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Home , Imidogen

Electronic Structure & Spectroscopy of NH+ Jose´ M. Amero & Gabriel J. Vazquez´

Centro de Ciencias F´ısicas Universidad Nacional Autonom´ a de Mexico´ Cuernavaca

– p.1/24 Results

Doublets, quartets & sextets : an overview The ﬁve known electronic states Five new bound states

Reactions forming NH+ in space Spectroscopic data relevant in the search for NH+ Conclusions

Outline

Generalities of NH+ Details of calculations

– p.2/24 Reactions forming NH+ in space Spectroscopic data relevant in the search for NH+ Conclusions

Outline

Generalities of NH+ Details of calculations

Results

Doublets, quartets & sextets : an overview The ﬁve known electronic states Five new bound states

– p.2/24 Outline

Generalities of NH+ Details of calculations

Results

Doublets, quartets & sextets : an overview The ﬁve known electronic states Five new bound states

Reactions forming NH+ in space Spectroscopic data relevant in the search for NH+ Conclusions

– p.2/24 Generalities of NH+

Cation of the imidogen radical NH Both, free radical & ion ⇒ extremely reactive ⇒ very short lifetime Exists in ﬂames & combustion plasmas Important in astrophysics Observed only in emission

– p.3/24 NH+ an elusive astrophysical species

Missing in the august 2004 NRAO list (125 observed intestellar & circumstellar molecules) Snow looked for the C2Σ+→X2Π UV line (2889 A)˚ could not observe it ! We are not aware of searches for NH+ in the visible

– p.4/24 NH+ an elusive astrophysical species

NH+ listed in the 1999 UMIST database for astrochemistry (modelling) Numerous possible precursors of NH+ : + + + NH3, HNC, N2H , HCNH , HC3NH , NH2, NH, . . . Various mechanisms proposed for the formation of NH+

– p.5/24 Postulated/observed diatomic cations

+ + + + + H2 PH O2 CCl PO HeH+ SH+ CN+ NS+ SO+ CH+ HCl+ CO+ SiC+ ClO+ + + + + + NH C2 NO SiN S2 + + + SiO+ + OH N2 CP SiS SiH+ CS+ PN+

Only 3 species observed ! (out of 28)

⇒ more observational effort required !

– p.6/24 Why NH+ has not been observed in space ?

Abundance of NH+ most likely very low ! ⇒ awaiting for progress in detector sensitivity Absorption & emission lines obscured by those of more abundant species ? Signal below noise level ? Observations from above the Earth’s atmosphere seem compulsory Not enough observational effort ? ⇒ visible, IR, submilimeter, MW, radio

– p.7/24 Puzzling ! Details of the calculations

Electronic structure calculations

Ab initio SCF MRSD–CI

Bonn–Wuppertal package

Basis : DZ + POL + Ryd (3s,3p,3d,4s) + s,p bond

– p.8/24 2 A1

SCF MO diagram of NH

0.1642 4π 4b1 4b2

0.0526 1δ 7a 1a 0.0304 5σ 1 5a 2 4σ 1 0.0068 4a1 -0.0529 3π -0.0953 LUMO 2π

-0.5371 HOMO 1π -0.5501 3σ 3a1 Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)Orbital energies (Hartrees)

-1.0422 2σ 2a1

-15.6120 1σ 1a1 – p.9/24 The ﬁrst electronic states of NH+

The ground state 7e

One–open–shell 1σ22σ23σ21π

The ﬁrst excited states 3σ → 1π

Three–open–shell 1σ22σ23σ1π2 σπ2 ⇒ 4Σ−, 2Σ−, 2∆, 2Σ+ Only states observed !

– p.10/24 Surprising:

From the inﬁnity number of electronic states of NH+, only the states arising from the 3σ → 1π excitation have been observed !

– p.11/24 Calculated states of NH+

49 electronic states

18 doblets 22 quartets 9 sextets

– p.12/24 Doublet electronic states of NH+

– p.13/24 Attributes of the lowest doublet elec- + 2 tronic states of NH at re(X Π)

