Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules

The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.     

Diffusion and solubility of some interstitial impurities in deformed metals

Summary The problem of impurity diffusion accompanying segregation phase nucleation on dislocations has been studied using the approximation of the local equilibrium with respect to the impurity distribution between the volume solution and dislocation regions. It has been shown that the known experimental data on diffusion and solubility of some interstitial impurities in cold-worked b.c.c. and f.c.c. metals and alloys can be described in the framework of the dislocation trap model. The characteristics of the impurity segregation regions near dislocations have been obtained from the treatment of the diffusion and solubility data for the systems. On the basis of the crystallographic and thermodynamic considerations the possibility of the existence of such segregation phase regions along dislocations in the systems in question has been shown.     

Calculation of rotation matrices for real spherical harmonics

N. G. Chernyshevskii Saratov State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 1, pp. 128–130, January–February, 1994.     

Interaction of oxygen adsorbed on silver film with hydrogen and ethylene

Kinetic data on hydrogen interaction with adsorbed oxygen testify to the uniformity and constancy of the oxygen bond with the silver surface. The surface reaction of ethylene epoxidation proceeds when the surface coverage by oxygen is higher than a certain threshold value, which is close to 0.4 for silver films at 333 K.     

Limiting-type theorem for conditional distributions of products of independent unimodular 2×2 matrices

We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments.     

DFT Calculation of the Structure of the Coordination Unit of Chlrophyll-Containing Proteins

In a DFT/B3LYP study (6-31G(d) basis set), the structure, IR spectra, and thermodynamic parameters of Mg-porphin-imidazole and Mg-khlorin-imidazole complexes, serving as models of the coordination unit of chlorophyll in proteins, have been calculated. When an axial ligand is added, the Mg atom goes out of the plane of the tetrapyrrole macrocycle, the deviation being 0.34 Å. The frequency of the out-of-plane vibrations of Mg in the complexes increased by 50 cm⁻¹, and the frequencies of the two in-plane vibrations decreased by 25 cm^{− 1}–30 cm⁻¹. IR vibrational spectra have been simulated.Original Russian Text Copyright © 2004 by M. D. Elkin, O. D. Ziganshina, K. V. Berezin, and V. V. Nechaev__________Translated from Zhurnal Strukturnoi Khimii, Vol. 45, No. 6, pp. 1132–1135, November–December, 2004.