The RCMC method can also estimate the propagation of a given initial distribution up to t MAX . To do this, the traffic volume index Λ i has been introduced as an
index to estimate the transition volume of population for MINi, where Λ i is the sum
of the population inflow to and outflow from MINi during M times of contraction
procedures [69]. This Λ i makes it possible to distinguish MINs with population
inflow/outflow from those without that at given initial conditions (population,
temperature, and reaction time). Specifically, a reference to Λ i during the automated
reaction path search allows automatic determination of kinetically important ones
among the obtained MINs. Then, the search continues only from kinetically important MINs, eliminating kinetically meaningless regions. This treatment improves the
search efficiency dramatically. It should be pointed out, however, that because the Λ i
value changes every time when the search expands the reaction path network, it is
necessary to re-evaluate the Λ i value using the RCMC method whenever a new TS is
found. The automated reaction path search based on this treatment can also be
regarded as on-the-fly kinetic simulation.
3 Applications of the AFIR Method
3.1 Transition State Sampling Using the MC-AFIR Method
One of the advantages of the AFIR method is the TS sampling. To elucidate the
mechanism of catalytic reactions, especially the origin of the selectivities, such as
chemo-selectivity and stereoselectivity, the TSs affording the major and minor
products need to be computed. As mentioned above, the ratio of each product is
proportional to the Boltzmann distribution of the corresponding TS. Thus, some
pre-selected TSs are not enough to predict the ratio of the products. All the TSs
having low activation barriers must be gathered exhaustively. In the case of geometrically rigid systems, the geometry of TSs could be prejudged based on the
experience of researchers. In the case of flexible systems, however, it is difficult to
prejudge the TS geometries because there could be a number of TSs whose geometries are slightly different.
One of the flexible systems is the lanthanide complex in solution. Lanthanide
tri-cations (Ln
3+ ) have characteristic electron configurations: open-shell 4f electrons
are shielded by closed-shell 5s and 5p electrons from outside. Thus, Ln
3+ does not
have a rigid coordination sphere, which allows the flexible coordination numbers
and structures. In fact, the coordination number of water molecules around Ln
3+ in
solution is still a topic for open discussion because the value depends on the
experimental measurements [70–72]. The Ln
3+ complexes are also gathering attention as water-tolerant Lewis acid catalysts. Though the first Ln
3+ -catalyzed reaction
in water solution, called the Kobayashi modification of the Mukaiyama aldol
reaction (Scheme 1) [73, 74], was reported in 1994 and a number of experimental
measurements were performed to understand the mechanism, there were unsolved
questions concerning the role of water. One question is why the product yield of the
Artificial Force-Induced Reaction Method for Systematic Elucidation of. . .
65
index to estimate the transition volume of population for MINi, where Λ i is the sum
of the population inflow to and outflow from MINi during M times of contraction
procedures [69]. This Λ i makes it possible to distinguish MINs with population
inflow/outflow from those without that at given initial conditions (population,
temperature, and reaction time). Specifically, a reference to Λ i during the automated
reaction path search allows automatic determination of kinetically important ones
among the obtained MINs. Then, the search continues only from kinetically important MINs, eliminating kinetically meaningless regions. This treatment improves the
search efficiency dramatically. It should be pointed out, however, that because the Λ i
value changes every time when the search expands the reaction path network, it is
necessary to re-evaluate the Λ i value using the RCMC method whenever a new TS is
found. The automated reaction path search based on this treatment can also be
regarded as on-the-fly kinetic simulation.
3 Applications of the AFIR Method
3.1 Transition State Sampling Using the MC-AFIR Method
One of the advantages of the AFIR method is the TS sampling. To elucidate the
mechanism of catalytic reactions, especially the origin of the selectivities, such as
chemo-selectivity and stereoselectivity, the TSs affording the major and minor
products need to be computed. As mentioned above, the ratio of each product is
proportional to the Boltzmann distribution of the corresponding TS. Thus, some
pre-selected TSs are not enough to predict the ratio of the products. All the TSs
having low activation barriers must be gathered exhaustively. In the case of geometrically rigid systems, the geometry of TSs could be prejudged based on the
experience of researchers. In the case of flexible systems, however, it is difficult to
prejudge the TS geometries because there could be a number of TSs whose geometries are slightly different.
One of the flexible systems is the lanthanide complex in solution. Lanthanide
tri-cations (Ln
3+ ) have characteristic electron configurations: open-shell 4f electrons
are shielded by closed-shell 5s and 5p electrons from outside. Thus, Ln
3+ does not
have a rigid coordination sphere, which allows the flexible coordination numbers
and structures. In fact, the coordination number of water molecules around Ln
3+ in
solution is still a topic for open discussion because the value depends on the
experimental measurements [70–72]. The Ln
3+ complexes are also gathering attention as water-tolerant Lewis acid catalysts. Though the first Ln
3+ -catalyzed reaction
in water solution, called the Kobayashi modification of the Mukaiyama aldol
reaction (Scheme 1) [73, 74], was reported in 1994 and a number of experimental
measurements were performed to understand the mechanism, there were unsolved
questions concerning the role of water. One question is why the product yield of the
Artificial Force-Induced Reaction Method for Systematic Elucidation of. . .
65