Electronic structure of pseudo-Ge

To test the results of the pseudopotential, modify Vnuc() to return the value of Eq. (1), and run ``broyden.c'' with the electronic configuration

  /* Specs for pseudo-Ge */
 Z=4.;
 lmax=1;

 nmax=ivector(0,lmax);
 nmax[0]=0;
 nmax[1]=0;

 nmaxmax=0;
 for (l=0; l<=lmax; l++)
   if (nmax[l]>nmaxmax) nmaxmax=nmax[l];

 F=dmatrix(0,lmax,0,nmaxmax);
 F[0][0]=2.;
 F[1][0]=2.;

This configuration corresponds to a core (nucleus plus core electrons) with a net charge of four, and 2 valence electrons in the lowest s state (``1s'') and two in the lowest p state (``2p'').
Hint: To handle the case $r=0$, you may wish to use $\lim_{r\rightarrow 0} V_{ps}(r) = -\frac{Z_v\lambda}{1+e^{\lambda r_c}}$.

To verify the suitability of the pseudopotential, compare the pseudo 1s eigenvalue with the all-electron 4s eigenvalue and the pseudo 2p with the all-electron 4p eigenvalues. Compare the corresponding pseudo- and all-electron wave functions by copying the output file ``psis'' to ``psis_pseudo'' and running ``pseudo.m'' from within octave. Finally, take note of the pseudo total energy and the difference between the pseudo 1s and pseudo 2p energies. The next problem will compare these last two quantities with the output of the $d=3$ dimensional code.