Role of resonances in building cross sections: Comparison between the Mittag–Leffler and the T‐matrix Green function expansion approaches

Peaks in collision cross sections are often interpreted as resonances. The complex dilation method, as well as other methods relying on analytic continuation of the scattering formalism, can be used to clarify whether these structures are true resonances in the sense that they are poles of the S‐matrix and the associated Green function. The performance of the Mittag–Leffler expansion and T‐matrix Green function expansion methods are formally and computationally compared. The two methods are applied to two model potentials. Eigenenergies, s‐wave residues, and cross sections are computed with both methods. The resonance contributions to the cross sections are further analyzed by removing the residue contributions from the Mittag–Leffler and Green function expansion sums, respectively. It is suggested that the contribution of a resonance to a cross section should be defined through its S‐matrix residue. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Fluxional processes in diamagnetic and paramagnetic allyl dicarbonyl and 2-methylallyl dicarbonyl molybdenum histidinato complexes as revealed by spectroscopic data and density functional calculations

This work describes a detailed study on the structure and dynamics of pseudooctahedral low-valent complexes of the type [Mo(His-N(epsilon)-R)(eta-2-R'-allyl)(CO)(2)] (His=N(delta),N,O-L-histidinate; R=H, R'=H (1); R=C(2)H(4)CO(2)Me, R'=H (2); R=H, R'=Me (3); R=C(2)H(4)CO(2)Me, R'=Me (4)). These diamagnetic 18-electron complexes were comprehensively characterized spectroscopically and by X-ray crystallography. In the solid state, the (substituted) allyl ligand is in an endo position in all compounds, but it is trans to the His-N(delta) atom in 1 and 2, whereas it is trans to the carboxylate O atom for the 2-Me-allyl compounds 3 and 4. In solution, both isomers are present in a solvent-dependent equilibrium. The third isomer (allyl trans to His-NH(2)) is not spectroscopically observed in solution. This is in agreement with the results from density functional (DFT) computations (BPW 91 functional) for 1 and 3, which predict a considerably higher energy (+6.3 and +5.9 kJ mol(-1), respectively) for this isomer. A likely path for isomerization is calculated, which is consistent with the activation energy determined by variable temperature NMR measurements. At least for 3, the preferred path involves several intermediates and a rotation of the 2-Me-allyl ligand. For the paramagnetic 17-electron congeners, DFT predicts the exo isomer of 3(+) with the 2-Me-allyl ligand trans to the carboxylate O atom to be by far the most stable isomer. For 1(+), an endo-exo equilibrium between the isomers with the allyl ligand trans to the carboxylate O atom is suggested. These suggestions are confirmed by EPR spectroscopy on the electrochemically generated species, which show signals for one- (4) and two- (2) metal-containing compounds. The appearance of the EPR spectra may be rationalized by inspection of the SOMOs from DFT calculations of the species in question. The notion of a metal-centered oxidation is also substantiated by IR spectroelectrochemistry and by UV/Vis spectra of the 17-electron complexes. Upon depleting the metal of electron density, the stretching vibrations of the carbonyl ligands shift more than 100 cm(-1) to higher wavenumbers, and the carbonyl vibration of the metal-coordinated carboxylate shifts by about 50 cm(-1). A color change from yellow to green upon oxidation is observed visually and quantified by the appearance of a new band at 622 nm (2(+)) and 546 nm (4(+)), respectively.     

Ferrocenoyl peptides with sulfur-containing side chains: synthesis, solid state and solution structures

The synthesis and full characterization of a number of amino acid and dipeptide derivatives with sulfur-containing side chains derived from ferrocene carboxylic acid and ferrocene-1,1′-dicarboxylic acid is presented. In particular, compounds Fc-CO-(Aaa)_n-OMe (4) and Fe[C₅H₄-CO-(Aaa)_n-OMe]₂ (3) with (Aaa)_n = Cys(Bzl) (a), Cys(Bzl)-Cys(Bzl) (b), Cys(p-OMe-Bzl) (c), Cys(p-OMe-Bzl)-Cys(p-OMe-Bzl) (d), Met (e), and Met-Met (f) were prepared. Also, the free acid derivatives Fe[C₅H₄-CO-Met-OH]₂ (6e) and Fc-CO-Met-OH (7e) were prepared and characterized. The solid state structures of 3a, 4b, and 4e were determined by single crystal X-ray diffraction. Compound 3a shows a 1,3′ substitution pattern on the Cp rings in the solid state. Structures in solution were determined by NMR, IR and CD spectroscopy, with particular emphasis on the question of hydrogen bonding and helical chirality of the metallocene. As an example, the full assignment for the Cp signals in the disubstituted derivative 3a was achieved by simulation of the ¹H NMR signals from the cyclopentadienyl ring in combination with 2D-NOESY spectra. In solution, 3a has the known 1,2′ substitution pattern, which is stabilized by intramolecular hydrogen bonds.     

