Journal of Molecular Spectroscopy 221 (2003) 149–155

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Rotational spectrum of CoF in the X3U4 electronic ground state

Toshiaki Okabayashi* and Mitsutoshi Tanimoto

Department of Chemistry, Faculty of Science, Shizuoka University, Oya 836, Shizuoka 422-8529, Japan

Received 3 March 2003; in revised form 25 June 2003

Abstract

The rotational spectrum of the CoF radical in the X 3U4 state was observed by employing a source modulation microwave

spectrometer. The CoF radical was generated in a free space cell by a dc glow discharge in CF4 and He. The cobalt atoms were

supplied by the sputtering reaction from cobalt powder placed over a lower surface of the cylindrical electrodes. The transitions with

J ¼ 11–10 to 17–16 were measured in the region between 250 and 400GHz. The effective rotational, centrifugal distortion, and

hyperfine constants were obtained by a least-squares analysis.

� 2003 Elsevier Inc. All rights reserved.

1. Introduction

Transition metal compounds have often high elec-

tronic-orbital and electron spin angular momenta due totheir d-electrons. The d-electrons thus cause a large

number of low lying electronic excited states. These elec-

tronic states and their substates result in remarkably

complex spectra observed by a high resolution spectro-

scopic method. It is interesting to observe high resolution

spectrum of such species in order to understand their

electronic properties fromanalysis of hyperfine constants.

However, it is difficult to produce the transition metalcompounds in the gas phase abundantly enough to ob-

serve rotational spectrumwhich is oneof themost suitable

method to observe hyperfine-resolved spectrum. Thus,

the electronic spectra with unresolved hyperfine structure

have been mainly employed to study such species [1,2].

The diatomic transition metal halides MX (M¼transition metal; X¼F, Cl, Br, and I) are highly ionic

species represented as MþX�. All unpaired electronsmainly exist on the metal atom because of the closed

shell structure of the X� ion. The electronic states

strongly reflect the character of metal ions Mþ. Thus,the transition metal halide is one of the simplest pro-

totypes to understand metal–ligand bonding.

Cobalt monofluoride (CoF) is one of such halides

that have scarcely been studied by any spectroscopic

* Corresponding author. Fax: +81542373384.

E-mail address: sctokab@ipc.shizuoka.ac.jp (T. Okabayashi).

0022-2852/$ - see front matter � 2003 Elsevier Inc. All rights reserved.

doi:10.1016/S0022-2852(03)00201-7

methods until recently. However, the electronic spectra

of CoF have been studied by two groups lately. The first

reliable spectrum was reported by Adam et al., who

observed the visible [18.8]3Ui–X 3Ui transition with highresolution LIF spectroscopy and carried out the rota-

tional analysis, initially using a Hund�s case (c) basis set[3] and later a case (a) basis set [4]. Ram et al. [5,6] re-

ported high resolution Fourier transform spectrum of

the C3Di–X 3Ui, D3Di–X 3Ui, G3Ui–X 3Ui, and G3Ui–C3Di

bands in the near-infrared region.

Recently, we have carried out millimeter- and sub-

millimeter-wave spectroscopic studies on several transi-tion metal halides such as CrF(X 6Rþ) [7], FeCl(X 6Di)

[8], NiF(X 2Pi) [9], and CuF (X 1Rþ) [10] which were

efficiently generated by the sputtering reaction of

metallic targets. As an extension of our interest in

transition metal halides, we report millimeter- and sub-

millimeter-wave spectroscopy of the CoF (X 3Ui) radical

in the present paper.

2. Experimental

The present experiment was carried out using a source-

modulated microwave spectrometer [11]. Millimeter- and

submillimeter-wave radiations were generated by multi-

plying the output of klystrons. The radiation transmitted

through a free space cell was detected by an InSb detectorcooled at 4.2 K by liquid helium. The cell contained a pair

of cylindrical electrodes for a dc glow discharge. The cell

395268.5 (MHz) 395274.5

CoF (X 3Φ4) J=17-16 F1=19.5-18.5

F=20-19 F=19-18

Fig. 1. Rotational transitions of CoF in the ground X 3U4 states.

