聯氨與四氧化二氮自燃反應機制的研究

國

立

交

通

大

學

分子科學研究所

碩

士

論

文

聯氨與四氧化二氮自燃反應機制的研究

Ab Initio Study of the Mechanism for

the Hypergolic Reaction of

Hydrazine with Dinitrogen Tetroxide

研究生 賴科余

指導教授 林明璋 院士

聯氨與四氧化二氮自燃反應機制的研究

Ab Initio Study of the Mechanism for

the Hypergolic Reaction of

Hydrazine with Dinitrogen Tetroxide

研 究 生：賴科余 Student：Ke-Yu Lai

指導教授：林明璋 院士 Advisor：Prof. M.C. Lin

國 立 交 通 大 學

分子科學研究所

碩 士 論 文

A Thesis

Submitted to Institute of Molecular Science

Department of Applied Chemistry, College of Science, National Chiao Tung University in partial Fulfillment of the Requirements

for the Degree of Master

in

Applied Chemistry September 2009

Hsinchu, Taiwan, Republic of China

Acknowledgement

首先感謝院士在這兩年中的指導，無論是在研究上或是在做人處事上，常常 都指引著我向前，並且提供許多的資源讓我進行研究，與許多實驗室的合作也讓 我學到如何溝通與協調，非常感謝老師當初讓我有這個機會可以進入這間實驗室 學習。另外，感謝帶我進入量子計算的欣聰學長，不厭其煩地讓我常常纏著問問 題，以及感謝禎翰學長在實驗上的指導與教導我如何處理人生道路上的起起伏伏， 很懷念與你們在工作一整天後的夜晚，在便利商店外喝著飲料討論問題與談天的 日子;感謝雯妃學姊在研究上的許多協助，能找到可以一起討論研究到眼睛發亮的 同伴真好；感謝 AD 總是一起熬夜做實驗，最欣賞你的直言直語，可以讓我們暢所 欲言，還有小結巴廢彬，帶給大家那麼多的歡樂；感謝志翰與冠霖讓我不是孤軍 奮戰，雖然總是被我碎碎念，還是非常認真地做實驗，與你們一起做實驗讓我信 心十足!還有雯傑一起討論，一起做手指運動紓發壓力，是我們最好的夥伴。總是 一起相約去打球的老王、馬哥、阿布、偉志、巨砲還有 Alonso，感謝你們的照顧， 跟你們學習到很多不同領域的知識與解決問題的想法，在做實驗時你們總是最棒 的友軍!雖然跟小朱還有欣瑜領域不同，不過與你們相處很開心，很高興與你們一 起走過這兩年；另外感謝林鵬老師與文碩學長在實驗上毫不保留地教導。跟老師 一起爬山出遊、與大夥一起打球賽、一起熬夜做實驗、還有每天收不停地失敗計 算，這些日子非常感謝大家的照顧與陪伴，有你們真好! 最後我要感謝我的父母，不論在什麼時候都守護著我，感謝你們的栽培!以及 在英國求學的怡孜，在我挫折的時候，提供我溫暖的支持，陪我一起走過。有許 許多多的人在這段時間中幫助我、砥礪我、陪伴我，非常感謝你們讓我成長、一 起擁有歡笑!

i

Abstract

Hydrazine and dinitrogen tetroxide reaction is a spontaneously ignited combustion reaction, and the propellants are practically used in the space shuttle of NASA. However, the mechanism of this hypergolic combustion system is still unknown theoretically and experimentally. In the practical system, the reactants are not only composed of N2H4(C2) and N2O4(D2h) molecules, and they also contain

trans-ONONO2(Cs), cis-ONONO2(Cs) and NO2(C2v) molecules which can react with

hydrazine when the liquid N2O4 oxidizer is ejected into reaction chamber with high

velocity. We consider these four bimolecular reactions by using ab-initio calculations with the Gaussian03 code. The geometries of all stationary points on the potential energy surfaces (PESs) are optimized by B3LYP/6-311++G(3df,2p). Moreover, the single-point calculations, including G3B3, CCSD(T), and G2M methods, correct the relative energies to give better values for the kinetic calculations. The G2M method provides the good prediction as CCSD(T)/6-311++G(3df,2p), and it also has smaller differences comparing with experimental data. The G2M(CC1) and G2M(CC3) schemes are chosen for the smaller and larger reaction system, respectively.

The geometries of cis- and trans-ONONO2 molecules are unknown

experimentally. The PES of N2O4 isomerization has been studied; the energy barrier

between the cis-isomer and N2O4(D2h) is lower than that between the trans-isomer and

N2O4(D2h) by 20.15 kcal/mol. The energy of transition state (TS) between cis- and

trans-ONONO2 is only 1.71 kcal/mol; thus cis-trans isomerization can occur rapidly.

In the bimolecular reactions, the major and lower-energy channels are the hydrogen abstraction reactions, and the mechanism for breaking the N-O bond of NO2

or N2O4 molecule needs much higher energies. In the N2H4 + NO2 reaction, the

ii

kcal/mol barrier. The rate constant predicted by transition state theory is 3.20×10-25T3.74exp(-1662.5/T) cm3/(molecule．sec) at 100K - 4000K. In the N2H4 +

N2O4 reaction, the hydrogen transfer reaction accompanies with bonds breaking and

forming via a ring-like TS. The energy barriers of transition state in most of the reaction channels are higher than 10 kcal/mo; however, the N2H4 + trans-ONONO2 reaction

occurs by hydrogen transfer via a six-member ring TS without an intrinsic barrier. In this lowest-energy channel, the energy of transition state is predicted to be lower than intermediate by 2.66 kcal/mol at the G2M(CC3) level. However the difference is only 0.16 kcal/mol at the B3LYP/6-311++G(3df,2p) level, which is confirmed by IRC calculation; therefore, it may be caused by the zero-point energy correction and computational errors. This lowest-energy channel produces HONO2 + H2NN(H)NO

with 15.57 kcal/mol exothermicity. Moreover, another lower-energy channel of N2H4 +

N2O4(D2h) reaction is also exothermic, and the products are trans-HONO and

H2NN(H)NO2. Furthermore, the decomposition reactions of H2NN(H)NO and

H2NN(H)NO2 molecules provide another possibility producing the active species. The

direct dissociation reaction to form N2H3 and NO radicals is the most possible path for

H2NN(H)NO molecule, where it needs to overcome a small rotation TS with 6.28

kcal/mol barrier height and undergoes the dissociation reaction with 27.83 kcal/mol energy. On the other hand, the H2NN(H)NO2 can overcome a five-member ring TS,

with a barrier is 26.6 kcal/mol barrier, and decompose to trans-N2H2 and trans-HONO.

Besides, it is also possible to directly dissociate to N2H3 and NO2 with 38.23 kcal/mol

energy.

The hypergolic reaction of N2O4 with N2H4 is therefore believed to be initiated

iii

Table of Contents

I. Introduction 1

1.1 Chemical properties of hydrazine and dinitrogen tetroxide ₂

1.2 Review of NASA reports ₆

1.3 Isomers of N2O4 11

1.3.1 Isomerization of N2O4 11

1.3.2 Temperature induced autoionization ₁₃ 1.3.3 Ab-initio studies of N2O4 isomers 15

1.4 References ₁₈

II. Computation Methods ₂₀

2.1 Ab-initio Calculations ₂₀

2.1.1 Modified GAUSSIAN-2 (G2M) ₂₁

2.1.2 Gaussian-3 theory using DFT geometries and zero-point energies

(G3B3) ₂₄

2.2 Kinetic Calculation ₂₆

2.3 Reference ₂₇

III. Results and Discussions 28

3.1 N2H4+NO2 reaction 28

iv

3.1.2 PES of the N2H4 + NO2 reaction 29

3.1.3 Kinetic calculation ₃₄

3.2 N2O4 isomerization reaction 46

3.2.1 The geometries of N2O4 isomers 46

3.2.2 PES of N2O4 isomerization 50

3.3 N2H4+N2O4 reaction 68

3.3.1 N2H4 + trans-ONONO2 and N2H4 + cis-ONONO2 reactions 68

3.3.2 Decomposition of H2NN(H)NO molecule 86

3.3.3 N2H4+N2O4 (D2h) reaction 97

3.3.4 Decomposition of H2NN(H)NO2 molecule 107

3.3.5 The single-point energies in N2H4+N2O4 isomeric reactions 118

3.4 Reference ₁₂₀

IV. Conclusion 123

v

List of Tables

Table1-1: Physical properties of N2H4, N2O4, and NO2 1

Table1-2: The equilibrium constant of 2NO2←→N O2 4 _{at three temperatures 3}

Table1-3: Equilibrium distance (in Å), bond angle (in deg), harmonic frequencies (in cm-1)and zero-point vibrational energies (kcal/mol) for NO2. 5

