Introduction

Creating a pseudo orbital

4. Without loss of generality we can assume that c[3] is equal to 1. Now we can solve the linear equation

   a    a         c         - x
    11   12        1           1
              *         = 
   a    a         c         - x
    21   22        2           2
   

   by using Gaussian Elimination.

5. After having gained c[1] and c[2] we calculate:

      oo   2
   int    P   dr  =  y
      0    3S
   

6. Normally y is not equal to 1.0 (as mentioned in our preconditions), because we previously set c[3] to 1.0). Therefore we have to normalize the solution by calculating:

           c              c              c
            1              2              3
   d   =  ----;   d   =  ----;   d   =  ----;
    1      y       2      y       3      y
   

7. Finally, the new data values d[1], d[2] and d[3] of the pseudo orbital 3S are stored in the atom data structure.