9 Exploring Potential Energy Surfaces: Critical Points and Molecular Dynamics

9.3 Constrained Optimization

(June 30, 2021)

Constrained optimization refers to the optimization of molecular structures (transition state or minimum-energy) in which certain parameters such as bond lengths, bond angles or dihedral angles are fixed. Jon Baker’s Optimize package, implemented in Q-Chem, makes it possible to handle constraints directly in delocalized internal coordinates using the method of Lagrange multipliers (see Appendix A). Features of constrained optimization in Q-Chem are:

  • Starting geometries need not satisfy the requested constraints.

  • Constrained optimization is performed in delocalized internal coordinates, which is typically the most efficient coordinate system for optimization of large molecules.

  • Q-Chem’s free-format $opt section allows the user to apply constraints with ease.

Constraints are imposed via the $opt input section, whose format is shown below, and the various parts of this input section are described below.

Note:  As with the rest of the Q-Chem input file, the $opt section is case-insensitive, but there should be no blank space at the beginning of a line.

$opt
CONSTRAINT
stre  atom1  atom2  value
...
bend  atom1  atom2  atom3  value
...
outp  atom1  atom2  atom3  atom4  value
...
tors  atom1  atom2  atom3  atom4  value
...
linc  atom1  atom2  atom3  atom4  value
...
linp  atom1  atom2  atom3  atom4  value
...
ENDCONSTRAINT

FIXED
atom   coordinate_reference
...
ENDFIXED

DUMMY
idum   type   list_length   defining_list
...
ENDDUMMY

CONNECT
atom   list_length   list
...
ENDCONNECT
$end