Table1-4: Bond distance (in Å), bond angle (deg), harmonic frequencies (cm-1),

zero-point vibraional energies (kcal/mol) for the N2O4 dimer. 5

Table1-5: Energetics (in kcal/mol) of the reaction ₆

Table1-6: Gas evolution from the low temperature reaction of N2H4+N2O4 7

Table1-7: The correspondence between D and D’. ₁₂

Table1-8: Frequency and vibrational assignment of infrared bands of ONONO2 (D) in

an oxygen matrix. (NO2 refers to the nitro group, and O=N-O- to the nitrite

group of D). ₁₂

Table1-9: Estimated activation barrier (kcal/mol) at the QCI and DFT (in parentheses)

level of theories. ₁₆

Table2-1: Formulas for the recommended G2M methods. ₂₂

Table2-2: Comparison of the accuracy and the range of applicability for various

modified Gaussian-2 (G2M) methods. ₂₃

vi

Table2-4: Comparison of average absolute deviations in kcal/mol. ₂₅ Table3-1: Moments of inertia (IA, IB, IC) and vibration frequencies of the species

computed at the B3LYP/6-311++G(3df,2p) level ₃₉

Table3-2: Relative energies of species predicted at various theoretical levels. ₄₁ Table3-3: Comparison of geometries (bond length in Å and bond angle in deg) of N2H4

by different computational methods and experimental results. ₄₂ Table3-4: Calculated and Experimental Vibrational Frequencies (in cm-1) of N2H4 43

Table3-5: Calculated and Experimental bond lengths (in Å), bond angles (in deg), and

vibrational Frequencies (in cm-1) of NO2. 44

Table3-6: Fitting expressions for the rate constants of the N2H4+NO2 reactions

employing transition-state theory. ₄₄

Table3-7: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in

N2O4 isomerization computed at B3LYP/6-311++G(3df,2p). 58

Table3-8: Relative energies of species in N2O4 isomerization reaction at various

theoretical levels. ₅₉

Table3-9: The heat of dissociation for N2O4 to 2NO2 at 0K and one atmosphere. 60

Table3-10: Comparison of geometries (bond length in Å and bond angle in deg) of N2O4

by different computational methods and experimental results. ₆₁ Table3-11: Calculated and Experimental Vibrational Frequencies (in cm-1) of N2O4 62

vii

Table3-12: Calculated (B3LYP) and Experimental Vibrational Frequencies (in cm-1) of

cis-ONONO2. 63

Table3-13: Calculated Vibrational Frequencies (in cm-1) of the cis-ONONO2 and

cis-ONONO2_2 structures. 64

Table3-14: Calculated Vibrational Frequencies (in cm-1) of the cis-ONONO2_3

structures. ₆₅

Table3-15: Computational and Experimental Vibrational Frequencies (in cm-1) of

trans-ONONO2 66

Table3-16: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in

trans-ONONO2 + N2H4 and cis-ONONO2 + N2H4 reactions computed at

B3LYP/6-311++G(3df,2p). ₈₁

Table3-17: Relative energies of species in trans-ONONO2 + N2H4 reaction and

cis-ONONO2 + N2H4 reaction predicted at various theoretical levels. 83

Table3-18: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in the

major channel of trans-ONONO2 + N2H4 reaction computed at

PW91PW91/6-311++G(3df,2p). ₈₄

Table3-19: Relative energies of species in the major channel of the trans-ONONO2 +

N2H4 reaction at various theoretical levels. 85

viii

H2NN(H)NO decomposition computed at B3LYP/6-311++G(3df,2p) 94

Table3-21: Relative energies of species in H2NN(H)NO decomposition computed at

various theoretical levels. ₉₅

Table3-22: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in the

N2O4 (D2h) + N2H4 reaction computed at B3LYP/6-311++G(3df,2p). 104

Table3-23: Relative energies of species in N2O4 (D2h) + N2H4 reaction computed at

various theoretical levels. ₁₀₆

Table3-24: Moments of inertia (IA, IB, IC) and vibration frequencies of the species in

H2NN(H)NO2 decomposition computed at B3LYP/6-311++G(3df,2p). 115

Table3-25: Relative energies of species in H2NN(H)NO2 decomposition computed at

various theoretical levels. ₁₁₇

Table3-26: The heats of formation based on experimental and computational studies. 119 Table3-27: The heats of reaction of N2H4+NO2 and N2H4+N2O4 reaction computed by

ix

List of Figures

Fig1-1: Measured data for equilibrium constant of at 25, 35, and 45℃. ₄ Fig1-2: The infrared spectrum of N2O4 (high concentration) at -196℃ 6

Fig1-3: Separation model for the impinging hypergolic stream ₉

Fig1-4: Parallel injector spray pattern in the combustion reaction. ₉ Fig1-5: Typical spray photographs for (a) stream mixing for high pressure, (b) stream

separation for high pressure. ₁₀

Fig1-6: The D structure can undergo a cis-trans isomerization to form D’. ₁₂

Fig1-7: Structures of N2O4 isomers 15

Fig3-1: The geometries in the PES are determined by B3LYP/6-311++G(3df,2p). ₃₈ Fig 3-2: Potential Energy Surface of the N2H4+NO2 reaction, whose energies are

calculated by G2M(CC1)//B3LYP/6-311++G(3df,2p). ₄₀

Fig3-3: Arrhenius plots of the calculated rate constants for various channels of the

N2H4+NO2 reaction. 45

Fig3-4: (a) The geometries in the PES of N2O4 isomerization are determined at B3LYP/

6-311++G(3df,2p) level, (b) PW91PW91/6-311++G(3df,2p) level, (c)

BHandHLYP/ 6-311++G(3df,2p) level, and (d) CCSD/6-311+G(d,p) The value

in parentheses is noted for Mulliken charge. ₅₆

x

G2M(CC1)//B3LYP/6-311++G(3df,2p). ₅₇

Fig3-6: Arrhenius plots and three-parameters fitting expressions for the rate constants. (a) The faster reaction is N2O4 to cis-ONONO2 via i-TS2, and the lower one is

N2O4 to trans-ONONO2 via i-TS1. 67

Fig3-7: (a) The stationary points in the PES of trans-ONONO2 + N2H4 reaction and

cis-ONONO2 + N2H4 reaction are optimized by B3LYP/6-311++G(3df,2p), and

(b) the stationary points on the major channel of trans-ONONO2 + N2H4 reaction

optimized by PW91PW91 /6-311++G(3df,2p). ₇₇

Fig3-8: Potential Energy Surface of trans-ONONO2 + N2H4 reaction and cis-ONONO2

+ N2H4 reactions, whose energies are calculated by G2M(CC3) //

B3LYP/6-311++G(3df,2p). ₇₈

Fig3-9: The IRC calculation of Cs-TS1 is determined by B3LYP/6-311++G(3df,2p) for

reverse direction. The highest point is the position of Cs-TS1, and the lowest

point is approaching to the Cs-Complex1. The energy difference is 0.00027

Hartree (0.17 kcal/mol). ₇₉

Fig3-10: The comparison for the major channel of trans-ONONO2 + N2H4 reaction

optimized by B3LYP/6-311++G(3df,2p) and PW91PW91/ 6-311++G(3df,2p). 80 Fig3-11: The stationary points in the PES of H2NN(H)NO decomposition are optimized

xi

by B3LYP/6-311++G(3df,2p) ₉₂

Fig3-12: Potential Energy Surface of H2NN(H)NO decomposition, whose energies are

calculated by G2M(CC1) // B3LYP/6-311++G(3df,2p). ₉₃

Fig3-13: The stationary points in the PES of N2O4 (D2h) + N2H4 reaction are optimized

by B3LYP/6-311++G(3df,2p) ₁₀₂

Fig3-14: Potential Energy Surface of the N2O4 (D2h) + N2H4 reaction, whose energies

are calculated by G2M(CC3) // B3LYP/6-311++G(3df,2p). ₁₀₃

Fig3-15: The stationary points in the PES of H2NN(H)NO2 decomposition are

optimized by B3LYP/6-311++G(3df,2p). ₁₁₃

Fig3-16: Potential Energy Surface of H2NN(H)NO2 decomposition, whose energies are

1

I.

