%40تخفیف

A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H2S ‏+ O3 Reaction& A Theoretical Study on the Dynamics of the C2H4+ S Reaction on an Interpolated Potential Energy Surface

Name: A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H2S ‏+ O3 Reaction&amp; A Theoretical Study on the Dynamics of the C2H4+ S Reaction on an Interpolated Potential Energy Surface
SKU: 14714
Price: 210000 IRR
Availability: InStock

تعداد181 صفحه در فایل word

Ph. D. Dissertation in Chemistry (Physical Chemistry)

A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H₂S ‏+ O₃ Reaction&

A Theoretical Study on the Dynamics of the C₂H₄+ S Reaction on an Interpolated Potential Energy Surface

In the first part, the kinetics and mechanism of the gas-phase reactions between H₂S with O₃ have been theoretically investigated. Three different pathways are suggested to be possible for the H₂S + O₃ reaction. The potential energy surface for each possible pathway has been studied by employing DFT and ab initio methods. The kinetics of three different pathways are also reported. Multichannel RRKM-SSA calculations have been carried out to calculate the individual and overall rate coefficients. Also, the rate coefficients were calculated using canonical variational transition state theory (CVT) and canonical variational transition state theory with small-curvature tunneling contributions (CVT/SCT) in the temperature range of 300–3000K. Curvilinear coordinates are utilized for vibrational frequency calculations at nonstationary points. Dual-level dynamics calculations are performed with the VTST-ISPE approach at the CCSD(T)/Aug-cc-pVTZ//MPWB1K/6-31+G(d,p) level. The major products are sulfur dioxide (SO₂) and water at lower temperatures, in good agreement with experimental reports, while at higher temperatures, formation of the other products like O₂, H₂SO, and radicals like SH, OH, cis/trans-HOSO and HO₃also become important.

In the second part, we have studied the dynamics of the C₂H₄+ S reaction on an interpolated potential energy surface. A theoretical study of the lowest singlet and triplet surfaces of C₂H₄S were done by using the GROW package of Collins and co-workers. We have used a modified form of the Shepard interpolation of ab initio molecular potential energy surface for these reactions. The ab initio calculations have been done using Becke three-parameter nonlocal exchange functional with the nonlocal correlation of Lee, Yang, Parr density functional theory. These surfaces are presented by an interpolation of second order Taylor expansion at 2000 molecular configurations. New data point selection methods were used to improve the convergence and accuracy of the interpolated surface. Classical trajectory studies on these surfaces reveal that the reaction rate has good agreement with previous reports.

دسته: زبان شناسی, علوم انسانی برچسب: A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H2S ‏+ O3 Reaction& A Theoretical Study on the Dynamics of the C2H4+ S Reaction on an Interpolated Potential Energy Surface

