equation15 and the value g value of AsH,
xx
HyperÐne structure
The ratios between the magnetic hyperÐne coupling constants
associated with hydrogen and deuterium of AsH and AsD,
b (D)/b (H) \ 0.1532(17) and c(D)/c(H) \ 0.150(12), are equal
m
I
G
2
o Sn o L o 0T o2
H
p
e
x
g
\
; Z z2 [
;
(4)
xx
i i
m
W (r ) [ W (r )
i
e n n e
0 e
F
F
where m and m are the masses of an electron and a proton,
to the ratio of the nuclear g factors of proton and deuteron,
0.153 506 1, which is calculated using the magnetic moments of
proton and deuteron with their corresponding nuclear spins,
k \ 2.792 845 6 k and k \ 0.857 437 6 k ,17 where k is the
e
p
respectively, I is the inertia moment at equilibrium structure,
Z is the atomic number of nucleus i, and z is the distance
between nucleus i and the centre of mass. Assuming that
the second term in the parentheses of eqn. (4) for AsD is
e
i
i
H
N
D
N
N
nuclear magneton.
equal to that of AsH, g
of AsD was calculated to
Second-order perturbation theory gives an expression for
xx
be 0.000 312(39) ] 1836. Thus, d values calculated were
the nuclear spinÈrotation coupling constant, C , by consider-
1
I
[135.8(171) MHz for AsH and [34.7(43) MHz for AsD.
ing the interaction of the nuclear magnetic moment of a
The Dunham correction was calculated using:15
nucleus with electrons and other nuclei in the molecule.14 In
the case of a diatomic molecule with nuclei I and J, C is given
I
G AB2BC A
c
B
by,
e
e
e
B ] d \ B 1 [
u2
e
2
e
e
u2
4B3
e
a
o S0 o L o nT o2
k q
0n
x
I
J
J
C \ 4hB ;
[ 4nB
(9)
A
[u x
B
DH
I
E [ E
I cr
e e
] 16a
[ 8a [ 6a2 ] 4a3
(5)
n
n
0
I
1
1
1
1
3B
e
where a is the matrix element of the nuclear spinÈorbit inter-
0n
where the anharmonic potential constant, a \ ([a u /6B 2)
action between the ground state, o 0T, and the excited elec-
1
e e
e
[1, c is the second-order rotationÈvibration coupling con-
tronic state, o nT, I , the nuclear spin of I, k , nuclear magnetic
e
I
I
stant. The second term of eqn. (5) was neglected because of its
moment, c, velocity of light, r , the internuclear distance and
J
small contribution. The vibrational parameters, u and u x ,
of AsD were derived from:14
q the net charge of the nucleus J plus the electrons in closed
shells around it. Because the spin density and the s character
e
e e
J
of the unpaired electron orbital around the As nucleus were
calculated at 96% and [0.1%, respectively,4 the unpaired
electrons mainly occupy the pn orbital of As. Therefore, the
Ðrst term of eqn. (9) can be estimated. Assuming the pure pre-
cession approximation, and that the dominant contribution is
u (AsD) \ u (AsH)[k(AsH)/k(AsD)]1@2
(6)
e
e
u x (AsD) \ B (AsD)[[a (AsD)u (AsD)/6B (AsD)2 ] 1]2
e e
e
e
e
e
\ u x (AsH)[k(AsH)/k(AsD)]
e e
(7)
only due to A 3%
i
Using values of the vibrational parameters, u (AsH) \
e
a
E
L (L ] I)
2155.503 cm~1 and u x (AsH) \ 39.2227(26) cm~1,7 d was
&%
C B Bh
(10)
e e
2
I
3% [ E
calculated to be 8.8 MHz for AsH and 2.2 MHz for AsD.
~
3&
Thus the adiabatic rotational constants, Bad, of AsH and AsD
C (As) for AsH or AsD was calculated to be 0.402 and 0.205
e
I
were obtained. The uncertainties in Bad and rad are mainly due
MHz respectively, using 29 880.65 cm~1 for E3% [ E
and
e
e
~
3&
to the large uncertainties in g .
834.1 MHz for the anisotropic hyperÐne parameter a .18
r
&%
The converted adiabatic equilibrium distances, rad, of AsH
and AsD still show a discrepancy beyond their uncertainties.
These values are comparable with the observed values,
e
0.471(17) MHz for AsH and 0.283(12) MHz for AsD.
The BornÈOppenheimer equilibrium distance, rBO, can be
e
derived from rad of AsH and AsD using:16
e
Summary
rad \ rBO[1 ] m (dad/M ] dad/M )]
(8)
e
e
e a
a
b
b
This microwave spectroscopic study presents precise molecu-
lar constants for AsH and AsD radicals; in addition, the
BornÈOppenheimer equilibrium bond length has been
derived. Their experimental spinÈrotation and nuclear spinÈ
rotation coupling constants are consistent with the values esti-
mated using second-order perturbation theory.
where m , M and M are the masses of an electron, nucleus a
e
a
b
and nucleus b, respectively, and dad and dad are the adiabatic
correction factors of nuclei a and b. Since data for normal
(AsH) and only one substituted isotope species are available
(AsD), the adiabatic correction of the arsenic nucleus with
a
b
much larger mass in eqn. (8) could be neglected. rB0 was deter-
e
mined to be 1.522 370(86) Ó and dad 1.46(17). The value of rB0,
H
e
The authors are grateful to Imtiaz K. Ahmad for her critical
reading of the manuscript. This study was supported by
Grants-in-Aid from the Ministry of Education, Science and
Culture (No. 04233107).
1.522 Ó, which Kawaguchi and Hirota estimated by simply
transferring the ratio rB0/r of PH to AsH4 is found to be
e
0
close to the present value.
Spin–Rotation coupling constants
References
Hensel et al. estimated the theoretically derived spinÈrotation
coupling constant c of AsH using second-order perturbation
theory, and stated that the theoretical value, [8892 MHz,
was consistent with the experimental value of [8195.4(72)
MHz.7 The experimental c value of AsD, [4179.68(18) MHz,
was compared with its theoretical value [4546 MHz, calcu-
lated from the rotational constant determined in this study,
1
2
3
S. Saito and M. Goto, Astrophys. J., 1993, 410, L53.
M. Goto and S. Saito, Chem. Phys. L ett., 1993, 211, 443.
R. N. Dixon and H. M. Lamberton, J. Mol. Spectrosc., 1968, 25,
12.
K. Kawaguchi and E. Hirota, J. Mol. Spectrosc., 1984, 106, 423.
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K. D. Hensel, R. A. Hughes and J. M. Brown, J. Chem. Soc.,
Faraday T rans., 1995, 91, 2999.
4
5
6
7
spinÈorbit coupling constant A \ [617.39 cm~1,3 and E
3%
[ E ~ \ 29 880.65 cm~1.3 Additionally, the ratios c(AsD)/
3&
8
9
B. Lindgren, Phys. Scr., 1975, 12, 164.
M. Beutel, K. D. Setzer, O. Shestakov and E. H. Fink, J. Mol.
Spectrosc., 1996, 178, 165.
c(AsH) \ 0.5092 and B (AsD)/B (AsH) \ 0.5094 are nearly
0
0
the same; this agreement is consistent with the statement that
the spinÈrotation coupling constant c is mainly due to the
second-order contribution from low-lying excited states.
10 L. G. H. Petersson and S. R. Langho†, J. Chem. Phys., 1986, 85,
3130.
1050
J. Chem. Soc., Faraday T rans., 1997, V ol. 93
Fujiwara, Hideo