Introduction

RNHNH2 and N2O4 (R = H, CH3, (CH2-CH3)) reaction systems have been

continuously used as propellants for rocket propulsions into space by NASA nowadays.

(1) _{The hydrazine (N}

2H4) and dinitrogen tetroxide (N2O4) reaction has an extremely

hypergolic property, which ignites spontaneously upon mixing without a source of ignition. A great many reports discussed this important reaction in early NASA research

(2-6)_{, and most of them highlighted the combustion process of the rocket, whose fuel and}

oxidizer are hydrazine and dinitrogen tetroxide, respectively. This reaction contains many complex and rapid reactions, which make up a kind of huge chemical soup of reactions, and the spectra of these reactions make it very difficult to separate the signals originating from many species. To our best knowledge, there is no recent paper which discusses the mechanism or kinetics of this reaction computationally or experimentally. The hydrazine and dinitrogen tetroxide have critical chemical properties as a combustion fuel and oxidizer, respectively, and some of their basic physical properties are presented in table1-1.

Table1-1: Physical properties of N2H4, N2O4, and NO2

Hydrazine (N2H4) Dinitrogen tetroxide

(N2O4)

Nitrogen dioxide (NO2)

Melting Point 1 °C (274 K, anhydrous) -51.7 °C (hydrate)

−11.2 ºC (261.9 K) 11.2 °C (62 K) Boiling Pont 114 °C (387 K, anhydrous)

119 °C (hydrate) 21.1 ºC (294.3 K) 21.1 °C (294 K) Density(g/cm3) 1.0045 (anhydrous) 1.032 (hydrate) 1.443 (liquid,21 ºC) 1.449 (liquid,20 ºC) 3.4 (gas, 22 ºC)

Appearance colorless liquid colorless gas brown gas

Solubility in water miscible miscible miscible

Refractive index 1.46044 (22 °C, anhydrous) 1.4284 (hydrate)

1.00112 1.449 (20 °C)

2

1.1 Chemical properties of hydrazine and dinitrogen tetroxide

Hydrazine (N2H4) is a toxic, flammable caustic liquid and strong reducing agent.

Its odor is similar to that of ammonia, but less strong. It is soluble in water, methanol, ethanol, UDMH (Unsymmetrical Dimethyl hydrazine ((CH3)2NNH2)), and

ethylenediamine, and therefore, it can be used with UDMH in the bi-fuel system. Hydrazine is found early and used as a storable liquid fuel, and it is replaced gradually by UDMH and MMA (Monomethyl hydrazine (CH3NHNH2)). Currently, it is used as a

monopropellant for satellite motors. Hydrazine can be made by different methods, and these are briefly described below.

-3 2 - -2 3 2 4 2

Raschig Process:

NH

OCl

NH Cl+OH

NH Cl+OH

NH

N H

Cl +H O

−

+

→

+

→

+

(1.1) 3 2 2 2 2 2 2 2 2 4 2

Bayer Process:

2NH

OCl

2Me C=O

Me C=N N=CMe

3H O+Cl

Me C=N N=CMe

2H O

N H

2Me C=O

− −

+

+

→

−

+

−

+

→

+

(1.2) 3 2 2 2 2 2 2 2 2 2 2 4 2

Produits Chimiques Ugine Kuhlmann Process (PCUK)

2NH

H O

2R C=O

R C=N N=CR

4H O

R C=N N=CR

2H O

N H

2R C=O

+

+

→

−

+

−

+

→

+

(1.3)

The MMA and UDMA originate from hydrazine in which one and two hydrogen atoms are replaced by one or two methyl groups, respectively. These two species are also easy to manufacture as N2H4, and are applied as common rocket fuels nowadays.

On the other hand, dinitrogen tetroxide (N2O4) is a powerful oxidizer, highly

toxic and corrosive, and it is manufactured by the catalytic oxidation of ammonia, in which steam is used as a diluting agent in order to reduce the reaction temperature. Next, the gases are cooled, and most of the water is condensed and removed. Furthermore, the nitric oxide (NO) is oxidized into nitrogen dioxide (NO2), and the remainder of the

3

water is removed as nitric acid. The above process is represented by eq. (1.4). This almost pure nitrogen dioxide gas is cooled to a low temperature and condensed into liquid, which keeps the equilibrium towards dinitrogen tetroxide (N2O4) as the

temperature decreased. The last cooling step is called a dimerization reaction, which is the eq. (1.5). o Pt catalyst 3 2 _750~900 2 2 2

4NH +5O

4NO+6H O

2NO+O

2NO

C

→

→

(1.4)

Therefore, the NO2 exists in equilibrium with N2O4.

2 2 4

2NO

_←



_

→

N O

_(1.5)

This equilibrium is famous, and is often used as a good example in many text books. Verhoek and Daniels (7) studied this effect in 1931, and the following equation is the representation of the dissociation constant, K_{N O2 4}. Fig1-1 and Table1-2 represent the equilibrium constant in this study.

2 4 2 4 2 4 2 4 2 N O 2 o N O o N O o N O 4 K = 1

where the is the measured pressure in atmosphere and is the degree of dissociation.

= ;

in which g is the weight of nitrogen tetroxide, M is the molecular

P P P P _{g RT} P P M V

α

α

α

α

− − = weight and R, T, and V have their usual meanings.

(1.6)

4

Fig1-1: Measured data for equilibrium constant of at 25, 35, and 45℃. (7)

Many papers discuss the N2O4 single molecule or the unimolecular dissociation reaction.

The most stable N2O4 geometry is D2h, and the N-N bond distance varies between 1.772

and 1.776, which is much longer than the N-N bond distance of hydrazine (1.434-1.449).

(8,9) _{The weak N-N bond is also evidenced by the low values of the enthalpies of the}

dissociation reaction, which are 12.7-12.9 kcal/mol at 0K(10,11) and 13.1-13.7 kcal/mol at 298K. (10-12) The activation energy barrier is also low. The dissociation energy, the reaction is very fast, and the experimental rate constants for the limiting low-concentration (k0) and high-concentration (k∞) regions are 4.5×106 cm3/mol-1 sec-1

and 1.7×105 1/sec at 298K, respectively.(13) The reason for the high rate constant is that the weak N-N bond undergoes an internal rotation (torsion) with a barrier height of about 3 kcal/mol. (14,15)

This dissociation reaction have been also calculated by an ab-initio calculation method (CCSD(T)/cc-PVTZ) to determine the rate constants, which are 0.62×101, 1.90× 103, and 1.66×105 1/sec at 250, 298.15, and 350K. (16) The following tables are the

2 2 4

5

geometries of NO2, N2O4, and the energetic properties of the reactionN O2 4→2NO2. Table1-3: Equilibrium distance (in Å), bond angle (in deg), harmonic frequencies (in cm-1)and zero-point vibrational energies (kcal/mol) for NO2. (16)

Table1-4: Bond distance (in Å), bond angle (deg), harmonic frequencies (cm-1), zero-point vibraional energies (kcal/mol) for the N2O4 dimer. (16)

6

Table1-5: Energetics (in kcal/mol) of the reaction N O_{2 4}→2NO₂ . Values in parentheses include the BSSE correction (basis set superposition error) in kcal/mol. (16)

1.2 Review of NASA reports

Weiss (2) studied the dinitrogen tetroxide and hydrazine reaction with an infrared spectrum at a low temperature, and he found some important elements of note, the first of which was, that the NO2 exists in pure N2O4 liquid at -196℃,which is shown in

Fig1-2. Although this situation is normal due to the equilibrium, it suggested that NO2 is

also one of the important liquid oxidants for this combustion reaction.