Table 1

Molecular constants of CoF (X 3U4)a

MW NIRb

B0 (MHz) 11635.32099(51) 11635.422(39)

D0 (kHz) 15.3437(10) 15.3553(26)

H0 (mHz) )6.038c )6.038(48)

150 T. Okabayashi, M. Tanimoto / Journal of Molecular Spectroscopy 221 (2003) 149–155

was surrounded by Helmholtz coils in order to cancel the

magnetic field of the Earth.

The CoF radical was generated in the free space cellby a dc glow discharge in CF4 and He. The cobalt atoms

were supplied by the sputtering reaction from cobalt

powder scattered over the lower surface of the elec-

trodes. The transition frequencies were predicted from

molecular constants recently obtained from the elec-

tronic spectra [5,6]. First we searched for the J ¼ 16–15

transition of the CoF radical in the lowest X 3U4 spin

component near 372GHz. Sixteen lines which showedremarkably paramagnetic behavior were observed be-

tween 372 025 and 372 140MHz. These lines appeared

when the cell temperature was below )150 �C and the

discharge current was above 300mA. With cooler cell

temperature and higher discharge current, the lines were

stronger. Accordingly the cell was cooled to the liquid

nitrogen temperature and the discharge current was set

to about 500mA. Optimum sample pressure was5mTorr of CF4 and 30mTorr of He. Under this con-

dition, the spectral lines were quenched within a minute

after the discharge was started.

If the carrier of these paramagnetic lines was the CoF

radical, it was quite reasonable that the 16 lines were

caused by the hyperfine interactions fromboth cobalt and

fluorine nuclei.Moreover,weobservedother J transitionsdue to this carrier, and therefore this specieswas identifiedas the CoF radical. No spectral lines were detected in the

higher spin substates, X 3U3 and X 3U2, which are, re-

spectively, located about 700 and 1400 cm�1 above the

lowest X 3U4 substate [4], because the signal-to-noise ratio

was poor. Finally, we observed 90 lines from J ¼ 11–10 to

17–16 transitions in the region between 250 and 400GHz.

Fig. 1 shows an example of the observed spectral line.

h4(Co) (MHz) 974.9(18)

h4D(Co) (MHz) )0.1675(11)eQq(Co) (MHz) )77.50(91)h4(F) (MHz) 233.52(32)aValues in parentheses are one standard deviation.bRef. [6].c Fixed in the analysis.

3. Analysis

The observed transition frequencies were analyzed by

a least-squares analysis using a Hund�s case (c) effective

Hamiltonian with two nonzero spin nuclei. The couplingscheme is F1 ¼ J þ ICo and F ¼ F1 þ IF.

The Hamiltonian employed is

Heff ¼ Hrot þ Hhf ; ð1Þwhere Hrot represents rotational energy including

centrifugal distortion, and Hhf hyperfine interaction. The

matrix elements are described as follows [12,13]:

hJXF1F jHrotjJXF1F i ¼ B0JðJ þ 1Þ � D0J 2ðJ þ 1Þ2

þ H0J 3ðJ þ 1Þ3 ð2Þ

and

hJ 0XF 01F jHhf jJXF1F i

¼ dF 01F1fhXðCoÞ þ hXDðCoÞ½JðJ þ 1Þ þ J 0ðJ 0 þ 1Þ�=2g

� ð�1ÞJ0þI1þF1

I1 J 0 F1J I1 1

( )ð�1ÞJ

0�X J 0 1 J

�X 0 X

!

� ½ð2J 0 þ 1Þð2J þ 1ÞI1ðI1 þ 1Þð2I1 þ 1Þ�1=2

þ dF 01F1

eQqðCoÞ4

ð�1ÞJ0þI1þF1

I1 J 0 F1J I1 2

( )ð�1ÞJ

0�X

�J 0 2 J

�X 0 X

!

� ð2J 0 þ 1Þð2J þ 1ÞðI1 þ 1Þð2I1 þ 1Þð2I1 þ 3ÞI1ðI1 � 1Þ

� �1=2

þ hXðFÞð�1ÞJþ2F 01þI1þI2þFþ1 I2 F 0

1 F

F1 I2 1

( )

�I1 J 0 F 0

1

1 F1 J

( )ð�1ÞJ

0�X J 0 1 J

�X 0 X

!

