Microwave spectra, nuclear field shift effects, geometries and hyperfine constants of bismuth mononitride, BiN, and bismuth monophosphide, BiP

Article abstract of DOI:10.1016/j.molstruc.2003.10.049

The diatomic molecules BiN and BiP have been prepared using a laser ablation technique and studied by Fourier transform microwave spectroscopy in the frequency range 7-22GHz. For BiN, only the J=1-0 transition fell within this range. Transitions for the ground and first excited vibrational states have been observed for both Bi¹⁴N and Bi¹⁵N. For BiP, which has only one isotopomer, the transitions J′-J″=1-0, 2-1 and 3-2 have been observed, but only for the ground vibrational state. Hyperfine structure has been observed for both nuclei in both molecules; the ²⁰⁹Bi nuclear quadrupole coupling constants show that the electronic structures are similar for the two molecules. Improved bond lengths have been obtained for both molecules. Density functional methods have been used to estimate the electron density at the bismuth nucleus in each molecule and hence allow an estimate of the uncertainty due to field shift effects in the experimentally derived bond lengths.

Full text of DOI:10.1016/j.molstruc.2003.10.049

Journal of Molecular Structure 695–696 (2004) 13–22
www.elsevier.com/locate/molstruc
Microwave spectra, nuclear field shift effects, geometries and hyperfine
constants of bismuth mononitride, BiN, and bismuth monophosphide, BiP
*
Stephen A. Cooke, Julie M. Michaud, Michael C.L. Gerry
Department of Chemistry, The University of British Columbia, 2036 Main Mall, Vancouver, BC, Canada V6T 1Z1
Received 30 July 2003; accepted 23 October 2003
Dedicated to Manfred and Brenda P. Winnewisser in recognition of their outstanding contributions to science, on the occasion of their 70th and 65th birthdays.
Abstract
The diatomic molecules BiN and BiP have been prepared using a laser ablation technique and studied by Fourier transform microwave
spectroscopy in the frequency range 7–22 GHz. For BiN, only the J ¼ 1–0 transition fell within this range. Transitions for the ground and
first excited vibrational states have been observed for both Bi14N and Bi15N. For BiP, which has only one isotopomer, the transitions
J0 –J00 ¼ 1–0; 2–1 and 3–2 have been observed, but only for the ground vibrational state. Hyperfine structure has been observed for both
nuclei in both molecules; the 209Bi nuclear quadrupole coupling constants show that the electronic structures are similar for the two
molecules. Improved bond lengths have been obtained for both molecules. Density functional methods have been used to estimate the
electron density at the bismuth nucleus in each molecule and hence allow an estimate of the uncertainty due to field shift effects in the
experimentally derived bond lengths.
q 2003 Elsevier B.V. All rights reserved.
Keywords: Nuclear field shift effects; Born–Oppenheimer breakdown; Hyperfine structure; BiN; BiP; Microwave spectra
1. Introduction
nine pairs [3–5,7–18], they have almost always been of
electronic transitions, usually at low resolution. Accord-
ingly, measurements of hyperfine structure are scarce; only
for PN has hyperfine structure been previously observed, in
molecular beam electric resonance experiments [15]. Yet all
the pnictides have non-zero nuclear spins capable of
generating hyperfine structure. Four of them (N, As, Sb
and Bi) have I $ 1; so quadrupole hyperfine structure
should be available to give information on the nature of the
bonding in the molecules. Interestingly Bi hyperfine
structure has been observed, in rotational spectra of the
bismuth monohalides (e.g. BiF and BiCl, etc.), and has
produced such information [19–23].
Bismuth nitride was first prepared in 1910 as a solid,
which was later found to be explosive [1]. Despite this early
characterization, it was later identified as a useful nitridizing
agent [2]. More recently, the diatomic molecule BiN has
been subject to some spectroscopic studies. Its matrix
isolation infrared specþtrum has beeþn observed [3],þas have
the a3Sþða11Þ 2 X1S ðX0þÞ; b5S ðb10þÞ 2 X1S ðX0þÞ;
b5Sþðb10þÞ 2 a3Sþða11Þ; near-infrared electronic tran-
sitions [4,5]. Bismuth phosphide has had a shorter history
in the literature, having first appeared as the focus of a mass
spectrometric study in 1973 [6]. For the diatomic molecule
BiP, the a3Sþða11Þ 2 X1SþðX0þÞ transition has also been
measured [7,8]. For both molecules, measurements of their
electronic spectra at high resolution have given accurate
rotational constants and equilibrium bond lengths [5,8].
