- 85 Downloads
Gradient extremals on N-dimensional energy hypersurfaces V=V(x1 ⋯ x n ) are curves defined by the condition that the gradient ∇V is an eigenvector of the hessian matrix ∇∇V. For variations which are restricted to any (N−1) dimensional hypersurface ∇V(x1⋯ x N ) = V0= constant, the absolute value of the gradient ∇V is an extremum at those points where a gradient extremal intersects this surface. In many, though not all, cases gradient extremals go along the bottom of a valley or along the crest of a ridge. The properties of gradient extremals are discussed through a detailed differential analysis and illustrated by an explicit example. Multidimensional generalizations of gradient extremals are defined and discussed.
Key wordsPotential energy surfaces Reaction paths
Unable to display preview. Download preview PDF.