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Hydrazine Oxidation in Aqueous Solutions I. N4H6 Decomposition

A peer-reviewed version of this preprint was published in:
Inorganics 2023, 11(10), 413. https://doi.org/10.3390/inorganics11100413

Submitted:

30 September 2023

Posted:

01 October 2023

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Abstract
A mixture of nonlabeled (14N2H4) and 15N labeled hydrazine (15N2H4) in an aqueous solution is oxidized to 15N2, 14N2, and 14N15N molecules, indicating the intermediate existence of the 14NH2-14NH-15NH-15NH2 with subsequent hydrogen transfers and splitting of side N-N bonds. Structures, thermodynamics, and electron characteristics of various N4H6 molecules in aqueous solutions are investigated using theoretical treatment at the CCSD/cc-pVTZ level of theory to explain the crucial part of the hydrazine oxidation reaction. Most N4H6 structures in aqueous solutions are decomposed during geometry optimization. Splitting the bond between central nitrogen atoms is the most frequent, but the breakaway of the side nitrogen is energetically the most preferred. The N-N fissions are enabled by suitable hydrogen rearrangements. Gibbs free energy data indicate the dominant abundance of NH3... N2... NH3 species. The side N atoms have very high negative charges, which should support hydrogen transfers in aqueous solutions. The only stable cyclo-(NH)4…H2 structure has a too high Gibbs energy and breaks the H2 molecule. The remaining initial cyclic structures are split into hydrazine and HN≡NH or H2N≡N species, and their relative abundance in aqueous solutions is vanishing.
Keywords: 
Coupled Cluster
;  
geometry optimization
;  
N-N bond splitting
;  
QTAIM analysis
;  
electron structure
Subject: 
Chemistry and Materials Science  -   Theoretical Chemistry

1. Introduction

Hydrazine N2H4 is a colorless flammable liquid that is used in industry and agriculture due to its reducing properties. It is used as a corrosion inhibitor in boilers, as a rocket propellant, antioxidant, catalyst, and pesticide precursor. In boiler water, it serves as an oxygen scavenger that reacts with oxygen into nitrogen and water only, which does not cause corrosion of ferrous metals. Unreacted hydrazine can be decomposed into ammonia, which can be corrosive to copper and copper-containing alloys [1]. Thus the knowledge of the exact mechanism of its oxidation is of practical importance so far.
Higginson and Sutton [2] studied the oxidation of 15N-enriched hydrazine by an excess of various oxidizing agents in aqueous solutions. Mass spectroscopic analysis of the evolved nitrogen for 28, 29, and 30 mass-number abundance (i.e. incidence of 14N2, 15N14N and 15N2 molecules, respectively) has shown that the proportion of 15N2 molecules decreased while that of 15N14N molecules increased depending on the oxidizing agent used. If the nitrogen produced by the reaction
2 N2H4 → N2 + 2 NH3
involves no N-N fission, the evolved N2 molecule originates in the same N2H4 molecule, and therefore it must have the same distribution of 15N isotopes as the hydrazine reactant. This implies that some of the nitrogen molecules are formed by a mechanism involving a N-N fission and the formation of nitrogen-containing radicals from two different hydrazine molecules as follows:
15NH2-15NH2 + 14NH2-14NH2 → 15NH2-15NH• + •14NH-14NH2 → 15NH2-15NH-14NH-14NH2
15NH2-15NH-14NH-14NH2 → 15NH3 + 15NH=14N-14NH2 → 15NH3 + 15N14N + 14NH3
15NH2-15NH-14NH-14NH2 → 15NH2-15N=14NH + 14NH3 → 15NH3 + 15N14N + 14NH3
Cahn and Powell [3] confirmed the randomized 15N14N composition obtained by one-electron oxidation of 15N enriched hydrazines with a number of oxidizing agents unlike exclusively four-electron oxidizing agents (acid iodate, alkaline ferricyanide) that produced unrandomized N2 molecules (all four hydrogen atoms must be removed from a single hydrazine molecule). Petek and Bruckenstein [4] observed that the electrooxidation of 15N labelled hydrazine (96.7% enrichment) at Pt electrode produced N2 molecules with the ratio of 14N15N/15N15N = 0.07±0.01 while in Ce(IV) solutions it was 0.9±0.2. A ratio of both isotopic forms between these two limits was produced by simultaneous electrooxidation and homogeneous oxidation with electrogenerated Ce(IV).
A bright yellow substance, stable under -178 oC, is formed after thermal decomposition of hydrazine at high temperatures and low pressures in a flowing system [5]. The authors suppose that it is tetrazane N4H6.
Based on polarographic and voltammetric studies of hydrazine in alkali solutions, Karp and Meites [6] suggested its two-electron oxidation to diimide with subsequent dimerization and decomposition as follows
2 N2H2 → N4H4 → NH4+ + N3-
The proposed mechan(3)ism is also capable of explaining the randomized 15N14N composition.
Ball [7] investigated the structure and some thermochemical properties of the cis- and trans-conformations of tetrazane NH2-NH-NH-NH2 using various-level ab initio methods. Unlike nearly planar trans-conformation, the cis-conformation should be denoted as a gauche structure (N-N-N-N dihedral angle of ca 90o).
The decomposition of hydrazine was studied at CCSD(T)-F12a/aug-ccpVTZ//ωB97x-D3/6-311++G(3df,3pd) level of theory [8]. A comprehensive analysis of the N4H6 singlet potential energy surfaces was performed. Three stable isomers NH2-NH-NH-NH2, NH2-NH-NH2=NH and NH2-NH2-N=NH2 and the transition states for H transfers between them were obtained as well. Stabilized NH2-NH-NH-NH2 formation becomes significant only at relatively high pressures and low temperatures due to decomposition into N2H3• + N2H3•. No direct reaction between NH2-NH-NH-NH2 and NH2-NH2-N-NH2 was found. NH3 eliminations from NH2-NH-NH-NH2 and NH2-NH2-N-NH2 are energetically preferred, but only NH2-NH2-N=NH2 has relatively small activation energy for this reaction (see Table 1).
It is evident that the N4H6 decomposition is crucial for the hydrazine oxidation with subsequent 15N14N molecules formation. It depends on the suitable N4H6 site of N-N bond splitting. At first, the NH2-NH-NH-NH2 isomer is formed by the reaction
N2H3• + N2H3• → NH2-NH-NH-NH2
In the next steps, H transfers and possible N-N bond splitting may proceed. The main aim of this study is a quantum-chemical study of N4H6 isomers in aqueous solutions at the solely Coupled Cluster level of theory and to determine the sites of the possible N-N fission in them. The thermodynamic properties of the decomposition reaction products enable us to predict the possible formation of 15N14N molecules in real systems. The electronic structure of the optimized structures will also be discussed.

