Systematics of f-element crystal-field interaction

Systematic behaviors of free-ion and crystal-field interactions are elucidated as a function of N, the number of f electrons in a lanthanide or actinide ion. Experimentally determined values of the free-ion interaction parameters are compared with those calculated based on Hartree-Fock theory. Comparison is also made between the lanthanide series in 4f^N configurations and the actinide series in 5f^N configurations. Variation in intra-ionic electrostatic interaction, spin-orbit coupling, and ion-ligand interaction is analyzed in comparison between the iso-f-electron lanthanide and actinide ions. Based on an exchange-charge model of crystal-field theory, crystal-field parameters of the f-element ions in various crystals are summarized in terms of point charge contribution and covalence effect. A systematic correlation is found between the free-ion parameters and the crystal-field strength. Increase of the crystal-field interaction results in a reduction in the free-ion parameters.     

Electrostatic interaction between ion-penetrable membranes in a salt-free medium

A set of coupled equations is given which determines the distributions of the electric potential and counterions in a system of two interacting identical ion-penetrable membranes of thickness d at separation h immersed in a salt-free medium containing only counterions. The solution to these coupled equations also gives the electrostatic repulsive force between the membranes. It is shown that the interaction force remains finite at h-->0, unlike the case of the interaction between two planar charged surfaces (d-->0), and that the interaction force becomes independent of the membrane fixed charge and membrane thickness d at very large h. Finally, an approximate single transcendental equation giving the solution to the coupled equations is derived.     

The computation of the representation matrices of the generators of the unitary group

A method is presented for the efficient computation of the representation matrices of the unitary group, U(n) in the Gelfand—Tsetlin basis (corresponding to the usual spin-symmetry adapted basis for an N electron CI). The present scheme is conceptually and computationally attractive in that it is formulated directly in terms of Weyl tableaux and also that it permits simultaneous basis vector generation and matrix element evaluation. In addition the basis vectors are ordered so that subsequent restriction to the three dimensional rotation group is facilitated. An illustrative example is also presented.Taken in part from a thesis submitted to the University of London in partial fulfilment of the requirements for the degree of PhD.     

Molecular modeling on recognition of sheared and normal DNA by novel metal complex Λ- and Δ-[Co(phen)2hpip]

Recognition of sheared and normal DNA by a novel metal complex [Co(phen)₂hpip]³⁺ (phen=1,10-phenanthroline, HPIP=2-(2-hydroxyphenyl)imidazole[4,5-f][1,10]phenanethroline) is studied by molecular modeling. Calculating results indicate that, this complex can specifically recognize DNA segment of sequence –MMNNMM– (M means mismatch base pairs and N means normal base pairs). Intercalating from minor groove between the middle normal duplex into the sheared DNA with the depth of 1.2 nm is of preference and enantioselectivity is observed. Comparison on the two DNA structures of optimal conformation and analysis on the interaction between DNA and the two tail ligands of the complex show that, the effect of the two neighboring mismatch duplexes on the structure of the middle normal base pairs and the steric interaction between the mismatch duplexes and the two tail ligands of the complex are the essential reason to the segment specificity. Investigation on the detailed energy terms indicate that, in effecting enantioselectivity, the electrostatic distribution of the complex is in the majority and steric interaction is at the next place. But, steric interaction is surely the only factor determining the intercalating from minor groove.     

Molecular intercalates

The paper deals with the relations between host lattices and guest molecules. Several types of interaction of the guest molecules and the host material are explained and some conclusions are made about the arrangement of various guest molecules in the van der Waals' gap.     

X-ray and IR spectroscopic studies of specific intermolecular interactions inN′-substituted isonicotinohydrazides

_N-Thenylidene- andN-(o-nitrobenzylidene)hydrazides of isonicotinic acid have been studied by X-ray structural analysis and IR spectroscopy. In the crystalline state, these molecules are linked through intermolecular N—H ... Np_y hydrogen bonds. Carbonyl groups are not involved in intermolecular hydrogen bonds. However, it was found that the C=O group participates in an attractive interaction with the sulfur atom of the thiophene group. The energy of this interaction is comparable with the energies of intermolecular C=O ... H—N hydrogen bonds in amides.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 4, pp. 896–900, April, 1996.     

