Understanding the Significance of Imaginary Frequencies in Chemical Reactions

[greisen]

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

 

[christianjb]

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.

 

[greisen]

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.

 

[christianjb]

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.