Hessian eigenvector

Close to a stationary point gc vanishes. One of the eigenvalues of the augmented Hessian Eq. (3.22) then goes to zero and the rest approach those of Gc. The zero-eigenvalue step becomes the Newton step and the remaining n steps become infinite and parallel to the Hessian eigenvectors. 

At stationary points there are GF. curves leading along the direction of all Hessian eigenvectors, and by tracing out GE paths it is possible to locate many stationary points... 

Slater determinant or similar approximate wave function Gradient component along a Hessian eigenvector Electric field... 

An arbitrary vector, y, can be written as a linear combination of the Hessian eigenvectors, ep... 

Interference from Hessian eigenvectors corresponding to overall translation or rotation is prevented by orthogonalization to these degrees of freedom. 

Expanding y in terms of the unknown Hessian eigenvectors as above reveals a lower bound for k(y) ... 

Search for a transition state along the Hessian eigenvector with the smallest nonzero eigenvalue. 

Wc have omitted the six freciuencies corresponding to rotational and translational motions of the whole cluster. One of the advantages of the INM analysis is that we can perform projections of the density of states. One can decompose the density of states spectrum, c.g., into molecular rotational and translational motion [39]. For molecular clusters it is interesting to explore the localization of the motion described by the Hessian eigenvectors at different frequencies. Even though the harmonic motion is inherently collective, certain motions can be attributed to a limited area. This is the case of non-homogeneous systems, where the spectral characteristics can be quite different for different spatial parts. We define a projector Parea... 

Here fi is the projection of the gradient along the Hessian eigenvector with eigenvalue Si (the gradient component pointing in the direction of the ith eigenvector). 

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