Resonances in Chemical Reactions : Theory and Experiment. Toshiyuki Takayanagi Saitama University Department of Chemistry

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1 Resonances in Chemical Reactions : Theory and Experiment Toshiyuki Takayanagi Saitama University Department of Chemistry

2 What is Chemical Reaction? Collision process between molecules (atoms) containing rearrangement of chemical bonding Theoretically Nuclear dynamics on the potential energy surface PES: Interaction potential energy between and atoms molecules PES is determined by quantized electron motions (within Born-Oppenheimer approximation)

3 Determination of accurate potential energy surfaces (PESs) of chemical reactions Solving electronic structure problems for given a nuclear configuration ab initio quantum chemistry calculations in chemistry field First-principles calc. in physics Many package programs: Gaussian, Molpro, Molcas etc. Very accurate calculations can now be possible for very small chemical systems PES for A + BC AB + C (potential energy function of nuclear configurations)

4 Outline of this talk Feshbach resonances in chemical reactions F + H 2 HF + H and F + HD HF/DF + D/H Vibrational adiabaticity and tunneling van der Waals resonances in chemical reactions Long-range attractive interaction Very sharp resonances Low-temperature behavior of reaction rate Interstellar chemistry, Cold reactions Resonances in atmospheric chemistry? Anomalous isotopic ratio of atmospheric ozone (also in interstellar chemistry : H/D ratio) Resonances in roaming reactions : Mg + H 2 MgH + H Resonances in DNA radiation damage (electron collision)

5 Feshbach Resonances in Chemical Reactions v=2 Vibrationally adiabatic potential Energy v=1 v=0 ( ) R(BC) A + BC(v) Potential energy surface AB(v) + C 1.0 R(A-BC) Reaction Probabilities from 2D calc. H + H 2 (v) -> H 2 (all-v) + H Reaction Coordinate Difficulty for predicting reactive resonances from topological features of potential surfaces Importance of dynamics calculations something happens at threshold energy Probability v=0 v= Total Energy / ev v=2

6 Resonance trajectory (classical picture) Other mechanisms Quasi-bound states in a potential well Energy A + BC(v) AB(v) + C Reaction Coordinate v = 1 van der Waals Resonance (hydrogen-bonding) Energy v = 0 A + BC(v) vdw or HB well AB(v) + C Reaction Coordinate

7 How to observe resonances in chemical reactions? Collision energy dependence of cross sections Nuclear Reaction for n U Electron Collision, e + N2 High-resolution molecular beam experiment (~ 0.01 ev) State-to-state differential cross sections Electron photodetachment measurement of anions

8 Collision energy dependence of cross sections Quantum results on Stark-Werner-PES 2.5 Cumulative Reaction Probability (a) J = 0 D HF(v=3, j ) j = 0 j = 1 j = 2 j = 3 j = 4 j = 5 j = 6 F + HD HF + D F + HD DF + H Total Energy / ev

9 Wave function of reactive resonance in F + HD 4 (a) F H D(003) Energy Vibrationally adiabatic potential energy curve r / a (b) (transient) Vibrationally excited state of linear triatomic molecule tunneling resonance state vibrationally adiabatic potential 2 F + HD Reaction coordinate HF + D γ / degree (c) R / a 0

10 Stabilization Diagram & State Density Extraction of resonance wave function θ = 37.3 deg. 4 ρ=6 Solving 3D eigenvalue problems using DVR representation in hyperspherical coordinates (r,q,f) DVR Grid points (50,100,200) 3 r' / au (a) Eres = ev Γ = ev (τ = 98 fs) State density / ev Energy / ev R' / au (b) (c) ρmax / a Energy / ev

11 State-to-state differential cross section measurements for F + H 2, HD HF(v = 2, j) HF(v = 2, j = 6) Science 311 (2006) 1440.

12 Differential cross sections

13 Vibrationally resolved cross sections Differential cross sections

14 Resonances in complex chemical reactions? Cl + CH 4 HCl + CH 3 case Vibrational mode dependence?

15 Resonances in Cl + CHD 3 HCl + CD 3? The effect of vibrational excitation. The answer is not clear. Further studies are needed.

16 Electron photodetachment spectra of molecular anions Information of transition-states, resonances

17 Resonances in Cl + CD4! DCl + CD3

18 Van der Waals resonances Cross Sections for the F + HD reaction (fine grid) Reaction Probabilities for each J Takayanagi, Chem. Phys. Lett. 433 (2006) 15.

