Lecture 4: Crossed-beam reactive scattering experiments Getting a collision by collision picture of a chemical reaction © 2014 D.J. Auerbach – All rights reserved How do we obtain information about the PES Through many methods: – Energy Requirements: Looking at what promotes a reaction: translation, vibration, rotation – Energy Disposal: Looking at the energy content of reaction products - are they vibrationally, rotationally, or translationally excited – Scattering Experiments: The most useful and definitive method has turned out to be scattering experiments Sept. 25, 2014 define the initial state of reactants measure the angular, energy, and quantum state distributions of products and compare to theory Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 2 Rutherford Experiment The power of scattering experiments Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 3 Discovery of the electron Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 4 Plum Pudding Model and Plum Pudding Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 5 Plum Pudding Model Prediction Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 6 Rutherford, Geiger, Marsden Experiment Ernest Rutherford Sept. 25, 2014 Hans Geiger Ernest Marsden Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 7 Geiger – Marsden Apparatus Geiger-Marsden apparatus photo" by Original work: Hans GeigerDepiction: Joachim Grehn - Metzler Physik. Licensed under Fair use of copyrighted material in the context of Geiger–Marsden experiment via Wikipedia http://en.wikipedia.org/wiki/File:Geiger-Marsden_apparatus_photo.jpg#mediaviewer/File:GeigerMarsden_apparatus_photo.jpg Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 8 Results Most of the particles (He+) went straight through. Occasionally, however one was deflected to large angles Very occasionally, an particle bounced back Rutherford said “It was as if you shot a 15 inch shell and a piece of tissue paper and it came back and hit you.” Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 9 Discovery of the Nucleus The positive and the vast majority (>99.9%) of the mass of the atom was concentrated in an extremely tiny nucleus Knowing the energy of the particle (7.7 MeV), Rutherford could place an upper limit on the size of the nucleus of 3.6x10-14 m Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 10 Stripping, Direct Rebound and Complex forming reactions being examples SCATTERING METHODS ALLOW US TO CLASSIFY REACTION TYPES Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 11 Scattering methods allow us to classify reaction types Stripping, Direct Rebound and Complex forming reactions being examples © 2014 D.J. Auerbach – All rights reserved Impact parameter What YT Lee liked to call ‘the aiming error’ Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 13 Geometric parameters of a molecular Collision consider scattering of two spherical particles sit on B so it appears to be at rest b impact parameter scattering angle vrel initial relative velocity v´rel final relative velocity Note how an attractive potential can steer molecules together. There is an orbital angular momentum L perpendicular to the plane of the collision of magnitude L = vrel b Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 14 Relation of scattering angle to impact parameter Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 15 Relation of scattering angle to impact parameter Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 16 Relation of scattering angle to impact parameter Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 17 Opacity function Back-scattering 1,2 1,2 1,0 1,0 P(b) P(b) 0,8 Arb. units 0,8 Arb. units Forward scattering 0,6 0,6 0,4 0,4 0,2 0,2 0,0 0,0 -4 -2 0 2 4 -4 -2 impact parameter (b) Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 0 2 4 impact parameter (b) 18 Scattering and the impact parameter, b Example of a stripping reaction K b large I I Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 19 Scattering and the impact parameter, b Example of a stripping reaction K K I b large b large I Reaction cross section (assuming every collision within ‘b’ reacts) ~ b Sept. 25, 2014 I I 2 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 20 Stripping reactions in molecular beam scattering Experiments Stripping reaction – Forward scattering in CM frame – usually attractive PES, early barrier; – direct reaction; – large impact parameters, b; – short lived TS. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 21 A Closer look We represent results by polar plots of velocities of products in Center of mass frame: Scattering angle is angle between reagent and product relative velocity vectors. Distance from CM represents product speed. Sept. 25, 2014 In this example - Angular distributions is forward scattered with respect to the original direction of the K atom Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 22 Rebound reaction Initial Conditions vrelative vF vH 2 F vF b small vH2 H-H Collision Occurs Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 23 Rebound reaction Initial Conditions vrelative vF vH 2 vHF F F vF H b small vH2 HH - vH H Linear momentum conserved mHF vHF mH vH Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 24 Rebound reactions in molecular beam scattering Experiments Rebound reaction – Backward scattering in CM frame; – Can be early or late barrier vD2 vF – small b – direct reaction; – short lived TS. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 25 Complex Forming Reaction H vO O vH2 1 O( D) Sept. 25, 2014 H + H2 OH + H Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 26 Complex Forming Reaction vO HH O O vH2 1 O( D) Sept. 25, 2014 HH + H2 OH + H Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 27 Complex Forming Reaction vO O O HHH O HH H vH2 Dissociation in all possible directions Memory of original direction forgotten 1 O( D) Sept. 25, 2014 + H2 OH + H Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 28 Complex forming reaction in molecular beam scattering Experiments Forward/backward scattering; long-lived complex (lifetime of many ps); Deep binding well on PES. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 29 A good homework problem (optional – extra credit) WHY FORWARD-BACKWARD SCATTERING AND NOT ISOTROPIC Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 30 Reaction rate in terms of opacity function P(b) is the so-called ‘opacity function’ – It is a function of impact parameter, b – This function may be different at different values of the relative (vrel ) ~ velocity The thermal rate constant – is the thermal average of the cross section times the velocity Sept. 25, 2014 P(b; v rel ) 2 b db k (T ) (vrel ) vrel PMB (v; T ) dvrel k (T ) (v) v Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 thermal 31 Opacity function for some reactions is independent of impact parameter 1.4 1.2 Arb. units 1.0 0.8 0.6 0.4 0.2 0.0 -4 -2 0 2 4 impact parameter The influence of the opacity function can be dramatic Determining the magnitude of the reaction cross section and Reaction rate constant Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 32 Maximum reaction rate This occurs when the opacity function is unity over a wide range of impact parameters. Long range interactions attract reactants. Once they get close to one another they react with 100% efficiency – E.g. Electron transfer reactions k (T ) (v) v PMB (v; T ) dv Sept. 25, 2014 3 𝑐𝑚 𝑘𝑚𝑎𝑥 ~10−10 𝑠 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 33 Crossed-beam reactive scattering experiments Getting a collision by collision picture of a chemical reaction © 2014 D.J. Auerbach – All rights reserved Last Modified 29.10.2010 34 10-6 Torr Molecular beam expansion 10-8 Torr 0.1-5 bar 10-4 Torr Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 35 Molecular beam expansion 10-4 Torr Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 36 Properties of the molecular beam expansions Velocities are large For pure gases vmost probable 2C p Tstag m 5kT For monoatomics vmost probable m He 1800 m/s at 300K 7kT vmost probable m H2 2900 m/s at 300K For Diatomics Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 37 Further properties of molecular beam expansions: “seeded beams” If you have a dilute mixture of heavy gas in a light gas. You get very high translational energies – e.g. I2 in H2 – mI2 = 254 vH2 = 2900 m/s – EI2 =11.5 eV vmost probable Sept. 25, 2014 2C p Tstag m Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 38 Number of collisions required for significant energy transfer Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 39 Translation is strongly cooled Dv/vMP = 0.05 is routine Dv/vMP = 0.005 is possible Production of He2 – weakest bound species – demonstrated in molecular beams Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 40 Rotation is strongly cooled Spectroscopy shows J=0 is dominant state in an HCl beam – (seeded in H2) – Rotational Temperature is 20K Ran, Q., et al., An advanced molecule-surface scattering instrument for study of vibrational energy transfer in gas-solid collisions. Review of Scientific Instruments, 2007. 78(10). Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 41 Rotation is strongly cooled Spectroscopy shows J=0 is dominant state in an HCl beam – (seeded in H2) – Rotational Temperature is 20K Ran, Q., et al., An advanced molecule-surface scattering instrument for study of vibrational energy transfer in gas-solid collisions. Review of Scientific Instruments, 2007. 78(10). Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 42 Crossed beams reactive scattering in F+H2 An instructive example Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 43 Scattering using crossed beams Two beam sources and a rotatable detector – Detector is a mass spectrometer or laser based state specific detector – Study angular scattering of reaction products in the lab frame – Time-of-flight to measure product speed To understand the collision dynamics, examine scattering in the centre-ofmass frame. Scattering distributions depend sensitively on the topography and nature of the PES Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 44 Crossed Molecular Beams Reactive Scattering Features A beam of F atoms is introduced Normal to a beam of H2 molecules A velocity selector is used to narrow the F atom velocity spread Reaction Products are observed by a rotatable mass spectrometer – Angular distributions and – TOF distributions using a choppper Sept. 25, 2014 Experimental arrangement Neumark, D.M., et al., Journal of Chemical Physics, 1985. 82(7): p. 3045-3066. Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 45 Basic information on F+H2 Thermochemistry Highly exothermic Energetics of the F+H2 reaction Tendency to produce vibrationally excited products. – See Pimentel chemical laser A small reaction barrier is located in the entrance channel of the reaction coordinate Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 46 More on the experiment Lee, Y.T., et al., MOLECULAR BEAM REACTIVE SCATTERING APPARATUS WITH ELECTRON BOMBARDMENT DETECTOR. Review of Scientific Instruments, 1969. 40(11): p. 1402-1408. Nobel Prize in Chemistry 1986 Experimental Overview An electron bombardment ionizer provides “universal detection” – Ion fragmentation must be sorted out. Sept. 25, 2014 Rotatable triple chamber design is crucial to reduce background Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 47 Newton Diagrams Center of Mass Demo Video - MIT Last Modified 29.10.2010 48 Newton Diagrams Center of Mass Demo Video - MIT Last Modified 29.10.2010 49 Newton diagrams for reactive scattering Newton diagrams show the relationship between the LAB and CM frames Lab frame CM frame vA lab velocity of A urel relative vel. of A + BC vBC lab velocity of BC urel' relative vel. of AB + C vAB lab velocity of AB uA relative velocity of A vC lab velocity of C uBC relative velocity of BC U velocity of CM uAB relative velocity of AB uC relative velocity of C CM scattering angle Sept. 25, 2014 lab scattering angle Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 50 Vector Addition in Newton Diagrams vF vCM Sept. 25, 2014 vrel vF vH 2 mF vF mH 2vH 2 mF mH 2 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 vH 2 51 Some reminders Translational Energy of Incidence vrel vF vH 2 1 Ecollision vrel vrel 2 mF mH 2 mF mH 2 Sept. 25, 2014 Transformation from Lab to CM frame vCM vCM vCM mF v F mH 2 v H 2 mF mH 2 u F vF u H 2 vH 2 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 52 Vector Addition in Newton Diagrams: Transformation from CM to Lab frame vF vCM vCM vCM Sept. 25, 2014 uF uH 2 mF v F mH 2 v H 2 mF mH 2 u F vF u H 2 vH 2 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 vH 2 53 Each vibrational channel has its own Newton Circle Ereleased Ereleased vF 1 1 mHF u HF u HF mH u H u H 2 2 0K DH reaction Ecollision Erovibrational energy of the products u HF So, HF formed in different vibrational states has different translational energy release and a different Newton Circle vH 2 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 54 Each vibrational channel has its own Newton Circle Ereleased Ereleased vF Sept. 25, 2014 1 1 mHF u HF u HF mH u H u H 2 2 By the way, The H atom is 0K DH reaction Ecollision momentum Erovibrationalmatched with HF energy of the products u HF And carries most of the kinetic energy So, HF formed in different mvibrational u HF has states H u H mHF different translational 1energy release 1and a 2 2 mH u H mHF u HF different Newton 2 2 Circle mH E H mHF E HF EH mHF 20 E HF mH Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 vH 2 55 A side note Actually every quantum state of HF produced in this reaction gives rise to its own Newton Circle. Every different rotational state of HF also has a different translational energy release. The tricky part is: Can you do an experiment to resolve them We will show later that this is possible. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 56 Newton Circles in the F+H2 reaction Things to Notice The CM angle is indicated The signal drops abruptly at 8°, 26° and 55° These are the edges of the Newton Circles for HF(v=3) and HF(v=2) formation Sept. 25, 2014 Experimental Angular distributions Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 57 TOF data allows you to see a cut along one angle. Sample Data – TOF distributions Sept. 25, 2014 Newton Circles Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 58 TOF and Angular Distributions TOF data at various angles Sept. 25, 2014 Angular distribution data Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 59 The experimentally derived product flux distribution Summary of