The 68 th International Symposium on Molecular Spectroscopy

The 68 th International Symposium on Molecular Spectroscopy, June 2013 The molecular frame electric dipole moment and hyperfine interaction in hafnium fluoride, Hf. F. Anh T. Le and Timothy C. Steimle* Department of Chemistry and Biochemistry, Arizona State University, Tempe, AZ 85287 Leonid Skipnikov and Anatoly V. Titov Petersburg Nuclear Physics Institute, Gatchina, 188300, Russia and Quantum Mechanics Division, St. Petersburg State University, St. Petersburg 198904, Russia. *Funded by NSF J. Chem. Phys. 138, 124313 (2013)

Electron’s Electric dipole moment measurement Pb. O, Yb. F, Pb. F, Th. O, WC, Hf. F+, Hf. H+, Pt. F+, Th. H+, Th. F+. . . The 3 D 1 state: small W-doubling easily polarized small Zeeman tuning. Minimizes systematic errors Focus on Hf. F (not Hf. F+ ): Ø Provide the hyperfine parameters, molecular dipole moments of Hf. F el Hf. F+ Calculate PNC needed information (Wa, Ws, Wd) el Hf. F(theory) Calculated hyp. parameters, molecular dipole moments Comparison Improve Experimental values (hyp. Parameters, molecular dipole moments)

Previous Related Work on Hf. F – not much Moskvitina et al. (1999): Spectrosc. Letts. , 1999, 32(5), 719 Identify 3 bands: 589 nm, 590. 6 nm, 593. 1 nm – Not analyzable Adam et al. (2004): J. Mol. Spectroc. 2004, 225, 1 Fine structure parameters for 9 bands in the range 17000 -24000 cm-1 Motivated by e. EDM experiments Barker et al. (2011): J. Chem. Phys. 2011, 134, 201102 REMPI study Hf. F, ZEKE study Hf. F+ Grau et al. (2012): J. Mol. Spectroc. , 2012, 272, 32 8 bands recorded, rotationally assigned, analyzed 13400 -14500 cm -1 Loh et al. (2012): J. Mol. Spectroc. 2012, 276 -277, 49 REMPI study, transition in the excited state up to 33000 cm-1

Experiment method Ablation laser Gated photon counter Skimmer Stark Plates Well collimated molecular beam Rot. Temp. <20 K Electric field > 4000 V/cm Resolution ~30 MHz CW dye laser

Overview %Abundance I g. N Q (m. Barns) 177 Hf 18. 60 7/2 0. 2571 +3365 179 Hf 13. 62 9/2 -0. 1574 +3793 180 Hf 35. 08 0 _ _ 19 F 100 1/2 5. 376 _ 177 Hf. F R(11/2) 180 Hf. F NOTE: highly overlapped with 180 Hf. F, Complicated spectra (WHY? Next slide) 179 Hf. F R(15/2) Q (2 H)= 2. 860(m. Barns) 180 Hf. F

Why are the spectra complicated ? (Cont. ) 177 Hf. F R(11/2) (I=7/2) J=6. 5 (v=1)[17. 9]2. 5 F 10 10 9 8 7 6 5 4 3 9 8 3 7, 6, 5, 4 9 8 7 6 5 4 3 2 J=5. 5 X 2 D 3/2 Rotation F J+I(7/2)=F Mag. hyperfine(177 Hf) 9 2 3 8 4 5, 7 6 [Mag. +Qua. ] (177 Hf)

Modeling the (1, 0)[17. 9]2. 5 -X 2 D 3/2 band system 1. Effective Hamiltonian Heff = Hso+ Hrot + Hmhf(Hf)+ He. Qq(Hf) 2. Matrix representation: Hund’s case (ab. J) coupled basis set: Eigenvalues & Eigenvectors Parameters: B, h 3/2(177, 179 Hf) and e. Qq 0(177, 179 Hf) for the X 2 D 3/2(v=0) state, T 00, B, h 5/2(177, 179 Hf) and e. Qq 0(177&179 Hf) for the [17. 9]2. 5(v=1) state

