CASTEP > Tasks in CASTEP > Setting up CASTEP calculations > Requesting electronic, structural, and vibrational properties > Requesting vibrational properties

CASTEP allows you to set up calculations that provide vibrational frequencies and eigenvectors at a selected set of q-vectors in the Brillouin zone. Two approaches to calculating these data are provided:

There are two predefined modes of calculation: the phonon dispersion spectrum along high symmetry directions and the phonon density of states spectrum, which is a prerequisite for the calculation of thermodynamic properties.

Phonon calculations take into account existing fixed atom constraints, regardless of the overall Task setting. Such fixed atoms are excluded from the calculation of vibrational properties, which corresponds to the "partial Hessian" approach. Constrained lattice dynamics approach is applied for both linear response and finite displacement approach.

You must check the Fix fractional position checkbox on the Atom tab of the Edit Constraints dialog, accessible from the Modify menu.

The linear response scheme treats atomic displacements as perturbations. In addition, an electric field response is evaluated to calculate a non-analytical correction to longitudinal optical (LO) phonon frequencies at the Γ-point. Longitudinal and transverse modes at the Γ-point are identical (no LO-TO splitting), unless this correction is applied.

The linear response scheme allows the calculation of phonon spectra in any commensurate or incommensurate q-vector of the reciprocal space, thus providing full flexibility in the choice of q-vectors to be used for calculations. Nevertheless, linear response calculations at a general q-vector are very time consuming and are often not necessary as a real space dynamical matrix that defines vibrational properties is often a short range property. This real space dynamical matrix can be calculated using a coarse Monkhorst-Pack mesh and then used to obtain the phonon spectrum at any given q-vector in the Brillouin zone. Thus, there two major modes of linear response calculations: direct and using interpolation.

The current version of CASTEP has a number of limitations related to phonon calculations. The only settings that are supported for linear response calculations or for finite displacement calculations that require LO-TO splitting correction are:

- Norm-conserving pseudopotentials (see the Setting up pseudopotentials topic)
- Non-spin-polarized calculations (see the Setting system parameters topic)

If any of these restrictions is violated by the current settings, an error message is displayed with an explanation of the problem. The offending setting must be changed in order to proceed with the phonon calculation.

Gradient-corrected exchange-correlation functionals are supported in linear response calculations, although the results may be less accurate than those obtained with LDA and the computational cost is noticeably higher.

CASTEP provides an alternative method of calculating phonon frequencies that is based on the finite displacements method (Montanari and Harrison, 2002). This technique is based on numerical differentiation of forces on atoms that are calculated for a number of unit cells with atomic displacements. CASTEP determines the optimum number of such displacements automatically, based on the crystal symmetry. Displacements with a very small magnitude give results that are similar to the linear response frequencies. An advantage of the finite displacements method is that it is also possible to investigate phonon anharmonicity by increasing the amplitude of the displacements. A further important advantage is that none of the linear response limitations mentioned above are relevant for finite displacements calculations. This method can be used to obtain vibrational frequencies for:

- Metallic systems
- Spin-polarized systems
- Any system treated with efficient ultrasoft potentials

It should be noted that the formalism can be implemented only at the commensurate q-points (at the cost of creating a supercell) and if the object of the calculation is to obtain dispersion results or a reasonable density of states, then an interpolation technique must be used. The current implementation of the finite displacements technique in CASTEP provides control, via a cutoff parameter, over the size of the supercell used to construct the real space dynamical matrix.

There is a limitation with the current implementation of the finite displacements method in CASTEP related to the treatment of the non-analytical term that is responsible for the LO-TO splitting in insulators. This term is currently calculated using linear response with an electric field as a perturbation; thus, all the computational restrictions mentioned in the previous section apply to finite displacements calculations if the LO-TO splitting is requested.

A LO-TO calculation imposes all the restrictions that apply when the linear response technique is used. You might want to proceed with finite displacement calculations without LO-TO splitting if these restrictions affect your study. In this case, only TO modes will be reliably produced when there is LO-TO degeneracy in the results.

