Gravitational index

Theses are calculated from the 3D molecular structure, which is defined with coordinates of all atoms in the molecule. The step from 2D to 3D description of molecules is the crucial one [40-42]. The 3D structure is an ambiguously defined quantity, which depends on molecular environment, i.e., it is different in crystal structure, in solutions, or in vacuo. If it is theoretically determined it depends on the computational method. However, the 3D structures form a basis for a broad range of descriptors. Examples are mass distribution descriptors such as moment of inertia or gravitation index, and shape indices such as shadow indices, surface area indices, and van der Waals indices [29,40,41]. 

Gravitational indexes Principal moments of inertia of a molecule Shadow areas of a molecule properties. 

In Formula (4.23), M is the molecular mass, m is the mass of the atom i, and r is the distance between the atom i and the center of mass. Using the tabulated values of the atomic mass m and interatomic distances r (distances that are a result of geometry optimization), a gravitational index I is calculated. 

The summation in Formnla (4.24) can be calculated for all atom pairs or only for all pairs of bonded atoms. The gravitational index is a measure of the spatial distribution of masses in the molecule and is similar to the geometrical principal moments of the inertia descriptor. An electronic index leie is calcnlated with a similar formula... 

Gravitation index (all atoms) 1001.7 Gravitation index (bonded atoms) 712.7 Electronic index (all atoms) 6.83 Electronic index (bonded atoms) 4.49 Wiener index 26.0 Randic index 2.87 Balaban index 2.10... 

Gravitation index (all atoms) 10420.2 Gravitation index (bonded atoms) 4265.5 Electronic index (all atoms) 29.55 Electronic index (bonded atoms) 12.69 Wiener index 4044.0 Randic index 20.35 Balaban index 0.83... 

Gravitation index (all atoms) 10297.0 Gravitation index (bonded atoms) 4216.75 Electronic index (all atoms) 43.63 Electronic index (bonded atoms) 21.84 Wiener index 4336.0 Randic index 18.59 Balaban index 0.94... 

---