The assignment of molecular infrared spectra from a laser magnetic resonance spectrometer

Mathematical techniques are presented which have proved useful in assigning the laser magnetic resonance pure-rotation spectrum of HO₂, i.e., useful in assigning an absorption spectrum obtained when molecular energy levels are Zeeman shifted by an external magnetic field until transition frequencies coincide with a fixed-frequency radiation source. The techniques described should have general applicability to the laser magnetic resonance vibration-rotation spectrum of any molecule in an orbitally nondegenerate electronic state and a doublet electronic spin state ($\text{S =}\text{1}\text{2}$). Equations involving both Zeeman line positions and Zeeman line intensities are presented. These allow the assignment of M_J quantum numbers, the determination of the spin-rotation interaction constant γ and rotational quantum number N for both the upper and the lower state, and the determination of the zero-field transition frequency. The equations can be used without prior knowledge of the molecular structure or energy levels.     

On the stability of parameters of molecular models in the parametric method of the theory of vibronic spectra

We have studied the stability of the system of parameters used in the parametric method of the theory of vibronic spectra of polyatomic molecules with respect to whether the initial structural-dynamic model of the ground state of a molecule is formed either by the fragmentary method or by direct quantum-chemical calculation. Modeling of excited states and spectra of the stilbene-h ₁₂ and stilbene-d ₁₂ molecules showed that, although the initial models of the ground states are significantly different, calculated changes in the geometry that occur upon excitation and electronic-vibrational spectra of the models are close and quantitatively agree with experiment. This indicates that the parameters of the method are stable and are applicable for performing predictive calculations of vibronic spectra based on models of the ground states created by different methods. We show that the fragmentary method has a considerable advantage, since models created by this method take into account the continuity of the structure in series of related compounds and calculations can be easily performed for molecules of arbitrarily high complexity. We show that direct quantum-chemical calculations are important in the case of molecules with unknown structural-dynamic models of fragments in the ground states.     

Analysis of Coriolis perturbations in the high-resolution infrared spectra of arsine (AsH3)

Numerical methods for the analysis of high-resolution infrared spectra of symmetric top molecules perturbed by Coriolis interactions between degenerate and nondegenerate vibrational levels are discussed in the second order of approximation. Application to the high-resolution infrared spectra of the AsH₃ molecule in the region of the fundamentals ν₁, ν₃ and ν₂, ν₄ yields considerably improved values of the molecular constants of AsH₃, including the band origins rotational constants, Coriolis coupling constants, centrifugal distortion constants, and the parameter of the K-type doubling effect.     

The kinetic theory of the perturbations in the isotropic universe

The short wave and long wave gravitational perturbations in the isotropic universe are considered by using the general relativistic kinetic theory. It is shown that the short wave perturbations propagate in the ultrarelativistic collisionless gas with the velocity of light.     

The commutator method for form-relatively compact perturbations

We present a variant of the conjugate operator method which can be used when the group generated by the conjugate operator leaves invariant only the form domain of the Hamiltonian. As an example, we get detailed spectral properties and a large class of locally smooth operators for two-body Schrödinger Hamiltonians with form-relatively compact potentials.     

The criteria for selecting a method for unfolding neutron spectra based on the information entropy theory

To further expand the application of an artificial neural network in the field of neutron spectrometry, the criteria for choosing between an artificial neural network and the maximum entropy method for the purpose of unfolding neutron spectra was presented. The counts of the Bonner spheres for IAEA neutron spectra were used as a database, and the artificial neural network and the maximum entropy method were used to unfold neutron spectra; the mean squares of the spectra were defined as the differences between the desired and unfolded spectra. After the information entropy of each spectrum was calculated using information entropy theory, the relationship between the mean squares of the spectra and the information entropy was acquired. Useful information from the information entropy guided the selection of unfolding methods. Due to the importance of the information entropy, the method for predicting the information entropy using the Bonner spheres' counts was established. The criteria based on the information entropy theory can be used to choose between the artificial neural network and the maximum entropy method unfolding methods. The application of an artificial neural network to unfold neutron spectra was expanded.     

New line narrowing effects in the infrared collision-induced spectra of molecular hydrogens in liquid neon

The first spectroscopic observation of the relative (solute-solute) diffusion in a fluid environment is reported. New, unusually sharp Q1q(J) lines developing against the diffuse background in the collision-induced fundamental IR bands of hydrogen isotopomers (H2, D2, and HD) dissolved in liquid Ne (T approximately 25 K) are studied as functions of the solute concentration x. In all cases, the Q1q intensity parabolically scales with x, accompanied by a striking narrowing of the line shapes. The narrowing, as revealed by the p-H2 solution studies, is due to a faster growth with x of the sharper solute-solute induced component of the single Q1q(0) line. The latter as well as other observed solute-solute lines are strongly narrowed by fast velocity decorrelations and are signatures of microscopic-scale diffusion. Also, a first observation of the solute-solvent induced J-->J + 4 transitions is reported.     

Consideration of the temperature dependence of infrared spectra in the context of classical specific heat theory

The dependence of harmonic frequencies on the temperature and broadening of vibrational energy levels is considered in the context of classical Debye and Einstein specific heat theories. Analytical expressions for the vibrational thermodynamic functions are derived with allowance for these factors. It is shown that consideration of these two factors leads to the fact that the average energy of low-frequency oscillators differs from the statistical temperature, and the high-frequency fluctuations give a nonzero contribution to the specific heat. These expressions are used to calculate the thermodynamic functions of liquid water, and reliable agreement with the experiment is obtained. Voronezh State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 81–88, June, 2000.     

Irreducible tensor operators and operations over them in the theory of molecular spectra

The explicit shape of symmetrized powers of three-dimensional representations of the groups Td and Oh is found in general form. Equations are obtained for calculating the vibrational commutators and matrix elements of irreducible tensor operators. Programs have been developed (in the C and FORTRAN languages) to remove the multiple-valued property of the vibrational-rotational Hamiltonian of spherical top molecules (CH₄, SiH₄, GeH₄, SF₆, and so on).Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 16–25, March, 1993.     

Quantum mechanical operator realization of the Stirling numbers theory studied by virtue of the operator Hermite polynomials method

Based on the operator Hermite polynomials method(OHPM), we study Stirling numbers in the context of quantum mechanics, i.e., we present operator realization of generating function formulas of Stirling numbers with some applications.As a by-product, we derive a summation formula involving both Stirling number and Hermite polynomials.