توضیحات

Subject	PAGE
Chapter one. Introduction and Literature Review ……………………………………	1
1.1 Kinetics of H₂S + O₃ Reaction ………………………………………………………	2
1.2 Dynamics of C₂H₄+ S Reaction …………………………………………………….	4
Chapter two. Theory and Methodology ………………………………………………	7
2-1 Potential Energy Surface (PES) …………………………………………………….	8
2-1-1 The Born-Oppenheimer Approximation …………………………………………	9
2-1-2 Methods to Calculate the Energy …………………………………………………	12
2-1-2-1 T1 Diagnostic …………………………………………………………………	16
2-2 Dynamics ……………………………………………………………………………	17
2-2-1 Interfacing the dynamics calculations to the potential energy surface …………..	18
2-2-1-1 Analytic Potential Energy Surfaces ……………………………………………	18
2-2-1-2 Straight Direct Dynamics ……………………………………………………..	19
2-2-1-3 Interpolated Variational Transition State Theory (IVTST) ……………………	19
2-2-1-4 Dual-Level Dynamics …………………………………………………………	20
2-3 Potential Energy Surfaces by Interpolation …………………………………………	21
2-3-1 Molecular Coordinates ……………………………………………………………	21
2-3-2 Local Shape of the PES …………………………………………………………..	23
2-4 Minimum Energy Path ………………………………………………………………	25
2-5 Collision Theory …………………………………………………………………….	27
2-6 Trajectory Calculation ………………………………………………………………	31
2-7 The Reaction Probability, Reaction Cross-Section and Rate Constant Calculations in Quasiclassical Trajectory Method (QCT) ………………………………………….	32
2-8 Rate Theory for Simple Barrier Reaction .………………………………………….	34
2-8-1 Conventional Transition State Theory ……………………………………………	34
2-8-2 Variational Transition State Theory ………………………………………………	37
2-8-3 Canonical Variational Transition State Theory ………………………………….	40
2-9 Validation Against Accurate Quantum Mechanical Dynamics …………………….	42
2-9-1 Tunneling and the Transmission coefficient ……………………………………..	42
2-9-2 Multidimensional Tunneling Corrections Based on the Adiabatic Approximation …………………………………………………………………………..	45
2-10 Unimolecular Reaction Theory ……………………………………………………	52
2-10-1 The Hinshelwood Revision of Lindemann Mechanism ………………………..	53
2-10-2 The RRKM Theory ……………………………………………………………..	55
2-10-3 Application of the RRKM Theory for Unimolecular Dissociation/Elimination Reactions – The Strong Collision Model ………………………………………………	57
2-10-4 Comparison of RRKM and Transition State Theories ………………………….	59
2-11 Chemically Activated Reactions …………………………………………………..	60
2-12 Statistical Mechanics ………………………………………………………………	63
2-13 Molecular Dynamics and Monte Carlo Simulations ………………………………	68
2-13-1 Molecular Dynamics ……………………………………………………………	69
2-13-2 Monte Carlo Simulations ……………………………………………………….	72

Chapter Three. Results and Discussion: Multichannel RRKM-TST and Direct-Dynamics CVT Study of the Reaction of Hydrogen Sulfide with Ozone …………….	74
3-1 Introduction …………………………………………………………………………..	75
3-2 Computational Method ………………………………………………………………	76
3-3 Geometries and Potential Energy Surfaces ………………………………………….	84
3-4 Calculation Methods of the Rate Constants …………………………………………	96
3-4-1 RRKM-SSA method for Rw1 to R9 ………………………………………………	96
3-4-2 Canonical Variational Transition State Theory Calculations ……………………..	105
3-4-2-1 Computational Details ………………………………………………………….	105
3-5 Conclusion ……………………………………………………………………………	123

Chapter Four. Results and Discussion: A Theoretical Study on the Dynamics of the C₂H₄+ S Reaction on an Interpolated Potential Energy Surface …………………….	125
4.1 Introduction …………………………………………………………………………..	126
4.2 Methods and computational details …………………………………………………..	128
4.2.1 Constructing the Potential Energy Surface ………………………………………..	128
4.2.2 Confident weights …………………………………………………………………	131
4.2.3 Iterative development of the PES ………………………………………………….	133
4.2.4 Ab initio calculations ………………………………………………………………	135
4.3 Classical Dynamics …………………………………………………………………..	144
4.4 The Iteration Procedure ………………………………………………………………	144
4.5 Calculation of thermal rate constants …………………………………………………	145
4.5.1 Rate Constant of Reaction R1 ……………………………………………………..	146
4.5.2 Rate Constant of Reaction R2 ……………………………………………………..	148
4.6 An ab initio investigation of spin-allowed and spin-forbidden pathways of the gas phase reactions of S (³P) + C₂H₄ ………………………………………………….	154
4.7 Canonical Variational Transition-State Theory Calculations for Dissociation of C₂H₄S (Reaction R1^‘) …………………………………………………………………..	158
4.8 Conclusion ……………………………………………………………………………	162
References ………………………………………………………………………………..	164

