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Size of imaginary frequency

  1. Aug 3, 2007 #1
    Hi,


    In the transition state of a chemical reaction defined as one imaginary eigenvalue of the hessian matrix - the size of my frequency is 1000i what can one say about the size of the imaginary frequency - is it related to energy in some way ? I have not been able to find any documents commenting on the size of the imaginary eigenvalue.

    Any help or advise appreciated. Thanks in advance

    Best regards,
     
  2. jcsd
  3. Aug 3, 2007 #2
    The eigenvalue is negative- the frequency is the sqrt of the eigenvalue, which is imaginary.

    The potential energy along the eigenvector direction is 1/2 q^2 w^2, which in your case is an 'upside-down' parabola.
     
  4. Aug 3, 2007 #3
    thanks - I am a little puzzled how to interpret to values when they are imaginary - if you have a C-H bond with frequency of 1300 cm^-1 you can say something about the energy of the bond or mode but when you have -1300 cm^-1 what to say about it than? I mean the bond/stretch should have the same energy but in one case it is denoted having a negative frequency instead of a positive.
     
  5. Aug 3, 2007 #4
    eigenvalue = w^2

    If the eigenvalue is negative- then w is imaginary.

    Energy = 1/2 q^2 w^2

    If the eigenvalue is negative then the energy goes as E= -1/2 q^2 |w^2|, i.e. the energy slopes downwards (along a parabola) if you move forward or backward along q.

    You can't tell anything about the dissociation energy from the frequencies- they can only tell you about the local curvature at the stationary point.
     
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