Multichannel Quantum Defect Theory Calculation of Vibrational Autoionization

Multi-channel Quantum Defect Theory Calculation of Vibrational Auto-ionization Resonance Widths of v = 1, n∗ ≈ 14 Ca. F Rydberg States Jun Jiang, Timothy J. Barnum, Stephen L. Coy, Robert W. Field MIT 6/18/2018

Overview Mulliken’s Rule Along each Rydberg series, the shape of the innermost lobe of the Rydberg orbital wavefunction is invariant. Its amplitude scales as n*-3/2. Almost all dynamics in Rydberg-land is determined by the shape and amplitude of this innermost lobe. Simple model: ligand-field theory for ”series terminus” states MQDT calculation of vibrational auto-ionization lifetime Provides both insights and accurate predictions

Vibrational Auto-ionization •

A brief description of Ca. F • Low lying Rydberg states (i. e. valence states): • Described by Ligand-Field Theory • Ca 2+-centered electron perturbed by F 4 s e- Ca 2+ F- Rice et al. , JCP, 82, 5023 (1985)

A brief description of Ca. F • Low lying Rydberg states (i. e. valence states): • Ligand-field theory • Ca 2+-centered electron perturbed by F 4 s + 4 p Ca 2+ F- Rice et al. , JCP, 82, 5023 (1985)

A brief description of Ca. F • “High” Rydberg states (n*>5): • Multi-channel Quantum Defect • Large ion-core dipole moment (~8. 5 D) • Significant l-mixing of hydrogenic wavefunctions Ca. F+

• Kay et al. , JCP, 134, 114313 (2011)

Vibrational Resonance Widths (ϒA) in the n*=14, v=1 region (N=11) 15 ps!! 50 -100 ps in agreement with experimental observations

The valence-precursor model & Mulliken’s Rule

n*=3. 17 n*= 1 st lobe ______ n*=3. 17

The valence-precursor model Molecular constants of the valence states • Mulliken JACS, 91, 4615 (1969) Gittins, MIT thesis (1987)

Ca. F+ has ~8. 5 D debye moment X, A, B Ry e- F- Ca 2+ C Ca 2+ Ry e- F- B’ Ry Ca 2+ e- F-

The ligand-field model X, A, B Ry e- F- Ca 2+ C Ca 2+ Ry e- F- B’ Ry Ca 2+ e- F-

Conclusions •

Acknowledgements • Alex Hull • Clare Keenan • John Muenter • Trevor Erickson • Liz Foreman • Gloria Clausen

X, A, B Ry e- F- Ca 2+ C Ca 2+ Ry e- F- B’ Ry Ca 2+ e- F-

X and B state wavefunctions from the ligand-field theory Rydberg electron

Ca. F+ has ~8. 5 D debye moment X, A, B Ry e- Ca 2+ F- C Ca 2+ Ry e- F- B’ Ry. Ca 2+ e- F-

X and B state wavefunctions from the ligand-field theory Rydberg electron

X and B state wavefunctions from the ligand-field theory