Subject: RE: CCL: GEOMETRY QUESTION

From: [email-masked]
Date: Tue, 20 Jul 99 10:58:12 EDT

The problem outlined below was recently proposed to the list for comment:

Given a fragment A-B-C, one wishes to attach a fourth atom, D, with the
available information being:

                r(BD)
                <(ABD)
                <(CBD)

how can one *uniquely* define the coordinates of D??

There is not enough information to define D uniquely.  Consider the situation
with the ABC fragment is constrained to the xy-plane:

                     A
                    /
                D--B
                    \
                     C

Unless the angles <(ABC), <(ABD), & <(CBD) sum to 360 deg., ther will be 2
solutions for the coordinates of D, differing in the algebraic sign for the 
z-coordinate.  In order to uniquely locate D one needs one additional piece
of information.  Two possibilities are:

        out-of-plane angle (signed) for the BD bond

        dihedral angle A-C-B-D (signed)

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                           FREDERIC A. VAN-CATLEDGE
                            Sr. Research Associate

Scientific Computing Division         ||   Office: (302) 695-1187 or 529-2076
Central Research & Development Dept.  ||          
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P. O. Box 80320                       ||
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