� ½ð2F 01 þ 1Þð2F1 þ 1Þð2J 0 þ 1Þð2J þ 1ÞI2ðI2 þ 1Þ

� ð2I2 þ 1Þ�1=2; ð3Þ

where I1 and I2 are nuclear spin quantum numbers of

cobalt(ICo ¼ 7=2) and fluorine(IF ¼ 1=2), respectively.

The molecular constants were determined by a least-

squares calculation. The standard deviation of the fitwas 29 kHz. The molecular constants determined are

listed in the second column of Table 1. The third column

T. Okabayashi, M. Tanimoto / Journal of Molecular Spectroscopy 221 (2003) 149–155 151

lists the constants reported by Ram et al. [6]. Therotational and centrifugal constants determined in

the present work well agree with those obtained from

the near infrared electronic transitions. The observed

and calculated transition frequencies are summarized

with their residuals in Table 2.

Table 2

Observed transition frequencies of CoF (X 3U4) in MHz

J 0–J F 01–F1 F 0–F Obs. Freq. O

11–10 7.5–6.5 7–6 256026.669

8.5–7.5 8–7 256009.764 )9.5–8.5 9–8 255987.677 )10.5–9.5 10–9 255960.165

11.5–10.5 11–10 255927.094 )12.5–11.5 12–11 255888.529 )13.5–12.5 13–12 255844.415 )14.5–13.5 14–13 255794.775 )

12–11 8.5–7.5 8–7

9.5–8.5 9–8 279235.919 )10.5–9.5 10–9 279216.544 )11.5–10.5 11–10 279192.964 )12.5–11.5 12–11 279165.144 )13.5–12.5 13–12 279133.059 )14.5–13.5 14–13 279096.775

15.5–14.5 15–14 279056.166

13–12 9.5–8.5 9–8 302476.571 )10.5–9.5 10–9 302462.624

11.5–10.5 11–10 302445.464

12.5–11.5 12–11 302424.965 )13.5–12.5 13–12 302401.231 )14.5–13.5 14–13 302374.130 )15.5–14.5 15–14 302343.673 )16.5–15.5 16–15 302309.873

14–13 10.5–9.5 10–9 325700.673

11.5–10.5 11–10 325687.849 )12.5–11.5 12–11 325672.640

13.5–12.5 13–12 325654.746

14.5–13.5 14–13 325634.198

15.5–14.5 15–14 325611.028

16.5–15.5 16–15 325585.083

17.5–16.5 17–16 325556.462

16–15 12.5–11.5 12–11 372140.053

13.5–12.5 13–12 372129.458

14.5–13.5 14–13 372117.094 )15.5–14.5 15–14 372103.048

16.5–15.5 16–15 372087.144 )17.5–16.5 17–16 372069.509

18.5–17.5 18–17 372050.024 )19.5–18.5 19–18 372028.770

17–16 13.5–12.5 13–12 395353.571 )14.5–13.5 14–13 395343.844

15.5–14.5 15–14 395332.632 )16.5–15.5 16–15 395320.023

17.5–16.5 17–16 395305.886 )18.5–17.5 18–17 395290.292 )19.5–18.5 19–18 395273.177

20.5–19.5 20–19 395254.504 )aObserved minus calculated frequency.b Excluded from the fit.

4. Results and discussion

Hyperfine splittings arising from the nuclear spins of

both cobalt and fluorine were observed in the present

experiment. The hyperfine parameters of Frosch and

Foley [14], a, bF and c, are represented as

)Ca F 0–F Obs. Freq. O)Ca

0.003 8–7 256019.667 0.009

0.004 9–8 256003.812 )0.0350.010 10–9 255981.954 )0.112b

0.001 11–10 255954.489 0.023

0.026 12–11 255921.147 0.012

0.010 13–12 255882.176 0.037

0.009 14–13 255837.539 0.012

0.016 15–14 255787.354 0.011

9–8

0.044 10–9

0.020 11–10 279211.557 0.032

0.018 12–11 279187.987 0.073

0.019 13–12 279159.898 )0.0120.028 14–13 279127.521 )0.0290.027 15–14 279090.809 )0.0520.020 16–15 279049.803 )0.059

