Introduction

Preconditions for creating a pseudo orbital

1. It is only possible to create a new pseudo orbital by using the data of already existing ones. For example, aluminium consists of three S-orbitals 1S, 2S and 3S, therefore only a 4S pseudo orbital can be calculated next.

2. The function of an orbital is defined as follows:

                        n       -alpha  *  r
                         k            k 
   P    =  sum   c  *  r    *  e               *  normalization
    ij        k   k
   

   where

   • i is the shell number, an element of the natural numbers.
   • j is the orbital type, an element of {S, P, D}.
   • k is an element of {1, .., #NumberDataValues}.
   • normalization is used to modify the Clementi-type orbitals of the RHF table into Slater-type orbitals.
   • c, n and alpha are data values.

3. The orbital functions are orthogonal, i.e.

      oo   2
   int    P    dr          =  1
      0    ij
   
   
      oo   
   int    P    *  P    dr  =  0
      0    ij      kj
   

   where

   • i, j are defined as above.
   • k is a shell number, an element of the natural numbers.