Next steps: RPA calculations (standalone) - Revision history

Matteo.dalessio: /* LFEs in periodic direction */

2025-05-20T14:33:23Z

LFEs in periodic direction

← Older revision		Revision as of 14:33, 20 May 2025
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	Plot the result:		Plot the result:
	$ gnuplot		$ gnuplot
	$ gnuplot> plot "o-q100.eps_q1_inv_rpa_dyson" u 1:2 w l t "RPA-~~LFA~~","o-q100.eps_q1_inv_rpa_dyson" u 1:4 w l t "noLFE", "o-q100.eel_q1_inv_rpa_dyson" u 1:4 w l ls 7 dt 2 t "EELS"		$ gnuplot> plot "o-q100.eps_q1_inv_rpa_dyson" u 1:2 w l t "RPA-LFE","o-q100.eps_q1_inv_rpa_dyson" u 1:4 w l t "noLFE", "o-q100.eel_q1_inv_rpa_dyson" u 1:4 w l ls 7 dt 2 t "EELS"
	[[File:CH-LFE4.png\|none\|600px\|Yambo tutorial image]]		[[File:CH-LFE4.png\|none\|600px\|Yambo tutorial image]]
	There is little influence of local fields in this case. This is generally the case for semiconductors or materials with a smoothly varying electronic density. We have also shown the EELS spectrum (''o-q100.eel_q1_inv_rpa_dyson'') for comparison.		There is little influence of local fields in this case. This is generally the case for semiconductors or materials with a smoothly varying electronic density. We have also shown the EELS spectrum (''o-q100.eel_q1_inv_rpa_dyson'') for comparison.

Giacomo.sesti: /* Non-local commutator */

2025-05-18T13:42:23Z

Non-local commutator

← Older revision		Revision as of 13:42, 18 May 2025
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	Note the warning in the output:		Note the warning in the output:
	<---> [WARNING] ~~Missing commutator with non-local pseudopotential contribution~~ in position and velocity dipoles		<---> [WARNING] [r,Vnl^pseudo] not included in position and velocity dipoles
	which also appears in the report file <code>r-6Ry_NoVnl_optics_dipoles_chi</code> as <code>[r,Vnl] included :no</code>. The difference is tiny:		which also appears in the report file <code>r-6Ry_NoVnl_optics_dipoles_chi</code> as <code>[r,Vnl] included :no</code>. The difference is tiny:
	[[File:CH-hBN-Vnl.png\|none\|500px\|Yambo tutorial image]]		[[File:CH-hBN-Vnl.png\|none\|500px\|Yambo tutorial image]]

Davide: /* Absorption versus EELS */

2022-04-01T12:39:15Z

Absorption versus EELS

← Older revision		Revision as of 12:39, 1 April 2022
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	See e.g.<ref>TDDFT from molecules to solids: The role of long‐range interactions, F. Sottile et al, International journal of quantum chemistry 102 (5), 684-701 (2005)</ref>		See e.g.<ref>TDDFT from molecules to solids: The role of long‐range interactions, F. Sottile et al, International journal of quantum chemistry 102 (5), 684-701 (2005)</ref>

			==Links==
			* Back to [[ICTP 2022#Tutorials]]
			* Back to [[CECAM VIRTUAL 2021#Tutorials]]


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Pedro at 16:12, 6 April 2021

2021-04-06T16:12:31Z

Show changes

Pedro at 15:53, 6 April 2021

2021-04-06T15:53:36Z

← Older revision		Revision as of 15:53, 6 April 2021
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	=== Choosing input parameters ===		=== Choosing input parameters ===
	Enter the folder for bulk hBN that contains the ''SAVE'' directory, run the initialization and generate the input file.		Enter the folder for bulk hBN that contains the ''SAVE'' directory, run the initialization and generate the input file.
	~~From~~ <code>yambo -h</code> ~~you should understand that~~ the correct option is <code>yambo -optics c</code> (or <code>yambo -o c</code>). Let's add some command line options:		You can type <code>yambo -h</code> and see the available options for different run-levels. For an RPA optical spectrum calculation the correct option is <code>yambo -optics c</code> (or <code>yambo -o c</code>). Let's add some command line options:

	$ cd YAMBO_TUTORIALS/hBN/YAMBO		$ cd YAMBO_TUTORIALS/hBN/YAMBO
Line 85:		Line 85:
	[[File:CH-hBN-6Ry.png\|none\|500px\|Yambo tutorial image]]		[[File:CH-hBN-6Ry.png\|none\|500px\|Yambo tutorial image]]