0.011 10–9 302471.372 0.000

0.008 11–10 302457.952 0.018

0.004 12–11 302440.972 0.009

0.054 13–12 302420.552 0.035

0.024 14–13

0.016 15–14 302369.305 )0.0150.009 16–15 302338.599 )0.0020.021 17–16 302304.448 )0.031

0.053 11–10 325696.130 0.053

0.059 12–11

0.006 13–12 325668.594 )0.0280.011 14–13 325650.728 0.000

0.019 15–14 325630.094 0.006

0.079 16–15 325606.719 0.008

0.056 17–16 325580.619 0.018

0.061 18–17

0.005 13–12 372136.472 )0.0470.025 14–13 372126.040 )0.083b

0.004 15–14 372113.853 )0.0270.037 16–15 372099.810 0.004

0.007 17–16 372083.794 )0.108b

0.011 18–17 372066.151 )0.0160.012 19–18 372046.583 )0.0120.022 20–19 372025.133 )0.043

0.010 14–13 395350.452 0.012

0.009 15–14 395340.841 )0.0220.024 16–15 395329.777 0.019

0.004 17–16 395317.131 )0.0030.018 18–17 395302.984 )0.0040.004 19–18 395287.336 0.020

0.001 20–19 395270.124 0.014

0.024 21–20 395251.358 0.000

� �152 T. Okabayashi, M. Tanimoto / Journal of Molecular Spectroscopy 221 (2003) 149–155

a ¼ 2lBgNlN1

K

Xi

li1

r3i o

; ð4Þ

bF ¼ 8p3gslBgNlN

1

n

Xi

hjWð0Þij2is; ð5Þ

and

c ¼ 3

2gslBgNlN

1

n

Xi

3 cos2 hi � 1

r3i

� �s

: ð6Þ

In the present study, however, we could not determine

the Frosch and Foley hyperfine parameters separately

because the transitions were observed only in the X ¼ 4

substate without X ¼ 3 and X ¼ 2 substates. Instead of

these three parameters, an effective magnetic hyperfine

constant h4 ¼ 3aþ bþ c was determined in the present

analysis, where hX ¼ aKþ ðbþ cÞR and b ¼ bF � c=3.The centrifugal distortion term h4D for the cobalt

hyperfine constant was needed to reproduce the ob-

served transition frequencies, but that for fluorine was

not necessary. Nevertheless, the h4D(Co) value seems to

be effectively determined because jh4DðCoÞ=h4ðCoÞj ’10�4 is much larger than D=B ’ 10�6. The apparently

large centrifugal distortion of hyperfine h parameter

often arises when a case (a) multiplet state is modeledusing a case (c) approach, or when the full spin–orbit

manifold cannot be observed. For example, this prob-

lem was found in the B4P state of the vanadium oxide

VO radical. The large hXD value of VO in the B4P(v ¼ 1) state found in the case (c) analysis was accounted

for as a second order cross term between the spin un-

coupling and Fermi contact operators in the case (a)

Hamiltonian [15]. In the later work, the analysis usingthe full case (a) Hamiltonian on a large data set for the

v ¼ 0 level did not need the hXD term any more [16].

In the case (a) Hamiltonian, the magnetic hyperfine

interaction is presented in [17].

hK0SR0J 0X0I jjHhf jjKSRJXIi¼ ½IðI þ 1Þð2I þ 1Þð2J 0 þ 1Þð2J þ 1Þ�1=2

� dKK0Xq

ð(

� 1ÞJ0�X0 J 0 1 J

�X0 q X

!

� aKdRR0dXX0

"þ bF ð � 1ÞS�R0 S 1 S

�R0 q R

� �

� ½SðS þ 1Þð2S þ 1Þ�1=2 þffiffiffiffiffi30

p

3cð � 1Þqð � 1ÞS�R0

�S 1 S

�R0 q R

� �1 2 1

�q 0 q

� �½SðS þ 1Þð2S þ 1Þ�1=2

#

þ dXq¼�1

dK0K�2ð � 1ÞJ0�X0

ð � 1ÞS�R0 J 0 1 J

�X0 q X

!

