Bethe-Salpeter equation tutorial. Optical absorption (BN) - Revision history

Fulvio: /* Coulomb truncation convergence */

2024-04-17T14:25:03Z

Coulomb truncation convergence

← Older revision		Revision as of 14:25, 17 April 2024
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	To analyze the data we will plot the dielectric screening and check how the different values of the screening change the absorption spectra.		To analyze the data we will plot the dielectric screening and check how the different values of the screening change the absorption spectra.
	In the folder <code>tutorials/bn/</code> you find the python script <code>~~bse_cutoff~~.py</code>. This script takes some time to be executed, you can run both variants without the cutoff and with the cutoff <code>-c</code> simultaneously to save time. You can run this script with:		In the folder <code>tutorials/bn/</code> you find the python script <code>bse_cutoff_bn.py</code>. This script takes some time to be executed, you can run both variants without the cutoff and with the cutoff <code>-c</code> simultaneously to save time. You can run this script with:

	python ~~bse_cutoff~~.py -r -t4 # without coulomb cutoff		python bse_cutoff_bn.py -r -t4 # without coulomb cutoff
	python ~~bse_cutoff~~.py -r -c -t4 # with coulomb cutoff		python bse_cutoff_bn.py -r -c -t4 # with coulomb cutoff
	where <code>-t</code> specifies the number of MPI threads to use. The main loop changes the <code>layer_separation</code> variable using values from a list in the header of the file. In the script you can find how the functions <code>scf</code>, <code>ncf</code> and <code>database</code> are defined.		where <code>-t</code> specifies the number of MPI threads to use. The main loop changes the <code>layer_separation</code> variable using values from a list in the header of the file. In the script you can find how the functions <code>scf</code>, <code>ncf</code> and <code>database</code> are defined.

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	You can also plot how the absorption spectra changes with the cutoff using:		You can also plot how the absorption spectra changes with the cutoff using:

	python ~~bse_cutoff~~.py -p		python bse_cutoff_bn.py -p
	python ~~bse_cutoff~~.py -p -c		python bse_cutoff_bn.py -p -c

	[[File:Bn bse cutoff.png\|bn bse cutoff]]		[[File:Bn bse cutoff.png\|bn bse cutoff]]

Fulvio: /* Excitonic wavefunctions in reciprocal space */

2022-03-31T14:26:16Z

Excitonic wavefunctions in reciprocal space

← Older revision		Revision as of 14:26, 31 March 2022
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	To run the BSE calculation do:		To run the BSE calculation do:

	~~<source lang="bash">~~python bse_bn.py -r~~</source>~~		python bse_bn.py -r
	Alternatively, you can run ~~<source lang="bash">~~ python bse_bn.py -r -c ~~</source>~~ to add the Coulomb cutoff.		Alternatively, you can run
			python bse_bn.py -r -c
			to add the Coulomb cutoff.

	Then, the absorption spectrum is readily plotted by running the auxiliary script		Then, the absorption spectrum is readily plotted by running the auxiliary script
	~~<source lang="bash">~~		python plot-bse.py
	python plot-bse.py
	~~</source>~~

	[[File:bse_abs_plt.png\|Yambo tutorial image]]		[[File:bse_abs_plt.png\|Yambo tutorial image]]

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	In order to proceed we will use the script <code>plot-excitondb.py</code>.		In order to proceed we will use the script <code>plot-excitondb.py</code>.
	After running it as		After running it as
	~~<source lang="bash">~~
	python plot-excitondb.py		python plot-excitondb.py
	~~</source>~~
	it will produce three plots.		it will produce three plots.

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	You can obtain plots for different excitonic states by changing the line		You can obtain plots for different excitonic states by changing the line
	~~<source lang=python>~~
	# List of states to be merged		# List of states to be merged
	states = [1,2]		states = [1,2]
	~~</source>~~

	in <code>plot-excitondb.py</code>.		in <code>plot-excitondb.py</code>.

	You may also want to test the script with a more converged calculation: to this end you can increase the number of kpoints in the nscf calculation by going to <code>gs_bn.py</code> and changing the line		You may also want to test the script with a more converged calculation: to this end you can increase the number of kpoints in the nscf calculation by going to <code>gs_bn.py</code> and changing the line
	~~<source lang=python>~~
	kpoints_nscf = [6,6,1]		kpoints_nscf = [6,6,1]
	~~</source>~~
	to your liking (for example to <code>12x12x1</code>).		to your liking (for example to <code>12x12x1</code>).

