A rigorous description of the energy spectrum of the isopropanol molecule taking into account the internal rotation of hydroxyl

Using the methods of a group chain, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal rotation of hydroxyl. The model is rigorous in the sense that its correctness is limited only by the correctness of a chosen symmetry of internal dynamics of the molecule.     

A rigorous description of the energy spectrum of the ammonia dimer. I. Taking into account the torsional and exchange motions

Using the methods of a symmetry group chain, a rigorous algebraic model for describing the energy spectrum of the ammonia dimer (NH₃)₂ is constructed with the torsional and exchange nonrigid motions taken into account. The model is rigorous in the sense that its correctness is limited only by the correctness of the chosen symmetry of internal dynamics of the dimer.     

A rigorous description of the energy spectrum of the ammonia dimer. II. Taking into account the inversional motion

Using the group chain methods, a rigorous algebraic model for describing the energy spectrum of the ammonia dimer (NH₃)₂ is constructed with an allowance for both the most important torsional and exchange nonrigid motions and the inversional nonrigid motion also taken into account. The model is rigorous in the sense that its correctness is limited only by the correctness of the chosen symmetry of internal dynamics of the dimer.     

Description of the torsional motion in the isotopically asymmetric ionic complexes ArH<Subscript>2</Subscript>D<Superscript>+</Superscript> and ArD<Subscript>2</Subscript>H<Superscript>+</Superscript>

The internal dynamics of the isotopically asymmetric ionic complexes ArH₂D⁺ and ArD₂H⁺ is considered to be a distorted dynamics of the isotopically symmetric ArH₃⁺ complex. By using the group chain methods, a rigorous algebraic model is constructed to describe the spectrum of the asymmetric complexes with an allowance for the torsional motion of the structure of hydrogen nuclei. The model is based on the geometrical group of symmetry of internal dynamics of the isotopically symmetric ionic complex, which is used here as a noninvariant group.     

Geometry of the internal dynamics of the 12C13CH 3 + carbocation

The internal dynamics of the ¹²C¹³CH₃⁺ isotopomer of the simplest carbocation is considered to be a distorted dynamics of its symmetric C₂H₃⁺ isotopomer. By using the group-chain methods and assuming quite naturally that the carbocation equilibrium structures continue to be planar and the nonrigid motion occurring between them is retained upon this isotopic substitution, a simple algebraic model is constructed to describe the spectrum of the ¹²C¹³CH₃⁺ isotopomer. The correctness of the model is limited only by that of the adopted geometrical symmetry of internal dynamics of the C₂H₃⁺ isotopomer.     

Description of the spectrum of the ethanol molecule with allowance for the mixing of its trans and gauche conformers

Based on symmetry methods, a rigorous model is, for the first time, obtained for describing the spectrum of the ethanol molecule CH₃CH₂OH in a given vibronic state with allowance for the mixing of its trans and gauche conformers due to the torsional motion of the hydroxyl group OH.     

Description of torsional motion in ionic complexes ArH<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> and ArD<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack>

An algebraic model that describes the internal dynamics of the ionic complexes ArH₃⁺ and ArD₃⁺ in the ground electronic-vibrational state taking into account the torsional motion of the structure of identical hydrogen nuclei is constructed by symmetry-group chain methods. It is important that the correctness of this model is only limited by the correctness of the choice of geometric symmetry of the internal dynamics of the ionic complex.     

Description of the spectrum of the ethanol molecule with allowance for the torsional motions of its hydroxyl and methyl groups

On the basis of symmetry methods, a rigorous model is, for the first time, obtained for describing the spectrum of the ethanol molecule CH₃CH₂OH in a given vibronic state with allowance for the simultaneous torsional motion of the hydroxyl group OH and the methyl group CH₃.     

Hamiltonian,symmetry group,and vibrational coordinates for the nonrigid molecule CXY2CCCXY2

A vibration-torsion-rotation Hamiltonian is derived for a molecule of the type CXY₂CCCXY₂ exhibiting nearly free internal rotation. The Hamiltonian obtained preserves many of the features of the ordinary Wilson-Howard vibration-rotation Hamiltonian and is based qualitatively on the idea of a slowly varying torsional reference configuration from which the atoms make rapid vibrational displacements. The appropriate molecular symmetry group for this molecule is found to be a double group of the simple Longuet-Higgins permutation-inversion symmetry group. The indeterminacy of symmetry species (single-valued vs double-valued) for coordinates used to describe the small amplitude vibrations is illustrated and clarified using a simple model for the skeletal bending vibrations.     

Internal dynamics of (H2O)2 and (D2O)2 dimers: II. Effective operators of physical quantities with account of inversion and exchange motions

Using the symmetry group chain methods, a model of the internal dynamics of (H₂O)₂ and (D₂O)₂ dimers that takes into account their real geometries and two nonrigid motions with the lowest energy barriers is constructed. The motions are the inversion motion (or the acceptor switching) and the exchange motion of the acceptor and donor via an intermediate trans configuration. The model rigorously describes the interactions of various motions and leads to a simple algebraic scheme of calculation of both the positions of the levels in the energy spectrum and the intensities of transitions between them. It is important that the correctness of the model is limited only by the trueness of the choice of the symmetry of the internal dynamics.     

Quantitative energy level correlations for linear,bent and internally rotating triatomic molecules

This paper is concerned with the study of the quantitative correlation of the rotation-bending energy levels of a linear or bent triatomic molecule with the energy levels of the molecule when there is free internal rotation of a diatomic fragment [as in, for example, Ar(HCl)]. The LiNC and KCN molecules are used as model systems. A correlation parameter γ_r is introduced to quantify the position a molecule occupies in these correlation diagrams; this parameter has the value +1 for an ideal bent molecule, ?1 for an ideal linear molecule, and ?3 for an ideal free internal rotor triatomic molecule. The rotation-bending energy levels of the HCN-HNC isomerization system, and of the double minimum HO₂ system, are also studied.