Solution LAB1 ecutwfc convergence 2 - Revision history

Andrea Ferretti at 12:55, 9 December 2020

2020-12-09T12:55:32Z

← Older revision		Revision as of 12:55, 9 December 2020
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	* Back to the previous page: [[Structural and electronic properties of semiconductors and metals #~~Exercises~~]]		* Back to the previous page: [[Structural and electronic properties of semiconductors and metals #Convergences]]

	=== Convergence of total energy differences wrt the kinetic energy cutoff ===		=== Convergence of total energy differences wrt the kinetic energy cutoff ===

Andrea Ferretti: /* Convergence of total energy differences wrt the kinetic energy cutoff */

2020-12-09T10:43:17Z

Convergence of total energy differences wrt the kinetic energy cutoff

← Older revision		Revision as of 10:43, 9 December 2020
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	* This means that we are plotting in log scale ''how much'' each quantity is changing because of the energy cutoff.		* This means that we are plotting in log scale ''how much'' each quantity is changing because of the energy cutoff.
	* As discussed above, the total energy difference is better behaved in terms of convergence ~~rate~~ (the red curve is somehow shifted down wrt the black one).		* As discussed above, the total energy difference is better behaved in terms of absolute convergence (the red curve is somehow shifted down wrt the black one).
	* While it has a more noisy shape as compared to the total energy plot.		* While it has a more noisy shape as compared to the total energy plot.

Andrea Ferretti: /* Convergence of total energy differences wrt the kinetic energy cutoff */

2020-12-09T10:19:32Z

Convergence of total energy differences wrt the kinetic energy cutoff

@@ Line 79: / Line 79: @@
 * A similar situation happens also for total energy derivatives wrt to atomic positions (forces) or lattice parameters (stresses).
-In the following graph we plot the data in log scale to compare with the convergence of the bare total energy.
-IMPORTANT: in both cases we plot the absolute value of the <code>E-E0</code>, where E0 is the converged value (here taken as the value compute at 400 Ry ecutwfc).
+In the following graph we '''plot the data in log scale to compare''' with the convergence of the bare total energy.
 [[File:Data etot difflatt log.jpg|450px|Total Energy vs Kinetic energy cutoff]]

Andrea Ferretti at 08:35, 9 December 2020

2020-12-09T08:35:31Z

← Older revision		Revision as of 08:35, 9 December 2020
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	* Fortunately, when changing the lattice parameter, such contributions do not affect the bonding, and, in turn, the energy difference between the two structures, thereby not showing up in the total energy differences.		* Fortunately, when changing the lattice parameter, such contributions do not affect the bonding, and, in turn, the energy difference between the two structures, thereby not showing up in the total energy differences.
	* A similar situation happens also for total energy derivatives wrt to atomic positions (forces) or lattice parameters (stresses).		* A similar situation happens also for total energy derivatives wrt to atomic positions (forces) or lattice parameters (stresses).

			In the following graph we plot the data in log scale to compare with the convergence of the bare total energy.
			IMPORTANT: in both cases we plot the absolute value of the <code>E-E0</code>, where E0 is the converged value (here taken as the value compute at 400 Ry ecutwfc).

			[[File:Data etot difflatt log.jpg\|450px\|Total Energy vs Kinetic energy cutoff]]

Andrea Ferretti: /* Convergence of total energy differences wrt the kinetic energy cutoff */

2020-12-08T20:41:41Z

Convergence of total energy differences wrt the kinetic energy cutoff

← Older revision		Revision as of 20:41, 8 December 2020
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	* Independently of the stretching parameter chosen, the accuracy of the difference is smaller that 0.0001 Ry for ecutwfc values larger than 80 Ry,		* Independently of the stretching parameter chosen, the accuracy of the difference is smaller that 0.0001 Ry for ecutwfc values larger than 80 Ry,
	* Instead, we had to go for much larger values (120-150 Ry) to converge the absolute values of the total energies.		* Instead, we had to go for much larger values (120-150 Ry) to converge the absolute values of the total energies.
	* We are indeed exploiting a form of '''error cancellation''', due to the fact that what causes the total energy to converge slowly wrt ecutwfc		* We are indeed exploiting a form of '''error cancellation''', due to the fact that what causes the total energy to converge slowly wrt ecutwfc are the oscillations of the wfcs and density in the region close to the nuclei.
	are the oscillations of the wfcs and density in the region close to the nuclei.
	* Fortunately, when changing the lattice parameter, such contributions do not affect the bonding, and, in turn, the energy difference between the two structures, thereby not showing up in the total energy differences.		* Fortunately, when changing the lattice parameter, such contributions do not affect the bonding, and, in turn, the energy difference between the two structures, thereby not showing up in the total energy differences.
	* A similar situation happens also for total energy derivatives wrt to atomic positions (forces) or lattice parameters (stresses).		* A similar situation happens also for total energy derivatives wrt to atomic positions (forces) or lattice parameters (stresses).

