Vibration-rotation Parameters Research Articles

A new approach to obtaining sum rules

A new approach to obtaining the sum rules satisfied by the phenomenological coefficients appearing in the metric tensor of the generalized coordinate space of a many-particle system is considered and applied to the vibration-rotation motion of a nonlinear molecule. The approach is based on the requirement of physical covariance of the Cartesian and generalized coordinate configuration spaces of the system. A partial criterion of this physical covariance is the condition that the curvature tensor of configuration space remains covariant, and this condition gives several sum rules for the vibration-rotation parameters. These sum rules are particular cases of those known previously.

The 10.4 μm CO 2 laser Stark spectra of the ν4 and the ν9 bands of 1,1 difluoroethylene

The ν 4 and the ν 9 bands of CF 2CH 2 have been studied using coincidences with the 10.4 μm band of the CO 2 laser and the 10.9 μm band of the N 2O laser. These resonances have been analyzed, together with recent microwave results, to give the following vibration-rotation parameters and dipole moments in the ν 4 and ν 9 states ν 4 CF 2CH 2 ν 9 CF 2CH 2 ν 0 925.7692 (2) 953.8057 (2) cm −1 A 10 971.99 (2) 11 026.918 (6) MHz B 10 414.98 (2) 10 436.381 (6) MHz C 5328.48 (2) 5346.100 (6) MHz μ 1.382 (1) 1.382 (1) D μ - μ 0 0.014 (2) 0.004 (1) D

The microwave spectrum of cyanoacetylene in ground and excited vibrational states

Microwave transitions are reported for ten isotopic species of cyanoacetylene in the ground, v 4, v 6, v 6 and v 7 vibrational states in the region 26·5-40·0 GHz. In addition millimetre-wave transitions of HCCCN and DCCCN in the ground v 5, v 6 and v 7 vibrational states in the region 54·5-211·8 GHz have been measured. The combined data have been analysed to yield Bv, Dv, γrs, γltlt′ and qt vibration-rotation parameters, for HCCCN and DCCCN. In addition millimetre-wave measurements pertaining to the v 6 + v 7 and v 5 + v 7 vibrational states have been analysed to give values for rtt′J and approximate values of gtt′ and rtt′ (t = 5, 6; t′ = 7). Rotational constants Bv in the first excited state of the fundamental vibrations v 4, v 5, v 6 and v 7 are combined with infra-red values for v 1, v 2 and v 3 to give Be for both HCCCN and DCCCN.

The microwave spectra of symmetric top polyacetylenes: 1,3,5-Heptatriyne, CH 3(CC) 3H and 1-cyano-2,4-pentadiyne, CH 3(CC) 2CN

The rotational spectra of 1,3,5-heptatriyne, CH 3(CC) 3H and 1-cyano-2,4-pentadiyne, CH 3(CC) 2CN have been studied in detail between 26.5 and 40.0 GHz. The molecules have long linear chains of heavy atoms and show characteristic C 3 v symmetric top spectra consisting of groups of R-branch lines at regular intervals separated by approximately 2 B 0. Six isotopic modifications of CH 3(CC) 2CN have been detected in natural abundance allowing r s substitution structural data to be derived for this species. Long linear polyacetylenic chains are quite flexible and this dynamic property manifests itself in the appearance of extended sequences of complex vibrational satellites associated with the bending of the chain. The vibrational ground state spectra as well as several low frequency vibrational satellites have been analyzed yielding various vibration-rotation parameters. For CH 3(CC) 3H B 0 = 778.2445 ± 0.0007 and for CH 3(CC) 2CN B 0 = 778.040 ± 0.001 MHz.

Stark spectroscopy with the CO 2 laser : The ν6 band of CD 3F

The ν 6 band of CD 3F has been studied using coincidences with the 10.4 μm band of the CO 2 laser, and the 10.9 μm band of the N 2O laser. Approximately half the 146 resonances measured have been studied using the Lamb dip techniques. These resonances have been analyzed, together with recent microwave results, to give the following vibration-rotation parameters and dipole moments in the ν 6 state: ν 0 911.49606 (8) cm −1 B 20 272.47 (4) MHz A-A 0 186.5 (14) MHz Aζ 0.61950 (8) cm −1 μ ν 6 1.8771 (7) D μ ν 6 -μ 0 0.0069 (7) D The Lamb dip spectra show examples of crossover bleaching and collisionally transferred saturation, and need high laser powers of several watts for their observation. The change in dipole moment shows that the absolute sign of ( ∂ μ ∂ q1 ) is negative.

