parameter α corresponds to the mean force that acts on the two Ar atoms in their
direct collision on the LJ potential with collision energy γ, in the area from the
minimum to the turning point.
It was shown with some examples that paths followed by the minimization of the
AFIR function were close to the actual reaction paths. In other words, the form of the
AFIR function was carefully designed so that paths obtained by the minimization of
the AFIR function resemble actual reaction paths as closely as possible. This made it
possible to obtain reaction paths just by repeating a simple task that is a minimization
of a single, continuous function.
To sum up, the approximate reaction path, called the AFIR path, can be obtained
by the minimization of the AFIR function in Eq. 1, which can be calculated only
from the following three input data: (1) compounds (starting structures) included in
the system; (2) definition of the fragmentation (A and B in Eq. 1), which usually
includes the reactive atoms in each compound; and (3) value of γ. From the AFIR
path, the real TSs as well as the local minima can be computed easily. It should be
noteworthy that the value of γ can be decided depending on the purpose. The small γ
value could be appropriate to the limited search of the AFIR paths with low
activation barriers. The search area could be extended by using the larger γ.
2.2 Three Calculation Schemes for the AFIR Method:
MC-AFIR, SC-AFIR, and DS-AFIR
There are three types of algorithms used in the AFIR method. The first is the
multicomponent-AFIR (MC-AFIR) algorithm, which is applicable to the systems
including two or more compounds. This algorithm takes the various initial structures, in which the mutual position and orientation of each compound are generated
randomly. Then, the AFIR function is minimized starting from these initial structures. If the system includes three compounds A, B, and C, force terms between A
and C and between B and C are added to Eq. (1). The number of force terms thus
increases depending on the number of compounds included in the system.
The second is the single-component AFIR (SC-AFIR) algorithm that automatically defines various fragments in a given system composed of either a single
molecule or a complex of multiple compounds and applies the artificial force
between all pairs of the defined fragments to induce various geometrical deformations. We note that such operations induce not only chemical bond reorganizations
but also conformational changes. For instance, an attractive force applied between
two methylene groups at different sites in a hydrocarbon first induces a structural
change to a conformer in which the two methylene groups are close to each other and
finally causes bond reorganizations between the two methylene groups. Fragments
are automatically defined for all the atoms included in a system; hence, their
combination becomes enormous in a large system. Therefore, an option is available,
where the users can specify a small number of atoms (called target atoms) from
Artificial Force-Induced Reaction Method for Systematic Elucidation of. . .
61
direct collision on the LJ potential with collision energy γ, in the area from the
minimum to the turning point.
It was shown with some examples that paths followed by the minimization of the
AFIR function were close to the actual reaction paths. In other words, the form of the
AFIR function was carefully designed so that paths obtained by the minimization of
the AFIR function resemble actual reaction paths as closely as possible. This made it
possible to obtain reaction paths just by repeating a simple task that is a minimization
of a single, continuous function.
To sum up, the approximate reaction path, called the AFIR path, can be obtained
by the minimization of the AFIR function in Eq. 1, which can be calculated only
from the following three input data: (1) compounds (starting structures) included in
the system; (2) definition of the fragmentation (A and B in Eq. 1), which usually
includes the reactive atoms in each compound; and (3) value of γ. From the AFIR
path, the real TSs as well as the local minima can be computed easily. It should be
noteworthy that the value of γ can be decided depending on the purpose. The small γ
value could be appropriate to the limited search of the AFIR paths with low
activation barriers. The search area could be extended by using the larger γ.
2.2 Three Calculation Schemes for the AFIR Method:
MC-AFIR, SC-AFIR, and DS-AFIR
There are three types of algorithms used in the AFIR method. The first is the
multicomponent-AFIR (MC-AFIR) algorithm, which is applicable to the systems
including two or more compounds. This algorithm takes the various initial structures, in which the mutual position and orientation of each compound are generated
randomly. Then, the AFIR function is minimized starting from these initial structures. If the system includes three compounds A, B, and C, force terms between A
and C and between B and C are added to Eq. (1). The number of force terms thus
increases depending on the number of compounds included in the system.
The second is the single-component AFIR (SC-AFIR) algorithm that automatically defines various fragments in a given system composed of either a single
molecule or a complex of multiple compounds and applies the artificial force
between all pairs of the defined fragments to induce various geometrical deformations. We note that such operations induce not only chemical bond reorganizations
but also conformational changes. For instance, an attractive force applied between
two methylene groups at different sites in a hydrocarbon first induces a structural
change to a conformer in which the two methylene groups are close to each other and
finally causes bond reorganizations between the two methylene groups. Fragments
are automatically defined for all the atoms included in a system; hence, their
combination becomes enormous in a large system. Therefore, an option is available,
where the users can specify a small number of atoms (called target atoms) from
Artificial Force-Induced Reaction Method for Systematic Elucidation of. . .
61