Ab initio calculations for photodissociation of diatomic molecules

Ab initio calculations for photodissociation of diatomic molecules Gerrit C. Groenenboom Theoretical Chemistry Institute for Molecules and Materials Radboud University Nijmegen The Netherlands Leiden 215 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 1 / 27

Experimental collaborators on photodissociation Dave Parker (Nijmegen): O 2 O( 3 P j ) + O( 3 P j ), O 2 O( 3 P j ) + O( 1 D 2 ), S 2 S( 3 P j ) + S( 3 P 2 ), OH O( 3 P j ) + H( 2 S) SH S( 3 P j ) + H( 2 S) NO 2 NO + O( 1 D) Wim van der Zande (Nijmegen): O 2 O ( 2 P j ) + O( 3 P j ) Simon North (Texas A&M): ClO Cl( 2 P j ) + O( 3 P j ) Maurice Janssen (VU): N 2 O NO + O( 1 D) Mark Brouard (Oxford): SO 2 O( 3 P) + SO( 3 Σ ) Roger Miller (North Carolina): (HCl) 2 HCl(j) + HCl(j ) (HF) 2 HF(j) + HF(j ) Gerard Meijer (Nijmegen): He + CO(A X ) He + CO(X ) www.theochem.ru.nl/cgi-bin/dbase/search.cgi?pr:photo Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 2 / 27

Overview Single channel photodissociation - direct dissociation of OH Multichannel photodissociation - predissociation of OD Correlated fine structure distributions - ClO Adiabatic model Diabatic model Multichannel treatment Absolute cross sections: Forbidden transitions, Herzberg I, O 2 Collision induced absorption, H 2 +H 2, N 2 +N 2, (O 2 +N 2 /O 2 ) Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 3 / 27

Direct dissociation: OH(X 2 Π) O( 3 P)+H Energy (ev) 1 5 1 2 Σ X 2 Π χ v (R) E ph = 5.1 ev = 243 nm Ψ (R;E) Bound state wave function: ] [ 2 2 2µ R + V 2 X (R) E ν χ ν(r) = Continuum wave function: ] [ 2 2 2µ R + V1(R) E Ψ (R; E) = 2 Transition dipole moment: 5 1 2 3 4 5 Interatomic distance (bohr) µ(r) = 1 2 Σ ˆµ x X 2 Π x Photodissociation cross section for ω = E E ν: σ(ω) = πω ɛ c Ψ (R; E) µ(r) χ ν(r) 2 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 4 / 27

Direct dissociation OD(X 2 Π) O( 3 P) + D( 2 S) Experiment Velocity map ion imaging Measure kinetic energy of O or D OD produced in discharge T rot 1K Populations of vibrational level: P ν (T ) e Eν/kT vib Fit to theory: T vib 17K Radenović, van Roij, Chestakov, Eppink, ter Meulen, Parker, Loo, Groenenboom, Greenslade, Lester, J. Chem. Phys. 119, 9341 (23) Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 5 / 27

Predissociation, OH(X 2 Π) O( 3 P) + H( 2 S) Velocity-map ion imaging experiment: H ε θ R O v Π Σ : I (θ) sin 2 θ Π Π : I (θ) cos 2 θ General: I (θ) 1 + βp 2 (cos θ) β = 1 β = 2. REMPI detection of fine structure states: O( 2 P J, J = 2, 1, ) Further complication, product alignment: JM, M = J,..., J I J (θ, ω) 1 + β J (ω)p 2 (cos θ) + γ J (ω)p 4 (cos θ) Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 6 / 27

OH predissociation proper quantum treatment Molecular electronic states: Ω = Λ + Σ: 2S+1 Λ Ω = X 2 Π 3/2, X 2 Π 1/2, 1 2 Σ 1/2, 1 4 Σ 3/2, 1 4 Σ 1/2, 1 4 Π 5/2, 1 4 Π 3/2, 1 4 Π 1/2, A 2 Σ 1/2 Multichannel expansion: Ψ J = SΛΩ 2S+1 Λ Ω JΩM c SΛΩJ (R) 2 2µ + ˆl 2 R 2 Hamiltonian: Ĥ = 2 + H 2µR 2 BO + H SO Born-Oppenheimer: H BO (5 potentials) Spin orbit coupling: H SO : Ω Ω (9 unique couplings) Coriolis coupling ˆl 2 : Ω Ω ± 1 (3 unique couplings) G. Parlant and D. R. Yarkony, J. Chem. Phys. 11, 363 (1999) Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 7 / 27

Predissociation of ClO(X 2 Π 3/2 ), correlated products ClO(X 2 Π 3/2 ) 28nm ClO(A 2 Π 3/2, v) Cl( 2 P 3/2,1/2 ) + O( 3 P 2,1, ) K. Dooley, M. Grubb, J. Geidosch, M. van Beek, G. Groenenboom, and S. North, PCCP 11, 477 (29) H. Kim, K. Dooley, G. Groenenboom, and S. North, PCCP 8, 2964 (26) I. Lane, W. Howie, A. Orr-Ewing, PCCP 1, 387 (1999); PCCP 1, 379 (1999) A. Toniolo, M. Persico, Pitea, J. Chem. Phys. 112, 279 (2) Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 8 / 27

