Why does the SCF not converge in a structure optimization with GAMESS of the thiourea molecule at the PM6 level of theory?
TL;DR: PM6 only works for elements up to fluoride in GAMESS.

I have played around with the GAMESS version installed at our cluster, the ancient 5 DEC 2014 (R1) and I came to the conclusion that there must be a 'bug' in the implementation of PM6 with GAMESS. (I reproduced the problem with 20 APR 2017 (R1); I have also downloaded 30 Jun 2019 (R1), but I won't try it as I think the result is the same.) When I tried it with Gaussian 16 Rev. B.01 on the PM6 level of theory it converged fine.

Actually, I have looked at the documentation, and it seems to be officially not supported (from INTRO.DOC):


Capabilities

   [...]
   3. Calculates semi-empirical MNDO, AM1, or PM3 models 
      using RHF, UHF, ROHF, or GVB wavefunctions.
   [...]



Or from INPUT.DOC:


        * * * semiempirical basis sets * * *

GBASIS = MNDO - selects MNDO model Hamiltonian
       = AM1  - selects AM1 model Hamiltonian
       = PM3  - selects PM3 model Hamiltonian
       = RM1  - selects RM1 model Hamiltonian
       = DFTB - selects tight binding Hamiltonian



I am pretty sure the error is associated with sulfur. I have tried a few molecules, among them $\ce{H3C-NH2}$, $\ce{(H3C)2NH}$, $\ce{(H3C)2CO}$ (see input below), urea, which converged fine. Whenever I tried a molecule containing sulfur the SCF seemed to be oscillating. I have tested $\ce{CS2}$, $\ce{SO2}$, $\ce{(H3C)2CS}$, and (obviously) thiourea. (With PM3 everything worked fine.)

My best guess is that they simply didn't finish implementing it. You could issue a support ticket on GitHub: issues. I found an article by (the here known) Jan Jensen from 2013: Project status: PM6 and PCM in GAMESS. And then from 2014: PM6, DFTB, GAMESS, enzyme design, protein-ligand binding, and protein structure validation. I stopped there.

I'd recommend using a different program, the obvious choice would be MOPAC (http://openmopac.net/). Gaussian has it implemented and a couple others probably too. Or you switch to a completely different method like xtb, HF-3c (in ORCA), DFTB (e.g. DFTB+), etc.. Depending on your system size, you can probably also get DFT based calculations done.

Here is also something related: GAMESS crash course?



 $CONTRL SCFTYP=RHF RUNTYP=OPTIMIZE MAXIT=100 MULT=1 COORD=UNIQUE
    NOSYM=1 $END
 $BASIS GBASIS=PM6 $END
 $DATA
 C3H6O
C1
CARBON      6.0      0.156332162        -0.059231571         0.417752882
OXYGEN      8.0      1.200569512        -0.535604279         0.831319560
CARBON      6.0     -0.037914597         1.466530485         0.340822109
HYDROGEN    1.0      0.279389785         1.860652999        -0.631337255
HYDROGEN    1.0     -1.089141584         1.742544046         0.481697509
HYDROGEN    1.0      0.545018653         1.982387227         1.112307247
CARBON      6.0     -1.053925162        -0.882111362        -0.061565447
HYDROGEN    1.0     -0.987243509        -1.102851552        -1.132983096
HYDROGEN    1.0     -1.121341433        -1.838731138         0.468944868
HYDROGEN    1.0     -1.993938204        -0.344384630         0.106761952
 $END