Calculations of partition functions for internal rotation of molecules

A simple numerical method for calculations of torsional energy for barriers of arbitrary forms was suggested. Within the framework of the Wigner-Kirkwood approximation, an analytic equation was derived for the partition function of a hindered top, which was used for interpretation and a comparison with numerically exact results.     

Barriers to internal rotation in asymmetric molecules: 2,3-Difluoropropene

The potential function for internal rotation in 2,3-difluoropropene has been obtained from the microwave spectrum of the gauche rotamer, the far- and mid-infrared spectra of both the gauche and cis rotamers and the absolute rotational intensity measurements of several gauche microwave transitions. It is found that the cis conformer is most stable by 145 ± 60 cm⁻¹. Both the cis-gauche and gauche(+)-trans-gauche(−) barriers are approximately 1000 cm⁻¹. A comparison between the potentials in 2,3-difluoropropene, propene, and several other fluoropropenes is made. The dipole moment of the gauche conformer is μ_a = 0.950 D, μ_b = 1.982 D, and μ_c = 1.135 D; μ_total = 2.67 D.     

Determination of the energy levels of total and internal rotation of arbitrary polyatomic molecules with a single internal rotation axis

An algorithm is developed for calculating the eigenvalues of the Hamiltonian operator in the case of asymmetric-asymmetric molecules with a common axis of internal rotation, taking into account the total and internal rotation of these molecules. The algorithm is based on the Ritz variational method. A program is written for reducing a symmetric band matrix to tridiagonal form with subsequent diagonalization of the resulting matrix.State Textile Academy, Ivanovo. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 81–88, October, 1995.     

Dichroism of absorption by impurity molecules with internal rotation in nematic liquid crystals

Expressions are obtained for the components of the permittivity tensor in the optical region for a nematic liquid crystal with impurity molecules having the internal rotation conformational degree of freedom. The dependence of the intensity and dichroism of the impurity absorption bands in isotropic and nematic phases on the parameters of conformational, orientation, and mixed conformation-orientation orders of molecules is found. The influence of the mutual correlation of conformational and orientation degrees of freedom of molecules on these parameters is studied. The dependence of the oscillator strengths of molecular transitions on the phase state of a medium and the orientation order of the impurity subsystem is analyzed. The self-consistent nature of molecular, structural, and spectral changes upon the nematic-isotropic liquid phase transition is demonstrated.     

Symmetry coordinates of nonrigid molecules

Motivated by Altmann’s definition of symmetry groups of nonrigid molecules, Wigner’s method of obtaining the symmetry coordinates of a molecule is extended to nonrigid molecules with free internal rotations. The molecule BF₂ CH₃ is exemplified.     

Spectral features of a nematic liquid crystal consisting of biaxial molecules with internal rotation

Expressions for the components of the optical permittivity tensor of a nematic liquid crystal consisting of biaxial π-conjugated molecules with a conformational degree of freedom (internal rotation) are obtained. A relationship between the intensity and dichroism of absorption bands in isotropic and nematic phases and the parameters of conformational, orientational, and mixed conformational and orientational orders of the molecules is established. A distribution function for the molecules is obtained that takes into account the mutual correlation of their conformational and orientational degrees of freedom. The effect of this correlation on the above-noted order parameters, the dichroism of the absorption bands, and the dependence of the measured oscillator strengths of molecular transitions on the character and degree of orientational order of biaxial molecules is studied. On the basis of comparison with experimental data, the relative role of different terms in the distribution function that are responsible for the correlation between the conformational and orientational degrees of freedom of the molecules is ascertained.     

Optical and structural anisotropy of a uniaxial nematic consisting of biaxial molecules with internal rotation

A relation is established between the refractive indices of a uniaxial nematic liquid crystal (LC) consisting of biaxial molecules with internal rotation and the properties of molecules and their structural ordering. It is shown that the correlation between the conformation degree of freedom associated with internal rotation of π-conjugate molecular fragments and the orientation degrees of freedom of the molecules as a whole leads to the existence of two mixed parameters of orientation-conformation order, which contribute to the optical anisotropy of the LC along with the parameters of the conformation and orientation order of the molecules. The effect of the correlation of the molecular degrees of freedom on the values of these order parameters and the properties of molecular polarizability is analyzed. The dependence of the polarizability of molecules on their orientation ordering in the LC is explained.     

