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

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7.1 Foundations of transition state theory 147 7.1.1 Basic assumptions of TST (1) The Born-Oppenheimer approximation (separation of electronic and nuclear motion) is a valid approximation. Thus we can describe the nuclear motion during the reaction on a single electronic potential energy surface (PES; see Fig. 7.2). 41 (2) The reactant molecules are in internal equilibrium (the quantum states are populated according to the Boltzmann distribution). (3) “Transition state” and “dividing surface“: a) Conventional TST (valid for so-called “type I” PES’s = PES’s with a distinctive energy barrier along the reaction coordinate (RC)): We can localize a distinctive “transition state” (TS) for the reaction at the saddle point on the PES that separates the reactant and product “valleys”. The TS is located at the maximum of the PES along the minimum energy path (MEP; see Fig. 7.3). b) Variational TST (version that can be used for so-called “type II” PES’s = PES’s without a clear energy barrier along the RC (we can’t localize a simple TS)): We can localize a 3 − 7-dimensional “dividing surface” (DS) on the 3 − 6-dimensional PES that separates the reactant and product regions on the PES in such a way that the “reactive flux” through the DS becomes minimal (Fig. 7.2). The TS is then placed at the point where the MEP intersects the DS. In this case, the position of the TS depends strongly on the finer details such as angular momentum (because of centrifugal barriers which move inwards with increasing or increasing ). (4) The motion along the minimum energy path across the TS (through the DS) can be separated from other degrees of freedom and treated as translational motion. AttheTS,wethereforehave1translationaldegreeoffreedom ‡ (the RC) and 3 − 7 (vibrational) degrees of freedom orthogonal to the RC. (5) Reactant molecules passing through the DS never come back (no recrossing). (6) The states of the TS are in quasi-equilibrium with the states of the reactant molecule even if we have no equilibrium between reactants and products (the individual molecules don’t know that this equilibrium is not present - this quasiequilibrium assumption can be dropped in dynamical derivations of TST; see below). I Conditions for TS at the saddle point: (1) has maximum along ‡ : =0and 2 0 (7.1) ‡ ‡2 y 1 imaginary frequency (criterion for TS in quantum chemical calculations)! 41 TST cannot be used at least in the simple form considered in this lecture when two potential surfaces are involved that are energetically close to each other (or even become degenerate) and the reaction involves a “non-adiabatic transition” between these two potentials.
7.1 Foundations of transition state theory 148 (2) has minimum along all 3 − 7 other coordinates: =0and 2 2 0 (7.2) y 3 − 7 real other frequencies. I Figure 7.2: Transition state theory: The dividing surface with minimal reactive flux. I Figure 7.3: Minimum energy path (MEP) and transition state (TS) of a simple atom transfer reaction.
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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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4.9 Femtosecond spectroscopy 92 I F
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4.10 References 94 5. Collision the
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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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