Gamess (US) frequently asked questions part 6: Obtaining proper SCF convergence (Anti-)ferromagnetic coupled Fe-S clusters

Obtaining SCF convergence of FeS clusters is a very demanding task.

The problem in FeS clusters is the arrangement of spins on the Fe atoms: if you have a cluster with 4 Fe atoms, each of them with 5 up-spins, and a total spin of zero, the arrangement of spins on the atoms could be

• Fe1 and Fe2  up-spin, Fe3 and Fe4 down-spin; or
• Fe1 and Fe4  up-spin, Fe2 and Fe3 down-spin; or
• Fe1 and Fe3  up-spin, Fe2 and Fe4 down-spin;

The problem is compounded if you have a mixture of Fe²⁺ and Fe³⁺, which may lead to 12 (or more) different spin arrangements, depending on the number of Fe²⁺ atoms. However, if you have a good guess SCF for one instance instance, you may simply substitute the coordinates of Fe2 with those of Fe4 to get a comparably good guess for the second instance, and so forth... This is the approach suggested by Greco, Fantucci, Ryde, de Gioia (2011) Int. J. Quantum Chem. 111, 3949-3960. Obtaining the guess for one of the instances is in itself quite difficult, and I usually follow the approach outlined by Szilagyi, R. K. and Winslow, M. A. (2006) J. Comput. Chem., 27: 1385–1397  .

It goes like this:

- obtain orbitals for bare Fe²⁺, Fe³⁺, S^2-, and isolated ligands, with proper spins on the Fe atoms (5/2 for Fe³⁺, 2 for Fe²⁺)

- Manually split the "alpha/up" and "beta/down" portions of the resulting  $VEC groups. For example, assuming you have a system with three Fe atoms (two Fe²⁺ and one Fe³⁺) with total spin S=5/2 and the $VEC groups for bare Fe²⁺ and bare Fe³⁺, you should cut the $VEC groups of Fe²⁺ and Fe³⁺ as:

$VEC  for the alpha (up) electrons of Fe²⁺   (let's call it "Fe2+_5_d_electrons")
$VEC  for the alpha (up) electrons of Fe³⁺   (let's call it "Fe3+_5_d_electrons")
$VEC  for the beta (down) electrons of Fe²⁺   (let's call it "Fe2+_1_d_electron")
$VEC  for the beta (down) electrons of Fe³⁺   (let's call it "Fe3+_0_d_electrons")

The total spin S=5/2 in this sample problem implies that  both Fe²⁺ atoms spins should annull each other, i.e., one Fe²⁺ is mostly "up" and the other is mostly "down". Building the new guess for the "up" electrons should therefore include:

"Fe2+_5_d_electrons" for one of the  Fe²⁺ ions,
"Fe2+_1_d_electrons" for the other  Fe²⁺,
"Fe3+_5_d_electrons" for the Fe³⁺

Building the new guess for the "down" electrons should  include:
"Fe2+_1_d_electrons" for the FIRST Fe²⁺ ions,
"Fe2+_5_d_electrons" for the other Fe²⁺,
"Fe3+_0_d_electrons" for the Fe³⁺

- combine the orbitals using the small utility called combo, which you may obtain from Alex Granovsky's Firefly website.

- Manually paste the "alpha" and "beta" guesses  into a single $vec group, which would be the proper guess.

- cross all your fingers and toes, and expect it to converge into the proper state. If it does not converge, change convergers (SOSCF=.T. DIIS=.F.), onset of SOSCF (SOGTOL=1e-3) , etc.

- after SCF optimization using this guess, manually scramble the ordering of Fe atoms in your input, to ascertain whether a lower energy solution can be obtained with a different spin distribution.



Good Luck!