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)