On the Interaction of Two Finite-Dimensional Quantum Systems

Interaction of quantum system S ^a described by the generalised × eigenvalue equation A| _s =E _s S ^a | _s (s=1,...,) with quantum system S ^b described by the generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) is considered. With the system S ^a is associated -dimensional space X ^a and with the system S ^b is associated an n-dimensional space X _n ^b that is orthogonal to X ^a . Combined system S is described by the generalised (+n)×(+n) eigenvalue equation [A+B+V]| _k = _k [S ^a +S ^b +P]| _k (k=1,...,n+) where operators V and P represent interaction between those two systems. All operators are Hermitian, while operators S ^a ,S ^b and S=S ^a +S ^b +P are, in addition, positive definite. It is shown that each eigenvalue _{k i} of the combined system is the eigenvalue of the × eigenvalue equation . Operator in this equation is expressed in terms of the eigenvalues _i of the system S ^b and in terms of matrix elements _s |V| _i and _s |P| _i where vectors | _s form a base in X ^a . Eigenstate | _k ^a of this equation is the projection of the eigenstate | _k of the combined system on the space X ^a . Projection | _k ^b of | _k on the space X _n ^b is given by | _k ^b =( _k S ^b –B)^–1(V– _k P})| _k ^a where ( _k S ^b –B)^–1 is inverse of ( _k S ^b –B) in X _n ^b . Hence, if the solution to the system S ^b is known, one can obtain all eigenvalues _{k i} } and all the corresponding eigenstates | _k of the combined system as a solution of the above × eigenvalue equation that refers to the system S ^a alone. Slightly more complicated expressions are obtained for the eigenvalues _{k i} } and the corresponding eigenstates, provided such eigenvalues and eigenstates exist.     

Operation of the quasi-optical gyrotron at harmonics of the gyrofrequency

This paper investigates the performance of a quasioptical gyrotron, when the electron beam interacts with the radiation fields at harmonics of the gyrofrequency. The nonlinear equations of motion are obtained in the slow-timescale. The expression for the linear gain is derived and the conditions for excitation are given (frequency threshold, optimal operating point, bean current and resonator quality thresholds). In the nonlinear regime, it is shown that maximum efficiencies comparable to those at the fundemental (50%) are possible, albeit at a prohitively high radiation field amplitude, while realistically feasible field amplitudes can give somewhat smaller, but nevertheless still high efficiencies (15%). Finally, the results are suplemented by empirical scaling laws, useful for experimental designs.     

Supramolecular Hybrids from Cyanometallate Complexes and Diblock Copolypeptide Amphiphiles in Water

The self-assembly of discrete cyanometallates has attracted significant interest due to the potential of these materials to undergo soft metallophilic interactions as well as their optical properties. Diblock copolypeptide amphiphiles have also been investigated concerning their capacity for self-assembly into morphologies such as nanostructures. The present work combined these two concepts by examining supramolecular hybrids comprising cyanometallates with diblock copolypeptide amphiphiles in aqueous solutions. Discrete cyanometallates such as [Au(CN)₂]⁻, [Ag(CN)₂]⁻, and [Pt(CN)₄]²⁻ dispersed at the molecular level in water cannot interact with each other at low concentrations. However, the results of this work demonstrate that the addition of diblock copolypeptide amphiphiles such as poly-(L-lysine)-block-(L-cysteine) (Lys_m-b-Cys_n) to solutions of these complexes induces the supramolecular assembly of the discrete cyanometallates, resulting in photoluminescence originating from multinuclear complexes with metal-metal interactions. Electron microscopy images confirmed the formation of nanostructures of several hundred nanometers in size that grew to form advanced nanoarchitectures, including those resembling the original nanostructures. This concept of combining diblock copolypeptide amphiphiles with discrete cyanometallates allows the design of flexible and functional supramolecular hybrid systems in water.