Extrapolations the GDIIS method

Newton-Raphson methods can be combined with extrapolation procedures, and the best known of these is perhaps the Geometry Direct Inversion in the Iterative Subspace (GDIIS), which is directly analogous to the DIIS for electronic wave functions described in Section 3.8.1. In the GDIIS method, the NR step is not taken from the last geometry but from an interpolated point with a corresponding interpolated gradient based on the previously calculated points on the surface. 

The interpolated geometry and gradient are generated by requiring that the norm of an error vector is minimum, subject to a normalization condition. 

The are two common choices for the error vector, either a geometry or gradient vector, with the latter being preferred in more recent work.  

The DIIS approach attempts to find a low-gradient point within the subspace already searched. For optimizing electronic wave functions, there is usually only one minimum 

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