in y(SW). The approximate mapping y(SW)-->y(SHS) is exploited to estimate the internal energy and structure factor of the SW fluid from those of the SHS fluid. Taking for y(SHS) the solution of the Percus-Yevick equation as well as the rational-function approximation, the radial distribution function g(r) of the SW fluid is theoretically estimated and a good agreement with our MC simulations is found. Finally, a similar study is carried out for short-range SW fluid mixtures.     

高电位胶体颗粒强相互作用的近似表达式

When surface potential of the particles, ,is high,sinh y can be approximated by ≈ey/2 in the nonlinear Poisson Boltzmann equation.Thus,we present a simple method of calculating the interaction force and energy per unit area between two dissimilar plates with high potentials at constant surface potential.These formulae could be applicable to the case of repulsive case,in which the derivative of y must vanish at an interior point,and a minimum ymin=u always exists.A turning point at ～kh≈2(1)e－y1/2 for the repulsion or attraction between dissimilar planar surfaces.These formulae are divergent at 阧∞,and zero point at kh≈2 .This means that they can only be used at 阧 < 2 and accurate location is at kh ≤ 4. 　　Agreement of the approximation for force,Eq.（13）,is good with the exact numerical values of the interaction of dissimilar plates given by Devereux [6] for high surface potentials.For y1 ≥5 kh ≤ 3.0 the relative errors of Eq.(13) are less than 5％,and for kh ≤ 3.5 relative errors are less than 10％.For the interaction energy,Eq.(15),the applicable range extends to kh =4.0.Beyond this range the error increases rapidly.The higher surface potential is the better the precision of Eq.（13）and Eq.( 15).The condition of the strong interaction has been satisfied.     

Synthesis and structure investigation of the antibiotic amoxicillin complexes of d-block elements

The study of some transition metals (M) and amoxicillin trihydrate (ACT) ligand complexes (M-ACT) that formed in solution involved the spectrophotometric determination of stoichiometric ratios and their stability constants and these ratios were found to be M:ACT = 1:1, 1:2 and 2:1 in some instances. The calculated stability constants of these chelates, under selected optimum conditions, using molar ratio method have values ranging from K(f) = 10(7) to 10(14). These data were confirmed by calculations of their free energy of formation deltaG, which corresponded to their high stabilities. The separated solid complexes were studied using elemental analyses, IR, reflectance spectra, magnetic measurements, mass spectra and thermal analyses (TGA and DTA). The proposed general formulae of these complexes were found to be ML(H2O)w(H2O)x(OH)y(Cl)2, where M = Fe(II), Co(III), w = 0, x = 2, y = 1, z = 0; M = Co(II), w = 0, x = 1, y = 0, z = 1; M = Fe(III), w = 0, x = 1, y = 2, z = 0; M = Ni(II), Cu(II) and Zn(II), w = 2, x = 0, y = 1, z = 0, where w = water of crystallization, x = coordinated water, y = coordinated OH(-) and z = Cl- in the outer sphere of the complex. The IR spectra show a shift of nu(NH) (2968 cm(-1)) to 2984-2999 cm(-1) of imino group of the ligand ACT and the absence of nu(CO) (beta-lactame) band at 1774 cm(-1) and the appearance of the band at 1605-1523 cm(-1) in all complexes suggest that 6,7-enolization takes place before coordination of the ligand to the metal ions. The bands of M-N (at 625-520 cm(-1)) and of M-O (at 889-7550 cm(-1)) proved the bond of N (of amino and imino groups) and O of C-O group of the ligand to the metal ions. The reflectance spectra and room temperature magnetic measurements refer to octahedral complexes of Fe(II) and Fe(III); square planner form of Co(II), reduced Co(III), Ni(II) and Cu(II)-ACT complexes but tetrahedral form of Zn-ACT complex. The thermal degradation of these complexes is confirmed by their mass spectral fragmentation. These data confirmed the proposed structural and general formulae of these complexes.     

