Computational Study on N-N Homolytic Bond Dissociation Enthalpies

Article pubs.acs.org/JPCA

Cite This: J. Phys. Chem. A XXXX, XXX, XXX−XXX

Computational Study on N−N Homolytic Bond Dissociation Enthalpies of Hydrazine Derivatives Yuanyuan Zheng, Wenrui Zheng,* Jiaoyang Wang, Huifang Chang, and Danfeng Zhu College of Chemistry and Chemical Engineering, Shanghai University of Engineering Science, Shanghai 201620, China S Supporting Information *

ABSTRACT: The hydrazine derivatives have been regarded as the important building blocks in organic chemistry for the synthesis of organic N-containing compounds. It is important to understand the structure−activity relationship of the thermodynamics of N−N bonds, in particular, their strength as measured by using the homolytic bond dissociation enthalpies (BDEs). We calculated the N−N BDEs of 13 organonitrogen compounds by eight composite high-level ab initio methods including G3, G3B3, G4, G4MP2, CBS-QB3, ROCBS-QB3, CBS-Q, and CBS-APNO. Then 25 density functional theory (DFT) methods were selected for calculating the N−N BDEs of 58 organonitrogen compounds. The M05-2X method can provide the most accurate results with the smallest root-meansquare error (RMSE) of 8.9 kJ/mol. Subsequently, the N−N BDE predictions of different hydrazine derivatives including cycloalkylhydrazines, N-heterocyclic hydrazines, arylhydrazines, and hydrazides as well as the substituent effects were investigated in detail by using the M05-2X method. In addition, the analysis including the natural bond orbital (NBO) as well as the energies of frontier orbitals were performed in order to further understand the essence of the N−N BDE change patterns.

1. INTRODUCTION Hydrazine and derivatives have been used in many technical and commercial areas due to their unique characteristics. Some simplest hydrazines, for example, monomethylhydrazine (MMH) and unsymmetrical dimethylhydrazine (UDMH), which have significant thermochemical properties of very high heat of combustion, can serve as common rocket propellants for space applications.1−3 Hydrazine derivatives are also classical and versatile building blocks in organic chemistry for the synthesis of biologically active N-containing heterocycle compounds such as α,β-diamino acids and monocyclic β-lactams.4−6 Besides, the amines7−11 obtained directly from hydrazine derivatives can be utilized as precursor materials for synthetic drugs12−14 and can be regarded as target molecules for the synthesis of xerographic, photographic materials, conducting polymers,15 etc. One of the most important hydrazine derivatives, the hydrazides, are common intermediates obtained in a growing number of synthetic routes and widely used in synthesizing active nitrogen-containing molecules, such as the α-amino acids and peptides and their derivatives, which are versatile building blocks for the construction of important biological and pharmaceutical units.16 Given to the many applications of hydrazine derivatives,17−28 it is important to understand the structure−activity relationship of the thermodynamics of N−N bonds, in particular, their strength as measured by using the homolytic bond dissociation enthalpies (BDEs). With the rapid development of quantum chemistry and computers in recent years,29 the theoretical methods such as composite methods, DFT methods, etc.,30−34 © XXXX American Chemical Society

have become powerful tools for calculating BDEs of organic compounds.35−37 For the theoretical studies on N−N BDEs, He and co-workers38 used ab initio calculations at M06-2X/cc-pvtz level to investigate the N−N BDEs of different conformational 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) and octahydro1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX) in the gas-phase, and the bonding strength was evaluated by the bond order (BO). Reynisson et al.39 calculated the N−N BDEs of the moieties found in drugs by B3LYP method, and the mean N−N BDEs for the six hydrazones and three nitrosamines are 255.4 and 146.7 kJ/mol, separately. The theoretical studies on N−N BDEs of hydrazines compounds were rarely reported. For example, Li et al.40 calculated the N−N BDE of 1,2-bis(2,4,6-trinitrophenyl) hydrazine at the B3LYP/6-31G* level, and the value is 202.6 kJ/ mol. Lu et al.41 used theoretical methods to calculate the N−N BDEs of oxygen-rich hydrazine derivatives and the values of H 2N−NH(NO2), H2 N−NH(H •HNO 3), (O 2N)HN−NH(NO2), (O3NH•H)HN−NH(H•HNO3), and (O2N)HN−NH(H•HNO3) are 367, 332, 385, 340, and 319 kJ/mol, respectively. In Reynisson’s research, the N−N BDEs of 11 hydrazine moieties were also calculated, and the mean value is 228.2 kJ/ mol.39 In the present study, the N−N BDEs of hydrazine and derivatives as well as the substituent effects were systematically investigated by using theoretical methods, which can provide a Received: December 10, 2017 Revised: January 19, 2018 Published: February 22, 2018 A

DOI: 10.1021/acs.jpca.7b12094 J. Phys. Chem. A XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry A Table 1. 13 N−N BDEs Calculated by Eight Composite High-Level ab Initio Methods (kJ/mol) entry

compounds

exptl

G3

G3B3

G4

G4MP2

CBSQB3

ROCBSQB3

CBS-Q

CBSAPNO

average of eight methods

1 2 3 4 5 6 7 8 9 10 11 12 13

ON−NO2 O2N−NO2 H2N−NH2 F2N−NF2 H3CHN−NH2 H2N−N(CH3)2 H3CHN−NHCH3 (H3C)2N−NHCH3 (H3C)2N−N(CH3)2 H2N−NO2 H3CHN−NO2 (H3C)2N−NO2 H2N(H3C)N−NO RMSEa

36.8 55.2 274.1 ± 1.7 87.9 ± 4.2 275.8 ± 8.4 259.8 ± 8.4 276.1 ± 12.6 254.4 249.4 230 209.2 183.3 179.6 10

31.3 53.4 257 83.4 254 251.9 259.2 255.2 239.5 212.2 213 202.4 146.7 3

40.4 58.8 257.5 87.7 254.1 251.4 258.9 253.7 236.9 212.4 212.1 200.4 137.2 2.6

38.6 55.1 259.3 88.6 254.4 250.1 257.5 250.4 231.8 212.8 209.6 194.7 134.1 3.4

37.9 51.5 259.6 81.6 254.1 249 256.3 248.5 228.9 209.3 205.5 189.8 130.8 5.8

36.6 56.1 266.7 92.7 261.8 258 264.9 258.8 240.7 218.6 217.4 204.6 138.2 4

36.4 54.2 264.7 90.3 259.9 256.1 263.1 256.9 238.8 216.7 215.5 202.7 138.2 2.2

36.9 56.6 269.3 92.2 262.1 258.2 259.5 261.2 242.2 219.8 218.3 205.4 138.5 4.7

34.7 49.6 267.1 81.9 259.5 255.2 262.5 256.6 239 212.6 211.1 198.3 137.0 3

36.6 54.4 262.7 87.3 257.5 253.7 260.2 255.2 237.2 214.3 212.8 199.8 137.6

a RMSE (root-mean-square error) = [Σ(xi − yi)2/N]1/2 (N = 13, xi represents the calculated or experimental data for each species, and yi represents the theoretical average of 13 N−N BDEs of eight composite high-level ab initio methods.

