Coriolis Coupling Coefficients Research Articles

The 130–500 GHz rotational spectrum of 2-cyanopyrimidine

The rotational spectrum of 2-cyanopyrimidine has been obtained from 130 GHz to 500 GHz. Over 7500 vibrational ground-state transitions have been assigned and least-squares fit to partial octic, A- and S-reduced Hamiltonians with low error (σfit = 36 kHz). The two lowest-energy fundamental modes, the out-of-plane (ν18) and in-plane (ν27) nitrile bending modes, form a Coriolis-coupled dyad similar to the analogous fundamental states of other cyanoarenes. The coupled dyad was least-squares fit to a partial octic, A-reduced Hamiltonian (σfit = 47 kHz) with over 6700 transitions for each vibrational state, including transitions that are perturbed or involved in resonances, as well as symmetry-allowed nominal interstate transitions resulting from Coriolis coupling. The spectroscopic information from these transitions enabled the determination of a highly precise energy separation (ΔE18,27 = 38.9673191 (77) cm−1) and six Coriolis-coupling coefficients (Ga, GaJ, GaK, GaJJ, Fbc, and FbcK). The spectroscopic constants and transitions presented in this work provide the foundation for future radioastronomical searches for 2-cyanopyrimidine.

Millimeter-wave spectrum of 4-cyanopyridine in its ground state and lowest-energy vibrationally excited states, ν20 and ν30

The rotational spectrum of 4-cyanopyridine (μa = 1.96 D) was recorded from 130 to 360 GHz, and the analysis of the ground state and two lowest-energy excited vibrational states was completed. Over 3900 new rotational transitions were measured for the ground state, allowing the determination of spectroscopic constants for a partial octic, distorted-rotor Hamiltonian. Over 5600 new transitions were measured for the Coriolis-coupled dyad, ν20 and ν30. A coupled-state least-squares fit of the dyad was obtained, which resulted in the precise determination of several parameters addressing the Coriolis coupling between the two states: Ga, GaJ, Fbc, and FbcK. With inclusion of these terms, numerous resonance transitions associated with selection rules ΔKa = 2 or ΔKa = 4 between vibrational states were assigned and fit to low error (σfit < 50 kHz). The precise energy difference between ν20 and ν30 was determined, ΔE = 18.806554 (11) cm−1, along with the Coriolis coupling coefficient ζ20,30a = 0.8432 (8). Determination of the spectroscopic and perturbation parameters for the vibrational states permits comparison to other arenes bearing –CN or –NC substituents and sharing a similar Coriolis-coupled dyad ~150 cm−1 above the ground state. This new data provides the foundation for an astrochemical search for 4-cyanopyridine in the interstellar medium.

The 130–370 GHz rotational spectrum of phenyl isocyanide (C6H5NC)

The analysis of phenyl isocyanide (C6H5NC, μa = 4.0 D) in its ground vibrational state and two lowest-energy excited vibrational states, ν22 (141 cm-1) and ν33 (155 cm-1), in the 130-370 GHz frequency region has been completed. Over 4500 new rotational transitions have been measured in the ground vibrational state for the most abundant isotopologue, resulting in the determination of the spectroscopic constants for a partial octic Hamiltonian with low error. The Coriolis-coupled ν22-ν33 dyad reported herein, containing over 3500 new transitions for each vibrational state, has been analyzed for the first time. The coupled-state least-squares fit utilizes seven coupling terms (Ga, Ga J, Ga K, Ga JJ, Ga JK, Fbc, and Fbc K) to address perturbation between the two vibrational states, including resonances and several nominal interstate transitions. This work results in precise determination of the energy separation between the two states, ΔE22,33 = 9.682 248(3) cm-1, and the Coriolis coupling coefficient, |ζ22,33 a| = 0.858(9). The precise rotational and distortion constants determined in this work provide the foundation for an astronomical search for phenyl isocyanide across the radio band.

FTIR spectrum of vinyl fluoride near 3.6 μm: rovibrational analysis of the ν4+ν7 band and modelling Coriolis resonances in a seven-level polyad

ABSTRACTThe Fourier transform infrared (FTIR) spectrum of vinyl fluoride, H2C=CHF, has been widely investigated in the region of the ν4+ν7 combination band around 2800 cm−1 at a resolution of 0.005 cm−1. This vibration of A' symmetry gives rise to an a/b-hybrid band with a predominant a-type component. The rovibrational structure is strongly perturbed and the analysis has been rather complicated since this combination band is involved at least in a seven-level interacting polyad, including the ν8+2ν10, 2ν8+ν10, 2ν7+ν9, ν7+ν8+ν12, ν5+ν9+ν10 and ν7+ν10+ν12 vibrational states. The study has been further complicated by the absence of transitions coming from the perturbers that were considered as dark states. The spectral analysis resulted in the identification of 936 transitions with J" ≤ 46 and Ka" ≤ 11, all belonging to the a-type component. Most of the assigned data have been fitted using the Watson's A-reduction Hamiltonian in the Ir representation and proper Coriolis perturbation operators. The model employed includes seven different resonances within a complex polyad resonant system and a set of spectroscopic constants for the ν4+ν7 combination band, for the dark states, and Coriolis coupling coefficients have been determined.

