Electronic structure and spectroscopy of HBr and HBr +

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Παίων Αλεξανδρίδης
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Lefebvre Brion 3 1 Universidad Nacional Autónoma de México Cuernavaca México 2

1 Electronic structure and spectroscopy of HBr and HBr + Gabriel J. Vázquez 1 H. P. Liebermann 2 H. Lefebvre Brion 3 1 Universidad Nacional Autónoma de México Cuernavaca México 2 Universität Wuppertal Wuppertal Germany 3 Institut des Sciences Moléculaire d Orsay Orsay France 71 st ISMS Urbana Champaign, Illinois June 2016 () 1 / 34

2 Outline Motivation Details of calculations Spectroscopic terms of HBr and HBr + Sample of HBr PECs (without/with spin orbit) Sample of HBr + PECs (without/with spin orbit) The mixed (E+V) Rydberg (ion pair) B 1 Σ + state Summary () 2 / 34

3 Motivation Hydrogen halides HX (X=Cl, Br, I) testing ground for molecular photodissociation/photoionization Display Rydberg valence mixing Relativistic spin orbit coupling due to (the K and L shells of) Br Changes in bonding, from covalent to ionic, with increasing internuclear distance HBr the least studied HX (HCl the most) No PECs available for HBr PECs required by Dr. Kvaran to shed light on the mixed double well Rydberg (ion pair) (E+V) B 1 Σ + state () 3 / 34

4 Ab initio electronic structure calculations of HBr and HBr + Type: SCF MRSD(TQ) CI SCF: C 2v symmetry Package: MRD CI a Core: Br relativistic effective core potential CI: 8 active e [two 4s and six 4p of Br] Br basis: cc pvqz + diffuse (two s, two p, one d) Excitations: S + D + (T, Q) Functions: H (6s5p1d) MOs HBr (X 1 Σ + ) Br (6s7p3d1f) Conf. HBr (X) 1σ 2 2σ 2 3σ 2 1π 4 4σ 2 5σ 2 2π 4 6σ 2 7σ 2 3π 4 1δ 4 8σ 2 4π 4 Total HBr 12s12p4d1f 82 atomic functions a Bonn-Wuppertal package, Buenker & Peyerimhoff () 4 / 34

5 Table: Spectroscopic terms of the Br atom a Term Configuration J Energy (ev) Exp. This work 4 D 4s 2 4p 4 ( 3 P 2)4d 7/ D 4s 2 4p 4 ( 3 P 1)5p 1/ D 4s 2 4p 4 ( 3 P 1)5p 3/ D 4s 2 4p 4 ( 3 P 1)5p 5/ S 4s 2 4p 4 ( 3 P 1)5p 1/ D 4s 2 4p 4 ( 3 P 2)5p 3/ D 4s 2 4p 4 ( 1 D)5s 3/ D 4s 2 4p 4 ( 1 D)5s 5/ P 4s 2 4p 4 ( 3 P 2)5p 1/ D 4s 2 4p 4 ( 3 P 2)5p 5/ D 4s 2 4p 4 ( 3 P 2)5p 7/ P 4s 2 4p 4 ( 3 P 2)5p 3/ P 4s 2 4p 4 ( 3 P 2)5p 5/ P 4s 2 4p 4 ( 3 P 0)5s 1/ P 4s 2 4p 4 ( 3 P 1)5s 3/ P 4s 2 4p 4 ( 3 P 1)5s 1/ P 4s 2 4p 4 ( 3 P 2)5s 3/ P 4s 2 4p 4 ( 3 P 2)5s 5/ / b 2 P 4s 2 4p 5 3/ a 35 Br: [Ar] 4s 2 3d 10 4p 5 ; b Aso = 3685 cm 1 () 5 / 34

