Objective:

 To calculate the torsion angle or dihedral angles of a molecule 

Theory:

 A molecule is a small chemical element that is made up of two or more atoms held together by chemical bonds. A molecule can be composed of either single kind of element (e.g. H2) or different kinds of elements (e.g. CO2). These bonds are formed as a result of the sharing or exchange of electrons among atoms of the molecule. Atoms have a tendency to attain more number of electrons towards itself thereby increasing stability. Bond length is the distance between the nuclei of two bonded atoms whereas bond angle is the angle formed betweeen two adjacent atoms in a molecule. They always range from 100- 180 degrees. Bond angle and bond length are the two important parameters which determine the shape and size of a molecule.  The geometry of a molecule can be characterised by analysing the bond length and bond angle. These parameters can vary in their lentgth depending upon their bond multiplicity. They are shorter for a triple bond than for a single bond. Bond angles too vary in their angles from molecule to molecule depending upon on the electron structures of the molecule.  Bond angles of molecules and ions are usually determined by VSEPR theory. Valence Shell Electron Pair Repulsion Theory or VSEPR theory are used to predict the shape of molecules based upon the extent of electron pair electrostatic repulsion. 

A dihedral angle or torsion angle is the angle between two planes. It defines the conformations around rotatable bonds. The dihedral angle changes only with the distance between the first and fourth atoms; the other inter atomic distances are controlled by the chemical bond lengths and bond angles. Its value range from -180 to +180 degrees. The torsion angle is considered to be positive if a clockwise rotation is performed with the molecule and it will be negative when an anti clockwise rotation is performed with the molecule in its plane. 

Figure 1: Schematic representaion of Bond length , bond angle and dihedral angle.

Avogadro is free open source molecular builder software designed for molecular modeling. It allows building of chemical structures, visualization and analysis of molecule, structure optimization, quantum mechanical calculations, electron density calculations, formatting of input and output files etc. Since it has an extensible plug-in based architecture, it helps to perform a wide range of applications. This software is licensed under GNU GPLv2. Avogadro is basically based on C++ language; its latest version uses python scripting. It uses Qt and OpenGL for graphical section and is introduced by Sourceforge service, which is available for Linux, Mac OS X and Windows platforms. It uses OpenBabel to load and save files which is a free software that is used to convert chemical file formats. Using Open Babel, different file types like PDB, CML, xyz, etc., can be opened with Avogadro after converting them to suitable file type supported by Avogadro.

Figure 2: Home Page of Avogadro