(a) Write a computer program that will perform the helium-atom SCF calculation of Section 14.3. Have the input to the program be ζ1, ζ2, and the initial guess for c11/c21. Do not use the Section 14.3 values of the integrals, but have the program calculate all integrals from ζ1 and ζ2. Have the program print c11, c21, e1, and e2 for each cycle of calculation. Use the convergence criterion that c11 and c21 each differ from the c11 and c21 values of the previous cycle by less than 10-5 atomic units.
(b) Use your program with ζ1 = 1.45 and ζ2 = 2.91 to find the number of iterations needed to reach convergence for each of these initial guesses for c11>c21:100, 10, 1, 0, -1, -10, -100.
(c) Run the program with ζ1 = 1.45363 and ζ2 = 2.91093 to verify the SCF energy given for these ζ's at the end of the Section 14.3 example.
(d) Run the program with ζ1 changed by +0.01 and by -0.01 from the value in (c), and verify that each EHF obtained is higher than that in (c). Repeat for ζ2.