Strong Coriolis coupling between [formula omitted] and [formula omitted] states of [formula omitted] studied by millimeter-wave spectroscopy

Rotational transitions in vibrational states v 5 = 1 and v 11 = 1 in the oblate CH 3 C 35 Cl 3 molecule have been studied at frequencies from 69 to 332 GHz. The two states belong to the second lowest wavenumber A-symmetry, and E-symmetry normal modes, and are accidentally very close in energy. They are thus strongly coupled by ( x - y ) Coriolis interaction, in addition to the l-type resonance in the degenerate v 11 = 1 state. The resulting rotational transitions form three characteristic band series, which show many manifestations of strong interstate coupling. Frequencies of well over 1000 transitions have been measured and fitted to within experimental accuracy, resulting in Δ E 5 , 11 = 2.41204 ( 3 ) cm −1, first values of the axial constants for this molecule, C 5 = 1709.966 ( 7 ) , C 11 = 1712.462 ( 7 ) MHz, and of values for the pertinent Coriolis coupling coefficients, ζ 11 c and ζ 5 , 11 b , which are in good agreement with results of ab initio calculations.

Anharmonic analysis of the vibrational spectra of some cyanides and related molecules of astrophysical importance

A detailed analysis of the vibrational spectra of carbonyl cyanide, diethynyl ketone and acetyl cyanide has been conducted in harmonic and anharmonic approximations. RHF, MP2 and density functional theory (DFT) methods with 6-311++G(2df,2p) basis sets and B3LYP functionals have been employed. Spectroscopic constants such as anharmonicity constants, rotational and centrifugal distortion constants, rotation–vibration coupling constants and Coriolis coupling coefficients have been calculated for each molecule and compared with the experimental data, where available. A close agreement between the calculated and experimental values of the spectroscopic constants has been obtained. Complete assignments have been provided to the fundamental bands, overtones and combination tones of the molecules. Density functional theory based anharmonic frequencies compare well with the experimental frequencies within ±18cm−1 on an average. RHF and MP2 methods, however, give much higher values for the frequencies that need scaling even in the anharmonic approximation.

Calculation of the τ dependence of the vibration–internal rotation–overall rotation interactions in CH3OH from molecular structure and molecular dynamics

The Guan and Quade theory for vibration-large-amplitude internal-motion-rotation interactions has been applied to the internal rotation problem in CH(3)OH. Through the molecular dynamics, the cos 3tau and sin 3tau dependence of the torsional-rotational coefficients in the effective Hamiltonian have been calculated from molecular structure. The internal rotation coordinate tau(') for the vibrationally distorted molecule is shown to have the necessary threefold symmetry for all values of tau('). For the methyl deformation modes, the vibrational dependence of the internal rotation potential energy is shown to have a threefold symmetry. The S(t) and S(t)S(t) dependence of the inertia tensor and Coriolis coupling coefficients has been developed in terms of curvilinear internal coordinates. The T transformation separating rotation from vibrations in zeroth order is then applied, the kinetic-energy tensor inverted to momentum space, and finally the effective torsion-rotation coefficients are calculated by Van Vleck perturbation theory. When compared to the empirical results, the kinetic-energy contributions to the cos 3tau and sin 3tau dependence of the coefficients are as follows: 54% of P(a)(2) is accounted for, 28% of P(a)P(b), 16% of P(a)P(c), and 91% of the asymmetry. The calculation is inadequate to account for the P(b)(2),P(c)(2), and P(b)P(c) coefficients, ranging from factors of 20-70, even with the incorrect sign for some of the terms. Anharmonic force contributions from the vibrations have not been used in the calculation since these forces are not known at this time.

Vibration-rotation interactions between overtone and combination levels of asymmetric-top molecules: Application to the infrared spectroscopy of formaldehyde and ketene

The conventional vibration-rotation Hamiltonian for an asymmetric-top molecule is rewritten by expanding the elements of the inverse inertial tensor about the equilibrium molecular geometry. The approach allows the identification of terms in the Hamiltonian that couple states differing by two, three, or four vibrational quanta and hence the calculation of dimensioned Coriolis xi coupling coefficients for interacting fundamental, overtone, and combination levels. The matrix elements that result from the application of the expanded Hamiltonian depend upon the harmonic vibrational wave numbers, equilibrium moments of inertia, Coriolis zeta parameters, and the derivatives of the elements of the inertial tensor matrix with respect to each of the normal coordinates. The Coriolis coupling coefficients may be calculated through evaluation of the summations that result from the appropriate terms. The validity of the approach is demonstrated through the calculation of coupling coefficients for interacting levels in formaldehyde and ketene. The uncertainty in the calculated values of the coupling coefficients is typically better than +/-6%, although the values calculated for interactions that involve low-frequency vibrational modes are less reliable. Comparisons are made between the calculated values and experimental results.

