Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonic model of a two-dimensional oscillator having Kratzer potential energy functionis used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interactionbetween the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a real polyatomic molecular species.     

Depicting the dehydration and dehydroxylation processes in very rare hydrogen arsenate minerals

Journal of Thermal Analysis and Calorimetry - The work represents a pioneering attempt to couple TG analysis and hot-stage t-ATR-FTIR spectroscopy to describe the dehydration and dehydroxylation...     

A perturbation theoretical method for determination of the dependence of the intramolecular X–H(D) potential on the hydrogen bond strength

A perturbation theoretical method is proposed that allows determination of the function describing the dependence of the intramolecular XH(D) potential on the hydrogen bond strength. Treating the XH(D) oscillators as mixed cubic–quartic oscillators in which the stretch–stretch couplings of the ν(X–H(D)) mode with the internal modes of the radical X may be neglected, and introducing the hydrogen bonding influence through the changes in the harmonic diagonal force constants (as proposed by Sceats and Rice [41]), it is possible to extract the analytical form of the function ) from the experimental versus correlations. The other parameters obtained by the empirical correlations, within this model, also have an exact physical meaning. The method is applicable to weak hydrogen bonds as well as to hydrogen bonds of intermediate strength, and, strictly speaking, to linear X– systems. However, extension to arbitrary geometry may be easily done. This revised version was published online in July 2006 with corrections to the Cover Date.     

The perturbation theory model of a spherical oscillator in electric field and the vibrational stark effect in polyatomic molecular species

The effect of external electrostatic fields on the spherical oscillator energy states was studied using stationary perturbation theory. Besides the spherical oscillator with ideal symmetry, also a variety of the deformed systems were considered in which the deformations may be induced by the external fields, but also by the short-range crystal lattice forces. The perturbation theory analysis was carried out using the field-dependent basis functions. Predicted spectral appearances and band splittings due to the deformations and external field influences were shown to be helpful in interpreting the experimental spectra of molecular oscillator possessing subsets of mutually orthogonal triply degenerate normal modes (such as, e.g. tetrahedral species). To verify the results of the perturbation theory treatments, as well as to provide a further illustration of the usefulness of the employed technique, a numerical HF/aug-cc-pVTZ study of the vibrational states of methane molecule in external electrostatic field was performed.     

Splitting of Spectra in Anharmonic Oscillators Described by Kratzer Potential Function

A perturbation theory model that describes splitting of the spectra in highly symmetrical molecular species in electrostatic field is proposed. An anahrmonie model of a two-dimensional oscillator having Kratzer potential energy function is used to model the molecular species and to represent the unperturbed system. A selection rule for the radial quantum number of the oscillator is derived. The eigenfunctions of a two-dimensional anharmonic oscillator in cylindrical coordinates are used for the matrix elements representing the probability for energy transitions in dipole approximation to be calculated. Several forms of perturbation operators are proposed to model the interaction between the polyatomic molecular species and an electrostatic field. It is found that the degeneracy is removed in the presence of the electric field and spectral splitting occurs. Anharmonic approximation for the unperturbed system is more accurate and reliable representation of a reaJ polyatomic molecular species.