Energy Minimization - Boundary Conditions

Boundary Conditions

The atoms in our system can have different degrees of freedom. For example, in case of a tube suspended over two supports, we need to fix certain number of atoms N* at the tube ends during the calculation. In this case, it is enough not to move these N* atoms in the step 4 or 8 in Figure 3, but we still calculate their interaction with other atoms in the steps 2 and 5. i.e. from mathematical point of view, we change the total number of variables in the energy function from 3N to 3N-3N*using the boundary condition, by which the values of these 3N* unknown variables are taken as known constants. Note that one can even fix atoms in only one or two directions in this way.

Moreover, one can equally adding other boundary conditions to the minimized energy function, such as adding external forces or external electric fields to the system. In these cases, the terms in potential energy function will be changed but the number of variables remains constant.

Here an example of the application of the energy minimization method in molecular modeling in nanoscience is shown in Figure 4.

Further information about the application of this method in nanoscience and Computational Codes programmed in Fortran for students is available in the following external links.