�S 1 S

�R0 q R

� �½SðS þ 1Þð2S þ 1Þ�1=2

): ð7Þ

Using this equation, the diagonal matrix element of3U4 and the off-diagonal elements between 3U4 � 3U3

are expressed by the following equations:

h3U4; JIF jHhf j3U4; JIF i ¼ 4 3a�

þ bF þ 2

3c�X ðJIF Þ

¼ 4h4X ðJIF Þ; ð8Þ

and

h3U4; JIF jHhf j3U3; JIF i ¼ bF

�� 1

3c�X ðJIF Þ

� ½2ðJðJ þ 1Þ � 12Þ�1=2

¼ bX ðJIF Þ½2ðJðJ þ 1Þ � 12Þ�1=2;ð9Þ

where X ðJIF Þ is an expression including several quan-

tum numbers as J , F , and I . With a spin-uncoupling

term included in the case (a) 3U matrix elements [22],

this off-diagonal element is approximately rewritten as

follows:

h3U4; JIF jH j3U3; JIF i ’ � ½B� bX ðJIF Þ�� ½2ðJðJ þ 1Þ � 12Þ�1=2: ð10Þ

Based on a second-order perturbation theory, the 3U4

energy is corrected by

DEð2Þ ’ 2ðJðJ þ 1Þ � 12ÞDEð3U4 � 3U3Þ

ðB2 � 2bBX ðJIF Þ þ b2X ðJIF Þ2Þ:

ð11ÞBy comparing Eq. (8) with Eq. (11), the second term in

Eq. (11) can be identified with the h4D term:

h4D ’ � bBDEð3U4 � 3U3Þ

’ � bB3A

: ð12Þ

Using the h4D(Co) and B0 values in Table 1 and

A ¼ �232:87 cm�1 [4], the off-diagonal b(Co) term is

estimated to be )302MHz. Although this value is not

very accurate, its absolute value is roughly close to that

of CoH (136MHz) [22]. This finding supports the as-

sumption that the present h4D(Co) value is an apparenteffective parameter arising when a case (a) multiplet

state is modeled using a case (c) coupling.

Electronic configuration of CoF has been proposed

as (core)ð9rÞ2ð1dÞ3ð4pÞ3 in [3], and the unpaired elec-

trons belong to the 1d and 4p orbitals. The 1d orbital is

constructed solely from a 3d(Co) orbital. On the other

hand, the 4p orbital is mainly constructed from a 3d(Co)orbital but includes small amounts of 4p(Co) and 2p(F)orbitals. Thus, the hyperfine constant h4(Co) reveals thecontributions of the 3d(Co) orbitals to the partially filled

1d and 4p orbitals. On the other hand, h4(F) representsthe contribution of the 2p(F) orbitals to the 4p orbital of

an unpaired electron.

If h1=r3io in Eq. (4) is approximately equal to h1=r3isin Eq. (6), a(F) and c(F) constants are related to a

T. Okabayashi, M. Tanimoto / Journal of Molecular Spectroscopy 221 (2003) 149–155 153

unique atomic constant P ðFÞ ¼ 4400MHz listed in [18].Since the 4p orbital does not include the contribution of

the 2s orbital of the fluorine, the bF (F) constant shouldbe close to zero. The a(F) and c(F) constants are thus

simplified to the following approximate equations:

aðFÞ ¼ 2lBgNlN1

32

1

r3

� �1d

�þ 1

r3

� �4p

�

¼ cF4p3

2lBgNlN1

r3

� �2ppðFÞ

" #

’ cF4p3

P ðFÞ; ð13Þ

and

cðFÞ ¼ 3

2gslBgNlN

1

2

3 cos2 h� 1

r3

� �1d

�

þ 3 cos2 h� 1

r3

� �4p

�

¼ 3cF4p4

gslBgNlN3 cos2 h� 1

r3

� �2ppðFÞ

" #

’ � 3cF4p10

PðFÞ; ð14Þ

where cF4p represents the contribution of the 2p(F) orbitalto the 4p orbital and the angular factor h3 cos2 h� 1i2ppis taken to be )2/5 [18]. The h4(F) value is derived as

follows:

h4ðFÞ ¼ 3aðFÞ þ bF ðFÞ þ2

3cðFÞ ¼ 4cF4p

5PðFÞ: ð15Þ

In order to reproduce the observed value h4ðFÞ ¼ 234MHz, we obtained cF4p ¼ 0:066. This value is consistent

with the prediction that the 4p orbital is dominantly

(’93%) constructed from the 3d(Co) atomic orbital.

