# 9.4 Application of External Forces

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),711 External Force is Explicitly Included (EFEI),817 and Enforced Geometry Optimization (EGO).1060 These methods are closely related, and the interested reader is referred to Ref. 908 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 9.8), 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. Example 9.9 EFEI calculation of hydrogen peroxide with a constant stretching force of 2.5 nN acting on each oxygen atom $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