The use of IR, magnetism, reflectance, and mass spectra together with thermal analyses in structure investigation of codeine phosphate complexes of d-block elements

Codeine is an analgesic with uses similar to morphines, but it is of much less effect, i.e., it had a mild sedative effect; codeine is usually used as the phosphate form (Cod.P) and is often administrated by mouth with aspirin of paracetamol. Due to its serious use, if it is in large dose, attention is paid in this research to the synthesis and stereochemistry of new iron, cobalt, nickel, copper, and zinc complexes of this drug in both solution and the solid states. The spectra of these complexes in solution and the study of their stoichiometry refer to the formation of 1:1 ratio of metal (M) to ligand (L). The steriochemical structures of the solid complexes were studied on the basis of their analytical, spectroscopic, magnetic, and thermal data. Infrared spectra proved the presence of MO bonds. Magnetic susceptibility and solid reflectance spectral measurements were used to infer the structures. The prepared complexes were found to have the general formulae [ML(OH)(x)(H2O)(y)](H2O)(z)H3PO4, M: Co(II), Ni(II), and Cu(II), x = 1, y = 0, z = 0; M: Fe(II), x = 1, y = 2, z = 1; Fe(III), x = 2, y = 1, z = 0; Co(III), x = 0, y = 2, z = 1; Zn(II), x = 1, y = 0, z = 3; and L: (Cod.P) of the general formula C18H24NO7P (anhydrate). Octahedral, tetrahedral, and square planer structures were proposed for these complexes depending upon the magnetic and reflectance data and were confirmed by detailed mass and thermal analyses comparative studies.     

Communication: rationale for a new class of double-hybrid approximations in density-functional theory

We provide a rationale for a new class of double-hybrid approximations introduced by Bre?mond and Adamo [J. Chem. Phys. 135, 024106 (2011)] which combine an exchange-correlation density functional with Hartree-Fock exchange weighted by λ and second-order M?ller-Plesset (MP2) correlation weighted by λ(3). We show that this double-hybrid model can be understood in the context of the density-scaled double-hybrid model proposed by Sharkas et al. [J. Chem. Phys. 134, 064113 (2011)], as approximating the density-scaled correlation functional E(c)[n(1/λ)] by a linear function of λ, interpolating between MP2 at λ = 0 and a density-functional approximation at λ = 1. Numerical results obtained with the Perdew-Burke-Ernzerhof density functional confirms the relevance of this double-hybrid model.     

Ultracold collisions and reactions of vibrationally excited OH radicals with oxygen atoms

We report a quantum dynamics study of O + OH (v = 1, j = 0) collisions on its ground electronic state, employing two different potential energy surfaces: the DIMKP surface by Kendrick and Pack, and the XXZLG surface by Xu et al. A time-independent quantum mechanical method based on hyperspherical coordinates has been adopted for the dynamics calculations. Energy-dependent probabilities and rate coefficients are computed for the elastic, inelastic, and reactive channels over the collision energy range E(coll) = 10(-10)-0.35 eV, for J = 0 total angular momentum. Initial state-selected reaction rate coefficients are also calculated from the J = 0 reaction probabilities by applying a J-shifting approximation, for temperatures in the range T = 10(-6)-700 K. Our results show that the dynamics of the collisional process and its outcome are strongly influenced by long-range forces, and chemical reactivity is found to be sensitive to the choice of the potential energy surface. For O + OH (v = 1, j = 0) collisions at low temperatures, vibrational relaxation of OH competes with reactive scattering. Since long-range interactions can facilitate vibrational relaxation processes, we find that the DIMKP potential (which explicitly includes van der Waals dispersion terms) favours vibrational relaxation over chemical reaction at low temperatures. On the DIMKP potential in the ultracold regime, the reaction rate coefficient for O + OH (v = 1, j = 0) is found to be a factor of thirteen lower than that for O + OH (v = 0, j = 0). This significantly high reactivity of OH (v = 0, j = 0), compared to that of OH (v = 1, j = 0), is attributed to enhancement caused by the presence of a HO(2) quasibound state (scattering resonance) with energy near the O + OH (v = 0, j = 0) dissociation threshold. In contrast, the XXZLG potential does not contain explicit van der Waals terms, being just an extrapolation by a nearly constant function at large O-OH distances. Therefore, long-range potential couplings are absent in calculations using the XXZLG surface, which does not induce vibrational relaxation as efficiently as the DIMKP potential. The XXZLG potential leads to a slightly higher reactivity (a factor of 1.4 higher) for O + OH (v = 1, j = 0) compared to that for O + OH (v = 0, j = 0) at ultracold temperatures. Overall, both potential surfaces yield comparable values of reaction rate coefficients at low temperatures for the O + OH (v = 1, j = 0) reaction.     