This finding means that the fluorine atom almost exists

as the closed shell F� ion and hardly possesses an

unpaired electron.

There are only scarce reports on hyperfine constants

for metal monofluoride radicals bearing unpaired elec-trons, except for alkaline earth fluorides like CaF [19]

and iron fluoride FeF [20]. Electronic configurations of

CaF and FeF are represented as (core)ð9rÞ1 and

(core)ð9rÞ1ð1dÞ3ð4pÞ2ð10rÞ1, respectively. The hyperfine

constant c(F) for CaF is represented as

cðFÞ ¼ 3

2gslBgNlN

3 cos2 h� 1

r3

� �9r

� �

¼ 3cF9r2

gslBgNlN3 cos2 h� 1

r3

� �2prðFÞ

" #

’ 6cF9r5

PðFÞ; ð16Þ

where cF9r represents the contribution of the 2p(F) orbitalto the 9r orbital and the angular factor h3 cos2 h� 1i2pr

is taken to be 4/5 [18]. To reproduce the experimentalvalue 41.2MHz [19], cF9r is obtained to be 0.008. Al-

though the cF9r value for CaF should not directly be

compared to the cF4p value for CoF (0.066), an ionic

molecule has qualitatively smaller orbital overlap be-

tween two bonding atoms than a covalent molecule.

Thus, the small value of cF9r probably reflects that CaF is

more ionic than CoF.

The similar expression can be given for FeF,

cðFÞ ¼ 3

2gslBgNlN

1

5

3cos2 h� 1

r3

� �9r

�

þ 3cos2 h� 1

r3

� �1d

þ 23cos2 h� 1

r3

� �4p

þ 3cos2 h� 1

r3

� �10r

�

¼ 3cF4p10

gslBgNlN cF9r3cos2 h� 1

r3

� �2prðFÞ

"

þ 2cF4p3cos2 h� 1

r3

� �2ppðFÞ

þ cF10r3cos2 h� 1

r3

� �2prðFÞ

#

’ 6

25cF9r�

� cF4p þ cF10rPðFÞ: ð17Þ

If cF9r ’ cF4p ’ cF10r can be assumed, an averaged cF

value for FeF is obtained to be 0.049 to reproduce the

experimental value 51.7MHz [20]. This value is in rough

agreement with the cF4p value of CoF (0.066), and FeFseems qualitatively as ionic as CoF.

It is notoriously difficult to estimate the molecular

hyperfine parameters from the atomic values for metal

containing molecules without a high-quality ab initio

work, because the molecular states are by no means

simply related to atomic states. However, we dare to

estimate the hyperfine constants a(Co), bF (Co) and

c(Co) from the hyperfine constants ajk3d of atomic cobalt[21] using a similar procedure.

aðCoÞ ¼ 2lBgNlN1

32

1

r3

� �1d

�þ 1

r3

� �4p

�

¼ 2þ cCo4p3

2lBgNlN1

r3

� �3dðCoÞ

" #

’ 2þ cCo4p3

� �a013d ; ð18Þ

bF ðCoÞ ¼8p3gslBgNlN

1

2½hjWð0Þj2i1d þ hjWð0Þj2i4p�

¼ 8p3gslBgNlN

1

2½hjWð0Þj2i3ddðCoÞ

þ cCo4p hjWð0Þj2i3dpðCoÞ�

’ 1þ cCo4p2

� �a103d ; ð19Þ

and

154 T. Okabayashi, M. Tanimoto / Journal of Molecular Spectroscopy 221 (2003) 149–155

cðCoÞ ¼ 3

2gslBgNlN

1

2

3 cos2 h� 1

r3

� �1d

�

þ 3 cos2 h� 1

r3

� �4p

�

¼ 3

4gslBgNlN

3 cos2 h� 1

r3

� �3ddðCoÞ

"

