61st Symposium on Molecular Spectroscopy June 19, 2006

-doubling in High Angular Momentum States: High Resolution Spectroscopy of CoF (X 3i)

M. A. Flory, P. M. Sheridan, M. A. Brewster, S. K. McLamarrah, L. M. ZiurysDepartment of Chemistry, Department of Astronomy, Steward Observatory

University of Arizona

T. C. SteimleDepartment of Chemistry and Biochemistry

Arizona State Universityand

J. M. BrownPhysical and Theoretical Chemistry Laboratory

University of Oxford

61st Symposium on Molecular Spectroscopy June 19, 2006

CoF Motivation

• Working on transition metal fluoride series – RE08 (ZnF)

• Interested in Co bonding– Recent studies of CoCl, CoCN, CoS, CoO

• CoCl highly perturbed

• While CoF previously studied, a complete, high- resolution spectrum is desired

– You never know what you’re going to get!

61st Symposium on Molecular Spectroscopy June 19, 2006

Past Studies of CoF• Several electronic and rotational studies

– T. Okabayashi & M. Tanimoto, J. Mol.Spec., 221, 2003– X. Zheng, J. Guo, T. Wang, L. Pei, Y. Chen, C. Chen, J. Mol.Spec., 220, 2003.– A. G. Adam & W. D. Hamilton, J. Mol.Spec., 206, 2001.– R. S. Ram, P. F. Bernath, & S. P. Davis, J. Chem. Phys., 104, 1996.– R. S. Ram, P. F. Bernath, & S. P. Davis, J. Mol.Spec., 173, 1995.– A. G. Adam, L. P. Fraser, W. D. Hamilton, & M. C. Steeves, Chem. Phys. Lett.,

230, 1994.

• No pure rotational spectrum of all 3 spin components– Hund’s Case (a) fit with 2 nuclear spins

• Co nuclear spin (I = 7/2)• F nuclear spin (I = 1/2)

– -doubling in = 3 and 2

61st Symposium on Molecular Spectroscopy June 19, 2006

• Radiation Source: Phase-locked Gunn oscillators and Schottky diode multipliers (65-660 GHz)

• Gaussian beam optics utilized to minimize radiation loss

• Reaction Chamber: Double walled, steel cell which contains a Broida-type oven

• Detector: InSb bolometer

• Radiation is modulated at 25kHz and detected at 2f

Direct Absorption Submillimeter Spectroscopy

61st Symposium on Molecular Spectroscopy June 19, 2006

61st Symposium on Molecular Spectroscopy June 19, 2006

• Co vapor produced in high temp Broida-type oven– m.p. = 1495 °C– Zircar insulating felt/alumina sleeve– Molybdenum posts

• Reacted with 10% F2 in He (25 mTorr mixture)

• No d.c. discharge required• No additional carrier gas used• Initial search based on B values

by Ram et al. (1996)

Gas-Phase Synthesis of CoF

61st Symposium on Molecular Spectroscopy June 19, 2006

= 4 = 3 = 2

Ener

gy

3ASO 6ASOJ=5J=4

• 3 Fine structure components• • J ≥

• Hyperfine levels• J + I (Co) = F1

• F1 + I (F) = F

J=5

J=4J=3

J=5

J=4

J=3J=2

F1 F

3i Energy Levels

61st Symposium on Molecular Spectroscopy June 19, 2006

372030 372080 372130 372180 372230

Frequency (MHz)372480 372530 372580 372630

= 4 = 3 *

* *

= 2

J = 16 15

CoF Spectra

680 individual lines measured from 14 rotational transitions in range 255-651 GHz

61st Symposium on Molecular Spectroscopy June 19, 2006

-doubling Theory for states• Not worked out for states

– Only seen in CoH (X 3i) = 3• Connect electronic states (6th order effect)• Case (a) Hamiltonian of the form (with J. Brown):

HD = /2(J+6 + J-

6) – /2(J+5S+ + J–

5S–) + /2(J+4S+

2 + J–4S–

2) – ñ/2(J+3S+

3 + J–3S–

3)

+ /2(J+2S+

4 + J–2S–

4) – /2(J+S+5 + J–S–

5) + /2(S+6 + S–

6)

˜ p ˜ q ˜ o m

~k

~l

~

where = q

= p + 6q

= o + 5p + 15q, etc.˜ o ˜ p ˜ q

and ˜ q

EEEEEEB

22

6

1

1111 )ˆ()ˆ(2)ˆ()ˆ()2()1(q

qqqqq LTJBTSTLTBAHD =

• Convert using Van Vleck transformation/Wigner-Eckart Theorem

61st Symposium on Molecular Spectroscopy June 19, 2006

-doubling for 3 states

e.g. 6; S ± 2; J, 4 HLD ; S ; J, = -( /2)[ {J(J + 1) – ( 4) ( 3)}{J(J + 1) – ( 3) ( 2)}{J(J + 1) –

( 2) ( 1)} {J(J + 1) – ( 1) }{S(S + 1) – ( ± 1) }{S(S + 1) – ( ± 1) ( ± 2)}]1/2

˜ o

• For 3 state, first 3 terms give a 3 x 3 matrix• = 2 diagonal term:

3 matrixX = J(J+1)

|34> |33> |32>

<34| - - /2 * X(X-2)(X-6)1/2(X-12)1/2

<33| sym. /2*X(X-2)(X-6) - /√2*X(X-2)(X-6)1/2

<32| sym. sym. *X(X-2)

˜ q

˜ q ˜ p

˜ o

• Simplifies to Hamiltonian matrix:

61st Symposium on Molecular Spectroscopy June 19, 2006

This work (= 3 & 4)

Okabayashi ( = 4) Adam (2001)

B 11638.2112(24) 11635.32099(51) 11643.9(7.8)

D 0.0154741(18) 0.0153437(10) 0.0151395a

H -6.038*10-9 a

A -6981350a -6981350(160)

AD 3.1779(23) 0 a

AH 0.0000345(41)

-20890a -20890(240)

4.128(98)*10-08

a(Co) 563.09(58) h(Co) = 974.9(18)

aD(Co) 0.0192(21)

bF(Co) -716.4(3.3)b

bFD(Co) -0.026(11)

eqQ -73(12) -77.50(91)

a(F) 94.7(3.5) h(F)= 233.52(32)

aD(F) 0.076(12)

bF(F) -34(22)b

bFD(F) -0.165(46)

rms 0.252

In MHz.a) Fixedb) hyperfine c set to 0

˜ q

• Hund’s case (a) Hamiltonian

Heff = HRot + HSO + HSS + H-d + Hhf(Co) + Hhf(F)

• In addition to -doubling terms, 2 nuclears spins not trivial (T.C. Steimle) • Preliminary results ( = 3 & 4) in good agreement with previous studies

• Hoping to finish by the end of the week!

Analysis

61st Symposium on Molecular Spectroscopy June 19, 2006

Lucy Ziurys Prof. J. M. Brown Prof. T. C. Steimle Prof. P. M. Sheridan Ziurys Group

Dr. Aldo Apponi Dr. DeWayne Halfen Shawn McLamarrah, Stefanie Milam, and Emmy Tenenbaum

Funding – NSF, NASA Laboratory Astronomy

Thanks to…