Symmetric Internal Rotor Research Articles

On the physical interpretation of torsion–rotational parameters for CH 3OD isotopomers

Using the formulation (Phys. Lett. A 207 (1995) 203) of the centrifugal distortion effects in terms of the potential parameters for a molecule that contains a threefold symmetric internal rotor, molecular parameters have been determined for the 12 C and 13 C isotopomers of CH 3OD with O-16, 17 and 18. The calculated parameters, especially the constants that represent interactions between torsion and rotation, are used to interpret the relationships among the terms in the reduced Hamiltonian and in the analysis of the observed torsion–rotational spectrum. Molecular parameters are calculated from several potential energy functions for methanol isotopomers to check the quality of these potentials. The dependence of torsion–rotational parameters on the mass of atom and the geometric parameters are addressed by comparisons of calculated values for various isotopomers of CH 3OD. The parameters are compared with the parameters that were obtained from several global fits to experimental spectrum data. The good agreement between the calculated torsion–rotational parameters and those derived from the global fits demonstrates that the derived formulae provide a useful tool for understanding the physical origins of the Hamiltonian parameters and the dependence of torsion–rotational parameters on fundamental molecular parameters.

Molecular parameters for C12 and C13-methanol isotopomers with O-16, 17, and 18

Torsion–rotational parameters have been determined for C12 and C13-methanol isotopomers CH3OH with O-16, 17, and 18 using a recent formulation [Duan and Takagi, Phys. Lett. A 207, 203 (1995)] of the centrifugal distortion effects from potential parameters for a molecule containing a threefold symmetric internal rotor. The calculated parameters, especially the constants representing interactions between torsion and rotation, are used to interpret the relationships among the terms in reduced Hamiltonian and in the analysis of the observed torsion–rotational spectrum. Molecular parameters are calculated from potential energy surfaces for methanol to check the quality of these surfaces. The calculated parameters are compared with parameters obtained from global fits to large experimental data sets. The good agreement between the calculated centrifugal distortion terms and those derived from fits to spectra demonstrates that the derived formulas provide a useful tool for understanding the physical origins and mass dependence of the molecular parameters.

The calculation of molecular parameters for a molecule with an internal rotor

A derivation for the formulas to calculate centrifugal distortion constants, based on a recent formulation [Duan and Takagi, Phys. Lett. A (1995)] of centrifugal distortion effects for a molecule containing a threefold symmetric internal rotor, is presented. Some constants which are independent of the barrier derivatives, especially the constants representing interactions between torsion and rotation, are given in terms of molecular structural parameters and force constants. These calculated constants are helpful in the reduction of the Hamiltonian and in the analysis of observed transitions. The derived formulas are applied to numerical calculations of the centrifugal distortion constants of methanol. It is shown that most of the calculated constants are in good agreement with those obtained from the fitting to experimental data.

Vibration-torsion-rotation polarizability tensor operator for a molecule with an internal rotor

The sequential contact transformation technique is applied to the vibration-torsion-rotation polarizability tensor operator for a molecule containing a threefold symmetric internal rotor. Detailed discussions about various types of polarizability tensor operators and corresponding vibration-torsion-rotation transitions are presented. The formalism of the transformed polarizability tensor operator makes it possible to analyze various high-order vibration-torsion-rotation interactions and their effects as well as to determine the intensities of transitions between vibration-torsion-rotation states within the Raman spectrum of the molecule. As an example, the transition matrix elements of the transformed polarizability tensor operators are discussed for CH3OH-like molecules.

Nuclear quadrupole coupling operator for a molecule with an internal rotor

The sequential contact transformation technique is applied to the nuclear quadrupole coupling operator for a molecule containing a threefold symmetric internal rotor in order to be consistent with the transformed vibration–torsion–rotation Hamiltonian to be used in the analysis of the spectra of the molecule. Various higher-order effects on the nuclear quadrupole coupling energies, such as the centrifugal distortion, the anharmonic corrections and so on, are formulated for a molecule containing one quadrupolar nucleus. The detailed discussion is presented of vibrational–torsional–rotational dependence of these higher corrections to the quadrupole hyperfine energies.

Centrifugal distortion effects for a molecule with two internal rotors

The centrifugal distortion effects for a molecule containing two symmetric internal rotors are formulated. The explicit expressions that relate the distortion constants to fundamental molecular parameters are given, which are applicable for analysing molecular structure from the parameters determined from a fit-to-observed spectrum or for calculating the centrifugal distortion constants from well known fundamental molecular parameters. The reduced torsion - rotation Hamiltonian is given for a molecule with two internal rotors with a symmetry plane which contains both internal rotation axes.

Vibration–torsion–rotation dipole moment operator for a molecule with an internal rotor

The sequential contact transformation technique is applied to the vibrational–torsional–rotational dipole moment operator for a molecule containing a threefold symmetric internal rotor in order to be consistent with the transformed Hamiltonian to be used in the analysis of the spectra of the molecule. The detailed discussion is presented of various types of dipole moments and corresponding vibration–torsion–rotation transitions. The transition matrix elements of the transformed dipole moment operator are given for CH3OH-like molecule.