þ cCo4p3 cos2 h� 1

r3

� �3dpðCoÞ

#

’�� 3ð2� cCo4p Þ

14

�a123d ; ð20Þ

where cCo4p is the contribution of the 3d(Co) orbital to the

4p orbital and the contribution of 4p(Co) is neglected.The angular factors h3 cos2 h� 1i3dd and h3 cos2 h� 1i3dpare assumed to be )4/7 and 2/7, respectively [18]. If

a01ð3d;3d84sÞ ¼ 617:9, a10ð3d;3d74s2Þ ¼ �69:4, a12ð3d;3d84sÞ ¼ 857:1MHz [21], and cCo4p ¼ 1� cF4p ¼ 0:934 are used, we

predict the hyperfine constants as aðCoÞ ¼ 604,

bF ðCoÞ ¼ �67, and cðCoÞ ¼ �196MHz. Using an

equation like Eq. (15), the h4(Co) value is calculated to

be 1614MHz. This value is quite different from theobserved value, 975MHz. If cCo4p is adjusted so as to

reproduce the observed value, cCo4p is obtained to be al-

most zero: this result means that the unpaired 4p orbital

is almost purely constructed from the 2p orbital of

fluorine and it is inconsistent with the fact that CoF is a

highly ionic species represented as CoþF�. Probably, the

valence orbitals of the CoF molecule are strongly de-

formed from the atomic cobalt 3d orbitals, and it seemsunsuitable to use the atomic hyperfine parameters of

cobalt for estimation of those of the CoF molecule.

Interestingly, the h4(Co) values of the CoH [22] and

CoCl [23] molecules are reported to be 1543 and

1318MHz, respectively. They are much closer to the

present estimated value 1614MHz. Since CoH and CoCl

as well as CoF seem to have the ionic structure repre-

sented as CoþX�, the similar procedure for hyperfineanalysis can be applied with small cCo4p values. Judging

from the observed h4(Co) value matching with the esti-

mated one, the orbitals of CoH and CoCl seem to be

better-behaving than those of CoF.

For the CoH molecule, experimental hyperfine

constants have also been reported as aðCoÞ ¼ 621,

bF ðCoÞ ¼ �16, and cðCoÞ ¼ �456MHz [22]. Although

a(Co) constant is in good agreement with the estimatedones, the experimental c(Co) value of CoH is not close

to the present estimation. One of the possible explana-

tions is that the angular factors h3 cos2 h� 1i in Eq. (20)

are quite different from the ideal case by the orbital

deformation caused by Co–H bonding. If this estimation

is true, it is likely that the a(Co) parameters of CoF and

CoH will have similar values each other. Indeed, an-

other ionic cobalt compound CoO (X 4Di) also has a

similar a(Co) value, 649MHz [24]. Using a(Co) of CoH,bF (Co) and c(Co) of CoF are estimated to be )497 and

)586MHz, respectively, to reproduce h4ðCoÞ ¼ 975 and

bðCoÞ ¼ �302MHz. The obtained c(Co) value is con-

sistent to that of CoH, )456MHz. On the other hand,

the obtained bF (Co) value is of anomalously large neg-

ative value, but it is not too large in consideration of

that of CoO, )183MHz. As mentioned above, however,

the present b(Co) value is too crude to derive accuratehyperfine parameters of Frosch and Foley. The obser-

vation of hyperfine splittings in other spin substates 3U3

and 3U2 is needed for further detailed discussion.

The electric quadrupole coupling constant eQq(Co) isobtained to be )77.50(91)MHz, which agrees with that

of CoH ()92.5(47)MHz [22]) within their three standard

deviations. This similarity means that the electric charge

distribution around the Co nucleus of CoF is quantita-tively similar to that of CoH. Another ionic cobalt

compound CoO (X 4Di) also has a negative eQq(Co)value )38MHz [24], but a more covalent species CoC

(X 2Rþ) has a large positive value, 303MHz [25]. Since

the eQq constant is affected by the distributions of core-

as well as valence-electrons, it is difficult to discuss the

constants quantitatively without a high-level ab initio

calculation when the orbital polarization is striking. Tounderstand these cobalt hyperfine constants including

eQq(Co) is a good subject of current theoretical calcu-

lations.

