among all bonds (merely 141.55 kJ/mol). It is comforting that none of the structural
parameters considered here indicates the N 7 =N 8 bond to be the weakest. However,
this also suggests that whenever exotic bonds (not listed in Table 1) are involved in a
bond breaking process, their BDEs should be calculated to verify the weakest bond
for certainty.
Data in Table 2 also show that MIEN alone can correctly single out the type of
bonds to which the trigger bond belongs. For instance, for the selected compounds,
the easiest bond to break is the C–NO 2 or N–NO 2 bond, but among which MIEN
sometimes incorrectly picks up the weakest bond. For CDNAPY, the C 4 –N 9 bond
has the smallest MIEN (0.1237) and its BDE is 278.67 kJ/mol, but it is the C 2 –N 8
bond that has the lowest BDE (248.56 kJ/mol) even with a bigger MIEN (0.1335).
Therefore, much sensible structural parameters other than the existing four aforementioned must be proposed for trigger bond identification.
In light of the general fact that WBO and MIEN are related positively to BDE
and inversely to R, W = WBO/R and M = MIEN/R were first conceived to be the
better alternatives. Such an idea comes with no surprise, because the numerator of
the 1/R a term on the right-hand side of Eq. (2) can be interpreted as WBO = 1 for
single bonds. Then, to take local chemical environment into consideration, Eq. (2)
might suggest a general relationship: BDE/R ∝ WBO/R. (Hereafter, numerical
values of bond-strength indicators will be quoted without units unless otherwise
noted.)
Unfortunately, the data shown in Table 2 again proclaim that the minima of
W and BDE still do not align well. For example, in PAM, the O 8 –C 17 bond has the
smallest W, but the C 2 –N 7 or C 4 –N 9 bond has the lowest BDE. In general, the
results of W closely resemble those of WBO.
Fortunately, the bonds with the smallest M enclose the bond with the lowest
BDE (see Table 2). For TNT, the C 1 –N 14 , C 3 –N 11 , and C 5 –N 8 bonds all have the
same smallest M value (0.10) and both of the C 1 –N 14 and C 5 –N 8 bonds have the
lowest BDE. For PNT, the C 3 –N 16 , C 4 –N 13 , and C 5 –N 10 bonds have the smallest
M (0.09) and, among them, the C 4 –N 13 bond is the weakest (BDE = 197.65 kJ/
mol). We then considered the product of W and M, K = W × M, as a new indicator.
According to M, for TNCr, the weakest bonds are the C 2 –N 8 and C 6 –N 12 bonds
(M = 0.11), whereas according to K, the weakest bond of TNCr is solely the C 2 –N 8
bond (K = 0.06) in agreement with its lowest BDE value. Overall, K outperforms
M only marginally (see Fig. 3).
Next, we observed an enlightening fact: ρ c can almost always single out the
weakest bond among the weaker bonds of the same type within a molecule identified by M and K (see Table 2). The only exception might be PNT: among the three
most weak bonds (C 3 –N 16 , C 4 –N 13 , and C 5 –N 10 ) sorted out by M and K, ρ c chooses
the C 5 –N 10 bond (BDE = 200.63 kJ/mol) to be the weakest whereas the C 4 –N 13
bond has the lowest BDE (197.65 kJ/mol). However, this is not a huge failure
because the difference in the BDEs of the three weak bonds of PNT is less than
3 kJ/mol, well within the error margin of the computational methods employed.
Nonetheless, such promising results strongly advocate that M and K, as two new
trigger bond indicators (TBIs), shall be first used to identify the set of most weak
Effective Bond-Strength Indicators
51
parameters considered here indicates the N 7 =N 8 bond to be the weakest. However,
this also suggests that whenever exotic bonds (not listed in Table 1) are involved in a
bond breaking process, their BDEs should be calculated to verify the weakest bond
for certainty.
Data in Table 2 also show that MIEN alone can correctly single out the type of
bonds to which the trigger bond belongs. For instance, for the selected compounds,
the easiest bond to break is the C–NO 2 or N–NO 2 bond, but among which MIEN
sometimes incorrectly picks up the weakest bond. For CDNAPY, the C 4 –N 9 bond
has the smallest MIEN (0.1237) and its BDE is 278.67 kJ/mol, but it is the C 2 –N 8
bond that has the lowest BDE (248.56 kJ/mol) even with a bigger MIEN (0.1335).
Therefore, much sensible structural parameters other than the existing four aforementioned must be proposed for trigger bond identification.
In light of the general fact that WBO and MIEN are related positively to BDE
and inversely to R, W = WBO/R and M = MIEN/R were first conceived to be the
better alternatives. Such an idea comes with no surprise, because the numerator of
the 1/R a term on the right-hand side of Eq. (2) can be interpreted as WBO = 1 for
single bonds. Then, to take local chemical environment into consideration, Eq. (2)
might suggest a general relationship: BDE/R ∝ WBO/R. (Hereafter, numerical
values of bond-strength indicators will be quoted without units unless otherwise
noted.)
Unfortunately, the data shown in Table 2 again proclaim that the minima of
W and BDE still do not align well. For example, in PAM, the O 8 –C 17 bond has the
smallest W, but the C 2 –N 7 or C 4 –N 9 bond has the lowest BDE. In general, the
results of W closely resemble those of WBO.
Fortunately, the bonds with the smallest M enclose the bond with the lowest
BDE (see Table 2). For TNT, the C 1 –N 14 , C 3 –N 11 , and C 5 –N 8 bonds all have the
same smallest M value (0.10) and both of the C 1 –N 14 and C 5 –N 8 bonds have the
lowest BDE. For PNT, the C 3 –N 16 , C 4 –N 13 , and C 5 –N 10 bonds have the smallest
M (0.09) and, among them, the C 4 –N 13 bond is the weakest (BDE = 197.65 kJ/
mol). We then considered the product of W and M, K = W × M, as a new indicator.
According to M, for TNCr, the weakest bonds are the C 2 –N 8 and C 6 –N 12 bonds
(M = 0.11), whereas according to K, the weakest bond of TNCr is solely the C 2 –N 8
bond (K = 0.06) in agreement with its lowest BDE value. Overall, K outperforms
M only marginally (see Fig. 3).
Next, we observed an enlightening fact: ρ c can almost always single out the
weakest bond among the weaker bonds of the same type within a molecule identified by M and K (see Table 2). The only exception might be PNT: among the three
most weak bonds (C 3 –N 16 , C 4 –N 13 , and C 5 –N 10 ) sorted out by M and K, ρ c chooses
the C 5 –N 10 bond (BDE = 200.63 kJ/mol) to be the weakest whereas the C 4 –N 13
bond has the lowest BDE (197.65 kJ/mol). However, this is not a huge failure
because the difference in the BDEs of the three weak bonds of PNT is less than
3 kJ/mol, well within the error margin of the computational methods employed.
Nonetheless, such promising results strongly advocate that M and K, as two new
trigger bond indicators (TBIs), shall be first used to identify the set of most weak
Effective Bond-Strength Indicators
51