2. Results and discussion

We consider possible linear isomers of N4H6 with the N1-N2-N3-N4 backbone and the composition N1Hm-N2Hn-N3Hp-N4Hq, where subscripts m, n, p, q denote the number of H atoms bonded to individual Ni, i = 1→ 4, atoms, and m + n + p + q = 6. We started geometry optimizations from anti- and syn-conformations of N1-N2-N3-N4. The optimized structures usually correspond to gauche-conformers or some N-N bonds are split (see Table 2). If N1 and N2 correspond to 15N atoms while N3 and N4 correspond to the 14N ones, then N1-N2 and N3-N4 fissions would lead to 15N14N molecules, unlike the N2-N3 fissions.
In the case of cyclo-N4H6 isomers we can use the same notation, but any N-N fission can lead to 15N14N molecules because of suitable H transfers within the cycle.
We introduce the notation Xmnpq for individual systems under study, where X = A, B, C, and D stands for anti-, syn-, cyclic, and gauche-structures and the indices m, n, p, and q are explained above. X = E denotes structures with N-N fissions, i.e., consisting of two or three molecules after geometry optimization. X = F stands for structures with N2-N3 fissions and subsequent N1-N4 bond formations. The N-N fissions in E and F systems are denoted by round brackets where the mutually bonded N atoms are included in the same bracket couple. The different structures with the same Xmnpq notation can be distinguished by additional letters a, b, c, etc. For example, E(22)(11)a and E(22)(11)b denote two different structures composed of H2N-NH2 and HN=NH molecules.
The N4H6 structures under study are in Table 2 divided into three groups according to the initial N1-N2-N3-N4 conformations. The H atom rearrangements during geometry optimizations are less frequent in the anti-conformations (starting A structures) than in the syn-conformations (starting B structures). In both groups the probability of N-N fissions is approximately 50%, and N2-N3 fissions prevail. On the other hand, the N1-N2 fissions lead to energetically much more preferred products such as E(3)(201), E(3)(102) and especially E(3)(00)(3). In the B1221 syn-conformation the mutual interaction of N1 and N4 causes the formation of the N1-N4 bond and N2-N3 fission leading to the structure of H2N2-N1H-N4H-N3H2 , i.e. F12)(21, in gauche-conformation or decomposition to more stable HN1=N4H and the H2N2-N3H2 species denoted as the F1)(22)(1 system.
The relative Gibbs free energies in Table 2 are related to the structure D2112a obtained by the reaction (5) in the first step. According to these data, the system E(3)(00)(3), which corresponds to 15NH3, 14NH3 and 15N14N molecules, is dominant among all N4H6 structures in aqueous solutions under normal conditions and the relative abundance of the remaining systems is vanishing. In general, the decomposed E systems are more stable than the remaining structures (see Table 2, Table 3 and Table 4, Figure 1 and Figure 2).
During the geometry optimization of the starting cyclic C structures (Table 2), only the least stable cyclo-(NH)4 structure, denoted as E1111, preserves its tetraatomic ring after removing a H2 molecule. The remaining C structures split into hydrazine and HN=NH in E(22)(11)d or H2N=N in E(22)(02). The disadvantage of cyclic structure preservation is indicated by preferring the above-mentioned F structures after N1-N4 bonding within geometry optimization of the starting B1221 syn-conformation.
The bonding in N4H6 structures can be described by individual bond lengths d (Table 3 and Table 4) as well as by the corresponding electron density ρ (Table 5 and Table 6) and ellipticity ε (Table 7 and Table 8) at their bond critical points BCP [9]. Bond strengths decrease with bond lengths d and increase with their BCP electron densities ρBCP. Their double bond character in acyclic structures increases with their BCP ellipticities εBCP.
The D1221 structure has an extremally long N2-N3 bond and the remaining N-N bonds are shorter than the average N4H6. The ρBCP(N2-N3) ~ 0.1 e/bohr3 corresponds to a very weak bond, the remaining N-N bonds are approximately three times stronger. The εBCP(N2-N3) ~ 0.1 is relatively high, and the remaining double N-N bonds have a ca double ellipticity.
The D2112a-c structures differ in N1-N2-N3-N4 dihedral angles, and their bond length alternation decreases with non-planarity of their backbone. Their ρBCP(N-N) values vary about ~ 0.3 e/bohr3 as in single N-N bonds. The εBCP(N2-N3) values decrease with non-planarity (~ 0.1 and less), while they are very small for the remaining N-N bonds, which correspond to single bonds.
