According to the data of QC computations a free molecule of BiDiMDAH molecule exists as single conformation of C2 symmetry with trans orientation of the methyl groups (see Fig. 1). The conformation with cis orientation of the methyl groups was found to be a transitional state. The instability of the TS may be connected with unfavorable electrostatic interactions of nitrogen atoms (the corresponding NPA charges were calculated to be ~ -0.4 e for the TS conformation). In order obtain a qualitative measure of overall atom-atom electrostatics NBO Natural Columbic Energy (NCE) concept was applied, yelling ΔE(es) = ΔENCE(cis) - ΔENCE (trans) = 34.1 kcal/mol, consistent with trans conformer advantage over cis.
The computed geometrical parameters of a stable BiDiMDAH conformation at B3LYP/6-31G(d,p), B3LYP/cc-pVTZ and MP2/cc-pVTZ levels of theory and the experimental values obtained by the XRD diffraction for the solid state are given in Table 2.
Table 2
Structural parameters for BiDiMDAH obtained by means of QC calculations and the XRD method.
|
method/basis
|
|
B3LYP/6-31G(d,p)
|
B3LYP/cc-PVTZ
|
MP2/cc-PVTZ
|
XRD
|
Bond lengths, Ǻ
|
|
|
|
|
N1-C2
|
1.479
|
1.475
|
1.473
|
1.480(2)
|
C2-C3
|
1.549
|
1.545
|
1.539
|
1.536(2)
|
C3-C4
|
1.549
|
1.545
|
1.539
|
1.540(2)
|
C4-N5
|
1.478
|
1.473
|
1.472
|
1.481(2)
|
N5-C6
|
1.461
|
1.456
|
1.457
|
1.468(2)
|
N1-C6
|
1.461
|
1.457
|
1.458
|
1.465(2)
|
N1-N5
|
1.506
|
1.503
|
1.518
|
1.522(1)
|
C6-C7
|
1.515
|
1.511
|
1.503
|
1.517(2)
|
C6-C13
|
1.542
|
1.539
|
1.519
|
1.534(2)
|
Bond angles, °
|
|
|
|
|
∠N1-C2-C3
|
109.0
|
109.0
|
109.4
|
109.4(1)
|
∠C2-C3-C4
|
104.6
|
104.7
|
104.8
|
103.8(1)
|
∠C3-C4-N5
|
109.0
|
108.9
|
109.4
|
109.3(1)
|
∠C4-N5-N1
|
108.7
|
108.7
|
108.3
|
107.6(1)
|
∠N5-N1-C2
|
108.6
|
108.6
|
108.2
|
107.8(1)
|
∠N5-C6-N1
|
62.0
|
62.1
|
62.8
|
62.5(1)
|
∠N1-N5-C6
|
59.0
|
58.9
|
58.6
|
58.6(1)
|
∠N5-N1-C6
|
59.0
|
58.9
|
58.6
|
58.8(1)
|
∠C4-N5-C6
|
116.0
|
116.2
|
114.2
|
115.0(1)
|
∠C2-N1-C6
|
115.6
|
115.7
|
113.4
|
114.9(1)
|
∠N1-C6-C7
|
123.0
|
122.6
|
122.6
|
122.3(1)
|
∠N5-C6-C7
|
123.5
|
123.3
|
123.4
|
122.0(1)
|
∠N1-C6-C13
|
113.4
|
113.8
|
113.2
|
112.1(1)
|
∠N5-C6-C13
|
111.8
|
111.6
|
111.4
|
112.1(1)
|
∠C7-C6-C13
|
113.6
|
113.8
|
114.0
|
115.4(1)
|
Torsion angles,°
|
|
|
|
|
N1-C2-C3-C4
|
-3.3
|
-2.3
|
-1.7
|
-13.8(1)
|
C2-C3-C4-N5
|
3.7
|
2.6
|
2.3
|
13.8(1)
|
C3-C4-N5-N1
|
-2.6
|
-2.0
|
-2.0
|
-8.9(1)
|
C4-N5-N1-C2
|
0.4
|
0.5
|
0.9
|
0.1(1)
|
N5-N1-C2-C3
|
1.9
|
1.1
|
0.6
|
8.8(1)
|
C6-N1-C2-C3
|
-61.8
|
-62.6
|
-62.4
|
-54.4(1)
|
C3-C4-N5-C6
|
61.2
|
61.9
|
61.1
|
54.0(1)
|
C4-N5-C6-N1
|
-97.0
|
-97.0
|
-97.4
|
-96.2(1)
|
N5-C6-N1-C2
|
97.1
|
97.1
|
97.7
|
96.4(1)
|
C2-N1-C6-C7
|
-16.4
|
-16.5
|
-16.2
|
-15.8(2)
|
C4-N5-C6-C7
|
15.8
|
15.4
|
15.3
|
16.5(2)
|
C2-N1-C6-C13
|
-159.7
|
-160.1
|
-159.2
|
-159.3(1)
|
C4-N5-C6-C13
|
157.2
|
156.7
|
156.7
|
159.6(1)
|
C7-C6-C13-C14
|
-171.1
|
-168.3
|
-168.7
|
-180.0(1)
|
N1-C6-C13-C14
|
-24.3
|
-21.4
|
-22.3
|
-33.8(1)
|
N5-C6-C13-C14
|
43.5
|
46.6
|
46.1
|
34.3(1)
|
N1-C6-C13-N8
|
-169.7
|
-166.6
|
-167.5
|
-180.0(1)
|
N1-C6-C13-N12
|
122.5
|
125.4
|
124.0
|
111.9(1)
|
N5-C6-C13-N8
|
-101.9
|
-98.6
|
-99.0
|
-111.9(1)
|
N5-C6-C13-N12
|
-169.7
|
-166.6
|
-167.5
|
-180.0(1)
|
N5-N1-C6-C13
|
103.2
|
102.9
|
103.1
|
104.2(1)
|
N5-N1-C6-C7
|
-113.6
|
-113.5
|
