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#1 2019-01-17 15:26:41

Leo
Member
Registered: 2018-11-20
Posts: 5

findTS and Hessian index ()

Dear all,
I am trying to optimize a transition state structure on S1. Firstly, I would like to ask if this input can fulfill such a task:

>   export MOLCAS_MAXITER = 100
>   Do   while

   &SEWARD
    DoAnalytical
   &ESPF
    External = Tinker
    lamorok
   &RASSCF; spin=1; nActEl=12   0   0;   Inactive=76;   Ras2=12
   JobIph; ciroot = 3 3 1; rlxroot = 2

> COPY $WorkDir/$Project.JobIph $InpDir
> COPY $Project.JobIph $Project.JobOld
> COPY $WorkDir/$Project.RunFile $InpDir

   &ALASKA
   &SLAPAF
    prfc
    FindTS
 TSConstraints
    d1  =  Dihedral  C26 C27 C28 C29
    d2  =  Dihedral  H46 C27 C28 C34
 Values
    d1 = -89.9 degrees
    d2 = -89.9 degrees
 End of TSConstraints
    maxstep = 0.1
    cartesian
    rHidden = 10.0

> End Do

I thougth that computing the gradient for root 2 would drive findTS to look for a 2nd order transition state.
I also have another question, which is the meaning of the numbers in bracket () next to the index of the Hessian matrix?

**********************************************************************************************************************
*                                    Energy Statistics for Geometry Optimization                                     *
**********************************************************************************************************************
                       Energy     Grad     Grad              Step                 Estimated   Geom       Hessian
Iter      Energy       Change     Norm     Max    Element    Max     Element     Final Energy Update Update   Index
  1   -868.83000127  0.00000000 2.002153 1.033024 dEdx185  0.048489* lnm020     -868.93006523 RS-RFO  None      0
  2   -868.82749150  0.00250977 1.252956 0.778178 dEdx177 -0.053951* lnm119     -868.85880292 RS-RFO  MSP       0
  3   -868.82375596  0.00373554 0.070123-0.040238 lnm185  -0.015692* lnm185     -868.82530410 RSIRFO  MSP       1
  4   -868.82484163 -0.00108567 0.050050 0.024209 lnm119  -0.026242* lnm020     -868.82651679 RSIRFO  MSP       1
  5   -868.82676886 -0.00192723 0.040982 0.022486 lnm119   0.020318* lnm119     -868.82777774 RSIRFO  MSP       1
  6   -868.82803368 -0.00126482 0.039985 0.021132 lnm119   0.039123* lnm006     -868.82996827 RSIRFO  MSP       1
  7   -868.82877549 -0.00074181 0.036540 0.019804 lnm119  -0.037504* lnm006     -868.83057403 RSIRFO  MSP       1
  8   -868.82647334  0.00230215 0.082184 0.046695 lnm185   0.045556* lnm119     -868.82949129 RSIRFO  MSP       1
  9   -868.82940517 -0.00293183 0.035694-0.023072 lnm185   0.025676* lnm119     -868.83010522 RSIRFO  MSP       1
 10   -868.83033149 -0.00092631 0.121776 0.083780 lnm185  -0.030940* lnm006     -868.83265257 RSIRFO  MSP       1(2)
 11   -868.82880642  0.00152507 0.028781-0.018277 lnm185   0.019724* lnm119     -868.82908249 RSIRFO  MSP       1(2)
 12   -868.83123804 -0.00243162 0.042171 0.023064 lnm185   0.026470  lnm001     -868.83153444 RSIRFO  MSP       1(3)

As expected, once the Hessian has a negative eigenvalue, the constraints are realized and the transition state structure optimization should take place, but
I havn't found on the manual which kind of information is encapsulated in the numbers in bracket.

Thank you for your help in advance!

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#2 2019-01-17 16:56:06

Ignacio
Administrator
From: Uppsala
Registered: 2015-11-03
Posts: 506

Re: findTS and Hessian index ()

Leo wrote:

I thougth that computing the gradient for root 2 would drive findTS to look for a 2nd order transition state.

Why? With a second-order TS I guess you mean a second-order saddle point (two negative Hessian eigenvalues). When you as for the gradient for root 2, you are simply exploring the potential energy surface of the second electronic state, but the TS is still a first-order saddle point.

I also have another question, which is the meaning of the numbers in bracket () next to the index of the Hessian matrix?

The program will "fix" the approximate Hessian it has available in order to obtain the correct number of negative eigenvalues (0 for minima, 1 for TS). The number in brackets is the number of negative eigenvalues before this fixing (if different from the desired). You should not be too worried by the fact that the number in brackets is larger than 1, since this is an approximate Hessian, but you should always compute the real Hessian at convergence, it may be that you arrived to a higher-order saddle point.

