Octopole moment

Doerksen R J and Thakkar A J 1999 Quadrupole and octopole moments of heteroaromatic rings J. Phys. Chem. A 103 10 009... 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

A comparison of MP2/6-31G structural parameters of 1,2-oxazole 19 (isox-azole) and 1,3-oxazole 20 with microwave data is provided by Kassimi et al. (Scheme 16) [96JPC8752]. The general agreement is excellent. The same authors investigated dipole moments, quadrupole moments, octopole moments, and dipole polarizabilities of 19 and 20 together with several oxadiazoles and oxatriazoles [96JPC8752, 99JPC(A) 10009]. For the mean polarizability of these species, they found the approximative formula... 

The dipole moments of both 3- and 4-phenylsydnones containing dimethylamino and nitro substituents were calculated (ah initio 3-21G basis set) the magnitude increases with the electron donor attached to the phenyl ring <1995JPC1923>. Quadrupole moments, octopole moments, and polarizability of 1,2,3-oxadiazole have been determined by ab initio calculations and simple models <1996JPC8752, 1999JPC10009>. 

All of the others are zero if the molecule has the orientation in the coordinate system that is used here. The value is positive, showing the same qualitative electronic distribution in C—H bonds as was seen for the other CH molecules we have examined. Quantitatively, the octopole moment is equivalent to a charge of0.204 e at the H-atom nuclei. 

An enlargement of the expansion yields the nuclear octopole moment (which vanishes exactly because of odd parity) and the nuclear hexadecapole moment (whose contribution is negligible). 

The HD states are characterized by the presence of alternating parity bands with very large moments of inertia because of the very large quadrupole and octopole moments (Blons et al. 1988). Assuming alternating parity bands with K = 3, 4, and 5 band heads, the fission probability between 5.2 and 5.5 MeV was fitted, resulting in the fit curve superimposed on the data in Pig. 5.14a. The corresponding normalized values are presented in Pig. 5.14c as a function of fi /20. The horizontal line represents the 99.9% (3(t) confidence level for the... 

The energy resolution has been considerably improved and one can clearly see the fine structure of the peaks. Experimentally, the very large quadrupole and octopole moments of the HD states should manifest themselves by the presence of alternating parity bands with very large moments of inertia (Blons et al. 1988). Assuming overlapping rotational bands with the same moment of inertia, inversion parameter (Ackermann et al. 1993) and intensity ratio for the members in a band, the spectrum was fitted in the same way as in the previous work (Krasznahorkay et al. 1998b). The result of the fit is shown in 5.21a. 

The expansion given in Eq. (3) can be continued to higher order, to include the octopole moment, the hexadecapole moment, and so on. In general the moment of rank n (the 2"-pole moment in the conventional but rather unsatisfactory terminology) is defined by [1]... 

Carbon tetrachloride has neither a dipole moment nor a quadrupole moment, but it does have an octopole moment. Provide a simple description of this moment. 

The quadrupole and octopole moments, the dipole polarizability, the first and second dipole hyperpolarizabilities, and the dipole-quadrupole and dipole-dipole-quadrupole polarizabilities were calculated using MPPT(4) theory [8]. 

---