Semiempirical calculations of TiO2 (rutile) clusters

The densities of states for small (TiO₂)_x-clusters, x = 1, 3, 6, 9, and 14, have been calculated by means of the INDO method. The shape of the valence bands' density of states (DOS ) are discussed in terms of the distribution of coordination numbers. A one-slab cluster with uniform distribution of the coordination numbers was used to compare our calculations with experimental spectra. The photoelectric DOS and DOS for a cluster with an oxygen vacancy are in very good agreement with experimental findings for the TiO₂ (001) surface. O1s core level shifts between a surfacelike and a bulklike oxygen atom have been estimated. It is concluded that the observed surface–bulk shift for the TiO₂ (001) surface contains a substantial relaxation contribution. © 1992 John Wiley & Sons, Inc.     

Self-consistent solution of the Dyson equation for atoms and molecules within a conserving approximation

We have calculated the self-consistent Green's function for a number of atoms and diatomic molecules. This Green's function is obtained from a conserving self-energy approximation, which implies that the observables calculated from the Green's functions agree with the macroscopic conservation laws for particle number, momentum, and energy. As a further consequence, the kinetic and potential energies agree with the virial theorem, and the many possible methods for calculating the total energy all give the same result. In these calculations we use the finite temperature formalism and calculate the Green's function on the imaginary time axis. This allows for a simple extension to nonequilibrium systems. We have compared the energies from self-consistent Green's functions to those of nonselfconsistent schemes and also calculated ionization potentials from the Green's functions by using the extended Koopmans' theorem.     

On the internally contracted multireference CI method with full contraction

The configuration interaction (CI ) method where the efficiency of the generators of the unitary group is most fully exploited is the internally contracted multireference CI method. In the most recent version of this method the semi-internal configurations were kept uncontracted, which means that the number of configurations can still be quite large. In the present study the necessary formulas are derived for the case where the semi-internal states are also contracted. The highest density matrix that appears in these formulas is of order 5, and the computational treatment of this large matrix is discussed in detail.     

Specific labeling of cell surface proteins with chemically diverse compounds

The specific and covalent labeling of fusion proteins with synthetic molecules opens up new ways to study protein function in the living cell. Here we present a novel method that allows for the specific and exclusive extracellular labeling of proteins on the surfaces of live cells with a large variety of synthetic molecules including fluorophores, protein ligands, or quantum dots. The approach is based on the specific labeling of fusion proteins of acyl carrier protein with synthetic molecules through post-translational modification catalyzed by phosphopantetheine transferase. The specificity and versatility of the labeling should allow it to become an important tool for studying and manipulating cell surface proteins and for complementing existing approaches in cell surface engineering.     

Das chlorsilylsubstituierte Silanimin Bu2SiNSiClBu2

In the thermolysis of the silaterazolines silatetrazoline ^tBu₂SiNSiCl^tBu₂ · ^tBu₃SiN₃ the silanimine ^tBu₂SiNSiCl^tBu₂ and the silyl azide ^tBu₃SiN₃ are formed quantitatively. The silanimine ^tBu₂SiNSiCl^tBu₂ has been trapped with Et₃NHF, Me₃NHCl, water, 1-butene, 2,3-dimethyl-1,3-butadiene, isobutene, methylvinyl ether, and ^tBu₂SiClN₃. The structure of the disiloxane (^tBu₂SiCl-NH-Si^tBu₂)₂O and of the bis(di-tert-butylchlorsilyl)-substituted silatetrazoline ^tBu₂SiNSiCl^tBu₂ · ^tBu₂SiClN₃ has been determined by X-ray structure analysis.     

UHF-CI studies of energy barriers for the abstraction and exchange reactions in the system H + CH4

UHF and CI calculations, using the direct CI method, and double-zeta plus polarization functions basis sets, have been performed on the more important parts of the energy hypersurface for CH₅. The abstraction H + CH₄ → H₂ + CH₃ and the inversion substitution reaction H′ + CH₄ → CH₃H′ + H have been studied in detail. The predicted barriers for these two reactions are 13.5 and 36.6 kcal/mol, respectively. The abstraction reaction is, in agreement with experiment, found to be almost thermo-neutral with a heat of reaction of 1.5 kcal/mol.     

Ab initio calculations on furan with a new computer program

Two ab initio calculations with different basis sets have been performed on the molecule furan, C₄H₄O. The calculations were done with a new computer program, REFLECT, which is presented. A preliminary analysis of the molecular wave functions has been made by looking at total and orbital energies and also by means of a population analysis. One inner shell ionization energy has been calculated by taking the difference in total energy for the molecule and the corresponding ion. The result is compared with the ionization energy obtained from Koopmans' theorem.