Ab initio Computation Revisited: Fweb Based Code for Educational Purposes

Abstract

We present an fweb based ab initio computation for educational purposes. As such we emphasized more on simplicity but without loss of generality and on readability than on efficiency of the code for this nontrivial problem. In order to check that our code worked we have tested the code to evaluate the total energies for some elements. We used our code to evaluate the total energies of hydrogen, carbon, oxygen atoms and O+. The total energies from our computation were compared to the available data from US National Institute of Standard and Technology (NIST). The results showed that our fweb based ab initio code has performed excellently. For the development of the code we used the density functional theory with local density approximation which gave a relatively simple but accurate prescription for the total energy of a system of electrons and nuclei. The rate of convergence to the final total energy will be presented in terms of total energy versus number of iterations with mixing factor α as a parameter. In the sense of self-consistent computation α is a measure of mixing between the previous and the new density value in order to get the density value for the next step computation in the iteration. Our computation shows that α = 0.55 gives the best performance.