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Table of Contents
How to run IC-QM/MM simulations for interface systems
Introduction
The image charge (IC) augmented QM/MM model in CP2K is designed for the simulation of adsorbate-metal systems. The adsorbate is treated by QM whereas the metallic substrate is described by classical force fields, see figure ##. The interactions between metal and adsorbate are described at the MM level of theory accounting for the polarization of metal and adsorbate by an IC approach. The charge distribution $\rho_m$ in the metal is modeled by a set of Gaussian charges (image charges) centered at the metal atoms,
Fig. ##: Nitrobenzene molecule on Au111. Separation in subsystems for IC-QM/MM.
\begin{equation}
\rho_m(\mathbf{r})= \sum_{a}{c_a g_a(\mathbf{r,R}_a)},
\label{eq:rhom}
\end{equation}
where $\mathbf{R}_\mathrm{a}$ is the position of metal atom $a$ and $g_a$ the spherical Gaussian function located at $a$. The expansion coefficients $c_a$ are unknown and determined in a self-consistent procedure imposing the constant-potential condition within a metal, i.e. the sum of $V_H(\mathbf{r})$ generated by the charge density $\rho(\mathbf{r})$ of the molecule and $V_m(\mathbf{r})$ generated by $\rho_m$ has to be constant within the metal,
\begin{equation}
V_{H}(\mathbf{r})+V_m(\mathbf{r})=\int \frac{\rho(\mathbf{r}')+\rho_m(\mathbf{r}')}{|\mathbf{r}'-\mathbf{r}|}
d\mathbf{r}'=V_0.
\label{eq:const_pot}
\end{equation}
In this expression $V_0$ is a constant potential that can be different from zero, if an external potential is applied.
The implementation is embedded in the Gaussian and plane waves scheme of CP2K naturally suited for periodic systems. Details of the theory and implementation are described in J. Chem. Theory Comput., 9, 5086 (2013).
Basic input
The IC method is specified in the QMMM section by
&QMMM : : &IMAGE_CHARGE MM_ATOM_LIST 1..576 EXT_POTENTIAL 0.0 &END IMAGE_CHARGE &END QMMM
The keyword MM_ATOM_LIST defines the list of MM atoms that carrying an image charge. These are typically all metal atoms. EXT_POTENTIAL corresponds to $V_0$ above and is set to 0.0V by default. Note that the QM and MM box must have the same size for an IC-QM/MM calculation.
Print options
The normalized IC coefficients, i.e. $q_a = c_a\left(\frac{\alpha}{\pi}\right)^{-\frac{3}{2}}$, where $\alpha$ is the width of the Gaussian, and detailed energy information can be printed out via
&QMMM : : &PRINT &IMAGE_CHARGE_INFO &END &END PRINT &END QMMM
Typical setup
The typical setup for an IC-QM/MM simulation is as follows: Adsorbed molecules are treated by DFT. MM-based interactions between metal and molecule are modeled with an empirical model reproducing dispersion, Pauli repulsion etc. The electrostatic interactions (induction)
Example input files
- H2O@Pt111: Pt111_1H2O.tar.gz