	~~Clearly there~~ is very little difference between the two spectra. This highlights an important point in calculating excited state properties: generally, fewer G-vectors are needed than what are needed in DFT calculations. Regarding the spectrum itself, the first peak occurs at about 4.4eV. This is consistent with the minimum direct gap reported by Yambo: 4.28eV. The comparison with experiment (not shown) is very poor however.		There is very little difference between the two spectra. This highlights an important point in calculating excited state properties: generally, fewer G-vectors are needed than what are needed in DFT calculations. Regarding the spectrum itself, the first peak occurs at about 4.4eV. This is consistent with the minimum direct gap reported by Yambo: 4.28eV. The comparison with experiment (not shown) is very poor however.

	If you made some mistake and cannot reproduce this figure, you should check the value of <code>[[Variables#FFTGvecs\|FFTGvecs]]</code> in the input file, delete the ''6Ry'' folder, and try again - taking care to plot the right file! (e.g. ''o-6Ry.eps_q1_ip_01''. The "_01" suffix means that while writing the output Yambo found another existing file with the name "o-6Ry.eps_q1_ip").		If you made some mistake and cannot reproduce this figure, you should check the value of <code>[[Variables#FFTGvecs\|FFTGvecs]]</code> in the input file, delete the ''6Ry'' folder, and try again - taking care to plot the right file! (e.g. ''o-6Ry.eps_q1_ip_01''. The "_01" suffix means that while writing the output Yambo found another existing file with the name "o-6Ry.eps_q1_ip").
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	[[File:CH-hBN-Vnl.png\|none\|500px\|Yambo tutorial image]]		[[File:CH-hBN-Vnl.png\|none\|500px\|Yambo tutorial image]]

	However, when your system is larger, with more projectors in the pseudopotential or more k-points (see the BSE tutorial), the inclusion of ~~''Vnl''~~ can make a huge difference in the computational load, so it's always worth checking to see if the terms are important in your system.		However, when your system is larger, with more projectors in the pseudopotential or more k-points (see the BSE tutorial), the inclusion of <math>V^\mathrm{NL}</math> can make a huge difference in the computational load, so it is always worth checking to see if the terms are important in your system.

	==Optical absorption in 2D BN: local field effects ==		==Optical absorption in 2D BN: local field effects ==
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	=== Background ===		=== Background ===
	[[File:Yambo-Cheatsheet-5.0_P7.png\|thumb\|Cheatsheet on LFE\|150px]]		[[File:Yambo-Cheatsheet-5.0_P7.png\|thumb\|Cheatsheet on LFE\|150px]]
	The macroscopic dielectric function is obtained by including the so-called local field effects (LFE) in the calculation of the response function. Within the time-dependent DFT formalism this is achieved by solving the Dyson equation for the susceptibility ~~''X''~~. In reciprocal space this is given by:		The macroscopic dielectric function is obtained by including the so-called local field effects (LFE) in the calculation of the response function. Within the time-dependent DFT formalism this is achieved by solving the Dyson equation for the susceptibility <math>\chi</math>. In reciprocal space this is given by:
	[~~[File:Yambo-CH7.png\|none\|x50px\|Yambo tutorial image]~~]
	The microscopic dielectric function is related to ~~''X''~~ by:		<math>\chi_{\mathbf{G}, \mathbf{G}^{\prime}}(\mathbf{q}, \omega) = \chi_{\mathbf{G}, \mathbf{G}^{\prime}}^{0}(\mathbf{q}, \omega)+\sum_{\mathbf{G}_{1}, \mathbf{G}_{2}} \chi_{\mathbf{G}, \mathbf{G}_{1}}^{0}(\mathbf{q}, \omega)\left[v_{\mathbf{G}_{1}}(\mathbf{q}) \delta_{\mathbf{G}_{1}, \mathbf{G}_{2}}+f_{\mathbf{G}_{1}, \mathbf{G}_{2}}^{x c}\right] \chi_{\mathbf{G}_{2}, \mathbf{G}^{\prime}}(\mathbf{q}, \omega)</math>
	~~[[File:Yambo~~-~~CH5.png\|none\|x30px\|Yambo tutorial image]]~~
			The microscopic dielectric function is related to <math>\chi</math> by:

			<math>\epsilon_{\mathbf{G}, \mathbf{G}^{\prime}}^{-1}(\mathbf{q}, \omega)=\delta_{\mathbf{G}, \mathbf{G}^{\prime}}+v_{\mathbf{G}}(\mathbf{q}) \chi_{\mathbf{G}, \mathbf{G}^{\prime}}(\mathbf{q}, \omega)</math>

	and the macroscopic dielectric function is obtained by taking the (0,0) component of the inverse microscopic one:		and the macroscopic dielectric function is obtained by taking the (0,0) component of the inverse microscopic one:
	~~[[File:Yambo~~-~~CH6.png\|none\|x60px\|Yambo tutorial image]]~~
			<math>\epsilon_{M}(\omega)=\lim _{\mathrm{q} \rightarrow 0} \frac{1}{\epsilon_{\mathrm{G}=0, \mathrm{G}^{\prime}=0}^{-1}(\mathbf{q}, \omega)}</math>

	Experimental observables like the optical absorption and the electron energy loss can be obtained from the macroscopic dielectric function:		Experimental observables like the optical absorption and the electron energy loss can be obtained from the macroscopic dielectric function:
	~~[[File:Yambo-CH8.png\|none\|x60px\|Yambo tutorial image]]~~

	In the following we will neglect the ~~''f~~ <~~sup~~> xc</~~sup~~>'' term: we perform the calculation at the RPA level and consider just the Hartree term (from ~~''v~~<~~sub~~>G</~~sub~~>'') in the kernel. If we also neglect the Hartree term, we arrive back at the independent particle approximation, since there is no kernel and ~~''X = X~~<~~sub~~>0</~~sub~~>''.		<math>\operatorname{Abs}(\omega)=\operatorname{Im} \epsilon_{M}(\omega) \quad \operatorname{EELS}(\omega)=-\operatorname{Im} \frac{1}{\epsilon_{M}(\omega)}</math>

			In the following we will neglect the <math>f^{xc}</math> term: we perform the calculation at the RPA level and consider just the Hartree term (from <math>v_G</math>) in the kernel. If we also neglect the Hartree term, we arrive back at the independent particle approximation, since there is no kernel and <math>\chi = \chi_0</math>.

	=== Choosing input parameters ===		=== Choosing input parameters ===
	Enter the folder for 2D hBN that contains the SAVE directory, and generate the input file. ~~From~~ <code>yambo -H</code> you ~~should understand that the correct option is~~ <code>yambo -~~o c -k hartree~~</code>. Let's start by running the calculation for light polarization ''q'' in the plane of the BN sheet:		Enter the folder for 2D hBN that contains the SAVE directory, and generate the input file. To include local the local fields variables in the input file the correct option is <code>yambo -o c -k hartree</code> (once again you can check it with <code>yambo -h</code>). Let's start by running the calculation for light polarization ''q'' in the plane of the BN sheet:
	$ cd YAMBO_TUTORIALS/hBN-2D/YAMBO		$ cd YAMBO_TUTORIALS/hBN-2D/YAMBO
	$ yambo ''(Initialization)''		$ yambo ''(Initialization)''
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	1.000000 \| 0.000000 \| 0.000000 \| # [Xd] [cc] Electric Field		1.000000 \| 0.000000 \| 0.000000 \| # [Xd] [cc] Electric Field
	%		%
	In this input file~~, we have~~:		In this input file:
	* We evaluate the q-->0 response function choosing the direction for the limit parallel in the plane of the hBN sheet		* We evaluate the q-->0 response function choosing the direction for the limit parallel in the plane of the hBN sheet;
	* A wider energy range than before, and ~~more~~ broadening		* We set a wider energy range than before, and a larger broadening;
	* ~~Selected~~ the Hartree kernel, and expanded G-vectors in the screening up to 3 Ry (about 85 G-vectors)		* We select the Hartree kernel, and expanded G-vectors in the screening up to 3 Ry (about 85 G-vectors);

