Simulating icosahedral gold clusters - Revision history

Miguel Caro: /* Computing the equilibrium lattice parameter of the reference structure */

2022-05-01T10:43:10Z

Computing the equilibrium lattice parameter of the reference structure

Miguel Caro: /* Setting up the gold cluster */

2022-05-01T10:41:11Z

Setting up the gold cluster

Miguel Caro: /* Setting up the gold cluster */

2022-04-01T07:08:29Z

Setting up the gold cluster

Miguel Caro: /* Setting up the gold cluster */

2022-04-01T06:09:48Z

Setting up the gold cluster

Miguel Caro: /* Setting up the gold cluster */

2022-04-01T06:08:07Z

Setting up the gold cluster

Miguel Caro at 06:06, 1 April 2022

2022-04-01T06:06:59Z

Miguel Caro: /* Computing the equilibrium lattice parameter of the reference structure */

2022-04-01T05:45:24Z

Computing the equilibrium lattice parameter of the reference structure

Miguel Caro: /* Computing the equilibrium lattice parameter of the reference structure */

2022-04-01T05:42:43Z

Computing the equilibrium lattice parameter of the reference structure

Miguel Caro at 05:35, 1 April 2022

2022-04-01T05:35:18Z

Miguel Caro: Created page with "In this tutorial we are going to use a GAP to optimize the structure of an icosahedral gold cluster and estimate its formation energy. In this tutorial we will make use of sta..."

2022-04-01T05:29:09Z

Created page with "In this tutorial we are going to use a GAP to optimize the structure of an icosahedral gold cluster and estimate its formation energy. In this tutorial we will make use of sta..."

New page

In this tutorial we are going to use a GAP to optimize the structure of an icosahedral gold cluster and estimate its formation energy. In this tutorial we will make use of static (single-point) calculations ([[turbogap predict]]) and [[geometry optimization]].

== Prerequisites for this tutorial ==

* A '''TurboGAP''' installation
* An [https://wiki.fysik.dtu.dk/ase/ ASE] installation
* Numpy
* A utility that can perform simple least-squares regression (I will use gnuplot, which lets me plot the fit at the same time)

== Computing the equilibrium lattice parameter of the reference structure ==

The thermodynamically stable crystal structure of gold is fcc. When we compute the formation energy of a gold nanocluster we will be referring its energy per atom to that of the fcc structure. Therefore, the first step in this tutorial is to find out the lattice parameter of fcc gold by computing the energy vs lattice parameter curve, and finding the minimum.

@@ Line 69: / Line 69: @@
   plot "e.dat" w l t "Data", a+b*x+c*x**2 t "Fit"
-I get <math>a_\text{opt} = 4.1536 \text{\AA}</math> and <math>E_\text{opt} = -3.0448 \text{eV}</math>, and the plot looks like this:
+I get <math>a_\text{opt} = 4.1536 \text{Å}</math> and <math>E_\text{opt} = -3.0448 \text{eV}</math>, and the plot looks like this:
 [[File:tutorial4_01.png|center|480px|]]

@@ Line 75: / Line 75: @@
 == Setting up the gold cluster ==
-Now that we now what is the reference fcc lattice parameter and its energy, let's construct an icosahedral gold cluster and relax it. We use ASE for constructing the cluster. ASE has a lot of useful functions for constructing clusters, surfaces and other common atomic structures:
+Now that we know what is the reference fcc lattice parameter and its energy, let's construct an icosahedral gold cluster and relax it. We use ASE for constructing the cluster. ASE has a lot of useful functions for constructing clusters, surfaces and other common atomic structures:
 <syntaxhighlight lang="python" line="line">

← Older revision		Revision as of 07:08, 1 April 2022
Line 109:		Line 109:
	mpirun -np 4 turbogap md		mpirun -np 4 turbogap md

