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Chemical Physics Letters 403 (2005) 223–227

Pure rotational spectrum of gold monoxide (AuO) in the X 2P3/2 state

Toshiaki Okabayashi a,*, Fumi Koto b, Kazuhiro Tsukamoto b,Emi Yamazaki b, Mitsutoshi Tanimoto b

a Center for Instrumental Analysis, Shizuoka University, Oya 836, Shizuoka 422-8529, Japanb Department of Chemistry, Faculty of Science, Shizuoka University, Oya 836, Shizuoka 422-8529, Japan

Received 25 November 2004; in final form 17 December 2004

Available online 18 January 2005

Abstract

The pure rotational spectrum of AuO in the X 2P3/2 state was observed by employing a source-modulated microwave spec-

trometer. The AuO radical was generated in a free space cell by the sputtering reaction from a gold sheet lining the inner sur-

face of a stainless steel cathode using a dc glow plasma of O2 and Ar. Observation of the rotational transitions in both the

ground and first excited vibrational states enabled to determine molecular constants by a least-squares fit. Other spectroscopic

parameters such as equilibrium bond length, re, and vibrational wavenumber, xe, were also derived from the obtained molec-

ular constants.

� 2005 Elsevier B.V. All rights reserved.

1. Introduction

Study on the relativistic effect in diatomic goldcompounds is of much interest, because the pro-

nounced local maximum contraction of the 6s shell

makes gold a unique element [1]. The relativistic effect

of such compounds has recently been a subject of

many theoretical studies, whereas experimental investi-

gations have thus far been quite limited. As for the

gaseous species investigated by high resolution spec-

troscopic methods, there are only few works exceptfor the closed-shell 1R+ species, e.g., gold monohalides

and monohydride. To the best of our knowledge, the

AuSi radical [2] is a sole open-shell species bearing a

gold atom studied by the high resolution spectroscopy

in the gas phase.

Millimeter- and submillimeter-wave spectroscopy is

a good method to investigate transient molecules bear-

ing transition metals. We have studied the gaseous

0009-2614/$ - see front matter � 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2005.01.003

* Corresponding author. Fax: +81 54 237 3384.

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

gold monohalides using a source-modulation micro-

wave spectrometer with a sputtering method [3,4].

The determined molecular constants have allowed thephysico-chemical properties of these closed-shell spe-

cies to be probed and have helped to understand the

nature of bonding of gold. To improve the under-

standing of diatomic Au species, we have extended

our studies to gold monoxide AuO in the open-shell2Pi electronic state.

The AuO radical was first observed spectroscopically

in 1977 by Griffiths and Barrow [5], who reported elec-tronic transitions of AuO in inert gas matrices in the vis-

ible region. Recently, Citra and Andrews [6] investigated

its infrared bands in inert gas matrices and determined

the vibrational constants. However, no spectroscopic

study was reported for the free AuO radical in the gas

phase. Three theoretical studies have been carried out

on the electronic ground and excited states of AuO [6–

8], giving estimates of several equilibrium molecularconstants.

In this Letter, we report on the first measurement of

the pure rotational spectrum of AuO in the electronic

224 T. Okabayashi et al. / Chemical Physics Letters 403 (2005) 223–227

ground state. Rotational and centrifugal distortion con-

stants have been determined and used to evaluate the

equilibrium bond distance, re, and the harmonic vibra-

tional frequency, xe.

2. Experimental

The present experiment was carried out using a

source-modulated microwave spectrometer [9]. Milli-

meter- and submillimeter-wave radiation was gener-

ated by multiplying the output of a klystron. The

radiation transmitted through a free space cell was de-

tected by an InSb detector cooled by liquid helium.The cell was equipped with a pair of cylindrical elec-

trodes for a dc glow discharge and was covered by a

cooling jacket made of copper through which liquid

nitrogen was circulated. To cancel the magnetic field

of the earth, electromagnetic coils were wound outside

the cell.