Similarly, the D2121a-d structures differ in the N1-N2-N3-N4 dihedral angles, with the N2-N3 bond length being longer and weaker than the remaining ones. The ρBCP(N-N) values varying about ~ 0.3 e/bohr3 correspond to single N-N bonds. The εBCP(N2-N3) values decrease with non-planarity (~ 0.1 and less), εBCP(N3-N4) ~ 0.2 is typical for double bonds.
The N-N bond properties in the A2202, D2202a-b, and D2022 structures (aside from reverse numbering of N atoms) vary with the N1-N2-N3-N4 dihedral angles. The N2-N3 bonds are the shortest in all these systems. The ρBCP(N-N) values varying about ~ 0.3 e/bohr3 typical for single N-N bonds but the εBCP(N2-N3) ~ 0.3 in all structures indicate a double bond character of this bond.
In A3021 the N-N bond lengths decrease with the distance from N1, and the BCP ellipticity values indicate the same trend in decreasing double bond character. However, the ρBCP(N-N) values about 0.3 e/bohr3 correspond to single N-N bonds.
Analogous trends are observed for D3012a-b structures.
In E1111 with N-N bond lengths of ca 1.5 Å and ρBCP(N-N) ~ 0.3 e/bohr3 typical for single N-N bonds, the εBCP(N-N) values 0.108 can be explained by mechanical strain in its four-membered ring rather than by its double bond character.
The remaining E systems consist of two or three independent molecules, interacting through weak hydrogen bonds only, which can be treated independently of their parent E structures. The possible biradical character of E(32)(10) can be excluded on the basis of its atomic charges (see later) which indicate the existence of [NH3-NH2]+ and [HN≡N]- charged species.
H2N-NH2 with the N-N distance of 1.45 Å, ρBCP(N-N) = 0.295 e/bohr3 and εBCP(N-N) = 0.008 in all E systems is typical for a single N-N bonding.
HN=NH with N-N distance of 1.245 Å, ρBCP(N-N) = 0.486 e/bohr3 and εBCP(N-N) = 0.189 in all systems E correspond to double N-N bonds.
Its isomer H2N=N has a N-N distance of 1.23 Å and ρBCP(N-N) = 0.497 e/bohr3 which correspond to the double N-N bond in contradiction with εBCP(N-N) = 0.020.
On the other hand, NH3-NH has a N-N distance of 1.47 Å and ρBCP(N-N) = 0.27 e/bohr3, which correspond to the single N-N bond in contradiction to the high εBCP(N-N) value of 0.156.
The [NH3-NH2]+ cation with the N-N distance of 1.446 Å, ρBCP(N-N) = 0.293 e/bohr3 and εBCP(N-N) = 0.089 corresponds to a single N-N bonding.
Its counterpart [HN≡N]- has a N-N distance of 1.242 Å and ρBCP(N-N) = 0.48 e/bohr3 which correspond to the double N-N bond in contradiction with the too low εBCP(N-N) = 0.072.
N2 has a N-N distance of 1.096 Å, ρBCP(N-N) = 0.714 e/bohr3 and εBCP(N-N) = 0.000 which is typical for the triple bond.
Finally, H2N-N=NH with N-N distances of 1.36 and 1.24 Å, ρBCP(N-N) values of 0.37 and 0.48 e/bohr3 as well as εBCP(N-N) values of 0.23 and 0.13, respectively, probably correspond to nearly double N-N bonds.
The F(11)(22) system is explained within the HN≡NH and H2N-NH2 structures above.
The F12)(21 structure (aside from different numbering of N atoms) corresponds to the D2112 structures explained above.
We have not discussed N-H bonding in the systems under study because of the too small differences in their bond lengths and BCP electron densities. However, their BCP electron densities are higher than those of N-N bonds except HN=NH, H2N=N, [HN≡N]- and N2. Increased εBCP(N-H) values can be ascribed mostly to a double bond character of neighboring N-N bonds, except εBCP(N-H) = 0.3 in NH3 molecules within the E(3)(102) systems.
The nitrogen atomic charges in the A and D structures (Table 9) are more negative on the N1 and N4 atoms (-0.65 to -0.82) than on the central N2 and N3 atoms (-0.35 to -0.50). Positive hydrogen atomic charges bonded to side N1 and N4 atoms increase with the number of bonded H atoms. The same trend holds for H atoms bonded to central N2 and N3 atoms which are more positive than the side hydrogens.
In the decomposed E systems (Table 10), negative N charges increase with the number of bonded H atoms. An analogous trend for positive H charges cannot be confirmed. Atomic charges are only slightly affected by hydrogen bonding. In the E(32)(10) system, the charges of its [NH3-NH2]+ and [HN≡N]- subsystems are +0.97 and -0.68, respectively. When the error of the electron density over atomic basins, the alternative biradical structure of the neutral E(32)(10) subsystems seems to be less probable.

