Category:Linear response

Apart from ground-state properties, VASP can compute how a system reacts to external perturbations. Currently, we can consider three types of perturbations:

1. external electric field
2. atomic displacements
3. homogeneous strains

If we restrict ourselves to the first order of the perturbation then we are in the linear regime and thus we talk about linear response. A central quantity in linear response is the dielectric function which relates an external electric field with the internal electric displacement. The response to atomic displacements includes phonons and electron-phonon interactions. The response to homogeneous strains is related to the elastic tensor and piezoelectric tensor when combined with a response to and external electric field.

Polarization, berry phases, and finite electric fields

The polarization in a periodic system can be computed using the berry phase formulation of the polarization (often referred to as the modern theory of polarization). With a method to compute the polarization, we can apply a finite electric field to the system. Strictly speaking, polarization, as well as the application of a finite electric field, are ground-state properties, however, because they can be used to compute the static dielectric tensor, born effective charges, and piezoelectric tensors which are response properties, we refer to this approach here.

Static response

Dielectric tensor

For the case where the external electric field is static, the static dielectric function is sufficient to determine the response. This static response can be computed by finite differences (LCALCEPS) of the polarization with respect to a finite external electric field or by using density functional perturbation theory (LEPSILON).

Both LEPSILON or LCALCEPS yield the same converged results for the dielectric tensor, however, the former can only be used for local or semi-local exchange-correlation functionals and applies to both semiconductors and metals while the second can be used for meta-GGA or hybrid but only for systems with a gap.

Dynamic response

There are different approaches and levels of theory implemented in VASP to compute the frequency-dependent dielectric tensor. The simplest of these is done using the Green-kubo formula and is activated using LOPTICS = .TRUE.. This however neglects local-field effects which means that it only reproduces calculations from DFPT or finite differences of a finite electric field when LRPA = .TRUE. when the frequency is zero (static limit). To include local field effects one should use ALGO = CHI.

X-ray absorption spectroscopy

Another case of interest is the absorption of electromagnetic radiation by core electrons as measured experimentally in X-ray absorption near edge spectroscopy (XANES). This is obtained from the frequency-dependent dielectric function with the particularity that core electrons are explicitly included in the calculation. The theory page describes the implementation details within the PAW method and the relevant literature.

Nuclear magnetic resonance (NMR)

Nuclear magnetic resonance is a widely used spectroscopy technique used to probe the structure and chemical composition of molecules and solids. VASP can compute chemical shielding shifts which is the ratio between the external and induced magnetic field compared to a reference compound, hyperfine tensors and electric field gradients.

How to

• X-ray absorption near edge spectra (XANES) spectra from the supercell core-hole method