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Rotational spectrum of FCO2 molecule with
resolved fs and hfs in its ground vibrational
and 2 B2 electronic ground states
a
y
z
states multiplicity MS 2 S 12 lt S ½
.. electron spin
The choice of the molecule-fixed axes system ?
IF 1/2
F
nuclear spin
(c)
(z)
(y)
b
x
C
O
O
It is an asymmetric top, which belong to C2v
point group
NKaKc ..asymmetric rotor levels
(two limit cases)
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MOLECULAR WAVE FUNCTION AND NUCLEAR SPIN
STATISTICS
total internal
? int ? el? vib? rot? ns
? el
.. electronic
? vib
..vibrational
? rot
..rotational
? ns
..nuclear-spin
?(? rve)
B2
B1
A1
A2
?(? int)
B2
B1
A1
A2
P.R.Bunker and Per Jensen, MOLECULAR SYMMETRY AND
SPECTROSCOPY
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ROTATIONAL LEVELS OF AN ASSYMETRIC TOP
2 2 0
2 2 1
2 1 1
2 1 2
2 0 2
1 1 0
1 1 1
1 0 1
0 0 0
N Ka Kc
G. Herzberg, MOLECULAR SPECTRA AND MOLECULAR
STRUCTURE II. INFRARED AND RAMAN SPECTRA OF
POLYATOMIC MOLECULES
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MOLECULAR WAVE FUNCTION IN QUANTUM NUMBER NOTATION

• int vgt SMSgt KNM gt IMI gt

uncoupled representation
S ½
I ½
electron spin, symmetric rotor and nuclear
spin wave functions

• int ? KNSJIFMF gt coupled representation

R.N. Zare, ANGULAR MOMENTUM
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HAMILTONIAN (Ir representation prolate, z a)
ROTATIONAL
Hrot A Na2 B Nb2 C Nc2
centrifugal distortion (A-reduction, J.K.G.
Watson, VIBRATIONAL SPECTRA and STRUCTURE)
Hrotcf - ?N N4 -?NK N2Na2 - ?K Na4 - dN N2
(N2 N-2 )
- 1/2 dK Na2 (N2 N-2 ) (N2 N-2 ) Na2
FINE (fs) AND HYPERFINE (hfs) STRUCTURE TERMS
? ?


electron spin rotational
Hsre ?aa NaSa ?bb NbSb ?cc NcSc
Wsre ? N S
? ?

Hssen Taa SaIa Tbb SbIb Tcc ScIc
Wssen T S I
electron spin nuclear spin

? ?
aFC S I
aFC S I
nuclear spin rotational

Hsrn Caa NaIa Cbb NbIb Ccc NcIc
classical energy
Hamiltonian (only diagonal terms considered)
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ELECTRON SPIN NUCLEAR SPIN INTERACTION
? ?

Hssen Taa SaIa Tbb SbIb Tcc ScIc
Wssen T S I

? ?
WFC aFC S I
H FC aFC S I
.. Fermi-contact type term
H FC a FC S I
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NUMERICAL ANALYSIS OF THE SPECTRA (Picketts
program)
( centrifugal distortion A-reduction )
Rotational constants
Units ab-initio study previous study Lille This work Lille Prague 1. 2.
A MHz 13772. 13752.667 (68) 13752.2758 (63) 13752.755(167)
B 11291. 11309.962 (52) 11310.2307 (55) 11309.853(136)
C 6192. 6192.8077 (21) 6192.80035 (58) 6192.8196( 68)
?N kHz 6.978 7.088 (124) 7.691 (18) 6.16( 76)
?NK 1.221
?K 13.231 21.26 (108) 15.682 (156) 29.1( 65)
dN 2.993 3.009 (62) 3.3119 (92) 2.54( 38)
dK 10.391 9.492 (237) 10.690 (34) 7.67(149)
?KJ Hz   -0.316 (48)
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NUMERICAL ANALYSIS OF THE SPECTRA (Picketts
program)
Fine structure constants
( centrifugal distortion A-reduction )
Units previous study Lille This work Lille Prague 1. 2.
eaa MHz -80.74 (33) -80.233 (211) -84.88(128)
ebb -788.67 (47) -789.868 (87) -782.9( 33)
ecc -44.005 (19) -44.2597 (227) -44.307(112)
?sN kHz   -0.0923 (297)
?sNK   -1.64 (45)
dsK   -3.80 (38)
aF MHz -208 (27) -243.7 (79) -165( 98)
½ Taa -95.25 (179) -27.16 (90) -712( 47)
¼ (Tbb -Tcc ) 8.85 (122) 6.008 (131) 86.8( 47)
J.M.Brown and T.J.Sears
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NUMERICAL ANALYSIS OF THE SPECTRA (Picketts
program)
( centrifugal distortion )
Hyperfine structure constants
Units previous study Lille This work Lille Prague 1. Units 2.
Caa MHz 8.744 (247) 12.990 (159) Caa MHz 11.18(107)
CaaJ   -0.02028 (142)
CaaK   0.02256 (238)
¼ (Cbb - Ccc) MHz -0.2793 (74) -0.3830 (115) Cbb MHz
¼ (Cbb - Ccc)J kHz   0.3769 (167) Ccc -0.929( 84)
¼ (Cbb - Ccc)K MHz   -0.01303 (81)
-14.9(37)
MICROWAVE AVG 0.039987 MHz, IR AVG
0.00000 MICROWAVE RMS 3.955783 MHz,
IR RMS 0.00000 END OF ITERATION 5 OLD,
NEW RMS ERROR 1.16633 1.16633