	===LFEs in periodic direction===		===LFEs in periodic direction===
	Now let's run the code with this new input file (CECAM in serial: about 2mins; parallel 4 tasks: 50s)		Now let's run the code with this new input file (CECAM in serial: about 2mins; parallel 4 tasks: 50s)
	$ yambo -F yambo.in_RPA -J q100		$ yambo -F yambo.in_RPA -J q100
	and let's compare the absorption with and without the local fields included. By inspecting the ''o-q100.eps_q1_inv_rpa_dyson'' file we find		and let's compare the absorption with and without the local fields included. By inspecting the ''o-q100.eps_q1_inv_rpa_dyson'' file we find that this information is given in the 2<math>^\mathrm{nd}</math> and 4<math>^\mathrm{th}</math> columns, respectively:
	that this information is given in the ~~2nd~~ and ~~4th~~ columns, respectively:
	$ head -n 40 o-q100.eps_q1_inv_rpa_dyson		$ head -n 40 o-q100.eps_q1_inv_rpa_dyson
	# Absorption @ Q(1) [q->0 direction] : 1.0000000 0.0000000 0.0000000		# Absorption @ Q(1) [q->0 direction] : 1.0000000 0.0000000 0.0000000
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	$ gnuplot> plot "o-q100.eps_q1_inv_rpa_dyson" u 1:2 w l t "RPA-LFA","o-q100.eps_q1_inv_rpa_dyson" u 1:4 w l t "noLFE", "o-q100.eel_q1_inv_rpa_dyson" u 1:4 w l ls 7 dt 2 t "EELS"		$ gnuplot> plot "o-q100.eps_q1_inv_rpa_dyson" u 1:2 w l t "RPA-LFA","o-q100.eps_q1_inv_rpa_dyson" u 1:4 w l t "noLFE", "o-q100.eel_q1_inv_rpa_dyson" u 1:4 w l ls 7 dt 2 t "EELS"
	[[File:CH-LFE4.png\|none\|600px\|Yambo tutorial image]]		[[File:CH-LFE4.png\|none\|600px\|Yambo tutorial image]]
	~~It is clear that there~~ is little influence of local fields in this case. This is generally the case for semiconductors or materials with a smoothly varying electronic density. We have also shown the EELS spectrum (''o-q100.eel_q1_inv_rpa_dyson'') for comparison.		There is little influence of local fields in this case. This is generally the case for semiconductors or materials with a smoothly varying electronic density. We have also shown the EELS spectrum (''o-q100.eel_q1_inv_rpa_dyson'') for comparison.

	===LFEs in non-periodic direction===		===LFEs in non-periodic direction===

Pedro at 15:22, 6 April 2021

2021-04-06T15:22:31Z

← Older revision		Revision as of 15:22, 6 April 2021
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	=== Background ===		=== Background ===
	The dielectric function in the long-wavelength limit, at the independent particle level (RPA without local fields), is essentially given by the following:		The dielectric function in the long-wavelength limit, at the independent particle level (RPA without local fields), is essentially given by the following:
	~~<math>~~

	\epsilon_{\alpha,\alpha}(\omega) = 1 + \frac		<math>\epsilon_{\alpha, \alpha}(\omega)=1+\frac{16 \pi}{\Omega} \sum_{c, v} \sum_{\mathbf{k}} \frac{1}{E_{c \mathbf{k}}-E_{v \mathbf{k}}} \frac{\left\|\left\langle v \mathbf{k}\left\|\mathbf{p}_{\alpha}+\mathrm i\left[V^{\mathrm{NL}}, \mathbf{r}_{\alpha}\right]\right\| c \mathbf{k}\right\rangle\right\|^{2}}{\left(E_{c \mathbf{k}}-E_{v \mathbf{k}}\right)^{2}-(\omega+\mathrm i \gamma)^{2}}</math>
	</math>
	~~[[File:CH1.png\|none\|x50px\|Yambo tutorial image]]~~
	In practice, Yambo does not use this expression directly but solves the Dyson equation for the susceptibility ''X'', which is described in the [[Local fields]] module.		In practice, Yambo does not use this expression directly but solves the Dyson equation for the susceptibility ''X'', which is described in the [[Local fields]] module.

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	===Non-local commutator===		===Non-local commutator===
	Last, we show the effect of switching off the non-local commutator term (the term with <math> V^\mathrm{NL} </math> in the equation ~~({{EquationNote\|1}}))~~ due to the pseudopotential. As there is no option to do this inside yambo, you need to hide the database file. Change back to the ''q \|\| (1 0 0)'' direction, and launch yambo with a different <code>-J</code> option:		Last, we show the effect of switching off the non-local commutator term (the term with <math> V^\mathrm{NL} </math> in the equation at the start of this tutorial due to the pseudopotential. As there is no option to do this inside yambo, you need to hide the database file. Change back to the ''q \|\| (1 0 0)'' direction, and launch yambo with a different <code>-J</code> option:
	$ mv SAVE/ns.kb_pp_pwscf SAVE/ns.kb_pp_pwscf_'''OFF'''		$ mv SAVE/ns.kb_pp_pwscf SAVE/ns.kb_pp_pwscf_'''OFF'''
	$ yambo -F yambo.in_IP -J '''6Ry_NoVnl''' -o c ~~''(change~~ to q \|\| ~~100)''~~		$ yambo -F yambo.in_IP -J '''6Ry_NoVnl''' -o c

