C. Richard Quade

Microwave rotational spectrum and internal rotation in gauche ethyl alcohol

The microwave torsional–rotational spectra of several species of gauche ethyl alcohol have been assigned and analyzed. The species studied are CH3CH2OH, CH3CH2OD, CH2DCH2OH, and CH2DCH2OD, both methyl symmetric and asymmetric forms of the last two species. Rotational coefficients have been determined for all species. For the normal species, the components of the dipole moment have been determined as ‖μa‖=1.264±0.010 D, ‖μb‖=0.104±0.008 D, and ‖μc‖=1.101±0.016 D. The tunneling frequency between the two gauche substrates is measured to be Δ=97 734.3 MHz and the gauche–trans energy difference is measured to be 41.2±5.0 cm−1 for the normal species. The first three coefficients in the Fourier expansion of the hydroxyl internal rotation potential energy are determined to be V1=57.0 cm−1, V2=0.8 cm−1, and V3=395.0 cm−1. The barrier to methyl internal rotation for gauche CH3CH3OH is The barrier to methyl internal rotation for gauche CH3CH3OH is determined to be V3=1331 cm−1. Analysis of the interaction between me...

The microwave spectrum of CH2DOH

The torsional–rotational spectrum of CH2DOH has been investigated in order to gain fuller understanding of the internal rotation parameters as well as to provide molecular radio astronomers with a set of measured transition frequencies which can be used for an interstellar search for the molecule. a‐ and b‐dipole transitions have been assigned within the three substates of the torsional ground state and c‐dipole transitions have been assigned from the e1 to the o1 substate. The potential energy coefficient V1=12±1 cm−1 has been determined with V2 constrained to zero. Although the torsional wave functions are by no means sharp, the molecule does localize to symmetric and asymmetric forms.

An internal axis approach for the internal rotation problem in asymmetric-asymmetric molecules: Application to the microwave torsional-rotational spectra of CH2DOH and CHD2OH

Abstract The IAM theory of the previous paper is used to calculate the torsional-rotational term values for CH 2 DOH and CHD 2 OH that have been observed experimentally. The Cal. — Obs. differences are found to contain predominantly rigid rotor terms that cannot be developed from the molecular structure. These terms have their origin in the interaction of internal rotation and rotation with the other vibrations of the molecules. A slightly modified molecular structure, due to the deuterium substitution, is determined for each species from the analysis. The best potential energy coefficients are CH 2 DOH CHD 2 OH V 1 = 8.80 cm −1 V 1 = −9.21 cm −1 V 2 = 2.42 cm −1 V 2 = −2.29 cm −1 V 3 = 373.22 cm −1 V 3 = 373.28 cm −1

An internal axis approach for the internal rotation problem in asymmetric-asymmetric molecules: Theoretical formulation

Abstract An internal axis (IAM) formulation for internal rotation in molecules has been developed when both the top and frame have planes of symmetry. The rotational coefficients are expanded in Fourier series after the internal axis system has been defined by coordinate transformations. The final form of the Hamiltonian has an extremely clean form which is suitable for computer solution. In the accompanying paper the theory is applied to the analysis of the microwave torsional-rotational spectra of CH 2 DOH and CHD 2 OH and then in a second paper to the prediction, assignment, and analysis of the spectrum of CHD 2 OD.

The interaction of a large amplitude internal motion with other vibrations in molecules. The effective Hamiltonian for the large amplitude motion

A theory for the interaction of a large amplitude internal motion (LAM) with the small amplitude vibrations in molecules is formulated. Valence internal coordinates are used for the development of the kinetic and potential energies in terms of the usual G−1, G, and F matrices with all three being functions of the internal coordinates. A coordinate transformation is defined that separates the large amplitude internal motion from the other vibrations in zeroth order in the kinetic energy but at the same time modifies the force constants for the 3N‐7 vibrations. The higher order momentum coupling between the large and small amplitude vibrations is developed. Expressions are obtained for the small amplitude coordinate dependence of the kinetic energy coefficient for the large amplitude motion. A Van Vleck transformation is used to obtain the effective Hamiltonian of the large amplitude motion for the vth vibrational state of the other vibrations. The effective Hamiltonian is suitable as a parametric equation ...

