When refining transition states, and TS is not wanted, the McIver-Komornicki gradient norm minimization [9,10] routines, POWSQ and SEARCH, can be used by including SIGMA. These are very rapid routines, but do not work for all species. If the gradient norm is low, i.e., less than about 5 units, then SIGMA will probably work; in most cases where TS does not work, NLLSQ is recommended. SIGMA first calculates a Hessian matrix, a slow step, then works out the direction of fastest descent, and searches along that direction until the gradient norm is minimized. The Hessian is then partially updated in light of the new gradients, and a fresh search direction found. Clearly, if the Hessian changes markedly as a result of the line-search, the update done will be inaccurate, and the new search direction will be faulty. SIGMA should be avoided if at all possible when non-variationally optimized calculations are being done.

If the Hessian is suspected to be corrupt within SIGMA, it will be automatically recalculated. This frequently speeds up the rate at which the transition state is located. If you do not want the Hessian to be reinitialized--it is costly in CPU time--specify LET on the keyword line.