Volume 60, Issue 3

By using a new more general ansatz with the aid of symbolic computation, we extended the unified algebraic method proposed by Fan [Computer Phys. Commun. 153, 17 (2003)] and the improved extended tanh method by Yomba [Chaos, Solitons and Fractals 20, 1135 (2004)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations. The efficiency of the method is demonstrated on the (2+1)-dimensional Broer-Kaup- Kupershmidt equation.

The mapping method is used with the aid of the symbolic computation system Mathematica for constructing exact solutions of the modified Kawahara equation. By this method the modified Kawahara equation is investigated and new exact traveling wave solutions are obtained. The solutions obtained in this paper include Jacobi elliptic solutions, combined Jacobi elliptic solutions, solitary wave solutions, periodic wave solutions, trigonometric solutions and rational solutions.

The spin Hamiltonian g factors and the hyperfine structure constants for V 2+ in CsMgX 3 (X = Cl, Br, I) are theoretically studied by using the perturbation formulas of these parameters for a 3d 3 ion in octahedral symmetry, based on the cluster approach. In such formulas, the contributions from the s-orbitals of the ligands were usually neglected. Here they are taken into account. The theoretical results (particularly the g factor for CsMgI 3 ) show a significant improvement compared with those in absence of the ligand s-orbital contributions in the previous studies.

In order to avoid divergence of its self-energy the free electron at rest is described as a relativistic continuum of finite extent. It has the form of an axisymmetric torus of finite aspect ratio, which rigidly rotates around its axis of symmetry with superluminal speed (v > c). It is shown that there is a class of stationary solutions of the free-boundary value problem. The parameter dependence of these solutions is related to experimental data.

MINDO/3-FORCES calculations were carried out for the radical ions of benz[a]anthracene. Both ions exhibit C s symmetry with C-C bond alternation in all four rings. The obtained equilibrium geometry was applied for the calculation of all 3N − 6 vibration frequencies of each ion, and for the analysis of their normal coordinates. The so calculated frequencies of the radical cation were close to the experimental frequencies and those of the ab initio calculations. They fall in the ranges νCHstr. (3034 - 3087 cm −1 ), νCCstr. (1237 - 1609 cm −1 ), δCH (1142 - 1216 cm −1 ). Interesting correlations could be obtained for the frequencies of similar vibrations, e. g. ν sym CHstr. >ν asym CHstr. Exception is the frequency of vibration of CHα in ring A for the radical cation and the same bond in ring D for the radical anion. The vibration frequencies for the CH bonds depend on the σ -electron densities of the corresponding carbon atoms, i. e. νCH. + str. >νCHstr. >νCH. − str., where σ −ρ Ċ + >σ −ρ C >σ −ρ Ċ − . For the C-C stretching vibrations the relation ν(C-C)str. >ν(C-C). − str. >ν(C-C). + str. holds, with the exception of the C β -C β bond, for which the relation ν(C-C)str. >ν(C-C). + str. >ν(C-C). − str. is found. As for the in-plane and out of-plane deformations, the following general correlations δ (CH) >δ (CH). − >δ (CH). + and γ (CC) >γ (CC). − >γ (CC). + .

MINDO/3-FORCES calculations were carried out for the vibration frequencies and IR absorption intensities of phenanthrene radical ions. The obtained frequencies were compared with the experimental values possible. It was found that the C-H stretching frequencies are directly related to the carbon σ -electron densities of the relevant atoms.

The partitioning of π-electrons into rings of benzenoid hydrocarbons is examined in the case of fibonacenes. It is demonstrated that the π-electron contents (ECs) of the hexagons of fibonacenes satisfy the following peculiar regularities: Let h be the number of hexagons, and EC(i) the electron content of the i-th hexagon. Then EC(i) is maximal for i = 1 and i = h, and minimal for i = 2 and i = h−1 . Going from the end towards the center of the fibonacene chain, EC(1) >EC(3)> EC(5)> · · · and EC(2)< EC(4) <EC(6) <· · · and EC(1)> EC(2)< EC(3) >EC(4) <EC(5) >EC(6) <· · · . For large values of h, the asymptotic values of EC(1) and EC(2) are 5.146 and 3.798, whereas of the central ring(s) 4 π-electrons.

