Inertial defect

Five isotopomers of Sia were studied in Ref (20), and are labeled as follows Si- Si- Si (I) Si- Si- Si (II) Si- Si- Si (III) Si- "Si- Si (IV) Si- Si- °Si (V). Rotational constants for each (both corrected and uncorrected for vibration-rotation interaction) can be found towards the bottom of Table I. Structures obtained by various refinement procedures are collected in Table II. Two distinct fitting procedures were used. In the first, the structures were refined against all three rotational constants A, B and C while only A and C were used in the second procedure. Since truly planar nuclear configurations have only two independent moments of inertia (A = / - 4 - 7. = 0), use of B (or C) involves a redundancy if the other is included. In practice, however, vibration-rotation effects spoil the exact proportionality between rotational constants and reciprocal moments of inertia and values of A calculated from effective moments of inertia determined from the Aq, Bq and Co constants do not vanish. Hence refining effective (ro) structures against all three is not without merit. Ao is called the inertial defect and amounts to ca. 0.4 amu for all five isotopomers. After correcting by the calculated vibration-rotation interactions, the inertial defect is reduced by an order of magnitude in all cases. 

In a previous study of cyclic SiCs, a residual inertial defect of only slightly smaller magnitude was found, despite the fact that an extremely high level of calculation (surpassing that in the present study) was used to determine the vibration-rotation interaction contributions to the rotational constants. This was subsequently traced to the so-called electronic contribution, which arises from a breakdown of the assumption that the atoms can be treated as point masses at the nuclear positions. Corrections for this somewhat exotic effect were carried out in that work and reduced the inertial defect from about 0.20 to less than 0.003 amu A. However, the associated change in the rotational constants had an entirely negligible effect on the inferred structural parameters. Hence, this issue is not considered further in this work. 

Identity element, 387-388 Identity operation, 54, 395 Improper axis of symmetry, 53 Improper rotation, 396 Index of refraction, 132 INDO method, 71, 75-76 and ESR coupling constants, 380 and force constants, 245 and ionization potentials, 318 and NMR coupling constants, 360 Induced dipole moment, 187 Inertial defect, 224-225 Inertia tensor, 201... 

Rotational analysis of the ultraviolet bands has been carried out in different degrees by several authors (Brand, 1956 Callomon and Innes, 1962 Dieke and Kistiakowsky, 1934 Parkin et al., 1962). A negative inertial defect A (= Ic — Ia — Ib) in the vibrationless excited state proves conclusively that the structure is pyramidal at equilibrium (Robinson and DiGiorgio, 1958). The structural parameters are summarized in Table 7. 

Quadratic and cubic potential constants have been obtained from IR frequencies, isotopic shifts, inertial defects, Coriolis constants and centrifugal distortion, assuming the geometry from microwave data. The quadratic force field is characterized by four symmetry force constants F which are related to the inner force constants by the following equations... 

The moments 7 = l°g- g (harm) can be calculated from the ground state moments if the harmonic force field is known, although the present application is not very sensitive to uncertainty in the force-field [65]. The moments 7 are geometrically more consistent than the I°g (e.g., the inertial defect, Eq. 15c, expressed by the 7 practically vanishes for a planar molecule). For the present purpose, the substitution coordinates gsa, the substitution moments Ig, and the mass dependence moments Ig must be adequately redefined in accordance with the use of the moments lzg instead of I°g, but the important result, Eq. 99, remains unchanged. 

The microwave spectrum of vibrationally excited COFj has been obtained [1435] the rotational constants and inertial defects obtained were used to resolve the ambiguity in the absoiute assignment of its r 3 and r 3 bending modes vide infra). 

The dipole moments of the oxazole molecule determined by dielectric218 and Stark-effect measurements in the microwave spectrum233 are 1.4 and 1.5 0.1 D, respectively. On the basis of small inertial defects in oxazole, Mackrodt et al.m have concluded that the molecule is planar. There is a complete lack of data on the dipole moment of simple alkyl-substituted oxazoles. On the other hand, the values of the dipole moments of a number of aryl-substituted oxazoles have been reported (see Table V). As might be expected, a nitro substituent into the para position of a phenyl ring attached to oxazole increases the value of dipole moment by 2.0-3.5 D. 

Brown and Crofts analyzed the microwave spectra of tellurophene for three isotopic constitutions of the molecule (C4H4l30Te, C4H4l28Te, C4H4126Te). The line frequencies, computed from the rotational constants obtained from least-squares fitting of low J transitions agree well with those observed. The constancy of the A rotational constant for the three isotopic species indicates that the tellurium atom is on the a axis. This, with the very small inertial defects, is consistent with a planar molecular structure of C2Ksymmetry. Stark shift measurements correspond to a dipole moment of 0.186 D. 

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