High-resolution laser magnetic resonance and infrared-radiofrequency double-resonance spectroscopy of NO and its isotopes near 5.4 μm

The fundamental band of NO has been investigated by the laser magnetic resonance method, in which the absorption lines from an NO sample located inside the laser cavity were Zeeman tuned into resonance with fixed CO laser transitions. Saturation dips with a width of <2 MHz were observed, allowing the resolution of hyperfine and Λ-doubling structure in the NO spectrum. Transitions due to the weak 2-1 “hot” band and the 2 Π 1 2 ← 2 Π 1 2 satellite band of 14N 16O were observed, as were transitions due to the 15N 16O, 14N 18O, and 14N 17O isotopic species in natural abundance. Data from the present work were combined with previous measurements to obtain a consistent set of vibration-rotation parameters for five isotopic species of NO. An infrared-radiofrequency double-resonance spectrum was observed which allowed the precise (∼20 kHz) measurement of some hyperfine Λ-doubling transitions within the v = 1 state of 14N 16O.

Stark spectroscopy with the CO 2 laser: The ν3 band of CD 3F

The ν 3 band of CD 3F has been studied using coincidences with the 10.4 μm band of the CO 2 laser. The majority of the 150 resonances measured have been studied using the Lamb dip technique. These resonances have been analyzed, together with recent microwave results, to give the following vibration-rotation parameters and dipole moments in the ν 3 state. 12CD 3F ν 0 992.29882 (19) cm −1 B 20395.77 6 ± 0.08 MHz A-A 0 −35.73 ± 0.61 MHz D J 33.8 ± 0.5 kHz D JK 203.9 ± 7 kHz μ ν3 1.8964 ± 0.0015 D μ ν3 − μ 0 0.02617 ± 0.0005 D The change in dipole moment on excitation of ν 3 is much smaller than in 12CH 3F and 13CH 3F and cannot be explained by the diatomic model used previously. The model has been extended to allow for the change in ∂μ ∂q 3 caused by the increased mixing of ν 2 and ν 3 in the deuteride, and shows that this is the primary cause of the small dipole moment change.

Laser Stark spectroscopy in the 10 μm region: The ν3 bands of CH 3F

Laser Stark spectroscopy of the ν 3 band of CH 3F has been carried out using coincidences with the 9.4 μm band CO 2 laser lines. About 350 Stark resonances were measured for the ν 3 fundamental bands of 12CH 3F and 13CH 3F. About 30 of them were measured by using a Stark-Lamb dip technique to increase the resolution and the accuracy of the data. These Stark resonances, together with the recent results of infrared-microwave two-photon Lamb dip measurements, were analyzed to give the following vibration-rotation parameters and the dipole moments in the ν 3 state, 12CH 3F 13CH 3F ν 0 1048.610767 (62) 1027.493191 (69) cm −1 B 25197.57 ± 0.03 24542.07 ± 0.43 MHz A - A 0 −294.09 ± 0.60 −288.81 ± 0.37 MHz D J 55.5 ± 1.2 56 ± 12 kHz D JK 575 ± 63 464 ± 24 kHz μ 1.9054 ± 0.0006 1.9039 ± 0.0006 D About 30 Stark resonances corresponding to the hot band 2 ν 3 ← ν 3 of 12CH 3F have also been observed. The analysis of the hot band resonances provided accurate vibration-rotation parameters and the dipole moment in the 2 ν 3 state. Observation of the hot band demonstrates the high sensitivity of laser Stark spectroscopy; we have been able to observe molecules of the order of 10 8 in the optical path easily. An approximate vibration-rotation calculation was used to discuss the observed dependence of the dipole moment and the vibration-rotation parameters on the vibrational state.

A method for calculating vibrational transition probabilities

Relative vibrational transition probabilities for diatomic molecules can be calculated by methods utilizing band intensity observations or by methods not requiring such data. To date the latter class has been represented solely by the linear dipole moment function approximation. In this paper a second such method is developed. It makes use of the wave function expansion technique of Trischka and Salwen. Its critical assumption is the approximate equivalence of the Morse and simple harmonic potentials in the region about the potential minimum. This assumption is sufficient to remove all ambiguity in the relative signs of the matrix elements of the dipole moment. Further, it provides a relation through which the relative magnitudes of the matrix elements can be calculated. It is shown that this method is equivalent to using Morse eigenfunctions with a dipole moment function which departs from linearity in a manner that is qualitatively correct, at least in the region of the equilibrium configuration. The method is compared extensively with the linear approximation and with experiment. Insofar as the limited intensity data now available can show, it is generally superior to the linear approximation. The method can be of use in deriving Taylor coefficients for the expansion of the dipole moment function and in obtaining vibration-rotation interaction parameters. It also provides a new method for obtaining absolute values of transition probabilities. The experimental data required for this are values of the permanent dipole moment in two different vibrational levels. The procedure is illustrated by the calculation of the fundamental band strength of lithium hydride. The linear approximation and the present method are compared briefly with two methods which require intensity data. These are the quadratic and cubic approximations to the dipole moment function. It is suggested that the extent and the accuracy of the intensity data presently available is not sufficient for these methods to be of general use. Relative transition probabilities calculated by the present method are tabulated for all bands with v′ ≦ 9 for OH, HCl, and CO. The computational procedure used is outlined. It is not suitable for hand calculation but can be programmed for a high-speed computing machine with relative ease. On a large machine about one minute is required to compute the entire contents of each table.