Point Group Theory

This Section is based on the original work of Peter Bischof in the UMNDO program, and made available to me by Dr David Danovich.

Some point-group theory has been added to MOPAC. The main functionalities added are:

'Normal' symmetry relationships are now automatically recognized if AUTOSYM is specified.
The symmetry of the system is printed both at the start of the run and at the end. If the point-group changes, the change will be shown in the different point-group symbols.
Molecular orbitals will be characterized by Irreducible Representation (I.R.).
Normal coordinates generated in the vibrational calculation will be characterized by I.R.
State functions will be characterized by I.R.
All rotation groups up to order 8, except D_8d, are available.
The cubic groups T, T_h, T_d, O, O_h, I, and I_h are available.
The infinite groups C $_{infty v}$ , D $_{infty h}$ and R₃ are available.
In FORCE or vibrational frequency calculations, symmetry will be used to accelerate the calculation, thus a calculation of benzene would involve two atoms, a C and a H atom, to be calculated, rather than the normal 12 atoms.
In vibrational frequency calculations, the Hessian or force matrix will be symmetrized.

$begin{displaymath}F_{ij}=frac{1}{h}sum_hR(h)^TF_{ij}'R(h)end{displaymath}$

This eliminates the normal small deviations from exact symmetry (a qualification appears elsewhere) .