7

By means of the experiment at low temperature, this reaction could occur under control. The experiment was started at -196℃ and slowly warmed up, and the infrared spectra began to change at around -78℃. After continuously increasing the temperature, the concentration of NO2 increased more than the quantity in the equilibrium state, and

the spectra was more complex than it was at a lower temperature. However, the heat of the system did not increase to the same temperature until at -54℃. Therefore, comparing the results of the infrared spectrum and the calorimeter; Weiss suggests that (1) the initial formation of adducts in the lower temperature made the spectrum change, (2) increasing the concentration of NO2 may be the result of adduct formation,

(3) the decomposition of adducts made the free-radical reaction occur and a large amount of heat and gas was released. Table1-6 presents the summary of the species in the spectrum at different temperatures. However, Weiss also indicates that there are contradictions between the results and the assumptions of the reaction mechanism. Furthermore, there were some species in the spectra which could be not identified.

8

In the end, the simple miscibility experiments had been done, and there were some principle factors when the N2H4-N2O4 impinging jets were diverted by the

interaction between the two propellants. The factors causing this phenomenon were: (1) Immiscibility of two reactants,

(2) Rapid reaction rate between N2O4 and N2H4,

(3) The high heat evolution and large gas volume generated by the reaction, and the heat can make the product gases expand and the propellants vaporize.

Therefore, the way to resolve the immiscibility problem is to increase the ratio of the contact surface and the volume of the two reactants as much as possible, since this would be very important for achieving better performance of the combustion system. This part is a different topic from the reaction kinetic, and another NASA reports (3-6) tried to solve it. Although these reports did not focus on the reaction mechanism, they could still offer the experimental conditions to make a better computational assumption. In the real rocket system, the N2O4 and N2H4 are in the

liquid phase, which stays with the cooler system, and are ejected into the combustion chamber with a high flow velocity. In order to achieve the best performance by means of a good mix of two propellants, the ratio of N2O4/ N2H4 should be optimized, and the

type of the injector, including the arrangement of the injector positions of the two propellants and the impingement angles of the injecting direction for every injector.(3-5) Furthermore, the injecting velocity and temperature of the propellants, the size of the nozzle, and the pressure of the combustion chamber are also very important elements which affect the performance.(6) Therefore, it can be understood that the combustion reaction occurs as the N2O4 and N2H4 collide with each other at very high momentum,

9

phase. The temperature of the chamber is over 3000℃ after continuous reaction. The following figures are the photographs of the combustion reaction.

Fig1-3: Separation model for the impinging hypergolic stream (4)

10 (a)

(b)

Fig1-5: Typical spray photographs for (a) stream mixing for high pressure, (b) stream separation for high pressure. (6)

11

1.3 Isomers of N

2

O

4

In the gas phase, the association of NO2 produces the N2O4 dimer, which is a

stable molecule. Infrared and Raman spectral techniques were used to record the vibrational frequencies of the molecules. The existence of unstable forms of the dinitrogen tetroxide was proposed by Fateley, Bent, and Crawfold (17), and they studied

NO2 at helium temperature in six types of matrices. Apart from bands belonging to NO2

and stable N2O4 (D2h), other bands were assigned to an unstable isomer of N2O4.

Baldeschwieler (18) repeated Fateley’s work, which was a similar work at liquid-hydrogen temperature. Furthermore, Hisatune, Devlin, and Wada (19) reported that unstable molecules appeared to be formed when pure NO2 gas was deposited at

liquid-nitrogen temperature. 1.3.1 Isomerization of N2O4

St. Louis and Crawford (20) used infrared spectra to study NO2 suspended in

oxygen and argon matrices at helium temperature, and assign the absorption spectra of NO2, N2O4 (D2h), and three unstable forms of N2O4, including N2O4 (D2d)and another

two ONO-NO2 isomers based on the relative optical density measurements and the

temperature dependence of the bands. They called the two conformers of ONO-NO2 as

D and D’, where D and D’ are notations for cis-ONO-NO2 and trans-ONO-NO2.

However, it is actually difficult to identify which one is cis- or trans- ONONO2.

Subsequent papers have applied the same notation, but sometimes the meanings of the notation would change from each other. They assumed that the ONO-NO2 molecule is

planar as in similar cases of stable N2O4 and stable N2O2, and they calculated the

12

also assumed the bonding structures, as Fig1-6, and most subsequent researchers followed this assumption. After warming up from the temperature of existence D, they also found another isomer D’, and the bands of D’ were near to D. It appeared that D was isomerized to D’, a molecule with a structure close to D. The following tables are the absorption spectra of D and D’.

Fig1-6: The D structure can undergo a cis-trans isomerization to form D’.

Table1-7: The correspondence between D and D’.

Table1-8: Frequency and vibrational assignment of infrared bands of ONONO2 (D) in

13 1.3.2 Temperature induced autoionization

Parts and Miller (21) first observed that the heterolytic dissociation of ONO-NO2

produced the nitrosonium-nitrate NO+NO3- complex in a solid state form by the infrared

spectra. Bouduan, Jodi, and Loewenschuss (22) also observed this complex by the Raman spectra, and NO+NO3- complex could produce as spontaneously as N2O4 trapping in an

Ne matrix. They suggested that autoionization is an intermolecular rather than intramolecular process. The results indicate that, when a solid matrix is warmed to about 180K, an almost complete conversion occurs to the ionic NO+NO3- which remains

stable over the full temperature range of 15-180K. There was no evidence that the unsymmetrical forms, D and D’ of ONO-NO2, are observed prior to the transformation

to the ionic form. Even though the unsymmetrical isomers exist in the matrix, all unsymmetrical and symmetrical N2O4 still undergo the temperature induced ionization

in the mean time.

However, Jones, Swanson, and Agnew (23) also reported a similar experiment with the infrared spectra, but they indicated the mechanism of the temperature induced autoionzation was intramolecular, contrary to that of Bolduan et al. (22) The experiment used the gas which was an equilibrium mixture of NO2 and N2O4 at room temperature to

make the low pressure deposition at various temperatures onto a CsBr window. The spectra were observed as the matrix samples were heated to different temperatures. The results showed that temperature induced that autoionization only occurred with the two less stable isomers of ONO-NO2, D and D’ existing. The frequencies of these isomers

were shifted towards those NO+NO3- relative to the more stable nitrite form. In addition,

the bulk of N2O4 did not undergo autoionization at low pressure and at temperatures

14

In fact, the band assignments for the solid N2O4 isomers in the matrix are far less

conclusive than N2O4 (D2h) gas. In earlier researches, there is no systematic correlation

between the different conditions as the solid sample is formed, such as its composition and the effect of the temperature cycling on such solid samples. Therefore, A. Givan and A. Loewenschuss(24-27) have also tried to solve this open question, and the results appear to clarify some of the conflicting points. In their work, the Raman and Fourier transform infrared spectra had been used to detect the matrices which included different preparation processes, such as controlling deposition rates, substrate material, deposition temperatures, and temperature cycling as parameters. They found similar results as Jones et al(23) that there was no evidence of the conversion to the ionic form of either an ordered or disordered N2O4(D2h) layer, and the existence in the solid of the D’

isomer was directly related to the formation of ionic nitrosonium nitrate (NO+NO3-) and

nitrogen dioxide (NO2). With temperature cycling, up to 150K, the NO3- bands increased

in intensity while the D’ features decreased. On the other hand, the summary of the relationship between the deposition rate and temperature for the species appearing in the solid matrix was that lowering the deposition temperature increased the relative amount of the monomer, and increasing the deposition temperature favored the D’ formation in the solid. Givan and Loewenschuss also suggested a mechanism of the formation of D and D’,(24,25) and proposed that the formation of temperature induced autoionization is an intermolecular process. Although these experimental results offered different mechanisms of autoionization, it is still open to question, because of the uncertain assignments for the results of the Raman or infrared spectra. The existence of D and D’ isomers (cis- and trans-ONONO2) and the NO+NO3- complex appearing from

15 1.3.3 Ab-initio studies of N2O4 isomers

Stirling (28), McKee (29) and many other researchers (30-33) have calculated the conformations and characterizations of N2O4 isomers, which include O2N-NO2(D2h),

cis-ONO-NO2(Cs), trans-ONO-NO2(Cs), cis-perp-cis ONO-ONO(C2), cis-perp-trans

ONO-ONO(Cs), and trans-perp-trans ONO-ONO(C2), and the geometries are shown in

Fig1-7. McKee (29) also calculated the N2O4 Potential Energy Surface (PES) as Fig.1-8,

and the estimated activation energy in Table1-9.

