Dipole Moment in periodic systems and Wannier Functions

General and efficient algorithms for obtaining maximally localized Wannier functions

Physical Review B, 61(15):10040.
Gerd Berghold, Christopher J Mundy, Aldo H Romero, Jürg Hutter, and Michele Parrinello (2000)


Recent advances in the theory of polarization and the development of linear-scaling methods have revitalized interest in the use of Wannier functions for obtaining a localized orbital picture within a periodic supercell. To examine complex chemical systems it is imperative for the localization procedure to be efficient; on the other hand, the method should also be simple and general. Motivated to meet these requirements we derive in this paper a spread functional to be minimized as a starting point for obtaining maximally localized Wannier functions through a unitary transformation. The functional turns out to be equivalent to others discussed in the literature with the difference of being valid in simulation supercells of arbitrary symmetry in the Γ-point approximation. To minimize the spread an iterative scheme is developed and very efficient optimization methods, such as conjugate gradient, direct inversion in the iterative subspace, and preconditioning are applied to accelerate the convergence. The iterative scheme is quite general and is shown to work also for methods first developed for finite systems (e.g., Pipek-Mezey, Boys-Foster). The applications discussed range from crystal structures such as Si to isolated complex molecules and are compared to previous investigations on this subject.

URL: http://dx.doi.org/10.1103/PhysRevB.61.10040

Maximally-localized Wannier functions for disordered systems: Application to amorphous silicon

Solid State Communications, 107(1):7–11.
Pier L Silvestrelli, Nicola Marzari, David V, Michele erbilt, and Parrinello (1998)


We use the maximally-localized Wannier function method to study bonding properties in amorphous silicon. This study represents, to our knowledge, the first application of the Wannier-function analysis to a disordered system. Our results show that, in the presence of disorder, this method is extremely helpful in providing an unambiguous picture of the bond distribution. In particular, defect configurations can be studied and characterized with a novel degree of accuracy that was not available before. Author Keywords: A. disordered systems; A. semiconductors; C. point defects; D. electronic states (localized)

URL: http://dx.doi.org/10.1016/S0038-1098(98)00175-6

Ab initio infrared spectrum of liquid water

Chemical Physics Letters, 277(5-6):478-482.
Pier L Silvestrelli, M. Bernasconi, and Michele Parrinello (1997)


An ab initio calculation of the infrared spectrum of liquid water has been performed using Car-Parrinello molecular dynamics and evaluating the electronic polarization by means of the Berry phase formulation. The major features of the spectrum are in good agreement with experiments and are shown to arise from specific vibrational motions of the water molecules. The effect of quantum corrections to the spectrum is discussed.

URL: http://dx.doi.org/10.1016/S0009-2614(97)00930-5