Subject: rules of thumb in optimiz.

From: Patrick Bultinck <[email-masked]>
Date: Fri, 20 May 1994 17:31:10 +0200 (MET DST)

Dear netters,

As you may have seen in my other message, I have sent an appendix to the 
summary on the use of symmetry in optimizations of molecular geometries. 
As became clear soon after I sent my original question there is no real 
conclusive answer that is superb to another.

Another thing I would like to know, since I have to do quite some 
extensive optimizations is on the use of the initial Hessian.

As most of you will know there is a big dependance for the number of 
required steps in an optimization (and so CPU-time) on the value of the 
initial Hessian (energy second derivative matrix).

This is pointed out by e.g. Schlegel in Ab Initio methods in Quantum 
Chemistry, p 249 in Advances in chemical physics, LXVII (1987) p.249.
He states (and this will be no suprise for you) that "an accurate initial 
estimate initial estimmate of the second derivative matrix can improve 
the rate of convergence significantly ...".

Now what better initial Hessian than the one computed analytically or 
numerically for the starting geometry.
Another possibility would be to use the one calculated at a lower level 
(of theory or basis set). This is possible through the fact that hessians 
are always 3N*3N (N=number af atoms).
Another widely used one is to use some sort of positive diagonal matrix 
that will be updated during the optimization, so that the number of steps 
is exceeded significantly, but no initial hessian has to be calculated.

My question is simple,

What is the opinion of the more experienced quantum chemists on the use 
of different approaches to find an initial hessian ? (a summary will be 
sent, so that all netters can hear all sorts of opinions... like last time)

Are there any simple rules of thumb that will approximately tell you what 
will be the relative time needed for the computation of the Hessian 
relative towards the number of steps it will require to find a half-good 
initial Hessian starting from e.g. a positive definite diagonal matrix ?  
(given basis set and number of atoms).

Hoop I havnt tijped to manny erreurs in my massage...

Patrick, University of Ghent, Belgium.