L-type Doubling Constants Research Articles

The microwave spectrum of 1-chloro-3,3,3-trifluoro-propyne

The microwave spectra of four isotopic species of 1-chloro-3,3,3-trifluoro-propyne (CF 3-CC-C1) have been investigated in natural abundance. The rotational, centrifugal distortion, rotational-vibrational interaction, quadrupole coupling and l-type doubling constants have been obtained. The structure giving the best fit to the four moments of inertia is: r 0(C-Cl) = 1.627 ± 0.009 Å, r o(CC) = 1.199±0.005 Å, r o(C-C) = 1.453±0.002 Å and r o(C-F) = 1.336±0.006 Å with the angle FCF assumed to be 107.0 ± 1.0°. A partial r s structure is also given, which indicates that the C-C or the CC distances, or both, are unusually short. The dipole moment is determined to be 1.73 ± 0.20 D. The results are compared to those for related molecules.

Millimeter wave rotational spectrum of HCNO in vibrationally excited states

A millimeter wave spectrometer equipped with a free space cell and on-line computer averaging has been employed to measure the absorption spectrum of H 12C 14N 16O in the frequency range from 40 to 300 GHz. For each rotational transition up to J = 11 → 12, all of the l-components of transitions in the following vibrational states have been observed and analyzed: 0000 02 0, 2, 0000 03 1, 3, 0002 0, 20 0, and 000(11) 0, 2. The method of analysis, carried out on the basis of the Nielsen-Amat formulation of the rotation-vibration interaction in linear molecules, is discussed. The unperturbed rotational constants B v and D v as well as several vibration-rotation constants were determined using sum rules valid for each group of perturbed levels and lines. The vibrational anharmonicity constants g l t l t′ were determined for the first time from pure rotational transitions. The following constants were obtained: gl 5l 5(v 5=2)=−24.2±3.0 cm −1, gl 4l 4(v 4=2)1.28±0.30 cm −1 gl 5l 5(v 5=3)=−6.24±0.14 cm −1, gl 4l 5(v 5=1; v 5=1)=1.63±0.50 cm −1; An interpretation of the results of this analysis, especially for the v 5 = 2 and v 5 = 3 states, is given. The observed anomalies indicate the presence of a potential function with a hump disturbing the isotropic two-dimensional oscillator potential for ν 5, the low-lying degenerate bending mode. In the case of the combination state 000(11) 0, 2 the vibrational l-type doubling constants r 45 (0) = −0.81 ± 1.00 cm −1 and r 45 (1) = 0.6565 ± 0.0027 MHz have been evaluated for the first time from millimeter wave rotational transitions.

On the Validity of the P–R Separation Method in the Presence of l-Type Resonance

A resonance calculation computer program has been applied to a quantitative investigation of the effects of strong l-type resonances on the envelopes of degenerate (E) infrared bands of symmetric tops. The immediate object of these calculations has been to establish whether l-type resonance is likely to be a serious source of error in the P–R separation method of determining η constants. Attention has been directed mainly to bands where (C − Cη − B) is close to zero so that the mutually perturbing levels are nearly degenerate. The effect of assuming l-type doubling constants, q, much larger than those observed has been examined. All of our calculations suggest that uncertainties in the P–R separation method arising from this source are small and comparable to those deriving from other known sources, such as the neglect of α constants in the method. An explanation for these results in terms of line by line shifts is advanced.

The microwave spectra of chlorobromoacetylene, chloroiodoacetylene, and chlorodiacetylene

The microwave spectra of 35Cl-CC- 79Br, 35Cl-CC- 81Br, 37Cl-CC- 79Br, 37Cl-CC- 81Br, 35Cl-CC-I, 37Cl-CC-I, 35Cl-CC-CC-H,and 37Cl-CC-CC-H in natxiral abundance are reported. The molecules were all found to be linear. The structure of chlorobromoacetylene was obtained: r(C-Cl) = 1.628±0.005 Å; r(CC) = 1.209 ± 0.008 Å; r(C-Br) = 1.790 ± 0.005 Å. The quadrupole coupling constants were obtained for the bromine nuclei of chlorobromoacetylene, for the iodine nucleus of chloroiodoacetylene, and for 35Cl of chlorodiacetylene. A least squares treatment yielded the rotational constants, vibration-rotation interaction and l-type doubling constants for several low frequency modes of the three molecules.