3. RESULTS AND DISCUSSION 3.1. Evaluation of Composite High-Level Methods. Considering the high precision of composite high-level methods in thermodynamic property calculation,84 the N−N BDEs of 13 compounds with experimental values85 in which no more than eight non-hydrogen atoms are included were calculated by using eight composite high-level ab initio methods, containing two different series of Gn (G3, G3B3, G4, and G4MP2) and CBS (CBS-QB3, ROCBS-QB3, CBS-Q, and CBS-APNO). The corresponding BDE results are shown in Table 1. Moreover, the 13 N−N BDE values calculated by eight composite high-level ab initio methods as well as the experimental values are all distributed in Figure 1.

better understanding for the N−N formation and cleavage of hydrazine derivatives and more valuable guidance for the further experimental researches in corresponding reactions.

2. COMPUTATIONAL METHODS The N−N bond cleavage of hydrazine derivatives is shown in the following reaction. The enthalpy change of this reaction at 1 atm and 298.15 K42 in the gas phase represents the homolytic bond dissociation enthalpy (BDE) of the N−N bond. R 2R1NNR3R 4(g) → R 2R1N•(g) + R 4R3N•(g)

The enthalpy of each species can be calculated by the following equation: H(298 K) = E + ZPE + Htrans + Hrot + H vib + RT

In this equation, ZPE represents the zero point energy. The Htrans, Hrot, and Hvib are the standard temperature correction terms calculated with equilibrium statistical mechanics with harmonic oscillator and rigid rotor approximations.43,44 In the benchmark calculations, the composite high-level ab initio methods, including Gaussian-n (Gn) series (G3,45 G3B3,46,47 G4,48 and G4MP249) and complete-basis-set (CBS) series (CBS-QB3,50,51 ROCBS-QB3,52 CBS-Q,53 and CBSAPNO54,55), which are suitable for systems of less than eight non-hydrogen atoms as well as the 25 kinds of DFT methods including B3LYP,51 B3LYP-D3,56 CAM-B3LYP,57 BP86,58 B3P86,59 B3PW91,60 B97D,61 B97D3,62 M05-2X,63 M06-2X,64 M06-HF, 65 MPW1B95, 66 MPW1KCIS, 67 TPSS1KCIS, 68 TPSSLYP1W,69 M11,70 N12,71 MN12-L,72 MN12-SX,73 PBE1W,74 PBE1PBE,74 SOGGA11,75 SOGGA11-X,76 WB97,77 and WB97-X77 were selected. For all of the DFT calculations, the geometry optimization and the frequency calculation of molecules and the corresponding radicals were conducted at the B3LYP/6-31+G(d) level due to its high accuracy and lower computational cost;78−82 at the same time the correct nature of the stationary points was confirmed and the zero-point vibrational energies (ZPEs) were extracted. The basis set of single-point energy calculation by 25 DFT methods is 6-311+ +G(2df,2p). All above calculations were performed by the Gaussian09 programs.83

Figure 1. Thirteen N−N BDE distributions calculated by eight theoretical methods as well as their experimental values.

It can be intuitively seen from Figure 1 that for the 13 N−N BDEs there are small differences between the eight high-level ab initio methods and that there is very good self-consistency between them. Considering the excellent self-consistency between the different series of high level methods, the average values of the eight composite methods for the 13 N−N BDEs B


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The Journal of Physical Chemistry A Table 2. Correlations between the Theoretical with Experimental N−N BDEs by 25 DFT Methods (kJ/mol)a DFT methods

MD

MAD

RMSE

DFT methods

MD

MAD

RMSE

B3LYP B3LYP-D3 CAM-B3LYP BP86 B3P86 B3PW91 B97D B97D3 M05-2X M06-2X M06-HF MPW1B95 MPW1KCIS

−23.4 −9.1 −10.7 −1.8 1.6 −11.5 −11.4 −5.2 0.8 17.1 36.9 1.4 −5.9

26.9 19.9 19.4 21.9 18.1 21.5 23.6 22.6 7.3 19.9 38.9 16.3 20.3

32.1 23.0 23.1 25.6 21.8 25.4 27.3 25.8 8.9 26.0 45.1 19.7 24.0

TPSS1KCIS TPSSLYP1W M11 N12 MN12-L MN12-SX PBE1W PBE1PBE SOGGA11 SOGGA11-X WB97 WB97-X

−16.5 −38.5 19.4 8.4 15.2 16.4 −4.9 −1.5 −6.9 −5.4 0.6 0.6

24.4 40.4 22.5 20.3 20.7 20.0 22.7 17.4 23.4 17.2 11.9 16.9

28.7 46.3 28.3 25.7 27.0 26.3 26.2 20.9 28.1 20.6 14.1 20.0

MD (mean deviation) = Σ(xi − yi)/N; MAD (mean absolute deviation) = Σ|xi − yi|/N; RMSE (root-mean-square error) = [Σ(xi − yi)2/N]1/2 (N = 58, xi represents the calculated data for each species, and yi represents the experimental or standard reference values accordingly).

