17.5 Using additional point-group symmetry

Since MOLPRO can handle only Abelian point-groups, there may be more symmetry than explicitly used. For instance, if linear molecules are treated in $C_{2v}$ instead of $C_{\infty v}$, the $\delta_{(x^2-y^2)}$-orbitals appear in symmetry 1 ($A_1$). In other cases, a linear geometry may occur as a special case of calculations in $C_S$ symmetry, and then one component of the $\pi$-orbitals occurs in symmetry 1 ($A'$). The program is able to detect such hidden ``extra'' symmetries by blockings in the one-electron hamiltonian $h$ and the overlap matrix $S$. Within each irreducible representation, an ``extra'' symmetry number is then assigned to each basis function. These numbers are printed at the end of the integral output. Usually, the extra symmetries are ordered with increasing $l$-quantum number of the basis functions. This information can be used to determine and fix the extra symmetries of the molecular orbitals by means of the SYM command.

SYM, $irrep,sym(1),sym(2),,,sym(n)$

$sym(i)$ are the extra symmetries for the first $n$ orbitals in the irreducible representation irrep. For instance, if you want that in a linear molecule the orbitals 1.1 to 3.1 are $\sigma$ and 4.1, 5.1 $\delta$, the SYM card would read (calculation done with X,Y as symmetry generators):

SYM,1,1,1,1,2,2

If necessary, the program will reorder the orbitals in each iteration to force this occupation. The symmetries of occupied and virtual orbitals may be specified. By default, symmetry contaminations are not removed. If irrep is set negative, however, symmetry contaminations are removed. Note that this may prevent convergence if degenerate orbitals are present.