PC GAMESS/Firefly-related discussion club

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Alex Granovsky
gran@classic.chem.msu.su

I think I need to make one additional comment here...

>>>Well, it depends. I apply Firefly not only for isolated molecules, but also
>>>for molecules coupled to metal leads and on metal surfaces. Especially
>>>in the last case the large number of metal atoms should (or may) be frozen.
>>>The "lost time" in this case can be longer than useful time. :(
>>>

>>Let us assume the Hessian has the following structure:

>>|AA|AF|
>>|FA|FF|

>>where A is for active (i.e., non-frozen) and F is for frozen atoms.
>>Even with infinitely large masses of frozen fragments,
>>one still needs not only AA block, but also the entire
>>off-diagonal blocks (namely |AF| and |FA| where |AF| = transpose(|FA|));
>>and only |FF| block is not needed.
>>This means that all these additional vibs are not completely useless at all.

In seminumeric (a.k.a. numeric) mode, the Hessian matrix is computed
column by column (i.e., the information on each ivib is used to
fill the corresponding column of the Hessian). It is indeed possible
(and is very easy to implement) to limit the program to run over A block
displacements only. This will give information on |AA| and |FA| blocks.
One then could use the |AF| = transpose(|FA|) identity to complete the
required blocks of Hessian matrix.

However, as rows of Hessian matrix are calculated using finite
differences, the resulting, complete Hessian is not actually
symmetric as it should be, and hence, it has to be  symmetrized.
The symmetrization naturally results in symmetric Hessian,
in addition, there are some cancellation of errors due to
finite difference approach as the result of symmetrization.

What this means is that in practical calculations |AF| is only
approximately equal to transpose(|FA|) before symmetrization
of Hessian matrix. And to perform symmetrization, we need to compute
both these blocks.