1. Observations of low-lying states of NiD; multi-isotope analysis
ISMS Urbana 2017
Session MH-10
Observations of low-lying states of NiD;
multi-isotope analysis
Mahdi Abbasi , Alireza Shayesteh
School of Chemistry, University of Tehran, IR IRAN
Amanda Ross, Patrick Crozet
Institut Lumière Matière*, Université de Lyon, France
Revised Abstract
“An experiment giving “not quite enough” information makes for complications in
what we thought would be a straightforward analysis prior to multiple potential fits"
*Unité mixte CNRS & U. Lyon 1

2. Introduction to the Electronic States of NiH (& NiD)
E 103 cm-1 2Φ 2Π 2Δ
2Σ-
4Φ, 4Σ-
4Δ, 4Π
2Σ+
Spectroscopy : strong transitions in the Visible
2ΛΩ – X1 2Δ5/2, with ΔΛ = ΔΩ. Stockholm & MIT groups, NiH, NiD Adakkai Kadavathu et al, Phys. Scr. 35 (3), 277 (1987)
O’Brien group isotopesNiH laser spectroscopy
L.C. & J.J. O'Brien, Astrophys. J. 621 (1), 554 (2005).
Ab initio : Zou & Liu J. Comp. Chem (2007)
Marian, JCP (1990)
Three lowest states of NiH (or NiD) are 2Λ only. Dominant configuration Ni+(3d8)−H−
Ground state X1 2Δ5/2. Spin-orbit effects mix 2Σ+, 2Π, 2Δ.
“Supermultiplet” model Gray et al. JCP (1991) 20 16 12 8 4
1445 2F 4F
3/2
5/2
7/2
9/2
1507
cm-1 2D 1

3. Introduction to the Electronic States of NiH (& NiD)
E 103 cm-1 2Φ 2Π 2Δ
2Σ-
4Φ, 4Σ-
4Δ, 4Π
2Σ+
Spectroscopy : strong transitions in the Visible
2ΛΩ – X1 2Δ5/2, with ΔΛ = ΔΩ. Stockholm & MIT groups, NiH, NiD Adakkai Kadavathu et al, Phys. Scr. 35 (3), 277 (1987)
O’Brien group isotopesNiH laser spectroscopy
L.C. & J.J. O'Brien, Astrophys. J. 621 (1), 554 (2005).
Ab initio : Zou & Liu J. Comp. Chem (2007)
Marian, JCP (1990)
Three lowest states of NiH (or NiD) are 2Λ only. Dominant configuration Ni+(3d8)−H−
Ground state X1 2Δ5/2. Spin-orbit effects mix 2Σ+, 2Π, 2Δ.
“Supermultiplet” model Gray et al. JCP (1991) 20 16 12 8 4
1445 2F 4F
3/2
5/2
7/2
9/2
1507
cm-1 2D 1b

4. Introduction to the Electronic States of NiH (& NiD)
Ab initio picture from Zou & Liu J. Comp. Chem (2007)
24000
16000
8000
R(Å)
E cm-1 2

5. Introduction to the Electronic States of NiH (& NiD)
Ab initio picture from Zou & Liu J. Comp. Chem (2007)
24000
16000
8000
R(Å)
E cm-1 2

6. FT dispersed fluorescence in NiD (much weaker than in NiH)
Pump transitions
B(Ω=5/2) – X1 2Δ5/2
Q(2.5) P(5.5) 2-0
F (Ω=7/2) – X1 2Δ5/2
Q(2.5) 0-0
NiD formed in discharge source. cw dye (R6G, R110) laser tuned to known resonances.
5% D2 in argon was TOO DILUTE! Recording times > 3 hrs 3
532 nm pump laser
TSL
Wavemeter
WA 1500 OF
FTS (Bomem DA3)
~ 50 scans
SP 380
Ring dye laser 
Pierced mirror pc
λ/2 polarizer
Sputter source
to primary pump
5% D2 in Ar
Res 0.04 cm-1

7. FT-resolved fluorescence from NiD (example)
Plenty of rotational relaxation. More overlap of systems than in NiH. 4

8. After some Loomis-Wood/combination differences sessions
Some new information on some excited states. More on low-lying electronic states. Effective parameter fits OK for RMSD, but reveal strange ΔGv and parity doubling. 5

9. Some numbers effective parameters (cm-1) for NiDOK
Not really OK 6

10. Reduced term energy plot for the low-lying states
NiD term energies
2Δ5/2 seems regular, observe v = 0-5
2Δ3/2 strong apparent anharmonicity, observe v = 0-3
2Π3/2 can’t tell, observe only v = 0, 1
New information.
2Π3/2
2Δ3/2
2Δ5/2 @ 7a

11. Reduced term energy plot for the low-lying states
NiD term energies
2Δ5/2 seems regular, observe v = 0-5
2Δ3/2 strong apparent anharmonicity, observe v = 0-3
2Π3/2 can’t tell, observe only v = 0, 1
No transitions assigned to Ω" = ½ states.
Compare with NiH ?
New information.
2Π3/2
2Δ3/2
2Δ5/2 @ 7b