a

corresponding results are listed in the Supporting Information. The mean deviation (MD), mean absolute deviation (MAD), and root-mean-square error (RMSE) values of the 25 DFT methods are listed in Table 2. It can be seen that M05-2X gave the highest accuracy with the smallest RMSE value of 8.9 kJ/mol, and the MD and MAD values are 0.8 and 7.3 kJ/mol, respectively. The second superior method is WB97, and the RMSE, MD, and MAD values are 14.1, 0.6, and 11.9 kJ/mol, respectively. The TPSSLYP1W method exhibits the worst precision with the largest RMSE value of 46.3 kJ/mol, and the MD and MAD are −38.5 and 40.4 kJ/mol, respectively. The B3LYP is obviously not suitable for calculating the N−N BDEs with high RMSE value of 32.1 kJ/mol, even though it is considered as one of the most popular DFT methods in organic molecular calculation. By comparison, the corrected B3LYP methods of B3LYP-D3 and CAM-B3LYP can provide better precision, and the RMSE values are 23.0 and 23.1 kJ/mol, separately. The excellent linear relationship between the 58 N− N BDEs calculated by M05-2X with the experimental values is depicted in Figure 2 in which the correlation coefficient square (R2) is 0.978. According to the above analysis, we selected the

were calculated, and the root-mean-square error (RMSE) values of the eight methods as well as the experimental values from the average values are listed in Table 1. It can be seen that for the eight composite methods, the RMSE values range from 2.2 kJ/ mol (ROCBS-QB3) to 5.8 kJ/mol (G4MP2), while for the experimental values, the RMSE reaches to 10 kJ/mol. Especially, we also can see that for N-nitrosodimethylamine (entry 13), the experimental and average theoretical N−N BDEs are 179.6 and 137.6 kJ/mol, respectively, and the difference is as high as 42.0 kJ/mol. Besides, there are large differences (>10 kJ/mol) between the experimental with average theoretical values for more than half of the 13 N−N BDEs, and the disparities between them can also be intuitively seen from Figure 1. In addition, there are also large uncertainties for the experimental BDE values itself, for example, the uncertainty of 12.6 kJ/mol is found in entry 7. Therefore, we think it is more reasonable to consider the averages of the eight high-level ab initio methods as the standard reference values for the 13 N−N BDEs in the following DFT evaluations. 3.2. Evaluation of Different DFT Methods. The composite high-level ab inito methods have been used to calculate the BDEs of small systems with high precision, which cannot meet the requirement of larger compounds including over eight non-hydrogen atoms. Hence, the density functional theory (DFT) method becomes a good choice for the BDE calculation on account of no serious spin-contamination and relatively low CPU-costs.86 In order to choose an optimal DFT method for calculating the N−N BDEs of hydrazine derivatives, we extended our training set by adding 45 N−N BDEs of organonitrogen compounds such as nitro- or nitroso-substituted amines with experimental values apart from the 13 N−N BDEs with standard reference values mentioned above in Table 1. For the 58 N−N BDE calculations, the 25 DFT methods were chosen, in which the global-hybrid meta-GGA such as BB1K, MPW1B95, TPSS1KCIS, MPW1KCIS, M05-2X, M06-HF, and M06-2X, the hybrid GGA like SOGGA11-X, the range-separated hybrid NGA like N12-SX, the range-separated hybrid meta-GGA like M11, the range-separated hybrid meta-NGA like MN12-SX, and the generalized gradient approximations (GGA) such as PBE1W and SOGGA11 are included. In addition, there are some functionals with dispersion correction such as B3LYP-D3 a nd B97D and long-range correction like CAM-B3LYP. Furthermore, these functionals such as N12, M11, MN12-L, MN12-SX, SOGGA11, and SOGGA11-X were produced after 2010. The

Figure 2. Correlation relationship between M05-2X and experimental 58 N−N BDEs. C


Article

The Journal of Physical Chemistry A Table 3. N−N BDEs, ΔBDEs, and Wiberg Bond Orders (N−N) of Cycloalkylhydrazines

M05-2X method to predict the N−N BDEs as well as the substituent effects of hydrazine derivatives in the following discussions. 3.3. Prediction of N−N BDEs in Cycloalkylhydrazines. One of the species of hydrazine derivatives, cycloalkylhydrazines, is of great interest in organic reactions. For example, cyclopropylhydrazines can be used for privileged scaffolds in library design and drug discovery as well as common rocket propellants due to the combination of hydrazine with cyclopropyl fragments, which has an additional three-membered ring strain. 87 Furthermore, several monocyclopropylhydrazines were reported to be lysine-specific demethylase 1 (LSD1) inhibitors.88,89

Therefore, in order to achieve the purpose of systematically comparing the N−N BDE change patterns of cycloalkylhydrazine family, the N−N BDEs from cyclopropylhydrazines to cyclohexylhydrazines were all calculated by the M05-2X method. The corresponding results are listed in Table 3, and the BDE value distribution from cyclopropylhydrazines to cyclohexylhydrazines is depicted in Figure 3. In Table 3, there are five theoretically possible cycloalkylhydrazines of mono- (entries 1− 4), 1,1-di- (entries 5−8), 1,2-di- (entries 9−12), tri- (entries 13− 16), and tetrasubstituted (entries 17−20). In order to better investigate the BDE change patterns, the ΔBDE values (ΔBDEs = BDE(mono-) − BDEs (1,1-di-, 1,2-di, tri-, and tetra-)) are also D


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The Journal of Physical Chemistry A

As an example, the molecular optimized conformations of cyclohexylhydrazines from mono- to tetrasubstituted are depicted in Figure 4 in which the corresponding bond angles are shown. It can be seen that the H−N−C bond angles in mono-, 1,2-di-, and trisubstituted are around 109.00°, and the C−N−C bond angles in 1,1-di-, trisubstituted are 119.00° and 116.41°, the two C−N−C bond angles in tetracyclohexylhydrazine are 115.00° and 125.30°. Comparing the H−N−C bond angles, the larger C−N−C bond angles show that the numbers of the substituted cyclohexyl groups on N atom have a large effect on the cyclohexylhydrazines conformations. Especially, in tetracyclohexylhydrazine with the smallest N−N BDE value of 147.7 kJ/mol, there is about 10.00° difference between the two C−N−C bond angles, and the largest value of 125.30° is found for all the C−N−C bond angles in cyclohexylhydrazines. In addition, one of the structural parameters, the two dihedral angles values in cycloalkylhydrazines, which can demonstrate the three-dimensional configuration on N−N bond center, is listed in Table 4. For the same compound, there is little difference between the two dihedral angle values on the N−N center, except for the tetracyclohexylhydrazine. For example, the two dihedral angles values of 1,2-dicyclobutylhydrazine (n = 2) are 123.0° and 123.9°, and there is only 0.9° difference, which indicated that the two N atoms in the N−N center exhibit the nearly identical three-dimensional configuration. While in tetracyclohexylhydrazine (n = 4), there is great difference between the two dihedral angle values (137.1° and 178.8°), which shows that the three-dimensional configurations of the two N atoms in the N−N bond center are different, one is planar, and the other is pyramidal. The particularity of the configuration on the N−N bond center of the tetracyclohexylhydrazine may lead to the especially small N−N BDE value of 147.7 kJ/mol. In addition, for the same substituted type from cyclopropylhydrazines (n = 1) to cyclohexylhydrazines (n = 4), it is found that the most obvious pyramidal configurations on N−N center are displayed in cyclopropylhydrazines (n = 1). For example, for 1,1disubstituted type from n = 1 to 4, the ∠H4H5N6N3 dihedral angles are 109.1°, 118.2°, 118.9°, and 122.4°, respectively, and the ∠C1C2N3N6 dihedral angles are 116.4°, 132.7°, 123.0°, and 137.0°, respectively. The disruption of overall planarity of the cyclopropyl scaffold is caused by the increased sp3 character, three-dimensionality favoring noncoplanarity, and less crystal packing.90 Besides, the additional ring strain of the cyclopropyl ring including the angular strain (von Baeyer strain) and torsional strain (Pitzer strain), and the transannular van der Waals interaction of nonbonded atoms may play an important role in N−N configurations.91 Therefore, these properties of cyclopropyl scaffold may lead to the molecular instability of