Higher-order variations of ℓ-type doubling constants and centrifugal distortion constants for HCN and OCS

The v- and J-dependences of the ℓ-type doubling constant q v and of the centrifugal distortion constant D v for linear XYZ molecules have been formulated by means of Amat and Nielsen's fourth-order theory of vibration-rotation interactions. Practical applications of the formulas have been carried out for HCN, OCS and their isotopic species by using anharmonic potential functions involving cubic and quartic terms.

Microwave spectra of nitrogen trifluoride in the excited vibrational states: Equilibrium structure

The microwave spectra of two isotopic species of the NF 3 molecule were investigated in the excited vibrational states. The vibration-rotation interaction constants α v B for the ν 1, ν 2, ν 3 and ν 4 states were found to be −43.45, +38.65, +78.81, and +4.48 MHz for 14NF 3 and −38.41, +40.14, +75.67, and +4.64 MHz for 15NF 3, respectively. The equilibrium rotational constant, B e , was then derived to be 10761.9 1 ± 0.2 MHz for 14NF 3 and 10710.6 3 ± 0.2 MHz for 15NF 3, from which the equilibrium structure was determined to be r e (N-F) = 1.365 ± 0.002 A ̊ and α e (∠FNF) = 102°22′ ± 2′. A set of linear relations was derived between cubic potential constants from the observed α v B and ℓ-type doubling constants.

The anharmonic constants and average structure of ammonia

The cubic and quartic potential constants for NH 3 and ND 3 have been calculated by assuming intramolecular potential functions of internal coordinates and by means of the nonlinear transformation of the internal coordinates into the normal coordinates. The ordinary F matrix elements in the internal-symmetry coordinate system and the Morse-like parameters representing the anharmonicity of the NH bond-stretching vibrations are taken into account in the valence force model, and in addition the hydrogen—hydrogen potential terms are assumed in the vander Waals model. A majority of the cubic constants, the vibration—rotation interaction constants α, and the l-type doubling constants q t calculated by these models agree essentially with the experimental values reported by Benedict and Plyler. The comparison has indicated that almost all the third-order potential constants in the internal coordinate system ignored in the valence force model should have small negative values, as observed for several bent XY 2 molecules. Possible orders of magnitude of these constants have been estimated. The vibrational anharmonic constants χ have been estimated in a similar manner from the cubic and quartic constants. The zero-point average structure is derived from the experimental rotational constants to be: r z (NH) = 1·024 0 Å, α z (HNH) = 107·3 2°, and r z (ND) = 1·020 6 Å, α z (DND) = 107·2 2°.

Infrared spectra of the methyl halides. Methyl fluoridenear 4100 Cm −11

High resolution infrared spectra of methyl fluoride between 3900 and 4500 cm −1 have been obtained and analyzed. The parallel band near 4011 cm −1 has been assigned to ν 1 + ν 3 , and the perpendicular band near 4060 cm −1 has been assigned to ν 3 + ν 4. Several perturbations were observed in ν 3 + ν 4 , and one of them has been interpreted as a combination of a first-order Coriolis effect with ν 1 + va and ℓ-type doubling in the K = ℓ = ± 1 upper states of ν 3 + ν 4. A set of molecular constants which reproduce the transition frequencies of the nonmeasurably perturbed transitions has been obtained together with a value for 14 X and the ℓ-type doubling constant for ν 3 + ν 4.

Vibration—Rotation Interaction in Symmetric-Top Molecules and the Splitting between A1 and A2 Levels

The main purpose of this paper is to reformulate the theory of vibration—rotation interaction in symmetric-top molecules in a way which is more accessible to practicing spectroscopists than the current contact transformation formalism. Also it is pointed out that the many accurately measured l-type doubling constants can provide information on the cubic as well as the quadratic potential constants. In Sec. I, analytical expressions for the splitting between the A1 and the A2 rovibrational states are derived starting from the Wilson—Howard equation. Although the result agrees with Grenier—Besson's formula, the method of derivation is new in the following three points: (1) The scheme of orders of magnitude of the terms appearing in the rovibrational Hamiltonian has been made in a definite way. (2) Symmetry considerations and the relations between various rovibrational constants have been fully used in the derivation. (3) The standard perturbation method is used instead of the contact transformation. In order to facilitate the understanding of the perturbation procedure, ``interaction diagrams'' are introduced and fully used. In Sec. II, several discussions of the l-type doubling of symmetric rotors are given. First a physical interpretation of the l-type doubling is discussed in Sec. II. A, and then the existence of a close analogy between the treatments of vibration—rotation interaction and vibronic interaction is pointed out in Sec. II. B. The above arguments lead to the conclusion that, because of certain anharmonic vibrational terms, the average structure of a symmetric-top molecule in the first excited state of a degenerate vibration is no longer symmetric. An interpretation of this effect is presented. Finally it is emphasized that the observed l-type doubling constants provide information on the anharmonic potential constants which are not obtainable from α. A numerical example for the NH3 molecule is given and it is shown that the anharmonic vibrational contribution to the l-type doubling is in fact large.