配合物[Fe(CO)x(Ph2Ppy)y(HgCl2)z](x=3, 4; y=1, 2; z=0, 1, 2)的Fe-Hg相互作用及31P化学位移的理论研究

用密度泛函理论PBE0法计算配合物[Fe(CO)x(Ph2Ppy)y(HgCl2)z](1: x=4, y=1, z=0; 2: x=3, y=2, z=0; 3: x=4, y=1, z=1; 4: x=3, y=2, z=1; 5: x=4, y=1, z=2; 6: x=3, y=2, z=2)的几何构型, 用PBE0-GIAO法计算配合物1~6的31P化学位移. 计算结果表明, 含2个Ph2Ppy的配合物5和6的Fe—Hg相互作用略大于含单个Ph2Ppy的配合物3和4. 含2个HgCl2的配合物4和6存在Fe—Hg σ键, 比含单个HgCl2的配合物3和5的Fe—Hg相互作用强, 配合物3和5的Fe—Hg相互作用以Fe→Hg和Fe←Hg离域为主. 配合物3中Fe的负电荷比5的小, 故配合物5的Fe—Hg相互作用比配合物3的强且Fe→Hg离域比较显著, 而配合物3的Fe←Hg离域更显著. Fe—Hg相互作用增大了双核配合物中P核周围的电子密度, 其31P化学位移比相应的单核配合物小, 且含2个HgCl2的双核配合物的31P化学位移更小. 含单个Ph2Ppy的配合物的31P化学位移小于含2个Ph2Ppy的配合物.     

Semiclassical glory analyses in the time domain for the H + D2(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D reaction

We make the first application of semiclassical (SC) techniques to the plane-wavepacket formulation of time-domain (T-domain) scattering. The angular scattering of the state-to-state reaction, H + D(2)(v(i) = 0, j(i) = 0) → HD(v(f) = 3, j(f) = 0) + D, is analysed, where v and j are vibrational and rotational quantum numbers, respectively. It is proved that the forward-angle scattering in the T-domain, which arises from a delayed mechanism, is an example of a glory. The SC techniques used in the T-domain are: An integral transitional approximation, a semiclassical transitional approximation, a uniform semiclassical approximation (USA), a primitive semiclassical approximation and a classical semiclassical approximation. Nearside-farside (NF) scattering theory is also employed, both partial wave and SC, since a NF analysis provides valuable insights into oscillatory structures present in the full scattering pattern. In addition, we incorporate techniques into the SC theory called "one linear fit" and "two linear fits", which allow the derivative of the quantum deflection function, Θ?(')(J), to be estimated when Θ?J exhibits undulations as a function of J, the total angular momentum variable. The input to our SC analyses is numerical scattering (S) matrix data, calculated from accurate quantum collisional calculations for the Boothroyd-Keogh-Martin-Peterson potential energy surface No. 2, in the energy domain (E-domain), from which accurate S matrix elements in the T-domain are generated. In the E-domain, we introduce a new technique, called "T-to-E domain SC analysis." It half-Fourier transforms the E-domain accurate quantum scattering amplitude to the T-domain, where we carry out a SC analysis; this is followed by an inverse half-Fourier transform of the T-domain SC scattering amplitude back to the E-domain. We demonstrate that T-to-E USA differential cross sections (DCSs) agree well with exact quantum DCSs at forward angles, for energies where a direct USA analysis in the E-domain fails.     

On the distorted wave approximation for chemical reactions

Various procedures for constructing transition amplitudes for chemical reactions in the distorted wave approximation are demonstrated. Calculations are performed for the collinear reaction H+H₂(ν = 0) → H₂(ν = 0) + H at low energies. Comparison is made with exact results after unitarization is invoked through (1) exponential unitarization and (2) the Condon approximation. In the threshold region the Condon approximation gives quite reasonable agreement with exact results.     

Synthesis, characterization and electronic spectra of cefadroxil complexes of d-block elements

Cefadroxil (CD) is an essential pharmaceutical drug used in curing many diseases. Due to its popular use in many pharmaceutical forms, attention is paid in this research to the synthesis and stereochemistry of new iron, cobalt, nickel, copper, and zinc complexes of this drug both in solution and the solid states. The spectra of these complexes in solution and the study of their stoichiometry refer to the formation of 1:1 and 1:2 ratios of metal (M) to ligand (L). The calculated stability constants (Kf) of these complexes (1.5x10(7) to 5x10(13)) and the change in free energy of formation (deltaGf=2.5-12.5 kcal mol(-1) degree(-1)) are indicative of their high stability. The stereo chemical structure of the solid complexes was studied on the basis of their analytical, spectroscopic, magnetic, and thermal data. Infrared spectra proved the presence of M-N and M-O bonds. Magnetic susceptibility and solid reflectance spectral measurements were used to infer the structure. The prepared complexes were found to have the general formulae [ML(OH)x(H2O)y](H2O)z-M: Fe(II), x=0, y=2, z=1; M: Fe(III) and Co(III), x=1, y=2, z=1; M: Co(II) and Zn(II), x=0, y=1, z=0; M: Ni(II) and Cu(II), x=1, y=0, z=1; L: CD. Octahedral and tetrahedral structures were proposed for these complexes depending upon the magnetic and reflectance data and were confirmed by detailed mass and thermal analyses comparative studies.     