	Then, run again the following commands (nscf calculation, regeneration of yambo database, new BSE calculation).		Then, run again the following commands (nscf calculation, regeneration of yambo database, new BSE calculation).
	~~<source lang=bash>~~
	python gs_bn.py -n		python gs_bn.py -n
	rm -r database		rm -r database
	python bse_bn.py -r -t 4		python bse_bn.py -r -t 4
	~~</source>~~
	As for the plotting, you may want to increase the value of <code>lpratio</code> in <code>plot-excitondb.py</code> to ensure that the interpolation works, as well as reduce the value of <code>scale</code> for a nicer plot in the hexagonal BN.		As for the plotting, you may want to increase the value of <code>lpratio</code> in <code>plot-excitondb.py</code> to ensure that the interpolation works, as well as reduce the value of <code>scale</code> for a nicer plot in the hexagonal BN.
	The lines to be changed are		The lines to be changed are
	~~<source lang=python>~~
	exc_bands_inter = yexc.interpolate(save,path,states,lpratio=5,f=None,size=0.5,verbose=True)		exc_bands_inter = yexc.interpolate(save,path,states,lpratio=5,f=None,size=0.5,verbose=True)
	~~</source>~~
	and		and
	~~<source lang=python>~~
	yexc.plot_exciton_2D_ax(ax,states,mode='hexagon',limfactor=0.8,scale=160)		yexc.plot_exciton_2D_ax(ax,states,mode='hexagon',limfactor=0.8,scale=160)
	~~</source>~~
	Then, you can run <code>plot-excitondb.py</code> again.		Then, you can run <code>plot-excitondb.py</code> again.

Fulvio: /* Coulomb truncation convergence */

2022-03-31T14:24:11Z

Coulomb truncation convergence

Fulvio: /* BSE convergence of optical spectra */

2022-03-31T14:23:11Z

BSE convergence of optical spectra

← Older revision		Revision as of 14:23, 31 March 2022
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	We create a dictionary with different values for each variable. The python script (<code>bse_conv_bn.py</code>) will then create a reference input file with the first value in each parameter's list. It will then create input files with the other parameters changing independently according to the values specified on the list:		We create a dictionary with different values for each variable. The python script (<code>bse_conv_bn.py</code>) will then create a reference input file with the first value in each parameter's list. It will then create input files with the other parameters changing independently according to the values specified on the list:

	~~<source lang="python">~~#list of variables to optimize the dielectric screening		#list of variables to optimize the dielectric screening
	conv = { 'FFTGvecs': [[10,10,15,20,30],'Ry'],		conv = { 'FFTGvecs': [[10,10,15,20,30],'Ry'],
	'NGsBlkXs': [[1,1,2,3,5,6], 'Ry'],		'NGsBlkXs': [[1,1,2,3,5,6], 'Ry'],
	'BndsRnXs': [[1,10],[1,10],[1,20],[1,30],[1,40]] }~~</source>.~~		'BndsRnXs': [[1,10],[1,10],[1,20],[1,30],[1,40]] }

	To run a calculation for each of the variables in the dictionary, we first define the <code>run</code> function		To run a calculation for each of the variables in the dictionary, we first define the <code>run</code> function

	~~<source lang="python">~~
	def run(filename):		def run(filename):
	"""		"""
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	if not os.path.isfile("%s/%s/done"%(folder,path)):		if not os.path.isfile("%s/%s/done"%(folder,path)):
	shell.run()		shell.run()
	~~</source>~~
	which together with the optimize function in the class <code>YamboIn</code>,		which together with the optimize function in the class <code>YamboIn</code>,
	~~<source lang="python">~~y.optimize(conv,folder='bse_conv',run=run,ref_run=False)~~</source>~~		y.optimize(conv,folder='bse_conv',run=run,ref_run=False)
	will run and manage the calculations as defined in the dictionary. All calculation files and outputs will be in their respective directories inside the folder <code>bse_conv</code>.		will run and manage the calculations as defined in the dictionary. All calculation files and outputs will be in their respective directories inside the folder <code>bse_conv</code>.

