Write a computer program that will calculate the optimum value of the orbital exponent k for the H+2 trial function (13.54) for a given R value. Have the program calculate W1 + 1/R [where W1 is given by (13.63)] for k ranging from 0 to 3 in steps of 0.001 and have the program pick the k value that gives the smallest W1 + 1/R. Write the program so that the value of R, the initial and final values of k, and the interval between k values are input from the keyboard for each run. Use the program to find k to the nearest 0.001 for R values of 0.5, 1.0, 2.0, 3.0, 4.0, and 6.0. Use the calculated energies to plot the U1R2 curve predicted by this trial function. (For more efficient ways to find the minimum of a function of one variable, see Press et al., Chapter 10.)