3. Method

Geometry optimizations of various isomers of neutral N4H6 molecules were performed at the CCSD (Coupled Cluster using Single and Double substitutions from the Hartree-Fock determinant) [10] level of theory and cc-pVTZ basis sets [11]. The effects of the aqueous solution were taken into account within the SMD (Solvation Model based on the solute electron Density) solvation model [12]. The optimized structures were tested by vibrational analysis on the absence of imaginary vibrations. Gaussian16 (Revision B.01) software [13] was used for all quantum-chemical calculations.
The electron structure of the systems under study was evaluated in terms of Quantum Theory of Atoms-in-Molecules (QTAIM) [9] using AIM200 software [14]. The bond strengths were compared according to the electron densities ρ at the bond critical points (BCP). The BCP bond ellipticities εBCP were evaluated as
εBCP = λ1/λ2 -1
where λi are the eigenvalues of the Hessian of the BCP electron density within the sequence λ1 < λ2 < 0 < λ3. Atomic charges were obtained by integration over atomic basins up to 0.001 e/bohr3.
Visualization and geometry modification were performed using MOLDRAW software (https://www.moldraw.software.informer.com, accessed on 9 September 2019) [15].

4. Conclusions

We have shown that most N4H6 structures in aqueous solutions are decomposed during geometry optimization. Splitting the bond between central nitrogen atoms is the most frequent, but the breakaway of the side nitrogen is energetically the most preferred. The N-N fissions are enabled by suitable hydrogen rearrangements. The initial H2N-NH-NH-NH2 structure (D2112) has a very weak central N-N bond, which explains the high degree of reversibility of the reaction (5). The most stable system NH3…N2…NH3 (E(3)(00)(3) system) might be obtained by transfers of both H atoms bonded with central nitrogens to the side N atoms. According to [8], such double H transfer was not found by quantum-chemical calculations in vacuo, and must be decomposed into several steps and this instantaneous decomposition should be slowed down. Furthermore, our calculations show that the transfer of the third H atom to the side nitrogen is very energetically disadvantageous, as indicated by the Gibbs energies of the structures NH3-N = NH2-NH and NH3-N = NH-NH2 (A3021 and D3012, respectively, see Table 2). In aqueous solutions, H atom transfers can be mediated by H2O, H3O+ and/or OH- species. We have shown that side N atoms have very high negative charges that should support such hydrogen transfers.
The experimentally observed formation of 15N14N molecules [1,2,3,4] is enabled by side N-N fissions. We have shown that the Gibbs free energy data (Table 2) indicate the dominant abundance of NH3... N2... NH3 species (E(3)(00)(3) system) in aqueous solutions, which explains the mentioned observations.
The 15N14N molecules can also be created by the decomposition of cyclic N4H6 structures. We have shown a high instability of such species. The only stable cyclo-(NH)4…H2 structure (E1111) has a too high Gibbs energy and breaks the H2 molecule instead. The remaining initial cyclic structures are split into hydrazine and HN≡NH (E(22)(11)d) or H2N≡N species (E(22)(02), see Table 2) and their relative abundance in aqueous solutions is vanishing.
We can deduce from the QTAIM analysis of our systems that single, double and triple N-N bonds exhibit BCP electron densities of ca 0.2, 0.5 and 0.7 e/bohr3 with BCP ellipticities of ca 0, 0.2 and 0, respectively. The bonds in the N4H6 structures often exhibit significant deviations from these values.
Our study did not solve all problems related to hydrazine oxidation in aqueous solutions. The role of various water forms and the corresponding transition states should also be investigated. An alternative reaction pathway through N4H4 [6] according to reaction (4) is worth a study as well. Further theoretical studies in these fields are desirable.

Author Contributions

Methodology, software, investigation, writing—original draft preparation, writing—review and editing, M.B.; conceptualization, supervision, project administration, funding acquisition, A.M. All authors have read and agreed to the published version of the manuscript.

Funding

This publication was supported by the Competence Center for SMART Technologies for Electronics and Informatics Systems and Services, ITMS 26240220072.

Institutional Review Board Statement

Not applicable.

Data Availability Statement

All necessary research data are presented in the article.

Acknowledgments

The authors thank the HPC center at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High Performance Computing (SIVVP Project No. 26230120002, funded by the European Region Development Funds), for computing facilities.

Conflicts of Interest

The authors declare no conflict of interest.

Sample Availability

Not applicable.