	To check which options are available in the script <code>bse_conv_bn.py</code>, run		To check which options are available in the script <code>bse_conv_bn.py</code>, run
	~~<source>~~$ python bse_conv_bn.py~~</source>~~		$ python bse_conv_bn.py
	which will give you the following list:		which will give you the following list:
	~~<source>~~
	~~usage: bse_conv_bn.py [-h] [-r] [-a] [-p] [-e] [-b] [-u] [-t THREADS]~~

	~~Test the yambopy script.~~

	optional arguments:		usage: bse_conv_bn.py [-h] [-r] [-a] [-p] [-e] [-b] [-u] [-t THREADS]
	-h, --help show this help message and exit
	-r, --run run BSE convergence calculation		Test the yambopy script.
	-a, --analyse analyse results data
	-p, --plot plot the results		optional arguments:
	-e, --epsilon converge epsilon parameters		-h, --help show this help message and exit
	-b, --bse converge bse parameters		-r, --run run BSE convergence calculation
	-u, --nohup run the commands with nohup		-a, --analyse analyse results data
	-t THREADS, --threads THREADS		-p, --plot plot the results
	number of threads to use		-e, --epsilon converge epsilon parameters
	~~</source>~~		-b, --bse converge bse parameters
			-u, --nohup run the commands with nohup
			-t THREADS, --threads THREADS
			number of threads to use

	So, in order to converge the screening, you will need to run		So, in order to converge the screening, you will need to run

	~~<source lang="bash">~~$ python bse_conv_bn.py -r -e~~</source>~~		$ python bse_conv_bn.py -r -e

	By default we have set up the total number of threads to be equal to 2. If you have access to more, you can change this using the <code>-t</code> option shown on the list, followed by the number of threads you want to use.		By default we have set up the total number of threads to be equal to 2. If you have access to more, you can change this using the <code>-t</code> option shown on the list, followed by the number of threads you want to use.
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	As you can see, the python script is running all the calculations changing the value of the input variables. You are free to open the <code>bse_conv_bn.py</code> file and modify it according to your own needs. Using the optimal parameters, you can run a calculation and save the dielectric screening databases <code>ndb.em1s*</code> to re-use them in the subsequent calculations. For that you can copy these files to the SAVE folder. <code>yambo</code> will only re-calculate any database if it does not find it or some parameter has changed.		As you can see, the python script is running all the calculations changing the value of the input variables. You are free to open the <code>bse_conv_bn.py</code> file and modify it according to your own needs. Using the optimal parameters, you can run a calculation and save the dielectric screening databases <code>ndb.em1s*</code> to re-use them in the subsequent calculations. For that you can copy these files to the SAVE folder. <code>yambo</code> will only re-calculate any database if it does not find it or some parameter has changed.

	Once the calculations are done you can plot resulting optical spectra by running ~~<source>~~$ python bse_conv_bn.py -a~~</source>~~ followed by ~~<source>~~$ python bse_conv_bn.py -p -e~~</source>.~~ It will search the folder <code>bse_conv</code> for all calculations you performed previously and plot the results, using the class <code>YamboAnalyser</code> class.		Once the calculations are done you can plot resulting optical spectra by running
			$ python bse_conv_bn.py -a
			followed by
			$ python bse_conv_bn.py -p -e
			It will search the folder <code>bse_conv</code> for all calculations you performed previously and plot the results, using the class <code>YamboAnalyser</code> class.

	[[File:Bse-hbn-conv-2.png\|x750px\|Yambo tutorial image]]		[[File:Bse-hbn-conv-2.png\|x750px\|Yambo tutorial image]]

	Alternatively, you can obtain the same plots by running the the following script: ~~<source>~~$ python plot-bse-conv.py ~~</source>~~		Alternatively, you can obtain the same plots by running the the following script:
			$ python plot-bse-conv.py
	If you want to, you can now add new entries to the lists in the dictionary, specially the <code>BndsRnXs</code>, which usually requires a lot of bands to achieve convergence. Keep its number less than or equal to the number of bands in the nscf calculation, re-run the script and plot the results again. You can also test if some variables can converge with smaller values than the ones you used up to now.		If you want to, you can now add new entries to the lists in the dictionary, specially the <code>BndsRnXs</code>, which usually requires a lot of bands to achieve convergence. Keep its number less than or equal to the number of bands in the nscf calculation, re-run the script and plot the results again. You can also test if some variables can converge with smaller values than the ones you used up to now.

