Conjugate Gradient and Hybrid Searches

Conjugate gradient and hybrid conjugate gradient/eigenvector-following routines are now available for minimization, transition state searches and pathway calculations. These methods will generally be much faster than eigenvector-following for large systems if diagonalisation of the Hessian is the slowest step. A conjugate gradient minimization using only first derivatives can be specified by the keyword CGMIN. A hybrid conjugate gradient/eigenvector-following transition state search can be specified by CGTS. In the latter algorithm an eigenvector-following step is taken along the eigenvector corresponding to the smallest eigenvalue, which is determined by iteration if second derivatives are available, or a variational method if not. A conjugate gradient minimization is then performed in the tangent space, but it is not necessary for this optimization to converge accurately except in the vicinity of the transition state. Hence it may be most efficient to set the maximum number of conjugate gradient steps allowed in the tangent space optimization below the default value of 100.

The Hessian index can be checked after a conjugate gradient or hybrid search by calculating eigenvalues iteratively until the smallest positive eigenvalue is found. Checking is turned on by the keyword CHECKINDEX. This keyword now works with NOHESS. It is possible to use an alternative line minimization routine rather than the default from Numerical Recipes with the keyword MYLINMIN.

Pathways can be calculated by stepping off a transition state using an eigenvector-following step along the eigenvector corresponding to the smallest Hessian eigenvalue calculated by iteration, followed by conjugate gradient minimization. The keyword CGSTEP must be specified to do this, along with CGTS. If the PUSHOFF parameter is set then it is used in the usual way. The sign of the MODE parameter, if set, specifies whether the initial step is parallel or antiparallel to the eigenvector located.