Hessian matrix

The choice of the initial Hessian matrix has a great effect on the convergence of the structure optimization. At present, there are three choices for the Hessian matrix in statpt. For minimization, a diagonal matrix or approximate Hessian matrix from a forcefield calculation using uff(see Section 5.4) can be used. For transition state optimizations you have to provide either the ``exact'' Hessian or results from the lowest eigenvalue search (LES, see Section 11). Note also that you can calculate the Hessian with a smaller basis set and/or at a lower wavefunction level, and use it for higher level structure optimization. Usually, a Hessian matrix calculated in a minimal basis using RI-DFT is good enough for all methods implemented in TURBOMOLE.

statpt automatically takes the best choice of the Hessian from the control file. For minimizations it first looks for the exact Hessian and then for the UFF Hessian. If none of them is found it takes the scaled unit matrix. For transition state optimization the exact Hessian has a higher priority than the results of LES.

The results of LES can be used to obtain an initial Hessian matrix for transition state optimizations involving large molecules, where calculation of the full Hessian is too expensive. Note, that LES calculations for statpt, in addition to the $les keyword require the following keywords to be added manually in the control file:

 
   $h0hessian
   $nomw

The default Hessian update for minimization is bfgs, which is likely to remain positive definite. The powell update is the default for transition state optimizations, since the Hessian can develop a negative curvature as the search progresses.