The second moment of 1 H NMR absorption spectra was calculated for three samples of [(NH 2 ) 2 CS] 2 (C 5 H 5 NH) + NO 3 − , two of which were deuterated at different positions. The calculations were performed for different rotations and oscillations, and for a wide range of frequencies of these motions. These frequencies were then transformed into temperatures resulting in the temperature dependence of the second moment. The calculations were undertaken in order to analyze the experimental results obtained in our laboratory. Special attention was paid to molecular reorientations through unequal potential barriers. Comparison of the second moment values calculated for different models of rotation with the experimental ones enabled a deeper insight into the internal motion in this material as a function of temperature.

The force constants of the internal coordinates of planar XY 3 and tetrahedral XY 4 molecules were calculated using the GF matrix method. The matrix solutions were carried out by means of a computer program built relative to the Newton-Raphson method, and the calculations were listed in tables. For tetrahedral XY 4 molecules having the same Y atom it was found that the force constants decrease with the increasing mass of the X atom, and this was attributed to the slowing of the molecule with increasing mass of the centre X atom.

Molecular dynamics simulations of molten (La 1/3 , K)Cl at 1123 K have been performed in order to investigate the correlation between simulated dynamical properties such as the self-exchange velocity (ν), the self-diffusion coefficient (D) and the electrical conductivity (κ) and the corresponding experimental values. The simulated results revealed that v and D of potassium decrease with increasing mole fraction of lanthanum, as expected from the experimental internal cation mobilities, b. The decrease of b K , ν K and D K is ascribed to the tranquilization effect by La 3+ , which strongly interacts with Cl − . In contrast, b La , ν La , and D La increase with increasing concentration of La 3+ . The distorted linkage of the network structure of [LaCl 6 ] 3− units was disconnected with increasing the concentration of the alkali chloride. This might be attributed to the stronger association of La 3+ with Cl − due to the enhanced charge asymmetry of the two cations neighboring Cl − . The sequence of the calculated v’s, D’s, and κ’s is consistent with those of the referred experimental results.

A formula for the calculation of the three g factors of 3d 9 ions in an orthorhombic field D 2h has been derived. Using it to investigate the EPR g factors of the Cu 2+ ions in single crystals of Cu 0.5 Zr 2 (PO 4 ) 3 , the variation of the g factors on changing the angle α between the x- and y-axis has been explained. According to that, it can be confirmed that the angle α of the D 2h distortion is about 62.6°. PACS: 71.70C; 76.30F

The molar enthalpies of mixing (Δ mix H m ) of liquid PrCl 3 -LiCl and NdCl 3 -LiCl mixtures have been measured at 1044 K. For both systems these enthalpies are negative in the whole composition range, with a minimum at x PrCl3 and x NdCl3 ≈ 0.4. The results are compared with existing mixing enthalpy data on lanthanide chloride-alkali metal chloride systems and discussed in terms of complex formation in the melts.

The complex formation between cobalt(II) and chloride ions in molten NH 4 NO 3 ・2.61H 2 O, NH 4 NO 3 ・CH 3 CONH 2 ・1.61H 2 O and NH 4 NO 3 ・2.61CH 3 CONH 2 has been investigated. Absorption spectra of cobalt(II) chloride containing variable amounts of ammonium chloride were recorded at 45 to 60 °C. In the absence of chloride, the solutions show spectra typical for octahedral co-ordination of cobalt(II). Addition of chloride caused a shift of the absorption maximum toward lower energies and an increase of the molar absorption coefficient with increasing chloride concentration. The position of the absorption maximum and the intensity of the absorption indicate tetrahedral or severely distorted octahedral co-ordination. The stability constants for [Co(NO 3 ) 4 ] 2− , [Co(NO 3 ) 2 Cl 2 ] 2− and [CoCl 4 ] 2− complex formation in NH 4 NO 3 ・2.61CH 3 CONH 2 are reported.