The two molecules BiN and BiP are part of an extensive
series of mixed pnictides (e.g. PN, AsN, AsP, etc.).
Although there have been spectroscopic studies on all
Calculation ab initio of nuclear quadrupole coupling
constants is an active area of research [24,25]. In some
cases, even, the experimental coupling constants are
combined with ab initio calculations to refine the nuclear
quadrupole moments [26]. The bismuth pnictides can be
expected to provide something of a harsh testing ground for
such calculations, for several reasons (see Refs. [27,28]).
The molecules are triply bound in the ground state but not in
some of the excited electronic states. The large number of
*
Corresponding author. Tel.: þ1-6048-223-266; fax: þ1-6048-222-847.
E-mail address: mgerry@chem.ubc.ca (M.C.L. Gerry).
0022-2860/$ - see front matter q 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.molstruc.2003.10.049

14
S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
electrons in Bi results in a very high density of low-lying
electronic states. Also, effects due to relativity are
significant.
3. Theoretical calculations
All calculations were performed using the Amsterdam
Density Functional package developed by Baerends et al.
[33–36]. A recent development in density functional theory
involves the use of a statistically averaged orbital exchange-
correlation potential (SAOP) [37] as opposed to using an
exchange-correlation potential, Vxc; derived from the
exchange-correlation functional, Exc: The SAOP approach
has been used in this study. The details and benefits of this
method along with other examples of its use may be found
elsewhere [37,38]. Potential energy curves and hence the
equilibrium bond lengths for BiN and BiP were calculated
taking relativistic effects into account using the zero order
regular approximation [39,40].
The present paper describes the measurement and
analysis of the Fourier transform microwave (FTMW)
spectra of BiN and BiP. The aim has been to take advantage
of the high resolution of the technique to improve the
precision of the rotational constants and geometries, and to
obtain the first values of the Bi, N and P hyperfine constants.
Though greater precision in the bond lengths has indeed
been obtained, it has made it necessary to consider effects of
Born–Oppenheimer breakdown, including the effect of
nuclear size, on the accuracy and meaning of the resulting
values. Similarly, hyperfine structure due to all three
elements has been observed and interpreted; the Bi nuclear
quadrupole coupling constants are contrasted to those of the
bismuth monohalides.
It was of interest to calculate the derivative of the
electron density at the bismuth nucleus with respect to the
internuclear separation in the molecule. This was achieved
by performing several single point electron density
calculations at different bond lengths and then fitting a
polynomial to the obtained points. The details of this latter
type of calculation are given elsewhere [41]. When
calculating electron densities at the bismuth nucleus, it is
evident that a suitable all electron basis set must be used; a
pseudo-potential or frozen core approximation was not used
because the core electrons make a significant contribution to
the electron densities at the nucleus. In the present study, the
large, all-electron, quadruple-zeta quadruply polarized
(QZ4P) basis sets of Slater-type orbitals (STOs) were used
in all the calculations for all three atoms, N, P and Bi. The
use of STOs over Gaussian-type orbitals (GTOs) is also
advantageous in calculating electron densities at nuclei
because of the poor representation of electron probability
near the nucleus by GTOs.
2. Experiments
Details of the Balle–Flygare FTMW spectrometer and
the modification for the study of metal-containing species
have been given fully elsewhere [29–31]. In the present
experiments, a 5 mm diameter rod was carefully
machined from a brittle lump of Bi. This rod was then
held by a rotating support inside a specially designed
adapter between a solenoid valve (General Valve,
Series 9) and an end mirror of the Fabry–Perot cavity.
One experimental cycle consisted of the following events.
The solenoid valve admitted a pulse of gas, during which
radiation was applied to the rod from a Nd:YAG laser at
1064 nm. The resulting metal vapour reacted with NH3 or
PH3 at concentrations of , 1% in Ar, and the mixture
was injected into the cavity as a supersonic jet. The
resulting product molecules were stabilized in the
collision-free jet.
4. Results and analysis
A pulse of microwaves was then applied to the sample
from an antenna in the center of one of the end mirrors.
