IC T IC-1/26 Lecture-4B Reaction Rate Theory  E reaction coordinate E + + k A B AB

IC T IC-2/26 Lecture-4B Partition Functions Similarly can we separate the internal motions of a molecule in Part involving vibrations, rotation and nuclei motion, and electronic motion i.e. for a mulecule we have Now we create a system of many molecules N that are in principle independent and as they are indistinguishable we get an overall partition function Q

IC T IC-3/26 Lecture-4B Partition Functions Summary 

IC T IC-4/26 Lecture-4B Partition Functions What was the advantage of having the Partition Function?

IC T IC-5/26 Lecture-4B Surface Collisions Consider a box with volume V What are the numbers?

IC T IC-6/26 Lecture-4B Surface Collisions How many are successful in reacting? Simple Maxwell-Boltzman distribution

IC T IC-7/26 Lecture-4B Transition State Theory Consider the following reaction : How? We assume that R and R # are in Equilibrium R P R#R# q `# is a frequency or trial factor in the reaction coordinate

IC T IC-8/26 Lecture-4B Transition State Theory By splitting the partition function in the transition state Assuming

IC T IC-9/26 Lecture-4B Transition State Theory R P R#R# q` # =q `# v q # 0 e -  E/kT q `# Which basically is the Arrhenius form If q 0 # ~ q  ~1x10 13 s -1 Relation to Thermodynamics The partition function q # can conveniently be split further:

IC T IC-10/26 Lecture-4B Transition State Theory Think of some examples Temperature dependence of prefactor

IC T IC-11/26 Lecture-4B Transition State Theory on Surfaces An atom adsorbs into a 2-dim mobile state, we have N g gas atoms, M sites on the surface, and N # atoms in the transition state Indirect adsorption of atoms:

IC T IC-12/26 Lecture-4B Transition State Theory on Surfaces Now what is K # ?

IC T IC-13/26 Lecture-4B Transition State Theory on Surfaces This corresponds to the collision on a surface since the atoms are still free to move in two dimensions

IC T IC-14/26 Lecture-4B Transition State Theory on Surfaces Direct adsorption of atoms: M is total number of sites M´ is number of free sites Why?

IC T IC-15/26 Lecture-4B Transition State Theory on Surfaces

IC T IC-16/26 Lecture-4B Transition State Theory on Surfaces Notice adsorption always result in loss of entropy There may also be steric hindrance leading to reduced S

IC T IC-17/26 Lecture-4B Transition State Theory on Surfaces What happens in the regime between direct and indirect adsorption? The atoms breaks free of the site and start to diffuse around in Eventually

IC T IC-18/26 Lecture-4B Transition State Theory on Surfaces Indirect adsorption of molecules: Notice that if the precursor is sufficiently loose S 0 (T)=1.

IC T IC-19/26 Lecture-4B Transition State Theory on Surfaces Direct adsorption of molecules:

IC T IC-20/26 Lecture-4B Transition State Theory on Surfaces

IC T IC-21/26 Lecture-4B Transition State Theory on Surfaces Reactions between surface species:

IC T IC-22/26 Lecture-4B Transition State Theory on Surfaces The reverse process:

IC T IC-23/26 Lecture-4B Transition State Theory on Surfaces Considering both processes and equilibrium: Notice how the K eq is alone determined from initial and final state partition functions.

IC T IC-24/26 Lecture-4B Transition State Theory on Surfaces Desorption:

IC T IC-25/26 Lecture-4B Transition State Theory on Surfaces System Prefactor s -1 E a kJ/mol CO/Co(0001) CO/Ni(111) CO/Ni(111) CO/Ni(111) CO/Ni(100) CO/Cu(100) CO/Ru (001) CO/Rh(111) How?

IC T IC-26/26 Lecture-4B Transition State Theory on Surfaces If the details of the transition state can be determined can the rate over the barrier be calculated. Details of the transition state are difficult to access: Low concentration Short lifetime. Often determined by ``First Principle´´ calculations, but are only accurate to say 0.1 eV or 10 kJ/mol.