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Re^5: Optimization of conical intersection with penalty function method: how to control the gap?

Alex Granovsky

Dear Evgeniy,

I doubt if it is possible to converge CoIns to 0.0001 Hartree using
penalty-based methods. Try to converge to 0.001 Hartree first.
Quick search with Google Scholar seems to show that most people uses
gap of 0.001 Hartree or so when they searches for CoIns.

As to optimal parameters of penalty function, it is rather easy to
construct a mathematical model of penalty function-based optimization
because the functional form of penalty function is known. One just
needs to use some approximations for PESs and voila!

Note, the larger is B (a "strength" of penalty function) the worse is
convergence of penalty-based methods. You'd probably need to severely
limit the maximum allowed geometry optimization step size.

Kind regards,

On Sun Oct 23 '16 2:23pm, GrEv wrote
>Dear Alex,

>Thanks for your answer! I wonder how much should I increase the B parameter to converge to a conical intersection with a smaller gap (0.0001)? With the default value of B (3.5) the gap is ~0.003.

>Best regards,
>On Sat Oct 22 '16 11:23pm, Alex Granovsky wrote
>>Dear Evgeniy,

>>SHIFT0 and SHIFT variables are primary used by Lagrange multiplier-
>>based code.

>>SHIFT can be used with penalty function based code but has very
>>little impact on the energy gap when gap is large and shift
>>is small. It is intended to trace rather large differences between
>>states like 0.1 or 0.05 Hartree.

>>Kind regards,
>>On Sat Oct 22 '16 7:39pm, GrEv wrote
>>>Dear Alex,

>>>Thanks very much for your reply.
>>>Just a curios question, what does the SHIFT option do?

>>>Best regards,

>>>On Sat Oct 22 '16 6:00pm, Alex Granovsky wrote
>>>>Dear Evgeniy,

>>>>there is no direct control over the energy gap for penalty-based CoIn
>>>>optimization procedures. The gap can be controlled indirectly using
>>>>parameters defining a penalty function. The larger is the "strength"
>>>>of penalty function the smaller will be the gap. With Firefly, the
>>>>strength is controlled by the parameter B of $mcaver group.

>>>>Kind regards,
>>>>On Sat Oct 22 '16 11:50am, GrEv wrote

>>>>>I am doing optimization of the minimum energy conical intersection using the penalty function method, with the following input (from the manual, p. 176) :

>>>>>$STATPT OPTTOL=0.00005 NSTEP=500 method=qa trmax=0.05 dxmax=0.05
>>>>> HSSEND=.f. $END

>>>>>Using this input I found a conical intersection (CoIn), with the final gap between the states of 0.003. I'd like however to have a smaller gap, let's say 0.0001. How this could be done. I've tried to use the SHIFT option in $MCAVER, setting SHIFT=0.0001. It however didn't do the job. I got a CoIn with almost the same gap as before.
>>>>>Many thanks!


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