1997 (Marzari & Vanderbilt)  : Wannier function projection methods

• These methods enable a more qualitative view of the electron density by projecting the Bloch wavefunctions into localized Wannier functions [1], which is especially useful when it comes to transition metal systems, but not limited to these.
• This description enables DFT practitioners to "talk" to the modelling community, since now we can approximate the physics and chemistry of the system in terms of orbitals.
• Two major milestones are the description of the maximally localized Wannier functions (MLWF) method by Marzari and Vanderbilt [2] and its community open-source implementation as Wannier90 [3].
• There are still ongoing work to perfect the method (such as alternative projection criteria), and to apply it to study other (more exotic) material systems. For instance, recently it has been used to describe the effective physics of the spin liquid candidate $\alpha$-$RuCl_3$ [4].

References:

[1] G.H. Wannier, Phys. Rev. 52, 191 (1937), doi:10.1103/PhysRev.52.191

[2] N. Marzari & D. Vanderbilt, Phys. Rev. B 56, 12847 (1997), doi:10.1103/PhysRevB.56.12847; N. Marzari et al., Rev. Mod. Phys. 84, 1419 (2002), doi:10.1103/RevModPhys.84.1419

[3] A.A. Mostofi et al., Comput. Phys. Commun. 178, 685 (2008), doi:10.1016/j.cpc.2007.11.016; A.A. Mostofi et al., Comput. Phys. Commun. 185, 2309 (2014), doi:10.1016/j.cpc.2014.05.003; G. Pizzi et al., J. Phys. Cond. Mat. 32(16), 165902 (2020), doi:10.1088/1361-648X/ab51ff

[4] C. Eichstaedt et al., Phys. Rev. B 100, 075110 (2019), doi:10.1103/PhysRevB.100.075110

1997 (Marzari & Vanderbilt): MLWF

• These methods enable a more qualitative view of the electron density by projecting the Bloch wavefunctions into localized Wannier functions [1], which is especially useful when it comes to transition metal systems, but not limited to these.
• This description enables DFT practitioners to "talk" to the modelling community, since now we can approximate the physics and chemistry of the system in terms of orbitals.
• Two major milestones are the description of the maximally localized Wannier functions (MLWF) method by Marzari and Vanderbilt [2] and its community open-source implementation as Wannier90 [3].
• There are still ongoing work to perfect the method (such as alternative projection criteria), and to apply it to study other (more exotic) material systems. For instance, recently it has been used to describe the effective physics of the spin liquid candidate $\alpha$-$\ce{RuCl_3}$ [4].

References:

[1] G.H. Wannier, Phys. Rev. 52, 191 (1937), doi:10.1103/PhysRev.52.191
[2] N. Marzari & D. Vanderbilt, Phys. Rev. B 56, 12847 (1997), doi:10.1103/PhysRevB.56.12847; N. Marzari et al., Rev. Mod. Phys. 84, 1419 (2002), doi:10.1103/RevModPhys.84.1419
[3] A.A. Mostofi et al., Comput. Phys. Commun. 178, 685 (2008), doi:10.1016/j.cpc.2007.11.016; A.A. Mostofi et al., Comput. Phys. Commun. 185, 2309 (2014), doi:10.1016/j.cpc.2014.05.003; G. Pizzi et al., J. Phys. Cond. Mat. 32(16), 165902 (2020), doi:10.1088/1361-648X/ab51ff
[4] C. Eichstaedt et al., Phys. Rev. B 100, 075110 (2019), doi:10.1103/PhysRevB.100.075110