Geometry Direct Inversion in the Iterative

Figure 14.11 An example of a function and the associated gradient norm known of these is perhaps the GDIIS (Geometry Direct Inversion in the Iterative Subspace) which is directly analogous to the DIIS for electronic wave functions... 

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. 

CPR = conjugate peak refinement GDIIS = geometry direct inversion in the iterative subspace GE = gradient extremal LST = linear synchronous transit LTP = line then plane LUP = locally updated planes NR = Newton-Raph-son P-RFO = partitioned rational function optimization QA = quadratic approximation QST = quadratic synchronous transit SPW = self-penalty walk STQN = synchronous transit-guided quasi-Newton TRIM = trust radius image minimization TS = transition structure. 

Csaszar P and Pulay P 1984 Geometry optimization by direct inversion in the iterative subspace J. Moi. Struct. (Theochem) 114 31... 

GDIIS. - Another approach based on the Hessian and devised for structure optimization is the GDIIS,25 i.e., geometry optimization using direct inversion in the iterative subspace. GDIIS is a special version, devised for structure optimization, of DIIS. It has, e.g., been described by Farkas and Schlegel.26... 

As well as the EF algorithm, the PQS package has another algorithm for structure minimization GDllS (Csaszar and Pulay 1984). This is an extension of Pulay s ubiquitous DllS (Direct Inversion in the Iterative Subspace) procedure for accelerating SCF convergence (Pulay 1980, 1982), only applied instead to geometry optimization. 

The best known of these is perhaps the GDIIS (geometiy direct inversion in the iterative subspace). In this case the inteipolated geometry and associated gradient are generated by requiring that the norm of an enor vector is a minimum, subject to a normalization condition ... 

Included in the methods discussed below are Newton-based methods (Section 10.3.1), the geometry optimization by direct inversion of the iterative subspace, or GDIIS, method (Section 10.3.2), QM/MM optimization techniques (Section 10.3.3), and algorithms designed to find surface intersections and points of closest approach (Section... 

The GDIIS method (geometry optimization by direct inversion of the iterative subspace) is an alternative approach for predicting the change in the geometry that is comparable in efficiency to the quasi-Newton methods. A linear combination of the current and previous points is chosen so that the Newton step is a minimum ... 

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