1. 70th International Symposium on Molecular Spectroscopy
On the Stark Effect in Open Shell Complexes Exhibiting Partially Quenched Electronic Angular Momentum
70th International Symposium on Molecular Spectroscopy
Gary E. Douberly and Christopher P. Moradi
Department of Chemistry, University of Georgia Athens, Georgia, USA

2. Stark Effect: Closed-Shell Symmetric Top
Parity conserving basis
∆𝑀=0; ∆𝐾=0; ∆𝐽=0,±1

3. Stark Effect: Closed-Shell Symmetric Top
Stark field leads to an interaction that couples opposite parity levels that are degenerate at zeroth order. This leads to a linear stark effect for states having K not equal to zero.
First-Order (Linear) Stark Effect

4. Stark Effect: Closed-Shell Symmetric Top
Second-Order (Quadratic) Stark Effect
States differing in J by one are non-degenerate at zeroth order, but are coupled via Stark effect. The Stark shift is ~quadratic with field, i.e. second-order (quadratic stark effect)

5. Stark Effect: Closed-Shell Symmetric Top
𝐴=1 c m −1
𝐵=0.1 c m −1
|𝐽,𝐾 = |2,1,±
𝑴=±𝟏
|𝐽,𝐾 = |3,0
|𝐽,𝐾 = |1,1,±
𝑴=±𝟏
𝑴=𝟎
𝑀=0
|𝐽,𝐾 = |2,0
𝑀=±1
𝑀=±2
|𝐽,𝐾 = |1,0
𝑀=0
|𝐽,𝐾 = |0,0
𝑀=±1
𝑀=0

7. theory ≈ 140 cm  1
gas ≈−148 cm  1

8. He = 165(1) cm1

9. Origin of Angular Momentum Quenching
2B2
2B2
𝐻 𝑞 = 𝜌 2 [ T 𝑳 + T −2 2 𝑳 ]
𝜌≈−150 cm −1
2B1
𝐻 𝑞 = ε 1 cos 𝜑 + ε 2 cos 2𝜑 ⋯

10. unquenched 𝜓 𝑒𝑙 ∝ 𝑒 ±𝑖𝜑 𝜓 𝑒𝑙 𝑳 𝑧 𝜓 𝑒𝑙 =±ℏ quenched
𝜓 𝑒𝑙 ∝ (𝑒 𝑖𝜑 + 𝑒 −𝑖𝜑 )
𝜓 𝑒𝑙 𝑳 𝑧 𝜓 𝑒𝑙 =0
quenched
2B2
21/2
𝐴 𝑆𝑂 2 + 𝜌 2 𝜌
𝐴 𝑆𝑂
23/2
unquenched
𝜓 𝑒𝑙 ∝ 𝑒 ±𝑖𝜑
𝜓 𝑒𝑙 𝑳 𝑧 𝜓 𝑒𝑙 =±ℏ
2B1
Increasing 𝜌
Barrier to free orbital motion decouples spin angular momentum from OH axis
Case (a) coupling Case (b) coupling

11. Parity conserving Hund’s case (a) basis 𝑠=1/2; 𝑙=1.
𝐻 = 𝐻 𝑟𝑜𝑡 + 𝐻 𝑆𝑂 + 𝐻 𝐶𝐷 + 𝐻 𝑞
|𝐽,𝑃,𝜆, 𝜎,𝜖 = |𝐽,𝑃,𝜆, 𝜎 + 𝜖 −1 (𝐽−1/2) |𝐽,−𝑃,−𝜆, −𝜎
𝐻 𝑞 = 𝜌 2 [ T 𝑳 + T −2 2 𝑳 ]
𝐽𝑃𝑀𝜆𝜎𝜖 𝐻 𝑞 𝐽 ′ 𝑃 ′ 𝑀 ′ 𝜆 ′ 𝜎 ′ 𝜖 ′ = 𝜌 2 𝛿 𝐽, 𝐽 ′ 𝛿 𝑃, 𝑃 ′ 𝛿 𝑀, 𝑀 ′ 𝛿 𝜆, −𝜆 ′ 𝛿 𝜎, 𝜎 ′ 𝛿 𝜖, 𝜖 ′
𝑯 𝑺𝑶 + 𝑯 𝒒 = 𝐴 𝑆𝑂 /2 𝜌/2 𝜌/2 −𝐴 𝑆𝑂 /2
𝜟𝑬≡ 2𝐵 2 − 2𝐵 1 = 𝐴 𝑆𝑂 2 + 𝜌 2
2B2
2B1
J. Chem. Phys. (2004) 121, 3019; J. Chem. Phys. (2015) 142,

