🚀 go-pugleaf

In article <247@gtss.UUCP> chas@gtss.UUCP (Charles Cleveland) writes:
>
>Well this is entirely charming :-).  Not to mention encouraging.  I
>applaud all the people you mention in the text I have deleted and
>professionally respect the quality of their work.  But totally apart
>from quantum mechanical questions, we can't even take an arbitrary
>simple potential (of the order of Lennard-Jonesium, for example) and
>predict what crystal structure it prefers.  Even classically.  At zero
>degrees.  

These points are all well taken with regard to cystal structures as well as
fluids and amorphorous solids, but the methods I was referring to are used
to study molecules composed of a modest number of atoms (up to a few dozen).
Certainly there is a lot of chemistry that involves the study of much 
larger systems, but there are many cases where quantum mechanical  
calculations have been indepensible to experimental chemists; not as simple 
qualitative tools, but in providing accurate chemical properties.
These cases include the determination of the ground structure and electronic 
state of the methylene radical, CH2, (initially incorrectly assigned by Herzberg),
the assignment of the infrared spectrum of the hydronium ion (H30+), and the
confirmation of the decay channel of glyoxal, and many others.


>       Of course given two structures, we can tell which is lowest
>in energy, but that's a different question.  The real problems is to
>find the structure without restricting the problem to certain preconceived
>possibilities.  

Perhaps I was overzealous in proclaiming quantum chemistry to be fully
ab initio (no, we don't calculate the electron mass, fine structure constant, ...
:-) since the molecular structures and electron states we use as starting 
points are based on experiment, semi-empirical rules (Hund's, etc.), and
experience.  However, starting from these initial configurations the 
structures are optimized (see below).  It is possible that this approach 
could lead to a gross error (perhaps the structure of benzene really shouldn't 
be cyclic), but by and large this approach has been very successful (the 
results are eventually confirmed by experiment).

>The problem is not merely computational.  In the case of finding the
>structure which minimizes the energy of a set of atoms interacting
>with some given set of potentials, we don't even know how to express
>the problem in a way conducive to its general solution.  Of course if
>we did, the problem of finding the global minimum would still be of
>staggering computational difficulty, simply by virtue of the vast number
>of degrees of freedom in the calculation.

  The problem of finding the global minimum for a particular molecule is
indeed a difficult one.  However, such optimizations are routinely carried
out and you will find that nearly all published theoretical molecular structures
have been optimized to where the energy gradients (dE/dRi  Ri=coords of each
atom in system) are on the order of 10**-6 a.u. (hartrees/bohr), i.e. very small. 
The number of degrees of freedom is large (3 * # atoms), but not vast, since the 
systems routinely studied are limited to only a dozen or so atoms.
The methods used for these optimizations are standard multi-dimension 
minimization methods such as Newton-Raphson using gradients and hessians 
calculated either analytically or by finite differences.
 
I don't want to oversell the utility of ab initio quantum chemistry, 
but to indicate the it plays only a minor, qualitative role in modern
chemistry is simply incorrect.  If you look in the Journal of Chemical
Physics or JACS (certainly among the flagship journals of chemistry) you
will find *many* articles (10-12 an issue in JCP) where these methods are being
used for the quantitative prediction of chemical properties.  

Thanks for raising some interesting points.

                                  --Mike Colvin