On the normal vibrations of nonrigid molecule B(CH3)3

Treating the symmetry operations as transformations in higher dimensional space, it is shown that Wigner’s method can be straightaway extended to study the vibrations of nonrigid molecules exhibiting free or nearly free internal rotations. The molecule B(CH₃)₃ is illustrated.     

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.     

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.     

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.     

Vibration-internal rotation-rotation Hamiltonian of an asymmetric top molecule with C3v internal rotor

An expression for the kinetic energy part of the vibration-torsion-rotation Hamiltonian of an asymmetric top molecule containing a C_3v internal rotor has been derived. The terms for various interactions in the molecule, viz. Coriolis interaction between rotation (both overall and internal rotation) and vibration, centrifugal distortion and anharmonicity of molecular vibrations induced by the internal, and overall rotation of the molecule, have been formulated. For a planar molecule with C_s symmetry we have obtained the vibrationally averaged rotation-internal rotation Hamiltonian. Diagonalization of this Hamiltonian for a particular vibrational state will yield the rotation-internal rotation energy levels and hence the transition frequencies. These data will be useful for analysis of high-resolution infrared spectra obtained by laser or Fourier transform spectroscopy of nonrigid molecules with internal rotor. We also present a set of quartic centrifugal distortion coefficients associated with rotation and internal rotation. These data will be helpful for evaluation of vibrational potential constants of the orthorhombic asymmetric top molecules.     

Correlation between energy levels of linear and bent X2Y2 molecules

The permutation-inversion group developed by Longuet-Higgins is extended to a classification of the vibronic, torsional, and rotational wavefunctions of a nonrigid X₂Y₂ molecule by introducing a symmetry operation $\text{T}\text{?}$, which rotates the top half of the molecule by 2π and, accordingly, the molecule-fixed x axis by π. Since the energy levels of linear (D_∞h) and bent (C_2h, C_2h, and C₂) forms of X₂Y₂ are classified according to a set of common symmetry operations of this extended permutation-inversion group, their energy levels can be correlated, including those of nonrigid forms such as a quasilinear system or a free internal rotor. Nuclear spin weights and selection rules are derived.     

Vibrational spectra and normal coordinate analysis on structure of chlorambucil and thioguanine

A normal coordinate analysis on chlorambucil and thioguanine has been carried out with a set of symmetry coordinates following Wilson’s F-G matrix method. The potential constants evaluated for these molecules are found to be in good agreement with literature values thereby confirming the vibrational assignments. To check whether the chosen set of vibrational frequencies contribute maximum to the potential energy associated with the normal coordinates of the molecule, the potential energy distribution has been evaluated.      

Critical phenomena in the rotational spectra of H2X molecules

Using the method of generating functions for the effective rotational Hamiltonian of H₂X molecules, an expression for estimating the critical value J _c of the rotational quantum number is obtained, starting with which the formation of four-level clusters in a molecule is possible. The analysis made in the harmonic approximation for rotational operators and for a particular form of generating functions showed the impossibility of clusterization for nonrigid H₂X molecules with strong centrifugal effects.     

Permutation-inversion symmetry of C70 fullerite in the high-temperature phase

The permutation-inversion symmetry group of C₇₀ fullerite in its high-temperature phase is constructed with allowance for the rotation of its constituent molecules, and the local symmetry group of a rotating molecule in the crystal is identified. Irreducible representations of these groups are constructed that are compatible with the principle of wave-function symmetry with respect to permutations of identical nuclei. A group-theoretic classification is made of the quantum states of a rotating molecule and of the crystal in the high-temperature phase of C₇₀ fullerite. Selection rules are derived for electronic, vibrational, and rotational spectra in terms of irreducible representations of the permutation-inversion symmetry group of the crystal. Fiz. Tverd. Tela (St. Petersburg) 39, 1895–1901 (October 1997)     

Local modes of silane within the framework of stretching vibrational polyads

We define stretching relative equilibria (RE) of silane and other similar tetrahedral molecules in terms of the dynamical polyad symmetry which assumes the resonance condition 1:1 between the two stretching vibrational modes ν₁ and ν₃ of the molecule. Exploiting symmetry and topology arguments and reducing the dimension of the classical mechanical system, we find these RE. One of them, with local symmetry C_3v and minimal energy within a polyad, corresponds to the local modes. We give the upper energy limit of the local mode localization within a polyad.     

Structural features of the polymer-like phase of AC60 fullerides

A new approach is proposed for describing the deformation of the C₆₀ molecule in the polymer-like phase of the fullerides AC₆₀ (A=K, Rb). A discrete basis of orientational states of the molecule is introduced, and orientational ordering is described on the basis of a phenomenological theory. A symmetry analysis of the molecular vibrations in the Fm3m phase is performed. It is shown that small rotations of the C₆₀ can occur at a phase transition. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 2, 110–115 (25 July 1996)     

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.     

