Calculation of band gap using QMMM

[jts2t... at gmail.com]

Hello every Developer and Researcher,
I tried the example in https://www.cp2k.org/exercises:2017_ethz_mmm:qmmm 
several days ago. It is a geo_opt example of 48 KCl atoms using QMMM 
method. And I also look up the paper listed in the tutorial and tried to 
calculate the band gap of the system. But the result is not satisfactory. 
If I use 1-layer QM atoms (16 atoms), the HOMO - LUMO gap is as following
HOMO - LUMO gap [eV] :    4.926845
 HOMO - LUMO gap [eV] :    4.668970
 HOMO - LUMO gap [eV] :    4.734728
 HOMO - LUMO gap [eV] :    4.728571
 HOMO - LUMO gap [eV] :    4.733307
 HOMO - LUMO gap [eV] :    4.692899
 HOMO - LUMO gap [eV] :    4.722199
 HOMO - LUMO gap [eV] :    4.681768
 HOMO - LUMO gap [eV] :    4.678310
 HOMO - LUMO gap [eV] :    4.700719
 HOMO - LUMO gap [eV] :    4.662065
 HOMO - LUMO gap [eV] :    4.685438
 HOMO - LUMO gap [eV] :    4.663563
 HOMO - LUMO gap [eV] :    4.662155
 HOMO - LUMO gap [eV] :    4.662057
 HOMO - LUMO gap [eV] :    4.662044
 HOMO - LUMO gap [eV] :    4.662065
 HOMO - LUMO gap [eV] :    4.662064
 HOMO - LUMO gap [eV] :    4.662034
 HOMO - LUMO gap [eV] :    4.662058
 HOMO - LUMO gap [eV] :    4.662063
 HOMO - LUMO gap [eV] :    4.662052

If I use 2-layer QM atoms (32 atoms), the result is 
HOMO - LUMO gap [eV] :    4.782295
 HOMO - LUMO gap [eV] :    4.271173
 HOMO - LUMO gap [eV] :    4.447092
 HOMO - LUMO gap [eV] :    4.470585
 HOMO - LUMO gap [eV] :    4.499691
 HOMO - LUMO gap [eV] :    4.487309
 HOMO - LUMO gap [eV] :    4.495278
 HOMO - LUMO gap [eV] :    4.486996
 HOMO - LUMO gap [eV] :    4.481340
 HOMO - LUMO gap [eV] :    4.481181
 HOMO - LUMO gap [eV] :    4.481379
 HOMO - LUMO gap [eV] :    4.481309
 HOMO - LUMO gap [eV] :    4.481298
 HOMO - LUMO gap [eV] :    4.481304
 HOMO - LUMO gap [eV] :    4.481308
 HOMO - LUMO gap [eV] :    4.481297
 HOMO - LUMO gap [eV] :    4.481311

If I use full QM,
HOMO - LUMO gap [eV] :    4.934751
 HOMO - LUMO gap [eV] :    4.683587
 HOMO - LUMO gap [eV] :    4.923171
 HOMO - LUMO gap [eV] :    4.941706
 HOMO - LUMO gap [eV] :    4.934531
 HOMO - LUMO gap [eV] :    4.924194
 HOMO - LUMO gap [eV] :    4.916435
 HOMO - LUMO gap [eV] :    4.917274
 HOMO - LUMO gap [eV] :    4.915809
 HOMO - LUMO gap [eV] :    4.916783
 HOMO - LUMO gap [eV] :    4.913765
 HOMO - LUMO gap [eV] :    4.916681
 HOMO - LUMO gap [eV] :    4.914778
 HOMO - LUMO gap [eV] :    4.916037
 HOMO - LUMO gap [eV] :    4.918605
 HOMO - LUMO gap [eV] :    4.916562
 HOMO - LUMO gap [eV] :    4.916525

The question is the 2-layer QM atoms should be more approaching to the 
result of full QM than the 1-layer atoms. But the fact is the opposite. The 
setting about printing the HOMO-LUMO gap is as follows
&MO_CUBES
        NHOMO 1
        NLUMO 1
        WRITE_CUBE F
&END MO_CUBES

The most possible reason I can think of is something wrong appear in the 
setting of full QM calculation.
Thanks for your reply ! 



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