posted on 2021-11-05, 18:07authored byMarjory
C. Clement, Xiao Wang, Edward F. Valeev
We describe a robust method for determining
Pipek–Mezey
(PM) Wannier functions (WF), recently introduced by Jónsson
et al. (J. Chem. Theor. Chem.2017,13, 460), which provide some formal advantages over the
more common Boys (also known as maximally-localized) Wannier functions.
The Broyden–Fletcher–Goldfarb–Shanno-based PMWF
solver is demonstrated to yield dramatically faster convergence compared
to the alternatives (steepest ascent and conjugate gradient) in a
variety of one-, two-, and three-dimensional solids (including some
with vanishing gaps) and can be used to obtain Wannier functions robustly
in supercells with thousands of atoms. Evaluation of the PM functional
and its gradient in periodic linear combination of atomic orbital
representation used a particularly simple definition of atomic charges
obtained by Moore–Penrose pseudoinverse projection onto the
minimal atomic orbital basis. An automated “canonicalize phase
then randomize” method for generating the initial guess for
WFs contributes significantly to the robustness of the solver.