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	The dictionary of convergence in this case is:		The dictionary of convergence in this case is:

	~~<source lang="python">~~#list of variables to optimize the BSE		#list of variables to optimize the BSE
	conv = { 'BSEEhEny': [[[1,10],[1,10],[1,12],[1,14]],'eV'],		conv = { 'BSEEhEny': [[[1,10],[1,10],[1,12],[1,14]],'eV'],
	'BSENGBlk': [[0,0,1,2], 'Ry'],		'BSENGBlk': [[0,0,1,2], 'Ry'],
	'BSENGexx': [[10,10,15,20],'Ry']}		'BSENGexx': [[10,10,15,20],'Ry']}
	~~</source>~~

	All these variables do not change the dielectric screening, so optionally you can calculate it once (using the previous section to determine converged parameters) and put the database in the <code>SAVE</code> folder to make the calculations faster. Otherwise the dielectric screening will be computed for each run (in the case of this tutorial, this is still quite fast). This is a slightly advanced use of <code>yambo</code>, so it is better to leave till you are more familiar with the code and its flow.		All these variables do not change the dielectric screening, so optionally you can calculate it once (using the previous section to determine converged parameters) and put the database in the <code>SAVE</code> folder to make the calculations faster. Otherwise the dielectric screening will be computed for each run (in the case of this tutorial, this is still quite fast). This is a slightly advanced use of <code>yambo</code>, so it is better to leave till you are more familiar with the code and its flow.
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	To run the convergence calculations for the BSE Hamiltonian write:		To run the convergence calculations for the BSE Hamiltonian write:

	~~<source lang="bash">~~$ python bse_conv_bn.py -r -b~~</source>~~		$ python bse_conv_bn.py -r -b
	Once the calculations are done you can plot the optical absorption spectra:		Once the calculations are done you can plot the optical absorption spectra:

	~~<source lang="bash">~~		$ python bse_conv_bn.py -a
	$ python bse_conv_bn.py -a		$ python bse_conv_bn.py -p -b
	$ python bse_conv_bn.py -p -b
	~~</source>~~

	[[File:Bse-hbn-conv-1.png\|x750px\|Yambo tutorial image]]		[[File:Bse-hbn-conv-1.png\|x750px\|Yambo tutorial image]]

Fulvio at 14:20, 31 March 2022

2022-03-31T14:20:34Z

← Older revision		Revision as of 14:20, 31 March 2022
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	Before you start this tutorial, make sure you have run the scf and nscf runs. If you have not, you can calculate the relax <code>-r</code>, scf <code>-s</code> and nscf <code>-n</code> using the <code>gs_bn.py</code> file:		Before you start this tutorial, make sure you have run the scf and nscf runs. If you have not, you can calculate the relax <code>-r</code>, scf <code>-s</code> and nscf <code>-n</code> using the <code>gs_bn.py</code> file:
			$ python gs_bn.py -r -s -n
	~~<source lang="bash">~~$ python gs_bn.py -r -s -n~~</source>~~
	Once that is over, you can start the tutorial.		Once that is over, you can start the tutorial.

Fulvio: /* Excitonic wavefunctions in reciprocal space */

2020-01-30T23:41:41Z

Excitonic wavefunctions in reciprocal space

← Older revision		Revision as of 23:41, 30 January 2020
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	kpoints_nscf = [6,6,1]		kpoints_nscf = [6,6,1]
	</source>		</source>
	to your liking (for example to <code>12x12x1<\code>).		to your liking (for example to <code>12x12x1</code>).

	Then, run again the following commands (nscf calculation, regeneration of yambo database, new BSE calculation).		Then, run again the following commands (nscf calculation, regeneration of yambo database, new BSE calculation).

Fulvio: /* Excitonic wavefunctions in reciprocal space */

2020-01-30T23:40:57Z

Excitonic wavefunctions in reciprocal space

← Older revision		Revision as of 23:40, 30 January 2020
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	kpoints_nscf = [6,6,1]		kpoints_nscf = [6,6,1]
	</source>		</source>
	to your liking (for example to 12x12x1).		to your liking (for example to <code>12x12x1<\code>).

	Then, run again the following commands (nscf calculation, regeneration of yambo database, new BSE calculation).		Then, run again the following commands (nscf calculation, regeneration of yambo database, new BSE calculation).

