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 20 24 June 2016 () 1 / 34
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
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
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
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 7/2 9.800 4 D 4s 2 4p 4 ( 3 P 1)5p 1/2 9.778 2 D 4s 2 4p 4 ( 3 P 1)5p 3/2 9.754 2 D 4s 2 4p 4 ( 3 P 1)5p 5/2 9.734 2 S 4s 2 4p 4 ( 3 P 1)5p 1/2 9.680 4 D 4s 2 4p 4 ( 3 P 2)5p 3/2 9.514 2 D 4s 2 4p 4 ( 1 D)5s 3/2 9.411 2 D 4s 2 4p 4 ( 1 D)5s 5/2 9.409 4 P 4s 2 4p 4 ( 3 P 2)5p 1/2 9.399 4 D 4s 2 4p 4 ( 3 P 2)5p 5/2 9.385 4 D 4s 2 4p 4 ( 3 P 2)5p 7/2 9.363 4 P 4s 2 4p 4 ( 3 P 2)5p 3/2 9.299 4 P 4s 2 4p 4 ( 3 P 2)5p 5/2 9.258 2 P 4s 2 4p 4 ( 3 P 0)5s 1/2 8.551 2 P 4s 2 4p 4 ( 3 P 1)5s 3/2 8.329 4 P 4s 2 4p 4 ( 3 P 1)5s 1/2 8.292 4 P 4s 2 4p 4 ( 3 P 2)5s 3/2 8.047 4 P 4s 2 4p 4 ( 3 P 2)5s 5/2 7.865.................................. 1/2 0.456 b 2 P 4s 2 4p 5 3/2 0.000 a 35 Br: [Ar] 4s 2 3d 10 4p 5 ; b Aso = 3685 cm 1 () 5 / 34
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 1 13.934 4s 2 4p 3 ( 4 S )4d 2 13.827 4s 2 4p 3 ( 2 D )5s 3 13.684 4s 2 4p 3 ( 2 D )5s 2 13.598 4s 2 4p 3 ( 2 D )5s 1 13.567 4s 2 4p 4 ( 4 S )4d 0 12.918 4s 2 4p 3 ( 4 S )4d 1 12.912 4s 2 4p 3 ( 4 S )4d 4 12.905 4s 2 4p 3 ( 4 S )4d 2 12.903 4s 2 4p 3 ( 4 S )4d 3 12.899 4s 2 4p 5 0 12.427 4s4p 5 1 12.249 4s 2 4p 3 ( 4 S )5s 1 12.208 4s 2 4p 5 2 11.956 4s 2 4p 3 ( 4 S )5s 2 11.644 0 3.455 1 D 4s 2 4p 4 2 1.498................................ 0 0.475 3 P 4s 2 4p 4 1 0.388 2 0.000 () 6 / 34
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
12 11 HBr 100000 90000 10 80000 9 8 7 6 1 Π 3 Σ + 70000 60000 50000 5 4 3 2 1 0 3 Π 40000 H + Br( 3 P o) 30000 20000 10000 X 1 Σ + 2 3 4 5 6 7 8 9 0 10 [MXLSYX73 () 8 / 34
120000 HBr Omega states 110000 100000 90000 80000 70000 60000 50000 40000 30000 [MXL73 20000 10000 0 2 3 4 5 6 7 8 9 10 () 9 / 34
150000 140000 % 130000 120000 110000 100000 90000 80000 70000 60000 50000 2 3 4 5 6 7 () 10 / 34
150000 140000 & 130000 120000 110000 100000 90000 80000 70000 60000 50000 2 3 4 5 6 7 () 11 / 34
150000 140000 % 130000 120000 110000 100000 90000 80000 70000 60000 50000 2 3 4 5 6 7 () 12 / 34
110000 100000 90000 80000 % & 13 14 % 70000 60000 50000 2 () 3 4 5 6 7 8 9 10 11 12 15 16 17 18 13 / 34
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 ) 9.800 3,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 1/2 ) 9.778 1,3 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 3/2 ) 9.754 1,3 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 5/2 ) 9.734 1,3 [Σ (1)] H( 2 S1/2 )+Br( 2 S 1/2 ) 9.680 3,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 3/2 ) 9.514 1,3 [Σ + (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 3/2 ) 9.411 1,3 [Σ + (1), Π(1), (1)] H( 2 S1/2 )+Br( 2 D 5/2 ) 9.409 3,5 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 4 P 1/2 ) 9.399 3,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 5/2 ) 9.385 3,5 [Σ (1), Π(1), (1)] H( 2 S1/2 )+Br( 4 D 7/2 ) 9.363 3,5 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 4 P 3/2 ) 9.299 3,5 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 4 P 5/2 ) 9.258 1,3 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 2 P 1/2 ) 8.551 1,3 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 2 P 3/2 ) 8.329 3,5 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 4 P 1/2 ) 8.292 3,5 [Σ (1), Π(1) H( 2 S1/2 )+Br( 4 P 3/2 ) 8.047 3,5 [Σ (1), Π(1)] H( 2 S1/2 )+Br( 4 P 5/2 ) 7.865.................................................... H( 2 S 1/2 )+Br( 2 P 1/2 ) 0.456 1,3 [Σ + (1), Π(1)] H( 2 S1/2 )+Br( 2 P 3/2 ) 0.000 a Energies referred to the lowest dissociation limit. () 15 / 34
