Jure Zupan, Marjan Vračko, Marjana Novič
National Institute of Chemistry, 1000 Ljubljana, Hajdrihova 19, Slovenia
New uniform and reversible spectrum-like representation of 3D chemical structures is explained. On a simple example of 3D structure of ethane, both the coding and decoding procedures are explained in detail. The spectrum-like representation is based on the projection of atoms specified by co-ordinate triplets [xi, yi, zi] on an arbitrarily large sphere using a Lorentzian shaped function dependent on atoms’ position in the space. The new structure representation of a molecule with N atoms is defined as n-dimensional vector S = (s1,s2,..si,...sn) with each component defined as a cumulative intensity si, at a given point i on the circle with and arbitrary radius. The cumulative intensity si (the i-th point on the circle at angle phii.) is a sum of N contributions sji of each atom j in the molecule.
, i=1...number of divisions on a circle
The intensity function sji can be any bell shaped function. In our case
the Lorentzian shape with maximum at angle phij, maximal intensity proportional
to the sigmaj, and having the width, sigmaj, related to the type of the
new representation atom was chosen. The new representation is suitable
for studying (modeling) various properties on a series of molecules having
common skeletons or common structural parts. The changes of a new representation
if a substituent on a given molecule is rotated is shown on an examples.