Predissociation of ClO, adiabatic model Molecular states: 2S+1 Λ Ω Atomic states: Cl(J Cl, Ω Cl ) + O(J O, Ω O ) Model: correlate Ω = Ω Cl + Ω O Expected to work for low kinetic energy Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 9 / 27

Predissociation of ClO, diabatic model Atomic fine structure states: J Cl Ω Cl J O Ω O Russel-Saunders coupling for atoms (Ω i = Λ i + Σ i ): J i Ω i = Λ i Σ i L i Λ i S i Σ i L i Λ i S i Σ i J i Ω i, i = Cl, O Coupled atomic spin gives molecular spin (Σ = Σ Cl + Σ O ) SΣ = Σ Cl Σ O S Cl Σ Cl S O Σ O S Cl Σ Cl S O Σ O SΣ Orbital part Λ = Λ Cl + Λ O : LΛ = Λ Cl Λ O L Cl Λ Cl L O Λ O L Cl Λ Cl L O Λ O LΛ Fine structure branching in diabatic or sudden limit: P (LΛSΣ) J Cl,J O = J Cl Ω Cl J O Ω O LΛSΣ 2 Ω Cl Ω O = Ω Cl Ω O Λ Cl Λ O Σ Cl Σ O L Cl Λ Cl S Cl Σ Cl J Cl Ω Cl L O Λ O S O Σ O J O Ω O S Cl Σ Cl S O Σ O SΣ L Cl Λ Cl L O Λ O LΛ 2 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 1 / 27

Results for ClO fine structure branching Coupled channel, Fermi golden rule: Γ (n) v ;J Cl J O = 2π A2 Π 3/2 (v ) Ĥ A,n Ψ JCl Ω Cl J O Ω O 2. Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 11 / 27

Results for ClO fine structure branching Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 12 / 27

Results for ClO fine structure branching Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 13 / 27

Forbidden transitions: oxygen Herzberg I, II, and III Potential Energy (ev) 3 2 1 1 2 3 A 3 Σ u + A 3 u c 1 Σ u B 3 Σ u 226 nm b 1 Σ g + 5 Σu 5 Πu 1 Π u 3 + 2 Σu 1 3 Π u O( 3 P j ) + O( 1 D 2 ) O( 3 P ja ) + O( 3 P jb ) 4 5 X 3 Σ g a 1 g 2 2.5 3 3.5 4 4.5 5 R (bohr) Herzberg I: A 3 Σ + u X 3 Σ g Herzberg II: c 1 Σ u X 3 Σ g Herzberg III: A 3 u X 3 Σ g B. Buisse, W. van der Zande, A. Eppink, D. Parker, B. Lewis, and S. Gibson, J. Chem. Phys. 18, 7229 (1998) Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 14 / 27

Pathways for Herzberg I transition Spin-orbit through 3 Σ u, (2 states) X 3 Σ g,1 Spin-orbit through 3 Π u, (3 states) 3 SO Σ u,1 A 3 Σ + u,1 X 3 Σ g, X 3 Σ g,1 Orbit-rotation through 3 Π u, (3 states) X 3 Σ g, X 3 Σ g,1 X 3 Σ g,1 Spin-orbit through 3 Π g, (2 states) X 3 Σ g, SO X 3 Σ SO g,1 Orbit-rotation through 3 Π g, (2 states) X 3 Σ g, X 3 Σ g,1 OR OR X 3 Σ OR g,1 Spin-orbit through 3 Σ + g, (1 state) X 3 Σ g,1 SO 3 Πu,1 SO A 3 Σ + u,1 3 Πu, SO A 3 Σ + u, 3 Πu,1 OR A 3 Σ + u, 3 Πu, OR A 3 Σ + u,1 3 Πu,2 OR A 3 Σ + u,1 3 Πg, A 3 Σ + u,1 3 Πg,1 A 3 Σ + u, 3 Πg,1 A 3 Σ + u, 3 Πg, A 3 Σ + u,1 3 Πg,2 A 3 Σ + u,1 3 + Σ g,1 A 3 Σ + u,1 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 15 / 27

