[PPT] - Theory of collision-induced absorption (CIA) for electronic PowerPoint Presentation

SLIDE 1

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs.

Tijs Karman Ad van der Avoird Gerrit C. Groenenboom

Theoretical Chemistry, Institute for Molecules and Materials, Radboud University, Nijmegen, The Netherlands

June 21, 2017

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 1 / 18

SLIDE 2

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

O2 electronic transitions X 3Σ−

g → a1∆g, b1Σ+ g

X 3Σg

−

b 1Σg

+ 1∆g

a

A band, 760 nm "M1,E2" 1.27 μm "M1,E2" 1.06 μm no lines

“For collisional induction of these bands a foreign molecule is more or less as expedient as an O2 molecule. The specific properties of the collisional partner hardly matter as long as it is not absent.”

L. Frommhold, Collision-Induced Absorption in Gases

(Cambridge Univ. Press, Cambridge, 1994).

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 2 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

O2 − X2 transition mechanism

Roto-translational and vibrational transitions: Quadrupole induction

No intensity for spin-forbidden transitions!

O2 − N2

O2(X 3Σ−

g ) + N2(1Σ+ g )

S′′

tot=1

+hν → O2(a1∆g, b1Σ+

g ) + N2(1Σ+ g )

S′

tot=0

⇒ Spin-orbit coupling must be involved

O2 − O2 (paramagnetic partner)

O2(X 3Σ−

g ) + O2(X 3Σ− g )

S′′

tot=0,1,2

+hν → O2(a1∆g, b1Σ+

g ) + O2(X 3Σ− g )

S′

tot=1

⇒ Additional exchange-induced contribution

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 3 / 18

SLIDE 4

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Line-shape calculations

Theory:

First line-shape calculations for electronic transitions
Previously: Roto-translational and vibrational transitions

6 8 10 12 14 16 −60 −40 −20 20 40 60 80 100 R/a0 V/cm−1 Final state Initial state Dipole overlap Dipole moment Potential energy

Potentials used to calculate

scattering wave functions

Dipole surfaces used to

calculate dipole coupling

Thermally average initial states
Energy difference initial and

final states set by frequency

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 4 / 18

SLIDE 5

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Electronic states O2 − O2

O2 − O2(X 3Σ−

g , a1∆g, b1Σ+ g )

Nearly degenerate states:

Two components of a1∆g
Excitation on molecule A or B

Requires diabatization

[Karman et al. JCP 144, 121101 (2016)]

Triplet-dimer diabatic states

|X 3Σ−

g |b1Σ+ g

|b1Σ+

g |X 3Σ− g

Coupled
|X 3Σ−

g |a1∆g,+2

|X 3Σ−

g |a1∆g,−2

|a1∆g,+2|X 3Σ−

g

|a1∆g,−2|X 3Σ−

g

             Coupled

|X 3Σ−

g |X 3Σ− g

[F12-MRCI / π + π∗ active space]

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 5 / 18

SLIDE 6

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

O2 − O2 triplet potential energy surfaces

5 6 7 8 9 10 R/a 0 5000 10000 15000 V/cm -1 (a) X 3Σg

+ X 3Σg
X 3Σg
+ a 1∆g

X 3Σg

+ b 1Σ+

g

6 7 8 9 10 R/a 0

100
50

50 100 V/cm -1 (c) 5 6 7 8 9 10 R/a 0

150
100
50

50 100 150 200 V/cm -1 (b ) 5 6 7 8 9 10 R/a 0

150
100
50

50 100 150 200 V/cm -1 (d)

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 6 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Exchange-induced transition dipole moment

Adiabatic

30 60 90 120 150 180

Dihedral angle / deg

0.2 0.4 0.6 0.8 1

Transition dipole / a.u.

×10 -3

Diabatic

30 60 90 120 150 180

Dihedral angle / deg

0.2 0.4 0.6 0.8 1

Transition dipole / a.u.

