Calculation of coordinates from molecular geometric parameters and the concept of a geometric calculator.

Authors: Essén, H., Svensson, M
Document Type: Article
Pubstate: Published
Journal: Computers and Chemistry
Volume: 20   389-395
Year: 1996


Three different geometric parameters, distance r(i,j), angle theta (i,j,k), and dihedral (or torsion) angle phi (i,j,k,l), are commonly used to specify the shape of a molecule. Given Cartesian coordinates it is simple to calculate such parameters. The, non-trivial, inverse problem of finding coordinates when given such parameters is considered here. When a triple of such geometric parameters is given to specify the position of an atom, n, relative to reference atoms i,j,k,..., with known positions, five qualitatively different cases arise: r(n,i), theta (n,i,j), phi (n,i,j,k), theta (j,n,i) and phi (k,n,i,j). Each such geometric coordinate specifies n to lie on a certain type of surface. To calculate its position one must find the point of intersection of three such surfaces. A program, EVCLID that can perform these calculations is integrated with an interactive set of routines that constitute a geometric calculator and editor. It works on (three-dimensional) points and has a number of input, display and output options. It can translate, rotate, reflect, invert and scale as well as edit the point set or subsets.