Obtaining converged molecular orbitals (or better, molecular spinors-MS) is an essential step in each ab-intio quantum chemical calculation. We provide you with some tricks on how to 'convince' the system to get converged MS for a chosen state.
Basis set requirements
First and important step: make sure that you have appropriate basis set for your chemical system. Basis set should be large enough to describe properly the electronic structure.
Next parameters you can vary is the occupation of shells. If you are not getting converged molecular spinors, for instance, you have high-spin open-shell system, remove one or more electrons from your system.
Repeat the removing if necessary in order to obtain converged MS for the charged system.
Use them as the starting set (-incmo flag form pam) for your system. Sometimes this could help. If not, continue playing with the occupation of spinors (for open-shells prefer the average occupation of several degenerate spinors instead of one) and/or increase your basis set.
Generally it is very hard to get converged excited state using the very basic single-determinant Hartree-Fock method. You might try it either by dynamical overlap selection method (see SCF keywords) or directly by placing electrons into lowest unoccupied spinors.
Oscillating SCF energies
Sometimes it happens that the SCF energy is oscillating between two values for many iterations. A purely pragmatic solution to this problem is to restart the calculation from the oscillating state and experiment with either dynamic overlap selection (.OVLSEL) or the number of error vectors used in the DIIS procedure (.MXDIIS).
Hf2 + , Ta3 + , W4 + with broken orbital degeneracies
A typical symmetry breaking problem was encountered in Tel Aviv for Lanthanide ions.
Hf2 + , Ta3 + , W4 + are converging closed shell systems with the electronic structure of Yb (Z=70). The first lanthanide in the line with the same electronic structure, Lu+, is not converging.
One observes broken degeneracies of their atomic p,d,f... shells (using four- and two-component Hamiltonians), even for spin-free and Levy-Leblond Hamiltonian. However, the Yb closed shell atom, whose electronic structure is emulated, comes out with proper degeneracies.
The reason for this problem is that the start guess for orbitals is based on a bare nucleus or other simple model Hamiltonian. In the first diagonalization this Hamiltonian gives orbitals that do not have the expected order 4f, 6p but rather 6p, 4f. The program then proceeds by occupying the three 6p orbitals, complemented by a remaining four 4f orbitals. This density does not have the correct spherical symmetry and offsets the SCF procedure yielding a symmetry-broken solution.
One should provide a better starting guess, e.g. by first calculating the highly-charged ion with a Xenon configuration. This gives a symmetric density that can be used as starting guess (using the DFCOEF file) for the real calculation. Some care is needed with this restart as also the orbitals for the Xe-like ion may have an undesired order. This may require use of the MO selection options of the program (see the manual).
Solution for Hf2 +
The idea behind (though not exactly following Work-around is to fix the wrong order of orbitals which is causing the degeneracy.
The 'default' wrong order of forming molecular orbitals is for s-shell (LUMO) beeing inserted after the first d-shell (HOMO).
One has to apply the MJ-selection for the linear symmetry, or the orbital reordering scheme to have s- separated from d-orbitals.
It is possible to get converged MOs not only for linear, but also for D2h and C2v symmetries. However, for the C2v it takes many iterations.