[CP2K-user] [CP2K:22330] Stabilizing/finding C2v-like Be_Ga acceptor state in CP2K HSE calculations

[Asif Billah]

Hi CP2K community,

I am studying Be substituting Ga in wurtzite GaN using CP2K/GPW with HSE + 
ADMM. 

Based on previous resources, it is possible to obtain three different 
configurations for Be in GaN.
C3v: one long axial Be-N bond
pseudo-C3v: one long basal Be-N bond
C2v: distortion of the two adjacent acceptor-nitrogen bonds, not a single 
bond is significantly long

I am trying to locate the shallow C2v like acceptor configuration, but so 
far my relaxations either converge to the deep C3v or pseudo-C3v polaronic 
states.

I have already found stable/converged neutral C3v and pseudo-C3v branches. 
In the 72-atom cell at α = 0.335, the pseudo-C3v branch is with one long 
basal Be-N bond around 2.56 Å. The C3v branch has one long axial Be-N bond 
around 2.59 Å. These two states can be obtained easily where the initial 
structure will be by distorting the Be atom such that there will be a long 
basal or axial bond. 

The shallow C2v state of Be_Ga acceptor results from the distortion of the 
two adjacent acceptor-nitrogen bonds, having the C2v symmetry of the atomic 
structure. The hole in this case is anisotropically delocalized in the 
(0001) wurtzite plane of GaN.

Hence, for the C2v search, I am giving an initial structure by distorting 
the Be atom along a bisector direction involving the axial N neighbor and 
one basal N neighbor. However, it starts to collapse to the C3v/pseudo-C3v 
state.

My question is: does anyone have advice on how to better initialize or 
constrain the search for the shallow C2v acceptor state in CP2K? Is it 
possible to obtain C2v state? In particular, I would appreciate suggestions 
on:

1. Better initial distortion pattern for C2v in wurtzite GaN
2. Better spin/localization initialization for the hole
3. Any CP2K-specific GEO_OPT/HSE/ADMM settings that help avoid collapse 
into C3v or pseudo-C3v

Any guidance would be very helpful. Thank you!

Ps:
My current setup is:

System: Be_Ga in wurtzite GaN
Cell sizes tested: 72 atoms, moving to 108 and 300 atoms
Run type: GEO_OPT, fixed cell
Functional: HSE-style screened hybrid
alpha = 0.335
omega = 0.1058354422 bohr^-1   # approximately 0.2 Å^-1
MGRID cutoff = 600 Ry
REL_CUTOFF = 60 Ry
SCF: OT-CG, FULL_ALL preconditioner
q = 0: UKS TRUE, MULTIPLICITY 2
q = -1: UKS FALSE
HFX: four-center HFX + ADMM

Basis/pseudopotential setup:

Ga: DZVP-MOLOPT-PBE0-GTH-q13 + admm-dz-q13, GTH-PBE0-q13
N : DZVP-MOLOPT-PBE0-GTH-q5  + admm-dz-q5,  GTH-PBE0-q5
Be: DZVP-MOLOPT-PBE0-GTH-q4  + admm-dz-q4,  GTH-PBE0-q4

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