12. |𝐽,𝑃,𝜆, 𝜎,𝜖 = 1 2 |𝐽,𝑃,𝜆, 𝜎 + 𝜖 −1 (𝐽−1/2) |𝐽,−𝑃,−𝜆, −𝜎
𝑯 = 𝑯 𝒓𝒐𝒕 + 𝑯 𝑺𝑶 + 𝑯 𝑪𝑫 + 𝑯 𝒒
|𝐽,𝑃,𝜆, 𝜎,𝜖 = |𝐽,𝑃,𝜆, 𝜎 + 𝜖 −1 (𝐽−1/2) |𝐽,−𝑃,−𝜆, −𝜎
𝑯= 𝐴+ 𝐵+𝐶 4 +𝐴 𝑆𝑂 2 𝜌 2 ∓ 𝐵+𝐶 2 𝜌 2 ∓ 𝐵+𝐶 𝐴+ 𝐵+𝐶 4 −𝐴 𝑆𝑂 𝐵+𝐶 4 −𝐴 𝑆𝑂 2 𝜌 2 ∓ 𝐵−𝐶 2 𝜌 2 ∓ 𝐵−𝐶 𝐴+ 𝐵+𝐶 4 +𝐴 𝑆𝑂 2
𝐽= 1 2 ; 𝜖=±1; 𝜔=𝜆+𝜎
|𝑃= 1 2 ,𝜔=+3/2
|𝑃= 1 2 ,𝜔=−1/2
|𝑃= 1 2 ,𝜔=+1/2
|𝑃= 1 2 ,𝜔=−3/2
Parity splittings arise from off-diagonal matrix elements as  increases.
J.S terms in Hrot and Hq couple different electronic states and lead to case b limit
𝐽,𝑃,𝜆,𝜎, 𝜖 𝐻 𝑟𝑜𝑡 𝐽,𝑃,𝜆,𝜎,𝜖 =𝐴 𝑃 2 + 𝜔 2 −2𝑃𝜔 + 𝐵+𝐶 2 [𝐽 𝐽+1 − 𝑃 2 ]

13. 2B2
Δ𝐸≡ 2𝐵 2 − 2𝐵 1 = 𝐴 𝑆𝑂 2 + 𝜌 2
2B1

14. gas =−148 cm  1 cm-1 Parity Doubling |𝑷= 𝟏 𝟐 ,𝝎=+𝟑/𝟐 |𝑷= 𝟑 𝟐 ,𝝎=+𝟑/𝟐

15. theory =−148 cm  1

16.  a-type simulations Trot = 0.35 K Half-integer quantum numbers (J, P)
like a symmetric top in a degenerate
electronic state 
Integer quantum numbers (N, Ka)
like an asymmetric top with
spin-rotation interaction a
Trot = 0.35 K b

17. He = −165(1) cm1
J. Chem. Phys. (2015) 142,

18. Accepted last week

19. a b
− 𝜇 𝑎 𝐸 2 𝐽 ′ +1 2𝐽+1 1/2 −1 𝑀−𝑃 𝐽 1 𝐽′ −𝑀 0 𝑀′ 𝐽 1 𝐽′ −𝑃 0 𝑃′ 𝛿 𝜆 ′ 𝜆 𝛿 𝜎 ′ 𝜎 𝛿 𝜖 ′ −𝜖

20. a-type
OH stretch
Angular Momentum Quenching
4 kV/cm

21. Large parity splitting at zero field = Second-order Stark Effect
B2 nuclear spin isomer
A1 nuclear spin isomer
No parity splitting at zero field = First-order Stark Effect
He = −165(1) cm1

23. Elaser
EStark
M = ±1

24. Acknowledgments
Paul Raston; Tao Liang; Mark Marshall (Amherst College)
Support: U.S. Department of Energy, Office of Science (BES-GPCP)

26. Elaser
EStark
M = 0

27. b-type
CH stretch
Elaser
EStark
Elaser
EStark
M = 0
M = ±1

28.  b-type simulations Trot = 0.35 K Half-integer quantum numbers (J, P)
like a symmetric top in a degenerate
electronic state 
Integer quantum numbers (N, Ka)
like an asymmetric top with
spin-rotation interaction a
Trot = 0.35 K b

29. He = −165(1) cm  1

30. theory = 148 cm  1

31. Helium solvation affects electronic states differently
2B2
2B1
Δ𝐸≡ 2𝐵 2 − 2𝐵 1 = 𝐴 𝑆𝑂 2 + 𝜌 2
𝚫 𝑬 𝑯𝒆 =𝟐𝟏𝟔 𝐜 𝐦 −𝟏
𝚫 𝑬 𝑯𝒆 − 𝚫 𝑬 𝒈𝒂𝒔 =+𝟏𝟒 𝐜 𝐦 −𝟏
theory = 148 cm1
gas = 148(1) cm1
He = 165(1) cm1
Helium solvation affects electronic states differently

32. Helium solvation effect is also evident in OH infrared spectrum.
Gas Helium
21/2
ASO
ASO+ (>10 cm-1)
23/2
Helium solvation effect is also evident in OH infrared spectrum.
The Q(3/2) to R(3/2) spacing is larger than in gas phase, indicative of a larger effective splitting between 23/2 and 21/2 states.
The 23/2 state has a free energy of solvation larger than for 21/2.
P.L. Raston, T. Liang, GED, J. Phys. Chem. A (2013) 117, 8103.