4. Results and Discussions
In this investigation, we will determine whether a reaction is
non-competitive or competitive as well as distinguish the
torquoselectivity along the reaction coordinate of given reactions in
order to understand either TSIC or TSOC preferences. To begin with, we
propose to use chemical topological properties of reactions instead of
using a universally conventional method, which is based on activation
energy, see Table 1 and Figures (1-4(c)) . According to∆ TS < 1.0 kcal/mol shown in this table results thatReaction 1 is competitive while the other three reactions,Reactions (2-4) , are non-competitive reactions. As mentioned
earlier, we decide to use some plots such as, metallicity
ξ(r b), stress tensor polarizability
ℙσ, ellipticity ε, total local energy densityH (r b), and stress tensor
λ3σ that contain chemical topological properties of
reactions. From the examination of these plots, consider that the TSIC
and TSOC reactions of the ring-opening C2-C3/C2–C3 BCP s ofReactions (1-4) exhibit degeneracy or non-degeneracy that could
assist in predicting either non-competitive or competitive reactions,
see Figures (1-4) . The plots of the variation of the
metallicity ξ(r b) with the IRC related to the
ring-opening C2-C3/C2–C3 BCP s, found for
ξ(r b) > 1, indicate degeneracy forReaction 1 and non-degeneracy for remain reactions,Reactions (2-4) , see Figures (1-4(d)) respectively.
This degenerate and non-degenerate behavior in the metallicity
ξ(r b) suggests that in fact Reaction 1is a competitive reaction and Reaction 2 , Reaction 3 ,
and Reaction 4 are non-competitive reactions on the chemical
basis of metallicity being a key factor in understanding the electronic
reorganization of the ring-opening BCP along the reaction
pathways. In addition, based on the transition state theory and previous
researches outcomes, we obtain that for all four reactions, the
transition state and maximum metallicity ξ(r b)
relevant to the ring-opening C2-C3/C2–C3 BCP s do not
simultaneously occur 48. Subsequently, the degeneracy
results from other QTAIM measures such as ellipticity ε and the total
local energy density H (r b) are in
confirmation with metallicity ξ(r b) results
which indicate that Reaction 1 is a competitive reaction andReaction 2 , Reaction 3 , and Reaction 4 are
non-competitive reactions, see Figures (1-4(e)) andFigures (1-4(f)) respectively.
In the following, investigation the plots of variation of stress tensor
polarizability ℙσ with the IRC demonstrate an apparent
differentiation among all four reactions. In other words, we can
conclude from the degenerate and non-degenerate behavior of the stress
tensor polarizability ℙσ corresponding to the
ring-opening C2-C3/C2–C3 BCP s that Reaction 1 is a
competitive reaction and Reaction 2 , Reaction 3 , andReaction 4 are non-competitive reactions, see Figures
(1-4(g)) . Additionally, we obtain the same behavior as was happened for
the metallicity ξ(r b) that the saddle point and
transition state do not coincide precisely with each other. Moreover,
the plots of examination of the variation of the stress tensor
λ3σ with the IRC for all four reactions are considered
which display similar evaluation with QTAIM measures mentioned above;
see Figures (1-4(h)) .
From this part of our survey, we can conclude that besides activation
energy which is a conventional method, we introduce some different
measures such as, ξ(r b), ε,H (r b), ℙσ,
λ3σ, which could be suitable indicators to predict that
each reaction is non-competitive or competitive.
Inspired by the theoretical predictions, we decided to evaluate the
tendency of each non-competitive reaction to determine if it is either
TSIC or TSOC reactions. Hence, using the eigenvector-following path with
length, which is nominated as helicity length H relevant to the
shared-shell ring-opening BCP of each of the Reactions
(1-4) pathways was determined, see Figures (1-4(j))respectively.
According to what has been discussed in the theory section, the
ellipticity εi values along the bond-paths
(r ) associated with shared-shell BCP s could demonstrate if
the bond is a single or double bond character not the same for the
closed-shell BCP s. This has been done to decide the inclination
for either the transition state (TS) outward conrotatory (TSOC) or the
transition state inward conrotatory reaction pathway (TSIC). To gain
predictions of the TSIC or TSOC product preference, we will analyze the
bond paths of the shared-shell ring-opening BCP s of the TSIC and
TSOC reaction pathways before they alter to closed-shell BCP s or
rupture completely. Subsequently, the plots of the variation of the
bond-path length (BPL) with the IRC for both TSIC and TSOC reactions of
the ring-opening C2-C3/C2–C3 BCP were evaluated. In addition,
the non-degeneracy and degeneracy trend of each reaction shows thatReaction 1 is degenerate while in opposite Reaction 2 ,Reaction 3 , and Reaction 4 show significant
differences for the corresponding variations and exhibit non-degenerate
values. Therefore, in agreement with the QTAIM and stress tensorBCP properties, we demonstrate Reaction 1 as a
competitive reaction and Reaction 2 , Reaction 3 , andReaction 4 as non-competitive reactions, see Figures
(1-4(i)) respectively. The favored TSIC or TSOC pathway is determined
by the greater length H, which is constructed from thee2 eigenvector tip paths alongside the
bond- path (r ) for a pair of TSIC and TSOC pathways that are
being compared. Larger deviations of the tips are associated with
greater deviations of the tips from the original orientation of thee2 at the BCP of TSIC or TSOC
pathways. Notice that e1 ande2 eigenvectors are associated with the
least and most preferred direction of ρ (r ) accumulation.
As a result, a larger value of H is relating to the most easily
distorted molecular graph and accordingly determines the preference for
either the TSIC or TSOC pathways. Consequently, we introduce that for
the shared-shell ring-opening BCP s, greater H lengths predict the
preferred TSIC or TSOC reaction pathway. Besides, the variation of the H
with the IRC for the TSIC and TSOC for all four reactions were display
similar behavior like QTAIM and stress tensor measures that are
discussed above. According to the results that obtained from the
variation of the H plots, we suggest that Reaction 1 is a
competitive reaction and Reaction 2 , Reaction 3 , andReaction 4 are non-competitive reactions, see Figures
(1-4(j)) respectively. However, the helicity length H values
demonstrate subtle differences amidst TSIC and TSOC reaction pathways.
Consequently, the torquoselectivity preferences of Reaction 2 ,Reaction 3 , and Reaction 4 are TSOC, TSOC, and TSIC
respectively based on the Longer H values, which is in confirmation with
the experimental results shown in Table 1 , Figures
(1-4) .