Chapter 2
Theoretical Backgrounds
of Interaction-induced Theory
At present, a lot of fine manuals and books may be recommended to study the
theoretical backgrounds of interaction of atoms and molecules [1–11]. However, in
the main, the research and educational works are devoted to description of the
energy of interacting molecules. At the same time, it is obvious that the knowledge
of the electric and magnetic properties of interacting molecules [3–9] are also of
interest. In accordance with the title of the book we focus on electric interactions as
the strongest ones. Of course, the weak magnetic interactions are of interest for
some specific problems of interacting molecules [2, 3], however, that is a special
topic. In the short book it is not possible to describe in details the modern
interaction-induced theory of molecules. Nevertheless, the general backgrounds of
this theory are needed to be given to facilitate the reading of the book. In the next
sections of this chapter some main definitions and formulas used in the book are
given.
2.1 Multipole Electrical Moments
2.1.1 Coordinate System
In the book we will use for all molecular van der Waals complexes the Cartesian
coordinate system (X, Y, Z) related to the complex (Fig. 2.1). The origin of this
coordinate system (O A ) is usually placed on the molecule A. The vector R is directed
from the point O A of the molecule A to any point O B of the molecule B. The relative
orientation of molecules in a complex is determined by local coordinate systems (x A ,
y A , z A ) and (x B , y B , z B ) placed, accordingly, on the separate molecules A and B of the
complex. The rotations of the molecules A and B are described by Euler angles,
which determine the positions of the local coordinate systems (x A , y A , z A ) and
(x B , y B , z B ) with respect to the complex coordinate system (X, Y, Z).
© 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_2
3
Theoretical Backgrounds
of Interaction-induced Theory
At present, a lot of fine manuals and books may be recommended to study the
theoretical backgrounds of interaction of atoms and molecules [1–11]. However, in
the main, the research and educational works are devoted to description of the
energy of interacting molecules. At the same time, it is obvious that the knowledge
of the electric and magnetic properties of interacting molecules [3–9] are also of
interest. In accordance with the title of the book we focus on electric interactions as
the strongest ones. Of course, the weak magnetic interactions are of interest for
some specific problems of interacting molecules [2, 3], however, that is a special
topic. In the short book it is not possible to describe in details the modern
interaction-induced theory of molecules. Nevertheless, the general backgrounds of
this theory are needed to be given to facilitate the reading of the book. In the next
sections of this chapter some main definitions and formulas used in the book are
given.
2.1 Multipole Electrical Moments
2.1.1 Coordinate System
In the book we will use for all molecular van der Waals complexes the Cartesian
coordinate system (X, Y, Z) related to the complex (Fig. 2.1). The origin of this
coordinate system (O A ) is usually placed on the molecule A. The vector R is directed
from the point O A of the molecule A to any point O B of the molecule B. The relative
orientation of molecules in a complex is determined by local coordinate systems (x A ,
y A , z A ) and (x B , y B , z B ) placed, accordingly, on the separate molecules A and B of the
complex. The rotations of the molecules A and B are described by Euler angles,
which determine the positions of the local coordinate systems (x A , y A , z A ) and
(x B , y B , z B ) with respect to the complex coordinate system (X, Y, Z).
© 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_2
3