State Character Dominant/(chief) Conﬁguration(s) VIE(AIE) VEE(AEE) excitation eV eV 2 + † 2 2 2 2 2 Σ (α) V 3σ → 1π10σ 0.19 2σ 1πx10σ + 0.19 2σ 1πy10σ (30.00) (16.69) 2 2 2 2 +0.07 2σ3σ 1πx + 0.07 2σ3σ 1πy 42Σ+ (β)† RV 1π → 9σ 0.28 2σ23σ29σ + 0.20 2σ23σ211σ (30.47) 17.64(17.16) 2 † 2 2 2 2 2 3 ∆ V 3σ → 1π10σ 0.20 2σ 1πx10σ + 0.19 2σ 1πy10σ (28.32) 18.93(15.02) 2 2 0.30 2σ 1πx1πy10σ + 0.22 2σ 3σ1πx2πy 2 2 2 3 Π VR 3σ → 10σ 0.51 2σ 3σ1πx10σ + 0.11 2σ 3σ1πx9σ 28.27 14.36 22Σ+ VR 1π → 10σ 0.44 2σ23σ210σ + 0.10 2σ23σ29σ 26.61 12.81 2 2 2 2 2 2 Π V 3σ → 1π 0.91 2σ 1πx1πy 21.33 7.83 2 + 2 2 2 2 1 Σ (C) V 3σ → 1π 0.45 2σ 3σ1πx + 0.45 2σ 3σ1πy (17.77) 4.54(4.46) 2 2 2 2 2 1 ∆ (B) V 3σ → 1π 0.46 2σ 3σ1πx + 0.46 2σ 3σ1πy (16.37) 3.11(3.06) 2 0.92 2σ 3σ1πx1πy 2 − 2 1 Σ (A) V 3σ → 1π 0.92 2σ 3σ1πx1πy (16.18) 3.11(2.87) 2 2 2 1 Π (X) V 0.89 2σ 3σ 1πx (13.31) 0.00(0.00)

– p.14/24 Quartet electronic states of NH+

– p.15/24 Sextet electronic states of NH+

– p.16/24 Observed electronic states of NH+

Molecular parameters of X2Π

T E 22 re (A)˚ 1.067 1.0692 8 −1 Be (cm ) 15.62 15.68 −1 20 ωe (cm ) 3166 3047

6 De (eV) ≥ 4.54 4.664

N+(3P)+H(2S) IP (eV) 13.34 13.476 18

16 Ionization energy (eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV) Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy 2 Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)

2 X Π

13.34 0

N 2 4 6 ∞ r (N-H) a.u. – p.17/24 Observed electronic states of NH+

Molecular parameters of a4Σ−

T E 22 re (A)˚ 1.088 1.093 8 −1 Be (cm ) 15.32 15.013 −1 20 ωe (cm ) 2796 2672

6 De (eV) 3.72 3.664

N+(3P)+H(2S) Te (eV) −113 354 18 IP (eV) 13.29 —- 4

− 4 + 1 a4Σ N( S)+H ( S) 16 Ionization energy (eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV) Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy 2 Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)

2 X Π

13.34 0

N 2 4 6 ∞ r (N-H) a.u. – p.17/24 Observed electronic states of NH+

Molecular parameters of A2Σ−

T E 22 re (A)˚ 1.244 (1.2704) 8 −1 Be (cm ) 11.71 (11.1105) −1 20 ωe (cm ) 1766 1706.9

6 De (eV) ≥ 1.70 —-

N+(3P)+H(2S) Te (eV) 2.87 (2.67) 18 IP (eV) 16.18 16.16 4

− 4 + 1 a4Σ N( S)+H ( S) 16 − A2Σ Ionization energy (eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV) Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy 2 Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)

2 X Π

13.34 0

N 2 4 6 ∞ r (N-H) a.u. – p.17/24 Observed electronic states of NH+

Molecular parameters of B2∆

T E 22 re (A)˚ 1.130 (1.1519) 8 −1 Be (cm ) 14.18 13.8 −1 20 ωe (cm ) 2506 2371

N(2D)+H+(1S) 6 De (eV) ≥ 3.25 —- B2∆ N+(3P)+H(2S) Te (eV) 3.06 (2.846) 18 IP (eV) 16.37 16.34 4

2 X Π

13.34 0

N 2 4 6 ∞ r (N-H) a.u. – p.17/24 Observed electronic states of NH+

Molecular parameters of C2Σ+

T E 22 re (A)˚ 1.150 1.164 8 −1 Be (cm ) 13.70 13.231 N+(1D)+H(2S) −1 20 ωe (cm ) 2373 2310

+ C2Σ N(2D)+H+(1S) 6 De (eV) ≥ 2.17 —- B2∆ N+(3P)+H(2S) Te (eV) 4.46 4.28 18 IP (eV) 17.77 —- 4

− 4 + 1 a4Σ N( S)+H ( S) 16 − A2Σ Ionization energy (eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV)(eV) Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy Ionization energy 2 Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)

2 X Π

13.34 0

N 2 4 6 ∞ r (N-H) a.u. – p.17/24 New bound electronic states of NH+

28 36Π 40 1 + X Σ

24 NH++ 36

20 32 2 + 2 β Σ A1

α2Σ+ 16

28 32∆

24Π 12 24 Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV)Ionization energy (eV) Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)Excitation energy (eV)