After a suitable delay, any radiation emitted by the
molecules relaxing within the cavity was collected and
digitized. The solenoid valve, the laser, and the switches
controlling the radiation and data acquisition were inter-
faced to a personal computer, which allowed the chronology
of events to be controlled very precisely. The number of
cycles required to record a transition varied from 10 to
several hundred. These time-domain spectra were converted
to the frequency domain using a fast Fourier transform.
Because the jet and the axis of propagation of the
microwaves were coaxial, each line was doubled by the
Doppler effect. Line widths were typically 7–10 kHz
(FWHM). Precise frequencies were determined from fits
to the time-domain (‘decay’) signals [32]. The frequencies
of all measured lines were referenced to a Loran frequency
standard accurate to one part in 1010, and are estimated to be
accurate to ^1 kHz.
Using the rotational constants of BiN and BiP from the
literature [5,8], searches were undertaken for rotational
spectra of each molecule in the appropriate spectral regions.
For both molecules, lines were found which required the
presence of both constituent atoms.
In each case, all the transitions were dominated by
hyperfine structure due to 209Bi (I ¼ 9=2; 100% abundance).
For BiN, each component showed further hyperfine
structure due to nitrogen, dominated by nuclear quadrupole
coupling for 14N, or by nuclear spin-rotation coupling for
15N. For BiP, each Bi hyperfine component was further
resolved by 31P spin-rotation coupling. Examples are given
in Figs. 1 and 2. For both Bi14N and Bi15N, the J ¼ 1–0
transition was measured for the ground and first excited
vibrational states. For BiP, three J0 –J00 transitions could be
measured, but the lines were relatively weak and only
the ground vibrational state could be observed. The
measured frequencies and corresponding quantum number

S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
15
assignments are given for BiN and BiP in Tables 1 and 2,
respectively. In both cases, the hyperfine splittings due to Bi
were much larger than those due to N or P. Consequently,
the quantum numbers given follow the coupling scheme
J þ IBi ¼ F1; F1 þ IPn ¼ F (Pn ¼ N or P).
4.1. Initial analysis of the spectra
Initially, spectroscopic constants were determined sep-
arately for each isotopomer of each molecule in each
vibrational state, using Pickett’s global least squares fitting
program SPFIT [42]. The Hamiltonian operator used was:
1
1
6
2
4
^
^
H ¼ BvJ 2 DvJ 2 QBi : 7EBi
2
QN : 7EN
6
þ IBi·CBi·J þ IPn·CPn·J
ð1Þ
Here Bv and Dv are the rotational constant and centrifugal
distortion constant of vibrational state v: The third and
fourth terms represent the nuclear quadrupole coupling
terms of Bi and N, with coupling constants eQqBi and eQqN;
respectively; clearly the fourth term was needed only for
Bi14N. Similarly, the fifth and sixth terms represent the
nuclear spin-rotation coupling energies for Bi and Pn ( ¼ N
or P), with coupling constants CðBiÞ and CðPnÞ; respect-
ively. The resulting spectroscopic constants are in Tables 3
and 4 for BiN and BiP, respectively. For BiN, since only the
J ¼ 1–0 transition could be measured, the distortion
constant D0 was fixed at 8.99 kHz from the electronic
spectrum [5].
Fig. 1. Detail of the spectrum for the J ¼ 1–0 transition of Bi14N, v ¼ 0;
showing a hyperfine component due to 209Bi ðI ¼ 9=2Þ which is split into
three further components by 14N ðI ¼ 1Þ: The Doppler splitting at this
frequency is <100 kHz. The measurement consists of 4k data points,
required 600 averaging cycles and is displayed as a 4k tranformation, i.e.
there is no zero-filling.
4.2. Molecular geometries
Although bond lengths of BiN and BiP have been
determined previously [5,8], the increased spectral resol-
ution of microwave spectroscopy allows them to be
evaluated with greater precision, which in turn may provide
fundamental insights into the molecular properties. Since
the data sets for the two molecules are somewhat different,
they are treated separately.
4.2.1. Geometry of BiN
For BiN, there are enough data to evaluate an equilibrium
ðreÞ bond length. The initial determination used the
following simple expression
ꢀ
ꢁ
ꢀ
ꢁ
ꢀ
ꢁ
2
3
1
2
1
2
1
2
Bv ¼ Be 2 ae v þ
þ ge v þ
2ee v þ
ð2Þ
in which Bv; Be are the rotational constants for vibrational
state v and at equilibrium, respectively; ae; ge and ee are
vibration–rotation constants. It was applied to each
isotopomer separately using the constants in Table 3, with
ge and ee held fixed at the values of Breidohr et al. [5]:
20.387(10) and 20.016(1) MHz, respectively. The result-
ing values of Be and ae are in Table 5; they agree well with
those of Ref. [5].
