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.     

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.     

Interrelationship of the Torsional and Rotational States of Asymmetric Nonrigid Molecules

The incorrectness of solution of a torsional-rotational equation for asymmetric nonrigid molecules in the system of internal axes is shown; this incorrectness is caused by the broken interrelationship between the torsional quantum number and the parity of the rotational quantum number K.     

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.     

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.     

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.     

Application of the instanton method for analyzing tunneling splitting spectra of nonrigid molecular systems

General formalism and basic ideas of the instanton method are described. The potentialities of the method are demonstrated by calculating the tunneling splitting of the ground vibrational level for nonrigid molecules with two and three equivalent minima on their potential-energy surface. Some advantages of the application of the instanton method as compared to the well-known semiclassical approximation for describing the spectra of tunneling splitting of a nonrigid molecular system are proved.     

Torsion-vibration interaction in CH3OH

The strong torsion-vibration interaction in CH₃OH has traditionally been dealt with by letting the torsional barrier height depend on vibrational excitation, and letting the vibrational energy depend on torsional excitation. By including an explicit interaction term in the Hamiltonian this is avoided, and apart from an anomaly which is presumably caused by the OH bending mode, the relative location of the vibrational ground state and the CO stretch state is well reproduced for torsional states n = 0, 1, and 2 by adjusting a single interaction constant.     

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.     

Torsional coupling in pyruvic acid

New assignments of rotational transitions in the first excited state of the skeletal torsion were made and showed an unexpected interchange in the sequence of energy levels for the internal rotation of the methyl group. This fact is traced back to a strong coupling between the skeletal torsion and the methyl torsion. A two dimensional flexible model for torsional motion was developed which could account for the observations. The model includes structural relaxation and torsional potential energy coupling and allowed successful prediction and further assignments of transitions in the second excited state of the skeletal torsion.     

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.     

Torsional barriers and nonlinear optical properties of 2-, 3-, 4-phenylpyridine molecules

The torsional barriers and nonlinear optical properties for all phenylpyridine molecules were calculated by using Hartree-Fock (HF) theory and Becke three-parameter functional (B3LYP) hybrid approaches within the density functional theory framework with the 6-31++G(d, p) basis set, and via the GAUSSIAN 98W. The torsional barrier computations show that dihedral angle between the two rings increases with the number of H-H vicinal interactions and torsional barriers with dihedral angles for 3-, 4-phenylpyridines are too similar for both HF and B3LYP level calculations. Also, HOMO-LUMO energy gaps, polarizabilities, anisotropy of polarizabilities, and static hyperpolarizabilities are calculated as a function of dihedral angle between benzene and pyridine rings. The study reveals that the phenylpyridines show very low nonlinear optical properties. The calculated torsional barrier, equilibrium dihedral angle and molecular dipole moment results for these molecules were compared with available experimental and other results determining from different computational methods.     

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.     

Molecular torsion: Comparison of harmonic oscillator and free rotor bases

In this work we describe a method of solving the eigenvalue problem of torsional motion in polyatomic molecules by expanding the eigenfunctions in a harmonic oscillator basis. By comparing the eigenvalues obtained with a harmonic oscillator basis and those calculated with a free rotor basis, it is found that a basis with only 5–7 oscillator functions will reproduce the low-lying energy levels for large torsional barriers with the same accuracy as a basis with about 10 free rotor functions. The method has been applied to a calculation of the barriers to internal rotation for methyl ammonium chloride. The barriers were obtained from a least squares fit of the torsional frequencies of methyl ammonium chloride and seven of its deuterated derivatives, treating the molecule as a double rotor. The method is recommended for the calculation of large rotational barriers from spectroscopic data on systems in any state of aggregation, and may therefore be useful in the testing of theoretical models.     

Torsional mechanics of single walled carbon nanotubes with hydrogen for energy storage and fuel cell applications

Torsional mechanics of single walled carbon nanotubes(SWCNTs) encapsulated with hydrogen molecules was investigated in this study, using the molecular dynamics(MD) simulation approach. The torsional properties of hydrogen stored SWCNTs were crucial for determining the durability and lifetime of SWNCTs-based energy storage and proton exchange membrane fuel cell(PEMFC) applications. The influence of hydrogen storage concentration, SWCNT geometry, vacancy defects, temperature variation and varying boundaries of rotated as well as fixed groups on the torsional mechanics of SWCNT was investigated. The results and conclusions provide an insight into the torsional properties of SWCNTs with hydrogen storage that could be used for the development of SWCNTs-based hydrogen storage devices and PEMFC applications.     

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.     

On the definition of intramolecular motions

The restrictions imposed when defining separate types of internal motions in rigid and nonrigid molecules are considered. These restrictions are based on the symmetry properties of intramolecular dynamics. It is shown that the violation of these restrictions gives rise to physically incorrect consequences.