10.3 Constrained Optimization

10.3.6 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),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.

Example 10.8  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