-113.9
|
-112.2(1)
|
C6-N1-N5-C4
|
109.7
|
109.9
|
107.7
|
108.9(1)
|
C6-N5-N1-C2
|
-109.2
|
-109.4
|
-106.8
|
-108.8(1)
|
N1-N5-C6-C13
|
-105.8
|
-106.3
|
-106.0
|
-104.3(1)
|
N1-N5-C6-C7
|
112.8
|
112.4
|
112.7
|
112.7(1)
|
N1-C6-C7-H21
|
44.8
|
46.2
|
49.6
|
96.6(1)
|
N1-C6-C7-H22
|
-77.3
|
-75.6
|
-72.3
|
-23.4(1)
|
N1-C6-C7-H23
|
166.1
|
167.5
|
170.9
|
-143.4(1)
|
The average values of BiDiMDAH bond lengths and bond angles obtained by QC calculations are similar to those for solid state (see Table 2), the computed values of torsion angles are in most cases particularly the same that in the crystal. However, there is a noticeable difference within the 5‑memberred ring: the values of the N5-N1-C2-C3 and the C2-C3-C4-N5 torsion angles are by about 8° and 11° bigger in the crystal than in a free molecule. There is also a difference in the conformation of the hydrogen atoms of the both methyl groups (confer Fig S7 of the ESI). Thus, though the structure of BiDiMDAH in a free state resembles the one in the crystal, it has a different positions of methyl hydrogens and possess flatter skeletons of the both 5-membered rings, comparing with the solid state.
According to the results of QC computations and XRD analysis the essentially planar skeletons of the 5-ring moieties are observed. This fact may be caused by the two possible tendencies. The first tendency is connected with the n(N)→σ*(C–C) and the n(N) →σ*(C–H) anomeric effects, stabilizing the boat conformation of the 6-membered rings. Thus, the lone pair of the N1 atom interacts with the C2–C3 and the C2–H16 antibonding orbitals n(N1)→σ∗(C2–C3 has E(2)=3.6 kcal mol−1 and the n(N1) → σ∗(C2–H16) interaction has E(2) = 4.3 kcal mol−1) and the lone pair of the N5 atom interacts with the C3–C4 and the C4–H20 antibonding orbitals (n(N5) → σ∗(C3–C4) has E(2) = 3.6 kcal mol−1 and the n(N5) → σ∗(C4–H20) interaction has E(2) = 4.3 kcal mol−1). The second tendency is the steric repulsion of the H21 atom of the methyl group and the H17, the H19 and the H15 atoms of the 5-membered ring. Thus, NBO STERIC analysis reveals the corresponding pairwise steric exchange energies: 2.26 kcal mol−1 for the C7–H21 and the C3–H17 bonds, 1.58 kcal mol−1 for the C7–H21 and the C4–H19 bonds, and 1.15 kcal mol−1 for the C7–H21 and the C2–H15 bonds, respectively. The interatomic distance between H21 and H17 is equal to 2.06 Å according to B3LYP/G(d,p), 2.08 Å according to B3LYP/ cc-PVTZ, and 2.00 Å according to MP2/cc-PVTZ levels of theory. That is a little bit less than the sum of the two atomic Wan der Waals radii [53] or natural atomic Wan der Waals radii of the H atoms [44]. However, AIM computations didn’t reveal a critical point between the corresponding H atoms as well as natural bond critical point analysis [54] applied as implemented into NBO 7.0 program. Therefore, it seems that the steric repulsion of the H atoms is the leading force, which causes the flattering of the 5-membered ring in order to achieve the minimal H…H distance which the sum of the Wan der Waals radii permit. The steric hindrance of BiDiMDAH molecule is also confirmed with its high value of standard enthalpy of formation in the gas phase calculated from commonly used atomization approach by the means of Gaussian-4 computations, which yielded (BiDiMDAH, g) = 443.8± 5.0 kJ/mol.