Figure 3. N−N BDEs (kJ/mol) of cycloalkylhydrazines.

listed in Table 3. Comparing with the monocycloalkylhydrazines, the N−N BDEs decrease as the ring numbers increase. For example, for the cyclohexylhydrazines, the ΔBDE values of 1,1di-, 1,2-di-, tri-, and tetrasubstituted are −17.2, −19.0, −65.9, and −131.6 kJ/mol, respectively, and the very large BDE difference of more than 100 kJ/mol is found. In addition, from cyclopropylhydrazines to cyclohexylhydrazines for each substituted type of the five, it can be seen that the largest N−N BDEs are found in cyclobutylhydrazines. For example, for the 1,1disubstituted (entries 5−8), the BDE values from cyclopropylhydrazines to cyclohexylhydrazines are 255.8, 277.0, 266.9, and 262.1 kJ/mol, respectively. The smallest N−N BDEs are found in cyclopropylhydrazines for mono-, 1,1-di-, 1,2di-, and trisubstituted types, for example, for the 1,2-disubstituted (entries 9−12), the BDE values from cyclopropylhydrazines to cyclohexylhydrazines are 217.0, 260.6, 259.5, and 260.3 kJ/mol, separately. Exceptionally, in the tetra-substituted type (entries 17−20), the BDE of cyclohexylhydrazine is the smallest of 147.7 kJ/mol, which is the minimum of all the cycloalkylhydrazines in Table 3. It also can be discovered that for the dicycloalkylhydrazines, the N−N BDE values of 1,2-disubstituted (RHNNHR) are less than that of 1,1-disubstituted (NH2−NR2), and the disparities between the two disubstituted hydrazines are 38.8, 16.4, 7.4, and 1.8 kJ/mol for cyclopropyl-, cyclobutyl-, cyclopentyl-, and cyclokexylhydrazines, respectively, in which the BDE difference decreases as the ring size increases. Besides, the Wiberg bond orders of N−N bond are listed in Table 3, and the values are around 1.000 for all of the cycloalkylhydrazines.

Figure 4. Molecular optimized conformations at the B3LYP/6-31+G(d) level of cyclohexylhydrazines from mono- to tetra-substituted. E


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The Journal of Physical Chemistry A Table 4. Dihedral Angles of Cycloalkylhydrazines

Figure 5. Natural charges distributions in molecules of cyclopropylhydrazines

depicted in Figure 6. From mono- to tetra-substituted cycloalkylhydrazines, the HOMO energy values increase as the N−N BDEs decrease. For instance, the BDE values of mono-, di-, tri-, and tetra-substituted cyclobutylhydrazines are 289.8, 277.0, 226.1, and 190.0 kJ/mol, separately, and the corresponding HOMO energy values are −8.24, −7.45, −7.25, and −6.97 eV, respectively. Similarly, for the cyclobutylhydrazines with larger N−N BDE, the HOMO energies are smaller than cyclohexylhydrazines for the same substituted type. For tetracyclohexylhydrazine, in which the N−N BDE is the smallest at 147.7 kJ/ mol, the HOMO energy is the largest of −6.43 eV. The smaller HOMO energies indicate that the molecules are less likely to be activated, and the N−N bond becomes more stable. 3.4. Prediction of N−N BDEs in N-Heterocyclic Hydrazines. The N−N cleavages of the N-heterocyclic hydrazines play an indispensable role in the synthesis of drugs and biologically active compounds. For example, in the tandem hetero[4 + 2]cycloaddition/allylboration three-component reaction of substituted 3,6-dihydro-2H-pyridin-1-ylamines, the α-hydroxyalkylated piperidines products can be provided,93 which are the common unit presence in several naturally occurring alkaloids and azasugar analogue.94 The chemoselective room temperature E1cB N−N cleavage of oxazolidinone hydrazides can give the chiral α-secondary amine, which provides

cyclopropylhydrazines, which thus results in the smaller N−N BDE values. The natural charges distributions of atoms in molecules of cyclopropylhydrazines by the natural bond orbital (NBO)92 analysis at the M05-2X/6-311++G(2df,2p) level are shown in Figure 5. For mono-, 1,1-di-, 1,2-di-, tri-, and tetraclopropylhydrazines, the natural charges of the two N atoms are −0.699 and −0.513, −0.658 and −0.401, −0.495 and −0.495, −0.502 and −0.397, and −0.380 and −0.389, separately. It is found the absolute natural charges of the N atoms decrease as the substituted ring numbers increase, i.e., for −NH2, −NHR, and −NR2 (R = cyclopropyl) groups in the cyclopropylhydrazines, the values are around −0.650, −0.500, and −0.400, separately. The reduced absolute natural charge of N atom makes the molecules unstable, and the N−N BDEs become smaller. Furthermore, the same phenomena were also found in other cycloalkylhydrazines. In addition, the N−N BDE change patterns can be interpreted by the energies of frontier orbitals of the highest occupied molecular orbital (HOMO) of the cycloalkylhydrazines from monosubstituted to tetra-substituted. The mono-, di(1,1disubstituted as example), tri-, and tetra-substituted cyclobutylhydrazines and cyclohexylhydrazines were taken as examples, and the HOMO figures as well as the energies are F


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Figure 6. HOMOs of cyclobutylhydrazines and cyclohexylhydrazines from mono- to tetra-substituted.

