Transition Metal Complexes

Many transition metal complexes are characterized by the presence of an open shell.  Thus an octahedral Ti(III) complex is likely to have one unpaired electron in the 3d shell of Ti, and have the state ²T_2g.  For example, the complex [Ti^III(H₂O)₆]³⁺ is expected to have a ground state ²Tg, and this is, in fact, correctly predicted.

Calculation of metal complexes is made difficult for several reasons:

1. The systems often involve multiple open shells, e.g. high and low spin complexes.  To allow for this, extended C.I. calculations were necessary.
2. The Jahn-Teller effect predicts that calculated systems should distort so as to lower the symmetry. To prevent this distortion in systems where the Jahn-Teller effect is small (the left hand side of the transition metal series), "average over configurations" was used.  This is done automatically if the system is of high symmetry and the symmetry is conserved by use of symmetry constraints.  In all other cases, the Jahn-Teller effect is allowed to distort the geometry.
3. Many textbooks and journal articles incorrectly refer to the next higher point-group when discussing complexes.  Thus hexaquo complexes are considered as having octahedral symmetry, Oh,  instead of the correct Th symmetry.  Because the symmetry analyzer is unaware of this, the symmetry printed is often in variance with that reported.
4. In solids, the effect of the next layer of ions is often important.  In the hexahalo complexes, the next layer consists of metal ions, and  is only slightly further away than the halide ions.  This effect is always present in solids where the complex is not electroneutral, e.g. in [M^IIIX₆]^3- ions in the solid MX₃. To allow for this, two special entities are provided, these have the symbols At (Astatine) and Fr (Francium).  The entity "At" behaves like a point-charge with a charge of -0.5, and "Fr" behaves like a point-charge with a charge of +0.5.  These entities should only ever be used in even numbers, so that the total charge is an  integer. A more realistic model of the [M^IIIX₆]^3- system could be constructed by adding eight Fr entities, arrayed at the vertices of a cube.  This would give rise to the complex [M^IIIX₆M^+1/2₈]⁺. 

The following table shows the results of PM6 calculations of the ground state of various high symmetry transition metal complexes.  Where the calculated heat of formation is zero, the calculated state is the same as the state expected.  Where the calculated ΔH_f is positive, the state expected is calculated to be an excited state, and the value is the energy of that state, in kcal.mol^-1,  above the calculated ground state, in other words, it is a measure of the error.

The following table shows the results of PM6 calculations of the energy of excitation, in  kcal.mol^-1,  from one state to another of  various high symmetry transition metal complexes, and the comparison with the values observed by experiment..

In almost all cases, the crystal field splitting is too small.  This appears to be a fault in the set of approximations used.