Subject: RESPONSE TO QUESTION ABOUT NEG FREQS

From: "E. Lewars" <[email-masked]>
Date: Mon, 31 Aug 1998 17:36:25 -0400 (EDT)

1998 August 31

Re the question:

>                 31-AUG-1998 15:30:49.21
>From:  IN%"[email-masked]"  "patrick"
>To:     IN%"[email-masked]"
>CC:
>Subj:   CCL:Frequency calculation of transition state
>
>
>Hi!  How are you?  During computation of frequency of molecules at
>transition state, one of frequencies is negative.  Why?  Is it a rule for
>identification of transition state?  Is it possible if two or more
>frequencies are negative when molecules are at transition state?
>
>Thank you for your attention.
>
>Patrick Pang
=====================

The number of "negative" (actually, imaginary) frequencies that an optimized
structure has is a basic feature of its nature, i.e. it tells whether you have
a minimum (no imag. freqs), a transition state or first-order saddle point
(1 imag freq), or a hilltop i.e. a second or higher-order saddle point
(two or more imag freqs). The imaginary number arises because along the
reaction path the second derivative of E with respect to geometry is negative
at the stationary point (draw it), i.e the force constant for this vibrational
mode is negative. To calculate the normal-mode freqs we need the square root
of the force constant (and the masses of the atoms) [look up the simple
equation for a diatomic molecule], and the square root of a negative number is
what mathematicians call imaginary (printed as a negative number in most
outputs).    For good introductions see
"Exploring Chemistry with Electronic Structure Methods", J. B. Foresman and
A. Frisch, 1st or 2nd Ed.

"Ab Initio Molecular Orbital Theory", W. J. Hehre, L. Radom, P. v.R. Schleyer,
J. A. Pople

  E. Lewars
===============