16

Fig1-7: Potential energy surface for the formation of ONO-ONO and N2O4 from

2NO+O2 at the QCI level theory. (29)

Table1-9: Estimated activation barrier (kcal/mol) at the QCI and DFT (in parentheses) level of theories. a (29)

These isomers are only the stationary points from computation, and only N2O4(D2h),

trans-ONONO2, and cis-ONONO2 have been observed in experiments. However, there

17

most stable state N2O4 (D2h). Therefore, the computational work can only be compared

with the results of the vibrational frequencies in the Raman or infrared spectra for cis-ONONO2 and trans-ONONO2 molecules. The geometries of cis-ONONO2 and

trans-ONONO2 molecules are assumed to be planar and Cs symmetry, as discussed in

section 1.3.1 (20). No other papers discuss this important assumption further, and thus, it may be still an open question needing to be resolved in experiments.

Since there is a possibility of the existence of NO2, trans-ONONO2, and

cis-ONONO2 with the N2O4 (D2h) as oxidizers, the N2H4+NO2, N2H4+cis-ONONO2,

N2H4+trans-ONONO2, and N2H4+N2O4(D2h) reactions should be considered for this

combustion system. After all, in order to account for the hypergolic phenomenon in the reactions, the products of these reactions have to be produced as reactive radicals fast and exothermically to make the reactions occur violently.

18

1.4 References

(1) Martin J. L. Turner, Rocker and Spacecraft Propulsion, 3rd ed (2009)., Springer Berlin Heidelberg.

(2) Harold G. Weiss, Technical report: A basic study of the nitrogen tetroxide -

hydrazine reaction, Jet Propulsior Laboratory Contract No. BE4-229751 (1965)

(3) Martin Herscb, Performance and stability characteristics of nitrogen tetroxide –

hydrazine combustors, NASA Technical Note D-4776 (1968)

(4) B.R. Lawver and B. P. Breen, Hypergolic stream impingement phenomena –

nitrogen tetroxide / hydrazine, NASA-CR-72444 (1968)

(5) Marshall C. Burrows, Mixing and reaction studies of hydrazine and nitrogen

tetroxide using photographic and spectral trchniques, NASA-TN-D-4467 (1968)

(6) L.B. Zung and J.R. White, Combustion process of impinging hypergolic

propellants, NASA-CR-1704 (1971)

(7) Frank H. Verhoek and Ferrington Daniels, J. Am. Chem. Soc., 53 (4), 1250 (1931) (8) F.B.C. Machado and O. Roberto-Nero, Chem. Phys. Lett., 352, 120 (2002)

(9) K. Kohata, T. Kukujama, and K. Kuchitsu, J. Phys. Chem. 86, 602 (1982) (10) W.F. Giauque and J.D. Kemp, J. Chem. Phys., 6, 40 (1938)

(11) I.C. Hisatsune, J. Phys. Chem., 65, 2249 (1961)

(12) A. Gutman and S.S. Penner, J. Chem. Phys. 36, 98 (1962) (13) M. Cher, J. Chem. Phys. 37, 2564 (1962)

(14) C.H. Bibart and G.E. Ewing, L. Chem. Phys., 61, 1284 (1974)

(15) L. Koput, J.W.G. Seibert, and B.P. Winnewisser, Chem. Phys. Lett. 204, 183 (1993)

19 Phys. 118, 4060 (2003)

(17) W.G. Fateley, H.A. Bent, and B. Crawford, J. Chem. Phys. 31, 204 (1959) (18) J.D. Baldeschwieler, PhD. Thesis, University of California (Berkeley), 1959 (19) I.C. Hisatsune, J.P. Devlin, and Y. Wada, J. Chem. Phys., 33, 714 (1960) (20) R. V. St. Louis and B. Craeford, J. Chem. Phys., 42, 857, 1965

(21) L. Parts and J.T. Miller, J. Chem. Phys. 43, 136 (1965)

(22) F. Bolduan, H.J. Jodi, and A. Loewenschuss, J. Chem. Phys., 80, 1739 (1984) (23) L. H. Jones, B.I. Swanson, and S.F. Agnew, J. Chem. Phys., 82, 4389 (1985) (24) A. Givan and A. Loewenschuss, J. Chem. Phys., 90, 6135 (1989)

(25) A. Givan and A. Loewenschuss, J. Chem. Phys., 91, 5126 (1989) (26) A. Givan and A. Loewenschuss, J. Chem. Phys., 93, 866 (1990) (27) A. Givan and A. Loewenschuss, J. Chem. Phys., 93, 7592 (1990) (28) A. Stirling, I. Papai, J. Mink, J. Chem. Phys., 100, 2910 (1994) (29) M.L. McKee, J. Am. Chem. Soc., 117, 1629-1637 (1995)

(30) E.D. Glendening and A.M. Halpern, J. Chem. Phys., 127, 164307 (2007) (31) X. Wang, Q. Qin, K. Fan, J. Molecular Structure, 432, 55-62, (1998)

(32) I.I. Zakharov, A.I. Kolbasin, O.I. Zakharova, I.V. Kravchenko, and v.i. Dyshlovoi, Theoretical and Experimental Chemistry, 44, 26 (2008)

(33) X. Wang, Q. Qin, J. Molecular Structure, 76, 77-82 (2000)

(34) A.S. Pimentel, F.C.A. Lima, and A.B.F. da Silva, J. Phys. Chem. A, 111, 2913-2920 (2007)

20

II. Computation Methods

2.1 Ab-initio Calculations

The equilibrium geometries, including reactants, complexes, transition states (TS), and products, have been optimized at the B3LYP/6-311++G(3df,2p) level in both NO2+N2H4 and N2O4+N2H4 reactions. The zero-point energies and the harmonic

vibrational frequencies have been also determined by the B3LYP method, which is the Becke’s three-parameter nonlocal exchange functional (1) with the nonlocal correlation functional of Lee, Yang, and Parr (2). All the stationary points have been positively identified for local minima (number of imaginary frequencies NIMAG=0), transition states (NIMAG=1), and higher order top (NIMAG>1). In order to confirm that the transition states have connected between the correct complexes (intermediates), we use the intrinsic reaction coordinate (3) (IRC) calculations at the B3LYP/6-311++G(3df,2p) level.

In order to obtain the more reliable energies, we have used the higher level computational methods to calculate the single-point energies with structures optimized by B3LYP/6-311++G(3df,2p). In the NO2+N2H4 reaction, the CCSD(T)/6-311+G(d,p),

CCSD(T)/6-311G(3df,2p), the CC1 scheme of modified G2 (G2M) (4), and G3B3 (5,6) have been employed to achieve more reliable evaluation of energies. In the N2O4+N2H4

reaction, there are four nitrogen atoms, four oxygen atoms, and four hydrogen atoms; hence, the higher-level ab-initio calculations could only be done by a large amount of computational resources. Due to the limitation of the resource, we have only calculated the single-point energies by CCSD(T)/6-311+G(d,p) and the CC3 scheme of modified G2 (G2M) method. In the Potential Energy Surface (PES), the total energy of each equilibrium geometry is composed of the zero-point energy determined by

21

B3LYP/6-311++G(3df,2p) and the single-point energy calculated by high-level ab-initio calculations. All of the ab-initio calculations have been performed by the Gaussian03 program, and the calculation theories are summarized in Appendix II.

2.1.1 Modified GAUSSIAN-2 (G2M)

This method is developed by Mebel and coworkers; it improves the G2 method in many places. First, for the open shell species, G2 uses the unprojected MPn energies, but spin-projected MPn energies are expected to be more reliable than UMPn ones, especially for the systems with large spin contamination. However, the spin contamination problems occur not only on UMPn methods but also on the (unprojected) QCISD(T) method. On the other hand, the zero-point energy (ZPE) of the G2 method is from HF/6-31G* method, and it is better to include the electron correlations. Therefore, G2M method improves the G2 method by using PUMPn, CCSD(T) methods, and the ZPE at B3LYP levels. The following eq. is the G2M(CC1) and G2M(CC3) methods.

