Optics at the independent particle level

In this tutorial you will learn how to calculate optical spectra at the independent particle level for bulk hBN.

Background

The dielectric function in the long-wavelength limit, at the independent particle level (RPA without local fields), is essentially given by the following:

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.

Prerequisites

Cheatsheet on linear response

• You must first complete the How to use Yambo modules

You will need:

• The SAVE databases for bulk hBN
• The yambo executable
• gnuplot, for plotting spectra

Choosing input parameters

Enter the folder for bulk hBN that contains the SAVE directory, run the initialization and generate the input file. From yambo -h you should understand that the correct option is yambo -optics c (or yambo -o c). Let's add some command line options:

$ cd YAMBO_TUTORIALS/hBN/YAMBO
$ yambo               (initialization)
$ yambo -F yambo.in_IP -o c

This corresponds to optical properties in G-space at the independent particle level: in the input file this is indicated by (Chimod= "IP").

Optics runlevel

For optical properties we are interested just in the long-wavelength limit q = 0. This always corresponds to the first q-point in the set of possible q=k-k' -points. Change the following variables in the input file to:

% QpntsRXd
 1 |  1 |                   # [Xd] Transferred momenta
%
ETStpsXd= 1001               # [Xd] Total Energy steps

in order to select just the first q. The last variable ensures we generate a smooth spectrum. Save the input file and launch the code, keeping the command line options as before (i.e., just remove the lower case options):

$ yambo -F yambo.in_IP -J Full
...
<---> [04] Dipoles
<---> [DIP] Checking dipoles header
<---> [WARNING] DIPOLES database not correct or missing
<---> [x,Vnl] computed using 4 projectors
<04s> Dipoles: P, V and iR (T) |########################################| [100%] 04s(E) 04s(X)
<04s> [DIP] Writing dipoles header
<04s> [WARNING] Only commutator with non-local pseudopotential contribution included in position and velocity dipol
<04s> [05] Optics
<04s> [LA] SERIAL linear algebra
<04s> [DIP] Checking dipoles header
<04s> [X-CG] R(p) Tot o/o(of R):    5499   52992     100
<05s> Xo@q[1] |########################################| [100%] --(E) --(X)
<05s> [06] Timing Overview
<05s> [07] Memory Overview
<05s> [08] Game Over & Game summary
 
$ ls
Full   SAVE  yambo.in_IP   r_setup
o-Full.eel_q1_ip  o-Full.eps_q1_ip  r-Full_optics_*

Let's take a moment to understand what Yambo has done inside the Optics runlevel:

1. Compute the [x,Vnl] term
2. Read the wavefunctions from disc [WF]
3. Compute the dipoles, i.e. matrix elements of p
4. Write the dipoles to disk as Full/ndb.dip* databases. This you can see in the report file:

$ grep -A20 "WR" r-Full_optics_chi 

yambo 4.5 (or before)

[WR./Full//ndb.dip_iR_and_P]
Brillouin Zone Q/K grids (IBZ/BZ):  14   72   14   72
RL vectors                   (WF): 1491
Electronic Temperature        [K]: 0.0000000
Bosonic    Temperature        [K]: 0.0000000
X band range           :   1  100
RL vectors in the sum  : 1491
[r,Vnl] included       :yes
...

yambo 5.0

[WR./Full//ndb.dipoles]---------------------------------------------------------
 Brillouin Zone Q/K grids (IBZ/BZ)                :   14   72   14   72
 RL vectors                                       :  1491 [WF]
 Fragmentation                                    : yes
 Electronic Temperature                           :  0.000000 [K]
 Bosonic    Temperature                           :  0.000000 [K]
 DIP band range                                   :    1  100
 DIP band range limits                            :   8   9
 DIP e/h energy range                             : -1.000000 -1.000000 [eV]
 RL vectors in the sum                            :  1491
 [r,Vnl] included                                 : yes
 Bands ordered                                    : yes
 Direct v evaluation                              : no
 Approach used                                    : G-space v
 Dipoles computed                                 : R V P
 Wavefunctions                                    : Slater exchange(X)+Perdew & Zunger(C)
- S/N 003471 ---------------------------------------------- v.05.00.01 r.19547 -

5. Finally, Yambo computes the non-interacting susceptibility X₀ for this q, and writes the dielectric function inside the o-Full.eps_q1_ip file for plotting

Energy cut off

Before plotting the output, let's change a few more variables. The previous calculation used all the G-vectors in expanding the wavefunctions, up to 1491 (~1016 components). This corresponds roughly to the cut off energy of 40Ry we used in the DFT calculation. Generally, however, we can use a smaller value. We use the verbosity to switch on this variable, and a new -J flag to avoid reading the previous database:

$ yambo -F yambo.in_IP -J 6Ry -V RL -o c

Change the value of FFTGvecs and also its unit from RL (number of G-vectors) to Ry (energy in Rydberg):

FFTGvecs= 6           Ry    # [FFT] Plane-waves

Save the input file and launch the code again:

 $ yambo -F yambo.in_IP -J 6Ry

and then plot the o-Full.eps_q1_ip and o-6Ry.eps_q1_ip files:

$ gnuplot
gnuplot> plot "o-Full.eps_q1_ip" w l,"o-6Ry.eps_q1_ip" w p

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 FFTGvecs 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).

q-direction

Now let's select a different component of the dielectric tensor:

$ yambo -F yambo.in_IP -J 6Ry -V RL -o c
...
% LongDrXd
0.000000 | 0.000000 | 1.000000 |        # [Xd] [cc] Electric Field
%
...
$ yambo -F yambo.in_IP -J 6Ry -V RL

This time yambo reads from the 6Ry folder, so it does not need to compute the dipole matrix elements again, and the calculation is fast. Plotting gives:

$ gnuplot
gnuplot> plot "o-6Ry.eps_q1_ip" t "q || x-axis" w l,"o-6Ry.eps_q1_ip_01" t "q || c-axis" w l

The absorption is suppressed in the stacking direction. As the interplanar spacing is increased, we would eventually arrive at the absorption of the BN sheet (see Local fields tutorial).

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 -J option:

$ 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

Note the warning in the output:

<---> [WARNING] Missing non-local pseudopotential contribution

which also appears in the report file, and noted in the database as [r,Vnl] included :no. The difference is tiny:

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.

Summary

From this tutorial you've learned:

• How to compute a simple optical spectrum
• How to reduce the computational load through reducing the G-vector/energy cut off and removing the Vnl term
• How to plot different components of the dielectric tensor
• How to use the -J option to neatly label and organise files and databases

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