The AuO radical was generated in the free space cell

by a dc glow discharge in O2 with Ar just like in our pre-vious experiment on PtO [10]. Gold atoms were supplied

by sputtering from a gold sheet lining the inner surface

of a stainless steel cathode. The cell was cooled to the li-

quid nitrogen temperature for the efficient AuO genera-

tion. Optimum sample pressure was 1 mTorr of O2 with

4 mTorr of Ar. Under these experimental conditions, the

lines of AuO in the ground state were strong enough to

be observed easily. The spectrum showed hyperfine split-ting due to the nuclear spin of gold. The discharge cur-

rent was set to about 400 mA. Weaker lines in the first

excited vibrational state were also observed, and the

line-intensity in the v = 1 state was about seven times

weaker than that in the ground state. In spite of a care-

ful examination, spectral lines in the higher spin substate

X 2P1/2 could not be detected. In total, we observed 13

rotational transitions of AuO between 149 and388 GHz. Fig. 1 displays a sample of the observed

spectrum.

149210 149217(MHz)

F=6–5F=7–6

F=8–7F=9–8

AuO (X 2

Π3/2) J=7.5–6.5

Fig. 1. Rotational spectrum of AuO observed near 149 GHz.

3. Analysis

The observed transition frequencies were analyzed by

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

Hamiltonian. The Hamiltonian employed is

H eff ¼ H rot þ Hhf ; ð1Þwhere Hrot represents rotational energy including cen-

trifugal distortion, and Hhf hyperfine interaction.

The matrix elements are described as follows [11]:

hJXF jH rotjJXF i ¼ BvJðJ þ 1Þ � DvJ 2ðJ þ 1Þ2 ð2Þand

hJ 0XF jHhf jJXF i¼ fhX þ hXD½JðJ þ 1Þ þ J 0ðJ 0 þ 1Þ�=2g

� ð�1ÞJ0þIþF I J 0 F

J I 1

� �ð�1ÞJ

0�X J 0 1 J

�X 0 X

� �

� ½ð2J 0 þ 1Þð2J þ 1ÞIðI þ 1Þð2I þ 1Þ�1=2

þ eQq4

ð�1ÞJ0þIþF I J 0 F

J I 2

� �ð�1ÞJ

0�X J 0 2 J

�X 0 X

� �

� ð2J 0 þ 1Þð2J þ 1ÞðI þ 1Þð2I þ 1Þð2I þ 3ÞIðI � 1Þ

� �1=2; ð3Þ

where I is the nuclear spin quantum number of gold

(I = 3/2). The molecular constants were determined by

a least-squares calculation, in which data of overlapped

lines were less weighted. The standard deviations of the

fit were about 10 kHz for both the ground and firstexcited vibrational states. The molecular constants

determined are listed in Table 1. The observed and cal-

culated transition frequencies with their residuals are

summarized in Table 2.

4. Results and discussion

In the present study, we observed the rotational spec-

trum of AuO in the X 2P3/2 substate but not that in the

X 2P1/2 substate. The present molecular constants,

therefore, are effective constants perturbed by the

X 2P1/2 substate. However, in a usual 2P radical, the

molecular constants in the X 2P3/2 substate have similar

values to those in the X 2P1/2 substate. For example, in

Table 1

Molecular constants of AuO in the X 2P3/2 statea

v = 0 v = 1

Bv (MHz) 9948.9266(12) 9856.8209(24)

Dv (kHz) 11.4247(29) 11.4917(62)

h3/2 (MHz) �46.50(37) �46.38(83)

h3/2D (kHz) �17.9(45) �11.6(41)

eQq (MHz) 201.9(29) 201.9b

a Values in parentheses represent 1 SDb Fixed in the analysis.

