L. Skála

The parity non-conserving energy difference between enantiomers and a consequence of the CPT theorem for molecule-antimolecule pairs

Abstract The energy difference between a chiral molecule and its antimolecule arising from parity non-conserving weak interactions is discussed. Calculations of this energy difference for methane derivatives are reported and results from the non-empirical Hartree-Fock and extended Huckel method are compared.

Analytic solutions of the Schrödinger equation for the modified quartic oscillator

No analytic solutions of the Schrödinger equation are known for the quartic anharmonic oscillator. We show in this paper that there are closely related modified quartic oscillators with the potential depending on |x| for which analytic solutions for some states exist. These results can be extended to the higher order oscillators

Theory of excitation energy transfer in the primary processes of photosynthesis I. General results

Abstract A general theory of the excitation energy transfer in the primary processes of photosynthesis based on the generalized master equation is formulated. The work provides a general theoretical description of four different regimes of the excitation energy transfer, analyzes the contribution of these regimes to the quantum yield characterizing the total efficiency of the transfer processes, presents a general analysis of mutual relations of nine experimental observables, takes into consideration limitations following from a finite experimental resolution and clarifies question what information on the excitation energy transfer processes can be obtained from experimental observables.

Maximum differences of electron density of states of finite and infinite crystals

The formulae determining the maximum differences of the integrated density of states and of the moments of the differential density of states of a finite and of the corresponding infinite crystal in the LCAO method are given and discussed in detail. The binding energies of one-, two- and three-dimensional model of a crystal are shown as an illustration of the general theory.

From finite to infinite crystals: Analytic solution of simple tight binding model of finite sc, fcc and bcc crystals of arbitrary size

The electronic structure of finite sc, fcc and bcc crystals having a rectangular parallelepiped geometry is investigated here. In all three cases, analytic formulae for the energies and wave functions are obtained. It is shown that the results for the fcc and bcc lattice in the tight binding first nearest neighbour approximation can directly be obtained from those for the sc lattice in the third nearest neighbour approximation. Further it is shown for the crystals in question that the concept of the Brillouin zone has a good meaning not only for the infinite crystals but also for the finite ones. The mutual relation of real and Born-Kármán boundary conditions and the transition finite-infinite crystal in both directions are investigated and discussed in detail.

Theory of excitation energy transfer in the primary processes of photosynthesis. II. Group symmetry analysis of the bacterial light-harvesting complex

Abstract A group symmetry analysis of the Pauli master equation for the excitation energy transfer in the cyclic arrangement of N (N= 6– 36) antenna Bchl molecules surrounding the bacterial reaction center of Rhodopseudomonas viridis is performed. The group theory allows to find analytic expressions for the most important observables (the antenna and reaction center fluorescence intensities and the quantum yield of the transfer to the charge transfer state) and to express their dependence on N. The time dependence of the fluorescence intensities is given by two exponentials, however, a single-exponential approximation can be used for t>t0 = 4–25 ps. The quantum yield of the excitation energy transfer to the reaction center charge transfer state is high (0.71– 0.98) for the whole range of physically acceptable values of the Forster radius R0 = 46–96 A.

From finite to infinite crystals: Some electronic properties of BCC clusters

Using results obtained within the framework of the tight binding nearest neighbour approximation (Bílek O.,Skála L., Czech. J. Phys.B 28 (1978), 1003) the analytical formulae for the band width, binding energy per atom, charge orders and bond orders of bcc clusters having a rectangular parallelepiped geometry are given. Numerical results for the number of atoms in the cluster in the range 9-2×106 illustrate the convergence of these properties. The asymptotical form of the formulae yields further detailed information. The band width and bond orders converge more quickly than the binding energy while the charge orders are equal to unity independently of the size of the cluster.

Interpolation formula for physical properties of polypeptides as a function of the number of amino acid residues

Abstract A simple interpolation formula for the evaluation of physical properties of polypeptides as a function of the number of the amino acid residues is suggested. The formula is applied to a model calculation of the band width and total π-electron energy of the exciton states of a finite helical polypeptide as well as to the interpolation of the binding energy and dipole moment known from the peptide quantum chemical analysis. The number of the amino acids necessary to achieve 10%, respectively 1% convergence of the interpolated quantities to their limit values is also calculated. Finally, the formula is used to discuss the increasing experimental tendency to take on the α-helical conformation in a series of the sequential peptides (L-lysyl-L-alanyl-L-alanine) n with their i

Effect of geometrical arrangement on experimental quantities in primary processes of photosynthesis

Abstract The effect of the number of antenna chlorophyll a molecules, their orientation and the dimensions of the reaction center on experimental quantities in a model of the antenna core based on the Pauli master equation is investigated. Results of numerical calculations, as well as analytic expressions for observables applicable from a few picoseconds after the excitation are given anddiscussed. The effect decreases with increasing time and from a few picoseconds it is very small.

On the nematic-isotropic phase transition in liquid amyl-ethoxy-cyanstilbene

Measurements of the index of refraction were used to evaluate the temperature dependence of the order parameterS in amyl-ethoxy-cyanstilbene (AECS). The results obtained may be described successfully in the frame of the Landau theory of phase transitions.