[CP2K-user] IC-QMMM with single charge in front of a metal plane: open boundary corrections

[Katharina Doblhoff-Dier]

Dear CP2K community,

I am confused about the IC-QMMM method as implemented in CP2K. I am not 
100% sure whether my question is related to my misunderstanding of the 
method (as implemented) or on how to use it.
Originally, my confusion came from my not-understanding of the parameter 
V_0 (i.e., EXT_POTENTIAL in the CP2K implementation): In periodic boundary 
conditions, this parameter does not seem to make much sense to me: 
Depending on the average potential in the quantum region, defining V_0 will 
make the charge Q on the metal adapt in such a way that the average 
potential in the cell is zero (I know that the latter is logic, but in view 
of this, the physical meaning of V_0 becmes unclear to me):

[image: tmp1.png]

Alternatively, if a charge is put into the QM part (e.g. an H2+) and V0 is 
adjusted such that the total charge Q on the metal is exaclty -1, a 
spurious field will result over the cell (due to Ewald summation) and 
again, V_0 does not have an obvious physical meaning. 

[image: tmp2.png]

Considering that the periodic boundary conditions lead to lots of spurious 
stuff, I then tried to go to MT boundary corrections or the IMPLICIT 
poisson solver as implemented in CP2K. This gave me the following results 
(note that I shifted the green and the blue curve by 0.4V for better 
comparison)

red:      IMPLICIT poissn solver with Neumann BC at z=0 and z=60 and 
homogeneous Dirichlet BC at z=30
green:  MT (Martyna-Tuckerman) poisson solver (shifted by 0.4V)
blue:    normal Ewald summation (shifted by 0.4V)

[image: tmp3.png]


The corresponding V_0 (optimized such that Q=-1) were 1.11V for IMPLICIT 
boundary conditions, 1.24V for MT boundary conditions and -0.37V for 
periodic boundary conditions. While for periodic boundary conditions (blue 
line) this can be seen to correspond to the potential in the metal part, 
this is not the case for MT boundary conditions (green), where the 
potential in the metal varies from about -0.4 to -0.5 (remember that I 
shifted the curves by 0.4 volt) and for IMPLICIT boundary conditions. 
Overall, to me, it looks as if the IC-QMMM method was ignoring the boundary 
conditions and optimizing the charges for the periodic boundary conditions 
and then keeping them fixed no matter what I set as POISSON_SOLVER. In the 
MT boundary condition case (geen) we can thus see the influence of the 
charges shieding the (spurious) field in periodic boundary conditions 
(hence the slope in the metal part, which has the same slope as the average 
field in the periodic solver).


Finally, I decided that, in principle, it should be possible to find an 
energy minimum when Q_image=-Q_QM (as also shown in the original paper by 
Siepmann and Sprik). With none of the boundary conditions could I find this 
minimum correctly. However, here comes my non-understanding of Eq. 4 in the 
paper by Golze, Iannuzzi, ..., and Hutter 
(https://pubs-acs-org.ezproxy.leidenuniv.nl:2443/doi/10.1021/ct400698y) 
into play: Here, the energy is written as:


[image: tmp4.png]

I would have thought this to be a grand canonical energy (grand canonical 
only in the charges on the metal) expression, where the last term accounts 
for the -N_i*mu_i term. Again, this does not seem physical to me if I think 
of a capacitor (or a charge+image charge in a box that is periodic in x and 
y, as I would then expect a correction for the charges in the QM region too 
(unless the vacuum potential on the QM side is zero and open boundary 
conditions are used, but likely this is wrong and this may be where my 
entire confusion starts.


So summarizing, this boils down to a few questions:

1.) can the IC-QMMM method be combined with poisson solvers other than 
periodic? If so, how? I simply set the poisson solver in the MM and the DFT 
part.

2.) What do I need to do in order to find an energy minimum for 
Q_image=-Q_QM?

3.) What is the meaning of V_0 and why is it substracted in the energy 
expression.


Any physical insight is appreciated!
Thank you and best regards,
Katharina
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20200624/e784bbb4/attachment.htm>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tmp1.png
Type: image/png
Size: 61511 bytes
Desc: not available
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20200624/e784bbb4/attachment.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tmp2.png
Type: image/png
Size: 29616 bytes
Desc: not available
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20200624/e784bbb4/attachment-0001.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tmp3.png
Type: image/png
Size: 12821 bytes
Desc: not available
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20200624/e784bbb4/attachment-0002.png>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tmp4.png
Type: image/png
Size: 2942 bytes
Desc: not available
URL: <https://lists.cp2k.org/archives/cp2k-user/attachments/20200624/e784bbb4/attachment-0003.png>