Cluster Growth: Cobalt Clusters
*******************************

ReaxFF Nanoscience Cluster growth Binding sites

Here we show a biased structure search strategy for investigating the
structural evolution and growth pattern of single-atom clusters. The
strategy consists of adding one atom to the lowest energy structures
of the n-atoms (frozen) and get the binding site with the largest
binding energy, which is a good approximation to the (n+1)-cluster
global minimum structure.

The strategy is illustrated using the Co.ff ReaxFF force field for the
growth mechanism Co_8+Co-->Co_9.

The tutorial is divided into two parts: In the first part, we obtain
the global minimum for the Co_8 cluster by using the Basin Hopping
subtask. In the second part, we fix the coordinates of the Co_8 global
minimum, add a Co atom and use the Process Search subtask to obtain
all reaction mechanisms involving it, and with them, the corresponding
binding sites. The structure associated with the highest binding
energy is the best approximation to the Co_9 global minimum structure,
and the binding-sites lattice will give us insights into the growth
mechanism behind it. The gradual population of the binding sites shows
the structural evolution and the growth pattern of these kinds of
clusters.

Hereafter, we will use the PES exploration task in the AMS driver with
the ReaxFF engine. Configure this by following the steps below:

   **1.** Start AMSinput (**SCM → New Input**).
   **2.** In AMSinput, select the ReaxFF panel: [image: ADFPanel][image] **→** [image: ReaxFFPanel][image].
   **3.** Select the **Task → PES Exploration**.
   **4.** Select **Periodicity → None**.
   **5.** Select the **Force field → Co.ff**.


Global Optimization of Co_8
===========================

We need an initial guess for the structure of the Co_8 cluster. Thus,
create a random structure composed of 8 atoms of Co by using the
drawing tools of AMSinput. Avoid a planar configuration for the
cluster’s atoms; to do so, take some atoms out of that plane
individually if needed. The difficulty is that planar configurations
usually converge to a transition state during optimization instead of
a local minimum. Then, use the **Pre-optimize** button on the main
panel to get the closest local minimum, make sure to pre-optimize the
full structure. Make sure that you have a non-flat structure with none
of the atoms collapsed. Otherwise try rebuilding an 8-atom cluster
again. This step is summarized in the following Figure:

[image]

The initial structure is not important, but more iterations may be
needed to get the same results. For this tutorial, we suggest starting
with the same local minimum to improve reproducibility.

   **1.** Delete your current structure by clicking **Select → Select all** and pressing the **Delete** key.
   **2.** Copy & paste the coordinates below into AMSinput.
   **3.** Press the **Pre-optimize** button again.

   Co      -0.57747929       3.09962106      -1.40010667
   Co      -1.94268805       1.60982864      -0.21835532
   Co       0.68130178      -0.28713038       1.61855474
   Co       0.41911715       1.21862699      -0.30327160
   Co       1.35380790       3.40899190      -0.11445733
   Co       1.88623229       1.82216225       1.57360827
   Co       0.56876970      -1.15098318      -0.59251345
   Co       2.52877908       0.02596128       0.06823723

To setup the Basin Hopping calculation, follow these steps:

   **1.** Select **Task → PES Exploration**.
   **2.** Click on [image: MoreBtn][image] next to the **Task** to specify the **PES Exploration** settings.
   **3.** On the PES Exploration page, select **Job → Basin Hopping**.
   **4.** Set **Num expeditions** to "10".
   **5.** Set **Num explorers** to "4".
 [image]

Details on the different settings can be found in the PES exploration
page in the AMS driver manual. For the purpose of this tutorial we
will leave everything at the default values, except the number of
expeditions and the number of explorers per expedition.

We have now finished the setup of the calculation and we are ready to
run it:

   **1.** Select **File → Save As** and give it an appropriate name (e.g. "Co8_BH")
   **2.** Select **File → Run**
   **3.** Wait for the calculation to finish (this should take a few seconds)

We can visualize the explored energy landscape by using AMSmovie:

   **1.** Select **SCM → Movie**
   **2.** In AMSmovie, make a double click on the Energy axis and change the units to eV (if it not yet eV). **Y Axis → Units: eV** then OK.
 [image]

With some luck, the lowest energy state should be at "-0.927817"
Hartree. If so, we have caught the global minimum successfully! You
can pass the mouse over a state to show the value of the relative
energy. The lowest relative energy should  be at 0 eV.