References

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Figure 1. Optimized geometries of stable A and D structures (N – blue, H – white).
Figure 1. Optimized geometries of stable A and D structures (N – blue, H – white).
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Figure 2. Optimized geometries of stable E systems (N – blue, H – white).
Figure 2. Optimized geometries of stable E systems (N – blue, H – white).
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Table 1. Reaction, ΔEr, and activation, Ea, energy data of elementary reactions on the N4H6 potential energy surface [8].
Table 1. Reaction, ΔEr, and activation, Ea, energy data of elementary reactions on the N4H6 potential energy surface [8].
Reaction ΔEr (kJ/mol) Ea (kJ/mol
N2H4 + H2N=N → NH2-NH-NH-NH2 -103.6 50.6
N2H4 + H2N=N → NH2NH2N=NH2 29.0 55.4
NH2-NH-NH-NH2 → NH2NH=N + NH3 7.5 178.7
NH2-NH-NH-NH2→ NH2-N=NH + NH3 -102.5 214.1
NH2-NH2-N=NH2→ NH2-N=NH + NH3 -245.1 38.7
NH2-NH-NH-NH2→ NH2-NH-NH2=NH 151.1 158.6
NH2-NH-NH2=NH → NH2-NH2-N=NH2 -18.5 74.4
N2H3• + N2H3• → NH2-NH-NH-NH2 -152.9 0.2
NH2-NH=NH•+ NH2• → NH2-NH-NH-NH2 208.9 0.2
NH=NH2-NH• + NH2• → NH2-NH-NH2=NH 682.7 0.2
NH2-N=NH2• + NH2• → NH2-NH2-N=NH2 37.9 2.8
Table 2. N1-N2-N3-N4 dihedral angles (Θ1234), absolute (G298) and relative (ΔG298) Gibbs free energies at 298.15 K of the optimized N4H6 structures obtained from the starting ones. The most stable structure is highlighted in bold.
Table 2. N1-N2-N3-N4 dihedral angles (Θ1234), absolute (G298) and relative (ΔG298) Gibbs free energies at 298.15 K of the optimized N4H6 structures obtained from the starting ones. The most stable structure is highlighted in bold.
Starting Optimized Θ1234 [o] G298 [Hartree] ΔG298 [kJ/mol] Remarks
A2112 D2112a 168.3 -222.09177 0.00
A2121 D2121a -161.4 -222.04654 118.75
A2211 E(22)(11)a -33.7 -222.10760 -41.56 H2N-NH2 + HN=NH
A2202 A2202 -179.9 -222.04618 119.71
A2220 E(22)(20)a 146.5 -222.07817 35.7 H2N-NH2 + H2N=N
A1221 D1221 -168.5 -222.00357 231.58
A3210 E(32)(10) 14.3 -222.04629 119.42 H3N-NH2 + HN=N
A3201 E(22)(11)b -142.8 -222.10755 -41.43 H2N-NH2 + HN=NH, 1→3 H rearrangement
A3201 E(3)(201)b -26.5 -222.1489 -150.04 NH3 + H2N-N=NH
A3111 D2112b 75.6 -222.09311 -3.52 1→4 H rearrangement
A3120 E(31)(20) -21.4 -222.03229 156.16 H3N-NH + H2N=N
A3102 E(3)(102)a -177.1 -222.14926 -150.94 NH3 + HN=N-NH2
A3012 D3012a 88.8 -222.04832 114.07
A3021 A3021 176.8 -221.99866 244.46
A3003 E(3)(00)(3) 60.4 -222.26295 -449.44 2NH3 + N2
B2112 D2112c 72.0 -222.09665 -12.80
B2121 D2121b -65.0 -222.04530 122.02
B2121 D2121c -44.8 -222.04982 110.13
B2211 E(22)(11)a -33.7 -222.10760 -41.56 H2N-NH2 + HN=NH
B2202 D2202a 73.7 -222.05056 108.21
B2220 E(22)(20)b -32.9 -222.07820 35.64 H2N-NH2 + H2N=N
B1221 F12)(21 75.8 -222.09760 -15.30 N2-N3 fission, N1-N4 bonding
B1221 F1)(22)(1 -33.3 -222.10756 -41.45 H2N-NH2 + HN=NH, N1-N4 bonding
B3210 E(22)(11)c -34.0 -222.10754 -41.41 H2N-NH2 + HN=NH, 1→4 H rearrangement
B3201 D2202b 80.1 -222.04758 116.02 1→4 H rearrangement
B3201 E(3)(201) -26.5 -222.14892 -150.04 NH3 + H2N=N-NH
B3111 D2112b 75.6 -222.09311 -3.52 1→4 H rearrangement
B3120 D2121d 68.8 -222.04651 118.82 1→4 H rearrangement
B3102 E(3)(102)b -20.6 -222.14678 -144.42 NH3 + HN=N-NH2
B3012 D3012b -59.7 -222.04910 112.02
B3021 D2022 -73.8 -222.05056 108.21 1→4 H rearrangement
B3003 E(3)(00)(3) 60.4 -222.26235 -449.44 2 NH3 + N2
C2211 E(22)(11)d 12.3 -222.10759 -41.45 H2N-NH2 + HN=NH
C2202 E(22)(02) 29.6 -222.07822 35.58 H2N-NH2 + N=NH2
C2121 E1111 23.1 -221.99631 250.64 Cyclo-N4H4 + H2
Table 3. Interatomic distances (in Å) in the optimized Amnpq and Dmnpq structures.