Fulvio at 23:28, 30 January 2020

2020-01-30T23:28:16Z

← Older revision		Revision as of 23:28, 30 January 2020
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	<code>FFTGvecs</code>: number of planewaves to include. Usually we need fewer planewaves than the total used in the self-consistent cycle that generated the ground state in the <code>scf</code> run. Reducing the total number of planewaves used diminishes the amount of memory per process that you are going to need.		<code>FFTGvecs</code>: number of planewaves to include. Usually we need fewer planewaves than the total used in the self-consistent cycle that generated the ground state in the <code>scf</code> run. Reducing the total number of planewaves used diminishes the amount of memory per process that you are going to need.

	<code>BndsRnXs</code>: number of bands to calculate the screening. Typically you need many more ~~bands~~ for the screening to converge.		<code>BndsRnXs</code>: number of bands to calculate the screening. Typically you need many bands (hundreds or even more) for the screening to converge.

	<code>NGsBlkXs</code>: number of components for the local fields. Averages the value of the dielectric screening over a number of periodic copies of the unit cell. This parameter ~~increases~~ greatly increases the cost of the calculation and thus should be increased slowly.		<code>NGsBlkXs</code>: number of components for the local fields. Averages the value of the dielectric screening over a number of periodic copies of the unit cell. This parameter greatly increases the computational cost of the calculation and thus should be increased slowly.

	</blockquote>		</blockquote>

Fulvio at 23:25, 30 January 2020

2020-01-30T23:25:36Z

← Older revision		Revision as of 23:25, 30 January 2020
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	In this tutorial we will deal with different aspects of running a Bethe-Salpeter (BSE) calculation for optical absorption spectra using yambopy. We continue using hexagonal boron nitride to illustrate how to perform convergence tests, and how to compare and analyse the results.		In this tutorial we will deal with different aspects of running a Bethe-Salpeter (BSE) calculation for optical absorption spectra using yambopy. We continue using hexagonal boron nitride to illustrate how to perform convergence tests, and how to compare and analyse the results.

	Before you start this tutorial, make sure you have run the scf and nscf runs. If you have not, you can calculate the scf <code>-s</code> and nscf <code>-n</code> using the <code>gs_bn.py</code> file:		Before you start this tutorial, make sure you have run the scf and nscf runs. If you have not, you can calculate the relax <code>-r</code>, scf <code>-s</code> and nscf <code>-n</code> using the <code>gs_bn.py</code> file:

	<source lang="bash">$ python gs_bn.py -s -n</source>		<source lang="bash">$ python gs_bn.py -r -s -n</source>
	Once that is over, you can start the tutorial.		Once that is over, you can start the tutorial.

Fulvio: /* BSE convergence of optical spectra */

2020-01-21T17:18:19Z

BSE convergence of optical spectra

← Older revision		Revision as of 17:18, 21 January 2020
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	Up to this point we have been focused on the variables which control the static screening. We still need to deal with the variables which setup the Bethe-Salpeter auxiliary Hamiltonian matrix. Once this matrix is set up, <code>yambo</code> will use a diagonalisation algorithm to obtain the excitonic states and energies. The relevant variables for this process are:		Up to this point we have been focused on the variables which control the static screening. We still need to deal with the variables which setup the Bethe-Salpeter auxiliary Hamiltonian matrix. Once this matrix is set up, <code>yambo</code> will use a diagonalisation algorithm to obtain the excitonic states and energies. The relevant variables for this process are:

	<blockquote><code>BSEBands</code>: number of bands to generate the transitions. Should be as small as possible as the size of the BSE auxiliary hamiltonian has (in the resonant approximation) dimensions <code>NkNvNc</code>. Another way to converge the number of transitions is using <code>BSEEhEny</code>. This variable selects the number of transitions based on the electron-hole energy difference.		<blockquote><code>BSEBands</code>: number of bands to generate the transitions. Should be as small as possible as the size of the BSE auxiliary hamiltonian has (in the resonant approximation) dimensions <code>NkNvNc</code>.

			Another way to converge the number of transitions is using <code>BSEEhEny</code>. This variable selects the number of transitions based on the electron-hole energy difference (it's the one we are going to use).

