A gradient extremal is defined as a locus of points in the contour space where the gradient is extremal [10]. These gradient extremals connect stationary points on a molecular potential energy surface and are locally characterized by requiring that the molecular gradient is an eigenvector of the mass-weighted molecular Hessian at each point on the line. From a stationary point there will be gradient extremals leaving in all normal coordinate directions, and stationary points on a molecular potential surface may thus be characterized by following these gradient extremals. The implementation of this approach in DALTON is described in Ref. [10].
Before discussing more closely which keywords are of importance in such a calculation and how they are to be used, we give an example of a typical gradient extremal input in a search for a first-order transition state along the second-lowest mode of a mono-deuterated ethane molecule:
**DALTON INPUT .WALK *WALK .GRDEXT .INDEX 1 .MODE 2 .ISOTOP 8 1 1 2 1 1 1 1 1 1 **WAVE FUNCTIONS .HF *END OF INPUT
The request for a gradient extremal calculation is controlled by the keyword .GRDEXT . In this example we have chosen to follow the second-lowest mode, as specified by the keyword .MODE .
As the calculation of the gradient extremal uses mass-weighted
coordinates , it is recommended to
specify the isotopic constitution of
the molecule. If none is specified, the most abundant
isotope of each atom is used by default. In this example the
molecule has the second-most abundant isotope of atom number 3, which,
according to the description of the calculation should correspond
to a deuterium isotope. The rest of the atoms in the molecule is of
the most abundant isotope. See also Sec. 
.
A requirement in a gradient extremal calculation is that the calculation is started on a gradient extremal. In practice this is most conveniently ensured by starting at a stationary point, a minimum or a transition state. The index of the critical point -- that is, the number of negative Hessian eigenvalues -- sought, need to be specified (by the keyword .INDEX ), as the calculation would otherwise continue until a critical point with index zero (corresponding to a minimum), is found.