E(G2M(CC1))= ( ) (2 ) ( ) ( , 1) [ 4 / 6 311 ( , )] ( ) [ 4 / 6 311 ( , )] (2 ) [ 4 / 6 311 (2 , )] ( ) [ ( ) / 6 311 ( , )] [ 2 / 6 311 (2 , bas bas bas bas bas E E E df E CC E HLC CC ZPE E E PMP G d p E E PMP G d p E E df E PMP G df p E E CC E CCSD T G d p E E PMP G df p + ∆ + + ∆ + ∆ + ∆ + ∆ + = − ∆ + = − + − ∆ = − − ∆ = − − ∆ = − + )] [ 2 / 6 311 (2 , )] [ 2 / 6 311+ ( , )]+ [ 2 / 6 311 ( , )] ( , 1)= 0.00019 E PMP G df p E PMP G d p E PMP G d p E HLC CC xn_β n_α − − − − − ∆ − −

where the PMPn stands for the spin-projected PUMPn energies for open shells and restricted RMPn energies for closed shell. The ∆E(HLC,CC1), the higher level correction, is defined by the number of α and β valence electrons, with n_α ≥n_β. Furthermore, the x value for ∆E(HLC,CC1) is optimized for each of modified G2

22

schemes, minimizing the average absolute deviation of calculated atomization energies from experiment values for the G2 sample set of molecules. The ZPE is determined at the B3LYP level, which is the same method as geometry optimization. The G2M(CC3) is similar with G2M(CC1) but with some simplification.

' ' ' ' E(G2M(CC3))= ( ) (2 ) ( ) ( , 3) [ 4 / 6 311 ( , )] ( ) [ 4 / 6 311 ( , )] (2 ) [ 2 / 6 311 (2 , )] [ 2 / 6 311 ( , )] ( ) [ ( ) / 6 311 ( , )] bas bas bas bas E E E df E CC E HLC CC ZPE E E PMP G d p E E PMP G d p E E df E PMP G df p E PMP G d p E CC E CCSD T G d p E E + ∆ + + ∆ + ∆ + ∆ + ∆ + = − ∆ + = − + − ∆ = − − − ∆ = − − ∆ = [ 2 / 6 311 (2 , )] [ 2 / 6 311 (2 , )] [ 2 / 6 311+ ( , )]+ [ 2 / 6 311 ( , )] ( , 3)= 0.19 UMP G df p E UMP G df p E UMP G d p E UMP G d p E HLC CC xn_β n_α − + − − − − − ∆ − −

The following tables are the summary of the other branch methods in G2M, including the parameters.

23

Table2-2: Comparison of the accuracy and the range of applicability for various modified Gaussian-2 (G2M) methods.(4)

24

2.1.2 Gaussian-3 theory using DFT geometries and zero-point energies (G3B3)

The G3B3 method (5) is based on the Gaussian-3 theory (G3) and used the geometries and zero-point energies by B3LYP calculations. The G3 method uses geometries by MP2(FC)/6-31G(d) and scaled zero-point energies by HF/6-31G(d) followed by a series of single-point energy calculations at the MP2, MP4, and QCISD(T) levels. The detail of the G3 method is presented in the Table2-3. It includes a spin-orbit correction and a higher-level correction; therefore, the average absolute derivation between experimental data and G3 theory for 299 energies is 1.01 kcal/mol. It performs much more accurate and requires less computation time than the G2 theory. In the modified version of the G2 method, such as G2M (4), G2(MP2) (7), G2(MP2,SVP) (8) methods, they use different methods to determine the geometries and zero-point energies for getting better computation results. They suggested that using B3LYP methods has many advantages. First, the frequencies and zero-point energies obtained at the B3LYP level have improved much more than those obtained at the HF level, and B3LYP geometries may be easier and cheaper to obtain than MP2 geometries for larger systems. The accuracy of density functional theory for calculation of geometries has been examined in several studies. (9,10) For the above reasons, Redfern’s group presents variations of G3 and G3(MP2) theories that use the B3LYP density functional method for geometries and zero-point energies in place of the MP2/6-31G(d) geometries and scaled HF/6-31G(d) zero-point energies. These two variations were referred to as G3//B3LYP (G3B3) and G3(MP2)//B3LYP. On the other hand, there is another variation for zero-point energy calculations; that is introducing the new scaling factor. As the scaling factor is optimized (along with the high-level correction parameters), it gives a smallest average absolute derivation. The scaling factor in G3B3 is 0.925.

25

However, such a low scaling factor for B3LYP is clearly nonphysical and may compensate for other deficiencies. In the end, the new scaling factor for the zero-point energy was recommended to be 0.96. In the table2-3, we can realize clearly what the difference between G3 and G3B3 is.

Table2-3: Steps in G3, G3(MP2), G3//B3LYP, and G3(MP2)//B3LYP methods. (5)

By the comparing with the experimental energies of 299 species, the average results for these four methods are given in the following table.

26

2.2 Kinetic Calculation

The canonical Transition State Theory (cTST) is employed to calculate the rate constants for the biomolecular and unimolecular reactions. In addition, the quantum tunneling effects are included in the rate constant calculations with the Eckart tunneling model. With the transition state theory, the thermal rate constant of a reaction can be expressed as

( )

( )

( )

[

]

( )

TS TS B r B

Q

T

E

k T

k T

T

Exp

h

Q T

k T

κ

σ

−∆

=

Where κ( )T is the transmission coefficient accounting for the quantum tunneling effect;

σ

is the reaction symmetry number; Q_TS( )T and Q T_r( )are the total partition

functions of the transition state and reactants, respectively; ∆E_TS is the classical

energy barrier for the transition state at 0K. The conventional T, kB, and h are

temperature, Boltzmann constant and Planck constant, respectively. The details of partition functions are shown in Appendix 1.11. The kinetics of a reaction was computed by the Rate Program at the platform of Computational Science and Engineering Online (CSE-online)(11).

27

2.3 Reference

(1) (a) A. D. Becke, J. Chem. Phys. 98, 5648 (1993); (b) 96, 2155 (1992); (c) 97, 9173 (1992)

(2) C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988) (3) C. Gonzalez and H. B. Schlegel, J. Phys. Chem. 90, 2154 (1989)

(4) A. M. Mebel, K. Morokuma, and M. C. Lin, J. Chem. Phys. 103, 7414 (1995) (5) A. G. Baboul, L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys.

110, 7650 (1999)

(6) B. Anantharaman and C. F. Melius, J. Phys.Chem. A 109, 1734-1747 (2005) (7) L. A. Curtiss, K. Raghavachari, and J. A. Pople, J. Chem. Phys. 98, 1293 (1993) (8) (a) J. Smith and L. Radom, J. Phys. Chem. 99, 6468 (1995);

(b) L. A. Curtiss, P. Redfern, B. J. Smith, and L. Radom, J. Chem. Phys. 104, 5148 (1996)

(9) C. W. Bauschlicher, Chem. Phys. Lett. 246, 40 (1995)

(10) B. G. Johnson, P. M. W. Gill, and J. A. Pople, J. Chem. Phys. 98, 5612 (1993) (11) Computational Science and Engineering Online. http://www.cse-online.net/

28

III.

Results and Discussions

3.1

N

2

H

4

+NO

2

reaction

In the first section, we focus on N2H4 and NO2 reaction, which is one of the

possible reactions in the hydrazine and dinitrogen tetroxide combustion system, since the NO2 always co-exists with N2O4 in the equilibrium state. The characteristic bond

lengths and angles of optimized geometries in this reaction are discussed, including reactants, complexes, transitions states (TS), and products at the B3LYP / 6-311++G(3df,2p) calculation level, showed in Fig3-1. Next, we describe the reaction channels in the full potential surface energy surface (PES) of the N2H4+NO2 reaction,

whose energies obtained by G2M(CC1) calculation shown in Fig.3-2. Furthermore, the moments of inertia and vibrational frequencies are represented in Table3-1. Table3-2 displays the details of relative energies computed by various computational methods. Finally, we predict the rate constants for the reaction channels by mean of the Transition State Theory (TST).

3.1.1 Molecular Geometries of hydrazine and nitrogen dioxide

Reactants, hydrazine and nitrogen dioxide, are well-studied molecules, and we compare the geometries and vibrational frequencies with the computational and experimental data, as shown in Tables 3-3 to 3-5. In Table3-3, comparing with the experimental data, the N-N bond of N2H4 predicted by B3LYP is smaller by 0.015Å; at

the CCSD(T) level the agreement between theory and experiment is very good. In the case of the bond angles, both B3LYP and CCSD(T) methods have good predictions.

