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

2. Electron’s Electric dipole moment measurement PbO, YbF, PbF, ThO, WC, HfF +, HfH +, PtH +, PtF +, ThH +, ThF +... small  -doubling  easily polarized small Zeeman tuning. Minimizes systematic errors The 3  1 state : Focus on HfF (not HfF + ):  Provide the hyperfine parameters, molecular dipole moments of HfF  el HfF(theory) Calculated hyp. parameters, molecular dipole moments Experimental values (hyp. Parameters, molecular dipole moments) Comparison  el HfF + Improve PNC needed information (Wa, Ws, Wd) Calculate

3. Previous Related Work on HfF – not much Adam et al.(2004): J. Mol. Spectroc. 2004, 225, 1 Fine structure parameters for 9 bands in the range 17000-24000cm -1 Moskvitina et al.(1999): Spectrosc. Letts., 1999, 32(5), 719 Identify 3 bands: 589nm, 590.6 nm, 593.1 nm – Not analyzable Motivated by eEDM experiments Grau et al. (2012): J. Mol. Spectroc., 2012, 272, 32 8 bands recorded, rotationally assigned, analyzed 13400-14500cm -1 Barker et al. (2011): J. Chem. Phys. 2011, 134, 201102 REMPI study HfF, ZEKE study HfF + Loh et al. (2012): J. Mol. Spectroc. 2012, 276-277, 49 REMPI study, transition in the excited state up to 33000cm -1

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

5. %AbundanceIgNgN Q (mBarns) 177 Hf 18.607/2 0.2571+3365 179 Hf 13.629/2-0.1574+3793 180 Hf 35.080__ 19 F 1001/25.376_ Overview 177 HfF R(11/2) 179 HfF R(15/2) NOTE: highly overlapped with 180 HfF, Complicated spectra (WHY?  Next slide) Q ( 2 H)= 2.860(mBarns) 180 HfF

6. Why are the spectra complicated ? (Cont.) 177 HfF R(11/2) (I=7/2) J=5.5 X 2  3/2 J=6.5 (v=1)[17.9]2.5 Rotation Mag. hyperfine( 177 Hf)[Mag.+Qua.] ( 177 Hf) 9876543298765432 10 9 8 7 6 5 4 3 F 9 8 6 5,7 4 3 2 10 8 3 9 7,6,5,4 F J+I(7/2)=F

7. 1.Effective Hamiltonian H eff = H so + H rot + H mhf (Hf)+ H eQq (Hf) Modeling the (1,0)[17.9]2.5-X 2  3/2 band system 2. Matrix representation: Hund’s case (a  J ) coupled basis set: Eigenvalues & Eigenvectors Parameters: B, h 3/2 ( 177,179 Hf) and eQq 0 ( 177,179 Hf) for the X 2  3/2 (v=0) state,T 00, B, h 5/2 ( 177,179 Hf) and eQq 0 ( 177&179 Hf) for the [17.9]2.5(v=1) state

8. Observation & prediction 177 HfF R(11/2) Laser wavenumber (cm -1 ) LIF Signal Total Angular momentum, F Relative Energy Level(cm-1) X 2  3/2, J=5.5 (v=1)[17.9]2.5, J=6.5 ABCDEF abcd a b c d A B CDEF ΔF=+1 ΔF= 0 Observed Pred. 180 HfF

9. Observation & prediction of 179 HfF R(15/2) (v=1)[17.9]2.5, J=17/2 Relative Energy Level (cm-1) X 2  3/2, J=15/2 LIF Signal Laser wavenumber (cm -1 ) A B,C G D E F H I K ABCD E FGHI K ΔF= +1 Observed Pred. 180 HfF

10. Stark Shift (MHz) LIF Signal (v=1)[17.9]2.5, J=5/2 X 2  3/2, J=3/2 Electric Field Strength (V/cm) Energy Shift (MHz) 1732.0 V/cm || 1732.0 V/cm Field Free R(3/2) Observation-Stark Shifts 180 HfF ABCD acegbdfh DCBA geca hfdb ΔM F = 0 ΔM F = -1 ΔM F = +1

11. Determined parameters *CCSD(T) calculation - collaboration with Prof. Titov g I ( 177 Hf) g I ( 179 Hf) -1.59 h  ( 177 Hf) h  ( 179 Hf) -1.68(16) States X 2  3/2 h  ( 179 Hf) [17.9]2.5 (v=1) -0.00348(34) -0.01660(26) 0.02572(27) 0.00586(38) h  ( 177 Hf) Predicted ratio -1.55(3) Q( 177 Hf) Q( 179 Hf) 0.89 eQq 0 ( 177 Hf) eQq 0 ( 179 Hf) eQq 0 ( 177 Hf) eQq 0 ( 179 Hf) -0.0805(35) -0.2101 (43) -0.1998(36) -0.0774(30) 0.96(8)0.95(6) 0.0056(8)* -0.0930(66) * Para- meters

12. Discussion- Are the parameters realistic? 1.Field Free Spectra MO correlation diagram h 3/2 ( 177 HfF(experiment)): 176(11)MHz Unpaired e is Hf-centered (5d  2 ) Predicted molecular magnetic hyperfine parameter h 3/2 ( 177 Hf)=170 MHz Atomic hyperfine of Hf 3F3F [Xe].4f 14.5d 2.6s 2

13. …2  2  1  2  2  3/2  (X 2  3/2 )=1.66(1) D  ([17.9]2.5(v=1))=0.419(7) D Electron configuration of HfF 6s 2 (Hf)  ind  bond  tot Small  F-F- Hf + Why does HfF have small dipole moment? 2. Stark Spectra Discussion- Are the parameters realistic? (cont.) Determined molecular dipole moments: Elec. Neg. Hf: 1.3 F: 3.98 Large Dipole moment Experiment: Calculation CCSD(T):  (X 2  3/2 )= 1.63 D (collaboration with Prof. Titov)

14. Summary The molecular electric dipole moments of the [17.9]2.5(v=1) and X 2  3/2 (v=0) states from optical Stark spectrum The complicated spectra of (1,0)[17.9]2.5-X 2  3/2 have been recorded and completely analyzed to provide magnetic hyperfine and quadrupole parameters ab initio calculations using scalar-relativistic, coupled cluster, method with single and double cluster amplitudes (CCSD) of the 2 Δ 3/2 state properties were performed by Prof. Titov. Calculated values are in good agreement with the experimental values.

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