Roothaan Parameters

In open-shell calculations within the restricted Hartree-Fock ansatz (ROHF), the coupling between the closed and the open shells must be specified using two parameters a and b, which depend on the type of the open shell, the number of electrons in it (the electron configuration), but also on the state to be calculated. For example, there are three states arising from the $s^2\,p^2$ mathend000# configuration of an atom ($^3$ mathend000#P, $^1$ mathend000#D, $^1$ mathend000#S) which have different values of $a$ mathend000# and $b$ mathend000#. For the definition of these parameters and their use refer to Roothaan's original paper [22]. For simple cases, DEFINE sets these parameters automatically. If not, you have to enter them yourself. In this case, you will get the following message:

ROOTHAAN PARAMETERS a AND b COULD NOT BE PROVIDED ...
TYPE IN ROOTHAAN a AND b AS INTEGER FRACTIONS
OR ENTER val FOR AN AVERAGE OF STATES CALCULATION
OR ENTER  &  TO REPEAT OCCUPATION NUMBER ASSIGNMENT

Note that not all open shell systems can be handled in this way. It is possible to specify $a$ mathend000# and $b$ mathend000# for atomic calculations with $s^n, p^n, d^1$ mathend000#, and $d^9$ mathend000# configurations and for calculations on linear molecules with $\pi^n$ mathend000# and $\delta^n$ mathend000# configurations. Furthermore, it is possible to do calculations on systems with half-filled shells (where a=1, b=2). In the literature you may find tabulated values for individual states arising from $d^n$ mathend000# configurations, but these are not correct. Instead, these are parameters for an average of all states arising from these configurations. You can obtain these values if you enter val on the above question. For a detailed description see Section 6.3.