Dynamics of the chalcopyrite lattice

The symmetry properties of the normal modes of the chalcopyrite lattice are analyzed. The phonon spectra of chalcopyrite and sphalerite are compared. There is a discussion of the intensity of the IR absorption lines due to single-phonon processes. Selection rules are found for direct and indirect transitions. Carrier scattering by phonons is analyzed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 10, pp. 42–48, October, 1970.     

Phonons in Si3Ge1 and Si1Ge3 short-period superlattices

Oscillatory spectra and single-phonon state densities are calculated in the Keating atomic interaction model for the ultrathin superlattices Si₃Ge₁ and Si₁Ge₃. Fundamental features of the superlattice phonon spectra and their relationship to the spectra of Si and Ge crystals are analyzed. Conditions required for oscillation localization in the interface region are studied and the role of the Si-Ge bond in formation of interlayer oscillations is considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii. Fizika, No. 8, pp. 40–44, August, 1993.     

Line Positions and Intensities of the ν1+ ν2+ 3ν3, ν2+ 4ν3, and 3ν1+ 2ν2Bands of Ozone

Using a Fourier transform spectrometer, we have recorded the spectra of ozone in the region of 4600 cm⁻¹, with a resolution of 0.008 cm⁻¹. The strongest absorption in this region is due to the ν₁+ ν₂+ 3ν₃band which is in Coriolis interaction with the ν₂+ 4ν₃band. We have been able to assign more than 1700 transitions for these two bands. To correctly reproduce the calculation of energy levels, it has been necessary to introduce the (320) state which strongly perturbs the (113) and (014) states through Coriolis- and Fermi-type resonances. Seventy transitions of the 3ν₁+ 2ν₂band have also been observed. The final fit on 926 energy levels withJ_max= 50 andK_max= 16 gives RMS = 3.1 × 10⁻³cm⁻¹and provides a satisfactory agreement of calculated and observed upper levels for most of the transitions. The following values for band centers are derived: ν₀(ν₁+ ν₂+ 3ν₃) = 4658.950 cm⁻¹, ν₀(3ν₁+ 2ν₂) = 4643.821 cm⁻¹, and ν₀(ν₂+ 4ν₃) = 4632.888 cm⁻¹. Line intensities have been measured and fitted, leading to the determination of transition moment parameters for the two bands ν₁+ ν₂+ 3ν₃and ν₂+ 4ν₃. Using these parameters we have obtained the following estimations for the integrated band intensities,S_V(ν₁+ ν₂+ 3ν₃) = 8.84 × 10⁻²²,S_V(ν₂+ 4ν₃) = 1.70 × 10⁻²², andS_V(3ν₁+ 2ν₂) = 0.49 × 10⁻²²cm⁻¹/molecule cm⁻²at 296 K, which correspond to a cutoff of 10⁻²⁶cm⁻¹/molecule cm⁻².     

Asymptotic behavior of rotational energies of rigid X2Y-type molecules

In this study the asymptotic behavior of rotational energies of simple rigid molecules of X₂Y-type is considered. This behavior is obtained using various forms of an effective rotational Hamiltonian. The results of calculations for highly excited rotational energies of the molecules H₂O and CH₂ are presented.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 9–12, January, 1990.     

Model with uniquely deducible parameters for the combined analysis of two resonating vibrational states. Anharmonic resonances in molecules of asymmetric-gyroscope type

A model of an effective Hamiltonian with parameters that are uniquely deducible from the spectrum for the combined analysis of the rotational structure of two resonating vibrational states is proposed and validated. Anharmonic resonances in molecules of asymmetric-gyroscope type are considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 108–112, February, 1982.     

Investigation of the stability of the inverse spectroscopic problem of diatomic molecules

The stability and convergence of the inverse spectroscopic problem is investigated for diatomic molecules in the¹ electron state for a potential representation by series in the Dunham variable z_d=(r-r_e)/r_e, the Ogilvie-Tipping z_ot=(r-r_e)/(r + r_e), the Simmond-Parr-Finlan z_S= (r-r_e)/r and the Tucker z_t=sign (p)[1 -(r_e/r)^P]. None among the representations under investigation was that which would give a significant systematic improvement in stability as compared with others. The convergence is related to the selection of the initial approximation in the method of least squares, and is practically independent of the functional form of the potential. For the Dunham representation the solutions of the inverse problem yield quantities close to the true values of the expansion coefficients.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 98–101, May, 1984.     