8 N+(1D)+H(2S) 20 2 + C Σ N(2D)+H+(1S) B2∆ N+(3P)+H(2S) 4 − 4 + 1 a4Σ N( S)+H ( S) 16 − A2Σ 2 X Π

13.34 0 N 2 4 6 ∞ r (N-H) a.u. – p.18/24 Spectroscopic properties of the new bound states of NH+

Property Unit States 24Π 32∆ α2Σ+ β2Σ+ 36Π

re A˚ 1.428 1.562 1.551 1.228 2.642 −1 ωe cm 1601 3038 1863 2970 742 −1 Be cm 8.85 8.17 7.53 12.02 2.59

De eV ≥1.0 ≥1.10 ≥1.05 ≥0.69 ≥0.78

– p.19/24 Reactions that might be involved in the formation of NH+ in space

Reaction Process Region Rate constant NH+hν →NH++e PI 1.00 × 10−11 PI, λ < 919 A˚ C, ISM + −9 NH3+hν→NH +H2+e PI 6.9 × 10 NH+γ →NH++e CRI 1.30 × 10−17 H++NH→NH++H CT 2.10 × 10−9 LDC,MDC 1.0 × 10−9 N++NH→NH++N CT MDC,DMC 3.70 × 10−10 O++NH→NH++O CT MDC,DMC 3.60 × 10−10 + + −10 H2 +NH→NH +H2 CT 7.60 × 10 ∼ 1 × 10−9 + + −10 N2 +NH→NH +N2 CT 6.50 × 10 CN++NH→NH++CN CT 6.50 × 10−10 CO++NH→NH++CO CT 3.20 × 10−10 OH++NH→NH++OH CT 3.60 × 10−10

– p.20/24 Reactions that might be involved in the formation of NH+ in space

Reaction Process Region Rate constant He++HNC→NH++C+He IN 5.00 × 10−10 + + −10 He +NH2→NH +He+H IN 8.00 × 10 + + −10 He +NH3→NH +He+H2 IN 1.76 × 10 2.2 × 10−9 + + −9 N +H2→NH +H IN 1.00 × 10 DMC 0.48 × 10−9 N++HD→NH+, ND+ IN + + N +H2O→NH +OH IN C + + −11 N +H2S→NH +HS IN 5.70 × 10 N++HCO→NH++CO IN 4.50 × 10−10 ISC 0.45 × 10−9 + + −9 H2 +N→NH +H IN 1.90 × 10 N+(3P )+H(2S)→NH+(A2Σ−) RA DMC 3 × 10−7 →NH+(X2Π)+hν

– p.21/24 Spectroscopic data relevant in the search for NH+ in space

Spectral Upper state Lower state Transition Transition region energy VUV 24Π a4Σ− 24Π→a4Σ− 979 A˚ UV C2Σ+ X2Π C(v0=0)→X(v00=0) 2885 A˚ C(v0=1)→X(v00=0) 2725 A˚ C(v0=1)→X(v00=1) 2980 A˚ Visible B2∆ X2Π B(v0=0)→X(v00=0) 4348.5 A˚ A2Σ− X2Π A(v0=1)→X(v00=0) 4312.7 A˚ A(v0=0)→X(v00=0) 4628.9 A˚ A(v0=0)→X(v00=1) 5349.4 A˚ IR X2Π(v=1) X2Π(v=0) 1–0 3.17 µm (3150 cm−1) 4 − 2 00 0 00 −1 Far–IR a Σ X Π(v =0) a(v =0)–X(v =0) T0=354 cm −1 Tv∼550 cm 2 3 2 1 3 1 1 Submil. X Π 1 (v=0,J= ) X Π 1 (v=0,J= ) J= ←J= 1.019 GHz (34 cm− ) 2 2 2 2 2 2 2 2 Radio X Π 1 X Π 1 e←f 13.52GHz 2 2 1 1 −1 (Λ–doub) (v=0,N=1,J= 2 ,e) (v=0,N=1,J= 2 ,f) (0.451cm ) – p.22/24 Conclusions

The present study represents a substantial contribution to the knowledge of the electronic structure of NH+ We calculated 49 electronic states. The majority reported for the ﬁrst time Improved, more detailed potential energy curves Spectroscopic parameters of known bound electronic in good agreement with our theoretical values We found ﬁve new bound electronic states of NH+ Calculating many electronic states not a mere academic exercise ⇒ novel, interesting spectroscopic information can be obtained

– p.23/24 Conclusions

⇒ Challenge for experimentalists Detect the ﬁve new bound electronic states

(re, ωe, Be, VEE)

– p.24/24