Evaluation of the degree of restoration of broken Wigner’s <Emphasis Type="Italic">SU</Emphasis>(4) spin-isospin symmetry in nuclei

The Franzini-Radicati factor R was calculated on the basis of experimental data on the masses of nuclei in the mass-number range of 5 ≤ A ≤ 257. The values calculated for this factor made it possible to evaluate the degree of fulfillment of Wigner’s SU(4) spin-isospin symmetry in nuclei. An expression for the factor R was obtained on the basis of Wigner’s mass formula. This expression is isospin-dependent and takes into account odd-even variations in the mass. The formula for the factor R describes the separation of nuclei into threeWigner-type groups. The values calculated for the factor R were analyzed by the method of Student’s t criterion, and it was inferred from the results of this analysis that only for nuclei having odd values of the mass number A and an isospin in the range of T _z ≥ 53/2 is broken Wigner’s SU(4) spin-isospin symmetry restored, the confidence level being α = 0.01.     

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.     

Derivation of the nonrigid rotation-large-amplitude internal motion Hamiltonian of the general molecule

The nonrigid (effective) rotation-large-amplitude internal motion Hamiltonian (NRLH) of the general molecule with one or more large-amplitude vibrations has been derived to the order of magnitude κ²T_VIB. The derivation takes advantage of the idea of a nonrigid reference configuration and uses the contact transformation method as a mathematical tool. The NRLH has a form fairly similar to that of the effective rotation Hamiltonian of semirigid (i.e., normal) molecules. From a careful examination of the Eckart-Sayvetz conditions and of the Taylor expansions of the potential energy surface in terms of curvilinear displacement coordinates, three types of large-amplitude internal coordinates of different physical meaning (effective large-amplitude internal coordinates, real large-amplitude internal coordinates, and reaction path coordinates) are described. To test the ideas and the formulas the effective bending potential function of the C₃ molecule in its ground electronic and ground stretching vibrational state is calculated from the ab initio potential energy surface given by W. P. Kraemer, P. R. Bunker, and M. Yoshimine (J. Mol. Spectrosc. 107, 191–207 (1984)). The calculations were carried out by using either the effective or the real large-amplitude bending coordinate of C₃. The NRLH theory is compared to the nonrigid bender theory at a theoretical level as well as through the results of the test calculations.     

The large-amplitude motions in quasi-symmetric top molecules with internal C3v rotors: The vibration-torsion-rotation Hamiltonian of a two-top molecule

An expression for the vibration-torsion-rotation Hamiltonian of a molecule with triatomic nonrigid frame and two internal C_3v rotors has been derived. Three large-amplitude motions, namely skeletal bending and two torsions, are removed from the vibrational problem and are considered together with the rotational problem. The Hamiltonian obtained is applicable to any two-C_3v-top molecule with triatomic linear or bent frame. The zeroth-order skeletal bending-torsion-rotation Hamiltonian is derived and the method of solving the corresponding Schrödinger equation is discussed. The Hamiltonian obtained with only slight modifications is shown to be applicable to any single-C_3v-top molecule with a quasi-linear tetratomic nonrigid frame or to the problem of the large-amplitude bending motion in a pentatomic quasi-linear molecule.     

Supersymmetric preon models with three-fermion generations

A class of supersymmetric preon models is considered in which the hypercolour groupG _HC and the unbroken flavour groupG _f anomalies are zero without needing spectators. It is shown that forG _HC=SU(2) and SU(3) quarks and leptons as composites can be obtained satisfying ’t Hooft’s anomaly matching conditions. For the case ofG _HC=SU(3),G _f can accommodate a horizontal symmetry group to describe just three generations.     

Bifurcation in the rotational spectra of nonlinear symmetric triatomic molecules

A microscopic theory is proposed for bifurcation in the rotational spectra of nonlinear AB₂-type molecules. The theory is based on a study of small-amplitude vibrational and precessional motion near the stationary states of a rotating molecule. Bifurcation leads to the formation of fourfold clusters of levels in the upper parts of the rotational multiplets, disruption of the symmetry of the molecule, and a transition from normal to local valence vibrations. The role of the centrifugal force of inertia in the development of these effects is clarified. Bifurcation and the accompanying phenomena are studied in the hydride molecules H₂O, H₂S, H₂Se, and H₂Te using empirical molecular potentials. Zh. éksp. Teor. Fiz. 112, 1239–1256 (October 1997)