The 68th International Symposium
on Molecular Spectroscopy, June 2013
The molecular frame electric dipole moment and
hyperfine interaction in hafnium fluoride, HfF.
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
PbO, YbF, PbF, ThO, WC, HfF+, HfH+, PtH+, PtF+, ThH+, ThF+...
The 3D1 state:
small W-doubling easily polarized
small Zeeman tuning.
Minimizes systematic errors
Focus on HfF (not HfF+ ):

Provide the hyperfine parameters, molecular dipole moments of HfF
el HfF+
Calculate
PNC needed
information
(Wa, Ws, Wd)
el HfF(theory)
Calculated hyp.
parameters,
molecular
dipole moments
Comparison
Improve
Experimental
values (hyp.
Parameters,
molecular dipole
moments)
Previous Related Work on HfF –
not much
Moskvitina et al.(1999):Spectrosc. Letts., 1999, 32(5), 719
Identify 3 bands: 589nm, 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 17000-24000cm-1
Motivated by eEDM experiments
Barker et al. (2011):J. Chem. Phys. 2011, 134, 201102
REMPI study HfF, ZEKE study HfF+
Grau et al. (2012): J. Mol. Spectroc., 2012, 272, 32
8 bands recorded, rotationally assigned, analyzed 13400-14500cm-1
Loh et al. (2012):J. Mol. Spectroc. 2012, 276-277, 49
REMPI study, transition in the excited state up to 33000cm-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
gN
Q
(mBarns)
177Hf
18.60
7/2
0.2571
+3365
179Hf
13.62
9/2
-0.1574
+3793
180Hf
35.08
0
_
_
19F
100
1/2
5.376
_
177HfF
R(11/2)
180HfF
NOTE: highly overlapped with 180HfF,
Complicated spectra (WHY?  Next slide)
179HfF
R(15/2)
Q (2H)=
2.860(mBarns)
180HfF
Why are the spectra complicated ? (Cont.)
177HfF
R(11/2) (I=7/2)
J=6.5
(v=1)[17.9]2.5
F
10
9
8
7
6
5
4
3
10
9
8
3
7,6,5,4
9
9
8
7
6
5
4
3
2
J=5.5
X2D3/2
Rotation
F
J+I(7/2)=F
Mag. hyperfine(177Hf)
2
3
8
4
5,7
6
[Mag.+Qua.] (177Hf)
Modeling the (1,0)[17.9]2.5-X2D3/2 band system
1. Effective Hamiltonian
Heff = Hso+ Hrot + Hmhf(Hf)+ HeQq(Hf)
2. Matrix representation: Hund’s case (abJ) coupled basis set:
Eigenvalues &
Eigenvectors
Parameters: B, h3/2(177,179Hf) and eQq0(177,179Hf) for the X2D3/2(v=0)
state,T00, B, h5/2(177,179Hf) and eQq0(177&179Hf) for the [17.9]2.5(v=1)
state
Observation & prediction
177HfF
R(11/2)
(v=1)[17.9]2.5, J=6.5
Observed
180HfF
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
X2D3/2, J=5.5
Total Angular momentum, F
c b a
Observation & prediction of
180HfF
Observed
179HfF
R(15/2)
(v=1)[17.9]2.5,
J=17/2
ΔF= +1
Pred.
B,C
A
D
E
F
G
Laser wavenumber (cm-1)
H
I
K
Relative Energy Level (cm-1)
LIF Signal
K I H GF E D C B A
X2D3/2,
J=15/2
Observation-Stark Shifts
(v=1)[17.9]2.5, J=5/2
1732.0 V/cm ||
A
180HfF
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
X2D3/2, J=3/2
Electric Field Strength (V/cm)
Stark Shift (MHz)
Determined parameters
States
Parameters
hW(179Hf)
hW
(177Hf)
hW(177Hf)
hW
(179Hf)
X2D3/2
-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)
-0.0805(35)
-0.0930(66) *
-0.2101 (43)
eQq0(179Hf)
-0.0774(30)
-0.1998(36)
eQq0(179Hf)
gI(177Hf)
-1.59
gI(179Hf)
eQq0(177Hf)
eQq0(177Hf)
Predicted ratio
0.96(8)
0.95(6)
Q(177Hf)
Q(179Hf)
*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].4f14.5d2.6s2
3F
Unpaired e is Hf-centered (5d 2)
Predicted molecular magnetic
h3/2(177HfF(experiment)):
176(11)MHz
hyperfine parameter
h3/2(177Hf)=170 MHz
Discussion-Are the parameters realistic?(cont.)
2. Stark Spectra
Determined molecular dipole moments:
Experiment:
m(X2D
3/2)=1.66(1) D
m([17.9]2.5(v=1))=0.419(7) D
Calculation CCSD(T): m(X2D3/2)= 1.63 D
(collaboration with Prof. Titov)
Elec. Neg.
Hf: 1.3
F: 3.98
Large Dipole
moment
Why does HfF have small dipole
moment?
Electron configuration of HfF
…2s21d13s2 2D3/2
6s2(Hf)
Hf+
mind
mtot
Small m
mbond
F-
Summary
• The complicated spectra of (1,0)[17.9]2.5-X2D3/2 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 X2D3/2 (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 2Δ3/2 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:
Prof. Anatoly V. Titov (Petersburg Nuclear Physics
Institute)
Group members:
 Dr. Fang Wang
 Ruohan Zhang
Funding sources:
NSF