Fig. 2. Detail of the spectrum for the J ¼ 2–1 transition of BiP showing a
hyperfine component due to 209Bi ðI ¼ 9=2Þ which is split into two further
components by P ðI ¼ 1=2Þ: The Doppler splitting at this frequency is
<75 kHz. 1000 averaging cycles were required and the spectrum is
displayed in the same manner as Fig. 1.

16
S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
Table 1
Observed and calculated hyperfine transition frequencies for the J0 –J00
Table 1 (continued)
¼
Isotopomer
F0 –F00
v
Frequency
(MHz)
Observed–
calculated
(kHz)a
00
F10 –F1
1–0 rotational transition for Bi14N and Bi15N in the v ¼ 0 and 1 vibrational
states
00
Isotopomer
F10 –F1
F0 –F00
v
Frequency
(MHz)
Observed–
calculated
(kHz)a
Bi15
N
3–4
4–5
6–5
5–4
4–4
0
0
0
0
0
19,138.7238
19,138.7399
19,177.5894
19,177.6069
19,340.7457
20.58
0.58
7
2
9
2
–
–
Bi14
N
0
0
0
0
0
0
0
0
0
20,412.8991
20,413.0962
20,413.1880
20,451.7120
20,452.1547
20,452.2299
20,614.7280
20,614.8799
20,615.5345
0.51
20.27
20.24
20.49
0.20
7
2
9
2
7
2
9
2
–
–
–
–
–
–
7
2
9
2
7
2
9
2
9
2
11
2
11
2
9
2
0.47
–
7
2
9
2
5
2
7
2
11
2
9
2
20.47
0.00
–
11
2
9
2
11
2
9
–
–
2
9
9
–
2
2
11
2
9
2
13 11
–
–
–
2
2
7
2
9
2
3–4
4–5
6–5
5–4
4–4
1
1
1
1
1
19,001.6830
19,001.7003
19,039.6990
19,039.7144
19,199.1329
21.37
1.37
–
–
11
2
9
2
9
7
2
0.29
–
–
2
7
2
9
2
9
9
7
2
7
2
0.17
–
2
2
11
2
9
2
1.12
–
9
2
9
2
11 11
–
2
20.02
20.15
–
–
2
11
2
9
2
21.12
0.00
–
9
2
9
2
9
9
2
–
2
9
9
–
2
2
7
2
9
2
7
2
9
2
1
1
1
1
1
1
1
1
1
20,261.7991
20,261.9909
20,262.0876
20,299.7320
20,300.1688
20,300.2417
20,458.9014
20,459.0518
20,459.6970
0.04
21.50
1.46
–
–
–
–
–
–
For each isotopomer, the equilibrium bond length re was
then determined from the equation:
7
2
9
2
9
2
11
2
C2
pffiffiffiffiffi
where m is the reduced mass of the isotopomer in atomic
re ¼
ð3Þ
7
2
9
2
5
2
7
2
Bem
11
2
9
2
11
2
9
0.08
mass units, u, and C2 is given by:
sffiffiffiffiffiffiffiffiffiffiffiffi
–
–
2
1017hNA
8p2
11
2
9
2
13 11
–
C2 ¼
:
ð4Þ
21.21
1.14
–
–
2
2
With the fundamental constants recommended
˚
11
2
9
2
9
7
2
by CODATA in 1998 [43], C2 ¼ 710:9001379ð25Þ A
–
–
2
MHz1=2 u1=2. All the parameters determined by this procedure
are in Table 5. Because of the high precision of C2; the
9
9
7
2
7
2
0.30
uncertainties in re; <7 £ 1027 A, are dominated by the
–
˚
2
2
uncertainties in Be and in the 1993 atomic masses used [44].
The values given agree well with those of Ref. [5], but are
indeed more precise as shown in Tables 5 and 7.