Observation & prediction 177 Hf. F R(11/2) (v=1)[17. 9]2. 5, J=6. 5 Observed 180 Hf. F ΔF= 0 LIF Signal FE D C B Pred. dc b a Laser wavenumber (cm-1) A Relative Energy Level(cm-1) ΔF=+1 d F E D C B A X 2 D 3/2, J=5. 5 Total Angular momentum, F c b a

Observation & prediction of 180 Hf. F Observed 179 Hf. F R(15/2) (v=1)[17. 9]2. 5, J=17/2 Pred. B, C A D E F G Laser wavenumber (cm-1) H I K Relative Energy Level (cm-1) LIF Signal ΔF= +1 K I H GF E D C B A X 2 D 3/2, J=15/2

Observation-Stark Shifts (v=1)[17. 9]2. 5, J=5/2 1732. 0 V/cm || A 180 Hf. F B C ΔMF= +1 D ΔMF= 0 1732. 0 V/cm a b c d e f g ΔMF= -1 h Field Free R(3/2) Energy Shift (MHz) LIF Signal D C B A g e ca h fdb X 2 D 3/2, J=3/2 Electric Field Strength (V/cm) Stark Shift (MHz)

Determined parameters States Parameters h. W(179 Hf) h. W (177 Hf) h. W (179 Hf) X 2 D 3/2 -0. 00348(34) 0. 00586(38) 0. 0056(8)* -1. 68(16) [17. 9]2. 5 (v=1) -0. 01660(26) 0. 02572(27) -1. 55(3) g. I(177 Hf) -1. 59 g. I(179 Hf) e. Qq 0(177 Hf) -0. 0805(35) -0. 0930(66) * -0. 2101 (43) e. Qq 0(179 Hf) -0. 0774(30) -0. 1998(36) e. Qq 0(177 Hf) e. Qq 0(179 Hf) Predicted ratio 0. 96(8) 0. 95(6) Q(177 Hf) Q(179 Hf) *CCSD(T) calculation - collaboration with Prof. Titov 0. 89

Discussion-Are the parameters realistic? 1. Field Free Spectra MO correlation diagram Atomic hyperfine of Hf [Xe]. 4 f 14. 5 d 2. 6 s 2 3 F Unpaired e is Hf-centered (5 d� 2) Predicted molecular magnetic h 3/2 (177 Hf. F(experiment)): 176(11)MHz hyperfine parameter h 3/2(177 Hf)=170 MHz

Discussion-Are the parameters realistic? (cont. ) 2. Stark Spectra Determined molecular dipole moments: Experiment: m(X 2 D 3/2)=1. 66(1) D m([17. 9]2. 5(v=1))=0. 419(7) D Calculation CCSD(T): m(X 2 D 3/2)= 1. 63 D (collaboration with Prof. Titov) Elec. Neg. Hf: 1. 3 F: 3. 98 Large Dipole moment Why does Hf. F have small dipole moment? Electron configuration of Hf. F … 2 s 21 d 13 s 2 2 D 3/2 6 s 2(Hf) Hf+ mind mtot Small m mbond F-

Summary • The complicated spectra of (1, 0)[17. 9]2. 5 -X 2 D 3/2 have been recorded and completely analyzed to provide magnetic hyperfine and quadrupole parameters • The molecular electric dipole moments of the [17. 9]2. 5(v=1) and X 2 D 3/2 (v=0) states from optical Stark spectrum • ab initio calculations using scalar-relativistic, coupled cluster, method with single and double cluster amplitudes (CCSD) of the 2Δ 3/2 state properties were performed by Prof. Titov. Calculated values are in good agreement with the experimental values.

Thank you Advisor: Prof. Timothy C. Steimle Collaborations: ØProf. Anatoly V. Titov (Petersburg Nuclear Physics Institute) Group members: Ø Dr. Fang Wang Ø Ruohan Zhang Funding sources: NSF