Basin Hopping optimization is a global optimization that uses random
perturbations to jump basins, and a local search algorithm to optimize
each basin. So, results may vary given the stochastic nature of the
algorithm or differences in numerical precision. Consider running the
example a few times and compare the outcomes.

For the next step, we will use the Co_8 global minimum. So, copy its
geometry and paste it into a new AMSinput.

   **1.** Make a right-click on the lowest energy state and select the option **Copy Geometry** from the popup menu.
   **2.** Start a new AMSinput **SCM → New Input**.
   **3.** Paste the geometry by using **Edit → Paste** or just press **ctrl+v**.


Growth Mechanism Co_8+Co → Co_9
===============================

Firstly, we need the geometry of the Co_8 global minimum obtained in
the previous section. In case you skipped the previous section, just
copy-paste the following coordinates into AMSinput.

   Co      -0.03403571       1.12611646      -2.08186475
   Co      -1.53717952       1.78357073      -0.30583453
   Co       1.68546231      -0.17156299       1.49980432
   Co      -0.01541891       1.59507948       1.61007493
   Co       0.67964989       2.82625193      -0.46130535
   Co       2.34451750       2.13563230       1.20356390
   Co      -0.20262505      -0.26260499      -0.06462506
   Co       1.99747005       0.71459565      -0.76811757

The new AMSinput window does not know yet that we want to perform PES
explorations with the ReaxFF engine. Let us quickly restore the engine
settings we have used for the Basin Hopping earlier:

   **1.** In AMSinput, select the ReaxFF panel: [image: ADFPanel][image] **→** [image: ReaxFFPanel][image].
   **2.** Select the **Task → PES Exploration**.
   **3.** Select the **Force field → Co.ff**.
   **4.** Make sure **Periodicity** is set to **None**.

Using the drawing tools of AMSinput, add a new Co atom roughly on the
cluster's surface. Then, use the **Pre-optimize** button to get the
closest local minimum, making sure that only the new atom is selected,
and only that selection is optimized; we would like to keep the
structure of the Co_8 intact. Again, the initial structure is not
important, but more iterations may be needed to get the same results.
We suggest starting with the following coordinates to improve
reproducibility. But, we invite you to use the first option to compare
times and outcomes.

   Co      -0.03403571       1.12611646      -2.08186475
   Co      -1.53717952       1.78357073      -0.30583453
   Co       1.68546231      -0.17156299       1.49980432
   Co      -0.01541891       1.59507948       1.61007493
   Co       0.67964989       2.82625193      -0.46130535
   Co       2.34451749       2.13563230       1.20356390
   Co      -0.20262505      -0.26260499      -0.06462506
   Co       1.99747005       0.71459565      -0.76811757
   Co       3.01465991       2.87039628      -0.97767612

First, we would like to define two regions: 1) **adsorbate**,
corresponding to the added atom, and 2) **cluster**, corresponding to
the Co_8 global minimum. Then, we use the defined **cluster** region
to fix the coordinates of the Co_8.

   **1.** Use the panel bar **Model → Regions** command
   **2.** Select the added atom
   **3.** Click on the **'+'** button to add a new region
   **4.** Change the name **Region_1** into **adsorbate**
   **5.** Select the Co_8 atoms (**Select → Invert Selection**)
   **6.** Click on the **'+'** button to add a new region
   **7.** Change the name **Region_2** into **cluster**
   **8.** Use the panel bar **Model → Geometry Constraints and PES Scan** command
   **9.** Make sure at least one atom from the **cluster** region is selected
   **10.** Click on the **'+' cluster (fixed position)** button to to fix the coordinates of the Co_8
 [image]

In this step, we are interested in exploring all possible processes in
which the added atom may be involved. Here, we will use the Process
Search subtask for this aim. To clarify, we refer to processes as
paths that connect local minima through saddle points (transition
states). The subtask Process Search will start in the proposed local
minimum and try to find a nearby saddle point starting from a random
displacement of the added atom. If a saddle point is found, it will
perform a geometry optimization pushing the atom to the other side of
the saddle point to find the new local minimum to which the original
state is connected. This process is repeated several times, starting
from all the local minima discovered so far.