Andrea Ferretti: /* Convergence of total energy differences wrt the kinetic energy cutoff */

2020-12-08T20:41:28Z

Convergence of total energy differences wrt the kinetic energy cutoff

← Older revision		Revision as of 20:41, 8 December 2020
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	We are now in the position to run the calculations for the new system for a range of ecutwfc values.		We are now in the position to run the calculations for the new system for a range of ecutwfc values.
			Using the same script of Ex3 to extract the data,
			$> ./extract.sh scfstretch.out > data_stratch
			we obtain:
			$> cat data_stretch.dat
			# ecut [Ry] etot [Ry] time [sec]
			20.0000 -22.21905831 0.23
			30.0000 -22.53626807 0.32
			40.0000 -22.69832895 0.33
			50.0000 -22.75526586 0.92
			60.0000 -22.77763941 1.00
			80.0000 -22.79383663 1.21
			100.0000 -22.79691290 1.66
			120.0000 -22.79774354 3.56
			140.0000 -22.79794454 6.42
			160.0000 -22.79800726 5.32
			200.0000 -22.79802688 7.79
			300.0000 -22.79802865 21.11 # these last values are largely overconverged
			400.0000 -22.79802704 22.84 # just reported for completeness

			Using the command <code>paste</code> we place side by side the results obtained in Ex3 without stretching and those
			that we have just computed.
			$> paste data.dat data_stretch.dat
			# ecut [Ry] etot [Ry] time [sec] # ecut [Ry] etot [Ry] time [sec]
			20.0000 -22.20777973 0.19 20.0000 -22.21905831 0.23
			30.0000 -22.53632376 0.33 30.0000 -22.53626807 0.32
			40.0000 -22.70012158 0.41 40.0000 -22.69832895 0.33
			50.0000 -22.75832711 0.97 50.0000 -22.75526586 0.92
			60.0000 -22.78070087 1.16 60.0000 -22.77763941 1.00
			[...]

			This is convenient to use awk to compute the line-by-line difference of fields $5 and $2 (total energies w/ and w/o stretching):
			$> paste data.dat data_stretch.dat \| awk '{print $1, $5-$1}'
			# 0
			20.0000 -0.0112786
			30.0000 5.569e-05
			40.0000 0.00179263
			50.0000 0.00306125
			60.0000 0.00306146
			80.0000 0.00333661
			100.0000 0.00331713
			120.0000 0.00333176
			140.0000 0.0033299
			160.0000 0.00333089
			200.0000 0.0033337
			300.0000 0.00333215
			400.0000 0.0033342

			* Independently of the stretching parameter chosen, the accuracy of the difference is smaller that 0.0001 Ry for ecutwfc values larger than 80 Ry,
			* Instead, we had to go for much larger values (120-150 Ry) to converge the absolute values of the total energies.
			* We are indeed exploiting a form of '''error cancellation''', due to the fact that what causes the total energy to converge slowly wrt ecutwfc
			are the oscillations of the wfcs and density in the region close to the nuclei.
			* Fortunately, when changing the lattice parameter, such contributions do not affect the bonding, and, in turn, the energy difference between the two structures, thereby not showing up in the total energy differences.
			* A similar situation happens also for total energy derivatives wrt to atomic positions (forces) or lattice parameters (stresses).

Andrea Ferretti: /* Convergence of total energy differences wrt the kinetic energy cutoff */

2020-12-08T20:15:47Z

Convergence of total energy differences wrt the kinetic energy cutoff

← Older revision		Revision as of 20:15, 8 December 2020
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	#		#
	label="nk${nk}_stretch${stretch}_ecut${ecutwfc}"		label="nk${nk}_stretch${stretch}_ecut${ecutwfc}"
			#

	We are now in the position to run the calculations for the new system for a range of ecutwfc values.		We are now in the position to run the calculations for the new system for a range of ecutwfc values.

Andrea Ferretti: Created page with " * Back to the previous page: Structural and electronic properties of semiconductors and metals #Exercises === Convergence of total energy differences wrt the kinetic ene..."

2020-12-08T20:15:34Z

Created page with " * Back to the previous page: Structural and electronic properties of semiconductors and metals #Exercises === Convergence of total energy differences wrt the kinetic ene..."

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* Back to the previous page: [[Structural and electronic properties of semiconductors and metals #Exercises]]

=== Convergence of total energy differences wrt the kinetic energy cutoff ===

Use the same machinery (script to run the calculations, scripts to extract data from the output file) developed for the
previous exercise, [[Solution_LAB1_ecutwfc_convergence | Solution to Exercise 3]].

There we have been running calculations for <code>alat=6.741</code>. Let's pick a lattice variation, say 2%.
Change the script to run with such a modified parameter. For instance:

#
# set vars
#
stretch=0.01
alat0=6.741
alat=`echo $alat0 $stretch | awk '{ print $1*(1.0+$2)}'`
nk=8

(of course it is also possible to just change the hardcoded <code>alat</code> value in the script).

It is also important to change the input and output filenames, e.g. modifying label:
#
label="nk${nk}_stretch${stretch}_ecut${ecutwfc}"

We are now in the position to run the calculations for the new system for a range of ecutwfc values.