CCL: Optimization in Z-matrix vs Cartesian coordinates

 Sent to CCL by: "Jacco  van de Streek"
 [jacco.vandestreek~!~sund.ku.dk]
 > I initially supposed that a geometry optimization, if it is performed in
 > properly composed Z-matrix, takes less optimization steps than if it runs
 in
 > Cartesian coordinates. Is that wrong?
 For a molecular compound, if the alternative is x,y,z coordinates, that should
 be correct. A Z-matrix in principle allows for a more natural description of the
 degrees of freedom in terms of bonds, valence angles and torsions. As you write,
 this is only true for "a properly composed Z-matrix" because a
 Z-matrix description is not unique and Z-matrix descriptions in which e.g.
 rotatable torsions do not correspond to chemical torsions would get you into
 trouble even though the Z-matrices would all be mathematically equivalent.
 A trivial example where a Z-matrix description should be vastly superior to
 optimisation in x,y,z coordinates is as follows: imagine a fully
 energy-minimised biphenyl molecule. Now distort the molecule by changing the
 length of the central bond connecting the two phenyl rings by moving the two
 phenyl rings slightly apart (or closer), leaving the minimised geometry of the
 phenyl rings intact. A geometry optimisation in Z-matrix description should only
 change the central bond and this should converge very quickly, whereas a
 geometry optimisation in Cartesian coordinates will distort neighbours of the
 central atoms in the first step, which will ripple out to the extremes of the
 molecule and then back. At least that is the theory and the very little
 experimenting I have done and have heard/read about supports this.
 >  A properly constructed Z-matrix, as far
 > as I suppose, must use dummy atoms for each aromatic cycle in the
 > molecule (the dummy atom is placed in the center of a cycle).
 > I don't mean here the symmetry constraints. I want to compare the speed of
 > geometry optimization of a non-symmetrical molecule (C1) in Z-matrix and
 > Cartesian coordinates.
 > I have this question because I have implemented automatic generation of Z-
 > matrix in my program Chemcraft, and I wonder whether this feature can be
 > useful. I appreciate any suggestions, in which cases such feature can be
 > used.
 There is a more general method for choosing the optimal coordinates for an
 geometry optimisation, called "delocalised internal coordinates":
 Baker, J.; Kessi, A.; Delley, B. J. Chem. Phys. 1996, 105, 192.
 Best wishes,
 --
 Dr Jacco van de Streek
 Department of Pharmacy
 University of Copenhagen