Bond asymmetry parameters

Using the separation of the effective Hamiltonian into the unperturbed part and the perturbation, the total ionic contribution to the geminal is calculated exactly (vari-ationally). Only the bond polarity needs to be estimated perturbatively in the linear response approximation, but now the correlated ground state of the symmetric effective bond Hamiltonian is taken for evaluating the response function. In this context, it is convenient to use a dimensionless bond asymmetry parameter ... 

There have been a large number of determinations of molecular force constants, mean amplitudes of vibration, bond asymmetry parameters, Coriolis coupling constants (and inertia defects) and centrifugal distortion constants [146,152,259,271,304,581,840,1221,1222,1278,1312, 1416,1448,1449,1549,1550,1575-1578,1587,1618,1671,1682,1806,1807,1858,1931,1961,1984,2021,2045, 2108,2109-2111,2167a], as well as a determination of the atomic potential energy distribution... 

Several methods for the determination of the three constants Fn, F12, and Fgg in the symmetry block Ai from only two frequencies, Vi and vg, were discussed and applied to OFg, see [10, 35 to 38]. The formalism of the Green s function analysis [29] and the L-matrix approximation method [30 to 33] were applied [34]. The constants were also derived on the basis of a bond asymmetry parameter , which was used for the description of the spatial distribution of the binding forces in a molecule [48]. Forrib, see also [49]. Constants in terms of Keating s coordinates [55] were reported [56]. 

The microwave spectrum of isothiazole shows that the molecule is planar, and enables rotational constants and NQR hyperfine coupling constants to be determined (67MI41700>. The total dipole moment was estimated to be 2.4 0.2D, which agrees with dielectric measurements. Asymmetry parameters and NQR coupling constants show small differences between the solid and gaseous states (79ZN(A)220>, and the principal dipole moment axis approximately bisects the S—N and C(4)—C(5) bonds. 

If the field gradient has no axial symmetry, then a more complicated expression is found, involving an asymmetry parameter which is often moderate. In particular, the study of this parameter has been useful for the determination of resonance structures and for the understanding of the bonding in solid iodine. The contribution of each of the molecular electrons to q is given by a relation of the form... 

The temperature dependent T data are shown in Fig. 9. 7j values decrease from 28 ms at 21°C with increasing temperature, and show a minimum of 6.4 ms at 80° C. These results indicate the presence of the motion with a Larmor frequency of 30 MHz at this temperature. This minimum was found to be attributed to the flipping motion of a phenyl ring from the result of our other experiments discussed in later section.13 The jump rates of the flipping motion were estimated with a two-site jump model that a C-2H bond jumps between two equivalent sites separated by 180°, and that the angle made by the C-2H bond and the rotational axis is 60°. The quadrupole coupling constant of 180 kHz and the asymmetry parameter approximated to zero were used in the calculation. The calculated values for fitting with the... 

To calculate the nuclear quadrupole moment from the measured quadrupole splitting, it is necessary to know the electric field gradient, q, at the Te nucleus as well as the asymmetry parameter, rj. These can be calculated in the Townes and Dailey approximation (4) by knowing the chemical bonding in Te. 

Its magnitude is governed by the amount of electronic and nuclear nuclear charge that lies along the z axis along the C—bond. The shape of the interaction (electric field gradient tensor) is described by the asymmetry parameter (ti), which... 

The value of the density at the critical point pb, the values of the curvature, and the asymmetry of the curvature provide the information for a density-based classification of chemical bonding. Several parameters are used to classify a bond ... 

The apparently unanimous verdict in favour of halogen metal multiple-bond character given by nuclear quadrupole resonance methods is unfortunately somewhat shaken by the results of Grayheal and Green (5) who measured (Table 4) the Chlorine asymmetry parameters of the... 

The cyano group as a 71-acceptor substituent induces a shortening of the distal bond in the cyclopropyl ring. A mean asymmetry parameter = -0.017 (2) A has been found8. 

From the results shown in Table 1, the following conclusions can be drawn out Ci1 All the spectra correspond to non axially symmetric 31P tensors, (ii) the [dn - 033] difference ranges from 206 to 263 ppm and is definitely larger than the chemical shift difference observed in the liquid phase between a phosphonite and the corresponding thioxo-phosphonate, (iii) a linear relationship appears when the asymmetry parameter n is plotted against the intracyclic O-P-O bond angle a. 

Separate values of the parameters were deduced for ortho, meta and para substituents. These values are listed in Table 6. As most chemists would have anticipated the standard deviation of the predicted frequency for the orf/w-substituted iodobenzenes is much higher than for the meta or para derivatives. Likewise, of these two last series it is the /wra-substituted compounds that exhibit the greatest sensitivity to asymmetry parameter. This is probably due to steric factors that may deform the shape of the filled non-bonding p-orbitals on the iodine atom and it is unlikely that in this case the asymmetry parameter can be used as a measure of the -character of the carbon-iodine bond. The meta and para are certainly better candidates for study in this respect, but even here no clear picture of the carbon-iodine 7i-bond arises. 

The asymmetry parameters of substituted chlorobenzenes and iodobenzenes have been discussed above in Section III.A.3 (Tables 4 and 5). The asymmetry parameters of several systems are discussed below carbonyl chlorides in Section III.B.4, a variety of substituted vinyl chlorides in Section III.B.9 and methylene dichloride and chloroform in Section III.B.lO.c. There remain a number of measurements of asymmetry parameters30-33, mainly of aliphatic systems, that are not covered elsewhere and these are listed in Table 7. It will be seen that the asymmetry parameters of chlorine atoms bonded to saturated carbon atoms are always small, of the order of 0.05 or less, while if the chlorine atom is bonded to an sp2-hybridized carbon atom then the asymmetry parameter is generally equal to or greater than 0.1. 

The intermolecular distance between the hydrogen atoms and the chlorine atoms of adjacent molecules in crystalline chloroform has been obtained from a study of the relative linewidths of the 35C1 frequencies in the protonated and deuteriated species95. A Zeeman 35C1 NQR study96 of monocrystalline chloroform and methylene dichloride confirmed that the field-gradient principal z-axes coincide with the directions of the C—Cl bonds. The asymmetry parameters were small, as expected for aliphatic C—Cl bonds. 

For the aromatic derivatives, small values of the asymmetry parameter are found, reflecting the departure from axial symmetry of the environment of the iodine atom. In all cases, hp is very slightly less than Up, suggesting a small degree of rehybridization of the iodine atom away from pure pff bonding. There is no evidence for significant 7r-bonding. 

Coronene (9) is known to form a 7r-complex with a chain structure in which the iodine molecule bridges symmetrically between double bonds of adjacent coronene molecules26 the double bonds are perpendicular to the I-I axis. Such a structure explains the large value of the asymmetry parameter. 

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