19 Reaction induced by photoexcitation via vdw resonances Energy Cross Section A B Prereaction Process C Reaction van der Waals molecule Reaction Coordinate IR Laser Excitation Formation of van der Waals complexes A B A C B Dissociation C A Resonance State (Cl HF, Br HF, l HF etc) in low temperature helium nanodroplets Takayanagi, Phys. Chem. Chem. Phys. 1 (1999) Takayanagi, Chem. Phys. Lett. 338 (2001) 195. B C Cumulative Reaction Probability Partial Cross Section / arb. Computational results for prereaction processes for H HF, H DF, D HF van der Waals complexes x10-2 1x10-3 1x10-4 1x10-5 1x10-6 1x10-7 1x10-8 1x10-9 1x x x10-12 Prereaction of the D HF vdw molecule (a) (b) D HF(v=3, j ) j = 0 j = 1 j = 2 j = 3 j = 4 j = 5 j = 6 F + HD HF + D F + HD DF + H D HF + hν D + HF D HF + hν F + HD D HF + hν H + DF Total Energy / ev

20 van der Waals effects in Mu + F 2 Results of reduced dimensionality quantum reactive scattering calculations on model potential energy surfaces (with vdw vs. without vdw interaction) Mu F F With van der Waals force EXP. Mu F F Mu F F k / cm molecule s Repulsive force vs. vdw attractive force Tunneling distance is short Large tunneling probability Mu + F 2 MuF + F / T [K] van der Waals interaction plays an important role in rate constants at low temperatures Takayanagi et al, J. Phys. Chem. A 101 (1997) 7098.

21 van der Waals effects in low-energy collisions Interference Effect above Reaction Threshold Energy A + BC AB + C Threshold energy Energy Scattering wavefunction van der Waals resonance state Tunneling F + H 2, D 2 Effective Potential Reaction Coordinate "Importance of long-range interactions in chemical reactions at cold and ultracold temperatures" Weck and Balakrishnan, Int. Rev. Phys. Chem. 25 (2006)

22 Interstellar Chemistry : Low-temperature reactions CN + O 2 CN + C 2 H 6 CN + C 2 H 2 Georgievskii, J. Phys. Chem. A 111 (2007) I.W.M. Smith, Acc. Chem. Res. 33 (2000) 261.

23 Cold and Ultracold Molecules Faraday Discussion Vol. 142 "Molecular collisions, from warm to ultracold" D. Herschbach, Faraday Discuss. 142 (2009) 9-23.

24 Cold and Ultracold Molecules Xe + OH collision

25 Low-energy collision : CO + H2

26 Cold reaction of S( 1 D) + HD

27 Recombination Mechanism Collision-Induced Dissociation Recombination AB + M A + B + M (A, B: atom or molecule, M: third-body) Two important mechanisms 1) Sequential two-body mechanism A + B AB* (AB*: resonance state) AB* + M AB + M 2) Direct three-body mechanism A + B + M AB + M Energy AB* AB Rotational Barrier R(A-B)

28 H H translation energy distributions from close-coupling calculations dp/de j f = 6 j f = 0 j f = 2 j f = 4 (a) He + H 2 (v = 10, j = 0) He + H + H j f = 8 j f = 10 j f = 12 (b) Energy / ev dp/de j f = 7 j f = 1 j f = 5 j f = 3 (a) j f = 13 j f = 11 j f = 9 (b) He + H 2 (v = 11, j = 1) He + H + H j f = 15 j f = 17 j f = 19 (c) Energy / ev

29 Anomalous isotope effects in ozone formation reactive resonances? 16 O 16 O 16 O, 16 O 18 O 16 O, 18 O 16 O 18 O etc O + O 2 + M(N 2 ) O 3 + M(N 2 ) Babikov et al, Chem. Phys. Lett. 372 (2003)

30 Roaming dynamics in Mg + H 2 MgH + H Wave packet dynamics

31 Roaming dynamics in chemical reactions

32 DNA damage by low-energy electrons Electron irradia-on to Plasmid DNA Boudaïffa et al., Science, 287, 1658 (2000).

33 DNA damage by low-energy electrons Other dissociation channels can be seen at high energy Vibrational state

34 Mechanism of DNA damage Potential Energy Valence anion ( *) e Valence anion ( *) Neutral R B

35 Conclusions Resonances in chemical reactions have been experimentally observed in several systems due to advances in sophisticated experimental techniques. Resonances in chemical reactions may be very important in various fields!? Atmospheric and interstellar chemistry Anomalous isotope ratios More cold chemistry experiments in the future Resonances in DNA radiation damage (electron collision)