×10 -3

Diabatization critical for smooth electronic transition dipole surfaces

[Karman et al. JCP 144, 121101 (2016)]

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 7 / 18

SLIDE 8

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Exchange-induced transition dipole moment

5 5.5 6 6.5 7 R/a 0

10
5

5 10 15 20

µ⊥ / mDebye

a 1∆g, θA= π/4, θB=0 b 1Σ+

g , θA= π/4, θB=0

a 1∆g, θA= π/2, θB=0 b 1Σ+

g , θA= π/2, θB=0

—— MRCI dipole surface

- - CASSCF dipole surface

Exponential R-dependence How to obtain accurate intermolecular-exchange-induced dipole surfaces?

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 8 / 18

SLIDE 9

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Spin-orbit-induced transition dipole moment

Intramolecular (O2) spin-orbit coupling breaks spin symmetry |ΨX,0 =|X 3Σ−

g + CSO|b1Σ+ g

CSO =b1Σ+

g |ˆ

HSO|X 3Σ−

g

EX − Eb = 0.0134i (1) Transition quadrupole moment a1∆g|ˆ Θ|ΨX,0 = CSOa1∆g|ˆ Θ|b1Σ+

g

(2a) Ψb|ˆ Θ|ΨX,0 = CSO

b1Σ+

g |ˆ

Θ|b1Σ+

g − X 3Σ− g |ˆ

Θ|X 3Σ−

g

(2b)

Quadrupole-induced dipole moment a1∆g|ˆ µν|ΨX,0 ∝ a1∆g|ˆ ΘA|ΨX,0 αB R−4 (3a) b1Σ+

g |ˆ

µν|ΨX,0 ∝ b1Σ+

g |ˆ

ΘA|ΨX,0 αB R−4 (3b)

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 9 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Line-shape calculations (Revisited)

6 8 10 12 14 16 −60 −40 −20 20 40 60 80 100 R/a0 V/cm−1 Final state Initial state Dipole overlap Dipole moment Potential energy

Isotropic interaction approximation:

1 Calculate wave functions for

V ( rA, rB, R) → V0(R)

2 Calculate coupling using

full dipole surface

Isotropic theory extended to

electronic transitions

Anisotropy corrections from

classical statistical mechanics Intensities scaled to experimental results Empirical scaling within uncertainty of dipole surfaces

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 10 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Intensities scaled to experiment

7600 7700 7800 7900 8000 8100 8200 / cm -1 10 -9 10 -8 10 -7 10 -6 / cm -1 amagat -2

Log-scale

[Mat´ e et al. (1999)]

9000 9200 9400 9600 9800 / cm -1 2 4 6 8 10 / cm -1 amagat -2 10 -7

[Karman et al. (submitted)]

10600 10800 11000 11200 / cm -1 1 2 3 4 5 6 / cm -1 amagat -2 10 -8

[Spiering et al. (2012)]

12800 13000 13200 13400 13600 / cm -1 10 -10 10 -9 10 -8 10 -7 10 -6 / cm -1 amagat -2

Log-scale

[Tran et al. (2006)]

14200 14400 14600 14800 / cm -1 0.5 1 1.5 2 2.5 / cm -1 amagat -2 10 -8

[Spiering et al. (2011)]

O2 − O2 CIA

More intense
Broader line shape
Decays less rapidly with v ′

⇒ O2 − O2 dominated by exchange

SLIDE 12

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Line shape

7600 7700 7800 7900 8000 8100 8200

/ cm -1

10 -9 10 -8 10 -7 10 -6

/ cm -1 amagat -2

Log-scale

12800 13000 13200 13400 13600

/ cm -1

10 -10 10 -9 10 -8 10 -7 10 -6

/ cm -1 amagat -2

Log-scale Line shape “Fourier transform of the dipole function” O2 − O2 Exchange Short ranged exp(−αR) Broad spectrum O2 − N2 Spin-orbit Long ranged R−4 Narrower spectrum

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 12 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Analytical line-shape model

“Translational profile” for hard-sphere scattering at energy kT µ(R) ∝ exp(−αR) → VGExch(ω) = α2kk′ {(α2 + k′)2 + 2(α2 − k2)k′2 + k′4}2 µ(R) ∝ R−4 → VGSO(ω) = 1 kk′

G 3,1

1,3

a2 4 [k − k′]2

3

2

2 2

Where: k = √2µkBT, k′ =

2µ(kBT + ω)

a the hard-sphere radius, G ·,·

·,· the Meijer G function.

