Geometry Analysis Program
C. David Sherrill
School of Chemistry and Biochemistry
Georgia Institute of Technology
Last Revised on 5 June 2001
Goals: Write a computer program to take a set of atomic symbols and Cartesian coordinates
for a collection of atoms and determine all possible interatomic distances and bond angles. Assume
the coordinates are provided in Angstroms.
Procedure:
1. Read in Cartesian coordinates from an ASCII file in the so-called XYZ format. The first line
of this file is just an integer telling how many atoms there are in the file. Each subsequent
row icontains an atomic symbol (e.g., C, N, O) and a set of coordinates (xi,yi,zi) for atom
i.
2. Calculate all possible interatomic distances
Rij =q(xi−xj)2+ (yi−yj)2+ (zi−zj)2.(1)
3. Calculate all possible bond angles between atoms i,j, and k:
R2
ik =R2
ij +R2
jk −2Rij Rjk cosφijk ,(2)
cosφijk = ˆrji ·ˆrjk ,(3)
where
~rij = (xj−xi)ˆ
i+ (yj−yi)ˆ
j+ (zj−zi)ˆ
k(4)
For additional challenge, try the following: Define unit vectors ˆeij pointing in the direction
between atoms iand j, as
ˆeij =~rij /Rij .(5)
1. Calculate all possible out-of-plane angles,
sinθijkl =ˆelj ׈elk
sinθjlk
·ˆeli (6)
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