Appendix A
Transformation Rules of the Tensor
Components Under Coordinate System
Rotation
The relation between the tensor components in the coordinate system of the
complex M abc...d and the tensor components in the monomer coordinate systems
M a 0 b
0 c 0 ...d
0 are expressed by the use the rotation matrix
k ab ¼
cos / cos h cos v À sin / sin v À cos / cos h sin v À sin / cos v sin h cos /
sin / cos h cos v þ cos / sin v À sin / cos h sin v þ cos / cos v sin h sin /
À sin h cos /
sin h sin v
cos h
0
@
1
A
Here, the Euler angles /, h and v describe the rotations of any monomer
coordinate system relative the complex coordinate system.
As a result,
M abc...d ¼ k aa 0 k bb
0 k c_ c Á Á Á k dd
0 M a 0 b
0 c 0 ...d
0
© The Author(s) 2017
V.N. Cherepanov et al., Interaction-induced Electric Properties of van der Waals Complexes,
SpringerBriefs in Electrical and Magnetic Properties of Atoms, Molecules, and Clusters,
DOI 10.1007/978-3-319-49032-8
105