Hereafter, the five key bond-strength indicators (i.e., R, MIEN, BO, ρ c , and
BDE) of all single bonds of these molecules will be carefully compared to seek
better relationships among them. The end goal is to propose simple, sensitive
structural indicators suitable for identifying the trigger bond (or even better, all
weak bonds), thus saving both computational resources and time.
2 Computational Methods
Many studies [1–8, 16, 17], have already shown that the DFT-B3LYP method [18,
19] in combination with the 6-31G* basis set [20] is able to yield accurate energetics, structures, and other molecular properties. In this paper, the same method
was employed to obtain the fully optimized molecular geometries and electronic
structures, including MIEN and Wiberg bond order (WBO) [21, 22], of the chosen
compounds (Fig. 2) within the Gaussian09 program package [23]. To obtain the
values of ρ c , the Bader analysis was performed using AIMAll package [24].
Based on Hess’s law [25], conventional counterpoise correction methods [10,
11] were employed to calculate the BDEs according to Eq. (1). Unfortunately, any
existing counterpoise correction methods [10, 11] cannot address the situation when
a bond within a ring is broken. Instead of trying to contemplate suitable ghost atoms
and their linking strategies for ring opening scenarios, we simply supplemented
extra diffuse polarization basis functions to the existing basis sets for the atoms of
the broken bonds to roughly mimic the effects of ghost atoms. Taking the
four-membered ring of NMDACB for example, when breaking the C 1 –N 2 and
C 1 –N 3 bonds, the BSSE was calculated with additional aug-cc-pV5Z Diffuse (1s,
1p, 1d, 1f, 1g, 1h) basis functions [26] separately placed on the C 1 , N 2 , and N 3
atoms. Numerical tests confirmed that the magnitude of the resulting correction to
the BDEs from this basis-set local enhancement protocol was in line with the
procedure of existing counterpoise correction methods [10, 11].
3 Results and Discussion
Four commonly available major bond-strength indicators (i.e., R, MIEN, WBO, and
ρ c ) are listed along with BDEs in Table 2. For the selected compounds, nearly all
the bonds with the longest R or the smallest WBO do not possess the lowest BDE.
The bond with the lowest BDE is the C–NO 2 or N–NO 2 bond, but, according to
R and WBO, the weakest bond can draw from all sorts of candidates, e.g., C–C, C–H,
C–NO 2 , C–Cl, N–H, or O–C bond. Similarly, the smallest values of ρ c alone never
correspond to the weakest bonds either. This obviously illustrates that R, WBO, or ρ c
cannot be used separately to identify the trigger bond.
Particularly, because of AMNFMC containing the azido group (−N 7 =N 8
+
=N 9
−
),
when the N 7 =N 8 bond is broken to produce the N 2 gas, its BDE is the second lowest
50
G.-X. Wang et al.
BDE) of all single bonds of these molecules will be carefully compared to seek
better relationships among them. The end goal is to propose simple, sensitive
structural indicators suitable for identifying the trigger bond (or even better, all
weak bonds), thus saving both computational resources and time.
2 Computational Methods
Many studies [1–8, 16, 17], have already shown that the DFT-B3LYP method [18,
19] in combination with the 6-31G* basis set [20] is able to yield accurate energetics, structures, and other molecular properties. In this paper, the same method
was employed to obtain the fully optimized molecular geometries and electronic
structures, including MIEN and Wiberg bond order (WBO) [21, 22], of the chosen
compounds (Fig. 2) within the Gaussian09 program package [23]. To obtain the
values of ρ c , the Bader analysis was performed using AIMAll package [24].
Based on Hess’s law [25], conventional counterpoise correction methods [10,
11] were employed to calculate the BDEs according to Eq. (1). Unfortunately, any
existing counterpoise correction methods [10, 11] cannot address the situation when
a bond within a ring is broken. Instead of trying to contemplate suitable ghost atoms
and their linking strategies for ring opening scenarios, we simply supplemented
extra diffuse polarization basis functions to the existing basis sets for the atoms of
the broken bonds to roughly mimic the effects of ghost atoms. Taking the
four-membered ring of NMDACB for example, when breaking the C 1 –N 2 and
C 1 –N 3 bonds, the BSSE was calculated with additional aug-cc-pV5Z Diffuse (1s,
1p, 1d, 1f, 1g, 1h) basis functions [26] separately placed on the C 1 , N 2 , and N 3
atoms. Numerical tests confirmed that the magnitude of the resulting correction to
the BDEs from this basis-set local enhancement protocol was in line with the
procedure of existing counterpoise correction methods [10, 11].
3 Results and Discussion
Four commonly available major bond-strength indicators (i.e., R, MIEN, WBO, and
ρ c ) are listed along with BDEs in Table 2. For the selected compounds, nearly all
the bonds with the longest R or the smallest WBO do not possess the lowest BDE.
The bond with the lowest BDE is the C–NO 2 or N–NO 2 bond, but, according to
R and WBO, the weakest bond can draw from all sorts of candidates, e.g., C–C, C–H,
C–NO 2 , C–Cl, N–H, or O–C bond. Similarly, the smallest values of ρ c alone never
correspond to the weakest bonds either. This obviously illustrates that R, WBO, or ρ c
cannot be used separately to identify the trigger bond.
Particularly, because of AMNFMC containing the azido group (−N 7 =N 8
+
=N 9
−
),
when the N 7 =N 8 bond is broken to produce the N 2 gas, its BDE is the second lowest
50
G.-X. Wang et al.