Computational study of the vibrational spectra of alpha- and beta-Keggin polyoxometalates

The structures and vibrational frequencies of the alpha- and beta-isomers of the phosphomolybdate Keggin anion [PMo(12)O(40)](3-) have been calculated by using density functional theory. Good agreement between the calculated unscaled vibrational frequencies and those determined experimentally and between the calculated and observed IR traces has been obtained allowing the IR and Raman spectra to be assigned. For the alpha-isomer, the agreement with experiment using the current level of theory is superior to that obtained previously. For the beta-isomer, for which no non-empirical study has previously been reported, the agreement with experiment is slightly poorer but still allows the spectrum to be assigned unambiguously. To calculate the structure and vibrational spectra of these large molydate cluster ions requires large basis sets and a good treatment of electron correlation and relativistic effects. For the 53-atom [PMo(12)O(40)](3-) ions, the computational demands are very high, requiring several months computational time. The calculated IR spectral traces for the two isomers are quite similar due to the relative flexibility of the molybdates, where the slight weakening of the bonding of the rotated trimetallic unit to the rest of the cluster in the beta-isomer is compensated by contraction of the bonds within the unit, and the structure of the [MO(6)] and [PO(4)] units in the two isomers is nearly identical. The vibrations characteristic of the bridging Mo-O-Mo bonds involve both the "2-2" junctions between rotated [M(3)O(13)] units and the "1-2" junctions between rotated and unrotated units. The separation of "ligand" and "interligand" vibrations is not clear. The vibrational analyses confirm the high symmetry, namely T(d) and C(3v) for the alpha- and beta-isomers, respectively, assumed by previous workers in this field. The characteristic group frequencies for the Type I polyoxometalates containing both edge- and corner-sharing I octahedra have been identified.     

Molybdenum phosphide as an o-propylaniline hydrodenitrogenation catalyst: a first principles study

MoP has been shown experimentally to be an active catalyst in the hydrodenitrogenation of o-propylaniline. We investigate the structure and the energetics of the o-propylaniline adsorption on the Mo-terminated MoP(001) surface. Detailed information on the structure of the free MoP(001) surface and on the structure and adsorption energy of o-propylaniline on MoP(001) is obtained by using density functional theory. The transition state, reaction path, and the energy barrier are reported for one of the branches of the HDN reaction network that leads to the formation of propylbenzene by hydrogenolysis of the C-N bond.     

tBuP(NH2)2--a reactive synthon for the synthesis of molecular imidophosphinates of group 13 metals

Reactions of tBuP(NH(2))(2) with Group 13 trialkyls MR(3) (M=Al, Ga, In; R=Me, tBu) were investigated in detail. According to variable-temperature (VT) NMR investigations, the reaction proceeds stepwise with the initial formation of aminophosphane adducts, which subsequently react to give iminophosphorane adducts and finally the heterocyclic metallonitridophosphinates. BP86/TZVPP (DFT) calculations were performed to verify this reaction pathway, to elucidate the influence of the central Group 13 element on the stability of the reaction intermediates and the heterocycles, as well as to assess the thermodynamics of their formation. The relative stability of free and complexed aminophosphane RP(NH(2))(2) and iminophosphorane R(H(2)N)(H)P=NH (adducts) with P(III) and P(V) centers was studied in more detail with DFT and MP2 methods. In addition, the influence of the substituent R was investigated by variation of R from H to Me, tBu, F, and NH(2). In general, the aminophosphane form was found to be favored for the free ligand, however, upon complexation with MR(3) (M=Al, Ga; R=alkyl) both forms are almost equal in energy.     

Synthesis and stereochemical properties of chiral square complexes of iron(II)

The hexadentate, and ditopic ligand 2,5-bis([2,2']bipyridin-6-yl)pyrazine yields a chiral, tetrameric, square-shaped, self-assembled species upon complexation with Fe2+ ions. The racemate of this complex was resolved with antimonyl tatrate as the chiral auxiliary. The purity of the enantiomer was determined by NMR spectroscopy, by using a chiral, diamagnetic shift reagent, and by circular dichroism (CD). The CD spectrum was also calculated by time-dependent density functional theory, and the correlation that was found between CD spectrum and configuration was confirmed by X-ray cristallography. When a "chiralised" version of the ligand was used instead, the corresponding iron complex was obtained in diastereomerically pure form.     

Existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch systems with stocking

By means of Mawhin's continuation theorem of coincidence degree and Lyapunov functional, a set of easily verifiable criteria are established for the existence and global attractivity of positive periodic solutions for delay Lotka-Volterra competition patch system with stocking

     

On injective or dense-range operators leaving a given chain of subspaces invariant

In this paper we prove the existence of dense-range or one-to-one compact operators on a separable Banach space leaving a given finite chain of subspaces invariant. We use this result to prove that a semigroup of bounded operators is reducible if and only if there exists an appropriate one-to-one compact operator such that the collection of compact operators is reducible.

     

Uncorrelatedness and orthogonality for vector-valued processes

For a square integrable vector-valued process on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for are presented. The process is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for involving the biorthogonal representation for the conditional expectation of with respect to the usual product -algebra is presented.

     

Non-linear Semigroup of a Class of Abstract Semilinear Functional Differential Equations with a Non-Dense Domain

In this work, we are concerned with a general class of abstract semilinear autonomous functional differential equations with a non-dense domain on a Banach space. Our objective is to study, using the Crandall-Liggett approach, the solutions as a semigroup of non-linear operators.     

Fast topological analysis of 2D and 3D grids of data: application to the atoms in molecule (AIM) and the electron localization function (ELF)

The topological analysis of grids of data is used for determination of surfaces or volumes around maxima. The volumes are then related to chemical information such as atoms or bonds, and can be used for integration of local properties such as electronic population. The problem of global connectivity is reversed into the question of local connectivity yielding a linear scaling partition algorithm. Two packages are developed for a very fast analysis and partition of 2D or 3D grids of data, applications being made to C2H2, C2H4, C6H6, H2CO, and H2CS molecules using the Atoms in Molecule (AIM) or Electron Localization Function (ELF).     

External Fields, Density Functionals, and the Gibbs Inequality

By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space , we show that the corresponding equilibrium densities must also differ from each other somewhere in . We note that the basic equations of density functional theory arise naturally from a simple rearrangement and reinterpretation of the terms in the upper bound Gibbs inequality for such systems and briefly discuss some of the complications that occur when the intermolecular interactions of the two systems also differ.