Boys localization scheme

The Boys localization scheme uses the square of the distance between two electrons as the operator, and minimizes the expectation value. 

The operator used in the Boys localization scheme can be expanded as... 

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)... 

Hi) Three Q bonds (banana bonds). There are neither a nor n bonds, bnt the P-0 bond is a formal triple bond with the three curved regions of electron density between P and O in a symmetrical fashion. The remaining lone pair on the oxygen atom points away from phosphoras along the P-0 axis. The banana bond description originates from a Boys localization scheme [1,29-31] and from generalized valence bond calculations [6,32-34] for the phosphine oxide derivatives. 

Table 9.17. Centroids positions xu, X2i, isi), in a.u., and polarization fractions pi for functions Wi(r) in the SrZrOs crystal localized according to the Waimier-Boys mixed scheme [63]...

We have added SIC capabilities to the DFT package in Q-Chem [20]. Initially, this involves localizing the KS canonical orbitals with the Boys procedure [78] and using these to evaluate the self-interaction correction. Thus, the present scheme simply applies the correction perturbatively to the KS energy. Table 9 lists the corrected DFT barriers, evaluated at the re-optimized SIC geometries. 

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