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# Using Linear Combinations Of Original ZMAT Coordinates

A type of calculation that might arise is one in which it is desirable to use combinations of the ZMAT file internal coordinates. For example, suppose that you wanted to optimize the structure of planar vinylidene (CCH2) subject to the constraint that the two CCH bond angles (those equilvalent in the C2v equilibrium structure differ by 10 degrees. While it might be possible to obtain such a result by doing several different calculations, there are features in CFOUR that allow this to be done easily. An area of application in which such calculations are commonly needed is that associated with developing potential energy surfaces for nuclear motion calculations. The new NITROGEN program, developed by Changala, is the choice of the CFOUR developers for most variational nuclear motion calculations, and this code often makes use of such linear combinations of coordinates.

To specify an alternative set of internal coordinates to be used in an optimizations which are linear transformations of those given in the ZMAT file, include the string

%nitroq

in your ZMAT file (the name is motivated by NITROGEN). The syntax used to specify the coordinates and the associated optimization is best communicated by example. For the vinylidene calculation mentioned above, the body of the usual ZMAT specification might be

Vinylidene
C
C 1 R1
H 2 R2 1 A1
H 2 R3 1 A2 3 TX
R1=1.3
R2=1.1
R3=1.1
A1=120.
A2=130.
TX=180.

Note that the internal coordinates above all have different names which - for the moment - is necessary in this context.

The %nitroq field looks like this:

%nitroq
1. 0. 0. 0. 0. 0.
0. 1. 0. 0. 0. 0.
0. 0. 0. 1. 0. 0.
0. 0. 1. 0. 1. 0.
0. 0. 1. 0. -1. 0.
0. 0. 0. 0. 0. 1.
4
1 2 3 4

Here, the alternative coordinates are as follows:

1: R1
2: R2
3: R3
4: A1+A2
5: A1-A2
6: TX

Following the specification of these coordinates, the next entry is a 4 (on the seventh line). This is the number of alternative ("NITROGEN") coordinates that will be optimized. After this, those coordinates are specified. This calculation will do what is discussed above. It will optimize the structure of vinylidene subject to a fixed value of NITROGEN coordinate 5. As specified in the ZMAT file, this will be constrained to a value of ten degrees.
Sample input and output for this calculation are available. CFOUR is partially supported by the U.S. National Science Foundation.