Calculating the phonon dispersion produces phonon frequencies and eigenvectors along high symmetry directions in the Brillouin zone. The standard path for each lattice type is taken from Bradley and Cracknell (1972). The path can be modified using the Brillouin Zone Path dialog. The density of points along the path, which affects the appearance of the resulting chart, is controlled by the Quality setting in the Dispersion section on the CASTEP Phonon Properties Setup dialog.

To calculate phonon dispersion

- Choose Modules | CASTEP | Calculation from the menu bar to display the CASTEP Calculation dialog.
- Select the Properties tab.
- Check the Phonons checkbox in the list of properties, then select the Dispersion radio button which appears below the list.
- If required, check the Calculate LO-TO splitting checkbox.
- Select the technique to be used to calculate the phonon frequencies from the Method dropdown list.
- Click the More... button to display the CASTEP Phonon Properties Options dialog.
- For linear response calculations, specify the convergence criterion for the force constants in the Convergence
tolerance text box. If you do not want to carry out a direct calculation, check the Use interpolation
checkbox and specify the q-point separation in the q-vector grid spacing for interpolation text box.
For finite displacement calculations, specify the cutoff radius to be used to construct the appropriate supercell in the Supercell defined by cutoff radius text box.

- Optionally, adjust the density of q-vectors along the high symmetry directions used for the phonon dispersion calculation via the Quality control in the Dispersion section.
- If you wish to inspect or modify the Brillouin zone path used for the phonon dispersion calculation, click the Path... button to display the Brillouin Zone Path dialog and alter the path segments accordingly.
- Optionally, accelerate the calculation by using partial Hessian approach - apply fixed atom constraints to the atoms that are not essential to the calculation (for example substrate atoms in a molecule on surface calculations).

Calculating the phonon density of states produces phonon frequencies and eigenvectors on the regular Monkhorst-Pack mesh of q-vectors. This information is required to produce either the total or projected (partial) phonon density of states and, thus, to calculate thermodynamic properties. The quality of the q-vector set is controlled by the Quality setting in the Density of states section on the CASTEP Phonon Properties Options dialog.

To calculate the density of states

- Choose Modules | CASTEP | Calculation from the menu bar to display the CASTEP Calculation dialog.
- Select the Properties tab.
- Check the Phonons checkbox in the list of properties, then select the Density of states radio button which appears below the list.
- If required, check the Calculate LO-TO splitting checkbox.
- Select the technique to be used to calculate the phonon frequencies from the Method dropdown list.
- Click the More... button to display the CASTEP Phonon Properties Options dialog.
- For linear response calculations, specify the convergence criterion for the electronic eigenvalues in the Convergence
tolerance text box. If you do not want to carry out a direct calculation, check the Use interpolation
checkbox and specify the q-point separation in the q-vector grid spacing for interpolation text box.
For finite displacement calculations, specify the cutoff radius to be used to construct the appropriate supercell in the Supercell defined by cutoff radius text box.

- Optionally, adjust the density of Monkhorst-Pack q-vectors used for the phonon density of states calculation via the Quality control in the Density of states section.
- If you wish to inspect or modify the setup of the Monkhorst-Pack grid, click the More... button to display the Phonon Density of States Options dialog and alter the settings accordingly.
- Optionally, accelerate the calculation by using partial Hessian approach - apply fixed atom constraints to the atoms that are not essential to the calculation (for example, substrate atoms in a molecule on surface calculations).

If you choose quality gamma frequencies then eigenvectors will be only calculated at the Γ-point, which determines most of the experimental data on IR or Raman spectra. This can accelerate finite displacement calculations tremendously as no supercell is constructed for this case. However, the accuracy of thermodynamic properties obtained with this single q-vector is very poor as no acoustic degrees of freedom can be taken into account.