Analysis of Torsion in a Three-Top Molecule. Torsional Barrier and Moment of Inertia of Trimethyl Ethynyl Germane

Internal rotation effects for a large number of molecules containing one or two symmetric internal rotors have been investigated using microwave spectroscopy. The high resolution of molecular beam Fourier transform microwave spectroscopy revealed now the internal rotation fine structure in the rotational spectrum of trimethyl ethynyl germane, (CH3)3GeC=CH. After assigning the rotational transition J = 1 → 0 in the vibrational and torsional ground state to the symmetry species of the molecular symmetry group G162 , the torsional barrier V3 and the rotational constant B0 could be determined to (4.5±0.2) kJ/mol and (1823.370±0.010) MHz, respectively.

Higher-order effects in the vibration–torsion–rotation spectra of a molecule with an internal rotor

The sequential contact transformation technique is applied to the vibrational–torsional–rotational Hamiltonian for molecules containing a threefold symmetric internal rotor, which makes it possible to analyze various higher-order vibration–torsion–rotation interactions and their effects in the vibration–torsion–rotation spectra of the molecule. The formalism for the calculation of Hamiltonian coefficients is developed in terms of the fundamental molecular parameters. The resulting formulas are applicable to analyze the molecular structure. The theory presented is applied to the calculation of the quartic and sixtic centrifugal distortion constants of the molecule.

Theory of centrifugal distortion for a molecule with an internal rotor

A formal theory of centrifugal distortion for a molecule containing a three-fold symmetric internal rotor is formulated. The relationships between the distortion constants and the potential constants are discussed.

The microwave spectrum of tert-butyl isocyanate

The rotational spectrum of tert-butyl isocyanate, (CH 3) 3C-NCO, has been assigned using pulsed molecular beam microwave Fourier transform spectroscopy. The rotational constants are A = 4572.6 MHz (assumed), B = 1632.948 (15) MHz, C = 1630.493 (14) MHz; the barrier to internal rotation of the tert-butyl group (assumed to constitute a symmetric internal rotor, the NCO group forming the frame) is V 3 = 41.510 (15) cm −1, the moment of inertia of the internal top is I α = 111.388 (4) amu · A ̊ 2 , and the angle between the internal rotor axis and the a-principal inertia axis is θ = 24.169 (3)°. The nitrogen nuclear quadrupole coupling constants are χ aa = +2.6376 (4) MHz, χ bb = −1.4935 (7) MHz, χ cc = −1.1441 (7) MHz, χ ac = +0.1731 (15) MHz (the molecule has an ac-plane of symmetry). The principal elements of the coupling tensor are χ zz = +2.6455 MHz, χ xx = −1.4935 MHz, χ yy = −1.1520 MHz; the angle between both axis systems is 〈( az) = +2.615° (with the x-axis perpendicular to the symmetry plane).

Structure of methyl cyanoformate from microwave spectroscopy and a b i n i t i o calculations

The microwave spectra of seven isotopic species of methyl cyanoformate, CD3OC(O)CN, CD2HOC(O)CN, 13CH3OC(O)CN, CH318OC(O)CN, CH3O13C(O)CN, CH3OC(O)13CN and CH3OC(O)C15N have been measured and assigned. A barrier to internal rotation of 407±1 cm−1 (1164±3 cal/mol) has been obtained for seven symmetric internal rotor species from the internal rotation analyses. The rotational constants from nine isotopic species have been used to determine both rs and r0 structural parameters for the s-trans conformer (methyl group trans to the cyanide group). All independent structural parameters could be determined. Optimized structures were calculated for the s-trans conformer by ab initio Hartree–Fock gradient calculations with both the 3-21G and 6-31G* basis sets as well as with MP2/6-31G* calculations. With the 6-31G* basis set, the barrier to interconversion of the s-trans form to the s-cis form was calculated to be 4055 cm−1 (11.59 kcal/mol) with the s-trans conformer being more stable by 2364 cm−1 (6.76 kcal/mol). The barrier to internal rotation of the methyl group was calculated to be 442 cm−1 (1264 cal/mol).

The structure of methyl fluoroformate from microwave spectroscopy and AB initio calculations

The microwave spectra of three isotopic species of methyl fluoroformate, CD 3OCFO, CD 2HOCFO and CH 3 18OCFO have been measured and assigned. A barrier to internal rotation of 372±2 cm −1 has been obtained for three symmetric internal rotor species from internal rotation analyses. The rotational constants from five isotopic species have been used to determine an r 0 structure for the s- trans conformer (methyl group trans to fluorine). The s- cis conformation is not compatible with the experimental data as the data lead to an unrealistically large COC angle. The fully optimized structure from ab initio calculations with the 6-31G* basis set which include electron correlation at the MP2 level is compared with the experimental structure and with earlier results from RHF/6-31G* calculations.