Influence of Ru doping on the structure, defect chemistry, magnetic interaction, and carrier motion of the La(1-x)Na(x)MnO(3+delta) manganite

In this work, we report a structural, electrical, and magnetic characterization of the La(1-x)Na(x)Mn(1-y)Ru(y)O(3+delta) (LNMRO) system with x = 0.05 and 0.15 and y = 0, 0.05, and 0.15, also comprising an investigation of the role of the oxygen content on the related redox properties. The experimental investigation has been realized with the aid of X-ray powder diffraction, electron microprobe analysis, thermogravimetry, electrical resistivity and magnetization measurements, and electron paramagnetic resonance. We demonstrate that the effect of ruthenium doping on the studied LNMRO compounds is not only directly related to the Ru/Mn substitution and to the Ru oxidation state but also indirectly connected to the oxygen content in the sample. Our data show that ruthenium addition can "improve" electrical and magnetic properties of nonoptimally (low) cation-doped manganites, causing an increase of the T(C) value and the insurgence of magnetoresistance effect, as observed for the x = 0.05 and y = 0.05 sample (MR congruent with 60% at 7 T and at approximately 260 K).     

Lindstedt Poincare technique applied to molecular potentials

The Lindstedt–Poincare technique has traditionally been used to deal with oscillators with power-law potentials. We show how this method can be extended to deal with molecular potentials for which the frequency goes to zero as the energy approaches zero. The extension requires the use of an asymptotic analysis which is combined with perturbation theory. For the Morse potential, we get an exact answer while for the Lennard Jones class of potentials \({{\rm V}={\rm V}_0 \left[ {\left( {\frac{{a}}{{\rm x}}}\right)^{2{\rm n}}-\left({\frac{{\rm a}}{{\rm x}}}\right)^{{\rm n}}}\right]}\) , the answer is generally approximate with some values of n giving exact results. For the widely studied case, n=6, our approximation gives better than 1% accuracy at the lowest order of calculation. We show that as \({{\rm n} \rightarrow \infty}\) , the result tends to that for the Morse potential. We also point out that the time period obtained by us can be used to obtain the quantum mechanical energy levels of these potentials within the Bohr-Sommerfeld scheme.     

Synthesis, structures, magnetism and electrochemical properties of triruthenium-acetylide complexes

A series of triruthenium complexes with arylacetylide axial ligands Ru(3)(dpa)(4)(C(2)X)(2)(BF(4))(y)(dpa = dipyridylamido; X = Fc, y= 0 (1); X = Ph, y= 0 (2); X = PhOCH(3), y= 1 (3); X = PhC(5)H(11), y= 1 (4); X = PhCN, y= 0 (5); X = PhNO(2), y= 0 (6)) have been synthesized. The crystal structures show that the Ru-Ru bond lengths (2.3304(9)-2.3572(5)A) of these compounds are longer than those of Ru(3)(dpa)(4)Cl(2)(Ru-Ru=2.2537(1)A). This is ascribed to the formation of the stronger pi-backbonding from metal to axial ligand which weakens the Ru-Ru interactions and the bond order is reduced in the triruthenium unit. Cyclic voltammetry and differential pulse voltammetry show that compound exhibits electronic coupling between the two ferrocenyl units with DeltaE(1/2) close to 100 mV. Compounds 2-6 display three triruthenium-based reversible one-electron redox couples, two oxidations and one reduction, and the electrode potentials shift upon varying the substituents. A linear relationship is observed when the Hammett constants are plotted against the redox potentials.     

