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$_g^2$) 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] $^{\mbox{\rm singlet}}$ case. As a guide for expert users, complete ROHF TURBOMOLE input for O$_2$ for various CSFs (configuration state function) is given in Section 13.6. 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 ($k,m$):

$$E = 2 \sum_{k}h_{kk} + \sum_{k,l}(2J_{kl}-K_{kl})$$

$$+ f[ 2\sum_{m}h_{mm} + f\sum_{m,n}(2aJ_{mn}-bK_{mn}) + 2\sum_{k,m}(2J_{km}-K_{km}) ]$$

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.