3.36 DFPT - density functional perturbation theory module

This code has recently been reorganised by Connor Box, the original DFPT implementation in FHI-aims was written by Honghui Shang and coworkers at FHI. Please contact connor.box@warwick.ac.uk for any questions related to the current implementation of DFPT in FHI-aims.

To compute vibrational frequencies, phonon band-structures, or molecular polarizabilities accurately, we need to understand how the electronic structure responds to external influences, such as nuclear displacements ($\partial H_{ij}/\partial R_I$) or applied electric fields ($\partial H_{ij}/\partial \mu$). This response can be obtained through density-functional perturbation theory (DFPT), which assumes a linear response to external perturbations like lattice displacement or electric fields. While different perturbations require specific integrals, DFPT provides a general framework applicable to various response properties. A DFT calculation is carried out to obtain the ground-state electron density $\rho (r)$ before initiating the general DFPT computation. Similar to the SCF algorithm in DFT, DFPT requires self-consistent convergence of response properties via the Coupled Perturbed SCF algorithm (CPSCF), including density response $n^{(1)}(r)$, first-order response Hamiltonian ${𝑯}^{(1)}$, and wave function expansion coefficients, ${𝑼}^{(1)}$. This process is universal, with the only property-specific aspects involving integrations over the relevant perturbation operator (e.g., during the construction of ${𝑯}^{(1)}$). Once the first order density matrix is converged, various response properties such as phonon band-structures, phonon linewidth, or polarizability can be accurately determined.

We support DFPT calculations for:

• •

  For vibrations in non-periodic systems and phonons in periodic systems. See 3.37.

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  For homogeneous electric fields in non-periodic systems (polarizability) and in periodic systems (dielectric constant). See 3.38.

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  For electron-phonon coupling and electronic friction in non-periodic systems and periodic systems. See 3.40.

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  A different DFPT implementation allows calculations based on the response to magnetic fields. This implementation shares a few keywords, but is otherwise completely separate currently. See 3.46.

There are two key references that provide the technical background for this implementation of DFPT within FHI-aims:

1. 1.

   Lattice dynamics calculations based on density-functional perturbation theory in real space
   Honghui Shang, Christian Carbogno, Patrick Rinke, Matthias Scheffler
   Comp. Phys. Comm., 215, 26 (2017)

2. 2.

   All-Electron, Real-Space Perturbation Theory for Homogeneous Electric Fields: Theory, Implementation, and Application within DFT
   Honghui Shang, Nathaniel Raimbault, Patrick Rinke, Matthias Scheffler, Mariana Rossi, Christian Carbogno
   New J. Phys., 20, 073040 (2018)