Two-dimensional potential energy function for internal rotation in 1,2-dihydroxybenzenes

We have obtained an analytical expression for the two-dimensional potential energy function for internal rotation in 1,2-dihydroxybenzenes, allowing us to use perturbation theory methods to calculate and interpret the torsional spectra of these compounds. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 1, pp. 133–136, January–February, 2006.     

On hindered rotation of linear molecules

The quantum-mechanical model of a rigid dumb-bell subjected to a potential field of octahedral symmetry, known as Devonshire's model, is group-theoretically analysed. The low-lying energy states of the system are calculated by employing the Ritz-Galerkin method based on the Schrödinger equation of the system.     

Torsional, rotational, and torsional-rotational energy levels of arbitrary molecules with a single internal rotation axis

A program is developed to calculate the torsional-rotational energy levels of multi-atomic molecules containing symmetric or antisymmetric frame and rotor. The torsional-rotational, rotational, and torsional energy levels of the molecules H₂O₂ (asymmetric rotor), C₂H₆ (symmetric rotor), and CH₃NH₂ (asymmetric rotor) are calculated. The value obtained are compared with the corresponding systems of energy levels found by other authors. Ivanovo State Textile Academy, Ivanovo. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 42, No. I, pp. 71–80. January, 1999.     

Symmetry of electrostatic interaction between pyrophosphate DNA molecules

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.     

Hyperfine structure in internal rotor molecules

The theory of magnetic hyperfine interactions in internal rotor molecules with one internal degree of freedom has been developed as basis for the interpretation of hyperfine structure in the microwave spectra of these molecules. It has been shown that the internal rotation modifies the familiar nuclear spin-spin and spin-rotation interactions. Explicit expressions for the hyperfine energy matrix elements and coupling constants are derived for the methanol molecule.     

Line-widths in the vibration rotation spectra of diatomic molecules perturbed by tetrahedral molecules

The line-broadening phenomena for a diatomic polar molecule perturbed by a tetrahedral molecule are analysed. Two points are particularly studied and exemplified in the case of the vibration bands of HCl perturbed by CF₄ and by SiF₄.

(i) The influence of the electrostatic potential energy (i.e. dipole-octopole and quadrupole-octopole couplings) on reorientation during a collision is introduced, and it appears, to a large extent, to be competitive with the effect of the shorter range angle independent contributions to the potential. Consequently only a weak vibrational effect from the 0–1 to the 0–2 bands is observed when the octopole moment of the tetrahedral molecule is taken into account, in agreement with the experiments.

(ii) For the systems mentioned above the moments of inertia allow us to apply a convenient simplified formalism for the line-broadening calculations. In this formalism the rotational degrees of freedom of the perturber are considered as classical. The results of these theoretical considerations are in good agreement with the presently available experimental data.     

Fluorescence and internal conversion spectra for excited molecules in solutions

A study has been made of the effects of temperature on the fluorescence spectrum, quantum yield, and lifetime of the excited state for seven derivatives of phthalimide at 20 to –196°C; the solvents were ethanol, isobutanol, and dioxane. The thermal shift in the emission is accompanied by changes in the other two quantities; the probability of internal conversion is related to the position of the emission band, as is the barrier height for this process.We are indebted to Academician A. N. Sevchenko, of the Academy of Sciences of the Belorussian SSR, for direction in this work and to V. V. Zelinskii and I. I. Reznikova for the gift of the compounds.     

Far-infrared spectrum of the internal rotation in methylamine

The far-infrared spectra of the Q branches of hindered rotation of CH₃NH₂ were studied in the 80 to 280 cm^?1 spectral region with resolutions up to 0.12 cm^?1. Through the theoretical analysis 11 of the 12 b-type parameters I_a1, I_a2, V₃, V₆, k₁, k₂, k₃, k₄, k₅, k₆, k₇, D_KK are determined using a nonlinear least-squares fit. The agreement between the observed and the final theoretical spectrum is satisfactory considering that only Q-branch lines were studied. Experimentally more lines, especially at low frequencies, were observed which probably belong to P- and R-branch lines of clusters thereof.