LIST OF TABLES

Table	Page
3.1 Relative Energies of Various Species at Different Levels of Theory in kJ mol^-1 on the Singlet Surface ……………………………………………………………………….	93
3.2 Harmonic Vibrational Wave Numbers (cm^-1) and Moments of Inertia (amu Å²) for Various Species at the B3LYP/6-311+G(d,p) Level …………………………………….	94
3.3 Relative Energies of Various Species at Different Levels of Theory in kJ mol^-1 on the Triplet Surface ………………………………………………………………………..	95
3.4 Microcanonical Variational RRKM Results for Unimolecular Dissociation Reaction R4′ ………………………………………………………………………………………..	103
3.5 Microcanonical Variational RRKM Results for Unimolecular Dissociation Reaction R8 ………………………………………………………………………………………..	104
3.6 Microcanonical Variational RRKM Results for Unimolecular Dissociation Reaction R14 ……………………………………………………………………………………….	109
3.7 Microcanonical Variational RRKM Results for Unimolecular Dissociation Reaction R16 ……………………………………………………………………………………….	110
3.8 Rate Constants of the R12 Reaction (in s^-1) at mpwb1k method …………………….	113
3.9 Rate Constants of the R13 Reaction (in s^-1) at mpwb1k method …………………….	113
3.10 Rate Constants of the R15 Reaction (in s^-1) at mp2 method ………………………..	114
4.1 Relative Energies of Various Species on Triplet Surface of Reaction Sulfur and Ethylene at Different Levels of Theory in kJ mol^-1 ………………………………………	139
4.2 Relative Energies of Various Species at Different Levels of Theory in kJ mol^-1 on the singlet surface reaction sulfur and ethylene ………………………………………….	141
4.3 Summary of the trajectory calculations for reaction of sulfur and ethylene on triplet surface ……………………………………………………………………………………	160
4.4 Summary of the trajectory calculations for reaction of sulfur and ethylene on singlet surface ……………………………………………………………………………………	161

