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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions Theory of collision-induced absorption (CIA) for electronic transitions in the atmospherically relevant O 2 − O 2 and O 2 − N 2 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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions O 2 electronic transitions X 3 Σ − g → a 1 ∆ g , b 1 Σ + g + b 1 Σ g 1 ∆ g a A band, 760 nm "M1,E2" X 3 Σ g − 1.27 μ m "M1,E2" 1.06 μ m no lines “For collisional induction of these bands a foreign molecule is more or less as expedient as an O 2 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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions O 2 − X 2 transition mechanism • Roto-translational and vibrational transitions: Quadrupole induction No intensity for spin-forbidden transitions! • O 2 − N 2 O 2 ( X 3 Σ − g ) + N 2 ( 1 Σ + + h ν → O 2 ( a 1 ∆ g , b 1 Σ + g ) + N 2 ( 1 Σ + g ) g ) � �� � � �� � S ′′ tot =1 S ′ tot =0 ⇒ Spin-orbit coupling must be involved • O 2 − O 2 (paramagnetic partner) O 2 ( X 3 Σ − g ) + O 2 ( X 3 Σ − + h ν → O 2 ( a 1 ∆ g , b 1 Σ + g ) + O 2 ( X 3 Σ − g ) g ) � �� � � �� � S ′′ tot =0 , 1 , 2 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

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 100 Final state 80 • Potentials used to calculate 60 scattering wave functions Initial state 40 V/cm −1 • Dipole surfaces used to 20 Dipole moment calculate dipole coupling 0 Potential energy Dipole overlap −20 • Thermally average initial states −40 • Energy difference initial and −60 final states set by frequency 6 8 10 12 14 16 R/a 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. 4 / 18

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions Electronic states O 2 − O 2 O 2 − O 2 ( X 3 Σ − g , a 1 ∆ g , b 1 Σ + g ) Triplet-dimer diabatic states Nearly degenerate states: • | X 3 Σ − g �| b 1 Σ + g � � Coupled • Two components of a 1 ∆ g • | b 1 Σ + g �| X 3 Σ − g �  • Excitation on molecule A or B • | X 3 Σ − g �| a 1 ∆ g , +2 �     • | X 3 Σ − g �| a 1 ∆ g , − 2 �   Coupled • | a 1 ∆ g , +2 �| X 3 Σ − g �     • | a 1 ∆ g , − 2 �| X 3 Σ −  g �  Requires diabatization • | X 3 Σ − g �| X 3 Σ − g � [Karman et al. JCP 144 , 121101 (2016)] [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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions O 2 − O 2 triplet potential energy surfaces 15000 200 X 3 Σ g - + b 1 Σ + (a) g (b ) 150 100 10000 - + a 1 ∆ g X 3 Σ g V/cm -1 V/cm -1 50 0 5000 -50 -100 - + X 3 Σ g X 3 Σ g - 0 -150 5 6 7 8 9 10 5 6 7 8 9 10 R/a 0 R/a 0 100 200 (c) (d) 150 50 100 V/cm -1 V/cm -1 50 0 0 -50 -50 -100 -100 -150 6 7 8 9 10 5 6 7 8 9 10 R/a 0 R/a 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. 6 / 18

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions Exchange-induced transition dipole moment Adiabatic Diabatic × 10 -3 × 10 -3 1 1 0.8 0.8 Transition dipole / a.u. Transition dipole / a.u. 0.6 0.6 0.4 0.4 0.2 0.2 0 0 0 30 60 90 120 150 180 0 30 60 90 120 150 180 Dihedral angle / deg Dihedral angle / deg 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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions Exchange-induced transition dipole moment 20 a 1 ∆ g , θ A = π /4, θ B =0 15 b 1 Σ + g , θ A = π /4, θ B =0 —— MRCI dipole surface a 1 ∆ g , θ A = π /2, θ B =0 - - - CASSCF dipole surface 10 b 1 Σ + µ ⊥ / mDebye g , θ A = π /2, θ B =0 5 0 -5 -10 5 5.5 6 6.5 7 R/a 0 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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions Spin-orbit-induced transition dipole moment Intramolecular ( O 2 ) spin-orbit coupling breaks spin symmetry | Ψ X , 0 � = | X 3 Σ − g � + C SO | b 1 Σ + g � g | ˆ C SO = � b 1 Σ + H SO | X 3 Σ − g � = 0 . 0134 i (1) E X − E b Transition quadrupole moment � a 1 ∆ g | ˆ Θ | Ψ X , 0 � = C SO � a 1 ∆ g | ˆ Θ | b 1 Σ + g � (2a) � � � Ψ b | ˆ g | ˆ g | ˆ � b 1 Σ + Θ | b 1 Σ + g � − � X 3 Σ − Θ | X 3 Σ − Θ | Ψ X , 0 � = C SO g � (2b) Quadrupole-induced dipole moment µ ν | Ψ X , 0 � ∝ � a 1 ∆ g | ˆ � a 1 ∆ g | ˆ Θ A | Ψ X , 0 � α B R − 4 (3a) g | ˆ � b 1 Σ + µ ν | Ψ X , 0 � ∝ � b 1 Σ + Θ A | Ψ X , 0 � α B R − 4 g | ˆ (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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions Line-shape calculations (Revisited) Isotropic interaction approximation: 100 Final state 80 60 1 Calculate wave functions for Initial state r B , � 40 V ( � r A ,� R ) → V 0 ( R ) V/cm −1 20 2 Calculate coupling using Dipole moment 0 full dipole surface Potential energy Dipole overlap −20 • Isotropic theory extended to −40 electronic transitions −60 6 8 10 12 14 16 • Anisotropy corrections from R/a 0 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

Introduction Potentials & dipole moments Line-shape calculations & comparison to experiment Conclusions 10 -6 10 -6 / cm -1 amagat -2 10 -7 Log-scale / cm -1 amagat -2 Log-scale 10 -7 10 -8 10 -8 Intensities scaled to experiment 10 -9 10 -9 10 -10 7600 7700 7800 7900 8000 8100 8200 12800 13000 13200 13400 13600 / cm -1 / cm -1 [Mat´ e et al. (1999)] [Tran et al. (2006)] 10 -7 10 -8 10 2.5 8 2 / cm -1 amagat -2 / cm -1 amagat -2 6 1.5 1 4 0.5 2 0 0 14200 14400 14600 14800 9000 9200 9400 9600 9800 / cm -1 [Spiering et al. (2011)] / cm -1 [Karman et al. (submitted)] 10 -8 6 O 2 − O 2 CIA 5 / cm -1 amagat -2 4 • More intense 3 • Broader line shape 2 • Decays less rapidly with v ′ 1 0 ⇒ O 2 − O 2 dominated by exchange 10600 10800 11000 11200 / cm -1 [Spiering et al. (2012)]