9
2
9
2
11 11
–
2
20.05
20.25
–
–
2
In the Born–Oppenheimer approximation [45], re
values should be isotopically invariant; thus the isotopic
variations found in the re values give a measure of the limit
9
2
9
2
9
9
2
2
2

S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
17
Table 2
Table 2 (continued)
Observed and calculated rotational transitions of BiP in the vibrational
ground state
J0 –J00
F0 –F00
3–4
2–3
6–5
7–6
4–4
5–5
5–6
2–3
7–6
8–7
3–3
4–4
5–4
6–5
5–5
6–6
2–2
3–3
4–3
Frequency
(MHz)
Observed–calculated
(kHz)a
00
F10 –F1
J0 –J00
F10 –F1
F0 –F00
4–5
3–4
5–4
6–5
5–5
Frequency
(MHz)
Observed–calculated
(kHz)a
00
5
2
7
2
21,250.5103
21,250.5226
21,295.6308
21,295.6527
21,299.7559
21,299.7700
21,300.3662
21,300.4134
21,309.9485
21,309.9695
21,320.6847
21,320.6992
21,327.4545
21,327.4834
21,328.0651
21,328.0796
21,362.8999
21,362.9287
21,380.9618
21.49
–
–
7
2
9
2
1–0
7024.8448
7024.8665
7062.6377
7062.6661
7227.0059
21.18
20.50
24.54
22.02
20.63
–
–
5
2
7
2
3.62
7
2
9
2
13 11
–
2.87
2
2
11
2
9
2
–
13 11
–
21.45
2
2
11
2
9
2
–
9
9
2
21.67
–
–
–
–
2
9
9
–
9
2
9
2
20.64
2
2
9
2
11
2
0.42
11
2
9
2
2–1
5–4
6–5
5–5
3–4
2–3
6–5
7–6
3–3
4–4
5–5
6–6
14,168.9538
14,168.9782
14,169.5791
14,178.0967
14,178.1099
14,194.7562
14,194.7778
14,290.4952
14,290.5100
14,333.3124
14,333.3225
1.17
24.54
1.32
–
3
2
5
2
2.99
11
2
9
2
–
15 13
–
3.91
9
9
–
2
2
2
2
15 13
–
0.12
5
2
7
2
3.65
–
–
2
2
7
7
2
3.59
5
2
7
2
22.67
4.69
–
–
2
7
2
7
2
0.06
13 11
–
2
2
11
2
9
0.10
13 11
–
–
1.15
2
2
2
11
2
9
2
21.11
7
7
2
–
21.00
1.80
–
–
2
11 11
–
23.71
7
2
7
2
2
2
11 11
–
0.05
11 11
–
0.26
2
2
2
2
5
5
2
22.71
11 11
–
2
1.28
–
–
–
2
2
5
2
5
2
1.71
7
9
2
3–2
4–5
3–4
21,239.4643
21,239.4768
24.62
–
–
2
9
2
7
2
21.45
7
2
9
2
1.37
(continued on next page)

18
S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
Table 2 (continued)
isotopomer, the rotational energy is given by:
ꢀ
ꢁ
J0 –J00
F10 –F1
F0 –F00
5–4
Frequency
(MHz)
Observed–calculated
(kHz)a
X
00
k
1
2
l
Eðv; JÞ ¼
Ykl v þ
½JðJ þ 1Þꢀ :
ð5Þ
k;l
9
2
7
2
21,381.0004
21,433.0607
21,433.1154
21,434.1984
20.46
24.04
1.10
–
–
–
To the accuracy of the present work, with the exception
of Y01; each Ykl ¼ Uklm2ðkþ2lÞ=2; with Ukl being a mass-
independent Dunham parameter. Y01 is given by
7
2
5
2
3–2
"
!
Bi
01
D
DN01
21
Y01 ¼U01m
1 þ me
þ
þ VBidkr2lBi;Bi
ꢁ
0
7
2
5
2
MBi
MN
#
4–3
þ VNdkr2lN;N
:
ð6Þ
ð7Þ
0
13 13
–
7–7
20.32
2
2
with
!
a
Zie2
driel
Observed–calculated residuals (kHz).
Vi ¼
3e0kere dr
re
of the approximation. The difference in the re values of
In Eqs. (6) and (7), me; e and e0 are the rest mass and charge
of the electron, and the permittivity of a vacuum,
respectively. The Di01 terms are Watson’s isotopically
independent Born–Oppenheimer breakdown terms for
atoms i [55]. Correspondingly the Vi are nuclear field shift
parameters, also isotopically independent [58, Eq. (25)] of
14
15
Bi N and Bi N, < 33ð14Þ £ 1027 A; is considerably
larger than the uncertainties in each individual re value.
