89.7 Theory for Gaseous bimolecular reaction Transition state theory tst) Extensive reading Levine, pp. 882-889 23.2 potential-energy surfaces
§9.7 Theory for Gaseous bimolecular reaction ---- Transition state theory (TST) Extensive reading: Levine, pp. 882-889. 23.2 potential-energy surfaces
89.7 Transition state theory (TST) 9.7.1 Brief introduction Quantum mechanics time Person Main contribution 1900 Max Planck black-body radiation 1905 Albert einstein Photoelectric effect oo Hydrogen Wave Function ():一, 1920s Erwin Schrodinger Early quantum theory Werner Heisenberg Max born 8 1927 Heitler-London Nature of chemical 回飞() 至 theory bond 圣兴#·
9.7.1 Brief introduction §9.7 Transition state theory (TST) Quantum mechanics time Person Main contribution 1900 Max Planck black-body radiation 1905 Albert Einstein Photoelectric effect 1920s Erwin Schrödinger Werner Heisenberg Max Born Early quantum theory 1927 Heitler-London theory Nature of chemical bond
89.7 Transition state theory (TST) 9.7.1 Brief introduction Polanyi mihaly Henry Eyring The transition state theory (TST), attempting to explain reaction rates on the basis of thermodynamics(potential energy -the nature of chemical bond), was developed by H. ring and M. Polanyi during 1930-1935 TST treated the reaction rate from a quantum mechanical viewpoint involves the consideration of intramolecular forces and intermolecular forces at the same time
The transition state theory (TST), attempting to explain reaction rates on the basis of thermodynamics (potential energy – the nature of chemical bond), was developed by H. Eyring and M. Polanyi during 1930-1935. TST treated the reaction rate from a quantum mechanical viewpoint involves the consideration of intramolecular forces and intermolecular forces at the same time. 9.7.1 Brief introduction Henry Eyring Polányi Mihály §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) 9.7.1 Brief introduction FEBRUARY. 1935 JOURNAL OF CHEMICAL PHYSICS VOLUME 3 The Activated Complex in Chemical Reactions HENRY EYRING, Frick Chemical Laboratory, Princeton Universily Received November 8, 1934) The calculation of absolute reaction rates isIformulated complex, in degrees of free SOME APPLICATIONS OF THE I TRANSITION rms of quantities which are a vanable from the potential the original molecules, lea STATE METHOD TO THE CALCULATION OF surfaces which can be constructed at the present time. The isotopes quite different ir REACTION VELOCITIES. ESPECIALLY IN probability of the activated state is calculated using ordi- simple kinetic theory, Th SOLUTION nary statistical mechanics. This probability multiplied by general statistical treatmen the rate of decomposition gives the specific rate of reaction. treatment are given The occurrence of quantized vibrations in the activated BY M. G. EVANS AND M. PolanYi Received 12th March, 1935 The calculation of absolute reaction rates is formulated I. Introduction in terms of quantities which are available from the potential surfaces which can be constructed at the influence of pressure on the velocity of chemical reactions in solution, e One of the main objects of this discussion will be to consider th present time. The probability of the activated state is established the fact that, in certain cases, the velocity of re action could calculated using ordinary statistical mechanics. This pressure could be atributed to secondary effects, which, in their turn, probability multiplied by the rate of decomposition explanation based on the change of association of the solvent(aqueous gives the specific rate of reaction alcohol), which may be applicable in special cases. The extensive work of Cohen 2 and his collaborators, however. removed to some extent
The calculation of absolute reaction rates is formulated in terms of quantities which are available from the potential surfaces which can be constructed at the present time. The probability of the activated state is calculated using ordinary statistical mechanics. This probability multiplied by the rate of decomposition gives the specific rate of reaction. 9.7.1 Brief introduction §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) 9.7.1 Brief introduction A+BC→A-B+C During reaction, energies are being redistributed among bonds: old bonds are being ripped apart and new bonds formed H+H-H→H…H…H →H…H…H( Is it strange??) →H…H…………H→HH+H This process can be generalized as: A+BC—[ABC->A-B+C Activated complex /Transition state
A + B⎯C → A ⎯ B + C During reaction, energies are being redistributed among bonds: old bonds are being ripped apart and new bonds formed. H + H–H → H∙∙∙∙∙∙∙∙∙ H∙∙∙∙H → H∙∙∙∙∙∙H∙∙∙∙∙∙H (Is it strange??) → H∙∙∙∙H∙∙∙∙∙∙∙∙∙∙∙∙H → H–H + H This process can be generalized as: A + B-C ⎯→ [ABC] ⎯→ A-B + C Activated complex / Transition state 9.7.1 Brief introduction §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) 9.7.1 Brief introduction Basic consideration A+bP ( Activated complex is in thermodynamic equilibrium with the molecules of the reactants- -to determine its concentration (2)The activated complex is treated as an ordinary molecule except that it has transient existence ( )Activated complex decomposes at a definite rate to form the product r=y≠CAB≠ Rate equation of TsT
