William-Stone-Misquitta

More recent methods (Gagliardi et al. 2004 LUlestolen and Wheatley 2007 Wheatley and Lillestolen 2008) have been more successful, but are either applicable only to the static polarizability or are too cumbersome to use routinely. Also very recently, distribution schemes were proposed by Williams and Stone (2003) and Misquitta and Stone (2006). These two methods have been combined into the Williams-Stone-Misquitta (WSM) method which has proved to be one of the most successful methods for obtaining distributed polarizabilities. This is what we will describe next. 

The WSM method involves three stages. In the first, the constrained density-fitting scheme (Misquitta and Stone 2006) is used to calculate distributed, non-local polarizabilities. These are then localized is stage two. And subsequently, in the final stage, refined using a method based on Ref Williams and Stone (2003). 

Step 3 The quality of the local polarizability model from the previous step can be dramatically improved using the method of Williams and Stone (2003). In this step, the local polarizabilities are refined by requiring them to reproduce a set of point-to-point polarizabilities which describe the response of the electrostatic potential at a point to the frequency-dependent potential produced by a unit oscillating point charge at another. Details of the refinement process are given in Misquitta and Stone (2008a) and Misquitta et al. (2008a). 

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