Table 5. N−N BDEs of N-Heterocyclic Hydrazines (kJ/mol)

depicted in Figure 7. It is found that the bond angles ∠C1N2C3 in the three N-heterocyclic hydrazines are 89.58°, 102.18°, and 111.31°, respectively; in the corresponding radicals, the bond angles ∠C1N2C3 are 89.36°, 107.18°, and 111.03°, separately. The large Δ-bond angle (∠C1N2C3(radicals) − ∠C1N2C3(molecules)) of 5.00° is found in the pyrrolidin-1ylamine with the smallest N−N BDE, by contrast, the Δ-bond angles are only −0.22° and −0.28° for the remaining two compounds. The natural spin densities of the three N radical centers by NBO analysis were also shown in Figure 7. We can see that the natural spin densities of three N radical centers are 0.943, 0.914, and 0.928, respectively, which are consistent with the change pattern of N−N BDEs. That is, the smaller natural spin densities denote the stronger spin delocalization and more stability of radicals, and the corresponding BDEs are smaller. In addition, comparing with the N-heterocyclic hydrazines containing one N-heterocycle, the BDEs of entries 4−9 are all smaller. For example, the N−N BDE of azetidin-1-ylamine

pivotal building blocks in medicinal and pharmaceutical chemistry programmes.95 Therefore, the N−N BDEs of several N-heterocyclic hydrazines were predicted by the M05-2X method, and the results are summarized in Table 5. For saturated N-heterocyclic hydrazines (entries 1−9), it is observed that the N−N BDEs of these hydrazines vary from 197.1 to 274.0 kJ/mol, and the difference between the maximum (entry 1) and the minimum (entry 5) is 76.9 kJ/mol. For the N-heterocyclic hydrazines of entries 1−3, in which only one N-heterocycle (azetidinyl, pyrrolidinyl, and piperidinyl) is included, the N−N BDE of pyrrolidin-1-ylamine is the smallest (254.1 kJ/mol) and that of azetidin-1-ylamine is the largest (274.0 kJ/mol). The same N−N BDE change pattern is found in entries 4−9, in which two N-heterocycles are included, that is, the azetidinyl can increase the N−N BDEs, while the pyrrolidinyl is beneficial for decreasing the BDEs. The optimized conformations of the three single N-heterocyclic hydrazines (entries 1−3) as well as the corresponding radicals at the B3LYP/6-31+G(d) level are G


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Figure 7. Optimized conformations as well as the NBO analysis results of single N-heterocyclic hydrazines and corresponding radicals

Figure 8. Natural charges of N atoms of five-membered N-heterocyclic hydrazines.

pyrrolidin-1-ylamine, 2,5-dihydro-pyrrol-1-ylamine, and pyrrol1-ylamine, the absolute natural charges of the N atoms on Nheterocycles are 0.406, 0.411, and 0.255, respectively. The smallest value of 0.255 is found in pyrrol-1-ylamine with the largest N−N BDE of 279.0 kJ/mol, and there is little difference between the values of pyrrolidin-1-ylamine and 2,5-dihydropyrrol-1-ylamine, which is consistent with the BDE change pattern. Similarly, for the five-membered N-heterocyclic hydrazines containing two heterocycles, the same phenomenon is found. The absolute natural charges of N atoms are 0.386, 0.402, and 0.231 for [1,1′]bipyrrolidinyl, 2,5,2′,5′-tetrahydro[1,1′]bipyrrolyl, and [1,1′]bipyrrolyl, separately, and the corresponding N−N BDEs are 197.1, 194.3, and 216.0 kJ/mol, respectively. In addition, for the two aromatic N-heterocyclic hydrazines of [1,2,4]triazol-4-ylamine and tetrazol-1-ylamine with the especially larger N−N BDEs, the absolute natural charges of the N atoms on the heterocycles are much smaller at 0.238 and 0.091, respectively. The discrepancy of the natural charge distributions may be responsible for the N−N BDEs difference between saturated and unsaturated N-heterocyclic hydrazines. 3.5. Prediction of N−N BDEs in Arylhydrazines. Arylhydrazines are the classical essential raw materials in

(entry 1) is 274.1 kJ/mol, while in [1,1′]biazetidinyl compound (entry 4), in which two azetidinyl cycles are included, the BDE value is deceased to 245.2 kJ/mol. Furthermore, comparing with the corresponding saturated N-heterocyclic hydrazines, for the unsaturated N-heterocyclic hydrazines of entries 10−13, it is found that the 2,5-dihydro-1H-pyrrolyl can decrease the N−N BDE a little, while the aromatic 1H-pyrrolyl can obviously increase the N−N BDE. For example, the N−N BDE of pyrrolidin-1-ylamine (entry 2) is 254.1 kJ/mol, while for 2,5dihydro-pyrrol-1-ylamine (entry 10) and pyrrol-1-ylamine (entry 11), the BDE values are 249.1 and 279.0 kJ/mol, respectively. Especially, for the aromatic unsaturated N-heterocyclic hydrazines of [1,2,4]triazol-4-ylamine and tetrazol-1-ylamine (entries 14−15), the N−N BDEs are up to 300 kJ/mol, which indicated that the high delocalization effect of the conjugated π-electrons on the aromatic N-heterocycles can strongly stabilize the molecules and that the N−N BDEs are greatly increased. In order to obtain a better understanding of the N−N BDE change patterns of the saturated and unsaturated hydrazines, the natural charges of five-membered N-heterocyclic hydrazine molecules were performed by NBO analysis, and the corresponding results are shown in Figure 8. We can see that for the five-membered single N-heterocyclic hydrazines of H


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Table 6. N−N BDEs (kJ/mol), qN × qN (e2), and Orbitals Energies (eV) of Phenyl Hydrazines and Naphthyl Hydrazines R = phenyl

R = naphthyl

ELUMO (eV)

EHOMO − ELUMO (eV)

qN × qN (e2)

entry

N−N BDEs (kJ/mol)

EHOMO (eV)

ELUMO (eV)

EHOMO − ELUMO (eV)

qN × qN (e2)

substituted type

compounds

entry

N−N BDEs (kJ/mol)

monosubstituted 1,1-disubstituted 1,2-disubstituted

H2N-NHR H2N-NR2 RHNNHR RHN-N2R R2N-NR2

1 2 3

240.0 214.7 189.8

−7.18 −7.06 −6.62

0.54 0.46 0.23

7.72 7.52 6.85

0.311 0.224 0.223

6 7 8

219.7 199.7 161.2

−7.50 −6.78 −6.58

−0.21 −0.36 −0.6

7.29 6.42 5.98

0.318 0.235 0.216

4 5

170.3 156.8

−6.79 −6.46

0.13 0.01

6.92 6.47

0.159 0.113

9 10

151.7 148.1

−6.56 −6.46

−0.71 −0.83

5.85 5.63

0.160 0.111

trisubstituted tetra-substituted

EHOMO (eV)