Results Vibrationally state resolved angular distributions V=1,2 backward scattered vH2 V=3 forward scattered Something fishy going on here. We will return to this Originally attributed to a reaction resonance – Long lived complex that can appear on a potential surface where there is no well Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 vF 60 Chemical Dynamics: Experimentally testing the standard model Striving for 1st principles understanding of chemical reactivity Approach – Measure angle and speed resolved scattering with as complete as possible control and characterization of initial and final quantum state Experimental Signatures: derive mechanisms from “signatures” and how they vary with incidence conditions. Sept. 25, 2014 Benchmarks for Theory: Compare measurements with theory to develop fundamental understanding. Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 61 The Ultimate Goals of the field of Chemical Dynamics Compare first principles calculations to the best possible experiments and derive the PES quantitatively Demonstrate reliable first principles theoretical modeling of chemical reactivity Predict new chemistry from a computer keyboard using established theoretical methods. 25.09.2014 62 Let’s look at the H+H2 system in more detail Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 63 The first attempt to calculate a potential energy surface Henry Eyring Michael Polanyi English translation in: World Scientific Series in 20th Century Chemistry - Vol. 8,“Über Quantum Chemistry Classic Scientific Papers, Hinne Hettema, Imperial einfache Gasreaktionen”, H. Eyring and M.byPolanyi, Sonderdruck aus Z. College Press. Abt. B 12, Heft 4 (1931). Phys. Chem., Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 64 Some comments about Eyring and Polanyi’s calculation The calculation was drastically simplified – The H atoms were restricted to move on a line: the co-linear approximation – The electronic Schrödinger equation was solved semi-empirically The computer had not yet been invented We must consider the PES only qualitatively correct. – In fact there are some qualitative problems with the PES Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 65 A closer look H1-H2 H3 (Products) H1 H2-H3 (Reactants) Transition State region Reaction Path Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 66 Experimental efforts to reveal the nature of the H3 PES Crossed beam reactive scattering DI was photolyzed by a polarized laser. A collimated D-atom beam was formed. This beam was crossed at 90° with an H2 beam A rotatable mass spectrometer detected scattered HD products at m/z=3 Continetti et al. 1990 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 67 Energy Diagram for the Continetti experiment Two Collision energies simultaneously: DI photolysis leads to two products – D+I(2P3/2); Etrans,D= 1.01 eV – D+I(2P1/2); Etrans,D= 0.53 eV Sept. 25, 2014 Threshold energy is higher than 0.43 eV due to zero point energy correction HD(v=0,1,2) are accessible Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 68 Experimental detail: D-atom TOF The laser is fired and the signal at m/z=2 (D+) is detected as a function time using a multichannel scaler. Ions are counted using a Daly style detector • Continetti et al. 1990 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 69 The Newton Diagram for D+H2 reaction according to Continetti vH2 vD Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 70 The Newton Diagram for D+H2 reaction according to Continetti vH2 vD HD Backward Sept. 25, 2014 HD Forward Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 71 TOF measurements of the reaction products Angles are measured with respect to the direction of the D atom beam Collision energy was 1.01 eV Continetti et al. 1990 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 72 Angle resolved reactive flux map HD is seen to be scattered roughly back in the direction from which the D atom came. significant ‘sideways scattering’ is also seen. This is also seen in the theoretical flux map Exp But Theory Continetti et al. 1990 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 73 H-atom Rydberg Atom Tagging Extremely high resolution velocity measurements Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 74 Rydberg atom tagging: Lifetimes of Rydberg states in H Karl Welge Uni Bielefeld Yang Xueming Dalian Institute of Chemical Physics Schnieder, L., et al., Hydrogen-exchange reaction h + d2 in crossed beams. Faraday Discussions, 1991. 91: p. 259-269. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 75 Field Ionization of high Rydberg states • Application of a small external field leads to emission of the electron. A Rydberg state 2.5 cm-1 below ionization • Hence the Rydberg may fly as a neutral and encounter a grid with an applied potential and be ionized with 100% efficiency • Notice the spatial extent of the wave function 5 m A Rydberg state 25 cm-1 below ionization with a 10V/cm external field • And the ease with which field ionization can be implemented Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 76 Lets think about TOF resolution t Definition R ; of TOF resolution t t l / v and t l / v so, t l /v l R t l / v l Sept. 25, 2014 For an H atom of one velocity, the uncertainty in the flight time is determined by the uncertainty in the flight distance For electron bombardment ionization (e.g. continetti) the size of the electron cloud For Rydberg tagging, the size of the focused laser beam Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 77 Energy Resolution – Homework problem Calculate the energy resolution of a Rydberg Atom Tagging experiment and compare to the energy spacing of rovibrational states of the product molecule. Parameters – – – – Sept. 25, 2014 Reaction D + H2 HD + H Flight path for Rydberg atoms = 0.5 m Tagging laser beam diameter 1 mm Tagging laser beam energy spread 0.5 cm-1. Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 78 Isotope selective lH= 1 21.5668237310 nm l D= 1 21.533755495 nm Separated Bandwidth ~0.5 cm-1 Sept. 25, 2014 by 22 cm-1 of laser Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 79 The Lyman- line is a doublet due to spin orbit splitting in the 2p state 2P state splits into – 2P3/2 – 2P1/2 Sept. 25, 2014 This can be used to interrogate the M state populations in the ground state. Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 80 From Schnieder, L., et al., HYDROGENEXCHANGE REACTION H + D2 IN CROSSED BEAMS. Faraday Discussions, 1991. 91: p. 259269. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 81 Rydberg state lifetimes can be dramatically lengthened Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 82 Generation of Lyman- Two photon resonance enhanced four wave mixing in Krypton. Argon added to improve phase matching J / pulse are produced from YAG pumped ns lasers 10-100 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 83 Extra Credit Homework Problem: Calculate the excitation probability H-Atom Lyman- Laser properties – trad= 1.6 ns – Pulse energy:10 J – l = 121.6 nm – Pulse duration: 5 ns – Spot size: 1 mm circular – Line-width: 0.2 cm-1 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 84 Advantages of Rydberg atom tagging High sensitivity: – You are utilizing the 1s-2p transition in H atom. There is no stronger transition in nature. – Detection Efficiency of high Rydberg states is close to 100% using field ionization – Essentially no Background High Resolution Time of Flight – By focusing the laser spot the uncertainty in the flight distance can be much less than one mm – Flight distances can be anywhere from 0.25 to 1 meter – No space charge effects Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 85 One more advantage: Detection of the H-atom is ‘kinematically’ favorable High (the highest) translational energy resolution is obtained © 2014 D.J. Auerbach – All rights reserved Previously we pointed out that the TOF resolution was limited this equation l R l But actually that is too simple Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 87 Other factors can degrade resolution Consider F+H2 Due to spreads in the F and H2 beam velocities, the CM velocity vector is blurred Even though ℓ 𝛿ℓ can be large. The results are blurred in velocity space to start with …. We say “you have to average over many similar but different Newton Diagrams” Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 88 The spreading of the Vcm has little influence on the spread in uH Since the H atom speed is so high, the Vcm blurring is a smaller fraction of its magnitude uH uHF mH uH mHF uHF Due to momentum conservation uH>>uHF Sept. 25, 2014 We call this a kinematic advantage Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 89 Carrying out the crossed beam scattering experiment • • • Parallel beam geometry: D2 beam crosses photolytic H-atom beam Photodissociation of molecular beam cooled HI creates a nearly mono-energetic H-atom beam Rydberg tagging in the collision volume probes D-atom product Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 90 First RAT data obtained by Welge in Bielefeld (@1990-1991) D atom Kinetic energy distribution D atom TOF data The reaction of H+D2HD(v) + D Individual vibrational states of HD resolved Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 91 Within a few years Rotational resolution was achieved In the H+D2 reaction one produces D + HD(v,J) HD(v, J) has two quantum numbers that determine the internal energy of the system – We neglect nuclear spin states Rydberg tagging allows each ro-vibrational channel to be resolved. And its angular scattering distribution to be observed Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 92 Theoretical approach to the H+H2 reaction Adiabatic potential energy surface