In 2009, three methods for optimizing the geometry of a molecule under a
constant external force were introduced, which were called *Force-Modified
Potential Energy Surface* (FMPES),^{685} *External Force is Explicitly
Included* (EFEI),^{780} and *Enforced
Geometry Optimization* (EGO).^{1000} These methods are closely
related, and the interested reader is referred to Ref. 864
for a detailed discussion of the similarities and differences between them. For
simplicity, we will stick to the term *EFEI* in this Section. An EFEI
calculation is a geometry optimization in which a constant that is equal to the
external force is added to the nuclear gradient of two atoms specified by the
user. The external force is applied along the vector connecting the two atoms,
thus driving them apart. The geometry optimization converges when the restoring
force of the molecule is equal to the external force. The EFEI method can also
be used in AIMD simulations (see Section 10.7), in which case the
force is added in every time step. The basic syntax for specifying EFEI
calculations is as follows.

$efei atom1 atom2 force1 atom3 atom4 force2 ... $end

Here, atom1 and atom2 are the indices of the atoms to which a force is applied. force1 is the sum of the force values that acts on atom1 and atom2 in nanoNewtons (nN). If this value is positive, a mechanical force of magnitude force1/2 acts on each of these atoms, thus driving them apart. If it is negative, an attractive force acts between the atoms. Optionally, additional pairs of atoms that are subject to a force can be specified by adding lines in the $efei section.

$molecule 0 1 O -0.7059250062 -0.1776745132 -0.0698000882 O 0.7059250062 0.1776745132 -0.0698000882 H 1.0662092915 -0.5838921799 0.4181150580 H -1.0662092915 0.5838921799 0.4181150580 $end $rem JOBTYPE opt EXCHANGE b3lyp BASIS 6-31G* $end $efei 1 2 5 $end