Integrated line cross section for O 2 Herzberg I Cross-sections in 1 26 cm 2 molecule 1 cm 1 Q Q11 Q Q22 Q Q33 15 1 calc exp 3 2 calc exp 3 2 calc exp 5 1 1 7 13 19 25 1 7 13 19 25 Q Q R12 R23 15 15 calc calc exp exp 1 1 5 5 1 7 13 19 25 1 7 13 19 25 Q Q P21 P32 1 1 calc calc 8 exp 8 exp 6 6 4 4 2 2 1 7 13 19 25 1 7 13 19 25 O O P12 P23 3 3 calc calc exp exp 2 2 1 1 1 7 13 19 25 1 7 13 19 25 1 1 7 13 19 25 S R21 3 calc exp 2 1 1 7 13 19 25 Potential Energy [ev] 12 9 6 3 3 6 X 3 Σ g A 3 Σ u + A 3 u c 1 Σ u 3 Σg + 3 Πu 3 Σ u 1 Π g 3 Π g 2. 2.5 3. R [a ] Experiment: M.-F. Mérienne et al., J. Mol. Spectrosc. 22, 171 (2). Theory: PhD thesis Mirjam van Vroonhoven, Nijmegen, 23 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 16 / 27

Collision induced absorption (CIA) V/cm 1 1 8 6 4 2 2 4 6 Final state Initial state Dipole overlap Dipole moment Potential energy 6 8 1 12 14 16 R/a H 2 (N)+H 2 (N ), Tijs Karman, A. van der Avoird, G. Groenenboom, J. Chem. Phys. (215), accepted N 2 (N)+N 2 (N ), Tijs Karman, E. Milliordos, K. Hunt, G. Groenenboom, A. van der Avoird, J. Chem. Phys. (215), accepted Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 17 / 27

Collision induced absorption, theory CIA absorption coefficient quadratic in monomer density Dominant contribution from continuum states (integral sign) [ ( α(ω, T ) = 2π2 3 c n2 ω 1 exp ω )] V g(ω, T ) k B T Spectral density: g(ω, T ) = i P (i) (T ) i ˆµ f 2 δ(ω f ω i ω). f Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 18 / 27

Multichannel expansion of wave function Coupled angular basis function (N A N B )NL; JM = M A,M B,M N,M L N A M A N B M B LM L N A M A N B M B NM N NM N LM L JM Expansion of the potential in coupled spherical harmonics V (R) = l 1,l 2,l [ [ ] (l) () V l1,l 2,l(R) C (l1) (ˆr A ) C (l2) (ˆr B )] C (l) (ˆR). Expansion of spherical components of the dipole moment µ ν (R) = l 1,l 2,l,λ [ [ ] (l) (1) D l1,l 2,l,λ(R) C (l1) (ˆr A ) C (l2) (ˆr B )] C (λ) (ˆR). ν Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 19 / 27

Approximation schemes Isotropic interaction approximation: separation of degrees of freedom. (Keep angular dependence of dipole surfaces) (N A N B )NL; JME col = (N A N B )NL; JM E col, L, R E col, L = 1 R U E col,l(r). Coupled-states approximation: neglect off-diagonal coriolis coupling. ˆL 2 = (Ĵ ˆN) 2 Ĵ 2 + ˆN 2 2Ĵ z ˆN z Coupled channels: Numerically exact calculation of the dipole coupling. Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 2 / 27

CIA H 2 H 2 Usual isotropic interaction accurate for H 2. 1 5 α/cm 1 amagat 2 1 6 1 7 1 8 T = 77 K T = 195 K T = 292 K 2 4 6 8 1 ω/cm 1 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 21 / 27

CIA N 2 N 2 Isotropic interaction approximation for high T. 1 1 1 4 α(t=3k) α/cm 1 amagat 2 1 2 1 3 1 4 1 5 1 3 α(t=228.3k) 1 2 α(t=126k) 1 1 α(t=93k) 1 6 α(t=78k) 1 7 5 1 15 2 25 ω/cm 1 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 22 / 27

CIA N 2 N 2 Large effects of anisotropy for low energy. Coupled-states approximation captures effect of anisotropy. 1 12 Isotropic interaction approximation Coupled states approximation Close coupling calculation 1 1 f(ω,e)/a.u. 1 8 1 6 1 4 1 1 1 1 1 1 2 1 3 E/K Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 23 / 27

CIA N 2 N 2, T=78 K 1 5 α/cm 1 amagat 2 1 6 Experiment Anisotropic theory Isotropic theory 1 7 5 1 15 2 ω/cm 1 Anisotropic calculations improve agreement with experiment (19 %). Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 24 / 27

CIA N 2 N 2 Bound-free contribution about 1 % at T = 78 K. Contribution about 1 % at T = 5 K. α/cm 1 amagat 2 1 5 1 6 1 7 1 8 Free free Bound free Bound bound Isotropic total 1 9 5 1 15 2 ω/cm 1 Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 25 / 27

Conclusion Photodissociation finestructure branching ratios Predissociation rates Forbidden transitions Collision induced absorption Question: what is most urgently needed in astrochemistry? Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 26 / 27

Acknowledgements Theory Nijmegen Mirjam van Vroonhoven (O 2 ) Mark van der Loo (OH, H 2 ) Marloes van Beek (ClO) Liesbeth Janssen (OH, SH) Tijs Karman (CIA) Prof. Ad van der Avoird (CIA) Funding: NWO Gerrit C. Groenenboom Leiden 215 Ab initio photodissociation 27 / 27