Molecular Modeling

In general, molecular modeling systems are computer programs which allow: building molecules from fragments (e.g., residues) and groups; displaying different graphic representations of molecules; translation and rotation of molecular objects on the screen; modifying molecular models by changing distances, angles and replacing/adding atoms and groups; refining geometry of molecules by molecular mechanics or similar methods; superimposing and comparing molecular objects; computation and display of molecular volumes, surfaces, electrostatic potentials and other properties; and preparing plots on various hardcopy devices. Molecular modeling systems also incorporate, or help in preparing, input data for specialized programs like molecular mechanics, dynamics, conformational searches, quantum methods, databases of chemical information, etc. They also provide means for the analysis and visualization of results from other specialized programs.

How to represent molecular geometri

Molecules are not static entities. Even at absolute zero temperature atoms in a molecule are actively vibrating. The molecular geometry represented by a static picture on the computer screen or a Dreiding model is therefore only an approximation. The term atom position is usually understood as a position of the atom nucleus, or rather as some kind of average position of the vibrating nucleus. The dimensions of an atom nucleus are negligible compared to average bond lengths, and since its mass is thousands of times larger than the mass of surrounding electrons, the nucleus is the true center of gravity of an atom. The major conceptual difficulty is to decide what is an average position of a nucleus. Nuclear vibrations are anharmonic, and hence, the time average position of a nucleus is not located half way between its extreme positions. Moreover, in molecules containing more than two atoms, nuclei vibrate not only along chemical bonds but also in directions perpendicular to them.Interatomic distances are usually expressed in Ångströms, since distances between chemically bonded atoms are of the order of 1 Å. Also,atomic units are frequently used: 1 a.u. = 1 Bohr = 0.529177249 Å. The simplest way to specify molecular geometry to the computer is to list cartesian coordinates for each atom. In most cases the right-handed coordinate system is used, whose axes are perpendicular to each other (i.e., orthogonal), as represented in figure below. Figure: Cartesian coordinate Cartesian coordinates are usually listed in 3-column format, X, Y, and Z coordinates for each atom. Cartesian coordinates are an efficient representation of molecular geometry for the computer, and have the advantage of including actual spatial orientation of the molecule. However, they lack the chemical contents for chemists. Chemists prefer to specify and analyze molecular geometry in terms of internal coordinates, i.e., bond lengths and bond angles. The most popular internal coordinates are shown in figure below: Internal coordinates are efficiently calculated by the computer from cartesian coordinates using the vector operations described above. The bond length , dij, is simply a distance between two bonded atoms i and j, i.e., the length of the vector between atom i and j The valence angle called also bond angle, tetaijk, between bonds originating on atom j. The valence angle is always positive and not larger than 180, it is the smaller of the two possible angles. Figure: Internal coordinates: a) bond length, b) valence angle, c) torsional angle. The torsional angle, is a dihedral angle, phiijkl between two planes passing through atoms i,j,k and j,k,l, respectively. It is an angle between vectors normal (i.e., perpendicular) to these planes, or alternatively, an angle between the lines drawn on these planes perpendicularly to the edge where planes.