Ray s asymmetry parameter

Fitting results for fs DFWM experiments of the formic acid dimer (ground state) rotational constants, CD constants, parametrized polarizability parameter cp, Ray s asymmetry parameter k and temperature T. ... 

A=5.4+0.4GHz B+C=1445.2 0.5MHz of the per-deuterated acetic acid dimer (CD3COOD)2 were extracted. It was not possible to determine the rotational constants B and C independently due to the symmetric prolate top nature of the dimeric structure (Ray s asymmetry parameter k=-0.965). More detailed consideration of the fs DFWM spectra taken in the gas cell and in a supersonic expansion for the acetic acid dimer are under way in our laboratory and will be presented in a forthcoming publication. 

Fig. 5.4 Correlation diagram for asymmetric-top levels. Ray s asymmetry parameter k is defined as k = (2B — A — C)/(A - C). The symmetric-top levels have been taken from Fig. 5.3 thus it is assumed that A =4.5C. Note that the 1], energy is independent of B and hence gives a horizontal line.

The relations between the different sets of parameters are given in [77Wat, 84Gor]. The notation of the centrifugal distortion constants permits to know which reduction is used, and therefore die rotational constants are simply called A, B, C (without the superscript A or S). There are six different ways (representations) to identify the (x, y, z) reference system with the (a, b, c) principal axis system. In practice two different representations are used T where x b, y=c, z=a and which is best for prolate molecules (Ray s asymmetry parameter x = (25- -C)/( -C)<0), and IIF where x=a, y b, z=c which is thought to be better for oblate molecules (k > 0). Representation IlF is also used where x = a, y = c, z = b but it is equivalent to representation HF. Many authors use codes written in F representation for oblate molecules, in particular for the analysis of infrared spectra. 

Based on the convention that < lb I the rotational constants will have the following ordering A > B C. The rotational constants can be ordered into a single, dimensionless number called Ray s asymmetry parameter, k. The Ray s asymmetry parameter scales asymmetric top molecules between prolate and oblate limits. 

Table 7-4. The rotational constants in MHz along with the Ray s asymmetry parameter, ic, for some near prolate molecules (A > B = C) are shown. Data obtained from W.H. Flygare, Molecidar Structure and Dynamics, Prentice-Hall, New Jersey, 1978.

X-Ray elucidation provided a final proof for the structure elucidation of 8-(4-chlorophenyl)-8-hydroxy-5-methyl-8/f-[l,4]thiazino[3,4-H[l,2,4]oxadiazol-3-one 49, which was obtained as a product of ring-transformation reaction <1997J(P2)2407>. This analysis revealed that the oxadiazole ring is planar, whereas the thiazine ring is in a distorted half-chair conformation with a displacement asymmetry parameter AC2 (S—G(3)) = 0.031. The structure analysis represents the first X-ray elucidation of a [l,4]thiazine ring fused to a [l,2,4]triazole moiety. 

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