Vibrations of excited molecules at combination and difference frequencies

In the context of the theory of molecular vibrations, by applying the direct product operation of matrices, an equation for the vibrations of vibrationally excited molecules at combination and difference frequencies is obtained. From the solution of this equation, elements of vibration patterns and expressions that can be used for the study of changes in the molecular structural parameters and the coefficients of kinematic interactions are determined. The formulas obtained are applied to the calculation of the anharmonic electro-optical parameters of the molecules of water H₂O and its two isotopes H₂ ¹⁷O and H₂ ¹⁸O. These calculations are performed in terms of the semiempirical quantum-chemical CNDO/2 method and by numerical differentiation of dipole moment functions by employing a cubic spline approximation.     

Germanium–vacancy color center in isotopically enriched diamonds synthesized at high pressures

We report on the high-pressure synthesis of novel nano- and microcrystalline diamonds with germanium–vacancy (Ge–V) color centers emitting at 602 nm. The synthesis was carried out in non-metallic growth systems C–H–Ge and C–H–O–Ge enriched with germanium and carbon isotopes. We demonstrate germanium and carbon isotope shifts in the fine structure of the luminescence, which allows us to unambiguously associate the center with the germanium impurity entering into the diamond lattice. We show that there are two ground-state energy levels with the separation of 0.7 meV and two excited-state levels separated by 4.6 meV in the electronic structure of the center and suggest a split-vacancy structure of this center. High-intensity and narrow-line emission of high-pressure synthesized small diamonds with Ge–V centers makes them promising candidates for single-photon emitters.     

Highly excited vibrations of molecules at combination and difference frequencies

An equation for highly excited vibrations of molecules at combination and difference frequencies is derived by means of modification of the basic equation for the normal vibrations of molecules by applying the direct product operation of matrices and using the properties of this operation with respect to the eigenvalues and eigenvectors of the multiplicand matrices. From the solution of the equation derived, the elements of vibration patterns are determined, which allow one to find expressions for the structural molecular parameters and the coefficients of kinematic interactions and to study their changes.     

Analytical perturbations of wave functions and energy levels of vibrational states of molecules

A method for investigating the excited vibrational states of molecules based on the analytical perturbation theory for linear operators is proposed. According to this theory, the similarity transformation of the total projector and the construction of the transforming function allow obtaining analytical representations of eigenvectors, and in the course of reduction, eigenvalues of the perturbed operator. Theoretical statements and formulas of contributions of analytical perturbations are applied to the investigation of vibrational-rotational interactions, determination of wave functions, and corresponding energy values of excited vibrational states of molecules.     

Heat capacity of high-purity isotope-enriched germanium-76 in the temperature range of 2–15 K

The heat capacity of high-purity isotopically-enriched germanium Ge-76 has been measured in the range of 2.5–15 K. In this range, the heat capacity of Ge-76 is 6–15% higher than the heat capacity of germanium of the natural isotopic composition, which is determined by a change in the average mass.     

Effect of mode interaction on spectroscopic parameters of molecular vibrations with combination frequencies

An equation has been obtained for excited vibrations with combination frequencies by modifying the equation for the normal vibrations of the molecules, using the direct product operation and its properties for the eigenvalues and eigenvectors of the cofactor matrices within matrix perturbation theory. From the solution of the equation, the elements of the vibrational mode tensor are determined, for which formulas are written (in terms of projectors of the matrix of the dynamic coefficients) that take into account their changes for excited vibrations. Using these formulas makes it possible to study the effect of perturbations on the change in the intramolecular and spectroscopic parameters of combination vibrations of the molecules. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 4, pp. 421–425, July–August, 2006.     

Influence of interactions of excited vibrations on the molecular parameters

The interaction of vibrations is studied by the algebraic method of perturbation theory. Formulas are derived that take into account the influence of interactions on the anharmonic spectroscopic parameters of excited vibrations with compound frequencies. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–32, March, 2008.     

Activity Coefficients of Ferrocenium Iodide in Aqueous-Organic Salt Solutions

Potentiometric titration at 298.2 was used to measure electrode potentials and to estimate standard EMFs and unified activity coefficients for ferrocenium iodide in aqueous-acetone and aqueousethanol solutions of various salt compositions.     

Spectroscopic Parameters of High Overtones of the Vibrations of Molecules

Based on the fundamental equation from the vibration theory of molecules and the operation of direct product of matrices and its properties for eigenvalues and eigenvectors, an equation of overtone vibrations for any high order has been obtained whose solution yields the matrices of vibration modes. Correlations determining changes in the structure parameters, just as expressions for the matrices of the coefficients of kinematic interaction and force constants, and for the parameters of vibrational-rotational interaction have been presented. Using the formulas obtained, the electro-optical parameters of water molecules H₂O and isotopes H₂ ¹⁷O and H₂ ¹⁸O have been calculated for overtones of up to the sixth order within the framework of the semiempirical quantum-chemical CNDO/2 method using the method of numerical differentiation by spline functions.     

Determination of oxygen and carbon impurities in polycrystalline silicon by IR spectrometry

The possibility of using infrared spectrometry for the determination of the total oxygen and carbon impurity in polycrystalline silicon of the natural isotope composition and that enriched with the ²⁸Si isotope was studied for samples synthesized by different methods. The results of determining these impurities by the optical method are compared to those obtained by independent methods of analysis. The conditions of IR spectrometric analysis of the silicon synthesized by deposition from the gas phase are determined. It is shown that, for IR spectrometry, the upper boundaries of the analytical range of oxygen and carbon in polycrystalline silicon are 1 × 10¹⁸ and 2 × 10¹⁸ cm^?3; and the limits of their detection are 8 × 10¹⁵ and 5 × 10¹⁵ cm^?3 at a sample thickness of 0.5 and 0.2 cm, respectively.