Constrained optimizations: linear combinations of internal coordinates

It is often desirable to carry out a geometry optimization in internal coordinates where two or more of the coordinates are required to maintain constant values relative to each other. The most simple case, where two internal coordinates a kept equal can be achieved by referencing both coordinates to a single variable in the GEOVAR block. Ensuring a different relationship, such as forcing one bond length in a molecule to be 0.5 Angstrom longer than another is more difficult to achieve. These kind of constraints can often be be managed through the creative use of dummy atoms but this is generally laborious and not always possible at all.

The CONSTRAINT keyword allows geometry optimizations with constraints defined by arbitrary linear combinations of internal coordinates to be performed quite straightforwardly. The keyword allows the linear combination to be constrained or used as part of a linear transit calculation with the constrained value being stepped as would a variable from the GEOVAR block.

CONSTRAINT
 Name1 Data1
 VAR11 Coef11
 VAR12 Coef12
 ...
 SUBEND
 Name2 Data2
 VAR21 Coef21
 VAR22 Coef22
 ...
 SUBEND
 ....
end

Namex

Identifier of the xth linear constraint.

Datax

Either of two formats
1) A single number, giving the value of the xth constraint
2) Two numbers, the first as in 1) and the second the final value in a linear transit calculation. The LINEARTRANSIT keyword must be present in the GEOMETRY block.

Varxy

Name of the yth variable in that is part of the xth constraint. Varxy must be defined in the GEOVAR block.

Coeffxy

Coefficient of Varxy in the linear combination defining the constraint. Thus:
Coeff11*Var11 + Coeff12*Var12 ...= Data1
The summation must be consistent with the initial values of the Varxy.

This procedure is only possible when the geometry is defined in terms of internal coordinates. Although the program will not complain, it makes no sense to have linear combinations containing both bonds and angles of course.

The number of linear constraints must be less than or equal to the number of entries in the GEOVAR block. Only internal coordinates involving QM atoms can be included at this stage.

As a geometry optimization is run, the force acting on the linear constraints will be printed immediately after the forces on the internal coordinates. The constraint forces may be useful in the search for a transition state for instance.