Variations of this magnitude are typical of many molecules
[46–52]; in particular, they were found earlier for the Pb-
chalcogenides and Tl-halides [53], which are valence
isoelectronic with the Bi-pnictides reported here.
ꢀ
atoms i; with atomic number Zi: The term ðdriel=drÞr is the
e
To account for this isotopic variation, the spectra of the
Pb and Tl compounds were initially analysed using the
approaches of Watson [54,55] and Bunker [56,57], which
consider the isotopic dependence of the re values as due to
adiabatic and non-adiabatic corrective effects. Further
analysis of the PbO and PbS data showed [58] that there
is a further correction which arises through consideration of
the Pb nucleus as possessing a finite size, as opposed to
being treated as a point charge. Tiemann et al. [58,59]
showed that this so-called field shift accounts for much of
the observed Born–Oppenheimer breakdown, and hence the
isotopic dependence of re; in both the Pb-chalcogenides and
Tl-halides. It was thus anticipated that field shift effects
should be significant for BiN and BiP as well.
derivative of the electron density at nucleus i evaluated at
the equilibrium bond length re: ke is the BiN harmonic
stretching force constant.
There is a different Y01 value for each isotopomer. For a
given isotopomer, the masses of the atoms are MBi and MN;
with corresponding reduced mass, m:
To apply Eq. (6), one isotopomer is selected as a
209 14
reference; for BiN, it is
Bi N. The parameters dkr2lii
0
then represent the change in the mean0square nuclear charge
ꢁ
radius on isotopic substitution i ! i : The parameter U01
applies to the reference isotope; it is given by
U01 ¼ U01ð1 þ VBikr2lBi þ VNkr2lNÞ
ð8Þ
ꢁ
where U01 is the isotopically independent Dunham par-
ameter and kr2lBi and kr2lN are the mean square charge radii
of the nuclei of the reference isotope.
As a result, the next analysis for BiN used the approach
proposed by Schlembach and Tiemann [59]. For each
Table 3
Spectroscopic parameters for Bi14N and Bi15
N
Spectroscopic constant
Bi14N
Bi15
N
v ¼ 0
v ¼ 1
v ¼ 0
v ¼ 1
Bv (MHz)
Dv (kHz)b
10,247.91169(34)a
8.99
10,171.39981(34)
8.99
9610.72417(48)
8.99
9541.27558(48)
8.99
eQqvðBiÞ (MHz)
CvðBiÞ (kHz)
eQqvðNÞ (MHz)
CvðNÞ (kHz)
894.5607(69)
176.54(17)
22.4512(65)
7.52(99)
873.5508(69)
175.56(17)
22.4179(65)
9.10(99)
894.8811(109)
165.67(20)
–
874.5600(109)
164.92(20)
–
216.9(20)
216.2(20)
a
Numbers in parentheses show one standard deviation in units of the least significant figure.
Fixed to the values given in Ref. [5].
b

S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
19
Table 4
Table 6
Calculated unsplit J0 –J00 ¼ 1–0 rotational transitions for Bi14N and Bi15
Spectroscopic parameters for BiP
N
in the v ¼ 0 and 1 vibrational states
Spectroscopic constant
Isotopomer
v
Frequency (MHz)
B0 (MHz)
3553.405332(243)a
1.083(5)
D0 (kHz)
Bi14N
0
1
20,495.7874a
20,342.7636
eQq0ðBiÞ (MHz)
CIðBiÞ (kHz)
CIðPÞ (kHz)
898.2172(46)
58.730(81)
Bi15N
0
1
19,221.4137
19,082.5165
23.65(64)
a
Numbers in parentheses indicate one standard deviation in units of the
least significant figure.
a
The line centers have been calculated from the constants given in
Table 4.
Bi
N
to Bi14N), U11 and D0N1; the constants U02; U21 and U31
were fixed at 21.55 u2 MHz, 266.65 u2 MHz and
29.98 u5/2 MHz calculated from Ref. [5]. In the first fit,
ꢁ
In general, U01; D01; D01; VBi and VN in Eq. (6) should be
fit to the experimental data. However, the data set for BiN
is somewhat restricted. Since Bi has only one isotope,
Bi
D
was set to zero, and U01; U11 and DN01 were determined.