Observation of Coriolis Coupling between ν2 + 4ν4 and 7ν4 in Acetylene X̃1Σ+g by Stimulated Emission Pumping Spectroscopy

Stimulated emission pumping (SEP) spectroscopy has been used to examine a low energy region (Evib ≈ 4400 cm−1) of X̃1Σ+g acetylene at higher resolution than was possible in previous dispersed fluorescence studies. The expected bright state, ν2 + 4ν4, is observed to be coupled to the nearly degenerate 7ν4 state by a Coriolis mechanism. A least-squares analysis yields values for zero-order vibrational energies, rotational constants, and a Coriolis-coupling coefficient that are all consistent with expectations. Calculated relative intensities of SEP transitions, accounting for interference due to axis-switching effects, are also consistent with observations. Implications of the observed Coriolis resonance with regard to global acetylene vibrational dynamics are also discussed.

A new method to evaluate force constants from experimental spectral data

AbstractAn iterative procedure is proposed to facilitate the determination of molecular vibrational force constants from the experimental fundamental frequencies. Proper restrictions are introduced to the force constants based on physical considerations for getting reasonable results. The experimental data of Coriolis coupling coefficients and isotopic frequency shifts are utilized to reduce the uncertainty of the calculated force constants when they are available. A series of various kinds of molecules have been calculated by this method and the results are satisfactory.

Potential energy surfaces for the ground electronic state of water, hydrogen sulfide, and hydrogen selenide

A curvilinear internal coordinate Hamiltonian is used to calculate vibrational term values of water, hydrogen sulfide, and hydrogen selenide variationally with Morse oscillator basis functions for the stretches and harmonic oscillator basis functions for the bend. Rotational parameters, a constants, are calculated with perturbation theory expressions. Potential energy parameters are optimized with the nonlinear least-squares method using vibrational term values, a constants, and Coriolis coupling coefficients as data. The model is applied to five isotopic species of water, five isotopic species of hydrogen sulfide, and to two isotopic species of hydrogen selenide. The observed vibrational and rotational data of the studied molecules are reproduced well

Vibration-rotation interactions and local modes in tetrahedral molecules

Vibration-rotation coupling in tetrahedral molecules is treated by using tensorial formalism in the T d point group and by expressing the vibrational part of the rovibrational operators in terms of “local” bond stretching coordinates and momenta. Due to the X -H stretching anharmonicity any realistic calculation of the rotational structures of the excited stretching states of an X H 4 molecule is much simpler by this approach than by the customary description of the X -H stretches in terms of ν 1 and ν 3 normal modes. The observed first-order Coriolis coupling coefficients of several excited states of CH 4 and SiH 4 are very well accounted for by considering the harmonic interaction with the ν 4 bending mode. A very high resolution spectrum of the 2 ν 3 band of SiH 4 is interpreted from P (4) to R (3) (i.3., about 40 transitions) with a rms deviation of 3 × 10 −3 cm −1 by using only two adjustable parameters in the effective vibration-rotation Hamiltonian.

The infrared spectrum of aminodifluoroborane, NH2BF2: Partial assignment of the fundamentals and analysis of the band near 1608 cm−1

The infrared spectrum of gas phase aminodifluoroborane, NH2BF2, has been observed for the first time. A partial assignment to the fundamental vibrations has been made. The [Formula: see text] band has been recorded at high resolution, and the rotational and centrifugal distortion constants of NH211F2 have been obtained in both the ground and 21 levels. A small rotational perturbation in the 21 level has been attributed to a perpendicular Coriolis interaction. Using a newly written least-squares fitting program, spectroscopic constants of the unseen level have been evaluated, including its band origin and the Coriolis coupling coefficient. Possible identities of the unseen level are suggested.