	<code>BSENGBlk</code> is the number of blocks for the dielectric screening average over the unit cells. This uses the static screening computed previously and controlled by the variable <code>NGsBlkXs</code>. So you <code>BSENGBlk</code> cannot be larger than <code>NGsBlkXs</code>.		<code>BSENGBlk</code> is the number of blocks for the dielectric screening average over the unit cells. This uses the static screening computed previously and controlled by the variable <code>NGsBlkXs</code>. So you <code>BSENGBlk</code> cannot be larger than <code>NGsBlkXs</code>.
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	<code>BSENGexx</code> in the number of exchange components. Relatively cheap to calculate, but should be kept as small as possible to save memory.		<code>BSENGexx</code> in the number of exchange components. Relatively cheap to calculate, but should be kept as small as possible to save memory.

	<code>KfnQP_E</code> is the scissor operator for the BSE. The first value is the rigid scissor, the second and third are the stretching for the conduction and valence respectively. The optical absorption spectrum is obtained in a range of energies given by <code>BEnRange</code> and the number of frequencies in the interval is <code>BEnSteps</code>.		<code>KfnQP_E</code> is the scissor operator for the BSE. The first value is the rigid scissor, the second and third are the stretching for the conduction and valence respectively. The optical absorption spectrum is obtained in a range of energies given by <code>BEnRange</code> and the number of frequencies in the interval is <code>BEnSteps</code>. Alternatively a quasiparticle energy database can be included from a previous GW calculation.
	</blockquote>		</blockquote>

← Older revision		Revision as of 14:24, 31 March 2022
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	In the folder <code>tutorials/bn/</code> you find the python script <code>bse_cutoff.py</code>. This script takes some time to be executed, you can run both variants without the cutoff and with the cutoff <code>-c</code> simultaneously to save time. You can run this script with:		In the folder <code>tutorials/bn/</code> you find the python script <code>bse_cutoff.py</code>. This script takes some time to be executed, you can run both variants without the cutoff and with the cutoff <code>-c</code> simultaneously to save time. You can run this script with:

	~~<source lang="bash">~~python bse_cutoff.py -r -t4 # without coulomb cutoff		python bse_cutoff.py -r -t4 # without coulomb cutoff
	python bse_cutoff.py -r -c -t4 # with coulomb cutoff~~</source>~~		python bse_cutoff.py -r -c -t4 # with coulomb cutoff
	where <code>-t</code> specifies the number of MPI threads to use. The main loop changes the <code>layer_separation</code> variable using values from a list in the header of the file. In the script you can find how the functions <code>scf</code>, <code>ncf</code> and <code>database</code> are defined.		where <code>-t</code> specifies the number of MPI threads to use. The main loop changes the <code>layer_separation</code> variable using values from a list in the header of the file. In the script you can find how the functions <code>scf</code>, <code>ncf</code> and <code>database</code> are defined.

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	In a similar way as what was done before we can now plot the dielectric function for different layer separations:		In a similar way as what was done before we can now plot the dielectric function for different layer separations:

	~~<source lang="bash">~~yambopy plotem1s bse_cutoff// # without coulomb cutoff		yambopy plotem1s bse_cutoff// # without coulomb cutoff
	yambopy plotem1s bse_cutoff_cut// # with coulomb cutoff~~</source>~~		yambopy plotem1s bse_cutoff_cut// # with coulomb cutoff

	[[File:Bn em1s cutoff cut.png\|Yambo tutorial image]]		[[File:Bn em1s cutoff cut.png\|Yambo tutorial image]]
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	You can also plot how the absorption spectra changes with the cutoff using:		You can also plot how the absorption spectra changes with the cutoff using:

	~~<source lang="bash">~~python bse_cutoff.py -p		python bse_cutoff.py -p
	python bse_cutoff.py -p -c~~</source>~~		python bse_cutoff.py -p -c

	[[File:Bn bse cutoff.png\|bn bse cutoff]]		[[File:Bn bse cutoff.png\|bn bse cutoff]]
Line 166:		Line 166:
	[[File:Bn bse cutoff cut.png\|bn bse cutoff cut]]		[[File:Bn bse cutoff cut.png\|bn bse cutoff cut]]

	As you can see, the spectra is still changing with the ~~vaccum~~ spacing, you should increase the vacuum until convergence. For that you can add larger values to the <code>layer_separations</code> list and run the calculations and analysis again.		As you can see, the spectra is still changing with the vacuum spacing, you should increase the vacuum until convergence. For that you can add larger values to the <code>layer_separations</code> list and run the calculations and analysis again.

	=== Excitonic wavefunctions in reciprocal space ===		=== Excitonic wavefunctions in reciprocal space ===