29

Therefore, the geometry by B3LYP calculation is still reliable as CCSD(T) does. Furthermore, in Table3-4, the vibrational frequencies are over-predicted by the B3LYP, MP2, and CCSD(T) methods; the most serious difference results from the MP2 method. In the high frequency region, B3LYP and CCSD(T) give similar values. The B3LYP method has a much serious over-prediction problem in the low frequency region, which is higher than 40 cm-1 on average. On the other hand, for the N-O bond of the NO2

molecule, the B3LYP method performs slightly better than the CCSD(T) and CASSCF methods. The errors of bond length between calculations and the experimental data are less than 0.01Å, and they have similar values in the bond angle. Moreover, the average error of vibrational frequencies predicted the B3LYP method is about 20 cm-1, which is a reliable prediction. Comparing with DFT calculation, the CCSD(T) and CASSCF methods need much computational resources, and the MP2 method suffers from spin contamination in many cases. Therefore, according to comparison between the DFT method (B3LYP) and the MP2, CCSD(T), CASSCF methods for prediction of geometries and vibrational frequencies of N2H4 and NO2 molecules, the former can not

only save computational resources for larger molecular systems, it can also have a reliable prediction.

3.1.2 PES of the N2H4 + NO2 reaction

There are four product channels in the N2H4+NO2 reaction, are presented in

Fig3-2. Three of them are hydrogen-abstraction reactions, and the other is the oxygen transfer reaction. In the hydrogen-abstraction channels, the products are similar, including cis-HONO+N2H3, trans-HONO+N2H3, and HNO2+N2H3 for channel-1,

30

intermediate in the combustion of many nitramine propellants, and hydrazinyl radical (N2H3) is very reactive with other species due to one unpaired electron in the open shell

configuration. Therefore, the N2H3 radical and HNO2 isomers can play an important role

in the hypergolic combustion reaction. In the N2H4+NO2 reaction, every channel starts

to react from complex1, which originates from the physical attraction of the two reactants. This intermediate is lower in energy by 2.50 kcal/mol relative to the reactants at the G2M(CC1) level, and the closest distance of the two molecules is 2.494 Å. The hydrogen bond between O and H may be the reason for the decrease in the energy of complex1, and this makes the N-O bond of NO2 and the N-N bond of N2H4 slightly

longer. Moreover, the NO2 and N2H4 in complex1 still maintain their symmetries.

In channel-1, in the beginning, complex1 is transformed to complex2 through TS1, the relative energy of which is 2.56 kcal/mol and is lower than complex2 by 0.81 kcal/mol. TS1 is a transition state to change the symmetry of N2H4, and the imaginary

frequency is only 114 cm-1, corresponding to a rotation motion. According to Table3-2, the energy difference between complex2 and TS1 is -0.7 to -0.8kcal/mol by single-point calculations. Therefore, we believe the small negative value should originate from a calculation error (less than 1 kcal/mol in normal situations). On the other hand, the increase in the energy of complex2 result from the structural change of N2H4 in

complex2, from C2 symmetry to its anti-form (C2h symmetry)(21), the energy of C2h

form is much higher than that of C2 symmetry. Therefore, the energy of complex2 is the

balance between creating hydrogen bonds and the high energy conformation of N2H4.

Since complex1 and complex2 are the physical attraction of the two reactant molecules, the bond lengths (N-H, N-N, and N-O) and bond angles (H-N-H) have only a small difference comparing with the separate single molecules, except that the bond angle of O-N-O decreases by 5 degrees due to the formation hydrogen bonds. To produce the

31

cis-HONO and N2H3, complex2 needs to cross over TS2, whose energy barrier is 4.2

and 7.6 kcal/mol at the G2M(CC1) level with respect to complex2 and the reactants, respectively. The intrinsic reaction coordinate (IRC) calculation of TS2 in the direction of the products indicates the formation of the O-H bond and the breaking N-H bond, resulting in the production of the cis-HONO and N2H3 radical. This hydrogen transfer

breaks the symmetry of complex2 and elongates the N-O bond to connect with the hydrogen into an N-O-H form, but the change in the other N-O bond is less significant. In the mean time, the N-N bond shortens by 0.9 Å to balance the loss of one electron. At the next step, complex3, the association complex of cis-HONO and the N2H3 radical,

dissociates to two independent molecules; with 8.4 and 9.5 kcal/mol energies predicted at G2M(CC1) and CCSD(T)/6-311G(3df,2p) levels of theory.

Comparing complex1 with complex2, the hydrogen is in a different position relating to NO2. For complex2, the two hydrogen atoms are in the inner side of the

N-O-N angle, whereas the hydrogen is in the outer side of O-N-O angle of complex1, as presented in Fig3-1. Therefore, the products are cis-HONO+N2H3 and

trans-HONO+N2H3 in channel-1 and channel-2, respectively. In channel-2, complex1

directly goes through TS3, whose energy barrier is 15.5 and 13.0 kcal/mol with respect to complex1 and the reactants at the G2M(CC1) level, producing complex4 (trans-HONO and N2H3). TS2 and TS3 have similar hydrogen transfers, but the position

of the hydrogen atom between the oxygen atom of NO2 and nitrogen atom of N2H4 is

different. The distances between the hydrogen and nitrogen of N2H4 are 1.144 Å and

1.083Å, and those between hydrogen and oxygen of NO2 are 1.395Å and 1.528Å for

TS2 and TS3, respectively. This means that the energy for hydrogen transfer will be higher as the hydrogen atom is closer to the nitrogen. On the other hand, TS2 and TS3 have the same tendencies in bond lengths and the bond angle of N2H3 and NO2, as

32

discussed above. The last step is also a dissociation of complex4 into N2H3 and

trans-HONO, whose energy is 10.5 and 12.2 kcal/mol predicted at the G2M(CC1) and CCSD(T)/6-311G(3df,2p) levels. Furthermore, the arrangement of the two molecules in complex3 and complex4 may mean that the hydrogen bonding in complex3 is weaker than in complex4. Therefore, the dissociate energy of complex4 is higher than that of complex3.

In channel-3, which also occurs by hydrogen transfer, it connects a hydrogen atom of N2H4 with the nitrogen atom of NO2. Complex1 twists its N-N bond of N2H4 to

form TS4, bringing the hydrogen atom closer to the nitrogen atom of NO2. The energy

of TS4 is 11.86 and 9.36 kcal/mol above complex1 and the reactants, respectively, at the G2M (CC1) level. The characteristic of bond lengths and angles in TS4 has the same trend as in TS2 and TS3. The IRC calculation of TS4 confirms the hydrogen transfer to form complex5, which is composed of N2H3 and HNO2. The dissociation energy from

complex5 to the two separated molecules is 11.8 and 13.7 kcal/mol predicted at the G2M(CC1) and CCSD(T)/6-311G(3df,2p) levels. Comparing the three products from channel-1 to channel-3, the dissociation energies are high and close. Therefore this infers that the physical attractions and the hydrogen bonding are similar and important in these three systems.

Channel-4 is the pathway in which oxygen is transferred to produce NO, instead of hydrogen transfer reaction; this process has to pass through a very high energy barrier via TS5, in which one N-O bond breaks in NO2, creating another N-O bond with N2H4.

The N-N bond in N2H4 decreases by 0.4Å, which is less than that in TS2, and the N-O

bond not involved in the oxygen transfer increases by 0.5Å at TS5. Furthermore, the oxygen is located in the middle of the nitrogen atoms of NO2 and the nitrogen atom of

33

106.5o, and the O-N-O angle of NO2 molecule is decreased from 134.5 o to 109.8o. Since

the NO double bond in NO2 is originally short (1.190Å), the elongation of this bond at

TS5 by over 0.25Å makes the energy barrier (which is 48.47 and 45.97 kcal/mol relative to complex1 and reactants, respectively) very high comparing with the transition states for the hydrogen transfer. After passing through TS5, complex6 consisting of NO and H2NN(O)H2 molecule. The H2NN(O)H2 isomerizes to

H2NN(H)OH via TS6, which is a more stable molecule obeying the Octet rule. The

unimolecular reaction via TS6 involves hydrogen migration from the nitrogen to the oxygen with releasing of energy giving the more stable molecule, H2NN(H)OH.