Table 3. Interatomic distances (in Å) in the optimized Amnpq and Dmnpq structures.
Structure N1-N2 N2-N3 N3-N4 N1-H N2-H N3-H N4-H
D1221 1.341 1.840 1.338 1.017 1.019
1.016		 1.015
1.021		 1.018
D2112a 1.423 1.467 1.431 1.012
1.018		 1.014 1.016 1.011
1.014
D2112b 1.432 1.419 1.440 1.012
1.015		 1.018 1.013 1.011
1.015
D2112c 1.424 1.428 1.437 1.013
1.017		 1.016 1.014 1.011
1.015
D2121a 1.413 1.480 1.412 1.011
1.017		 1.015 1.020
1.021		 1.018
D2121b 1.423 1.467 1.417 1.010
1.013		 1.018 1.017
1.020		 1.019
D2121c 1.413 1.504 1.409 1.013
1.024		 1.017 1.017
1.020		 1.020
D2121d 1.423 1.467 1.415 1.010
1.013		 1.018 1.016
1.021		 1.018
A2202 1.427 1.454 1.443 1.016(2×) 1.021(2×) - 1.013(2×)
D2202a 1.459 1.422 1.446 1.017(2×) 1.016
1.022		 - 1.012
1.013
D2202b 1.464 1.418 1.446 1.016
1.018		 1.017
1.021		 - 1.012
1.014
D2022 1.459 1.421 1.447 1.017(2×) 1.016
1.022		 - 1.012
1.013
A3021 1.463 1.452 1.433 1.016
1.024(2×)		 - 1.020
1.025		 1.019
D3012a 1.463 1.418 1.463 1.016
1.021(2×)		 - 1.013 1.015
1.017
D3012b 1.493 1.395 1.485 1.014
1.021(2×)		 - 1.021 1.014
1.017
Table 4. Interatomic distances (in Å) in the optimized Emnpq and Fmnpq systems.
Table 4. Interatomic distances (in Å) in the optimized Emnpq and Fmnpq systems.
System N1-N2 N2-N3 N3-N4 N1-H N2-H N3-H N4-H
E1111a) 1.476 1.481 1.481 1.023 1.017 1.017 1.017
E(22)(11)a 1.446 3.118 1.245 1.012
1.014		 1.011
1.014		 1.030 1.027
E(22)(11)b 1.446 3.465 1.245 1.011
1.014		 1.012
1.014		 1.030 1.027
E(22)(11)c 1.445 3.292 1.245 1.011
1.014		 1.012
1.014		 1.027 1.030
E(22)(11)d 1.446 3.116 1.245 1.012
1.014		 1.011
1.014		 1.030 1.027
E(22)(20)a 1.446 3.271 1.225 1.011
1.014		 1.013
1.014		 1.028
1.034		 -
E(22)(20)b 1.446 2.971 1.225 1.013
1.014		 1.011
1.014		 1.028
1.033		 -
E(22)(02) 1.447 3.276 1.225 1.011
1.014		 1.013
1.014		 - 1.028
1.033
E(31)(20) 1.468 2.750 1.230 1.018(2×)
1.029		 1.016 1.029
1.057		 -
E(32)(10) 1.445 3.035 1.242 1.018(2×)
1.021		 1.015
1.079		 1.076 -
E(3)(201) 3.088 1.350 1.249 1.013(3×) 1.006
1.022		 - 1.019
E(3)(102)a 3.117 1.243 1.365 1.013(3×) 1.026 - 1.008
1.014
E(3)(102)b 3.760 1.246 1.356 1.013(2×)
1.014		 1.032 - 1.007
E(3)(00)(3) 3.636 1.096 3.711 1.014(3×) - - 1.013(3×)
F(11)(22) 1.245 3.291 1.446 1.030 1.027 1.012
1.014		 1.011
1.014
F12)(21b) 1.430 3.017 1.424 1.012 1.012
1.018		 1.012
1.017		 1.017
Remarks: a)N1-N4 bond length of 1.476 Å; b)N1-N4 bond length of 1.432 Å.
Table 5. BCP electron density (in e/bohr3) of N-N and N-H bonds in the optimized Amnpq and Dmnpq structures.
Table 5. BCP electron density (in e/bohr3) of N-N and N-H bonds in the optimized Amnpq and Dmnpq structures.
Structure N1-N2 N2-N3 N3-N4 N1-H N2-H N3-H N4-H
D1221 0.3705 0.1281 0.3734 0.3450 0.3483
0.3528		 0.3467
0.3534		 0.3448
D2112a 0.3156 0.2911 0.3092 0.3459
0.3515		 0.3574 0.3551 0.3492
0.3518
D2112b 0.3092 0.3237 0.3036 0.3494
0.3508		 0.3527 0.3561 0.3484
0.3514
D2112c 0.3149 0.3165 0.3050 0.3472
0.3513		 0.3542 0.3552 0.3484
0.3515
D2121a 0.3212 0.2827 0.3080 0.3458
0.3516		 0.3544 0.3520
0.3527		 0.3415
D2121b 0.3149 0.2920 0.3074 0.3509
0.3517		 0.3524 0.3521
0.3551		 0.3404
D2121c 0.3224 0.2668 0.3133 0.3406
0.3505		 0.3542 0.3508
0.3556		 0.3404
D2121d 0.3149 0.2928 0.3086 0.3503
0.3521		 0.3523 0.3509
0.3559		 0.3417
A2202 0.3148 0.2864 0.2965 0.3478(2×) 0.3514(2×) - 0.3504
0.3503
D2202a 0.2928 0.3098 0.2951 0.3469
0.3474		 0.3499
0.3553		 - 0.3506(2×)
D2202b 0.2898 0.3107 0.2956 0.3447
0.3478		 0.3507
0.3549		 - 0.3501
0.3510
D2022 0.2949 0.3102 0.2930 0.3505
0.3507		 - 0.3498
0.3552		 0.3470
0.3474
A3021 0.2759 0.2964 0.2956 0.3431
0.3437
0.3480		 - 0.3499
0.3542		 0.3397
D3012a 0.2761 0.3196 0.2874 0.3454
0.3473