According to NBO analysis BiDiMDAH molecule also has relatively strong σ(C–N)→ σ∗ (N–N) (E(2) = 5.5 kcal mol− 1 ) and σ(N–N) → σ∗(C–N) (E(2) = 7.3 kcal mol− 1 ) interactions in the three-membered ring and some additional important types of conjugations. Thus, there is a strong interaction between N–N bonding orbital and the methyl antibonding C6–C7 orbital: σ(N–N) → σ∗(C6–C7) with E(2) = 6.1 kcal mol− 1. The lone pair of the N1 atom also interacts with antibonding orbital of the the C6–C7 bond (the n(N1) → σ∗(C6–C7) interaction has E(2) = 4.9 kcal mol− 1) as well as the lone pair of the N5 atom interacts with the antibonding orbital of the C6–C7 bonds (the n(N5) → σ∗(C6–C7) interaction has E(2) = 5.3 kcal mol− 1). Additionally, there are strong interactions between two C–H bonding orbitals of the methyl group and antibonding orbital C6–N5, namely σ(C7–H22) → σ∗(C6–N5) with E (2) = 7.0 kcal mol− 1 and σ(C7–H23) → σ∗(C6–N5) with E (2) = 7.2 kcal mol− 1.
The structure of BiDiMDAH was compared with the structures of similar compounds (see Table 3). The largest difference was found for the value of the torsional angle N5N1C2C3 in 1,5-diazabicyclo[3.1.0]hexane and 6.6′-bis(1,5-diazabicyclo[3.1.0]hexane). This two molecules lack the methyl group and subsequently there are no repulsion of the corresponding hydrogen atoms, leading to the flattening of the 5-membered ring. It is worth to notice, that the value of the N5N1C2C3 torsion angle is practically the same in BiDiMDAH and 6,6-dimethyl-1,5-diazabicyclo[3.1.0.]hexane, in which 5-membered ring moiety is also nearly flat, probably due to the H…H repulsions as supposed for BiDiMDAH molecule.
The analysis of the 1H and 13C 1D NMR spectra of BiDiMDAH showed that in solution the compound exists only in a single conformation (i.e., there are clear peaks of only one compound, Fig. S1 and S2, for 1H and 13C 1D NMR spectra, respectively).
The data of {1H-13C}HSQC and {1H‑1Н}gNOESY 2D spectra helped to enable all protons and carbon atoms to be assigned together with their inter relationships. The results of the heteronuclear correlation NMR {1H-13C}HSQC and {1H‑13C}HMBC spectra are presented in Table 4. These spectra show how far away each proton was found from a particular carbon atom, respectively, through one or 2–3 bonds.
Table 4
Selected {1H-13C}HSQC and {1H-13C}HMBC data for BiDiMDAH. Atom numeration is given in Fig. 1.
Atom number
|
13C NMR,
chemical shift, ppm
|
{1H-13C} HSQC
interactions
|
{1H-13C} HMBC
interactions
|
C2
|
48.4
|
H15, H16
|
H17, H18
|
C3
|
32.1
|
H17, H18
|
H16, H20
|
C4
|
48.4
|
H19, H20
|
H17, H18
|
C6
|
65.7
|
-
|
H15, H16, H19, H20,H21, H22, H23
|
C7
|
8.1
|
H21, H22, H23
|
-
|
The 2D NMR spectrum {1H-1H}gNOESY shows the spatial arrangement of protons relative to each other (Table 5, Fig S5 of the ESI). Protons H15, H17 and H19 have cross-peaks with proton H21.
Table 5
Partial data {1H- 1H}gNOESY for BiDiMDAH 4. Atom numeration is given in Fig. 1.
Atom number
|
1H NMR
chemical shift, ppm
|
Coupling constant
J, Hz
|
1H1НgNOESY
Interactions
|
H15
|
2.78–2.82, dt
|
11.7 (2JH15−H16)
7.1 (3J H15−H18)
|
H16, H17, H21
|
H16
|
3.18–3.23, dt
|
11.7 (2JH16−H15)
8.7 (3JH16−H17 )
|
H15, H17, H18
|
H17
|
1.76–1.82, m
|
-
|
Н15, H16, H18, H19, H20, H21
|
H18
|
2.07–2.13, m
|
-
|
H16, H17, H20
|
H19
|
2.78–2.82, dt
|
11.7 (2JH19−H20)
7.1 (3J H19−H18)
|
H17, H20
|
H20
|
3.18–3.23, dt
|
11.7 (2JH20−H19)
8.7 (3JH20−H17 )
|
H18, H19
|
H21, H22, H23
|
1.09, s
|
-
|
H21 − H15, H17, H19
|
The detected cross-peaks of proton H17 with proton H21 (Nuclear Overheuser effect) confirms of the endo-position of the methyl groups at the C ring atom in the diaziridine moiety.
Thus, the results of 1D and 2D NMR spectra reveal that in CDCl3 solution BiDiMDAH molecule exists only in a single conformation and the distances between H21 proton of the methyl group and the protons H17 of the ring moiety are small enough to produce Nuclear Overheuser effect. This fact supports that 6-membered rings of BiDiMDAH do not adopt a chair conformation, but rather a boat form is amiable.