−	In the <code>trajectory_out.xyz</code> file we can find the energy for this structure. I get <math>E = -~~4011~~.~~771073~~ \,\text{eV}</math> for <math>N = 1415</math> atoms. Therefore, the cohesive energy per atom is <math>e = -~~4011~~.~~771073~~/1415 \,\text{eV} + 3.0448 \,\text{eV} = 0.~~210~~ \,\text{eV}</math> versus fcc.	+	In the <code>trajectory_out.xyz</code> file we can find the energy for this structure. Check the energy of the relaxed cluster, i.e., the last frame in the trajectory file. I get <math>E = -4085.948634 \,\text{eV}</math> for <math>N = 1415</math> atoms. Therefore, the cohesive energy per atom is <math>e = -4085.948634/1415 \,\text{eV} + 3.0448 \,\text{eV} = 0.157 \,\text{eV}</math> versus fcc.

← Older revision		Revision as of 06:09, 1 April 2022
Line 109:		Line 109:
	mpirun -np 4 turbogap md		mpirun -np 4 turbogap md

−	In the <code>trajectory_out.xyz</code> file we can find the energy for this structure. I get <math>E = -4011.771073 \text{~eV}</math> for <math>N = 1415</math> atoms. Therefore, the cohesive energy per atom is <math>e = -4011.771073/1415 \text{~eV} + 3.0448 \text{~eV} = 0.210 \text{~eV}</math> versus fcc.	+	In the <code>trajectory_out.xyz</code> file we can find the energy for this structure. I get <math>E = -4011.771073 \,\text{eV}</math> for <math>N = 1415</math> atoms. Therefore, the cohesive energy per atom is <math>e = -4011.771073/1415 \,\text{eV} + 3.0448 \,\text{eV} = 0.210 \,\text{eV}</math> versus fcc.

← Older revision		Revision as of 06:08, 1 April 2022
Line 109:		Line 109:
	mpirun -np 4 turbogap md		mpirun -np 4 turbogap md

−	In the <code>trajectory_out.xyz</code> file we can find the energy for this structure. I get <math>E = -4011.771073 eV</math> for <math>N = 1415</math> atoms. Therefore, the cohesive energy per atom is <math>e = -4011.771073/1415 \text{eV} + 3.0448 \text{eV} = 0.210 eV</math> versus fcc.	+	In the <code>trajectory_out.xyz</code> file we can find the energy for this structure. I get <math>E = -4011.771073 \text{~eV}</math> for <math>N = 1415</math> atoms. Therefore, the cohesive energy per atom is <math>e = -4011.771073/1415 \text{~eV} + 3.0448 \text{~eV} = 0.210 \text{~eV}</math> versus fcc.

@@ Line 1: / Line 1: @@
-In this tutorial we are going to use a GAP to optimize the structure of an icosahedral gold cluster and estimate its formation energy. In this tutorial we will make use of static (single-point) calculations ([[turbogap predict]]) and [[geometry optimization]].
+In this tutorial we are going to use a GAP to optimize the structure of an icosahedral gold cluster and estimate its formation energy. In this tutorial we will make use of static (single-point) calculations ([[Documentation#turbogap predict|turbogap predict]]) and [[geometry optimization]].
 == Prerequisites for this tutorial ==
@@ Line 64: / Line 64: @@
   fit[4.1:4.2] a+b*x+c*x**2 "e.dat" via a,b,c
-  opt=-b/2/c
+  opt=-b/2/c; E_opt = a+b*opt+c*opt**2
-  print opt # this will tell you the lattice parameter at the optimum
+  print opt, E_opt # this will tell you the lattice parameter at the optimum
   set xlabel "Lattice parameter (A)"; set ylabel "Energy (eV)"
   plot "e.dat" w l t "Data", a+b*x+c*x**2 t "Fit"
-I get <math>a_\text{opt} = 4.154 \text{\AA}</math> and the plot looks like this:
+I get <math>a_\text{opt} = 4.1536 \text{\AA}</math> and <math>E_\text{opt} = -3.0448 \text{eV}</math>, and the plot looks like this:
 [[File:tutorial4_01.png|center|480px|]]

