Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

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6.3 Trajectory Calculations 143 6.3 Trajectory Calculations The “exact” dynamics of the molecules on a potential energy hypersurface can be followed by classical trajectory calculations. I Phase Space: 6-dimensional space spanned by the spatial coordinates ( )and the conjugated momenta ( ): ↔ (6.12) where = = · (6.13) I I Hamilton function: = + = 2 + () (6.14) 2 Note that depends only on and depends only on . Equations of motion: • for a 1 particle system: (1) = = = − () y · = − = − since contains only not . (2) y y • for an atomic system: = + = (6.15) (6.16) = 2 2 + (6.17) = 1 × = 1 µ × · 3X =1 · = = · (6.18) (6.19) 2 2 + ( 1 2 3−6 ) (6.20) · = − (6.21) · = (6.22) Thus we obtain a set of coupled differential equations which can be solved using the Runge-Kutta or Gear methods.
6.3 Trajectory Calculations 144 • Thermal rate constants ( ) follow by suitable averaging over the initial conditions ( vibrational states, rotational states, angles, ...). • Major problems: Zero-point energy? Tunneling? Surface crossings? I Figure 6.6: Trajectory calculations. I Figure 6.7: Trajectory calculations.
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Physical Chemistry 3: — Chemical
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iii 2.7 Temperature dependence of r
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v 7.1.2 Formal kinetic model 149 7.
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vii 12 Photochemical reactions 241
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ix Preface This scriptum contains l
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xi Disclaimer Use of this text is e
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xiii I Figure 2: Organisational mat
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xv I Figure 6: Recommended textbook
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1.2 Time scales for chemical reacti
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1.2 Time scales for chemical reacti
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1.3 Historical events 6 I Empirical
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1.4 References 8 2. Formal kinetics
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2.1 Definitions and conventions 10
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2.2 Kinetics of irreversible first-
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2.2 Kinetics of irreversible first-
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2.3 Kinetics of reversible first-or
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2.3 Kinetics of reversible first-or
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2.4 Kinetics of second-order reacti
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2.4 Kinetics of second-order reacti
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2.5 Kinetics of third-order reactio
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2.6 Kinetics of simple composite re
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2.7 Temperature dependence of rate
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3.1 Determination of the order of a
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3.2 Application of the steady-state
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3.2 Application of the steady-state
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3.4 Generalized first-order kinetic
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3.5 Numerical integration 58 I Surv
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3.5 Numerical integration 60 2 ord
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3.5 Numerical integration 62 3.5.5
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3.5 Numerical integration 64 , Func
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3.6 Oscillating reactions* 66 3.6 O
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3.6 Oscillating reactions* 68 • B
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3.6 Oscillating reactions* 70 (5) S
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3.6 Oscillating reactions* 72 I Fig
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3.6 Oscillating reactions* 74 [X]
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3.7 References 76 4. Experimental m
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4.3 The discharge flow (DF) techniq
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4.3 The discharge flow (DF) techniq
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4.4 Flash photolysis (FP) 82 4.4 Fl
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4.4 Flash photolysis (FP) 84 I Figu
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4.6 Stopped flow studies 86 4.6 Sto
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4.8 Relaxation methods 88 4.8 Relax
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4.9 Femtosecond spectroscopy 90 I F
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Page 109 and 110: 4.10 References 94 5. Collision the
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Page 115 and 116: 5.1 Hard sphere collision theory 10
Page 117 and 118: 5.2 Kinetic gas theory 102 I The 1D
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Page 123 and 124: 5.2 Kinetic gas theory 108 • Resu
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Page 131 and 132: 5.4 Advanced collision theory 116 W
Page 133 and 134: 5.4 Advanced collision theory 118 I
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Page 155 and 156: 6.2 Polyatomic molecules 140 I Figu
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Page 163 and 164: 7.1 Foundations of transition state
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Page 193 and 194: 8.2 Lindemann mechanism 178 8.2 Lin
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8.4 The specific unimolecular react
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8.5 Collisional energy transfer* 20
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8.6 Recombination reactions 202 8.7
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9.1 Chain reactions and chain explo
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9.1 Chain reactions and chain explo
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9.2 Heat explosions 208 • positiv
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9.2 Heat explosions 210 (3) We can
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9.2 Heat explosions 212 9.2.3 Explo
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9.2 Heat explosions 214 10. Catalys
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10.1 Kinetics of enzyme catalyzed r
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10.2 Kinetics of heterogeneous reac
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11.1 Qualitative model of liquid ph
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11.2 Diffusion-controlled reactions
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11.2 Diffusion-controlled reactions
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11.3 Activation controlled reaction
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11.4 Electron transfer reactions (M
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11.5 Reactions of ions in solutions
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11.5 Reactions of ions in solutions
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12.2 Fluorescence quenching (Stern-
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12.4 Radiationless processes in pho
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14 Combustion chemistry* 258 15. As
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16 Energy transfer processes* 260 1
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Appendix B 262 Appendix A: Useful p
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Appendix B 264 The Marquardt-Levenb
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Appendix C 266 • Convolution of t
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Appendix C 268 C.2 Application to t
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Appendix C 270 C.3 Application to p
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Appendix D 272 Final solutions for
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Appendix D 274 D.2 Special matrices
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Appendix D 276 I Multiplication by
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Appendix D 278 D.4 Coordinate trans
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Appendix D 280 D.5 Systems of linea
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Appendix D 282 D.6 Eigenvalue equat
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Appendix E 284 Secular equation: de
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Appendix E 286 Appendix E: Laplace
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Appendix F 288 Appendix F: The Gamm
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Appendix G 290 Appendix G: Ergebnis
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Appendix G 292 I Anschauliche Bedeu
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Appendix G 294 Ergebnis: = 1 X
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Appendix G 296 (2) Grenzfall für
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Appendix G 298 G.4 Mikrokanonische
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Appendix G 300 G.5 Statistische Int
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Appendix G 302 y = (G.7
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Appendix G 304 G.8 Zustandssumme f
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Appendix G 306 G.9 Zustandssumme f
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Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

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