Octupole moments

Many molecules, such as carbon monoxide, have unique dipole moments. Molecules with a center of inversion, such as carbon dioxide, will have a dipole moment that is zero by symmetry and a unique quadrupole moment. Molecules of Td symmetry, such as methane, have a zero dipole and quadrupole moment and a unique octupole moment. Likewise, molecules of octahedral symmetry will have a unique hexadecapole moment. 

Interaction BH-BH in the linear configuration, a) Electrostatic interaction energy and the first terms of its multipole expansion, Intermolecular distance, R,and quadrupole and octupole moments refer to the centers of mass, b) SCF interaction energy and its components. 

Now, conddering that by equation (38a) the traces of the octupole moment tensor vanish, we can re-write (45d) quite generally as follows ... 

This contribution is rather insignificant compared to the previously calculated one (196b) resulting from translational fluctuations alone, and can be of importaixe only in the case of tetrahedral molecules with a large octupole moment. 

Electric octupole (Figure 4). Three-dimensional space is defined in general by three distinct vectors ri, rs, rs and the electric octupole moment is consequently given by a tri-vector of the form qr r rs. The permanent... 

In analogy to the definition of electric dipole moment, electric multipole moments are also defined. In particular, the quadrupole moment Q and the octupole moment U are defined as ... 

A few comments on Table 5.2 seem appropriate at this point. CO has such a small dipole moment C 0+ that can be considered a quasi-quadrupolar molecule. NH3 has large axial quadrupole and octupole moments directed along the z symmetry axis. Besides by its dipole moment, H2O is characterized by a rather small (0.06< uo2) axial quadrupole moment and by a large transverse quadrupole moment (2.19e o2) perpendicular to the z symmetry axis, mostly due to the couple of lone pair electrons. LiH has the largest dipole moment and dipole polarizability. 

This was the start of a line of theoretical and experimental research that lasted in my group over several years. Davydov [212] had shown that in crystals each transition of a free molecule splits into transitions to sub-levels equal in number to molecules in the unit cell. There were new selection rules for the polarization properties in the crystal. The splitting between sublevels in leading order was proportional to the square of the transition moment. In strong transitions this was a dipole moment. In weak transitions, as we later showed, even the octupole moment could appear. 

Now in the pure electronically allowed system the intensity is so small that transitions caused by higher multipole interactions must be allowed for in addition to the very small transition dipole. In the naphthalene spectrum the next interaction term depends upon the the transition octupole moment. Thus the multipolar expansion of the intermolecular potential energy (3.4) cannot be cut off at the dipole term, as implied in (3.2) and (3.3)... 

U, Dinur,/. Comput. Chem., 12,91 (1991). Force Related Atomic Multipoles. Derivation of Atomic Quadrupole and Octupole Moments. 

A molecular electric potential exists because some types of atoms in a molecule attract electrons better than others. For instance, it is well known that fluorine attracts electrons more than hydrogen in HF, resulting in a nonzero dipole moment for this molecule. In the linear molecule carbon dioxide, electronic charge migrates toward the oxygens giving the molecule a measurable quadrupole moment. Even tetrahedral methane has a measurable octupole moment due to charge separation in its C —H bonds its dipole and quadrupole moments are zero by symmetry. 

---