[CP2K-user] [CP2K:13546] IC-QMMM with single charge in front of a metal plane: open boundary corrections

[Dorothea Golze]

Hi Katharina,

I am not sure if I understand your question correctly and what your
computational setup is.
The basic electrostatic consideration is that the potential should be
constant within a conductor. If no external potential is applied, the
electrostatic potential is zero within a metal, i.e., V_0=0. That is the
default. It can be also set to another value  in principle, e.g., maybe to
approximate the application of a potential to an electrode. But it seems
that's not what you want to do here. Note that the IC-QM/MM does not
introduce actual charges, only image charges. You can run with the normal
periodic solver when you have a (neutral) molecule on top of the metal (MM).
If you have a charged system in the QM part, then you need a solver like
MT, like in a standard QM calculation.

Best regards,
Dorothea

Am Mi., 24. Juni 2020 um 16:23 Uhr schrieb Katharina Doblhoff-Dier <
k.doblh... at lic.leidenuniv.nl>:

> 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
>
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