Brief Description

The spin-restricted open-shell Hartree-Fock method (ROHF) can always be chosen to systems where all unpaired spins are parallel. The TURBOMOLE keywords for such a case (one open shell, triplet e_g² ) are:

$open shells  type=1
  eg     1               (1)
$roothaan   1
  a=1  b=2

It can also treat more complicated open-shell cases, as indicated in the tables below. In particular, it is possible to calculate the [xy] ^singlet case. As a guide for expert users, complete ROHF TURBOMOLE input for O₂ for various CSFs (configuration state function) is given in Section 16.6. Further examples are collected below.

The ROHF ansatz for the energy expectation value has a term for interactions of closed-shells with closed-shells (indices k, l), a term for purely open-shell interactions (indices m, n) and a coupling term (k, m):

$$\sum_{{k}}^{} \sum_{{k,l}}^{}$$ E =

$$\sum_{{m}}^{} \sum_{{m,n}}^{} \sum_{{k,m}}^{}$$

where f is the (fractional) occupation number of the open-shell part (0 < f < 1), and a and b are the Roothaan parameters, numerical constants which depend on the particular configuration of interest.