(1) Activated complex is in thermodynamic equilibrium with the molecules of the reactants—to determine its concentration. (2) The activated complex is treated as an ordinary molecule except that it has transient existence. (3) Activated complex decomposes at a definite rate to form the product. Basic consideration AB r c = Rate equation of TST 9.7.1 Brief introduction §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) 9.7.2 Potential energy surfaces According to the quantum mechanics, the nature of the chemical interaction (chemical bond) is a potential energy which is the function of interatomic distance (r) The function can be obtained by solving Schrodinger equation for a fixed nuclear configuration, i. e, Born-Oppenheimer approximation The other way is to use empirical equation. The empirical equation usually used for system of diatomic systems is the Morse equation
9.7.2 Potential energy surfaces According to the quantum mechanics, the nature of the chemical interaction (chemical bond) is a potential energy which is the function of interatomic distance (r): V V r = ( ) The function can be obtained by solving Schrödinger equation for a fixed nuclear configuration, i.e., Born-Oppenheimer approximation. The other way is to use empirical equation. The empirical equation usually used for system of diatomic systems is the Morse equation: §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) (I)Potential energy of diatomic systems Diatomic Molecules According to the Wave Mechanics Vibrational levels Philip M. morse Phys. Rev. 34, 57-Published 1 July 1929 ABSTRACT An exact solution is obtained for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to those required by Heitler and London and others. The allowed vibrational energy levels are found to be the experimental values quite accurately. The empirical law relating the normal molecular separation ro and the classical vibration frequency wo is shown to be ro wo= k to within a probable error of 4 percent, where K is the same constant for all diatomic molecules and for all electronic levels. By means of this law, and by means of the solution above, the experimental data for many of the electronic levels of various molecules are analyzed and a table of constants is obtained from which the potential energy curves can be plotted. The changes in the above mentioned vibrational levels due to molecular rotation are found to agree with the Kratzer formula to the first approximation
(1) Potential energy of diatomic systems §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) (1)Potential energy of diatomic systems orse equation ()=D{exp-2a(r-)-2exp[-a(r-0) The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the vibrational structure of the molecule than the qho (quantum harmonic oscillator) because it explicitly includes the effects of bond breaking. such as the existence of unbound states It also accounts for the anharmonicity of real bonds and the non-zero transition probability for overtone and combination bands. The morse potential can also be used to model other interactions such as the interaction between an atom and a surface ttps /en. wikipedia. org/wiki/Morse_potential
The Morse potential, named after physicist Philip M. Morse, is a convenient interatomic interaction model for the potential energy of a diatomic molecule. It is a better approximation for the vibrational structure of the molecule than the QHO (quantum harmonic oscillator) because it explicitly includes the effects of bond breaking, such as the existence of unbound states. It also accounts for the anharmonicity of real bonds and the non-zero transition probability for overtone and combination bands. The Morse potential can also be used to model other interactions such as the interaction between an atom and a surface. Morse equation: ( ) {exp[ 2 ( )] 2exp[ ( )]} 0 0 V r D a r r a r r = e − − − − − https://en.wikipedia.org/wiki/Morse_potential (1) Potential energy of diatomic systems §9.7 Transition state theory (TST)
89.7 Transition state theory (TST) (1) Potential energy of diatomic systems 000 decomposition De: the depth of the wall of potentiall asymptote dissociation energy of the bond Dissociation Energy Harmonic ro: equilibrium interatomic distance/ Morse bond length a: a parameter with the unit of cm-l can be determined from spectroscopy =1 Zero point energy: Eo=De-Do v=0 Internuclear Separation (r) r> ro, interatomIc attraction When r=ro, V(r=ro)=-D r∞,V(r>∞)=0
(1) Potential energy of diatomic systems De : the depth of the wall of potential/ dissociation energy of the bond. r 0 : equilibrium interatomic distance/ bond length; a: a parameter with the unit of cm-1 can be determined from spectroscopy. r > r0 , interatomic attraction, r < r0 , interatomic repulsion. decomposition asymptote Zero point energy: E0 = De -D0 When r = r0 , Vr (r = r0 ) = -De r→, Vr (r→) = 0 §9.7 Transition state theory (TST)