LIST OF FIGURES

Figure	Page
2.1 Illustration of how the steepest descent algorithm follows a path that oscillates around the minimum energy path ………………………………………………………..	27
2.2 Contour plot of a model bimolecular reaction that indicates the possible tunneling paths ………………………………………………………………………………………	51
2.3 Rate coefficient of reaction (2.84) at T=400 K as a function of pressure ……………	54
2.4 Schematic diagram of the Lindemann-Hinshelwood mechanism ……………………	55
2.5 Schematic energy diagram of a chemically activated reaction ………………………	61
2.6 Fraction of molecules that will be found at various energies above the ground- state energy for two different temperatures ……………………………………………………	68
3.1 IRC for reaction R1 at the B3LYP level ……………………………………………..	77
3.2 IRC for reaction R2 at the B3LYP level ……………………………………………..	77
3.3 IRC for reaction R3 at the B3LYP level ……………………………………………..	78
3.4 IRC for reaction R4 at the B3LYP level ……………………………………………..	78
3.5 IRC for reaction R5 at the B3LYP level ……………………………………………..	79
3.6 IRC for reaction R6 at the B3LYP level ……………………………………………..	79
3.7 IRC for reaction R7 at the B3LYP level ……………………………………………..	80
3.8 IRC for reaction R9 at the B3LYP level ……………………………………………..	80
3.9 IRC for reaction R10 at the B3LYP level ……………………………………………	81
3.10 IRC for reaction R11 at the B3LYP level …………………………………………..	81
3.11 IRC for reaction R12 at the B3LYP level …………………………………………..	82
3.12 IRC for reaction R13 at the B3LYP level …………………………………………..	82
3.13 IRC for reaction R15 at the MP2 level ………………………………………………	83
3.14 Optimized geometries of the stationary points at the MP2/Aug-cc-pVTZ level ……	89
3.15 Schematic of the PES of the reaction of H₂S + ¹O₃ at the CCSD(T)/Aug-cc-pVTZ level. The energies are corrected for ZPEs ………………………………………………	91
3.16 Schematic of the PES of the reaction of H₂S + ³O₃ at the CCSD(T)/Aug-cc-pVTZ level. The energies are corrected for ZPEs ………………………………………………	92
3.17 Arrhenius plot of the calculated rate constants for various channels of H₂S+O₃ reaction at 760 Torr pressure of N₂ ………………………………………………………	102
3.18 (a) Variation of frequencies along the MEP and (b) the vibrationally adiabatic ground-state potential , MEP , and ZPE for reaction R10 at the MPWB1K level ………………………………………………………………………………………	115
3.19 (a) Variation of frequencies along the MEP and (b) the vibrationally adiabatic ground-state potential , MEP , and ZPE for reaction R12 at the MPWB1K level ………………………………………………………………………………………	116
3.20 (a) Variation of frequencies along the MEP and (b) the vibrationally adiabatic ground-state potential , MEP , and ZPE for reaction R13 at the MPWB1K level ………………………………………………………………………………………	117
3.21 (a) Variation of frequencies along the MEP and (b) the vibrationally adiabatic ground-state potential , MEP , and ZPE for reaction R15 at the MPWB1K level ………………………………………………………………………………………	118
3.22 Thermally averaged transmission probability at 298 K for R10 reaction …………..	119
3.23 Thermally averaged transmission probability at 298 K for R12 reaction …………..	119
3.24 Thermally averaged transmission probability at 298 K for R13 reaction …………..	120
3.25 Thermally averaged transmission probability at 298 K for R15 reaction …………..	120
3.26 Arrhenius plot for reactions R10 and R11 at the CCSD(T)/Aug-cc-pVTZ level …..	121
3.27 Arrhenius plot at the CCSD(T)/Aug-cc-pVTZ level for channels R12-R16′ ………	122
4.1 A schematic representation of the twenty one bond lengths defining the C₂H₄S system, with atoms labeled as shown …………………………………………………….	130
4.2 Reaction probablity for reaction R1, as a function of the PES data set size …………	134
4.3 Reaction probablity for reaction R2, as a function of the PES data set size …………	135
4.4 Optimized geometries of the stationary points on triplet surface of reaction sulfur and ethylene at the B3LYP/cc-pVDZ level ………………………………………………	137
4.5 Relative energies of the stationary points in kJ mol^-1on triplet surface of reaction sulfur and ethylene at the CCSD(T)/aug-cc-pVTZ level …………………………………	138
4.6 IRC for reaction R1 at the B3LYP level ……………………………………………..	140
4.7 IRC for reaction R1^‘ at the B3LYP level ……………………………………………..	140
4.8 Optimized geometries of the stationary points at the B3LYP/cc-pVDZ level in Singlet Surface of reaction sulfur and ethylene ………………………………………….	142
4.9 Relative Energies of the Stationary Points in kJ mol^-1on Singlet Surface of Reaction Sulfur and Ethylene at the CCSD(T)/cc-pVDZ level ……………………………………	143
4.10 Reactive Cross Section as a function of relative kinetic energy for reaction R1 for 2000 trajectory …………………………………………………………………………..	150
4.11 Dependence on temperature of rate constant for the reaction R1 …………………	151
4.12 Reactive Cross Section as a function of relative kinetic energy for reaction R2 for 2000 trajectory …………………………………………………………………………..	152
4.13 Dependence on temperature of rate constant for the reaction R2 …………………..	153
4.14 The singlet and triplet potential energy profile of C₂H₄ + S system rigorous CCSD(T) level including ZPE ……………………………………………………………	156
4.15 IRC for the singlet and triplet surfaces of C₂H₄ + S system, Calculated at B3lyp/cc-pVDZ level …………………………………………………………………….	157
4.16 Arrhenius plot at the CCSD(T)/Aug-cc-pVTZ level for channels R1′ ……………..	159

TABLE OF SCHEMES

Scheme	Page
Scheme 1. Compelete Mechanism of The H₂S + O₃ Reaction …………………………..	85
Scheme 2. Calculated Rate coefficients from RRKM-SSA method …………………….	98