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#3 2019-01-17 17:10:05

niko
Member
From: Marseille
Registered: 2015-11-08
Posts: 43
Website

Re: findTS and Hessian index ()

Ignacio wrote:
Leo wrote:

I thougth that computing the gradient for root 2 would drive findTS to look for a 2nd order transition state.

Why? With a second-order TS I guess you mean a second-order saddle point (two negative Hessian eigenvalues). When you as for the gradient for root 2, you are simply exploring the potential energy surface of the second electronic state, but the TS is still a first-order saddle point.

I also have another question, which is the meaning of the numbers in bracket () next to the index of the Hessian matrix?

The program will "fix" the approximate Hessian it has available in order to obtain the correct number of negative eigenvalues (0 for minima, 1 for TS). The number in brackets is the number of negative eigenvalues before this fixing (if different from the desired). You should not be too worried by the fact that the number in brackets is larger than 1, since this is an approximate Hessian, but you should always compute the real Hessian at convergence, it may be that you arrived to a higher-order saddle point.

I would also add that QM/MM analytic Hessian is not available. Numerical Hessian should be feasible, however at a huge computational cost.

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#4 2019-01-17 17:34:23

Leo
Member
Registered: 2018-11-20
Posts: 5

Re: findTS and Hessian index ()

Dear Ignacio,
Thank you for your replay. Sorry for the mistake, I actually meant a 1st order saddle point (transition state).
Can you explain me or point me to some reference on how the algorithm works in "fixing" the hessian?

Thanks a lot for your help.

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#5 2019-01-17 17:47:50

Leo
Member
Registered: 2018-11-20
Posts: 5

Re: findTS and Hessian index ()

Dear Niko,

niko wrote:

I would also add that QM/MM analytic Hessian is not available. Numerical Hessian should be feasible, however at a huge computational cost.

It might be a stupid question, but is it possible to have a more precise idea of "huge computational cost"?

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#6 2019-01-18 11:49:49

niko
Member
From: Marseille
Registered: 2015-11-08
Posts: 43
Website

Re: findTS and Hessian index ()

Leo wrote:

Dear Niko,

niko wrote:

I would also add that QM/MM analytic Hessian is not available. Numerical Hessian should be feasible, however at a huge computational cost.

It might be a stupid question, but is it possible to have a more precise idea of "huge computational cost"?

Using a two-point formula, you need 2 analytic gradients per active (ie. non-frozen) coordinate -> 2*3*N gradient calculations for N active atoms. In any case, if N < number of QM and MM atoms, the normal mode analysis is valid only in the subspace spanned by the active nuclear coordinates.

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#7 2019-01-18 16:54:27

Ignacio
Administrator
From: Uppsala
Registered: 2015-11-03
Posts: 506

Re: findTS and Hessian index ()

Leo wrote:

Can you explain me or point me to some reference on how the algorithm works in "fixing" the hessian?

I think it just changes the sign of the eigenvalue and proceeds with the "fixed" Hessian.

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#8 2019-01-22 18:33:42

Leo
Member
Registered: 2018-11-20
Posts: 5

Re: findTS and Hessian index ()

Dear all,
excuse me for re-opening this topic, I was not sure if I had to open a new one (?).  Excuse me in advance for the large number of questions that I will bring up, but I think they are somehow linked together, and I am clearly missing something.
The calculation I was talking about has converged lately to a minimum energy structure. The final approximate hessian has three negative eigenvalue.
Do I still need to compute the real hessian? By that I mean, is there any chance that such a calculation willl end up being an actual transition state with one imaginary frequency? If not, should I try to set different constraint for the TS optimization?
Could you explain me why the algorithm can converge to a nth order saddle point?

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#9 2019-01-22 22:01:13

Ignacio
Administrator
From: Uppsala
Registered: 2015-11-03
Posts: 506

Re: findTS and Hessian index ()

Leo wrote:

Do I still need to compute the real hessian? By that I mean, is there any chance that such a calculation willl end up being an actual transition state with one imaginary frequency?

If you want to be sure, yes, you should compute the "exact" Hessian. It's quite possible that the approximate Hessian is wrong. Even if it had only 1 negative eigenvalue, it can still be wrong, so you should compute the Hessian.

On the other hand, it may be enough for you that you have a stationary point that links your desired reactants and products (which you verify by running an IRC), and that if there is a lower-order saddle point it would have lower energy, so you have an "upper bound".

If not, should I try to set different constraint for the TS optimization?

Different constraints, different starting structure, different settings (max step, cartesian/internal coordinates, etc.), different method (check "saddle" in gateway)...

Could you explain me why the algorithm can converge to a nth order saddle point?

The optimization will typically find the "closest" stationary point, regardless of its order. Minima are relatively easy to enforce, but saddle points are much trickier.

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