			Change

			%LonDrXd

			back to

			1.000000 \| 0.000000 \| 0.000000 \|

			and run

	$ yambo -F yambo.in_IP -J 6Ry_NoVnl		$ yambo -F yambo.in_IP -J 6Ry_NoVnl

	Note the warning in the output:		Note the warning in the output:
	<---> [WARNING] Missing non-local pseudopotential contribution		<---> [WARNING] Missing non-local pseudopotential contribution

Pedro at 13:56, 6 April 2021

2021-04-06T13:56:09Z

← Older revision		Revision as of 13:56, 6 April 2021
Line 5:		Line 5:
	=== Background ===		=== Background ===
	The dielectric function in the long-wavelength limit, at the independent particle level (RPA without local fields), is essentially given by the following:		The dielectric function in the long-wavelength limit, at the independent particle level (RPA without local fields), is essentially given by the following:
			<math>

			\epsilon_{\alpha,\alpha}(\omega) = 1 + \frac
			</math>
	[[File:CH1.png\|none\|x50px\|Yambo tutorial image]]		[[File:CH1.png\|none\|x50px\|Yambo tutorial image]]
	In practice, Yambo does not use this expression directly but solves the Dyson equation for the susceptibility ''X'', which is described in the [[Local fields]] module.		In practice, Yambo does not use this expression directly but solves the Dyson equation for the susceptibility ''X'', which is described in the [[Local fields]] module.
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	===Non-local commutator===		===Non-local commutator===
	Last, we show the effect of switching off the non-local commutator term (~~see ''[Vnl,r]''~~ in the equation ~~at the top of the page~~) due to the pseudopotential. As there is no option to do this inside yambo, you need to hide the database file. Change back to the ''q \|\| (1 0 0)'' direction, and launch yambo with a different <code>-J</code> option:		Last, we show the effect of switching off the non-local commutator term (the term with <math> V^\mathrm{NL} </math> in the equation ({{EquationNote\|1}})) due to the pseudopotential. As there is no option to do this inside yambo, you need to hide the database file. Change back to the ''q \|\| (1 0 0)'' direction, and launch yambo with a different <code>-J</code> option:
	$ mv SAVE/ns.kb_pp_pwscf SAVE/ns.kb_pp_pwscf_'''OFF'''		$ mv SAVE/ns.kb_pp_pwscf SAVE/ns.kb_pp_pwscf_'''OFF'''
	$ yambo -F yambo.in_IP -J '''6Ry_NoVnl''' -o c ''(change to q \|\| 100)''		$ yambo -F yambo.in_IP -J '''6Ry_NoVnl''' -o c ''(change to q \|\| 100)''

Pedro at 13:38, 6 April 2021

2021-04-06T13:38:48Z

← Older revision		Revision as of 13:38, 6 April 2021
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	Clearly there is very little difference between the two spectra. This highlights an important point in calculating excited state properties: generally, fewer G-vectors are needed than what are needed in DFT calculations. Regarding the spectrum itself, the first peak occurs at about 4.4eV. This is consistent with the minimum direct gap reported by Yambo: 4.28eV. The comparison with experiment (not shown) is very poor however.		Clearly there is very little difference between the two spectra. This highlights an important point in calculating excited state properties: generally, fewer G-vectors are needed than what are needed in DFT calculations. Regarding the spectrum itself, the first peak occurs at about 4.4eV. This is consistent with the minimum direct gap reported by Yambo: 4.28eV. The comparison with experiment (not shown) is very poor however.

	If you ~~make~~ some mistake, and cannot reproduce this figure, you should check the value of <code>[[Variables#FFTGvecs\|FFTGvecs]]</code> in the input file, delete the ''6Ry'' folder, and try again - taking care to plot the right file! (e.g. ''o-6Ry.eps_q1_ip_01'').		If you made some mistake and cannot reproduce this figure, you should check the value of <code>[[Variables#FFTGvecs\|FFTGvecs]]</code> in the input file, delete the ''6Ry'' folder, and try again - taking care to plot the right file! (e.g. ''o-6Ry.eps_q1_ip_01''. The "_01" suffix means that while writing the output Yambo found another existing file with the name "o-6Ry.eps_q1_ip").