A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H2S ‏+ O3 Reaction& A Theoretical Study on the Dynamics of the C2H4+ S Reaction on an Interpolated Potential Energy Surface

تعداد181 صفحه در فایل word

Ph. D. Dissertation in Chemistry (Physical Chemistry)

A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H2S ‏+ O3 Reaction&

A Theoretical Study on the Dynamics of the C2H4+ S Reaction on an Interpolated Potential Energy Surface

CONTENTS

Subject

PAGE

Chapter one. Introduction and Literature Review ……………………………………

1

1.1 Kinetics of H2S + O3 Reaction ………………………………………………………

2

1.2 Dynamics of C2H4 + S Reaction …………………………………………………….

4

Chapter two. Theory and Methodology ………………………………………………

7

2-1 Potential Energy Surface (PES) …………………………………………………….

8

2-1-1 The Born-Oppenheimer Approximation …………………………………………

9

2-1-2 Methods to Calculate the Energy …………………………………………………

12

2-1-2-1 T1 Diagnostic …………………………………………………………………

16

2-2 Dynamics ……………………………………………………………………………

17

2-2-1 Interfacing the dynamics calculations to the potential energy surface …………..

18

2-2-1-1 Analytic Potential Energy Surfaces ……………………………………………

18

2-2-1-2 Straight Direct Dynamics ……………………………………………………..

19

2-2-1-3 Interpolated Variational Transition State Theory (IVTST) ……………………

19

2-2-1-4 Dual-Level Dynamics …………………………………………………………

20

2-3 Potential Energy Surfaces by Interpolation …………………………………………

21

2-3-1 Molecular Coordinates ……………………………………………………………

21

2-3-2 Local Shape of the PES …………………………………………………………..

23

2-4 Minimum Energy Path ………………………………………………………………

25

2-5 Collision Theory …………………………………………………………………….

27

2-6 Trajectory Calculation ………………………………………………………………

31

2-7 The Reaction Probability, Reaction Cross-Section and Rate Constant Calculations in Quasiclassical Trajectory Method (QCT) ………………………………………….

32

2-8 Rate Theory for Simple Barrier Reaction .………………………………………….

34

2-8-1 Conventional Transition State Theory ……………………………………………

34

2-8-2 Variational Transition State Theory ………………………………………………

37

2-8-3 Canonical Variational Transition State Theory ………………………………….

40

2-9 Validation Against Accurate Quantum Mechanical Dynamics …………………….

42

2-9-1 Tunneling and the Transmission coefficient ……………………………………..

42

2-9-2 Multidimensional Tunneling Corrections Based on the Adiabatic Approximation …………………………………………………………………………..

45

2-10 Unimolecular Reaction Theory ……………………………………………………

52

2-10-1 The Hinshelwood Revision of Lindemann Mechanism ………………………..

53

2-10-2 The RRKM Theory ……………………………………………………………..

55

2-10-3 Application of the RRKM Theory for Unimolecular Dissociation/Elimination

Reactions – The Strong Collision Model ………………………………………………

57

2-10-4 Comparison of RRKM and Transition State Theories ………………………….

59

2-11 Chemically Activated Reactions …………………………………………………..

60

2-12 Statistical Mechanics ………………………………………………………………

63

2-13 Molecular Dynamics and Monte Carlo Simulations ………………………………

A Theoretical Investigation on the Potential Energy Surface, Kinetics and Mechanism of H₂S ‏+ O₃ Reaction&

A Theoretical Study on the Dynamics of the C₂H₄+ S Reaction on an Interpolated Potential Energy Surface

1.1 Kinetics of H₂S + O₃ Reaction ………………………………………………………

1.2 Dynamics of C₂H₄+ S Reaction …………………………………………………….

Chapter Four. Results and Discussion: A Theoretical Study on the Dynamics of the C₂H₄+ S Reaction on an Interpolated Potential Energy Surface …………………….

gas phase reactions of S (³P) + C₂H₄ ………………………………………………….

C₂H₄S (Reaction R1^‘) …………………………………………………………………..