is calculated from ab initio quantum theory of electrons in the presence of fixed nuclei. – Born-Oppenheimer Approximation employed – Large basis sets used to account as accurately as possible for electron correlation – 10-50 ab initio points calculated for each degree of freedom. Total number of points (10-50)3 that is, 103-5 points – Points fit to an analytical function with high accuracy The Schrödinger equation for the motion of the nuclei on the PES must be solved. – Alternatively one can carry out classical trajectory calculations Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 93 Comparison to the standard model Dashed line is classical approximation Solid and dotted lines quantum with two different PES Not surprisingly, classical mechanics doesn’t work that well But Quantum dynamics gives outstanding agreement with experiment and comparison of two potential surfaces is possible. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 94 The current master of this technique Yang Xueming Dalian Institute of Chemical Physics Dalian Rydberg Tagging instrument Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 95 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 96 Chemical Dynamics: an example Playing (Quantum) Billiards with Atoms H + H-D → H-H + D H Experiment Theory Yang and Skodje, Journal of Chemical Physics, 117 (18) 8341 -8361 (2002) Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 97 With this level of agreement we can state without qualms that the standard model of chemical reactivity works At least for the H+H2 system Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 98 End of Lecture 4 Crossed-beam reactive scattering experiments Getting a collision by collision picture of a chemical reaction Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 99 Extra Slides Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 100 The 4He Dimer: The World‘s Weakest Bound and Largest Ground State Molecule Butterfly of molecules. Like catching a butterfly, measuring the delicate molecule formed by two helium atoms requires a light touch. Since <R> is much greater than Rout the <R> dimer is a classically forbidden molecule Eb Expt. Theory Eb 1.1 0.2 1.62 0.03 mK R 52 4 47.1 0.05 Å Scatt High cross SR sect Sept. 25, 2014 H2 molecule: <R> = 0.74Å Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 101 “Simple” experiment Make a really strong expansion – High backing pressure – Low stagnation temperature Then you get some He clusters including the dimer But how do you detect it with breaking it apart? Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 102 Atom-Wave Diffraction (including Atom-Grating vdW Interaction) Using a grating He is a wave. At constant velocity He2 is a wave of half the wavelength ξ z Sept. 25, 2014 2 Re[] Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 103 Electron Microscope Picture of the SiNx Transmission Gratings 100 nm period 50 nm slit width View of the chip before the Si base is etched away App Sept. 25, 2014 Courtesy of Prof. H. Smith and Dr. Tim Savas ,M. I. T. Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 Courtesy of JP Toennie 104 Nano-Structure Gratings 1 um Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 Courtesy of JP Toennie 105 Transmission Grating Diffraction Apparatus S1 and S2 =5 microns S3= 20 microns Can discriminate against atoms with mass spectrometer set at mass 8 and larger Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 Courtesy of JP Toennie 106 Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 Courtesy of JP Toennie 107 Decreasing Source Temperature Slit fct Courtesy of JP Toennies Sept. 25, 2014 Kornilov and Toennies. Europhysics News 38, 22 (2007) Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 108 He-He Scattering Cross Section is Huge 8 a 2 T→0 where a 2 R a 100 Å 2 Å 250,000 Large cross section explains extreme cooling and sharp velocities of He atom beams Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 109 Measured Cross Sections as a Fct. of Velocity R Expect 2 3900 Å2 2 2 2 atom cross sec tion Magic nos Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 110 Measured Cross Sections as a Fct. of Velocity R Expect 2 3900 Å2 2 2 2 atom cross sec tion The Kr atom can pass through the middle of the molecule without its being affected Magic nos Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 111 The deflection angle gives you the mass Electron bombardment ionization destroys all clusters. All species are detected as He+ Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 112 He diffraction through a multislit grating Top Panel: The angular distribution of He: many diffraction orders seen Middle panel: P0 raised T0 lowered: two peaks between the He n=0 and 1 orders seen Lower panel: P0 raised T0 lowered further: Three peaks seen. Sept. 25, 2014 Lecture 4 -- Chemical Dynamics at Surfaces -- Dalian 2014 113