[molpro-user] Optg and Numerical Hessian

[Tsuneo Hirano]

Dear MOLPRO developers (and users),

When MOLPRO was upgraded from MOLPRO 2008 to MOLPRO 2009 and above, 
optg calculation at the MRCI level with symmetry constraint has 
become ‘illegal’ and the relevant job will be aborted.  We 
encountered this situation when we tried to optimize the geometry at 
the MR-SDCI level based on the SA-MCSCF natural orbitals using MOLPRO 
2010.1 (Patch level: 8).  An example of the input file is given as an 
attached file‘hco_cs_ts_Ap_opt_vdz_2010.inp.’  The error message 
from the MOLPRO 2010.1 for this input is;
-------------------
   method=MRCI  nstsym= 2  istsym(1)=1  isyref=1

   Numerical hessians for multireference methods can only be computed 
without symmetry.
   Use NOSYM !
   ? Error
   ? Illegal use of symmetry
   ? The problem occurs in numhess_mppx

   ERROR EXIT
   CURRENT STACK:      MAIN
-------------------
This error message came from the Lines 167-174 in the ‘numhess_mppx.f 
’of MOLPRO 2010.1.

The same input (with change in “symmetry,x; geometry={” to “ 
geometry = {x;”) successfully ran to the end using MOLPRO 2006.1 
(Patch level: 149).  The corresponding message is;
-------------------
   Numerically approximating hessian using central energy differences

   Task list generated. Total number of displacements:     12
-------------------

Generally speaking, numerical Hessian is simply the 2nd-order 
geometrical derivatives of the energy, and it does not matter by what 
methods the energy is calculated.  Therefore, with or without 
symmetry constraint, or for multi-reference or single-reference 
method, the numerical Hessian can be constructed once the energy that 
is specified by the ‘variable’ directive can be calculated for the 
given geometrical changes.

When symmetry constraint is imposed, the geometrical changes for the 
numerical Hessian should be done to keep the given symmetry.  This 
can be done by setting the z-matrix or xyz-type geometry 
specification symmetry-adaptive.  It is the responsibility of the 
user of MOLPRO to write a proper z-matrix or xyz-type geometry 
specification to keep the symmetry for any change of the geometry in 
the numerical evaluation steps for the Hessian.

The one who upgraded the optg codes might misunderstand what the 
numerical Hessian means or there might be some reason which I cannot think out.
It should be noted that Optg using numerical Hessian at the 
multi-reference level with symmetry constraint is very important.

Best wishes,
Tsuneo Hirano


************************************************
Tsuneo Hirano
Emeritus Professor of Chemistry, Ochanomizu University

e-mail:  hirano at nccsk.com
************************************************ 
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