Table 2

Observed transition frequencies of AuO in MHz

J 0–J00 F 0–F00 v = 0 v = 1

Obs. Freq. O � Ca Obs. Freq. O � Ca

7.5–6.5 6–5 149212.281 �0.006

7–6 149214.814 �0.021b

8–7 149215.188 0.031b

9–8 149215.188 0.105b

8.5–7.5 7–6 169102.019 0.000

8–7 169103.994 0.125b

9–8 169103.994 �0.039b

10–9 169103.994 �0.095b

10.5–9.5 9–8 208873.612 0.016 206939.041 �0.014

10–9 208874.718 0.036b 206940.271 0.122b

11–10 208874.718 0.001b 206940.271 0.079b

12–11 208874.718 �0.137b 206940.271 �0.067b

11.5–10.5 10–9 228755.044 �0.006 226636.210 0.011

11–10 228755.909 �0.006b 226637.162 0.089b

12–11 228755.909 �0.014b 226637.162 0.073b

13–12 228755.909 �0.159b 226637.162 �0.080b

12.5–11.5 11–10 248633.300 0.004 246330.120 0.002

12–11 248633.995 �0.004b 246330.885 0.056b

13–12 248633.995 0.004b 246330.885 0.055b

14–13 248633.995 �0.139b 246330.885 �0.096b

14.5–13.5 13–12 288378.993 �0.141b 285707.177 �0.062b

14–13 288379.593 �0.027b 285707.785 0.052b

15–14 288379.593 �0.003b 285707.785 0.066b

16–15 288379.593 �0.131b 285707.785 �0.070b

15.5–14.5 14–13 308245.970 �0.225b 305389.777 �0.131b

15–14 308246.529 0.100b 305390.330 0.016b

16–15 308246.529 �0.050b 305390.330 0.020b

17–16 308246.529 �0.169b 305390.330 �0.107b

19.5–18.5 18–17 387669.318 0.223b

19–18 387669.318 �0.001b

20–19 387669.318 0.025b

21–20 387669.318 �0.058b

a Observed minus calculated frequencies.b Blended line. Less weighted.

T. Okabayashi et al. / Chemical Physics Letters 403 (2005) 223–227 225

the IO radical [12], the difference between the equilib-

rium internuclear distances, re, in the X 2P1/2 and

X 2P3/2 substates is about 1%, and that in the vibra-

tional wavenumber, xe, is about 5%. Hence, the present

molecular constants in the X 2P3/2 substate can be used

to judge the reliability of theoretical calculations for the

AuO radical in the X 2Pi ground state.

The equilibrium rotational and centrifugal distortionconstants are obtained from the observed B0, B1, D0 and

D1 values: Be = 9994.9795(22) MHz and De = 11.3912

(53) kHz. The equilibrium internuclear distance, re, is

thus 1.84876171(23) A, which is in rather good agree-

ment with the recent theoretical calculations, 1.83–

1.87 A [6,8]. The earlier ab initio calculation [7] provided

a 0.1 A larger value.

The vibrational wavenumber xe and its anharmonicterm xexe of a diatomic molecule are represented as

[13,14]

xe ¼

ffiffiffiffiffiffiffiffi4B3

e

De

sð4Þ

and

xexe ¼ Be

aexe

6B2e

þ 1

� �2

: ð5Þ

The xe and xexe values are calculated to be 624.59(15)

and 5.0122(14) cm�1, respectively. The Kratzer equa-

tion, Eq. (4), usually applies to an unperturbed mole-

cule. Although the X 2P3/2 substate of AuO may be

slightly affected by the X 2P1/2 substate, the present xe

value is probably acceptable for the real AuO molecule.

In contrast, the Pekeris relationship, Eq. (5), applies

only to a Morse oscillator, and it is likely that the pres-

ent xexe value is subject to a systematic error.

The present xe value is compared with the previous

experimental and theoretical values in Table 3. The

Table 3

Comparison of molecular parameters of AuO

re (A) xe (cm�1) De ðkJ=molÞ References

Experimental (X 2P3/2)

mmW 1.84876171(23)a 624.59(15)a,b (233)c This work

Matrix-Vis. 699d [5]

Matrix-IR 619.2d [6]

MS 225 ± 15e [15]

Theoretical (X 2P)

BPW91 1.869 640.7 [6]

BDF 1.831 695 271 [8]

ZORA(MP) 1.864 632 274 [8]

CISD/SC 1.953 516 108.0 [7]

CEPA-1 1.946 497 146.5 [7]

a Values in parentheses represent 1 SDb Calculated value with the Kratzer relation, equation (4).c Estimated value under assumption of a Morse oscillator, equation (6).d Effective value including anharmonic terms.e D0

0 value excluding the zero-point energy.

226 T. Okabayashi et al. / Chemical Physics Letters 403 (2005) 223–227

present xe value is qualitatively consistent with the value

of matrix-IR (619 cm�1) [6], but somewhat smaller than

that of the matrix-Vis. (699 cm�1) [5]. The recent

BPW91 [6] and ZORA(MP) [8] calculations suggestthe xe value of about 640 cm�1, which qualitatively

agrees with the present value. On the other hand, the

earlier ab initio calculations [7] reported the somewhat

poor results of about 500 cm�1.

The dissociation energy De of a Morse oscillator is

estimated from the present vibrational parameters using

[13,14]

De ¼x2

e

4xexe: ð6Þ

The obtained dissociation energy is about 233 kJ/mol,which agrees well with both the indirect estimation by

the mass spectrometric method, 225 ± 15 kJ/mol [15],

and the recent BDF and ZORA(MP) calculations,

about 270 kJ/mol [8], but not with the earlier ab initio

study [7] as shown in Table 3.

