Testing whether the optimized structure really is a transition state structure (saddlepoint)
· But is this really
a transition state structure?
· Calculating
the frequencies will test this.
· There are (3N-6 =) 18 vibrational frequencies produced
by the normal mode analysis.
· As required,
there is one - and only one- imaginary frequency, of 315i cm-1.
· This really is
a TS.
This is output from Gaussian-98:
Full mass-weighted force constant matrix:
Low frequencies: -315.1485 -7.9068
Low frequencies: -3.6130 -3.5517
Low frequencies: -0.0014 -0.0011
Low frequencies: -0.0007 971.5755
*1 imaginary
frequencies(negative signs)*
·
There are 6
frequencies which are very close to zero, which correspond to the rotational
and translational degrees of freedom of the molecule.
· They are not
quite zero for numerical reasons.
A frequency calculation on staggered
ethane (after optimizing its geometry) gives no imaginary frequencies:
Full mass-weighted force constant matrix:
Low frequencies -3.9869 -3.9863
Low frequencies -0.0014 -0.0012
Low frequencies -0.0010 4.7730
Low frequencies 326.1954 889.4536
(again the 6 ‘frequencies’ corresponding to rotational and vibrational
motion are not exactly zero, but are very close to zero).