GDIIS method

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... 

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. 

Abstract It is shown that the system of unit vectors corresponding to the internal coordinates is non-orlhogonal generally. The deduction starts with the well-known ortho-normality of unit vectors of the Cartesian coordinates. The crucial point of the GDIIS method is discussed regarding a partially isomorphic relationship between two vector spaces. Some features of the pseudoinverse of the Elia-shevich-Wilsonian matrix B are deduced and discussed these are analogous to the conditions formulated originally for the elements of the B-matrix. 

O Equation 10.20-10.23 constitute a complete cycle of the GDIIS method. Convergence can be tested for in the usual way (based on the gradient and the displacement from the previous step) or on the norm of the GDIIS residuum vector. 

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 ... 

The GDIIS approach does not depend as critically on the quality of the Hessian as quasi-Newton methods. It can be... 

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