synthesizing indoles, which is one of the most common motifs in natural bioactive products, marketed drugs, and other functional molecules.96,97 A facile [3,3]-sigmatropic rearrangement of the achiral N,N′-binaphthyl hydrazines, one of the arylhydrazines, can afford enantiomerically enriched 2,2′-diamino-1,1′-binaphthalenes (biaryl amines) derivatives,98 which are useful ligands in transition-metal-catalyzed cross-coupling reactions.99 At first, the N−N BDEs of the five phenyl hydrazines and five naphthyl hydrazines calculated by the M05-2X method as well as the NBO analysis results are shown in Table 6. We can see that the N−N BDEs of the five phenyl hydrazines are in the range of 156.8− 240.0 kJ/mol, and there is a big difference of 83.2 kJ/mol between the maximum and minimum. It is obvious that the N−N BDEs greatly decrease with the increase of the phenyl numbers. For the two diphenylhydrazines, i.e., 1,1-diphenylhydrazine and 1,2-diphenylhydrazine, the N−N BDEs are 214.7 and 189.8 kJ/ mol, and there is a 24.9 kJ/mol disparity between them. Similarly, for the five naphthyl hydrazines, the N−N BDEs decrease with the increase of naphthyl numbers, and the BDE values change from 148.1 to 219.7 kJ/mol with the difference of 71.6 kJ/mol. The N−N BDE of 1,1-dinaphthylhydrazine (199.7 kJ/mol) is larger than that of 1,2-dinaphthylhydrazine (161.2 kJ/mol), and the difference between them is 38.5 kJ/mol. In addition, we find that for each of the five substituted types, the N−N BDE of naphthyl hydrazines is smaller than phenyl hydrazines. The values of qN × qN (qN indicates the natural charge of N atom in N−N bond) are also shown in the Table 6. We can see that for phenyl hydrazines and naphthyl hydrazines, the N−N BDEs are larger, the values of qN × qN are larger, too. Furthermore, the linear relationship between the N−N BDEs with qN × qN values was found and the correlation coefficient (R) is 0.884, which is shown in Figure 9. In addition, the natural spin densities of the four N radical centers (•NHR, •NR2, R = phenyl, naphthyl) are depicted in Figure 10. When R = phenyl, the natural spin densities of •NHR and •NR2 radical centers are 0.646 and 0.569, and when R = naphthyl, the corresponding natural spin densities are smaller with the values of 0.586 and 0.518, separately, which demonstrates that the stronger delocalization effect in the N radical centers for R = naphthyl makes the radicals more stable and the corresponding BDE values are smaller. Besides, the energies of frontier orbitals of the highest occupied molecular orbital (EHOMO), the lowest unoccupied molecular orbital (ELUMO) as well as the energy gaps between HOMO and LUMO (ELUMO − EHOMO) of molecules are listed in Table 6. It can be found that for both phenyl hydrazines and naphthyl hydrazines, the N−N BDEs are larger, the values of ELUMO − EHOMO are larger, too. The larger energy gaps between HOMO and LUMO indicate that the molecules are less likely to be activated, and the N−N bond becomes more stable. The linear relationship between the N−N BDEs with ELUMO −

Figure 9. Correlation between N−N BDEs with qN × qN of phenyl hydrazines and naphthyl hydrazines.

Figure 10. Natural spin densities of N radical centers.

EHOMO was obtained with the correlation coefficient (R) of 0.875, which is depicted in Figure 11. 3.6. Prediction of N−N BDEs in Hydrazides. One of the most common species of hydrazine derivatives, hydrazides, can provide amino acids, carbamates, or amines through the N−N bond cleavage in reactions, thus serving as a powerful and versatile tool for efficient synthesis of complex nitrogensubstituted natural products and pharmaceutical agents.100,101 For example, the AIDA and APICA, which are known antagonists of metabotropic glutamate receptors (mGluRs), Gprotein-coupled receptors associated with various neurodegenerative diseases,102,103 can be prepared by the samariuminduced N−N bond cleavage of formohydrazides. Herein, the N−N BDEs of the three kinds of hydrazides, i.e., formohydrazides (entries 1−5), methanesulfonyl hydrazides (entries 6− 10), and benzenesulfonyl hydrazides (entries 11−15) were calculated by the M05-2X method, and the results are shown in Table 7. For these three kinds of compounds, the N−N BDEs are in the range of 328.3−388.3 kJ/mol for formohydrazides, 305.5− 334.3 kJ/mol for benzenesulfonyl hydrazides, and 275.7−318.2 kJ/mol for methanesulfonyl hydrazides, respectively. The differences between the maximum and the minimum are 60.0, I


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Figure 12. Natural spin densities and ESOMO of corresponding radical centers.

energies of singly occupied molecular orbital (SOMO) of these radicals are also shown in Figure 12. Similarly, when R = −CHO, the absolute ESOMO values of the two radicals (•NHR and •NR2) are larger than R = −SO2CH3 and −SO2Ph. Therefore, for the three kinds of hydrazides, the stabilities of the corresponding radicals determine the order of the N−N BDE values. Furthermore, the N−N BDEs of some formohydrazide derivatives substituted by electron-donating groups (EDGs), electron-withdrawing groups (EWGs), and conjugated effect groups (CEGs) are listed in Table 8. In these formohydrazide derivatives, the EWGs of R can increase the N−N BDEs, and the EDGs of R can decrease the BDEs; especially, the BDE of CEG is the smallest. For example, when R = OH (entry 1), the N−N BDE is 344.3 kJ/mol, when R = CN (entry 7), the BDE value is 359.4 kJ/mol, and the minimum of 321.2 kJ/mol is found in the formohydrazide derivative of R = Ph (entry 11). In addition, our results (not listed in the table) indicated that for substituted methylsulfonyl hydrazides H2N−NHSO2CH2−R, the remote substituent effects of R are not obvious, which is also found in phenylsulfonyl hydrazides for different R positions on benzene ring (o-, m-, and p-). Besides, the SOMO energies of the corresponding radicals are also listed in Table 8. We can see that the N−N BDEs are larger, the absolute energies of SOMO are larger, too. The larger absolute energies of SOMO show that the radicals are more instable, and the corresponding BDE values are larger. Besides, the good linear relationship between the N−N BDEs and ESOMO with the correlation coefficient (R) of 0.960 was found, which is depicted in Figure 13. The natural charge distributions of the three formohydrazide derivatives as well as the natural spin densities of corresponding N radical centers were presented in the Figure 14. In the

Figure 11. Correlation between N−N BDEs with ELUMO − EHOMO of phenyl hydrazines and naphthyl hydrazines.