In the present study, lines in the first excited vibra-

tional state, which locates at about 600 cm�1 above

the ground state, have been observed for AuO. Theeffective vibrational temperature in the discharge plasma

is roughly estimated to be about 500 K from the relative

intensity ratio of the lines in the v = 0 and 1 states under

the assumption of the Boltzmann distribution. The spin

temperature often has a quite different value from the

vibrational temperature, but if spin temperature is as-

sumed to be the same with the vibrational one (about

500 K), the unobserved X 2P1/2 substate is estimatedto lie at least 800 cm�1 above the X 2P3/2 substate.

Hyperfine splitting arising from the nuclear spin of

gold was partly resolved in the present experiment.

The hyperfine parameters of Frosch and Foley [16], a,

bF and c, are represented as

a ¼ 2lBgNlN

1

r3

� o

; ð7Þ

bF ¼ 8p3gslBgNlN jWð0Þj2

D Es; ð8Þ

and

c ¼ 3

2gslBgNlN

3cos2h� 1

r3

� s

: ð9Þ

However, we could not determine the Frosch and Foley

hyperfine parameters separately, for the transitions were

observed only in the X = 3/2 substate. Instead of these

three parameters, an effective magnetic hyperfine con-

stant h3/2 = a + (b + c)/2 was determined, where

hX = aK + (b + c)R and b = bF � c/3.

It is difficult to estimate the molecular hyperfineparameters for metal-containing molecules from the

atomic values without a high-quality ab initio work,

because the molecular states are by no means simply

related to the atomic states. However, we dare to

estimate the hyperfine constants a, bF and c from

the hyperfine constants P(Au) = 132.0 MHz and

A(Au) = 2876 MHz of atomic gold [17]. If Æ1/r3æo in

Eq. (7) is approximately equal to Æ1/r3æs in Eq. (9),a and c constants are related to a unique atomic

constant P(Au). The angular factor h3cos2h� 1i5dpis taken to be 2/7 [17]. The h3/2 value is then derived

as follows:

h3=2 ¼ aþ 1

2bF þ

1

3c

¼ cspinP ðAuÞ þ cs2AðAuÞ þ cspin

7P ðAuÞ

¼ 8cspin7

P ðAuÞ þ cs2AðAuÞ; ð10Þ

T. Okabayashi et al. / Chemical Physics Letters 403 (2005) 223–227 227

where cspin represents the contribution of the 5d orbital

to the unpaired orbital and cs the s-character of the un-

paired electron. However, it is impossible to reproduce

the observed value h3/2 = �46 MHz, because the atomic

P(Au) and A(Au) have positive values. This finding

means that the behavior of an unpaired electron inAuO cannot be described using such a simple model.

The similar anomalies were also found in the cases of re-

lated species, CuO [18] and AgO [19]. Steimle et al.

[18,19] explained these anomalies in CuO and AgO in

terms of the perturbations from electronic exited states.

Similar phenomenon may also occur in the AuO radical.

For further discussion in detail, it is necessary to observe

the spectral lines in the other spin substate 2P1/2.The electric quadrupole coupling constant eQq is ob-

tained to be 201.9(29) MHz, which is rather larger than

those of AuF (�53.2 MHz [20]), AuCl (9.6 MHz [21]),

AuBr (37.3 MHz [21]), and AuI (78.3 MHz [22]). Since

the eQq constant of a gold compound such as AuCl

[23] is remarkably affected by the relativistic effect, it is

difficult to discuss the eQq constants quantitatively with-

out a high-level ab initio calculation. Theoretical inter-pretation of these gold hyperfine constants including

eQq is thus highly desired.

Acknowledgments

The research was supported by Japan Society for the

Promotion of Science through Grants-in-Aid for Scien-tific Research (Nos. 12740316 and 15656184). T.O.

thanks the Kawasaki Steel 21st Century Foundation

for financial support. E.Y. thanks the Japan Science

Society through the Sasagawa Scientific Research Grant

and the Hayashi Memorial Foundation for Female Nat-

ural Scientists through the Hayashi Fellowship. T.O.

and E.Y. also acknowledge the financial support from

the Hamamatsu Foundation for Science and Technol-

ogy Promotion.

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