# The optic utility¶

Frequency dependent linear optical dielectric function and second order nonlinear optical susceptibility.

This file explains the i/o parameters needed for the calculation of the frequency-dependent linear optical dielectric function and second-order nonlinear optical susceptibility, in the RPA approximation (sum-over-states using independent electronic states) thanks to the Optic utility of the Abinit package. The user is advised to be familiar with the main abinit help file before reading the present file.

A knowledge of the computation of the linear response d/dk perturbation, explained in the respfn help file, is also advised.

It will be easier to discover the present file with the help of the optic tutorial.

## 1 Introduction¶

The Optic utility allows the computation of the frequency-dependent linear optical dielectric function and second-order nonlinear optical susceptibility including the nonlinear susceptibility and the linear electro-optical coefficient. An introduction to such computations is given in [Sharma2004], online at http://arxiv.org/abs/cond-mat/0305016. Other useful references include [Hughes1996], [Draxl2006], online at http://arxiv.org/abs/cond-mat/0402523, and [Sharma2003], online at http://arxiv.org/abs/cond-mat/0211512.

Before going to the detailed explanation of the Optic utility, the user is advised to become familiar to the theory behind it, explained in these references. Familiarity at least with [Sharma2004] is strongly advised.

The specific purpose of the Optic utility is to read in the momentum matrix elements generated by Abinit (actually matrix elements of the dH/dk operator), and then use the approach of [Sharma2004] to determine the linear (Eq. 46) and nonlinear (Eqs. 49-51) optical response of the material under investigation.

Note that optic works in the independent-particle approximation (no excitons), and without local-field effects. For higher level of theories, use the Bethe-Salpeter equation, see the BSE tutorial. The intraband Drude term (for metals only) is also not included. Usually it has only small effect at visible frequencies, but important effect at smaller frequencies. See e.g. [Cazzaniga2010], Fig. 3.

## 2 How to run Optic¶

The use of Optic is quite simple:

optic < optic.files > optic.log


where the optic.files file contains three lines: the name of the input file, the name of an output file (actually unused), and the root name for all other output files. These files will be described in the next section.

However, before being able to use Optic, you must have obtained, from the main Abinit program, four different files, corresponding to the physical system that you want to study:

• The ground state wavefunction file, indexed with _WFK

• Three files containing the matrix elements of the dH/dk operators of the unperturbed wavefunctions, one for each direction of space

Supposing you have read the main Abinit help file, the production of the first file should not require any additional explanation. However, the way to obtain the three other files, containing the matrix elements of the dH/dk operators is worth explaining.

A straightforward relationship exists between the dH/dk matrix elements and the matrix elements of the momentum operator. The computation of the dH/dk matrix elements is the initializing step in the treatment of the response to an electric field in DFPT. The long-wave method as well as the Berry-phase treatment of electric field, allow to establish the equivalence between the off-diagonal matrix elements of the position operator, and the off-diagonal matrix elements of the derivative with respect to the wavevector (d/dk), for the periodic part of the Bloch functions (see for example section VI of [Gonze1997], and [Nunes2001]). Such calculation involve applying the dH/dk operator to the unperturbed wavefunctions, in the Sternheimer equation.

The main Abinit program has the capability to compute derivatives of wavefunctions with respect to their wavevector. This is explained in respfn help file. Such a calculation implies treating three d/dk perturbations, indexed by the numbers 3*natom+1, 3*natom+2 and 3*natom+3 (thus for example, for a unit cell with 2 atoms, perturbations number 7, 8 and 9). In the two-atom case, the associated files needed for Optic have the index _1WF7 , _1WF8 , and _1WF9. However, as mentioned above, the computation of the dH/dk matrix elements is only the initializing step in such calculations. Still, the dH/dk will be made available in such files.

The formalism implemented in Optic treats explicitly the eigenstates lying in the range of energy between the lowest occupied wavefunction and the highest one plus the maximal excitation energy (chosen by the user). All the other ones are neglected. This has two important consequences for the preliminary runs:

• The ground calculation must produce explicitly all the eigenstates and eigenvalues for that target range of energy, so it cannot be restricted to the occupied wavefunctions only

• One does not need the full change of Bloch wavefunctions with respect to d/dk, but only the matrix elements of dH/dk between the wavefunctions of this range of energy

Because of the latter, the computation of the response to d/dk perturbations is much shorter than usual: indeed, the matrix elements between the explicitly ground-state wavefunctions are computed at the very beginning of the abinit(respfn) run. It is not necessary to make a full calculation of the modification of the wavefunctions due to a change of wavevector. This explains why nstep has been set to 0 in such calculations.