ꢁ
VBi cannot be determined experimentally, because
0
01
dkr2lBi;Bi ¼ 0: Similarly, D01 is experimentally indetermi-
Bi
It is generally the case that the Di01 terms are of comparable
magnitude for both atoms [54] (e.g. PbS and TlCl [58,59]);
nate, but does add a small, potentially significant amount
which will need somehow to be accounted for in accurate
work. Because of the dependence of the Vi on atomic
Bi
01
therefore, D was fixed at the determined value of DN01; and
a new fit was carried out. The procedure was repeated until
it converged. Then a value of rev; the internuclear distance
of Bi14N with volume effects included, was obtained from:
number Zi; (see Eq. (7)), the term in VNdkr2lN;N is very small
0
and can be set to zero. Thus the expression for Y01 reduces to
ꢃ
ꢂ
me
me
h
21
Bi
01
ꢁ
ꢁ
U01
Y01 ¼ U01m
1 þ
D
þ
DN01
ð9Þ
¼
ð10Þ
8p2ðrevÞ2
All these parameters are given in Table 5.
MBi
MN
with U01 and DN01 as the parameters to be determined.
ꢁ
To obtain the isotopically independent internuclear
distance reBO of point-like nuclear charges, it was necessary
to obtain U01 using Eq. (8). As with the fits, the term in
VNkr2lN was set to zero. The value of kr2lBi ¼ 30:40ð73Þ fm2
was obtained from Bardin et al. [60,61]. The value for VBi
From the data in Table 1, line centers were determined
giving four ‘unsplit’ frequencies; these are given in Table 6.
Iterative fits to these frequencies were then carried out using
ꢁ
Eqs. (5) and (9). The fitting parameters were U01 (referred
was obtained by first evaluating ðdriel=drÞr with a DFT
Table 5
e
calculation using the method outlined in Section 3 above,
then applying Eq. (7). All the derived values are in Table 5.
Finally, by applying the equation of Bunker [57]:
Spectroscopic constants of BiN, determined by various procedures
Bi14
N
Bi15
N
Bi14N [5]
h
Use of Eqs. (2) and (3)
U01
¼
ð11Þ
Be (MHz)
10,285.85338(79)a
9645.13488(79)
68.6226(7)
10,285.88(6)
75.73(6)
8p2ðreBO 2
Þ
ae (MHz)
˚
re (A)
75.6859(7)
a value for reBO was obtained; it is also in Table 5.
1.93490793(67)
1.93490468(70)
1.93491(1)
Use of Eqs. (5) and (9)b
The uncertainties of the parameters in Table 5 again
reflect those of the spectroscopic constants and the atomic
masses. It would perhaps also be useful to consider those
introduced to the bond lengths by the assumptions and
ꢁ
U01 (u MHz)
135,004.17(10)
23598.290(25)
22.788(19)
U11 (u3/2 MHz)
DN01
rev (A)
1.93479418(72)c
˚
approximations made in the above procedure. In the fits, the
assumptions were that D ¼ DN01; and that the term
Born-Oppenheimer parameters from Eqs. (8) and (11)
Bi
01
!
Bi
dr
el
24 d
Bi
VNdkr2lNN could be ignored. Allowing D01 ¼ D0N1 ^ 1
˚
(A
)
32.7
3.19
0
produced a variation in re of ^3 £ 1026 A. If VN < 0:1VBi
dr
˚
re
VBi (106 fm22 d
)
and dkr2lNN < 1 fm2, then their product <3 £ 1027 and the
0
change in re < 3 £ 1027 A, which is indeed negligible.
U01 (u MHz)
reBO (A)
134,991.08(45)
1.9348880(33)c
˚
˚
Accordingly, the approximations give an uncertainty in
rev < 3 £ 1026A.
a
˚
Numbers in parentheses indicate one standard deviation in units of the
least significant figure. For derived parameters they represent the
uncertainties in the spectroscopic constants and atomic masses.
If the uncertainty in the DFT value for VBi < 20% [41],
and that of kr2lBi < 2%; the uncertainty contributed by
b
The Bi14N isotopomer was used as the reference isotopomer.
VBikr2lBi to reBO is <1025 A. If the value of VN < 0:1VBi
˚
c
The absolute uncertainties in rev < ^3 £ 1026 A and in re < ^1025
BO
˚
˚
A
(it has been calculated to be considerably less than this)
and kr2lN < 0:1kr2lBi; then neglect of VNkr2lN introduces
(see text).
d
Result of DFT calculation (see text).

20
S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
an uncertainty in reBO < 1027 A which is again negligible.
