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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
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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!
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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
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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
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61st Symposium on Molecular Spectroscopy June 19, 2006
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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
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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
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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
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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
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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:
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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
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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…