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 + [73 740.] V 1 Σ + [75 293.] g 3 Σ 1 [76 522.3] [1.415] g 3 Σ 0 + [75 378.4] [1.519] d 3 Π 0 [76 088.8] [1.4904] [2418.5] d 3 Π 1 [73 542.] d 3 Π 2 [73 440.] C 1 Π 70 527.6 1.465 2552. 52. b 3 Π 0 + [68 911.] [1.455] [2452] b 3 Π 0 [68 904.] 19680. b 3 Π 1 [67 088.4] 1.442 [2444.2] b 3 Π 2 [67 663.0] [1.473] t 3 Σ + 1 [60 522.3] repulsive A 1 Π 1 [50 440.] repulsive a 3 Π 0 [42 088.8] a 3 Π 1 [41 542.] a 3 Π 2 [40 000.] repulsive X 1 Σ + 0.0 1.41443 2648.975 45.2175 31523. a The values of Te in brackets correspond to ν 00 () 17 / 34
24 22 2 2 4 Σ Σ HBr + 200000 190000 180000 6WXEXIW,&V EFSZII: 170000 20 18 4 Π 2 Σ 2 Π 2 Σ + 2 Π 2 Σ + 2 H + Br + ( 1 S) H + + Br( 2 P o ) 160000 150000 140000 16 4 Σ H + Br + ( 1 D) 130000 14 2 Σ + H + Br + ( 3 P) 120000 110000 12 100000 X 2 Π -4,&V!I: 90000 2 3 4 5 6 7 8 9 10 () 19 / 34
70000 HBr + Omega-States 60000 50000 40000 30000 +7HSYFPIXWTPMXXMRK 20000 10000 0 2 3 4 5 6 7 8 9 10 () 20 / 34
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 ) 10.674 2,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 3/2, 2p)+Br + ( 3 P 1 ) 10.587 H(2)+Br + ( 3 P 1 ) 10.587 2,4 [Σ (1), Π(1)] H( 2 S1/2, 2s)+Br + ( 3 P 1 ) 10.587 2,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 1/2, 2p)+Br + ( 3 P 1 ) 10.587 H + +Br( 2 P 1/2 ) 10.335 2,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 3/2, 2p)+Br + ( 3 P 2 ) 10.198 H(2)+Br + ( 3 P 2 ) 10.198 2,4 [Σ (1), Π(1)] H( 2 S1/2, 2s)+Br + ( 3 P 2 ) 10.198 2,4 [Σ + (1), Σ (2), Π(2), (1)] H( 2 P 1/2, 2p)+Br + ( 3 P 2 ) 10.198 H + +Br( 2 P 3/2 ) 10.114 H + +Br( 4 P 1/2 ) 10.077 H + +Br( 4 P 3/2 ) 9.832 H + +Br( 4 P 5/2 ) 9.649 2 [Σ + (1)] H( 2 S1/2, 1s)+Br + ( 1 S 0 ) 3.455 H + +Br( 2 P 1/2 ) 2.241 H + +Br( 2 P 3/2 ) 1.784 2 [Σ + (1), Π(1), (1)] H( 2 S1/2, 1s)+Br + ( 1 D 2 ) 1.498............................................................. H( 2 S 1/2, 1s)+Br + ( 3 P 0 ) 0.475 H( 2 S 1/2, 1s)+Br + ( 3 P 1 ) 0.388 2,4 [Σ (1), Π(1)] H( 2 S1/2, 1s)+Br + ( 3 P 2 ) 0.000 a Energies referred to the lowest dissociation limit. b Energies of H + +Br are calculated as: IP(H) IP(Br)+EE(Br)= 13.598 11.813 + EE(Br)= 1.784 ev + EE(Br). () 22 / 34
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 [108 400.] repulsive B 2 Σ + [78 557.] repulsive 29 116. 1.6933 1384 26.2 13066. A 2 Σ + 28 421.2 1.6842 999.25 19.12 0.0 1.4484 2459. 44.3 31132. X 2 Π 0.0 1.4484 2441.52 47.40 31407. () 24 / 34
200000 180000 160000 HBr + H + Br+(1S) 2sig+ 2sig- 2Pi 4sig- 4Pi HBr 1 Σ + H + +Br - 1A1 1Pi 3Pi 3Sigma 140000 H+ + Br (2Po) H + Br+(1D) 120000 H(1s) + Br+ H+ + Br- H(2s) + Br 100000 H + Br+(2D)? H(2s) + Br- 80000 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 r / a 0 () 29 / 34
HBr, HBr + 140000 120000 100000 80000 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 r / a 0 () 31 / 34
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.) 81 145 V(m+10) 81 197.2 80 543 V(m+9) 80 638.0 80 076 E (v=1) 80 168.8 80 350 V(m+8) 80 029.7 79 770 V(m+7) 79 480.3 79 027 V(m+6) 78 940.2 78 471 V(m+5) 78 388.8 77 313 E(v=0) 77 939.9 78 232 V(m+4) 77 830.0 77 383 V(m+3) 77 343.8 76 589 V(m+2) 76 963.7 76 078 V(m+1) 76 516. 75 548 V(m) 75 293. The origin of the energies is the v =0 level of X 1 Σ + () 32 / 34
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
T H A N K S () 34 / 34