Once the energy landscape is obtained, we will also ask to calculate
the associated binding-sites lattice. Binding sites are defined as the
atoms' position from the "adsorbate" region which are neighbors of the
atoms in the region "cluster" and associated with a local minimum
configuration in the energy landscape. Additionally, two binding sites
are considered connected if the following two requirements are met: 1)
there is a transition state connecting two local minima associated to
these binding sites (notice that there may be multiple local minima
associated with the same binding site), and 2) there is at least an
atom (from the "adsorbate" region) that changes its position from the
first binding site to the second one mediated by the same transition
state described above. In this process, AMS will align as much as
possible all local minima and transition states to the input file's
structure but ignoring the atoms in the region "adsorbate" trying to
establish a common reference frame. If the structure of the region
"cluster" changes significantly for different configurations, the
binding sites may not be well defined. For this example, we have
frozen the Co_8 cluster region, which guarantees that we will not have
that issue.

To setup the Process Search calculation, follow these steps:

   **1.** Go to the **Model → PES Exploration** panel.
   **2.** On the **PES Exploration** page, select **Job → Process Search**.
   **4.** Set **Num expeditions** to "100".
   **5.** Set **Num explorers** to "4".

   **6.** Click on [image: MoreBtn][image] next to the **Structure Comparison**
   **7.** On the **PES Exploration Structure Comparison** page, set **Neighbors cutoff** to "5.0" Å

   **8.** Go to **Details → PES Exploration... → PES Exploration Binding sites calculation**
   **9.** On the **PES Exploration Binding sites calculation** page, select "cluster" as the **Reference region**
   **10.** Enable the calculation of the binding sites by selecting the option **Calculate** under the **Binding Sites** section.
   **11.** Set **Distance difference** to "0.5" Å.
 [image][image][image]

We have now finished the setup of the calculation and we are ready to
run it:

   **1.** Select **File → Save As** and give it an appropriate name (e.g. "Co8+Co_PS")
   **2.** Select **File → Run**
   **3.** Wait for the calculation to finish (this should take a few minutes). Click Yes when asked to load the binding sites in AMSinput.

In the AMSinput, we will see the binding-sites lattice superimposed to
the cluster's initial geometry:

[image]

Notice that the added atom is located over one of the binding sites.
The symbols used to represent the binding sites are related to the
number of atom neighbors (within a 5 Å of distance, see above
Neighbors cutoff option) and the colors with the average energy of the
contributing states. In our case, because there is only one type of
neighborhood, there is only one symbol: triangles. These binding sites
have three neighbors in the first coordination shell and three
neighbors in the second. Because of this, the labels are "N33".
Regarding their color, we have two groups: 1) Red for the most stable
adsorption-sites with the energy of around "-1.0333 Hartree", and 2)
Blue for the rest of the binding sites with the energy of "-1.0321
Hartree". These details can be seen from the panel **Details → PES
Exploration Binding Sites**:

[image]

We can visualize the explored energy landscape by using AMSmovie:

   **1.** In the AMSJobs window, select the job and click **SCM → Movie**
   **2.** In AMSmovie, double-click the Energy axis and change the units, e.g., to eV. **Y Axis → Units: eV** then OK.
 [image]

You should get a graphical representation of the states discovered
during the searching in the right panel. Minima are shown with a black
level, while transition states are shown using a red level. You can
move around the different states by clicking on them. The selected
state is shown on the left panel to appreciate details.

As a final comment, due to the stochastic nature of the algorithm
and/or differences in numerical precision, you can get different
results for the energy landscape exploration. In our example,
particularly, we have chosen "100" for **Num expeditions** to
guarantee that you can get the full set of critical points; 12 local
minima and 12 transition states.

Note:

  You can see the vibrational spectrum of any state by using right-
  click on it and then selecting **Open in module → Spectra** in the
  popup window. For the present calculation, only the frequencies of
  the modes related to the unconstrained atoms are available.

Note:

  You can remove any state by using right-click on it and then
  selecting **Delete level** in the popup window.

In the Figure below, we show the number of configurations obtained by
20 different runs as the number of expeditions increase. Notice that
at least "100" expeditions are required to guarantee you get the 24
configurations.

[image]
