Subject: SUMMARY HIGHER-ORDER SADDLE POINTS

From: Errol Lewars <[email-masked]>
Date: Mon, 10 Jan 2000 11:10:40 -0500

2000 Jan 10

Here is the summary of the replies [#1--#5] to my question on
higher-order saddle points (hilltops).

Thanks very much to all who wrote.

QUESTION
-------
Subject: 
            CCL:HIGHER-ORDER SADDLE POINTS
       Date: 
            Sun, 02 Jan 2000 14:41:31 -0500
       From: 
            Errol Lewars <[email-masked]>
Organization: 
            Trent University
         To: 
            [email-masked]

2000 Jan 02
Happy New Year!

Hello,

We know that a 1st-order saddle point (a transition state, with 1
imaginary frequency) connects two zero-order stationary points (two
minima, each with 0 imag freqs).

Question:
(1) What does an nth-order saddle point connect? Does it always join
2n stationary points, each of order (n-1)?
(2) Understandably, chemists concentrate overwhelmingly on minima and
transition states. But has anyone ever shown much interest in
higher-order saddle points?

Thanks

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

#1
Subject: 
        Re: CCL:HIGHER-ORDER SADDLE POINTS
  Date: 
        Mon, 03 Jan 2000 11:05:18 +0100 (MET)
  From: 
        [email-masked]
    To: 
        [email-masked] (Errol Lewars)

There is little interest in higher order saddle points since the
minimum energy path (between two structures) simply does not come
along there.

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=======
#2
Subject: 
        Re: CCL:HIGHER-ORDER SADDLE POINTS
  Date: 
        Mon, 03 Jan 2000 09:24:16 -0500 (EST)
  From: 
        [email-masked]
    To: 
        [email-masked]

The following paper may be of interest to you:

        "[18]Annulene: Extrema on the HF/6-31G Potential Energy Surface
        and Evidience for a D6h Structure form COrrelate Wavefunctions"
        by F. A. Van-Catledge & D. A. DIxon

It is published in the volume:

        "Henry C. McBay: A Chemical Festschrift", W. M. Jackson & B. J.
Evans, eds.,
         MIT Press, Cambridge MA, 1994

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 FREDERIC A. VAN-CATLEDGE, Sr. Research Associate
 Scientific Computing Division       
 Central Research & Development
 The DuPont Company                  
 P. O. Box 80320
 Wilmington DE 19880-0320            
 VOX: (302) 695-1187 or (302) 529-2076
 FAX: (302) 695-9658
 Internet: [email-masked]

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
==========
#3
Subject: 
        Re: CCL:HIGHER-ORDER SADDLE POINTS
  Date: 
        Mon, 03 Jan 2000 10:41:57 -0800 (PST)
  From: 
        George Vacek <[email-masked]>
    To: 
        [email-masked] (Errol Lewars)

%% (2) Understandably, chemists concentrate overwhelmingly on minima and
%% transition states. But has anyone ever shown much interest in
%% higher-order saddle points?

Check out the following two theoretical papers and the Zeeman papers
referenced therein.

``The Anomalous Behavior of the Zeeman Anticrossing Spectra of A 1Au
Acetylene: Theoretical Considerations,'' G. Vacek, C. D. Sherrill,
Y. Yamaguchi and H. F. Schaefer, J. Chem. Phys.  104, 1774-8 (1996).

``The A 1Au State and the T2 Potential Surface of Acetylene:
Implications for Triplet Perturbations in the Flourescence Spectra of
the A State,'' C. D. Sherrill, G. Vacek, Y. Yamaguchi, H. F. Schaefer,
J. F. Stanton and J. Gauss, J. Chem. Phys.  104, 8507-15 (1996).

Regards,
George

=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
George Vacek                    + Schrodinger, Inc. 
(503) 299-1150                  + 1500 SW First, Suite 1180
[email-masked]           + Portland, OR 97201
http://www.schrodinger.com/~vacek/ 

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art degenerated into the lowest kind of amusement and esthetic 
criticism into the cement of a social group that was vain, 
distracted, egotistic, and totally unoriginal 
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========
#4
Subject: 
  Date: 
        Mon, 03 Jan 2000 13:13:38 -0500 (EST)
  From: 
        [email-masked]
    To: 
        [email-masked]

Date: Mon, 3 Jan 2000 10:18:34 -0800
Message-Id: <[email-masked]
In-Reply-To: Errol Lewars <[email-masked]>
        "CCL:HIGHER-ORDER SADDLE POINTS" (Jan  2,  2:41pm)
References: <[email-masked]>
Reply-To: [email-masked]
X-Mailer: Z-Mail-SGI (3.2S.3 08feb96 MediaMail)
To: Errol Lewars <[email-masked]>
Subject: Re: CCL:HIGHER-ORDER SADDLE POINTS
Cc: [email-masked]

If I didn't understand wrong, an n-order saddle point means there are n
(orthogonal) curves passing over this point with negative curvature (and
all
others positive). This is a location where more than one type of
decomposition
can occur. That is, either A->B+C, or B'+C', or B''+C'', etc.

Happy New Year,

Liang
Wavefunction, Inc.
=========
#5
Subject: 
        Re: CCL:HIGHER-ORDER SADDLE POINTS
  Date: 
        Mon, 03 Jan 2000 06:57:53 +0530
  From: 
        "Prof. S. R. Gadre Faculty member" <[email-masked]>
    To: 
        [email-masked], [email-masked]

Dear Dr. Lewars : May I request you to kindly summarize the answers
to the interesting question posed by you recently?
Thanks and wishes for a happy 2000!..........Shridhar Gadree
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