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

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

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

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)

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

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

He = 165(1) cm1

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

unquenched 𝜓 𝑒𝑙 ∝ 𝑒 ±𝑖𝜑 𝜓 𝑒𝑙 𝑳 𝑧 𝜓 𝑒𝑙 =±ℏ quenched 𝜓 𝑒𝑙 ∝ 1 2 (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

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 = 1 2 |𝐽,𝑃,𝜆, 𝜎 + 𝜖 −1 (𝐽−1/2) |𝐽,−𝑃,−𝜆, −𝜎 𝐻 𝑞 = 𝜌 2 [ T 2 2 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, 134306.

|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 = 1 2 |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 2 𝐴+ 𝐵+𝐶 4 −𝐴 𝑆𝑂 2 0 0 0 0 0 0 0 0 𝐵+𝐶 4 −𝐴 𝑆𝑂 2 𝜌 2 ∓ 𝐵−𝐶 2 𝜌 2 ∓ 𝐵−𝐶 2 4𝐴+ 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 ]

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

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

theory =−148 cm  1

 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

He = −165(1) cm1 J. Chem. Phys. (2015) 142, 134306.

Accepted last week

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

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

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

Elaser EStark M = ±1

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

Elaser EStark M = 0

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

 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

He = −165(1) cm  1

theory = 148 cm  1

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

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.