Understanding the Significance of Imaginary Frequencies in Chemical Reactions

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Discussion Overview

The discussion centers on the interpretation of imaginary frequencies in the context of chemical reactions, particularly regarding their relationship to energy as indicated by eigenvalues of the Hessian matrix. Participants explore the implications of these imaginary frequencies and their significance in understanding transition states in chemical processes.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions the significance of an imaginary eigenvalue of 1000i in relation to energy, seeking clarification on how to interpret its size.
  • Another participant explains that the eigenvalue is negative, leading to an imaginary frequency, and describes the potential energy along the eigenvector direction as resembling an 'upside-down' parabola.
  • A different participant expresses confusion about interpreting negative frequencies, comparing them to positive frequencies associated with bond energies, and questions how to reconcile the two interpretations.
  • Further clarification is provided that the eigenvalue relates to the square of the frequency, and that negative eigenvalues indicate downward-sloping energy along a parabola, emphasizing that frequencies do not directly indicate dissociation energy but rather local curvature at stationary points.

Areas of Agreement / Disagreement

Participants exhibit some agreement on the mathematical relationships between eigenvalues, frequencies, and energy, but there remains uncertainty and confusion regarding the physical interpretation of negative frequencies and their implications for bond energies.

Contextual Notes

Limitations include the lack of consensus on how to interpret the physical significance of imaginary frequencies and their relationship to energy, as well as the dependence on specific definitions and assumptions regarding the curvature of potential energy surfaces.

Who May Find This Useful

Researchers and students in chemistry and related fields interested in the theoretical aspects of chemical reactions, particularly those studying transition states and vibrational analysis.

greisen
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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

 
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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.
 
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.
 
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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