Curvilinear coordinate formulation for vibration–rotation–large amplitude internal motion interactions. I. The general theory

A theory for vibration–rotation–large amplitude internal motion interactions is developed using curvilinear coordinates for the vibrational degrees of freedom. An essential feature to the theory is our coordination of two transformations developed previously for the separation of vibration from rotation and vibration from the LAM, in zeroth order. Series expansion in the vibrational coordinates is used to obtain the full vibration–rotation–LAM Hamiltonian. A Van Vleck perturbation approach is used to obtain the effective rotation–LAM Hamiltonian, HeffτR, for the molecule in the nth vibrational state. Reduction of the effective Hamiltonian has been made to (1) the zero angular momentum state of the molecule, (2) the zeroth order rotation–LAM Hamiltonian, and (3) the usual vibration–rotation Hamiltonian when the LAM takes on a small amplitude.

Microwave detection of direct trans to gauche transitions in CH2DOH

Abstract Additional lines have been assigned in the microwave torsional-rotational spectrum of CH 2 DOH. Of particular interest is the detection and identification of direct trans to gauche transitions to both gauche states. In terms of torsional substate, three R -type and three Q -type transitions have been assigned for e 0 ( trans ) to e 1 ( gauche ) and four R -type transitions have been assigned for e 0 ( trans ) to o 1 ( gauche ). Five additional lines have been assigned for e 1 ( gauche ) to o 1 ( gauche ) and seven additional lines have been assigned within the e 0 and o 1 substates. The torsion-rotation analysis gives the torsional energy level differences gauche - gauche = 101.9 GHz, trans - gauche (lower) = 280.5 GHz, and trans - gauche (upper) = 382.4 GHz. The torsional potential energy coefficients have been determined to be V 1 = 8.74 ± 0.01 cm −1 , V 2 = 2.49 ± 0.02 cm −1 , and V 3 = 373.45 ± 0.05 cm −1 .

Microwave detection of direct gauche to trans transitions in CHD2OH

A portion of the microwave torsional–rotational spectrum of CHD2OH has been assigned between 12.4 and 41.3 GHz. Of particular interest is the detection and identification of direct gauche to trans transitions from both gauche states as well as gauche to gauche transitions. The energy level system has three substates in the torsional motion with a rotational manifold for each torsional substate. In terms of torsional substate, ten Q‐type and three R‐type transitions have been assigned for e0 (gauche) to o1(gauche); 13 Q‐type for o1(gauche) to e1(trans); and four R‐type for e0(gauche) to e1(trans). Additional lines have been assigned within each torsional substate. Spectral analysis has been made using a phenomenological rotational Hamiltonian plus an internal axis torsion–rotation Hamiltonian in zeroth order. The approximate torsional energy level differences are gauche–gauche=184.7 GHz, gauche(upper)–trans=202.5 GHz, and gauche(lower)–trans=387.2 GHz. Two sets of potential energy coefficients, one with po...

Internal coordinate formulation for the vibration‐rotation energies of polyatomic molecules. II. Symmetric top molecules with a threefold axis

The theory of vibration‐rotation interactions in symmetric top molecules with a threefold axis has been developed using curvilinear internal coordinates for the vibrational degrees of freedom. General expressions for the inertial coefficients, Coriolis coupling coefficients, and vibrational kinetic energy anharmonic coefficients have been derived for planar and nonplanar XY3 molecules. A Van Vleck perturbation scheme is used to obtain the theoretical vibration‐rotation and vibration anharmonic spectroscopic coefficients. Applications are made in the analyses of the empirical spectroscopic coefficients for BF3 and NH3 in the determination of incomplete sets of improved anharmonic potential energy coefficients. In many respects it is found that the curvilinear internal coordinate approach to vibration‐rotation interactions has advantages over the Cartesian displacement coordinate approach for angle bending modes in the symmetric top molecules.

The microwave spectra of CH2DSH and CHD2SH

The microwave torsional‐rotational spectra of CH2DSH and CHD2SH have been measured and analyzed over the frequency range 12.5–48.0 MHz. a‐, b‐, and c‐dipole transitions have been assigned for both species which makes it possible to determine the tunneling frequency between the two gauche torsional levels for both species. An internal rotation analysis gives the torsional potential energy coefficients V1=−3.40±0.10 cm−1, V3=456.3±0.5 cm−1 for CH2DSH and V1=4.45±0.10 cm−1, V3=424.5±0.5 cm−1 for CHD2SH with V2 constrained to zero.