[Pw_forum] Physical meaning of two imaginary phonon frequencies at NEB saddle point and Transition State Theory

[JAY Antoine]

Dear Pascal, Dear Stefano, dear all

In a symetric system where two reactions A1->B1 and A2->B2 go trough the same saddle point, following the eigen vector responssible in each NEB is quite easy.
For example in NEB 1, here I plot the number of "negative" frequencies as a function of the path/15 steps
1      0      state A1
2      0
3      0
4      -1   inflexion point on the E({Ri}) curve
5      -1  This "negative" frequency w1 with eigen vector V1 is the one responsible of the transition A1->B1
6      -1
7     -2    here appear the frequency w2 responsible of the transition A2->B2
8     -2    saddle point that is a 2 dimension saddle in a 3Nat dimension space.
9     -2
10   -1
11   -1
12   -1  inflexion point on the E({Ri}) curve
13    0
14    0
15    0   state B1

the same for NEB2 by exchanging w1 and w2.
The two paths are separeted by high energy barriers that is always higher than the DeltaE of the saddle point except at the saddle point where this barrier is null.
Not that in this example I give 4 potential wells link together through the same saddle point (the reaction A1->A2 is also possible),
but it is mathematically possible to have even more potential wells as we are in a 3Nat dimension space.

For Stefano, the state 8 mathematically exists and is physically due to a high symmetry point, so I do not see why I should look for another saddle point.
NEB raffinement is un precise in this "plateau region".

For Pascal, following eigen vector V1 from the saddle point give me B1 (or A1 as a function of the sign of the imposed displacement) and following V2 give me B2 (or A2),
but the problem is to know the transition rate from the Delta E and the omega_i, I already know which eigen vector correspond to which path...


Antoine Jay



On Monday, November 13, 2017 20:27 CET, degironc <degironc at sissa.it> wrote:
  I think that if there are two unstable directions at the saddle point this means there is another saddle point with a lower Activation energy nearby. Just slide the neb downhill stefano   Sent from my Samsung Galaxy smartphone. -------- Original message --------From: Pascal Boulet <pascal.boulet at univ-amu.fr>Date: 13/11/2017 19:45 (GMT+01:00)To: PWSCF Forum <pw_forum at pwscf.org>Subject: *spam*Re: [Pw_forum] Physical meaning of two imaginary phonon frequencies at NEB saddle point and Transition State Theory Hello, My guess: you have to remove one of the imaginary frequencies (most probably the smallest one) by following the corresponding eigenvector (=moving the atoms accordingly). Then, you will have to make sure that the transition state connects the reactants and products you are interested in. HTH,Pascal Pascal Boulet—Professor in computational chemistry - DEPARTEMENT OF CHEMISTRYAix-Marseille University - ST JEROME - Avenue Escadrille Normandie Niemen - F-13013 Marseille - FRANCETél: +33(0)4 13 55 18 10 - Fax : +33(0)4 13 55 18 50Site : http://madirel.univ-amu.fr/pages_web_BOULET_PASCAL/infos - Email : pascal.boulet at univ-amu.fr   Le 13 nov. 2017 à 12:44, JAY Antoine <Antoine.JAY at isae-supaero.fr> a écrit : Dear all,
I have been using NEB to obtain the Delta E and phonon DOS at begining/end/saddle point to properly evaluate the vibrationnal entropy contribution in the transition state theory.
Commonly, one frequency in "negative" at the saddle point, the one that is "responssible" of the transition and the following of its eigen vector from the initial state give the minimum energy path.
However, when two phonon frequencies are "negatives" at the saddle point, that means that at least 3  energy minima are link together to the same saddle point.
The transition state theory cannot be applied there as the preexponential term is the ratio of the 3N-3 phonon frequencies of initial state over the 3N-4 frequencies of the saddle point, giving the dimension of a time (state life time)
Using 3N-5 frequencies without the two negatives ones would not have a physical meaning for the initial partition function.

Any idea on how to treat such a problem to evaluate the transition rate would be appreciated.

Best regards.

Antoine Jay _______________________________________________
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