**1.2 Derivatives**

For derivatives based Minimization methods, calculation of the derivatives of the energy is performed with respect to the different variables i.e. Cartesian or internal coordinates, as the case may be. These derivatives can be generated using either analytical or numerical procedures but derivatives obtained through analytical procedure are more preferred because these can be generated more readily and these are more exact. Although, if derivatives generated by only numerical procedure is available then one should use a non-derivative Minimization procedure as it is more efficient [3].

Although, in some situations it is always preferable to use derivatives generated though numerical procedure. By following way these can be generated: suppose there is a small alteration (*δx*i) in one of the coordinates *x*i and the energy calculation is performed for this new alteration the by dividing the alteration in energy (*δE*) by the alteration in coordinate (*δE / δx*j), the derivative *∂E/∂x*i is obtained. This rigorously yields the derivative at the mid-point between the two points *x*i and *x*i + *δx*i. A more correct value of the derivative at the point *x*i; could also be acquired (at the price of a further energy calculation) by assessing the energy at two points, *x*i + *δx*i and *x*i – *δx*i. The derivative is then obtained by dividing the variation with in the energies by 2*δx*i.