Vibration-rotation molecular constants for the ground and ( ν3 = 1) states of 32SF 6 from saturated absorption spectroscopy

An analysis has been made of the vibration-rotation structure of the ν 3 band of 32SF 6 from measurements, by saturated absorption spectroscopy, of the frequencies for 136 transitions in close coincidence with CO 2 and N 2O laser lines in the 28-THz region. After deconvolution of the fine structure lines from their hyperfine structures, the centers of vibration-rotation transitions are given with a 5-kHz uncertainty. They are analyzed using the tensor Hamiltonian of Moret-Bailly, developed to the fifth order of approximation. An iterative procedure, using full diagonalization of the Hamiltonian matrices, leads to a very accurate determination of 18 effective molecular constants of the ( v 3 = 1) excited state, together with 6 constants of the ground state (both for scalar and tensor terms). For instance, the inertial constant of the ground state is β 0 = B 0 = 0.0910842001(10) cm −1, the vibrational energy is α = ν 3 = 948.10252337(40) cm −1, and the Coriolis coupling coefficient is ζ 3 = 0.69344341(20). The recorded transitions, ranging from P(84) to R(94), are reproduced with a standard deviation σ d = 28 kHz ⋍ 0.93 × 10 −6 cm −1 . A few transitions remain out of the fit, and the possibility of resonances with close vibrational levels is briefly discussed. We also give the predicted positions for SF 6 transitions in close coincidence with laser lines of various isotopic species of CO 2.

Internal coordinate formulation for the vibration-rotation energies of polyatomic molecules. III. Tetrahedral and octahedral spherical top moleculesa)

The theory of vibration-rotation interactions in tetrahedral and octahedral spherical top molecules has been developed using curvilinear internal coordinates for the vibrational degrees of freedom. Integral to the development has been a derivation of the vibrational kinetic energy for configurations away from equilibrium when redundant coordinates are present in the symmetry coordinate basis. General expressions for the inertial coefficients, Coriolis coupling coefficients, and vibrational kinetic energy anharmonicity coefficients have been derived for both the tetrahedral and octahedral molecules. A Van Vleck transformation is used to obtain both the diagonal and off-diagonal theoretical vibration-rotation and vibration anharmonic spectroscopic coefficients to second order. Comparisons with the earlier work on methane by Gray and Robiette are good. Application is made in the partial determination of the anharmonic potential energy coefficients for SF6 and CF4. As has been found in our previous work, the curvilinear internal coordinate approach has definite advantages over the Cartesian displacement approach for the angle bending modes in the molecules.

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.

Normal coordinate analysis and spectroscopic constants of formic acid and its isotopes

A normal coordinate analysis has been performed for the molecule formic acid and its isotopes. The force constants have been computed assuming the GVFF. Using the force constants other spectroscopic constants such as mean square amplitudes of vibration, generalized mean square ampli¬ tudes of vibration, Coriolis coupling coefficients, centrifugal distortion constants have been calculated and presented here. With the aid of vibrational frequencies and the structural parameters, the thermodynamics functions such as heat content, heat capacity, free energy and entropy have also been evaluated.

Vibrational analysis of chlorine dioxide in the ground state, electrically excited state and ionic state

Based on the normal coordinate theory, the vibrational analysis of the ground state (Bt), the electronically excited state (A2) and singly ionised state (A,) of ClO2 has been carried out and the force constants corresponding to these three states have been evaluated by kinetic constants method employing the general valence force field. These force constants have been used to calculate the mean square amplitudes of vibration, Coriolis Coupling Coefficients and Centrifugal distortion constants of ClO2 in these three states.

Many-body perturbation theory electronic structure calculations for the methoxy radical. I. Determination of Jahn–Teller energy surfaces, spin–orbit splitting, and Zeeman effect

Many-body perturbation theory calculations of the electronic structure are reported for C3v and Jahn–Teller distorted conformations of the methoxy radical CH3O. The Jahn–Teller distortion reduces the energy relative to the minimum energy for the C3v structure by −0.64 kcal/mol. Furthermore, the dynamic Jahn–Teller effect reduces the calculated spin–orbit splitting from 78 to 37 cm−1. An analysis of the Jahn–Teller energy surface yields the e mode vibrational frequencies (ν4 = 2314, ν5 = 1066, ν6 = 792 cm−1) and Coriolis coupling coefficients (ζ4 = 0.065, ζ5 = −0.152, and ζ6 = 0.186) for the ground state. The orbital g factor g0 = 0.647 was calculated and used to determine the components of the g tensor for free methoxy and matrix-trapped methoxy. For free methoxy, g∥ = 2.645 and g⊥ = 0; for the matrix-trapped radical, experimental data was used to calculate the splitting 1.7 kcal/mol of the methoxy energy level caused by its site environment. This splitting quenches g∥ to a value of 2.096.

Normal coordinate analysis of the tetrafluoro-1,3 dithietane

A complete normal coordinate analysis has been performed for the tetra fluoro-1,3 dithietane which is planar belonging to D2h point group. The symmetric.F, and the internal valence force constant,f, matrices were derived in general case by using a GVFF and the results were applied to C2S2F4. In addition, mean amplitudes, generalised mean square amplitudes, the Coriolis coupling coefficients, the rotation distortion constants and the thermodynamic properties have also been evaluated.