$ZMAT

$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

IZMAT
=1 followed by two atom numbers. (I-J bond length)

=2 followed by three numbers. (I-J-K bond angle)

=3 followed by four numbers. (dihedral angle)
Torsion angle between planes I-J-K and J-K-L.

=4 followed by four atom numbers. (atom-plane)
Out-of-plane angle from bond I-J to plane J-K-L.

=5 followed by three numbers. (I-J-K linear bend)
Counts as 2 coordinates for the degenerate bend, normally J is the center atom. See $LIBE.

=6 followed by five atom numbers. (dihedral angle)
Dihedral angle between planes I-J-K and K-L-M.

=7 followed by six atom numbers. (ghost torsion)
Let A be the midpoint between atoms I and J, and B be the midpoint between atoms M and N. This coordinate is the dihedral angle A-K-L-B. The atoms I,J and/or M,N may be the same atom number.
(If I=J AND M=N, this is a conventional torsion).
Examples: N2H4, or, with one common pair, H2POH.

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, 2,3
SIJ(1) = 1.0, 1.0, 1.0,-1.0, 1.0
gives the matrix S=
1.01.00.0
0.00.01.0
1.0-1.00.0

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)


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