Module SCDM_WFs implements the selected columns of the density matrix (SCDM) method [1] for building localized Wannier Functions (WFs). Wannier90 [2] is a post-processing tool for the computation of the Maximally Localised Wannier Functions (MLWFs) [3,4,5], which have been increasingly adopted by the electronic structure community for different purposes. The reasons are manifold: MLWFs provide an insightful chemical analysis of the nature of bonding, and its evolution during, say, a chemical reaction. They play for solids a role similar to localized orbitals in molecular systems. In the condensed matter community, they are used in the construction of model Hamiltonians for, e.g., correlated-electron and magnetic systems. Also, they are pivotal in first-principles tight-binding Hamiltonians, where chemically-accurate Hamiltonians are constructed directly on the Wannier basis, rather than fitted or inferred from macroscopic considerations, and many other applications, e.g. dielectric response and polarization in materials, ballistic transport, analysis of phonons, photonic crystals, cold atom lattices, and the local dielectric responses of insulators, for reference see [3]. This module is a first step towards the automation of MLWFs. In the original Wannier90 framework, automation of MLWFs is hindered by the difficult step of choosing a set of initial localized functions with the correct symmetries and centers to use as an initial guess for the optimization. As a result, high throughput calculations (HTC) and big data analysis with MLWFs have proved to be problematic to implement.

This module is part of the newly developed Wannier90 utilities within the pilot project on Electronic Structure Functionalities for Multi-Thread Workflows. The module is part of the pw2wannier interface between the popular QUANTUM ESPRESSO code link and Wannier90. It will be part of the next version of QUANTUM ESPRESSO v.6.3 and Wannier90. Moreover, it has been successfully added in a developer branch of the AiiDA workflow [6] to perform HTC on large material datasets.

Practical application and exploitation of the code

The SCDM-k method [1] removes the need for an initial guess altogether by using information contained in the single-particle density matrix. In fact, the columns of the density matrix are localized in real space and can be used as a vocabulary to build the localized WFs. The SCDM-k method can be used in isolation to generate well localized WFs. More interestingly is the possibility of coupling the SCDM-k method to Wannier90. The core idea is to use WFs generated by the SCDM-k method as an initial guess in the optimization procedure within Wannier90. This module is a big step towards the automation of WFs and simplification of the use of the Wannier90 program. The module is therefore intended for all the scientists that benefit from the use of WFs in their research. Furthermore, by making the code more accessible and easier to use, this module will certainly increase the popularity of the Wannier90 code.

[1] A. Damle, L. Lin, L. Ying SCDM-k: Localized orbitals for solids via selected columns of the density matrix J.Comp.Phys. 334 (2017) 1
[2] A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, N. Marzari wannier90: A tool for obtaining maximally-localised Wannier functions Com. Phys. Comm. 178 (2008) 685
[3] N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, D. Vanderbilt Maximally localized Wannier functions: Theory and applications Rev. Mod. Phys. 84 (2012) 1419
[4] N. Marzari, D. Vanderbilt Maximally localized generalized Wannier functions for composite energy bands Phys. Rev. B 56 (1997) 12847
[5] I. Souza, N. Marzari, D. Vanderbilt Maximally localized Wannier functions for entangled energy bands Phys. Rev. B 65 (2001) 035109
[6] G. Pizzi, A. Cepellotti, R. Sabatini, N. Marzari, B. Kozinsky AiiDA: automated interactive infrastructure and database for computational science Comp. Mat. Sci. 111 (2016) 218