← Older revision		Revision as of 05:45, 1 April 2022
Line 68:		Line 68:
	set xlabel "Lattice parameter (A)"; set ylabel "Energy (eV)"		set xlabel "Lattice parameter (A)"; set ylabel "Energy (eV)"
	plot "e.dat" w l t "Data", a+bx+cx**2 t "Fit"		plot "e.dat" w l t "Data", a+bx+cx**2 t "Fit"
		+
		+	I get <math>a_\text{opt} = 4.154 \text{\AA}</math> and the plot looks like this:
		+
		+	[[File:tutorial4_01.png\|center\|480px\|]]

← Older revision		Revision as of 05:42, 1 April 2022
Line 40:		Line 40:
	species = Au		species = Au
	n_species = 1		n_species = 1
		+
		+	and run '''Turbogap''' in single-point mode:
		+
		+	mpirun -np turbogap predict
		+
		+	From the resulting <code>trajectory_out.xyz</code> we retrive the lattice parameters and energies with the following script:
		+
		+	<syntaxhighlight lang="python" line="line">
		+	from ase.io import read
		+	db = read("trajectory_out.xyz", index=":")
		+	f = open("e.dat", "w+")
		+	for atoms in db:
		+	e = atoms.info["energy"]
		+	a = atoms.get_cell()[0][1]*2
		+	print(a, e, file=f)
		+	</syntaxhighlight>
		+
		+	Run it an save the results to a file (I save the Python script to a file called <code>extract_energy.py</code> here:
		+
		+	python3 extract_energy.py > e.dat
		+
		+	We can open this file in gnuplot and use gnuplot's fitting capabilities to fit a second order polynomial to the data (I restrict the fitting domain to [4.1:4.2] to get a better fit):
		+
		+	fit[4.1:4.2] a+bx+cx**2 "e.dat" via a,b,c
		+	opt=-b/2/c
		+	print opt # this will tell you the lattice parameter at the optimum
		+	set xlabel "Lattice parameter (A)"; set ylabel "Energy (eV)"
		+	plot "e.dat" w l t "Data", a+bx+cx**2 t "Fit"

← Older revision		Revision as of 05:35, 1 April 2022
Line 11:		Line 11:

	The thermodynamically stable crystal structure of gold is fcc. When we compute the formation energy of a gold nanocluster we will be referring its energy per atom to that of the fcc structure. Therefore, the first step in this tutorial is to find out the lattice parameter of fcc gold by computing the energy vs lattice parameter curve, and finding the minimum.		The thermodynamically stable crystal structure of gold is fcc. When we compute the formation energy of a gold nanocluster we will be referring its energy per atom to that of the fcc structure. Therefore, the first step in this tutorial is to find out the lattice parameter of fcc gold by computing the energy vs lattice parameter curve, and finding the minimum.
		+
		+	This script will generate a series of Au fcc structures with lattice parameter between 3.8 and 4.3 Angstrom:
		+
		+	<syntaxhighlight lang="python" line="line">
		+	from ase.io import write
		+	from ase import Atoms
		+	import numpy as np
		+
		+	append = False
		+	for a in np.arange(3.8,4.3,0.01):
		+	atoms = Atoms("Au", positions=[[0,0,0]], cell=[[0,a/2,a/2],[a/2,0,a/2],[a/2,a/2,0]], pbc=True)
		+	write("fcc.xyz", atoms, append=append)
		+	append = True
		+	</syntaxhighlight>
		+
		+	We now have the <code>fcc.xyz</code> file containing all of these structures. Next, we retrieve the Au GAP potential from Zenodo:
		+
		+	<syntaxhighlight lang="bash" line="line">
		+	wget https://zenodo.org/record/6302852/files/gap_files.tar.gz
		+	tar -xvf gap_files.tar.gz
		+	</syntaxhighlight>
		+
		+	The following step is to set up an <code>input</code> file:
		+
		+	atoms_file = "fcc.xyz"
		+	pot_file = "gap_files/aurum.gap"
		+
		+	species = Au
		+	n_species = 1