Microwave Spectra and Equilibrium Structure of Carbonyl Sulfide

Abstract Microwave spectra have been measured for various vibrationally excited states of the OCS molecule. The l-type doubling constants obtained for the excited states of the bending vibration, ν2, have led to the determination of the zero-order coupling constant, qe. It has been shown that the qe value thus obtained is useful for the evaluation of the harmonic force constants. The Fermi resonances have been discussed; they lead to the conclusion that the effect due to the cubic constant, k223, cannot be ignored, nor can that due to k122 With due consideration for this situation, the equilibrium structure has been found to be: re(O–C)=1.1572±0.002 Å and re(C–S)=1.5606±0.002 Å.

Infrared Spectrum of Dideuteroacetylene (C_2D_2)

Thirty bands of C2D2 have been observed and measured between 1900 and 3300 cm−1. Twenty of these have been resolved well enough to permit extraction of rotational constants. The Δ2F values up to J35 for three Σg ground state bands were averaged and correlated with other data for a more reliable B0 = 0.84794 ± 0.00005 and D0 = 7.85 × 10−7 ± 0.4 × 10−7, where the indicated uncertainties are the probable errors of the coefficients. Better resolution and higher J values have reduced the uncertainty derived from other sources. The l-type doubling constants for ν41 and ν51 have been obtained from resolved Q branches and split P and R branches; they are q4 = 0.00316 and q5 = 0.00314 cm−1.

L-Type Doubling in Three π—π Bands of HCN

l-type doubling constants have been determined for the 0112–0110, 0113–0110, and 0311–0110 bands of HCN. The results, in units of 10—3 cm—1, are: 011201130311q′7.717.5415.4q′′7.517.267.21The accuracy of the constants is ±5% for the 0113 and 0311 bands, and ±1% for the 0112 band. The q′—q″ values obtained for the 0113 and 0112 bands agree within experimental error with the prediction of our empirical equation which relates q to the vibrational quantum numbers.

L-Type Doubling in Energy Levels of Carbon Dioxide Coupled by Fermi Resonance

In this paper we discuss the l-type doubling in levels of linear molecules which are coupled by Fermi resonance; in particular we consider here a triad of such levels in carbon dioxide. In principle, it becomes necessary to consider simultaneously the perturbations related to both anharmonic resonance interaction and l-type doubling. A further analysis reveals, however, that we are justified in carrying out an approximate solution, in which we first consider the resonance interaction as if l-type doubling did not occur and subsequently find the energy levels associated with +l and —l as a result of small perturbations on the two-fold degenerate levels involved. It appears that the applicability of the well-known formula Δν=qJ(J+1), in which q is the l-type doubling constant, is inherent to this approximation. The agreement between q values computed by our method and those obtained experimentally is very satisfactory indeed.

Rotation-Vibration Spectra of Diatomic and Simple Polyatomic Molecules with Long Absorbing Paths VII. The Spectrum of Dideuteroacetylene (C2D2) in the Photographic Infrared

Twelve absorption bands of C2D2 have been observed in the photographic infrared. Eleven of these bands show simple P and R branches with intensity alternation, i.e., they are Σu+—Σg+ bands while one band, without intensity alternation, is a difference band of type Π—Π. From the positions of the bands some of the vibrational constants ωi0 and xik are determined. In addition, from the rotational fine structure, the rotational constants B[v] and D[v] are determined. For B[0] the value 0.84787 cm−1 is obtained. The αi values are α1=+0.00578, α2=+0.00302, α3=+0.00455, α4=−0.00120, α5=−0.0026 cm−1. From the αi and B[0] one obtains Be=0.85075 cm−1. Combining Be(C2D2) with Be(C2H2) yields, for the internuclear distances in the acetylene molecule, re(C≡C)=1.2010×10−8 and re(C–H)=1.0637×10−8 cm in very satisfactory agreement with the values previously obtained from Be(C2HD) and Be(C2H2). Evidence for l-type doubling in C2D2 is given and approximate values for the l-type doubling constants q4 and q5 are obtained.