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 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.     

Rigorous description of an energy spectrum of the isopropanol molecule taking into account the internal rotation of methyl tops

By using the group chain methods, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal motion of hydroxil and two identical methyl tops. The model is rigorous in the sense that its correctness is limited only by the correctness of a symmetry chosen to describe internal dynamics of the molecule.     

Classification of energy levels of the ammonia dimer

Using the methods of a symmetry-group chain, the total classification of energy levels of the ammonia dimer (NH₃)₂ is constructed with the torsional, exchange, and inversional nonrigid motions taken into account.     

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.     

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.     

On the connection between the symmetry of internal dynamics of a nonrigid molecule and the geometry of its equilibrium configurations

For the example of nonrigid nitromethane and toluene molecules CH₃NO₂ and CH₃C₆H₅ in the ground electronic states, the possibility of using the observed symmetry properties of internal dynamics of a nonrigid molecule for the correct choice of its equilibrium configurations is considered in the case where different possible geometries of such configurations correspond to the same point group.     

Microwave spectra of the (HF)2, (DF)2, HFDF,and DFHF hydrogen-bonded complexes

The microwave spectra of the tunneling-rotation bands of the hydrogen-bonded complexes (HF)₂ and (DF)₂ have been measured in the 50- to 126-GHz region. In addition, the pure rotation spectra of both the HFDF and DFHF molecules have been obtained. Transitions with K = 0 through K = 2 have been observed for all isotopic species. The hydrogen fluoride dimer is a very nonrigid molecular species. In order to fit the observed transitions adequately, empirical expressions for the energy levels were used, and each K subband was separately fitted. Constants obtained from a Padé approximant fitting of the microwave data of (HF)₂ together with infrared ground state combination differences are given.     

On the relation between the energy level classification of a nonrigid molecule and the symmetry of its equilibrium configurations

The problem of changes in the energy level classification of a nonrigid molecule upon a change in its equilibrium configurations, in the case in which different possible geometries of such configurations correspond to different point groups, is considered for the example of the nonrigid dimethylacetylene molecule CH₃C₂CH₃ in the ground electronic state.     

Possibilities of the observation of the discrete spectrum of the water dimer at equilibrium in millimeter-wave band

Attempts of experimental observations of the water dimer spectrum at equilibrium conditions have lasted for more than 40 years since the dimeric hypothesis for extra absorption, but have not yielded any positive confirmed result. In the present paper a new approach is considered: using a high-resolution millimeter-wave spectrum of the water dimer at equilibrium, calculated by a rigorous fully quantum method, we show the potential existence of discernible spectral series of discrete features of the water dimer, which correspond to J+1←J, K lines of E₁ symmetry, already observed in cold molecular beam experiments and having, therefore, well-defined positions. The intensity of spectral series and contrast to the remaining continuum-like spectrum of the dimer are calculated and compared with the monomer absorption. The suitability of two types of microwave spectrometers for observing these series is considered. The collisional line-width of millimeter lines of the dimer at equilibrium is estimated and the width of IR dimer bands is discussed. It is pointed out that the large width of IR dimer bands may pose difficulties for their reliable observation and conclusive separation from the rest of absorption in water vapor. This situation contrasts with the suggested approach of dimer detection in millimeter-waves.     

Geometry of the internal dynamics of C<Subscript>2</Subscript>H<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> carbocation

Using the symmetry group chain methods, the internal dynamics of the simplest carbocation, C₂H ₃ ⁺ , is analyzed under the traditional assumptions that the equilibrium structures of the carbocation are planar and that the nonrigid motion between them is in-plane. This geometry of the internal dynamics is shown to agree with the data of the microwave spectroscopy on the splittings of rotational energy levels caused by the nonrigid motion. Previously, this statement was based on the model that violated the requirement of self-adjointness of operators of physical quantities.     

Internal rotation in acetaldehyde

The microwave spectrum of acetaldehyde has been investigated in the frequency range from 7 to 40 GHz. A rather complete assignment of rotational transitions in the ground and torsionally excited states has been found with the help of microwave-microwave double resonance techniques. The spectral data have been analyzed using three different models for the overall and internal rotation problem including a nonrigid model. The threefold component of the internal rotation barrier was determined to be V₃ = 400 ± 2 cm⁻¹. The sixfold contribution V₆ = −10.9 ± 0.3 cm⁻¹ could only be adjusted reliably from data for both ground and torsionally excited states using the nonrigid model. The methods of barrier determinations have been critically reviewed. In an appendix, the Hamiltonian for a nonrigid model is derived based on structure relaxation of the methyl top during internal rotation.     

Vibrational anharmonicity and the inversion potential function of NH3

The nonrigid bender formulation of the vibration-inversion-rotation Hamiltonian for an XY₃ pyramidal molecule (V. ?pirko, J. M. R. Stone, and D. Papou?ek, J. Mol. Spectrosc.60, 159 (1976)) is improved by allowing for anharmonicity in all the vibrations. To model the anharmonic potential function of an XY₃ molecule with a low barrier to inversion a Plíva-type empirical potential (J. Plíva, Collect. Czech. Chem. Commun.23, 777 (1958)) is used. A fitting procedure that involves the numerical integration of the effective inversion Schrödinger equation (the nonrigid bender equation) and diagonalization of some resonance matrices is used to determine the equilibrium structure and the anharmonic potential function of the ammonia molecule.     

Problem of mixing of stereoisomers in the hydrazine molecule N2H4

It is shown that the important consequence of nonrigid motions observed in the hydrazine molecule N₂H₄ is mixing of stereoisomers, although the geometrical symmetry group, taking into account these motions, similarly to the point group of one equilibrium configuration, has no improper transformations of the molecule as a whole. Here, an important point is that the geometrical group of a nonrigid molecule is the so-called noninvariance dynamical group. The effect of mixing of stereoisomers on the total picture of nonrigid motions is considered using the symmetry methods. In particular, it is shown that a nonrigid molecule exhibits properties of a symmetric top, whereas a rigid molecule represents an asymmetric top.     

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.     

Classification of energy levels of the isopropanol molecule

Using the methods of a symmetry group chain, an energy level classification is constructed for the nonrigid isopropanol molecule (CH₃)₂CHOH in the ground electronic state with an allowance for the internal motion of hydroxyl and two methyl tops.     

Complexes d'autoassociation du cyclohexanol. I - modele thermodynamique des solutions diluees.

Activity coefficients for cyclohexanol in diluted isooctane solutions at 25°C and 45°C are obtained from vapour pressure measurements, x_u = 10^?3 to 5.10^?2 (x_u mole fraction of cyclohexanol) ; enthalpies of mixing for the same composition range are obtained at 25°C. The results are interpreted in terms of the model of ideal association where open dimer and trimer, open and cyclic other i-mers are considered in a six parameters model : two standard enthalpies for formation of the H-bonds (Δ$\text{H}$_2o for the dimer and h for the stepwise formation for other bonds), four equilibrium constants (K_2o and K_3o for the dimer and trimer formation from the monomer, K_c for the cyclisation of an open i-mer and k for the stepwise formation of an open, or cyclic, i-mer higher than the trimer). The cyclic form of the tetramer is shown to be the predominent one.