Resonances in Chemical Reactions :

Theory and Experiment

Toshiyuki Takayanagi Saitama University

Department of Chemistry

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)

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)

Outline of this talk ・　Feshbach resonances in chemical reactions F + H2 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 + H2 MgH + H ・　Resonances in DNA radiation damage (electron collision)

Ene

rgy

A + BC(v)

AB(v) + C

v=0

v=1

v=2

Reaction Coordinate

Vibrationally adiabatic potential

(n1n2n3)

Potential energy surface

0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.50.0

0.2

0.4

0.6

0.8

1.0

v=2v=1v=0

H + H2(v) -> H2(all-v) + H

Prob

abilit

y

Total Energy / eV

×

R(B

C)

R(A-BC)

Reaction Probabilities from 2D calc.

Feshbach Resonances in Chemical Reactions

Difficulty for predicting reactive resonances from topological features of potential surfaces Importance of dynamics calculations something happens at threshold energy

van der Waals Resonance

(hydrogen-bonding)

Quasi-bound states in

a potential well

Reaction Coordinate

Ene

rgy

vdW or HB well

A + BC(v)

AB(v) + C

v = 0

v = 1

Reaction Coordinate E

nerg

y

A + BC(v) AB(v) + C

Resonance trajectory (classical picture)

Other mechanisms

How to observe resonances in chemical reactions ? 　　Collision energy dependence of cross sections

Nuclear Reaction for n + 235U Electron Collision, e + N2

・High-resolution molecular beam experiment (~ 0.01 eV) 　　State-to-state differential cross sections ・ Electron photodetachment measurement of anions

0.25 0.30 0.35 0.40

0.0

0.5

1.0

1.5

2.0

2.5

j = 6

j = 5

j = 0

j = 4

j = 3

j = 2

j = 1

D···HF(v=3, j )

F + HD → HF + D F + HD → DF + H

(a)

Total Energy / eV

Cum

ulat

ive

Rea

ctio

n Pr

obab

ility

Quantum results on Stark-Werner-PES Collision energy dependence of cross sections

J = 0

Wave function of reactive resonance in F + HD

1

2

3

4

(b)

r / a

0

1

2

3

4

(a)

4 5 6 7 8120

140

160

180

(c)

R / a0

γ / d

egre

e

F•••H•••D(003) (transient) Vibrationally excited state of linear triatomic molecule

Vibrationally adiabatic potential energy curve

Energy

F + HD HF + D

Reaction coordinate

resonance state tunneling

vibrationally adiabatic potential

Stabilization Diagram & State Density

5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.60.23

0.24

0.25

0.26

0.27

(a)

Ener

gy /

eV

5.90 5.95 6.00 6.05 6.10 6.15 6.20 6.250.25

0.26

(b)

6.25 6.30 6.35 6.40 6.45 6.50 6.55 6.600.25

0.26

(c)

ρmax / a0

0.23 0.24 0.25 0.26 0.27

1750

1800

1850

1900

1950Eres = 0.254 eVΓ = 0.00670 eV (τ = 98 fs)

Sta

te d

ensi

ty /

eV-1

Energy / eV

4 5 6 7 8

1

2

3

4θ = 37.3 deg.

ρ = 6

r' / a

u

R' / au

Extraction of resonance wave function

Solving 3D eigenvalue problems using DVR representation in hyperspherical coordinates (r,q,f) DVR Grid points ～ (50,100,200)　　

State-to-state differential cross section measurements for F + H2, HD

HF(v = 2, j = 6) HF(v = 2, j)

Science 311 (2006) 1440.

Differential cross sections

Vibrationally resolved cross sections

Differential cross sections

Resonances in complex chemical reactions ? Cl + CH4 HCl + CH3 case

Vibrational mode dependence ?

Resonances in Cl + CHD3 HCl + CD3 ?

The effect of vibrational excitation.

The answer is not clear. Further studies are needed.

Electron photodetachment spectra of molecular anions

Information of transition-states, resonances

Resonances in Cl + CD4 DCl + CD3

Van der Waals resonances Cross Sections for the F + HD reaction (fine grid)

Takayanagi, Chem. Phys. Lett. 433 (2006) 15.

