$ZMAT group (required if NZVAR is nonzero in $CONTRL)
This group lets you define the internal coordinates in which the gradient geometry search is carried out. These need not be the same as the internal coordinates used in $DATA. See $STATPT to freeze internals. You must input a total of M=3N-6 internal coordinates (M=3N-5 for linear molecules). NZVAR in $CONTRL can be less than M IF AND ONLY IF you are using linear bends.
It is also possible to input more than M coordinates if they are used to form exactly M linear combinations for new internals. These may be symmetry coordinates or natural internal coordinates. If NZVAR > M, you must input IJS and SIJ below to form M new coordinates. See DECOMP in $FORCE for the only circumstance in which you may enter a larger NZVAR without giving SIJ and IJS.
IZMAT is an array of integers defining each coordinate. The general form for each internal coordinate is code number,I,J,K,L,M,N
Example - a nonlinear triatomic, atom 2 in the middle:
$ZMAT IZMAT(1)=1,1,2, 2,1,2,3, 1,2,3 $END
This sets up two bonds and the angle between them.
The blanks between each coordinate definition are
not necessary, but improve readability mightily.
SIJ is a transformation matrix of dimension NZVAR x M, used to transform the NZVAR internal coordinates in IZMAT into M new internal coordinates. SIJ is a sparse matrix, so only the non-zero elements are given, by using the IJS array described below. The columns of SIJ will be normalized by GAMESS. (Default: SIJ = I, unit matrix)
IJS is an array of pairs of indices, giving the row and column index of the entries in SIJ.
example - if the above triatomic is water, using
IJS(1) = 1,1, 3,1, 1,2, 3,2, 2,31.0 | 1.0 | 0.0 |
0.0 | 0.0 | 1.0 |
1.0 | -1.0 | 0.0 |
which defines the symmetric stretch, asymmetric stretch, and bend of water.
references for natural internal coordinates:
P.Pulay, G.Fogarasi, F.Pang, J.E.Boggs
J.Am.Chem.Soc. 101, 2550-2560(1979)
G.Fogarasi, X.Zhou, P.W.Taylor, P.Pulay
J.Am.Chem.Soc. 114, 8191-8201(1992)