Requesting non-linear optical properties

Second harmonic generation (SHG) coefficients determine the efficiency of non-linear optical (NLO) materials for applications in optoelectronics. The formalism for CASTEP calculations of NLO properties is similar to that for Raman intensity calculations and relies on density functional perturbation theory. All the limitations currently in place for linear response calculations of vibrational properties also apply to the calculation of SHG coefficients, see Requesting vibrational properties for more information.

You can correct numerical values of the calculated SHG coefficients by taking into account systematic underestimation of the band gap in DFT calculations. Use the following workflow for calculation of nonlinear optical properties:

  1. Carry out an accurate geometry optimization calculation using a GGA exchange correlation functional, such as WC or PBE. Specify the Quality as Ultra-fine.
  2. Perform a band structure calculation for the relaxed geometry and extract the value of band gap.
  3. Obtain an estimate of a true band gap.

    Use an experimental band gap value when it is available, or perform a band structure calculation. For example, perform a band structure calculation with screened exchange (sX-LDA) functional or a hybrid functional, like HSE0. This can obtain a more accurate band gap than that calculated by a GGA calculation.

  4. Use the difference between a GGA band gap and a more accurate value to define the Scissors operator value; this effectively shifts the conduction bands up in a CASTEP calculation.

Calculation of non-linear optical properties is only reasonable for crystals without a center of symmetry.

The "Nonlinear Optical Susceptibility" section of the seed_NLO.castep output file provides the results of the SHG calculation. The 3 × 6 dij tensor reported can contain small numerical noise that violates crystal and Kleinman symmetry. In addition, the tensor's presentation might be in a non-standard lattice orientation, especially for hexagonal and trigonal lattice types. The same output file contains a symmetrized and, where relevant, rotated to standard representation dij tensor.

Numerical noise in the elements of dij tensor (that ought to be zero by symmetry) usually reflects the level of convergence with respect to the quality of k-point sampling of the Brillouin zone. If you encounter such noise, you should verify the convergence of the calculated values with respect to the number of k-points. Under-converged results can include significant errors, especially for crystals with small band gaps.

To request calculation of non-linear optical properties

  1. Choose Modules | CASTEP | Calculation from the menu bar to display the CASTEP Calculation dialog.
  2. Select the Properties tab.
  3. Select the Non-linear optical properties checkbox in the list of properties.
  4. Optionally, alter the accuracy of the calculation by changing the value of the Convergence tolerance.
  5. If you know the value of the scissors operator, enter this in the Scissors operator text box.
See Also:

Non-linear optical properties
Requesting vibrational properties
CASTEP Calculation dialog