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WARNING: Chemically significant eigenvalues (CSE) not well separated from internal energy relaxation eigenvals (IEREs).

Qian Xu
2025-03-16
2025-03-17
  • Qian Xu

    Qian Xu - 2025-03-16

    Dear all,
    I am using mesmer to simulate the reaction of R radicals with O2 and subsequent reactions in the atmosphere, and the simulation process is as shown in the following figure.

    The calculation shows an error “WARNING: Chemically significant eigenvalues (CSE) not well separated from internal energy relaxation eigenvals (IEREs).
    The last CSE = -3.10654e+08 and the first IERE = -1.70469e+09
    (last CSE)/(first IERE) ratio = 0.182235, which is less than an order of magnitude
    Results obtained from Bartis Widom eigenvalue-vector analysis may be unreliable”

    Also I found that in the output, R increases with time and even exceeds 1. I am not sure what is the reason for this and would appreciate your help! Thanks for your help!

    Xu Qian

     
  • struanr

    struanr - 2025-03-17

    Dear Dr. Qian,

    Thank-you for using MESMER.

    The calculation shows an error “WARNING: Chemically significant eigenvalues (CSE) not well separated from internal energy relaxation eigenvals (IEREs).
    The last CSE = -3.10654e+08 and the first IERE = -1.70469e+09
    (last CSE)/(first IERE) ratio = 0.182235, which is less than an order of magnitude
    Results obtained from Bartis Widom eigenvalue-vector analysis may be unreliable”

    This is a warning not an error. The origin of this warning is the eigenvalue spectrum of your systems and how it is used to calculate rate coefficients. For systems where the wells are deep compared to the ambient thermal energy the eigenvalues spectrum can be partitioned into two groups, the chemically significant eigenvalues (CSEs) which determine how the chemical species evolve and the internal energy relaxation eigenvalues (IEREs) which are larger in magnitude than the CSEs and govern the energy relaxation of the system. Under these conditions rate coefficients can be unambiguously determined using the Bartis-Widom algorithm. However, if these two groups begin to merge, such that the distinction between the two is less clear, the basis of the Bartis-Widom is eroded and so the rate coefficients derived become less well defined. Even so, the solution of the Master Equation, the evolution of the species, remains valid. In my experience the rate coefficients derived often remain useful even when these two groups of eigenvalues are not well separated.

    Also I found that in the output, R increases with time and even exceeds 1. I am not sure what is the reason for this and would appreciate your help! Thanks for your help!

    I think the reason for this observation is that the temperature of your system is quite low, so I think that you need to increase the precision of the calculation. I have reviewed your input and made a few changes and attach a .zip file and the results I obtained. You will see from this that most of the reaction proceeds almost entirely from R+O2 to P+HO2 via the lower transition state, the other reactions begin of minimal importance. I would remark that this appears to be a bimolecular reaction and so it is possible that MESMER is not the best tool to study this system. I doubt this system will show much pressure dependence. (Incidentally, in case you are looking at the plot of the concentrations in Firefox, the oscillations are because there are two P + HOO densities coming from the two transition states.)

    I hope this helps a little.

    With regards, Struan

     

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