89.7 Transition state theory (TST) 9.7.1 Brief introduction Basic consideration A+b<AB->P ( 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< ro interatomic repulsion 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)