0.3500		 - 0.3564 0.3463
0.3476
D3012b 0.2562 0.3362 0.2736 0.3446
0.3450
0.3501		 - 0.3488 0.3455
0.3497
Table 6. BCP electron density (in e/bohr3) of N-N and N-H bonds in the optimized Emnpq and Fmnpq systems.
Table 6. BCP electron density (in e/bohr3) of N-N and N-H bonds in the optimized Emnpq and Fmnpq systems.
System N1-N2 N2-N3 N3-N4 N1-H N2-H N3-H N4-H
E1111a) 0.2858 0.2828 0.2824 0.3506 0.3545 0.3566 0.3546
E(22)(11)a 0.2953 - 0.4863 0.3502
0.3529		 0.3500
0.3529		 0.3463 0.3483
E(22)(11)b 0.2953 - 0.4826 0.3500
0.3529		 0.3502
0.3529		 0.3462 0.3482
E(22)(11)c 0.2954 - 0.4863 0.3500
0.3529		 0.3503
0.3529		 0.3482 0.3462
E(22)(11)d 0.2953 - 0.4863 0.3502
0.3529		 0.3500
0.3529		 0.3463 0.3482
E(22)(20)a 0.2947 - 0.4970 0.3499
0.3529		 0.3501
0.3518		 0.3367
0.3422		 -
E(22)(20)b 0.2945 - 0.4967 0.3501
0.3517		 0.3499
0.3529		 0.3367
0.3423		 -
E(22)(02) 0.2945 - 0.4967 0.3500
0.3529		 0.3501
0.3517		 - 0.3367
0.3423
E(31)(20) 0.2696 - 0.4927 0.3382
0.3486
0.3493		 0.3426 0.3123
0.3412		 -
E(32)(10) 0.2929 - 0.4831 0.3471
0.3453
0.3474		 0.2909
0.3485		 0.3032 -
E(3)(201) - 0.3794 0.4825 0.3434
0.3435
0.3436		 0.3531
0.3368		 - 0.3503
E(3)(102)a - 0.4891 0.3669 0.3435(2×)
0.3436		 0.3448 - 0.3457
0.3521
E(3)(102)b - 0.4833 0.3719 0.3432
0.3435
0.3436		 0.3375 - 0.3345
0.3523
E(3)(00)(3) - 0.7140 - 0.3432
0.3433
0.3433		 - - 0.3435
0.3437
0.3442
F(11)(22) 0.4863 - 0.2954 0.3463 0.3482 0.3502
0.3529		 0.3500
0.3529
F12)(21b) 0.3096 - 0.3150 0.3573 0.3451
0.3515		 0.3470
0.3515		 0.3522
Remarks: a)N1-N4 BCP electron density of 0.2858 e/bohr3; b)N1-N4 BCP electron density of 0.3134 e/bohr3.
Table 7. BCP ellipticity of N-N and N-H bonds in the optimized Amnpq and Dmnpq structures.
Table 7. BCP ellipticity of N-N and N-H bonds in the optimized Amnpq and Dmnpq structures.
Structure N1-N2 N2-N3 N3-N4 N1-H N2-H N3-H N4-H
D1221 0.230 0.107 0.231 0.048 0.015
0.017		 0.015
0.016		 0.047
D2112a 0.003 0.149 0.024 0.045
0.050		 0.041 0.036 0.046
0.051
D2112b 0.040 0.039 0.012 0.046
0.051		 0.043 0.051 0.047
0.051
D2112c 0.027 0.046 0.015 0.044
0.047		 0.047 0.050 0.046
0.050
D2121a 0.027 0.123 0.198 0.048
0.051		 0.046 0.007
0.009		 0.073
D2121b 0.035 0.070 0.182 0.045
0.049		 0.034 0.011
0.015		 0.074
D2121c 0.026 0.074 0.192 0.039
0.048		 0.038 0.013(2×) 0.071
D2121d 0.025 0.069 0.178 0.045
0.050		 0.033 0.012
0.013		 0.073
A2202 0.060 0.302 0.089 0.036(2×) 0.008(2×) - 0.055(2×)
D2202a 0.045 0.288 0.084 0.034
0.035		 0.012
0.013		 - 0.053(2×)
D2202b 0.086 0.301 0.087 0.039
0.041		 0.010
0.082		 - 0.052
0.053
D2022 0.084 0.288 0.046 0.052
0.053		 - 0.012
0.013		 0.034
0.035
A3021 0.268 0.222 0.169 0.106
0.108
0.005		 - 0.006
0.009		 0.079
D3012a 0.267 0.124 0.064 0.006
0.007
0.008		 - 0.049 0.044
0.048
D3012b 0.248 0.113 0.123 0.004
0.005(2×)		 - 0.051 0.038(2×)
Table 8. BCP ellipticity of N-N and N-H bonds in the optimized Emnpq and Fmnpq systems.
Table 8. BCP ellipticity of N-N and N-H bonds in the optimized Emnpq and Fmnpq systems.
System N1-N2 N2-N3 N3-N4 N1-H N2-H N3-H N4-H
E1111a) 0.103 0.108 0.108 0.029 0.030 0.027 0.030
E(22)(11)a 0.008 - 0.189 0.047
0.049		 0.046
0.050		 0.004 0.004
E(22)(11)b 0.008 - 0.189 0.046
0.050		 0.047
0.049		 0.004 0.004
E(22)(11)c 0.008 - 0.189 0.046
0.050		 0.047
0.049		 0.004 0.004
E(22)(11)d 0.008 - 0.189 0.047
0.049		 0.046
0.049		 0.004 0.004
E(22)(20)a 0.008 - 0.021 0.046
0.049		 0.047(2×) 0.035
0.038		 -
E(22)(20)b 0.007 - 0.020 0.047(2×) 0.046
0.049		 0.035
0.038		 -
E(22)(02) 0.007 - 0.020 0.046
0.049		 0.047(2×) - 0.035
0.039
E(31)(20) 0.156 - 0.005 0.006
0.011
0.012		 0.080 0.029
0.035		 -
E(32)(10) 0.089 - 0.072 0.009
0.010(2×)		 0.027
0.045		 0.005 -