Acknowledgments

The research was supported by Japan Society for thePromotion of Science through Grant-in-Aid for Scien-

tific Research (No. 12740316). T.O. thanks the Kawa-

saki Steel 21st Century Foundation for financial

support. T.O. also acknowledges financial support from

the Hamamatsu Foundation for Science and Technol-

ogy Promotion.

References

[1] K.P. Huber, G. Herzberg, Molecular Spectra and Molecular

Structure. IV. Constants of Diatomic Molecules, Van Nostrand

Reinhold, New York, 1979.

[2] A.J. Merer, Annu. Rev. Phys. Chem. 40 (1989) 407–438.

[3] A.G. Adam, L.P. Fraser, W.D. Hamilton, M.C. Steeves, Chem.

Phys. Lett. 230 (1994) 82–86.

[4] A.G. Adam, W.D. Hamilton, J. Mol. Spectrosc. 206 (2001)

139–142.

[5] R.S. Ram, P.F. Bernath, S.P. Davis, J. Mol. Spectrosc. 173 (1995)

158–176.

[6] R.S. Ram, P.F. Bernath, S.P. Davis, J. Chem. Phys. 104 (1996)

6949–6955.

[7] T. Okabayashi, M. Tanimoto, J. Chem. Phys. 105 (1996) 7421–

7424.

T. Okabayashi, M. Tanimoto / Journal of Molecular Spectroscopy 221 (2003) 149–155 155

[8] M. Tanimoto, S. Saito, T. Okabayashi, Chem. Phys. Lett. 242

(1995) 153–156.

[9] M. Tanimoto, T. Sakamaki, T. Okabayashi, J. Mol. Spectrosc.

207 (2001) 66–69.

[10] T. Okabayashi, E. Yamazaki, T. Honda, M. Tanimoto, J. Mol.

Spectrosc. 208 (2001) 66–70.

[11] T. Okabayashi, M. Tanimoto, J. Chem. Phys. 99 (1993) 3268–

3270.

[12] E. Hirota, High-Resolution Spectroscopy of Transient Molecules,

Springer, Berlin, 1985.

[13] S. Yamamoto, S. Saito, J. Chem. Phys. 86 (1987) 102–105.

[14] R.A. Frosch, H.M. Foley, Phys. Rev. 88 (1952) 1337–1349.

[15] G. Huang, A.J. Merer, D.J. Clouthier, J. Mol. Spectrosc. 153

(1992) 32–40.

[16] A.G. Adam, M. Barnes, B. Berno, R.D. Bower, A.J. Merer, J.

Mol. Spectrosc. 170 (1995) 94–130.

[17] J.M. Brown, M. Kaise, C.M.L. Kerr, D.J. Milton, Mol. Phys. 36

(1978) 553–582.

[18] J.R. Morton, K.F. Preston, J. Mag. Reson. 30 (1978) 577–582.

[19] W.J. Childs, G.L. Goodman, L.S. Goodman, J. Mol. Spectrosc.

86 (1981) 365–392.

[20] M.D. Allen, L.M. Ziurys, J. Chem. Phys. 106 (1997) 3494–

3503.

[21] G.H. Guth€oohrlein, H.P. Keller, Z. Phys. D 17 (1990) 181–

193.

[22] S.P. Beaton, K.M. Evenson, J.M. Brown, J. Mol. Spectrosc. 164

(1994) 395–415.

[23] A.G. Adam, J.R.D. Peers, Y. Teng, C. Linton, J. Mol. Spectrosc.

212 (2002) 111–117.

[24] K.C. Namiki, S. Saito, J. Chem. Phys. 114 (2001) 9390–9394.

[25] M.A. Brewster, L.M. Ziurys, Astrophys. J. 559 (2001) L163–

L166.