9 Exploring Potential Energy Surfaces: Critical Points and Molecular Dynamics

9.5 Application of External Forces (EFEI)

(May 16, 2021)

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), 817 Ong M. T. et al.
J. Am. Chem. Soc.
(2009), 131, pp. 6377.
Link
External Force is Explicitly Included (EFEI), 932 Ribas-Arino J., Shiga M., Marx D.
Angew. Chem. Int. Ed. Engl.
(2009), 48, pp. 4190.
Link
and Enforced Geometry Optimization (EGO). 1196 Wolinski K., Baker J.
Mol. Phys.
(2009), 107, pp. 2403.
Link
These methods are closely related, and the interested reader is referred to Ref. 1036 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 (cf. Section 9.9), in which case the force is added in every time step.

Q-Chem 5.4 is the first version that uses a new syntax for specifying EFEI calculations, which requires the $rem variable DISTORT to be true (cf. Section 9.4):

$distort
   model efei
   force [atom1 atom2 force1]
   force [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 $distort section.

Example 9.13  EFEI calculation of benzene with two vectors along which a constant external force is applied

$molecule
   0 1
   C         -5.49560        1.38469        0.00000
   C         -5.63439       -0.00746        0.00000
   C         -4.22058        1.96056       -0.00000
   C         -3.08434        1.14430       -0.00000
   C         -3.22313       -0.24784       -0.00000
   C         -4.49816       -0.82372       -0.00000
   H         -4.60553       -1.90072       -0.00000
   H         -6.62079       -0.45297        0.00000
   H         -2.09795        1.58981       -0.00000
   H         -2.34411       -0.87933       -0.00000
   H         -6.37463        2.01617        0.00000
   H         -4.11321        3.03756       -0.00000
$end

$rem
   JOBTYPE      opt
   EXCHANGE     b3lyp
   BASIS        6-31G*
   DISTORT      true
   SYM_IGNORE   true
$end

$distort
   model       efei
   force       [1 5 8]
   force       [1 4 8]
$end

View output