Verification of boundedness for the powers of symplectic matrices with the help of averaging

Novosibirsk. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 3–13, November–December, 1992.     

Theoretical study of the structure of the CClF2NO and CCl2FNO molecules in the ground and lowest excited singlet and triplet electronic states

The potential energy surfaces of the nitroso compounds CClF₂NO and CCl₂FNO in the ground and lowest excited singlet and triplet electronic states were studied by various ab initio methods (including multiconfigurational methods). The equilibrium geometric parameters, vibrational frequencies, internal rotation potential functions, and rotational contours of bands in the S₁ S₀ vibronic spectrum of the CClF₂NO molecule were calculated. For the molecules under consideration, the quantum-mechanical problem on torsional motion was solved. The results of calculations are, on the whole, in good agreement with experiment.     

One- and Two-Dimensional Torsion-Inversion Models for the Fluoral Molecule (CF3CHO) in Excited Electronic States

The structure of the conformationally nonrigid fluoral molecule (CF₃CHO) in the ground (S₀) and lowest excited triplet (T₁) and singlet (S₁) electronic states was studied by ab initio quantum-chemical methods. The equilibrium geometric parameters and harmonic vibrational frequencies of the molecule in these electronic states were determined. The calculations demonstrated that the electronic excitation causes substantial changes in the molecular structure involving the rotation of the CF₃ top and the deviation of the CCHO carbonyl fragment from planarity. The quantum-mechanical problems for large-amplitude vibrations, namely, for the torsional vibration in the S₀ state and the torsional and inversion vibrations (nonplanar carbonyl fragment) in the T₁ and S₁ states, were solved in the one- and two-dimensional approximations. A comparison of the results of calculations revealed the correlation between the torsional and inversion motions.     

S 1 ←S 0 vibronic spectrum and the structure of the chloral molecule in theS 1 stateS 0 vibronic spectrum and the structure of the chloral molecule in theS 1 state

The vibronic absorption spectrum of chloral (CCl₃COH) vapors is studied in the region of S₁ ← S₀ electron transition (32,000–28,700 cm⁻¹). The 29,070 cm⁻¹ vibronic transition (not observed because of low intensity) is believed to be the ‘start’ of the electron transition. Several fundamentals are found in the S₀ and S₁ states. Inversion splitting of the zero vibrational level in the S₁ state of chloral, indicating a nonplanar structure of the carbonyl fragment, is found. The intensity ratio of the torsional transition bands indicates that the S₁ ← S₀ electronic excitation of the chloral molecule causes significant changes in the orientation of the −CCl₃ group relative to the molecular framework. The potential functions of internal rotation (S₀ and S₁ states) and inversion (S₁ state) of the chloral molecule are determined from experimental data. The potential barriers of internal rotation (S₀ and S₁ states) and inversion (S₁ state) are 380, 780, and 760 cm⁻¹ (4.5, 9.3, and 9.1 kJ/mole), respectively. M. V. Lomonosov Moscow State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 3, pp. 507–513, May–June, 1998.     

Vibronic spectra and S1 excited electronic state molecular structures for acetyl chloride and acetyl fluoride

Vapor-state absorption spectra have been recorded for acetyl fluoride and acetyl chloride and also for deuterated derivatives with path lengths up to 40 m. The origins of the S₁S₀ transitions have been derived, together with the torsional-vibration energy levels in the ground state S₀ and excited singlet state S₁. Fitting the calculated and observed rotational contours of the vibronic bands has been used to estimate the geometrical parameters in the S₁ states. The carbonyl groups in the S₁ states are nonplanar. The internal-rotation potentials have been determined for acetyl fluoride and acetyl chloride in the S₁ and S₀ states. The relative intensities of the torsional transitions in those states indicate that the minima in the potential energy are appreciably displaced along the torsional coordinate in the S₀ and S₁ states.Chemical Faculty, Lomonosov Moscow University. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 26–30, January–February, 1993.     

Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states. Part III: Theoretical investigation of oxalyl fluoride

We present a theoretical investigation of oxalyl fluoride (COF)₂ in the ground and the four lowest excited (two singlet and two triplet) electronic states of the n,π∗-type mainly with the CASPT2(8-6)/cc-pVTZ method. Geometries, vibrational frequencies, potential energy functions of internal rotation, and adiabatic electronic transition energies were obtained. The conformer energy difference and the barrier to internal rotation in the ground electronic state were extrapolated to the complete basis set limit. The planar trans and cis conformations were the most stable configurations for all five electronic states under study. We found that the allowed electronic transition of the cis conformer has a transition energy that is significantly higher than that predicted in previous studies. For the excited states, the internal rotation was found to be accompanied by significant non-planar distortion of both carbonyl fragments, indicating strong coupling between these molecular motions.     

Neutrino oscillations in the gravitational field

We calculate the gravitational correction to the phase difference between neutrino mass eigenstates for the spherically symmetric gravitational field described by the Schwarzschild metric. This correction was calculated in a number of works, but the results of these works differ from each other. Our result does not coincide with the results ever published. In this work, we make calculations in the simplest way and verify our result by several tests.     

The Clebsch–Gordan Coefficients with Respect to Various Bases for Unitary and Orthogonal Representations of SU(2) and SO(3)

We calculate the Clebsch–Gordan coefficients for orthogonal rather than unitary representations of the rotation group.     

Interpolation formulas for maxwell viscosity of certain metals as a function of shear-strain intensity and temperature

The purpose of this study is the construction of interpolation formulas for the dependence of Maxwell viscosity, a quantity which is the reciprocal of shear-strain relaxation time , on shear-strain intensity and temperature for several metals: iron, aluminum, copper, and lead. This function was interpolated in various temperature and deformation velocity ranges in accordance with available experimental data for iron (0 10⁷ sec^–1, 200 ° T 1500 °); aluminum (0 10⁷ sec^–1, 300 ° T 900 °); copper (0 10⁵ sec^–1, 300 ° T 1300 °); lead (0 10⁶ sec^–1, 90 ° T 400 °); temperatures in °K.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 114–118, July–August, 1974.