Reference Axis Systems and Symmetries

Unlike monopoles, all higher MTPs are intrinsically anisotropic (see Fig. 7.1]. Their orientation must be defined with respect to an axis system. Evidently, the choice of an axis system has no influence on the physics of the system and its choice may thus appear one guided by convenience. However, not all axis systems are equally advantageous, as, depending on the symmetry of the molecule, the number of nonzero MTPs differs. Beyond its aesthetic appeal, it stands to reason that such a scheme should help reduce the number of interactions between two MTP sites (see Eq. 7.6). A smaller number of concurrent MTP interactions may also help stabilize the torque propagation, though this remains very much unclear at the moment. 

As an example, the dipole-charge interaction energy between the O -component of a dipole moment on site a and a charge Qoo on site b is considered. From Eq. 7.6, one can write the energy as 00 = Qi.QooR- iK 

Due to the added complexity, fluctuating MTPs have been the subject of only a few studies. Not only do they require increased computational investment with respect to static MTPs, but such an approach entails even more parameters that need to be fitted. The simplest case where fluctuating MTPs may arise is in a diatomic molecule will be a simple linear function of rj = d which 

While the reproduction of fluctuating MTPs certainly helps describing a charge distribution with high accuracy, the sheer number of parameters—up to nine static MTP coefficients (Table 7.1) as well as the coefficients along all internal coordinates (Eq. 7.11) for each site—can seem daunting. As a compromise, we point 

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Figure 5.26 The complex Au(CN)2 showing the reference axis system and symmetry axes used in the main text.

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