50 100 150 200

/ cm -1

10 -3 10 -2 10 -1 10 0 Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 13 / 18

SLIDE 14

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Vibrational dependence

7600 7700 7800 7900 8000 8100 8200 / cm -1 10 -9 10 -8 10 -7 10 -6 / cm -1 amagat -2

Log-scale

9000 9200 9400 9600 9800 / cm -1 2 4 6 8 10 / cm -1 amagat -2 10 -7

Spin-orbit mechanism (O2 − N2)

O2 transition quadrupole:

Weak r-dependence

Suppression v ′ = 1 close to FCF ≈ 10−2

Exchange mechanism (O2 − O2)

Exponential geometry dependence dipole
Calculations including one vibrational

coordinate

Suppression v ′ = 1 around 0.2−0.7
Experiment: 0.6

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 14 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Temperature dependence X 3Σ−

g → a1∆g

Exchange-based mechanism

7600 7700 7800 7900 8000 8100 8200

/ cm -1

10 -10 10 -9 10 -8 10 -7

/ cm -1 amagat -2

T=300 K T=200 K T=100 K

Spin-orbit-based mechanism

7600 7700 7800 7900 8000 8100 8200

/ cm -1

10 -10 10 -9 10 -8 10 -7

/ cm -1 amagat -2

T=300 K T=200 K T=100 K

Exchange mechanism: Intensity increases with T.

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 15 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Uncertainty estimates

X 3Σ−

g → a1∆g

7600 7700 7800 7900 8000 8100 8200 / cm -1 10 -9 10 -8 10 -7 10 -6 10 -5 / cm -1 amagat -2 Experiment MRCI MRCI 0.7 bohr shift CASSCF CIS lCAS RAS (a)

X 3Σ−

g → b1Σ+ g

12750 13000 13250 13500 / cm -1 10 -10 10 -9 10 -8 10 -7 10 -6 / cm -1 amagat -2 Experiment MRCI MRCI 0.6 bohr shift CASSCF CIS lCAS RAS (b)

Different dipole surfaces:

Line shape unaffected
Intensity affected by up to factor 10
Scaling within “theoretical error bar”

Scaling factors MRCI theory to experiment, including anisotropy corrections

Transition cO2−O2

exch

cO2−O2

SO

cO2−N2

SO

X 3Σ−

g → a1∆g

4.5 1.0 1.6 X 3Σ−

g → b1Σ+ g

5.6 0.9 0.7

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 16 / 18

SLIDE 17

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Conclusions

First line-shape calculations for electronic transitions in molecular collisions

Line shape in good agreement with experiment
Intensities within large “theoretical error bars”
Large uncertainty intermolecular-exchange-induced transition dipole

Identified absorption mechanism (Exchange / SO)

Mechanism depends on collision partner (O2 − O2 / O2 − N2)
Qualitative differences
Intensity
Line shape
v ′-dependence
T-dependence

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 17 / 18

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Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Acknowledgements

Iouli Gordon (Harvard-Smithsonian CfA)
Wim van der Zande (RU Nijmegen, now at ASML)
David Parker (RU Nijmegen)
Piotr ˙

Zuchowski (Toru´ n)

Computer resources
Funding

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 18 / 18

SLIDE 19

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

References

Theoretical progress

Diabatization

[Karman et al. J. Chem. Phys. 144 121101 (2016)]

Potentials & dipoles

[Karman et al. Submitted]

Line-shape theory

[Karman et al. Submitted]

Absorption mechanism

[Karman et al. Submitted]

Experimental results

a1∆g(v ′ = 0) [Mat´

e et al. J. Geophys. Res.: Atmospheres 104 30585 (1999) ]

a1∆g(v ′ = 1) [Karman et al. Submitted ]
a1∆g(v ′ = 2) [Spiering et al. Phys. Chem. Chem. Phys. 14 9923 (2012) ]
b1Σ+

g (v ′ = 0) [Tran et al. J. Geophys. Res. 111 D15210 (2006) ]

b1Σ+

g (v ′ = 1) [Spiering et al. Phys. Chem. Chem. Phys. 13 9616 (2011) ]

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 19 / 18

SLIDE 20

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Scaling factors

Table : Scale factors for theoretical line shapes fit to experimental data. Classical statistical mechanical corrections for anisotropic interactions have been included.