E(3)(201) - 0.138 0.229 0.033(3×) 0.043
0.053		 - 0.008
E(3)(102)a - 0.218 0.118 0.326
0.327(2×)		 0.005 - 0.047
0.051
E(3)(102)b - 0.238 0.133 0.324(2×)
0.329		 0.001 - 0.041
0.052
E(3)(00)(3) - 0.000 - 0.033
0.034(2×)		 - - 0.033(3×)
F(11)(22) 0.189 - 0.008 0.004 0.004 0.047
0.049		 0.046
0.050
F12)(21b) 0.012 - 0.031 0.054 0.046
0.051		 0.045
0.047		 0.049
Remarks: a)N1-N4 BCP ellipticity of 0.103; b)N1-N4 BCP ellipticity of 0.041.
Table 9. Atomic charges of N and H (bonded to N in brackets) in the optimized Amnpq and Dmnpq structures. The asterisks denote the atoms included in hydrogen bonds as well.
Table 9. Atomic charges of N and H (bonded to N in brackets) in the optimized Amnpq and Dmnpq structures. The asterisks denote the atoms included in hydrogen bonds as well.
Structure N1 N2 N3 N4 H(N1) H(N2) H(N3) H(N4)
D1221 -0.657 -0.488 -0.485 -0.649 0.342 0.452
0.455		 0.444
0.457		 0.342
D2112a -0.699 -0.347 -0.367 -0.706 0.379
0.392		 0.391 0.382 0.391
0.404
D2112b -0.691 -0.357 -0.354 -0.726 0.378
0.394		 0.372 0.395 0.387
0.398
D2112c -0.711 -0.354 -0.368 -0.729 0.377
0.389		 0.382 0.396 0.389
0.401
D2121a -0.700 -0.341 -0.398 -0.787 0.394
0.413		 0.417 0.452(2×) 0.309
D2121b -0.704 -0.361 -0.394 -0.811 0.400
0.416		 0.405 0.470
0.560		 0.302
D2121c -0.709 -0.365 -0.412 -0.800* 0.396
0.407*		 0.406 0.463
0.468		 0.310
D2121d -0.707 -0.361 -0.395 -0.809 0.402
0.420		 0.408 0.458
0.471		 0.304
A2202 -0.664 -0.388 -0.435 -0.750 0.418(2×) 0.450(2×) - 0.362(2×)
D2202a -0.712 -0.404 -0.430 -0.760 0.409
0.410		 0.455
0.475		 - 0.361
0.364
D2202b -0.705 -0.397 -0.432 -0.737 0.407
0.411		 0.459
0.465		 - 0.357
0.367
D2022 -0.761 -0.430 -0.402 -0.711 0.361
0.365		 - 0.455
0.475		 0.409
0.410
A3021 -0.730 -0.368 -0.388 -0.824 0.460
0.461
0.496		 - 0.403
0.423		 0.286
D3012a -0.732 -0.436 -0.390 -0.739 0.449(2×)
0.472		 - 0.370 0.360
0.372
D3012b -0.762 -0.417 -0.384 -0.754* 0.444
0.466*
0.473		 - 0.345 0.376
0.378
Table 10. Atomic charges of N and H (bonded to N in bracket) in the optimized Emnpq and Fmnpq systems. Asterisks denote atoms included in hydrogen bonds as well.
Table 10. Atomic charges of N and H (bonded to N in bracket) in the optimized Emnpq and Fmnpq systems. Asterisks denote atoms included in hydrogen bonds as well.
System N1 N2 N3 N4 H(N1) H(N2) H(N3) H(N4)
E1111a) -0.345 -0.367* -0.373 -0.367 0.383 0.408 0.396* 0.403
E(22)(11)a -0.707 -0.727h -0.358 -0.348* 0.380
0.392h		 0.385
0.393		 0.409* 0.380
E(22)(11)b -0.727* -0.707 -0.360 -0.348* 0.384
0.393		 0.380
0.388*		 0.409* 0.380
E(22)(11)c -0.726* -0.706 -0.349h -0.360 0.384
0.393		 0.380
0.387*		 0.380 0.409h
E(22)(11)d -0.706 -0.726h -0.359 -0.347* 0.380
0.388h		 0.384
0.393		 0.409* 0.380
E(22)(20)a -0.732* -0.714 -0.519 -0.271* 0.380
0.393*		 0.387
0.395		 0.417
0.460*		 -
E(22)(20)b -0.713 -0.732* -0.517 -0.273* 0.380
0.393*		 0.387
0.395		 0.417
0.461*		 -
E(22)(02) -0.714 -0.732* -0.272* -0.517 0.380
0.393*		 0.387
0.395		 - 0.417
0.460*
E(31)(20) -0.751 -0.831* -0.543 -0.306* 0.447
0.452
0.491*		 0.315 0.408
0.511*		 -
E(32)(10) -0.718 -0.731 -0.426 -0.530* 0.496
0.508(2×)		 0.408
0.501*		 0.185
 -
E(3)(201) -1.079* -0.734 -0.035 -0.436 0.394(3×) 0.443
0.473*		 - 0.388
E(3)(102)a -1.076* -0.454 -0.033 -0.686 0.394(3×) 0.428* - 0.429
0.445
E(3)(102)b -1.084* -0.396 -0.030 -0.739 0.394
0.395
0.396		 0.352 - 0.445
0.470*
E(3)(00)(3) -1.077* 0.076* -0.049 -1.059 0.382
0.382*
0.384		 - - 0.373
0.380*
0.386
F(11)(22) -0.359 -0.347h -0.706 -0.725* 0.409h 0.380 0.380
0.388*		 0.393
0.394
F12)(21b) -0.356 -0.722 -0.702 -0.368 0.403 0.377
0.392		 0.371
0.395		 0.381
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