28.8, and 42.5 kJ/mol, separately. It can be seen that for each of the three compounds, the largest BDE is found in the trisubstituted type. Moreover, for the same substituted type, the N−N BDEs of formohydrazides are the largest, and the values of the benzenesulfonyl hydrazides are the smallest. The energies of the highest occupied molecular orbital (EHOMO) are also listed in Table 7. We can see that for each kind of the three hydrazides, the largest absolute value of EHOMO is found in trisubstituted type, which is consistent with the N−N BDE change pattern. For example, the N−N BDEs of five formohydrazides are 328.3, 364.0, 375.4, 388.3, and 380.4 kJ/ mol, respectively, and the corresponding EHOMO absolute values are 9.39, 9.82, 9.89, 10.10, and 10.01 eV, separately. The NBO analysis of natural spin densities of corresponding radicals are depicted in Figure 12. For the •NHR (R= −CHO, −SO2CH3, −SO2Ph) radicals centers, the natural spin densities are 0.874, 0.862, and 0.839, respectively, and for •NR2 radical (R = −CHO, −SO2CH3, −SO2Ph) centers, the values are 0.947, 0.904, and 0.879, separately. The natural spin densities of the corresponding radical centers of formohydrazides are the largest, which are in accordance with the change pattern of N−N BDEs among the three kinds of hydrazides. In addition, the orbital

Table 7. N−N BDEs (kJ/mol) and Orbital Energies (eV) of the Three Kinds of Hydrazides

formohydrazides

methanesulfonyl hydrazide

benzenesulfonyl hydrazide

entry

substituted type

compounds

N−N BDE (kJ/mol)

EHOMO (eV)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

mono1,2-di1,1-ditritetramono1,2-di1,1-ditritetramono1,2-di1,1-ditritetra-

H2N−NHCHO OHCHN−NHCHO H2N−N(CHO)2 OHCHN−N(CHO)2 (OHC)2N−N(CHO)2 H2N−NHSO2CH3 H3CO2SHN−NHSO2CH3 H2N−N(SO2CH3)2 H3CO2SHN−N(SO2CH3)2 (H3CO2S)2N−N(SO2CH3)2 H2N−NHSO2Ph PhO2SHN−NHSO2Ph H2N−N(SO2Ph)2 PhO2SHN−N(SO2Ph)2 (PhO2S)2N−N(SO2Ph)2

328.3 364.0 375.4 388.3 380.4 305.5 313.3 325.3 334.3 293.3 275.7 292.3 313.1 318.2 268.6

−9.39 −9.82 −9.89 −10.10 −10.01 −9.46 −9.89 −9.91 −9.95 −9.80 −8.94 −9.04 −9.26 −9.37 −8.84

J


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absolute value is smaller at 0.465; moreover, the absolute N natural charge of Ph is the largest value of 0.537. In addition, the natural spin densities of the three N radical centers of R = −OH, −CN, and −Ph after N−N bond cleavage are 0.884, 0.933, and 0.846, separately. Therefore, the different natural charge distributions in the molecules as well as the natural spin densities imparities in the corresponding radicals result in the different substituent effects. In addition to the above three kinds of hydrazides, there are many cyclic hydrazides that are common intermediates obtained in a growing number of synthetic routes in which the corresponding free amines or acyl-protected derivatives are the main purposes.104 In these reactions, the cleavage of the N−N bond appears as a key transformation. For example, the photochemically induced N−N bond cleavage of cyclic hydrazides can give rise to amines and amino acids, which are important pharmacophores in numerous biologically active compounds.105 In addition, the reaction of cyclic hydrazides with magnesium monoperoxyphthalate (MMPP) can afford the deaminated lactams in which the β-lactam ring can serve as a key substructure of the most widely used family of antibiotics.106 Based on the experimental researches, we calculated the N−N BDEs of several cyclic hydrazides by M05-2X method, and the results are shown in Table 9. For single (entries 1−6) and double (entries 7−12) cyclic hydrazides, the N−N BDE change patterns are the same. It can be seen that the largest N−N BDEs are found in the hydrazides containing the four-membered azetidinyl-2dione ring, and the corresponding BDE values for single and double cyclic hydrazides are 328.0 kJ/mol (entry 1) and 350.8 kJ/mol (entry 7) separately. Moreover, the five-membered oxazolidinyl-2-one ring can provide the smallest N−N BDEs for both single and double cyclic hydrazides, and the BDE values are 313.5 (entry 4) and 329.3 kJ/mol (entry 10), respectively. The SOMO energies of corresponding cyclic radicals are also listed in Table 9, and the largest and smallest absolute ESOMO values are found in the four-membered azetidinyl-2-dione ring and fivemembered oxazolidinyl-2-one ring, separately, which are consistent with the BDE change pattern. In addition, we found that the double cyclic hydrazides are more stable than single cyclic hydrazides. For example, the N−N BDE of 1-aminoazetidin-2-one (entry 1) is 328.0 kJ/mol, and in the [1,1′]biazetidinyl-2,2′-dione (entry 7), the BDE is 350.8 kJ/mol. In addition, the substituent effects of R including EDGs of −CH3, −OH, and −NH2 (entries 1−12), EWGs of −CN, −COOH, and −CF3 (entries 13−24) as well as CEG of Ph (entries 25−28) at different positions on the rings were investigated, and the corresponding N−N BDEs are listed in Table 10. It can be seen that for each of the five cyclic hydrazides

Table 8. N−N BDEs (kJ/mol) and Orbital Energies (eV) of Formohydrazide Derivatives

Figure 13. Correlation between N−N BDEs with E SOMO of formohydrazide derivatives.

−NHCOR groups, the natural charges of N atoms are different. When R is the EDG of −OH, the absolute N natural charge is 0.501, and when R is the EWG of −CN, the corresponding

Figure 14. Natural charges distributions of several formohydrazide derivatives and natural spin densities of corresponding N radical centers. K


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The Journal of Physical Chemistry A Table 9. N−N BDEs (kJ/mol) and Orbital Energies (eV) of Cyclic Hydrazides

including cycloalkylhydrazines, N-heterocyclic hydrazines, arylhydrazines, and hydrazides. The ranges of the N−N BDEs of these hydrazines are depicted in the Figure 16. In general, the N− N BDEs of hydrazides are larger, while those of arylhydrazines are smaller, and there is a wide BDE range of 194.3−372.6 kJ/ mol for N-heterocyclic hydrazines, while for arylhydrazines, there is a narrow BDE range of 148.1−240.0 kJ/mol.

