Subject: Transform to redundant internal Coord?

From: Cheol Choi <[email-masked]>
Date: Wed, 11 Oct 1995 18:19:03 -0400 (EDT)

Dear CCLers.

I have a simple question.

First of all, let me define some terms.

X : cartesian displacement coordinate
R : internal displacement coordinate
If I have N atoms, then I would have 3N of cartesians.
Also if I define nun-redundant internal coordinate, I would have
3N-6 or 5 internal coordnate.

There is A matrix which transform R into X.
X=A*R

In general, one could get the inverse (since A is not square matrix,
this is not exactly inverse matrix) of A like 
(Let me use B for inverse of A)

A=transpose(B)*inverse(B*transpose(B))
(This formula can only be used for direction independent quantities, such as
energy and only hold for nun-redundant internal coordinate.)

Now, my problem is this.
If I have redundant internal coordinate,which means that there are (is)
singularities in B matrix, I could not inverse the B*transpose(B).
Therefore I couldn't get the A matrix form B matrix.

Gaussian94 uses the redundant internal coordinate to optimize geometry.
It actually calculates the hessian matrix in redundant internal 
coordinate and also gives us the cartesian hessian matrix. So there might
be a transformation matrix between these coordinates.

Please, let me konw how to get such a transformation matrix.

Thank you in advance.

Cheol Ho Choi

Georgetown Univ.