Maximally localized Wannier functions MLWF

III.B. In order to analyze the wavefunction in a chemically more intuitive way, it is useful to localize it. In the framework of AIMD this is, for example, done by calculating the maximally localized Wannier functions (MLWF) and the corresponding expectation values of the position operator for a MLWF basis the so-called maximally localized Wannier centers (MLWCs), see Fig. 1 (67-72). With the help of the MLWC it is possible to compute molecular dipole moments (72-82). Furthermore, it is possible with the MLWC to obtain molecular properties, e.g., IR spectra (75,76,82-85). 

For the description of a solution of alanine in water two models were compared and combined with one another (79), namely the continuum model approach and the cluster ansatz approach (148,149). In the cluster approach snapshots along a trajectory are harvested and subsequent quantum chemical analysis is carried out. In order to learn more about the structure and the effects of the solvent shell, the molecular dipole moments were computed. To harvest a trajectory and for comparison AIMD (here CPMD) simulations were carried out (79). The calculations contained one alanine molecule dissolved in 60 water molecules. The average dipole moments for alanine and water were derived by means of maximally localized Wannier functions (MLWF) (67-72). For the water molecules different solvent shells were selected according to the three radial pair distributions between water and the functional groups. An overview about the findings is given in Tables II and III. 

The idea of distributed dipole moments has also been transferred to the dynamic domain and we shall discuss recent work from our laboratory in this section in more detail. With the help of maximally localized Wannier functions local dipoles and charges on atoms can be derived. The Wannier functions are obtained by Boys localization scheme [217]. Thus, Wannier orbitals [218] are the condensed phase analogs of localized molecular orbitals known from quantum chemistry. Access to the electronic structure during a CPMD simulation allows the calculation of electronic properties. Through an appropriate unitary transformation U of the canonical Kohn-Sham orbitals maximally localized Wannier functions (MLWFs)... 

The exploitation of localized orbitals for dispersion energy calculations has already been proposed since the early works on local correlation methods [41 5]. In classical and semiclassical models most often the atoms are selected as force centers only a few works exploit the advantages related to the use of two-center localized orbitals and lone pairs. A notable exception is the recent work of Silvestrelh and coworkers [46-50], who adapted the Tkatchenko-Scheffler model [16] for maximally localized Wannier functions (MLWF), which are essentially Boys localized orbitals for solids. It is worthwhile to mention that one of the very first use of the bond polarizabilities as interacting units for the description of London dispersion forces has been suggested as early as in 1969 by Claverie and Rein [51] see also [52],... 

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