12. Reduced term energy plot for the low-lying states
NiD term energies
NiH term energies
2Π3/2
2Δ3/2
2Δ5/2 @ 7b

13. Can the supermultiplet model be applied to NiD?
E 2Δ5/2 v=0
E 2Δ3/2 v=0
E 2Π3/2 v=0
E 2Π1/2 v=0
E 2Σ+ v=0
2Δ5/2 v=0
2Δ3/2 v=0
2Π3/2 v=0
2Π1/2 v=0
2Σ+ v=0
Assume Aso 603 cm-1 (Ni+) For NiD, Bv=0 ~ 3.5 cm-1 : off diagonal ME’s are not small! And … < 2Λ, v=0 | 2(Λ±1), v=0 > ≠ so this needs to be extended. 8

14. or <Λ'v'|(ħ2/2μr2)|Λ"v”>
Can the supermultiplet model be applied to NiD?
E 2Δ5/2 v=1
E 2Δ3/2 v=1
E 2Π3/2 v=1
E 2Π1/2 v=1
2Δ5/2 v=1
2Δ3/2 v=1
2Π3/2 v=1
2Π1/2 v=1
2Σ+ v=1
2Σ+ v=0
2Π1/2 v=0
2Π3/2 v=0
2Δ3/2 v=0
SCALE ME’s
<Λ'v'|Λ"v">
or <Λ'v'|(ħ2/2μr2)|Λ"v”>
Even when the off-diagonal matrix elements are SMALLER, effects can be large .
2Δ3/2 v=0 lies close to 2Δ5/2 v=1,
2Δ3/2 v=1 is close to 2Π3/2 v=0, itself VERY close to 2Δ5/2 v=2 9

15. Can the supermultiplet model be applied to NiD?
… et cetera
… et cetera
1° Fit NiD alone ?
2° Take parameters from NiH, mass-scale and see if we’re even close?
3° Take all available data and try again (and again …) 10

16. What are sensible restrictions in this context?
Fit 58NiH data only (literature)
Yij parameters for Av, Tv, Bv with i,j, ≤ 2 for 3 states ( > 20 parameters)
Dv via Kratzer relations (?)
Include effective spin-rotation terms to compensate truncation of ME’s with vΛ2 – vΛ1 > 2
« Some flexibility » in off-diagonal rotational terms (as few free parameters as possible)
RMS deviation > 5 x larger than estimated experimental uncertainty. 11

17. What are sensible restrictions in this context?
Fit 58NiH data only (literature)
Yij parameters for Av, Tv, Bv with i,j, ≤ 2 for 3 states ( > 20 parameters)
Dv via Kratzer relations (?)
Include effective spin-rotation terms to compensate truncation of ME’s with vΛ2 – vΛ1 > 2
« Some flexibility » in off-diagonal rotational terms (as few free parameters as possible)
RMS deviation > 5 x larger than estimated experimental uncertainty.
Combined analysis of 58NiD and 58,60,62NiH ?
Mass scaling of NiH parameters OK for 2Δ5/2 Dismal for 2Δ3/2
Fit of all data together fails to converge
Find a compromise. 12

18. Current status ? Combined analysis of NiD and NiH
This approach is NOT going to reproduce energy levels to experimental uncertainty.
Still requires many parameters (~70 free parameters, 120 are constrained)
Will be step toward multi-potential fits
RKR potentials
+ 58NiD
° 58NiH
Residuals from manually weighted fit
Term energy, cm-1 4 2 -2
obs—calc, cm-1
Model suggests 2Σ+ crosses 2Δ , contradicting ab initio work. 13

19. Outlook? How reasonable are predictions from this fit?
Lack of observation of and states in NiD is a major hindrance. Model predictions based on ‘current best’ parameters need testing.
Survey spectra & low res. dispersed fluorescence spectra of NiD formed in a cold laser ablation expt (Univ. New Brunswick) really lend credence !
Yag-pulsed dye laser pumps E (Ω=3/2) v=1, J=1.5
Shift from X1 2Δ5/2 v=0 J=2.5 /cm-1
X1 2Δ5/2 v=1
X2 2Δ3/2
v=0
W1 2Π3/2
v=2
v=1
2Σ+ v=0
Model predicts (cm-1) Obs ?
2Π1/2 v=
2Σ+ v=
2Σ+ v=
± ??? ± 30 ?
2Σ+ 2Π1/2? 14

20. Conclusions Acknowledgements
The model we are trying to use is still too ambitious for the data available.
Gaps in the data base need to be filled. Collisional good fortune in NiH did not re-visit for NiD.
Collision-free environment should determine a few rotationless energies.
Acknowledgements
All the work from Mahdi Abbasi who took the multi-isotope analysis beyond expectations
(subject initiated by funding for a research visit from Univ. Tehran, 2015)
Hospitality and much patience from colleagues at UNB Fredericton, tracking down elusive levels of NiD these past few days.
Support from CNRS, France and Harrison-McCain foundation, UNB Canada. 15