	===q-direction===		===q-direction===

Pedro at 13:35, 6 April 2021

2021-04-06T13:35:44Z

← Older revision		Revision as of 13:35, 6 April 2021
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	$ yambo -F yambo.in_IP -J Full		$ yambo -F yambo.in_IP -J Full
	...		...
	<---> [05] Optics		<---> [04] Optics
	<---> [LA] SERIAL linear algebra		<---> [LA] SERIAL linear algebra
	<---> [DIP] Checking dipoles header		<---> [DIP] Checking dipoles header
	<---> [x,Vnl] computed using 4 projectors		<---> [x,Vnl] computed using 4 projectors
	<---> [~~M 0.017 Gb~~] Alloc WF ( 0.~~016~~)		<---> [MEMORY] Alloc WF%c( 16.307001Mb) TOTAL: 17.951000Mb (traced)
	<---> [WF] Performing Wave-Functions I/O from ./SAVE		<---> [WF] Performing Wave-Functions I/O from ./SAVE
	<~~01s~~> Dipoles: P and iR (T): \|########################################\| [100%] ~~01s~~(E) ~~01s~~(X)		<---> Dipoles: P and iR (T): \|########################################\| [100%] --(E) --(X)
	<~~01s~~> [M ~~0.001 Gb]~~ Free WF ( 0.~~016~~)		<---> [MEMORY] Free WF%c( 16.307001Mb) TOTAL: 1.4700000Mb (traced)
	<~~01s~~> [DIP] Writing dipoles header		<---> [DIP] Writing dipoles header
	<~~01s~~> [X-CG] R(p) Tot o/o(of R) : ~~5501~~ 52992 100		<---> [X-CG] R(p) Tot o/o(of R) : 5499 52992 100
	<01s> Xo@q[1] \|########################################\| [100%] --(E) --(X)		<01s> Xo@q[1] \|########################################\| [100%] --(E) --(X)
	<01s> [06] Game Over & Game summary		<01s> [MEMORY]TOTAL not deallocated : 907.0000Kb
			<01s> [05] Timing Overview
			<01s> [06] Memory Overview
			<01s> [07] Game Over & Game summary

	$ ls		$ ls
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	# Write the dipoles to disk as ''Full/ndb.dip*'' databases. This you can see in the report file:		# Write the dipoles to disk as ''Full/ndb.dip*'' databases. This you can see in the report file:
	$ grep -A20 "WR" r-Full_optics_*		$ grep -A20 "WR" r-Full_optics_*
	[WR./Full//ndb.dip_iR_and_P]		[WR./Full//ndb.dip_iR_and_P]--------------------------------
	Brillouin Zone Q/K grids (IBZ/BZ): 14 72 14 72		Brillouin Zone Q/K grids (IBZ/BZ): 14 72 14 72
	RL vectors (WF): 1491		RL vectors (WF): 1491
	Electronic Temperature [K]: 0.0000000		Fragmentation :yes
	Bosonic Temperature [K]: 0.0000000		Electronic Temperature [K]: 0.0000000
	X band range : 1 100		Bosonic Temperature [K]: 0.0000000
	RL vectors in the sum : 1491		X band range : 1 100
	[r,Vnl] included :yes		X band range limits : 8 9
	~~...~~		X e/h energy range [ev]:-1.0000000 -1.0000000
			RL vectors in the sum : 1491
			[r,Vnl] included :yes

	<ol start="5">		<ol start="5">
	<li>Finally, Yambo computes the non-interacting susceptibility ''X<sub>0</sub>'' for this ''q'', and writes the dielectric function inside the ''o-Full.eps_q1_ip'' file for plotting</li>		<li>Finally, Yambo computes the non-interacting susceptibility ''X<sub>0</sub>'' for this ''q'', and writes the dielectric function inside the ''o-Full.eps_q1_ip'' file for plotting</li>

Davide: /* Optical absorption in hBN: independent particle approximation */

2021-04-06T12:07:09Z

Optical absorption in hBN: independent particle approximation

← Older revision		Revision as of 12:07, 6 April 2021
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	==Optical absorption in hBN: independent particle approximation ==		==Optical absorption in hBN: independent particle approximation ==

			[[File:HBN-bulk-3x3-annotated.png\|x200px\|Atomic structure of bulk hBN]]

	=== Background ===		=== Background ===