Reaction Probabilities for each J

Reaction induced by photoexcitation via vdW resonances

A C B

IR Laser Excitation

van der Waals molecule

Reaction

B A C A C B

Resonance State

A C B

Reaction Coordinate

Cross Section

Energy

Dissociation

Prereaction Process

Computational results for prereaction processes for

H•••HF, H•••DF, D•••HF　van der Waals complexes

Formation of van der Waals complexes

(Cl•••HF, Br•••HF, l•••HF etc) in low temperature

helium nanodroplets

0.25 0.30 0.35 0.401x10-12

1x10-11

1x10-10

1x10-9

1x10-8

1x10-7

1x10-6

1x10-5

1x10-4

1x10-3

1x10-2

Prereaction of the D···HF vdW molecule

(b)

Par

tial C

ross

Sec

tion

/ arb

.

Total Energy / eV

D···HF + hν → D + HF D···HF + hν → F + HD D···HF + hν → H + DF

0.0

0.5

1.0

1.5

2.0

2.5

j = 6

j = 5

j = 0

j = 4

j = 3

j = 2

j = 1

D···HF(v=3, j )

F + HD → HF + D F + HD → DF + H

(a)

Cum

ulat

ive

Rea

ctio

n Pr

obab

ility

Takayanagi, Phys. Chem. Chem. Phys. 1 (1999) 1099.

Takayanagi, Chem. Phys. Lett. 338 (2001) 195.

van der Waals effects in Mu + F2 Results of reduced dimensionality quantum reactive scattering calculations on model potential energy surfaces (with vdW vs. without vdW interaction)

3 -1 -1

0 5 10 15 10 -12

10 -11

10 -10 With van der Waals force

k / c

m m

olec

ule

s

1000 / T [K]

Without van der Waals force

Mu + F 2 ® MuF + F

EXP.

Energy

Reactants Products

Reaction coord.

Mu

Mu F F

F F

Mu F F

Tunneling

Repulsive force vs. vdW attractive force 　　Tunneling distance is short 　　　　→ Large tunneling probability 　van der Waals interaction plays an important role in rate constants at low temperatures

Takayanagi et al, J. Phys. Chem. A 101 (1997) 7098.

Scattering wavefunction

van der Waals resonance state

Tunneling

Ene

rgy

Reaction Coordinate

Interference Effect above Reaction Threshold Energy

Effective Potential

Threshold energy

A + BC AB + C

van der Waals effects in low-energy collisions

F + H2, D2

"Importance of long-range interactions in chemical reactions at cold and ultracold temperatures"

Weck and Balakrishnan, Int. Rev. Phys. Chem. 25 (2006) 283-311

Interstellar Chemistry : Low-temperature reactions

CN + O2 CN + C2H6

CN + C2H2

I.W.M. Smith, Acc. Chem. Res. 33 (2000) 261. Georgievskii, J. Phys. Chem. A 111 (2007) 3802.

Cold and Ultracold Molecules Faraday Discussion Vol. 142

"Molecular collisions, from warm to ultracold"

D. Herschbach, Faraday Discuss. 142 (2009) 9-23.

Cold and Ultracold Molecules

Xe + OH collision

Low-energy collision : CO + H2

Cold reaction of S(1D) + HD

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

R(A-B)

Energy

AB*

Rotational Barrier

AB

0.00 0.05 0.10 0.15 0.200.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

jf = 6

jf = 4

jf = 2

jf = 0

(a)

dP

/dE

0.00 0.05 0.10 0.15 0.200.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

jf = 12

jf = 10

jf = 8

He + H2(v = 10, j = 0) → He + H + H

(b)

Energy / eV

0.00 0.05 0.10 0.15 0.200.000

0.002

0.004

0.006

0.008

0.010

(a)

jf = 3

jf = 5jf = 7

jf = 1

0.00 0.05 0.10 0.15 0.200.000

0.001

0.002

0.003

0.004

0.005

(b)

jf = 11

jf = 13

jf = 9

dP/d

E

0.00 0.05 0.10 0.15 0.200.000

0.001

0.002

0.003

0.004

0.005

He + H2(v = 11, j = 1) → He + H + H

(c)

jf = 17

jf = 19

jf = 15

Energy / eV

HH translation energy distributions from close-coupling

calculations

16O16O16O, 16O18O16O,18O16O18O etc O + O2 + M(N2) O3 + M(N2)

Anomalous isotope effects in ozone formation reactive resonances ?

Babikov et al, Chem. Phys. Lett. 372 (2003) 686-691.

Roaming dynamics in Mg + H2 MgH + H

Wave packet dynamics

Roaming dynamics in chemical reactions

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

(2000).

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

Vibrational state

Mechanism of DNA damage

Valence anion (s*)

RA-B

Pote

ntia

l Ene

rgy

Neutral

Valence anion (p*)

e‐

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)