The preparation of dimolybdenum(V,V) complexes from molybdenum quadruply bonded metal-metal dimers

Oxidation of quadruply bonded metal-metal dimers in the presence of good π-accepting ligands results in the formation of Mo^V---Mo^V compounds of the type [MO₂(μ-X)₂(Y)(Y′)]²⁺ (X = O or S; Y,Y′ = O,O; S,S; O,S). Reaction of MO₂(O₂CCH₃)₄ with oxygen in the presence of Na₂mnt (mnt = 1,2-dicyanoethylene-2,2-dithiolate) gives [MO₂(μ-S)₂(O)(S)(mnt)₂]²⁻ (1). The compound crystallizes in the monoclinic space group P2₁/c, with cell dimensions a = 19.547(4), b = 15.210(4), c = 18.754(6) Å, β = 101.69(2)°, V= 5460(2) ų, and Z = 4. Similarly, oxidation of o-dichlorobenzene solutions of Mo₂Cl₄(CH₃CN)₄ and 4,4′-dimethyl-2,2′-dipyridyl (dmpby) or, more directly, the reaction of Mo₂Cl₄(dmbpy)₂ with oxygen leads to the formation of a red solid, which was characterized by X-ray crystallography to be Mo₂(μ-O)₂(O)₂(Cl)₂(dmbpy)₂ (2). Red diamond crystals, prepared by slow evaporation of CH₃CN solutions of 2, are trigonal and in the space group P3₁21 with cell dimensions a = 16.135(4), b = 16.135(4), c = 10.709(3) Å, V = 2414.4(13) ų and Z = 3. In both structures, the geometry about each of the molybdenum atoms is a distorted square pyramid with terminal oxygen or sulphur atoms at the apices and in a syn conformation. The molybdenum-molybdenum bond distances of 2.858(1) Å and 2.562(2) Å in structures of 1 and 2, respectively, are typical of other Mo^V---Mo^V dimers and indicative of a single Mo---Mo bond.     

Density functional theory investigations on the chemical basis of the selectivity filter in the K+ channel protein

The chemical-physical basis of loading and release of K(+) and Na(+) ions in and out of the selectivity filter of the K(+) channel has been investigated using the B3LYP method of density functional theory. We have shown that the difference between binding free energies of K(+) and Na(+) to the cavity end of the filter is smaller than the difference between the K(+) and Na(+) solvation free energies. Thus, the loading of K(+) ions into the cavity end of the selectivity filter from the solution phase is suggested to be selective prior to the subsequent conduction process. It is shown that the extracellular end of the filter is only optimal for K(+) ions, because K(+) ions prefer the coordination environment of eight carbonyl oxygens. Na(+) ions do not fit into the extracellular end of the filter, since they prefer the coordination environment of six carbonyl oxygens. Overall, the results suggest that the rigid C(4) symmetric selectivity filter is specifically designed for conduction of K(+) ions.     

Determination of the Dissociation Constants of Urocanic Acid Isomers in Aqueous Solutions

Summary. (E)- and (Z)-Urocanic acids are endogenous chemicals in the normal mammalian skin. The first and the second thermodynamic dissociation constants (pK _a1 and pK _a2) of urocanic acid isomers were determined using UV spectrophotometry in aqueous solutions. The values with standard deviation (pK _a1 = 3.43 ± 0.12 and pK _a2 = 5.80 ± 0.04) and (pK _a1 = 2.7 ± 0.3 and pK _a2 = 6.65 ± 0.04) were obtained to (E)- and (Z)-urocanic acids, respectively. The second dissociations were studied also by potentiometric titration in aqueous sodium chloride solutions up to the isotonic salt concentration (0.154 mol dm⁻³), and the second thermodynamic dissociation constants as well as activity parameters for both isomers were determined at temperature 25°C and for (E)-urocanic acid also at 37°C. The obtained pK _a2 values were close to those found by UV spectrophotometry. The equations for the calculation of the second stoichiometric dissociation constants of urocanic acid isomers on molality and molarity scale in aqueous sodium chloride solutions were derived. The obtained pK _a1 and pK _a2 values for (Z)-urocanic acid appear to be essentially lower than some previously reported values in literature. An erratum to this article is available at .     