6 Table: Spectroscopic terms of the Br + ion. Term Configuration J Energy (ev) Exp. This work 3 D 3 D 3 D 3 D 3 D 5 D 5 D 5 D 5 D 5 D 3 P 3 P 3 S 3 P 5 S 1 S 4s 2 4p 4 4s 2 4p 3 ( 4 S )4d s 2 4p 3 ( 4 S )4d s 2 4p 3 ( 2 D )5s s 2 4p 3 ( 2 D )5s s 2 4p 3 ( 2 D )5s s 2 4p 4 ( 4 S )4d s 2 4p 3 ( 4 S )4d s 2 4p 3 ( 4 S )4d s 2 4p 3 ( 4 S )4d s 2 4p 3 ( 4 S )4d s 2 4p s4p s 2 4p 3 ( 4 S )5s s 2 4p s 2 4p 3 ( 4 S )5s D 4s 2 4p P 4s 2 4p () 6 / 34

7 Lowest electronic states of HBr Excitation MO configuration Ginter s notation Character π 5dσ (σ 2 π 3 )5dσ n 3 Π i (2, 1, 0), N 1 Π (1) R g 3 Σ (1, 0 + ), G 1 Σ (0 ), f 3 i (2, 1, 0), F 1 (2) π 5pπ (σ 2 π 3 )5pπ e 3 Σ + (1, 0 ), E 1 Σ + (0 + ) R π 5pσ (σ 2 π 3 )5pσ d 3 Π i (2, 1, 0 ± ), D 1 Π (1) R π 5sσ (σ 2 π 3 )5sσ b 3 Π i (2, 1, 0 ± ), C 1 Π (1) R σ σ (σπ 4 )σ t 3 Σ + (1, 0 ), V 1 Σ + (0 + ) I P π σ (σ 2 π 3 )σ a 3 Π i (2, 1, 0), A 1 Π (1) V (σ 2 π 4 ) X 1 Σ + (0 + ) G () 7 / 34

8 12 11 HBr Π 3 Σ Π H + Br( 3 P o) X 1 Σ [MXLSYX73 () 8 / 34

9 HBr Omega states [MXL () 9 / 34

10 % () 10 / 34

11 & () 11 / 34

12 % () 12 / 34

13 % & % () / 34

14 Table: Molecular states correlating to the various dissociation limits of HBr. states Number of Limit Relative Relative states energy (ev) a energy (ev) b 3,5 [Σ + (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 7/2 ) ,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 1/2 ) ,3 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 3/2 ) ,3 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 5/2 ) ,3 [Σ (1)] H( 2 S1/2 )+Br( 2 S 1/2 ) ,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 3/2 ) ,3 [Σ + (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 3/2 ) ,3 [Σ + (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 5/2 ) ,5 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 4 P 1/2 ) ,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 5/2 ) ,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 7/2 ) ,5 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 4 P 3/2 ) ,5 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 4 P 5/2 ) ,3 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 2 P 1/2 ) ,3 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 2 P 3/2 ) ,5 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 4 P 1/2 ) ,5 [Σ (1), Π(1) H( 2 S1/2 )+Br( 4 P 3/2 ) ,5 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 4 P 5/2 ) H( 2 S 1/2 )+Br( 2 P 1/2 ) ,3 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 2 P 3/2 ) a Energies referred to the lowest dissociation limit. () 15 / 34

15 Table: Spectroscopic constants of the electronic states of HBr. a State T e (ev) R e (A) ω e (cm 1 ) ω ex e (cm 1 ) D e (cm 1) e 3 Σ + [ ] V 1 Σ + [ ] g 3 Σ 1 [ ] [1.415] g 3 Σ 0 + [ ] [1.519] d 3 Π 0 [ ] [1.4904] [2418.5] d 3 Π 1 [ ] d 3 Π 2 [ ] C 1 Π b 3 Π 0 + [ ] [1.455] [2452] b 3 Π 0 [ ] b 3 Π 1 [ ] [2444.2] b 3 Π 2 [ ] [1.473] t 3 Σ + 1 [ ] repulsive A 1 Π 1 [ ] repulsive a 3 Π 0 [ ] a 3 Π 1 [ ] a 3 Π 2 [ ] repulsive X 1 Σ a The values of Te in brackets correspond to ν 00 () 17 / 34