Shear modulus of sintered 'house of cards'-like assemblies of crystals

A cell model of a 'house of cards'-like assembly of crystals is used for the study of the evolution of the shear modulus during sintering. The crystals are assumed to have a lozenge shape. The cell model takes different crystal-crystal contacts into account. The force needed to separate two sintered crystals is calculated using the minimum surface area (MSA) approximation. By varying the thickness, long axis, and short axis of the crystals, it is possible to make space-filing configurations which have a nonzero shear modulus at crystal volume fraction that can be as low as phi = 0.03. This is significantly lower than the volume fractions phi > 0.52 that are found in studies where the MSA approximation is applied to assemblies of spherical particles. It is found that sintering may cause a nonlinear volume fraction dependence of the shear modulus, which depends on the shape of the crystals, the type of crystal-crystal contacts, and the character of the crystal assembly. The calculated shear modulus is analyzed using the phenomenological expression (phi - phi0)beta, where phi0 represents the volume fraction at the start of sintering. The exponent beta is found to vary between 1 and 2. The interpretation of the shear modulus using a fractal model is also discussed.     

Scattering by a hard sphere in a laser field

We consider the scattering of electrons by a hard sphere in the presence of a strong laser field. If the electrons are nonrelativistic and if the radiation field is treated as a monochromatic plane wave in the dipole approximation, the solution of our problem can be expressed in terms of well-known functions. The crux for finding this solution lies in the fact that in the potential-free region (V = 0) a space-translated solution can be written down and expressed in spherical polar coordinates. For this solution it is relatively easy to derive the matching equations on the surface of the scattering sphere of radiusR, whereV = ∞ and Ψ(R) = 0.     

Electronic relaxation of paramagnetic metal ions and NMR relaxivity in solution: critical analysis of various approaches and application to a Gd(III)-based contrast agent

The time correlation functions (TCFs) G(alphaalpha(t)[triple bond](Salpha(t)Salpha(0)) (alpha = x,y,z) of the electronic spin components of a complexed paramagnetic metal ion give information about the time fluctuations of its zero-field splitting (ZFS) Hamiltonian due to the random dynamics of the coordination polyhedron. These TCFs reflect the electronic spin relaxation which plays an essential role in the inner- and outer-sphere paramagnetic relaxation enhancements of the various nuclear spins in solution. When a static ZFS Hamiltonian is allowed by symmetry, its modulation by the random rotational motion of the complex has a great influence on the TCFs. We discuss several attempts to describe this mechanism and show that subtle mathematical pitfalls should be avoided in order to obtain a theoretical framework, within which reliable adjustable parameters can be fitted through the interpretation of nuclear-magnetic relaxation dispersion experimental results. We underline the advantage of the numerical simulation of the TCFs, which avoids the above difficulties and allows one to include the effect of the transient ZFS for all the relative magnitudes of the various terms in the electron-spin Hamiltonian and arbitrary correlation times. This method is applied for various values of the magnetic field taken to be along the z direction. At low field, contrary to previous theoretical expectations, if the transient ZFS has negligible influence, the longitudinal TCF GII(t) [triple bond] G(zz)(t) has a monoexponential decay with an electronic relaxation time T1e different from 1/(2D(r)), D(r) being the rotational diffusion coefficient of the complex. At intermediate and high field, the simulation results show that GII (t) still has a monoexponential decay with a characteristic time T1e, which is surprisingly well approximated by a simple analytical expression derived from the Redfield perturbation approximation of the time-independent Zeeman Hamiltonian, even in the case of a strong ZFS where this approximation is expected to fail. These results are illustrated for spins S = 1, 3/2, and 5/2 in axial and rhombic symmetries. Finally, the simulation method is applied to the reinterpretation of the water-proton relaxivity profile due to P760-Gd(III), an efficient blood pool contrast agent for magnetic-resonance imaging.     

Determination of oxygen in ternary uranium oxides by a gravimetric alkaline earth addition method

The applicability of a gravimetric method based on alkaline earth metal addition for the determination of oxygen in ternary uranium oxides of the type M—U—O (M=La, Ce and Th) is described. The oxide sample is mixed with MgO or Ba_2.8UO_5.8 and heated in air under suitable conditions. Because uranium is completely oxidized to the hexavalent state during the reaction, oxygen can be determined from the weight change. Oxygen in La_yU_1-y O_2+x is determined up to y = 0.8 with a standard deviation for x of ±0.006 with MgO. For Th_yU_1-y O_2+x, the value of x is determined with Ba_2.8UO_5.8 with a standard deviation of ±0.01 at y = 0.8. For Ce_yU_1-y O_2+x, the method can be applied only for low cerium concentrations where y = 0–0.2; the value for x with Ba_2.8UO_5.8 at y = 0.2 showed a standard deviation of ±0.002.