Conductivity Studies of <Emphasis Type="Italic">n</Emphasis>-Tetrabutylammonium Tetraphenylborate in 3-Pentanone in the Temperature Range from 283.15 to 329.15 K

The molar conductivities (Λ) of solutions of n-tetrabutylammonium tetraphenylborate (NBu₄BPh₄) in 3-pentanone have been measured in the temperature range from 283.15 to 329.15 K. The conductance data have been analyzed using the Lee-Wheaton conductivity equation with the distance parameter (a) set at Bjerrum’s pairing distance, and the limiting molar conductivities (Λ_o) and the association equilibrium constants (K _A) have been derived. The limiting ion conductivities (λ_±^o) have been evaluated according to the method of Krumgalz. The λ₊ ^o values have been compared with λ₊ ^o values calculated from the empirical equation of Gill. The thermodynamic functions, Gibbs energy (Δ G _A ^o), enthalpy (Δ H _A ^o) and entropy (Δ S _A ^o) for the process of ion-pair formation as well as the activation energy of the ionic movement (ΔH ^∗) have been evaluated. The obtained results are discussed in terms of ion-ion and ion-solvent interactions.     

Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion

Summary Conventional numerical methods, when applied to the ordinary differential equations of motion of classical mechanics, conserve the total energy and angular momentum only to the order of the truncation error. Since these constants of the motion play a central role in mechanics, it is a great advantage to be able to conserve them exactly. A new numerical method is developed, which is a generalization to arbitrary order of the discrete mechanics described in earlier work, and which conserves the energy and angular momentum to all orders. This new method can be applied much like a corrector as a modification to conventional numerical approximations, such as those obtained via Taylor series, Runge-Kutta, or predictor-corrector formulae. The theory is extended to a system of particles in Part II of this work.     

聚N-异丙基丙烯酰胺接枝聚苯乙烯高分子刷的构象

当长链高分子高密度接枝到一个表面上时,由于分子链间的相互作用使得接枝的高分子链扩张而形成伸直链的构象,这种形态被称为高分子刷.     

Electronic structure of strongly correlated systems: recent developments in multiconfiguration pair-density functional theory and multiconfiguration nonclassical-energy functional theory

Strong electron correlation plays an important role in transition-metal and heavy-metal chemistry, magnetic molecules, bond breaking, biradicals, excited states, and many functional materials, but it provides a significant challenge for modern electronic structure theory. The treatment of strongly correlated systems usually requires a multireference method to adequately describe spin densities and near-degeneracy correlation. However, quantitative computation of dynamic correlation with multireference wave functions is often difficult or impractical. Multiconfiguration pair-density functional theory (MC-PDFT) provides a way to blend multiconfiguration wave function theory and density functional theory to quantitatively treat both near-degeneracy correlation and dynamic correlation in strongly correlated systems; it is more affordable than multireference perturbation theory, multireference configuration interaction, or multireference coupled cluster theory and more accurate for many properties than Kohn–Sham density functional theory. This perspective article provides a brief introduction to strongly correlated systems and previously reviewed progress on MC-PDFT followed by a discussion of several recent developments and applications of MC-PDFT and related methods, including localized-active-space MC-PDFT, generalized active-space MC-PDFT, density-matrix-renormalization-group MC-PDFT, hybrid MC-PDFT, multistate MC-PDFT, spin–orbit coupling, analytic gradients, and dipole moments. We also review the more recently introduced multiconfiguration nonclassical-energy functional theory (MC-NEFT), which is like MC-PDFT but allows for other ingredients in the nonclassical-energy functional. We discuss two new kinds of MC-NEFT methods, namely multiconfiguration density coherence functional theory and machine-learned functionals.

This feature article overviews recent work on active spaces, matrix product reference states, treatment of quasidegeneracy, hybrid theory, density-coherence functionals, machine-learned functionals, spin–orbit coupling, gradients, and dipole moments.     

An FEM approximation for a fourth-order variational inequality of second kind

A fourth-order variational inequality of the second kind arising in a plate frictional bending problem is considered. By using regularization method, the original problem can be formulated as a differentiable variational equation, and the corresponding discrete FEM variational equation is presented afterwards. Abstract error estimates and error estimates of the approximation are derived in terms of energy norm and L^2-norm.     

Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space

This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.