Subject: CCL:What is EXACTLY a "resonance"?

From: Shu-Kun Lin <[email-masked]>
Date: Thu, 23 Jan 1997 11:54:15 +0100

Dear CCLers,

"What is EXACTLY a "resonance"?"is a very good question. Let's
go on a little bit. The whole book of Pauling's The Nature of the Chemical
Bond is about this concept. Pauling's definition is based on
Heisenburg's definition.

To my understanding, also as implied in
von Newmann's "Mathematical Foundation of Quantum Mechanics", respnance is
a dynamic process of mixing quantum states which can happen
in an equilibrium state (time-independent) of a molecular or
atomic system. Normally resonance happends among energetically
identical and in many cases configurationally identical
quantum states. If you think this problem deeply, there is a
big problem never solved so far: why a quantum system
spontaneously resonances among several states? What is the
driving force? Energy minimization (based on what kind of
electromagnetic interaction?), or entropy maximization
(based on what kind of formula of entropy of mixing of quantum states?)?

I tried to understand why resonance. The explanation of resonance
phenomena can be done if some more foundamental problem is
solved. I tried a lot lonely so far and almost lost my job because
I spent too much time on it. Interested colleagues may obtain
a couple of papers published last year by me and they are
downloadable from www.mdpi.org/lin.htm

Shu-Kun
---------------------------------------------------------
Dr. Shu-Kun Lin
Molecular Diversity Preservation International (MDPI)
Saengergasse 25, CH-4054 Basel, Switzerland
MDPI: www.mdpi.org/
Molecules: www.mdpi.org/molecules/
ECSOC-1: www.mdpi.org/ecsoc-1.htm
e-mails: [email-masked]
         [email-masked]
Tel. +41 79 322 3379, Fax  +41 61 302 8918
--------------------------------------------------------

---

From: Alain Kessi <[email-masked]>
Date: Thu, 23 Jan 1997 14:37:29 +0100

Shu-Kun Lin wrote:
>If you think this problem deeply, there is a

I rather thought there was no secret to that, the matter being simply
that the states you're looking at are not eigenstates of your
hamiltonian and therefore the hamiltonian has non-diagonal elements.
Hence the states couple, and there is a way to lower the energy by
taking linear combinations of those states. Of course, in most cases,
you will still not get the energy minimum (you can only scan the
subspace spanned by the states you put in), but still, you can get a
better approximation than the states you are currently looking at.

A classic example is the ammonia (NH3) maser, which can be described by
a potential with respect to the N position which has two equal energy
minima, separated by a wall of some given height. The minima correspond
to some pyramid and its mirror image. These two states, however, are not
eigenstates of the hamiltonian. If you write down the energy matrix (2
by 2 in this case) in the subspace they span, it's not diagonal, which
means that by diagonalizing the hamiltonian you'll find a state with
lower energy (and one with higher energy, accordingly).

Alain

-- Alain Kessi ([email-masked]), at Paul Scherrer Institut, Zurich
     ++++ stop the execution of Mumia Abu-Jamal ++++
 ++++ if you agree copy these 3 sentences in your own sig ++++
++++ see: http://www.xs4all.nl/~tank/spg-l/sigaction.htm ++++

---

From: "Richard P. Muller" <[email-masked]>
Date: Thu, 23 Jan 1997 09:28:48 -0800

I posted a message earlier this week asking for references to Java
utilities on the net, and have received many helpful replies.

I have created a web page, http://www-rcf.usc.edu/~rmuller/java.html, to
help chemists develop and use their own Java applications.

I have included some basic sites, links to a Java tutorial, links to
other chemistry sites, and a few simple scripts that I wrote myself. I
hope that chemists can download theses applets and experiment with them
for their own particular problems. 

The site is currently quite primative. I will expand it in the future.

If you have any applets, links, or any other suggestions for the site,
send them to me at [email-masked]. There seems to be a great deal
of interest in Java in the computational chemistry community. Anyone
interested in a mailing list?

Thanks for all of the help. 

Rick
-- 
Richard P. Muller, Ph.D.                  [email-masked]        
Department of Chemistry, SGM 418  http://www-rcf.usc.edu/~rmuller
University of Southern California             Office 213-740-7671
Los Angeles, CA  90089-1062                   FAX    213-740-2701