Fokker—Planck—Langevin and extended diffusion models of internal rotation in molecules. I. symmetric internal rotor

The effects of internal rotation in molecules containing a symmetric internal rotor have been investigated using both the Fokker—Planck—Langevin (FPL) and extended diffusion (EDJ) models of collision dynamics. Sample calculations are presented illustrating the effects of the magnitude of the internal barrier to rotation, the magnitude of the internal angular momentum correlation time, and the collision model chosen on correlation times and factors of importance to NMR relaxation. These include second-rank reorientational correlation times, dipole—dipole relaxation spectral densities (including the effects of modulation of the internuclear distance), and spin-rotational correlation factors. The presentation concentrates on the case where internal and overall motions are decoupled, but a general expression for the Liouville operator of an asymmetric molecule with a symmetric internal rotor is derived and the associated collision operators are discussed. The results show that the correlation times and factors are quite sensitive to the size of the barrier and the internal angular momentum correlation time.

Erratum: Contributions of the interaction of internal rotation with other vibrations to the effective potential energy for internal rotation in molecules with symmetric internal rotors [J. Chem. Phys. 7 3, 2107 (1980)

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Contributions of the interaction of internal rotation with other vibrations to the effective potential energy for internal rotation in molecules with symmetric internal rotors

The theory of vibration–large amplitude internal motion interaction in molecules is used to calculate these contributions to the effective Hamiltonian for internal rotation when the internal rotor has a threefold axis of symmetry. Calculations are made for four deuterium isotopic species of methyl alcohol, two isotopic species of acetaldehyde and trifluoroacetaldehyde, and perfluoroacetyl fluoride. The dynamic contribution to the potential energy coefficient V6 ranges from −3 to −6 cm−1. The potential energy coefficient V3 shows a dependence of a few tens of cm−1 upon the state of the perpendicular vibrations. A cos6τ dependence of the reduced torsional coefficient is of the order of 0.05% of 𝒢ττ. The mixing of internal rotation with other vibrations cannot account for the decrease in barrier for methyl alcohol with deuterium substitution; actually the calculation gives an increase in barrier of comparable magnitude to the decrease observed for CD3OH compared to CH3OH.

ChemInform Abstract: INFRARED ABSORPTION INTENSITIES OF TORSION‐ROTATION TRANSITIONS OF MOLECULES WITH SYMMETRIC INTERNAL ROTOR

The infrared absorption intensities of torsion-rotation transitions were theoretically derived on the basis of torsion-rotation interactions of molecules with symmetric internal rotor. The theoretical intensities depend upon molecular structure parameters and molecular dipole moment. Implications of the present theory are discussed on absolute intensities, orientations of dipole transition moment, band types (A, B, or C), and deuteration effects on absorption intensities of methyl torsional transitions. For propylene oxide and propylene sulfide, the far infrared spectra of the gaseous state were measured, and the experimental absorption intensities of methyl torsional vibrations were compared with theoretical intensities.

Infrared Absorption Intensities of Torsion–Rotation Transitions of Molecules with Symmetric Internal Rotor

Abstract The infrared absorption intensities of torsion-rotation transitions were theoretically derived on the basis of torsion-rotation interactions of molecules with symmetric internal rotor. The theoretical intensities depend upon molecular structure parameters and molecular dipole moment. Implications of the present theory are discussed on absolute intensities, orientations of dipole transition moment, band types (A, B, or C), and deuteration effects on absorption intensities of methyl torsional transitions. For propylene oxide and propylene sulfide, the far infrared spectra of the gaseous state were measured, and the experimental absorption intensities of methyl torsional vibrations were compared with theoretical intensities.

Zero-point Average Structure of a Molecule Containing Two Symmetric Internal Rotors. Acetone

Abstract The theory of vibrational correction to the observed moments of inertia of a molecule which contains an internal rotor has been extended to the case of two symmetric internal rotors, and applied to the analysis of the structure of acetone. The zero-point average structure has been determined by using the moments of inertia obtained by microwave spectroscopy and the bond distances from gas electron diffraction. The zero-point average parameters have been determined as follows: C–C 1.517±0.003 Å; C=O 1.210±0.004 Å; C–H 1.091±0.003 Å; ∠HGH 108° 30′±30′; ∠CCC 116° O′±15′. The isotope effects in the structure parameters have also been observed in terms of the increase caused by deuteration to be δ(DCD)+10′±12′; δ(CCC)−17′±2′. The tilt angle of the methyl top was determined to be 2° 1′±30′.

Zero-point average structure of a molecule containing a symmetric internal rotor

A theoretical formulation for the correction to observed effective moments of inertia for the effect of molecular vibration has been worked out for a molecule containing a symmetric internal rotor. The theory has been applied to acetaldehyde and the zero-point average structure has been determined. The barrier to internal rotation has also been examined without any ambiguity of effective I γ caused by zero-point vibrations. The values of the parameters of the zero-point average structure of acetaldehyde are CC 1.512 ± 0.004 A ̊ , CO 1.207 ± 0.004 A ̊ , CH ald 1.114 ± 0.009 A ̊ , CH Me 1.093 ± 0.006 A ̊ , ∠ CCO 124.2° ± 0.5°, ∠ CCH ald 115.3° ± 0.3° and ∠ HCH Me 109.6° ± 0.9°.