including 1-amino-azetidin-2-one, 1-amino-pyrrolidin-2-one, 1amino-1,5-dihydro-pyrrol-2-one, 1-amino-piperidin-2-one, and 1-amino-5,6-dihydro-1H-pyridin-2-one, the N−N BDEs of the α-substituted of N atom on the ring are the largest, regardless of R being EWG, EDG, or CEGs. For example, when R = −CH3, the N−N BDEs for 3- and 4-subsituted 1-amino-azetidin-2-one are 339.8 kJ/mol (entry 1) and 348.4 kJ/mol (entry 2), respectively, and when R = −CN, the corresponding BDEs are 351.3 kJ/mol (entry 13) and 359.5 kJ/mol (entry 14), separately. While for the 3-amino-oxazolidin-2-one, in which an O atom is included in the five-membered ring, the N−N BDE change patterns are different, and the β-substituted of N atom (αposition of O atom) can provide the largest BDEs. For example, when R = −CH3, the BDEs of 4- and 5-substituted positions are 329.9 kJ/mol (entry 2) and 336.0 kJ/mol (entry 3), respectively, and when R = −CN, the values are 334.7 kJ/mol (entry 14) and 343.7 kJ/mol (entry 15), separately. In addition, we found that for all of the cyclic hydrazides, there is no obvious substituent effect whether R is EDG, EWG, or CEG at the same position. The natural spin densities of the cyclic radicals of CH3-, CN-, and Ph-substituted 1-amino-azetidin-2-one and 3-amino-oxazolidin-2-one are shown in Figure 15. For the four-membered radicals of azetidinyl-2-one, the larger natural spin densities of N radical centers are found when the substituents −CH3, −CN, and −Ph are at the α-position of N atom, and the corresponding N− N BDEs are larger too. Differently, for the five-membered oxazolidinyl-2-one, the larger N−N BDEs are found when the substituents are at the β-position of N atom, and the corresponding natural spin densities are larger. Therefore, we speculate that the additional O atom in the oxazolidinyl-2-one ring affects the natural spin densities of N radical centers and thus leads to a different substituent effect. 3.7. Overall Evaluation of Different Hydrazine Derivatives. From the above, we have discussed and analyzed the N−N BDE change patterns of different kinds of hydrazine derivatives

4. CONCLUSION In our present study, the homolytic bond dissociation enthalpies (BDEs) were investigated through the theoretical calculations. First, 13 organonitrogen compounds in which less than eight non-hydrogen atoms are included were calculated by eight composite high-level ab initio methods including G3, G3B3, G4, G4MP2, CBS-QB3, ROCBS-QB3, CBS-Q, and CBS-APNO. Second, we extended the training set to 58 compounds, and 25 density functional theory (DFT) methods were selected for calculating the N−N BDEs. The DFT method of M05-2X was regarded as the most reasonable and accurate to predict the N−N BDEs with the smallest root-mean-square error (RMSE) values of 8.9 kJ/mol. Finally, the N−N BDEs of various hydrazine derivatives including the cycloalkylhydrazines, N-heterocyclic hydrazines, arylhydrazines, and hydrazides as well as the substituent effects were systematically investigated by using the M05-2X method. The major conclusions are summarized as follows: (1) In the N−N BDE prediction of cycloalkylhydrazines, the N−N BDEs of five theoretically possible types (mono-, 1,1-di-, 1,2-di-, tri-, and tetra-) from cyclopropylhydrazines to cyclohexanehydrazines were calculated. Comparing with the monocycloalkylhydrazines, the increase of the ring number can decrease the N−N BDEs. From cyclopropylhydrazines to cyclohexylhydrazines for each substituted type of the five, the largest N−N BDEs are found in cyclobutylhydrazines, and the smallest BDE L


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The Journal of Physical Chemistry A Table 10. N−N BDEs (kJ/mol) of Substituted Cyclic Hydrazides

values are found in cyclopropylhydrazines for mono-, 1,1di-, 1,2-di-, and trisubstituted types, exceptionally, in tetrasubstituted type, the BDE of cyclohexylhydrazine is the smallest. In addition, the analysis of the molecular optimized conformations, natural bond orbital (NBO), and the energies of frontier orbitals were performed for further explaining the N−N BDEs change patterns. (2) In the N−N BDE prediction of N-heterocyclic hydrazines, for saturated heterocyclic hydrazines, the five-membered

pyrrolidinyl is beneficial for decreasing the BDEs, while the four-membered azetidinyl can increase the BDEs. The N−N BDEs of double cyclic hydrazines are smaller than that of single cyclic hydrazines. For aromatic unsaturated heterocyclic hydrazines, the N−N BDEs are greatly increased. Besides, the NBO analysis disclosed the essences of the BDEs change patterns. (3) In the N−N BDE prediction of arylhydrazines, the N−N BDEs of the five phenyl hydrazines and five naphthyl M


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Figure 15. Natural spin densities of several N radical centers.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b12094. Fifty-eight N−N BDEs calculated by 25 DFT methods and the Cartesian coordinates of selected molecules and radicals (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86 21 67791216. Fax: +86 21 67791220. E-mail: [email protected]. ORCID

Wenrui Zheng: 0000-0003-0894-1430 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This project is sponsored by the Shanghai University of Engineering Science Innovation Fund for Graduate Students (No. 17KY0409). We also thank the Shanghai Supercomputer Center for the computational resources.

Figure 16. Ranges of N−N BDEs of each kind of hydrazine derivative.

hydrazines were calculated. The N−N BDEs greatly decrease with the increase of the phenyl (naphthyl) numbers, and for each of the five substituted types, the N− N BDEs of naphthyl hydrazines are smaller than that of phenyl hydrazines. Furthermore, the linear relationships between the N−N BDEs with ELUMO − EHOMO and qN × qN values were found, and the correlation coefficients (R) are 0.882 and 0.884, respectively. (4) In the N−N BDE prediction of hydrazides, the five formohydrazides, methanesulfonyl hydrazides, and benzenesulfonyl hydrazides, as well as the cyclic hydrazides are included. For each of the three noncyclic hydrazides, the largest BDE is found in the trisubstituted type; for the same substituted type, the N−N BDEs of formohydrazides are the largest, and the smallest BDEs are found in benzenesulfonyl hydrazides. For cyclic hydrazides, the five-membered oxazolidinyl-2-one ring can especially reduce the BDE values, and the N−N BDEs of double cyclic hydrazides are larger than that of single cyclic hydrazides. In addition, the different substituent effects of substituted cyclic hydrazides were exhibited. The analysis of ESOMO and NBO provides explanations of the N−N BDE change patterns.

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REFERENCES

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