16 Σ Σ HBr WXEXIW,&V EFSZII: Π 2 Σ 2 Π 2 Σ + 2 Π 2 Σ + 2 H + Br + ( 1 S) H + + Br( 2 P o ) Σ H + Br + ( 1 D) Σ + H + Br + ( 3 P) X 2 Π -4,&V!I: () 19 / 34

17 70000 HBr + Omega-States HSYFPIXWTPMXXMRK () 20 / 34

18 Table: Molecular states correlating to the various dissociation limits of HBr +. Molecular states Number of Limit Relative Relative molecular states energy (ev) a,b energy (ev) b 2,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 1/2, 2p)+Br + ( 3 P 0 ) ,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 3/2, 2p)+Br + ( 3 P 1 ) H(2)+Br + ( 3 P 1 ) ,4 [Σ (1), Π(1)] H( 2 S1/2, 2s)+Br + ( 3 P 1 ) ,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 1/2, 2p)+Br + ( 3 P 1 ) H + +Br( 2 P 1/2 ) ,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 3/2, 2p)+Br + ( 3 P 2 ) H(2)+Br + ( 3 P 2 ) ,4 [Σ (1), Π(1)] H( 2 S1/2, 2s)+Br + ( 3 P 2 ) ,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 1/2, 2p)+Br + ( 3 P 2 ) H + +Br( 2 P 3/2 ) H + +Br( 4 P 1/2 ) H + +Br( 4 P 3/2 ) H + +Br( 4 P 5/2 ) [Σ + (1)] H( 2 S1/2, 1s)+Br + ( 1 S 0 ) H + +Br( 2 P 1/2 ) H + +Br( 2 P 3/2 ) [Σ + (1), Π(1), (1)] H( 2 S1/2, 1s)+Br + ( 1 D 2 ) H( 2 S 1/2, 1s)+Br + ( 3 P 0 ) H( 2 S 1/2, 1s)+Br + ( 3 P 1 ) ,4 [Σ (1), Π(1)] H( 2 S1/2, 1s)+Br + ( 3 P 2 ) a Energies referred to the lowest dissociation limit. b Energies of H + +Br are calculated as: IP(H) IP(Br)+EE(Br)= EE(Br)= ev + EE(Br). () 22 / 34

19 Table: Spectroscopic constants of the electronic states of HBr + State T e (ev) R e (A) ω e (cm 1 ) ω ex e (cm 1 ) D e (cm 1 ) 2 2 Π [ ] repulsive B 2 Σ + [ ] repulsive A 2 Σ X 2 Π () 24 / 34

20 HBr + H + Br+(1S) 2sig+ 2sig- 2Pi 4sig- 4Pi HBr 1 Σ + H + +Br - 1A1 1Pi 3Pi 3Sigma H+ + Br (2Po) H + Br+(1D) H(1s) + Br+ H+ + Br- H(2s) + Br H + Br+(2D)? H(2s) + Br r / a 0 () 29 / 34

21 HBr, HBr r / a 0 () 31 / 34

22 Table: Calculated vibrational levels of the B 1 Σ + adiabatic potential compared to the observed a vibrational levels of V 1 Σ + and E 1 Σ + of HBr (cm 1 ) T 0,v (calc. adiab.) b Exp. label. T 0,v (exp.) V(m+10) V(m+9) E (v=1) V(m+8) V(m+7) V(m+6) V(m+5) E(v=0) V(m+4) V(m+3) V(m+2) V(m+1) V(m) The origin of the energies is the v =0 level of X 1 Σ + () 32 / 34

23 Summary A study of the electronic structure and spectroscopy of HBr and HBr + is underway We expect to generate useful data on this system, such as: PECs, excitation, ionization and dissociation energies, spectroscopic constants, transition moment properties, dipole moment functions,... () 33 / 34

24 T H A N K S () 34 / 34

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