In this computational work, we use G3B3, CCSD(T),and G2M methods to improve single-point energies based on the geometries at B3LYP/6-311++G(3df,2p). In Table3-2, the energies predicted by these methods are slightly different, but with the same trends. Based on few experimental data, we only compare the heats of the reaction for the cis-HONO+N2H3 and trans-HONO+N2H3 products. The experimental reference

for ∆fHoT of the N2H3 radical is the experimental study of Ruscic and Berkowitz(22). The

heat of reaction in N2H4
N2H3+H is 3.50±0.01 eV (80.8±0.3 kcal/mol), and ∆Hf of

N2H3 would be 55.3±0.3 kcal/mol after calculation with the values of ∆Hf(N2H4) and

∆Hf(H). Moreover, if we use the values of ∆Hf(N2H4) and ∆Hf(H) given in the NIST

database(23,24), the ∆Hf(N2H3) will be 55.333 kcal/mol, which is almost the same as the

study of Ruscic. On the other hand, the ∆Hf(N2H3) is computed as 56.2 and 53.7

kcal/mol at 0K and 298K by Matus et al.(25), but they do not compare with the experimental data. After applying the ∆Hf(trans-HONO), ∆Hf(cis-HONO), and

∆Hf(N2H3), which are -17.36(23), -16.84(23), 55.333 kcal/mol, respectively, the heat of the

reaction is 3.25 and 3.76 kcal/mol for the products trans-HONO+N2H3 and

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computational results, G3B3 and G2M(CC1) perform well, but the heat of reaction for trans-HONO+N2H3 is higher than that for cis-HONO+N2H3 at CCSD(T)

/6-311G(3df,2p). However, since the difference of two CCSD(T) values are less with the trans product energy slightly higher than the cis-counterpart than 0.7 kcal/mol, which is within the accuracy of these methods. Comparing the experimental data, the errors of the computational result are -0.32, -0.33, and 0.66 kcal/mol for ∆H(cis-HONO+N2H3) and 0.68, -0.32, and 0.51 kcal/mol for ∆H(trans-HONO+N2H3)

predicted at CCSD(T)/6-311G(3df,2p), G2M(CC1), and G3B3 methods, respectively. 3.1.3 Kinetic calculation

Based on the PES presented in the preceding section, we consider the N2H4+NO2 reaction to proceed through TS2-TS4 and calculate the rate constants by

employing the transition-state theory.(25,26) For these kinetic calculations, we use the barrier heights obtained at G2M(CC1) and molecular geometries of the reactants and transition states at B3LYP/6-311++G(3df,2p) presented in Table3-1. We use the conventional TST method with Eckart’s tunneling corrections. The Arrhenius plots of various rate constants are shown in Fig3-3, and the three-parameters fitting expressions for the rate constants are presented in Table3-6.

The lowest-energy channel is channel-1, N2H4+NO2→complex1→TS1→complex2

→TS2→complex3→cis-HONO+N₂H₃ (channel-1) The rate constant k1, which is controlled mainly by TS2, is the highest at any

temperature among the three channels. The activation energy is 7.6 kcal/mol, and channel-2 and channel-3 have similar reaction paths, namely

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N2H4+NO2→complex1→TS4→complex5→HNO₂+N₂H₃ (channel-3)

The activation energy of Channel-4 is too high and therefore, we do not calculate its rate constant. In Fig.3-3, the rate constants of channel-3 (k3) is higher than that of channel-2

(k2) at a low temperature, whereas the k2 is slightly lower than k3 at a high temperature.

Although the activation energy of channel-2 is higher than that of channel-3 by 3.6 kcal/mol, the A factor, which is also called the pre-exponential factor, and temperature dependence are also more important as temperature increases. Unfortunately, as mentioned in the introduction, there is no experimental result for comparison with our predicted values.

36 (a) Reactants

37

38 (d) Products

39

Table3-1: Moments of inertia (IA, IB, IC) and vibration frequencies of the species computed at the B3LYP/6-311++G(3df,2p) level.

Species or

Transition States Moments of inertia Ii(a.u) Vibrational Frequency υj (cm

-1₎ N2H4 12.4, 74.2, 74.3 439, 801, 974, 1114, 1294, 1323, 1674, 1686, 3462, 3471, 3562, 3568 NO2 7.4, 137.6, 145.0 767, 1395, 1703 complex1 189.1, 757.8, 919.2 36, 77, 78, 723, 155, 174, 434, 763, 805, 970, 1115, 1297, 1321, 1383, 1668, 1680, 1702, 3464, 3470, 3556, 3567 complex2 189.8, 799.2, 898.3 60, 69, 93, 93, 131, 164, 200, 627, 914, 999, 1113, 1158, 1314, 1483, 1600, 1633, 1686, 3400, 3473, 3491, 3555 complex3 134.9, 992.7, 1126.8 39, 47, 124, 133, 202, 252, 487, 688, 703, 976, 992, 1142, 1293, 1453, 1490, 1662, 1673, 3063, 3473, 3513, 3650 complex4 144.2, 838.5, 981.5 92, 94, 158, 196, 232, 251, 485, 702, 728, 932, 980, 1149, 1297, 1470, 1534, 1653, 1653, 1740, 3112, 3487, 3499, 3630 complex5 151.3, 786.0, 936.4 68, 120, 165, 216, 244, 266, 481, 720, 787, 1149, 1191, 1374. 1470, 1564, 1634, 1660, 2866, 3480, 3493, 3626 complex6 178.8, 618.4, 717.8 73, 106, 161, 239, 318, 371, 489, 841, 998, 1049, 1191, 1297, 1443, 1458, 1647, 1678, 1810, 3124, 3320, 3456, 3530 N2H3 8.8, 58.6, 66.5 548, 696, 1136, 1238, 1479, 1658, 3425, 3488, 3632 trans-HONO 19.0, 143.1, 162.1 590, 621, 819, 1303, 1783, 3773 cis-HONO 21.1, 135.9, 157.0 635, 695, 876, 1342, 1716, 3597 HNO2 16.7, 136.1, 152.8 796, 1060, 1410, 1514, 1650, 3173 H2NN(H)OH 41.4, 172.3, 194.6 290, 473, 793, 988, 1039, 1200, 1272, 1437, 1440, 1662, 1676, 3239, 3249, 3445, 3516 H2NN(O)H2 41.1, 177.7, 199.6 319, 455, 492, 795, 853, 1044, 1184, 1265, 1389, 1511, 1688, 3436, 3506, 3567, 3822 NO 0, 34.9, 34.9 1979 TS1 191.8, 809.1, 906.6 114i, 51, 68, 96, 117, 141, 191, 634, 910, 996, 1106, 1173, 1317, 1470, 1615, 1636, 1688, 3402, 3472, 3512, 3557 TS2 169.0, 692.1, 769.7 657i, 81, 144, 180, 260, 287, 466, 619, 782, 934, 1123, 1177, 1269, 1439, 1458, 1573, 1653, 1745, 3491, 3536, 3660 TS3 147.0, 730.7, 870.7 622i, 91, 118, 168, 204, 259, 374, 595, 805, 978, 1068, 1137, 1273, 1492, 1524, 1621, 1673, 2225, 3536, 3543, 3686 TS4 160.0, 682.4, 827.1 1053i, 81, 99, 215, 284, 331, 510, 679, 760, 823, 1115, 1210, 1306, 1375, 1497, 1550, 1665, 1741, 3451, 3512, 3582 TS5 149.4, 532.8, 615.8 1032i, 104, 208, 270, 291, 387, 655, 747, 856, 941, 1127, 1185, 1225, 1382, 1470, 1627, 1696, 3008, 3474, 3530, 3561 TS6 40.9, 182.8, 205.2 1694i, 312, 423, 798, 835, 947, 1157, 1186, 1320, 1453, 1688, 2757, 3428, 3517, 3548

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Fig 3-2: Potential Energy Surface of the N2H4+NO2 reaction, whose energies are calculated by G2M(CC1)//B3LYP/6-311++G(3df,2p).

0 kcal/mol G2M(CC1) TS2 TS3 TS5 Complex2 Complex3 N2H4(C2)+NO2(C2v) Complex1 Complex4 N2H3+cis-HONO N2H3+trans-HONO H2NN(O)H2+NO 18.55 2.93 3.43 7.57 3.37 -4.94 12.96 -2.50 -7.56 45.97 17.22 complex6 TS6+NO 47.53 -1.27 H2NN(H)OH+NO TS4 9.36 Complex5 -0.51 11.29 N2H3+HNO2

~

_~

TS1

~

_~

2.56