Franz Mark

Variational solution of the dirac equation within a multicentre basis set of gaussian functions

Abstract The Dirac equation for one-electron polynuclear systems is solved variationally within an analytical multicentre basis set. Each of the four components of the molecular spinor is expanded separately into a scalar basis set. The expansion coefficients are obtained from the variational principle. Calculations using gaussian functions are performed for hydrogen-like atoms and for hydrogen-ion-like molecules with constituents of nuclear charge Z = 1, 50 and 90.

Analytical relativistic hartree-fock equations within scalar basis sets

Abstract Analytical relativistic Hartree-Fock equations for closed-shell polyatomic systems are derived by expanding each component of the molecular one-electron spinors separately into a scalar basis set. Within the context of the elimination method non-relativistic reference eigenvalue equations are obtained which for a complete basis reduce to the non-relativistic Hartree-Fock-Roothaan equations. Calculations using gaussian basis functions are performed for He and H 2 .

Radiolysis of DNA in aqueous solution in the presence of a scavenger: A kinetic model based on a nonhomogeneous reaction of OH radicals with DNA molecules of spherical or cylindrical shape

SummaryTwo expressions are given for the survival dose of DNA exposed to high-energy radiation in aqueous solution in the presence of a scavenger. They are derived from a model where a diffusion controlled reaction of OH radicals occurs on the surface of the DNA macromolecules in competition with scavenging in the bulk of the solution. The DNA molecules are approximated either by spheres or by cylinders. The model based on molecules of spherical shape corresponds closely to that developed by van Rijn et al. [20]. Expressions obtained from the cylindrical model are used to account for the dependence on the scavenger concentration of some experimentally measured quantities, namely the survival dose and theG value for single-strand breaks upon Co γ-irradiation ofΦX 174 DNA and polyadenylic acid, respectively.

Interpretation of the resonance Raman spectra of linear tetrapyrroles based on DFT calculations

Abstract Raman spectra of linear methine-bridged tetrapyrroles in different conformational and protonation states were calculated on the basis of scaled force fields obtained by density functional theory. Results are reported for protonated phycocyanobilin in the extended ZZZasa configuration, as it is found in C-phycocyanin of cyanobacteria. The calculated spectra are in good agreement with experimental spectra of the protein-bound chromophore in the α-subunit of C-phycocyanin and allow a plausible and consistent assignment of most of the observed resonance Raman bands in the region between 1000 and 1700 cm −1 .

Raman spectroscopic analysis of isomers of biliverdin dimethyl ester.

The constitutional isomers of biliverdin dimethyl ester, IX alpha and XIII alpha, were studied by resonance Raman spectroscopy. The far-reaching spectral similarities suggest that despite the different substitution patterns, the compositions of the normal modes are closely related. This conclusion does not hold only for the parent state (ZZZ, sss configuration) but also for the configurational isomers which were obtained upon double-bond photoisomerization. Based on a comparison of the resonance Raman spectra, a EZZ configuration is proposed for one of the two photoisomers of biliverdin dimethyl ester IX alpha, while a ZZE, ssa configuration has been assigned previously to the second isomer.

Perturbational analysis of the regioselectivity in the acrolein dimerization

Abstract Using intermolecular SCF-perturbation theory, the controlling factors determining the regioselectivity in the acrolein dimerization are derived by a rigorous decomposition of the interaction energy. This partitioning of the interaction energy is performed up to a level where a comparison with frontier orbital models is possible. The regioselectivity is found to be determined by orbital interactions occuring via the terminal atoms and atoms involved in secondary Woodward-Hoffmann interactions.

THEORETICAL AB INITIO AND SEMIEMPIRICAL STUDIES ON BIOLOGICALLY IMPORTANT DI- AND OLIGOPYRROLIC COMPOUNDS. PYRROMETHENONE AND BILIVERDIN

Abstract Comparative ab initio (HF/6-31G ∗ and MP2/6-31G ∗ ) and semiempirical (AM1 and PM3) studies of pyrromethenone as a model of the non-hydrogen bonded part of biliverdin-related compounds have been performed. The structure and the relative energies of the conformational isomers formed by rotation around the single and double CC bonds of the methine bridge were calculated. It has been found that the geometry of the pyrromethenone molecule calculated at the MP2, HF and AM1 levels corresponds well with the X-ray data of 3,4-dimethyl-2,2′-pyrromethen-5(1 H )-one. The reliability of the AM1 method for the calculations of biliverdin-related molecules has been proven. Calculations of the ground state of octamethylbilindione and biliverdin IXα molecules as models of open-chain tetrapyrrolic chromophores have been carried out at the AM1 level. An analysis of the rotation barrier heights and the relative energies in a vacuum and in a chloroform solution has been performed on biliverdin-related molecules to estimate the energy and structure effects at the rotation around the C 5 C 6 single bond at the methine bridge.

Relativistic Gaussian basis sets for the atoms hydrogen to neon

Gaussian basis sets for use in relativistic molecular calculations are developed for atoms and ions with one to ten electrons. A relativistic radial wavefunction coupled to an angular function of l-symmetry is expanded into a linear combination of spherical Gaussians of the form rl exp (−αr2). One set of basis functions is used for all large and small components of the same angular symmetry. The expansion coefficients and the orbital exponents have been determined by minimizing the integral over the weighted square of the deviation between the Dirac or Dirac-Fock radial wavefunctions and their analytical approximations. The basis sets calculated with a weighting function inversely proportional to the radial distance are found to have numerical constants very similar to those of their energy-optimized non-relativistic counterparts. Atomic sets are formed by combining l-subsets. The results of relativistic and non-relativistic calculations based on these sets are analyzed with respect to different criteria, e.g. their ability to reproduce the relativistic total energy contribution and the spin-orbit splitting. Contraction schemes are proposed.

Zur Photodimerisierung von 3-Methyl-2-cyclopentenon

ZusammenfassungBei der Belichtung von 3-Methyl-2-cyclopentenon in Lösung entstehen die Isomeren Cyclobutane I, II, III und IV sowie zwei weitere Dimere, V und VI, die ein Oxocyclopentylcyclopentenon-Gerüst besitzen. Das Verhältnis der gebildeten Dimeren ist abhängig vom Lösungsmittel und von der Konzentration der belichteten Lösung. Die Logarithmen der Dimerenverhältnisse korrelieren linear mit demKirkwood-Onsager-Parameter des Lösungsmittels; der Konzentrationseinfluß läßt sich durch den gemessenenKirkwood-Onsager-Parameter der Lösung erfassen.AbstractIrradiation of 3-methyl-2-cyclopentenone in solution yields the isomeric cyclobutanes I, II, III and IV, and two other dimers with oxocyclopentyl-cyclopentenone structure (V and VI, resp.). The ratio of the dimers is dependent on the solvent and on the concentration of the irradiated solution. The logarithms of the dimer ratios are related linearly to theKirkwood-Onsager parameter of the solvent; the concentration effect can be correlated with the measuredKirkwood-Onsager parameter of the solution.

The relativistic energy correction of the H2+ molecule

From variational solutions of the Dirac and Schrodinger equation using extended Gaussian basis sets the relativistic energy correction ΔEr of H2+ at R = 2.0 [Bohr] is estimated to be − 7.366 [μHa]. The leading coefficients in a series expansion of ΔEr in powers of the fine structure constant are obtained numerically. It is concluded that the value of ΔEr was slightly underestimated in earlier calculations based on the Dirac equation, whereas it was slightly overestimated in those based on perturbation theory.