Transition cO2−O2

exch

cO2−O2

SO

cO2−N2

SO

X 3Σ−

g → a1∆g

4.54 1.04 1.61 X 3Σ−

g → a1∆g(v ′ = 1)

2.91 X 3Σ−

g → a1∆g(v ′ = 2)

0.16 X 3Σ−

g → b1Σ+ g

5.55 0.94 0.67 X 3Σ−

g → b1Σ+ g (v ′ = 1)

0.61

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 20 / 18

SLIDE 21

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Property-based diabatization

Multiple-property diabatization algorithm

1 Calculate a set of properties in the adiabatic representation, Ap 2 Calculate the same properties in a diabatic model, Dp

|ψAψB =

ˆ

R(ΩA)|ψA

⊗
ˆ

R(ΩB)|ψB

Compute properties from monomer contributions

3 Fit adiabatic-to-diabatic transformation, U, to

Ap = UDpU† ∀ properties p

[Karman et al. J. Chem. Phys., 144, 121101 (2016)]

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 21 / 18

SLIDE 22

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Classical statistical theory

Integrated intensities ∞

−∞

g(ω, T)dω ∝ Tr

exp
− V

kT

µ2
Roto-translational

[N2 − N2 JCP 142 084306 (2015)]

T-shaped geometry dominant
Anisotropic potential deeper
20 % increase at T = 78 K
No effect at T = 300 K
Electronic excitations
Contributions from parallel geometries
Qualitative differences potentials
Large effects, up to factor 4 at T = 300 K 4

6 8 10 12 14 −100 −80 −60 −40 −20 R/a0 V/cm−1

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 22 / 18

SLIDE 23

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

O2 − O2 transition density

Transition moment density ψ|ˆ µ|φ = −

drρψ←φ(r)r

ρψ←φ(r) =

dr2
dr3 · · ·
drnψ∗(r, r2, r3, · · · , rn)φ(r, r2, r3, · · · , rn)

H-shaped X 3Σ−

g → a1∆g transition

CASSCF in minimal π∗-shell active space Basis set: aVDZ

1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 10 1 1 10 10 1 1 1 x

4
3
2
1

1 2 3 4 z

6
4
2

2 4 6

Basis set: aVTZ

1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 10 10 1 10 10 1 10 10 x

4
3
2
1

1 2 3 4 z

6
4
2

2 4 6

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 23 / 18

SLIDE 24

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions

Convergence with method?

H-shaped X 3Σ−

g → a1∆g transition, aVTZ basis set

π∗-shell active space CASSCF

1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 10 10 1 10 10 1 10 10 x

4
3
2
1

1 2 3 4 z

6
4
2

2 4 6

π∗-shell active space MRCI

8
8
8
8
8
8
8
8
6
6
6
6
6
6
6
6
4
4
4
4
4
4
4
4
4
4
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 8 10 10 10 1 1 10 1 10 x

4
3
2
1

1 2 3 4 z

6
4
2

2 4 6

π + π∗-shell active space CASSCF

2
2
2
2
1
1
1
1
1
1
1
1

1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 10 1 10 10 10 10 x

4
3
2
1

1 2 3 4 z

6
4
2

2 4 6

π + π∗-shell active space MRCI

10
1
10
10
8
8
8
8
6
6
6
6
6
6
4
4
4
4
4
4
4
4
4
4
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 4 4 4 4 4 4 4 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 8 8 8 10 10 1 10 1 1 10 10 10 1 10 10 x

4
3
2
1

1 2 3 4 z

6
4
2

2 4 6

Tijs Karman, Ad van der Avoird, Gerrit C. Groenenboom Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O2−O2 and O2−N2 pairs. 24 / 18