High-order anharmonicity parameters in various representations of the diatomic potential function and exact relations between spectroscopic constants. application to the co molecule

Closed formulae for Born—Oppenheimer anharmonicity parameters a_n in terms of isotopically invariant constants U_mj are derived for Dunham, Simons—Parr—Finlan, Ogilvie—Tipping and Thakkar representations and are applied to the CO molecule. Models for a fit of vibration—rotation and pure rotational transitions based on the exact relations U_mj = f(U_k,o, U_k-1.1) and U_mj = α(U_k,1, U_k,2) are discussed.     

Update of the anharmonic force field parameters of the ozone molecule

A new set of spectroscopic constants of the ¹⁶O₃ molecule (ω_i, x_ij, y_ijk, γ^DD, _i^X, β_ij^X,…), which determine vibrational dependence of band centres and rotational parameters, is derived from recent accurate analysis of high-resolution experimental ro-vibrational spectra through the theoretical approach based on second-order perturbation expansions in normal coordinates accounting for Darling–Dennison resonance interactions. These values are used to update empirical values of anharmonic coefficients (k_ijl, k_ijlm) of the potential function expansion in normal coordinates. Quadratic f_rr, f_r, f_rr′, f as well as cubic f_rst and quartic f_rstl force constants in internal (bond lengths, bond angle) coordinates are also derived. A detailed discussion is devoted to the accuracy of parameter determination for each of four steps of calculations. It is emphasised that the conventional method based on the inversion of formulae of the perturbation theory gives the largest uncertainties at the last step of calculations: the determination of the anharmonic force field in internal coordinates.     

CRDS spectroscopy of O3. Part 2: Analysis of six interacting bands between 5930 and 6080 cm

The absorption spectrum of ¹⁸O₃ has been recorded in the 5930-6080 cm⁻¹ region using CW-Cavity Ring Down Spectroscopy. 1888 transitions belonging to five bands have been assigned. Three of them are A-type bands: 2ν₂ + 5ν₃, ν₁ + ν₂ + 5ν₃ and 5ν₁ + ν₃, and two bands are of B-type: 2ν₁ + ν₂ + 4ν₃ and 4ν₁ + 3ν₂. Despite a complex spectral pattern perturbed by many rovibrational resonances, it has been possible to find a suitable effective Hamiltonian model reproducing all the transition wavenumbers (corresponding to 1016 energy levels) with an rms deviation of 9.5 × 10⁻³ cm⁻¹. A set of 721 line intensities was determined and fitted to derive the effective transition moment parameters. This set of parameters and the experimental energy levels were used to generate a complete line list of 2795 transitions allowing to generate synthetic spectrum in good agreement with the experimental spectrum.     

Electron-phonon relaxation and excited electron distribution in zinc oxide and anatase

We propose a first-principles method for evaluations of the time-dependent electron distribution function of excited electrons in the conduction band of semiconductors. The method takes into account the excitations of electrons by an external source and the relaxation to the bottom of the conduction band via electron-phonon coupling. The methods permit calculations of the non-equilibrium electron distribution function, the quasi-stationary distribution function with a steady-in-time source of light, the time of setting of the quasi-stationary distribution and the time of energy loss via relaxation to the bottom of the conduction band. The actual calculations have been performed for titanium dioxide in the anatase structure and zinc oxide in the wurtzite structure. We find that the quasi-stationary electron distribution function has a peak near the bottom of the conduction band and a tail whose maximum energy rises linearly with increasing energy of excitation. The calculations demonstrate that the relaxation of excited electrons and the setting of the quasi-stationary distribution occur within a time of no more than 500?fs for ZnO and 100?fs for anatase. We also discuss the applicability of the effective phonon model to energy-independent electron-phonon transition probability. We find that the model only reproduces the trends in the change of the characteristic times whereas the precision of such calculations is not high. The rate of energy transfer to phonons at the quasi-stationary electron distribution also have been evaluated and the effect of this transfer on the photocatalysis has been discussed. We found that for ZnO this rate is about five times less than in anatase.