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.     

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.     

Intervalley electron scattering by phonons in (GaAs)<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>(AlAs)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(001) ultrathin superlattices

The electron scattering by short-wavelength and long-wavelength phonons in (GaAs) _m (AlAs) _n (001) superlattices with ultrathin layers (n, m = 1, 2, 3) has been investigated using the pseudopotential method and the phenomenological model of bonding forces. The deformation potentials have been found for intervalley electron transitions in the conduction bands of the superlattices and solid solutions of the corresponding compositions. It has been shown that, owing to the localization of the wave functions in the quantum wells Γ, L, and X, the intensity of intervalley electron transitions in the superlattices, as a whole, is higher than that of similar transitions in the solid solutions. As the content of light Al atoms in the superlattices increases, the deformation potentials monotonically increase for the X-X transitions and decrease for the L-L and X-L transitions. The potentials of the Γ-X and Γ-L transitions change nonmonotonically depending on the layer thickness due to the pronounced quantum-well effects in the deep Γ quantum wells of GaAs. The deformation potentials averaged over phonons and related valleys in the superlattices are close to the corresponding potentials in the solid solutions.     

The effect of data scaling on dual prices and sensitivity analysis in linear programs

In many practical situations scaling the data is necessary to solve linear programs. This note explores the relationships in translating the sensitivity analysis between the original and the scaled problems.     

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.     

Investigation of the stability of the direct spectroscopic problem of diatomic molecules with non-Dunham power series representation of the potential

The stability of the direct spectroscopic problem of the CO and HI molecules in the singlet electron ground state has been investigated with the potential represented in the Dunham (D), Ogilivie-Tipping (OT), Simons-Parr-Finlan (SPF), and Thakkar (T) form. Introducing the same relative error in the potential parameters of the various representations, we calculated the errors of the wave numbers of the vibration-rotation transition. The direct problem is most stable for T and SPF expansions. The result obtained is important for direct theoretical calculation of spectrum parameters which do not participate in the fitting.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 58–62, October, 1982.     

Fourier transform measurements of water vapor line parameters in the 4200-6600 cm region

New high-resolution water vapor absorption spectra were obtained at room temperature in the 4200-6600 cm⁻¹ spectral region by combining Fourier transform spectrometers (FTS) with single and multiple reflection cells. With absorption paths from 0.3 to 1800 m in pure and air diluted water vapor, accurate measurements of about 10400 lines in an intensity range from 10⁻²⁹ to 10⁻¹⁹ cm/molecule have been performed. Positions, intensities, self- and air-broadening coefficients and air-induced shifts were determined for the H₂¹⁶O, H₂¹⁷O, H₂¹⁸O and HDO isotopologues. The rovibrational assignment of the observed lines was performed with the use of global variational predictions and allowed the identification of several new energy levels. One major contribution of this work consists of the identification of 3280 new weak lines. A very close agreement between the new measured parameters and those listed in the database is reported as well as between the observations and the most recent variational calculations for the positions and the intensities. The present parameters provide an extended and homogeneous data set for water vapor, which is shown to significantly improve the databases for atmospheric applications, especially in the transmission windows on both sides of the band centered at 5400 cm⁻¹.     

A new modification of the method of investigation of vibration-rotation interactions in molecules

The superoperator generalization of contact transformations has been used. New forms are presented for derivation of an effective rotational Hamiltonian and for investigation of rotational structure of vibrational bands (symmetric rotors).     

Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy

Using the variational technique, eigensolutions of the radial Herman-Asgharian equation accounting for non-adiabatic terms are determined within the experimental accuracy of the high-resolution spectroscopy. This method, which is independent of the algebraic and numerical approaches currently used in the literature for a "direct-potential-fit" of diatomic rovibrational spectra, is shown to be useful for validation of available calculations and for resolving some controversial issues. Comparative discussions are reported in this paper for a dozen diatomic molecules.