CASTEP can be used to calculate vibrational frequencies of isolated molecules as well as the phonon dispersion of solids. It is recommended that only the Γ-point is used for electronic calculations and that the Γ-point is requested when performing either phonon dispersion or phonon density of states calculations. In addition, the all bands/EDFT electronic minimizer is known to be more efficient for studies of isolated molecules in supercell geometry than the density mixing minimizer. Therefore, it is recommended that you change the Electronic minimizer setting to All Bands/EDFT on the SCF tab of the CASTEP Electronic Options dialog when performing such calculations.

Calculations for "molecule in a box" systems that do not require geometry optimization can be sped up if the molecular symmetry is utilized. Use the Find Symmetry tool to find and apply the symmetry of the molecule to the supercell.

Do not calculate LO-TO splitting for a "molecule in a box" system. There is no physical meaning to this term when studying molecular, rather than crystalline, vibrations.

- Parameters for geometry optimization
The results of a phonon calculation will be inaccurate unless the geometry of the input structure is well converged. Geometry optimization to a true ground state requires that the forces are well converged.

In general, using a Quality setting of Ultra-fine for the geometry optimization on the Setup tab of the CASTEP Calculation dialog should be sufficient for the purposes of obtaining accurate forces, but the safest procedure is to investigate the convergence of the forces as a function of calculation parameters - primarily the k-point sampling. It is recommended that you carry out a series of single-point energy calculations using increasingly dense k-point meshes. Monitor the convergence of the forces until they converge to within the force tolerance criterion.

- Geometry optimization of the input structure
Once you have generated reasonably well-converged forces, you can carry out the geometry optimization. Use the same force convergence tolerance as for the force convergence test. A well-converged geometry optimization is of little value if the forces are inaccurate because of convergence errors.

You may wish to perform a fixed-cell or variable-cell geometry optimization, depending on your goals for the calculation. The lattice-dynamical problem is well defined in either case, but, of course, the pressure or stress will be different. You should also monitor the convergence of the stress before carrying out a variable-cell optimization (though the behavior is usually similar to the convergence of forces).

- Use of consistent electronic settings
To be a valid lattice dynamics calculation, the phonon run must use the same specification as the geometry optimization. If you want to change anything of significance, such as the cutoff, XC functional or k-point sampling, you must carry out a fresh geometry optimization using these new settings before starting the lattice dynamics run.

- Checking the convergence of the results
Unfortunately, following the above guidelines does not guarantee that your final phonon frequencies will be converged to any given tolerance. The only way to determine that this is the case is to actually check the convergence behavior of the final properties. This requires a subtle judgment of whether you are measuring a 'primary' change due to the convergence of force constants or a 'secondary' one consequent on the slightly different geometry.

As noted in the literature, and from experience, phonon frequencies are more sensitive to k-point convergence than geometries, assuming tolerance criteria of a few cm

^{-1}and a few hundredths of an angstrom. Acoustic phonons near the Γ-point are the most sensitive, as they depend on near-cancellation between large force constant terms in the dynamical matrix. Dielectric properties and Born charges tend to be more sensitive than phonons, on a fractional proportion tolerance.The ultimate convergence test would require geometry optimization performed for a denser k-point grid, followed by a new phonon calculation - this is the only way to determine whether the k-point sampling has an effect on the accuracy of the calculated vibrational frequencies.

Phonon spectra in metallic compounds are very sensitive to the details of the Fermi surface. To obtain reasonable spectra using linear response method for metals, the k-point sampling must be extremely dense: much denser than the Fine mesh. It is recommended to consider setting the Separation parameter on the k-points tab of the CASTEP Electronic Options dialog to less than 0.02. A clear sign of insufficient quality of k-point sampling is the presence of imaginary acoustic modes near the Γ-point.

Phonon density of states

Phonons

Linear response

Setting up a calculation on an isolated molecule

CASTEP Calculation dialog

Accelrys Materials Studio 8.0 Help: Wednesday, December 17, 2014