Dear ADF users,

Several users have reported convergence problems with certain types of
geometry optimizations in internal (Z-matrix) coordinates. Although we
consider geometry optimization a very important task and did recognize
this as a major bug, we had so far been unable to find the precise origin
of this problem. Now, Dr. Drew McCormack, in a cooperation with SCM, has
found the cause of the problems and fixed this particular bug. In the next
release of ADF this fix will of course be included.

Two problematic cases have been identified in the case of optimizations
in internal coordinates:

1) A dihedral angle which passes through 0 or 180 degrees leads to a
   severe deterioration in the Hessian, due to an incorrect Hessian
   update. This is the bug that has been fixed. The deterioration in
   the Hessian will lead to awkward steps during the Z-matrix optimization
   and to poor or no convergence.

   Work-arounds or solutions:
   ==========================

   As a temporary work-around until a new ADF version is released, we suggest
   the following options:

   a) perform the geometry optimization in Cartesian coordinates
   b) introduce 4 dummy atoms by hand, one in the center of mass, one along
      the x-axis, one along the y-axis, and one along the z-axis.
      Use these dummy atoms to avoid dihedral angles close to 0 or 180
      degrees.
   c) use the utility offered by Marcel Swart to perform the task under b)
   d) for those with a source code extension to their ADF license, you can
      contact us to obtain a modified and a new routine which contain the fix.

2) Bond angles near 0 or 180 degrees.
    Such angles are to be strictly avoided, because they will lead to
    numerical instabilities in ADF's optimization algorithm (for all
    ADF versions). Basically the idea of using dummy atoms can be applied
    here as well to avoid such angles.

    Problems arise also if the bond angle approaches 180 degrees during
    the optimization. In such a case it may be wise to restart with a
    suitable dummy atom included to avoid the 180 degree bond angle.

    If a bond angle passes 180 degrees, the situation may be even worse
    because this can be the cause of a flip in the dihedral angle which
    will cause severe convergence problems.

We trust that with this advice many geometry optimization problems
can be avoided. Of course, we greatly appreciate further reports of
problematic geometry optimizations which seem unrelated to the issues
mentioned above.

SCM is currently considering several ideas on further improvements in the
optimization algorithm, both for the choice of coordinates, and for the
inclusion of more general types of constraints. Such improvements will be
implemented in future versions of ADF, either by SCM itself, or through
cooperations with others.

We welcome any comments or suggestions on this topic.

Best regards,
Stan van Gisbergen
 
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Dr. S.J.A. van Gisbergen SCIENTIFIC COMPUTING & MODELLING NV
Phone: +31-20-4447626 Vrije Universiteit, Theoretical Chemistry
Fax: +31-20-4447629 De Boelelaan 1083
E-mail: vangisbergen_at_scm.com 1081 HV Amsterdam, The Netherlands
                               http://www.scm.com
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Received on 2002-08-23 16:01:26