## 3 Optic input file and input variables¶

A typical optic.files file is presented below:

optic.in     ! Name of input file
optic.out    ! Unused
optic        ! Root name for all files that will be produced


Please note that the format of input files for Optic has changed as of Abinit v8.0. Since very few input parameters are required for Optic, the optic.in file contains them with the namelist format. The order of the three parts, namely FILES, PARAMETERS and COMPUTATIONS must be kept unaltered.

    &FILES
ddkfile_1 = 'toptic_1o_DS4_1WF7',
ddkfile_2 = 'toptic_1o_DS5_1WF8',
ddkfile_3 = 'toptic_1o_DS6_1WF9',
wfkfile = 'toptic_1o_DS3_WFK'
/
&PARAMETERS
domega = 0.0003,
maxomega = 0.3,
scissor = 0.000,
tolerance = 0.002
/
&COMPUTATIONS
num_lin_comp = 1,
lin_comp = 11,
num_nonlin_comp = 2,
nonlin_comp = 123,222,
num_linel_comp = 1,
linel_comp = 123,
/


The list of input variables for the optic input file is presented in topic_Optic.

## 4 Optic output files¶

#### 4.1. Linear optical response data files¶

Name: case_a_b-linopt.out
Contains the following 3 data sets

• 1) Column 1 - energy(eV), column 2 - imaginary part of the ab component of the frequency-dependent linear dielectric tensor.
• 2) Column 1 - energy(eV), column 2 - real part of the ab component of the frequency-dependent linear dielectric tensor.
• 3) Column 1 - energy(eV), column 2 - absolute value of the ab component of the frequency-dependent linear dielectric tensor.
• 4) Column 1 - energy(eV), column 2 - imaginary part of the ab component of the frequency-dependent linear refractive index (kappa).
• 5) Column 1 - energy(eV), column 2 - real part of the ab component of the frequency-dependent linear refractive index (n).
• 6) Column 1 - energy(eV), column 2 - frequency-dependent reflectivity at normal incidence.
• 7) Column 1 - energy(eV), column 2 - absorption coeff (in m-1) = omega Im(eps) / c n(eps)

In the header of the file you can find information about the calculation.

In case nsppol==2, the spin-decomposition of items 1 and 2 above is provided in columns 3-4 for the imaginary part, and 3-5 for the real part (the spin-independent contribution delta(ab) is mentioned as well).

#### 4.2. Non-linear optical response data files¶

Name: case_a_b_c-ChiKIND1.out
KIND1:This can be TotIm, TotRe or TotAbs
Contains: column 1 - energy(eV), column 2 and 3 - imaginary (KIND1=TotIm), real (KIND1=TotRe) or absolute (KIND1=TotAbs) value of the abc component of the nonlinear optical susceptibility. Second column contains values in electro-static units (esu) and third column contains values in the SI units.

Name: case_a_b_c-ChiKIND2.out
KIND2:This can be Im, Re or abs
Contains: column 1 - energy(eV), column 2, 3 inter and column 4, 5 intra band contributions to the imaginary (KIND2=Im), real (KIND2=Re) or absolute (KIND2=Abs) value of the abc component of the nonlinear optical susceptibility. These components are labeled as inter and intra in Eqs. 49-51 in [Sharma2004]

All the values are in electro-static units (esu). In the header of all the above files you can find information about the calculation.

## 5 Troubleshooting¶

1) All I get are zeros in my *-linopt.out file. Why?

There are several possibilities.
Let us explore some of them here:

• (i) The component of the dielectric tensor that you are looking at could be zero due to symmetry of the crystal. Normally zz component is a good place to start. It is almost never zero. So check the file case__0003_0003-linopt.out.

• (ii) If the components zz is zero this is more serious, if you are using the default input file t57.in then please check that on the line number 10 the second number is 33. If you are not using the default input file please calculate the 33 (or zz) component and make sure it is not zero.

• (iii) If even zz component is zero then possibilities are endless maximum frequency on line number 6 of t57.in is too small, or the number of bands used for performing ground state calculation are too small.

2) All I get is zeros in my *-ChiKIND.out file. Why?

The two most common mistakes are:

• (i) You are calculating the second order response for material with inversion symmetry, so in this case all the components will be correctly zero or very small (order $10^{-15}$).

• (ii) Most components out of the 27 are zero due to the symmetry of the crystal. Please calculate a different component.