Table 7
˚
The uncertainty in reBO is thus < ^ 1025 A.
˚
Determined equilibrium bond lengths for BiN and BiP
˚
re (A)
Molecule
Method
4.2.2. Geometry of BiP
BiN X1Sþ
1.9349079(7)a
1.93489(1)
1.9367
Experimental re for Bi14Nb
For BiP, for which vibrational and isotopic data are not
available, only the ground state effective bond length r0
could be obtained from the present data, using B0 in Eq. (3).
c
reBO
DFT calc. This work
˚
1.93491(1)
1.940
Expt. Ref. [5]
The value is r0 ¼ 2:296152ð8Þ A. The re value obtained
˚
earlier is 2.29345(8) A [8].
Ab initio Ref. [27]
BiP X1Sþ
2.2961520(80)
2.2835
r0 value from expt. This work
DFT calc. This work
Expt. Ref. [8]
The spectroscopic constants in Table 4 allow the
harmonic stretching frequency of BiP to be estimated [62]
from v2 < ð4B03=D0Þ: The resulting value is 429.4 cm21, in
good agreement with the value from Ref. [8]
(ve ¼ 430:275ð2Þ cm21).
2.29345(8)
a
Numbers in parentheses indicate one standard deviation in units of the
least significant figure.
b
Obtained using the initial method outlined in this work (see text).
c
Derived from both theoretical and experimental properties (see text).
4.3. DFT results
Fig. 3 displays a plot of the potential energy curve and
the electron density at the Bi nucleus at different inter-
nuclear separations, both calculated using density functional
theory. From the potential energy curve for BiN, which has
these constants have roughly the same magnitudes in the
bismuth monohalides, the signs are reversed [19,20,23],
consistent with radical differences in the electronic
structures of the two sets of molecules. For BiCl [20],
eQqðBiÞ has been interpreted in terms of a simple Townes–
Dailey model [64] and the same approach will be used here.
The measured eQq value is given by:
been prepared using the HCTH/93 exchange-correlation
potential as outlined in
SAOP
xc
functional [63] and the V
Section 3, we have determined re for BiN to be 1.9367 A in
˚
good agreement with experiment. With identical methods
˚
ꢂ
ꢃ
1
for BiP, we determine re ¼ 2:2835 A which agrees with re
eQq ¼ nz 2 ðnx þ nyÞ eQqn10
ð12Þ
from electronic spectroscopy [8]. A summary of determined
bond lengths for BiN and BiP is given in Table 7.
2
where nx; ny and nz are the populations of the np valence
orbitals of the atom in question, with z being the internuclear
axis; eQqn10 is the coupling constant for a singly occupied
npz atomic orbital. For Bi, n ¼ 6; and eQq610 ¼ 1500 MHz;
for 14N, n ¼ 2; and eQq210 ¼ 210 MHz [65]. For N, P and
Bi atoms, the ground state electron configuration is [Ng]
ns2np3 (Ng ¼ noble gas), so each np orbital is singly
occupied and eQqðatomÞ ¼ 0:
5. Nuclear quadrupole coupling constants
The nuclear quadrupole coupling constants eQqðBiÞ and
eQqðNÞ for BiN and BiP are given in Table 8, in comparison
with values for some related diatomic molecules. Several
comparisons can be made.
The simple interpretation for eQqðBiÞ for the bismuth
monohalides was to say that the electronegative halogen
withdraws 6pz electron density from Bi, leaving nx ¼
ny ¼ 1 unchanged; this would make ½nz 2 1=2ðnx þ nyÞꢀ ¼
20:68; and account for the negative sign. The bond
would be largely ionic consistent with the eQqðClÞ value
in BiCl [20]. It should also be noted that in this model,
the 6px and 6py electrons stay localized on Bi, so that the
ground electronic state should be a triplet. This is indeed
the case, though Hund’s case (c) applies, and the ground
state is the 0þ component.
First we note that the values of eQqðBiÞ for BiN and BiP
are nearly identical, suggesting that the electron distribution
at Bi is essentially the same in both molecules. Although
For BiN and BiP, the interpretation is a little different. In
simple terms, the atoms are held together by a triple bond.
Furthermore, since eQqðBiÞ is the same for both BiN and
BiP, we will assume that the electronegativities of N and P
are not a factor, and consider the bonding to be fully
covalent. In this case nx ¼ ny ¼ 1; again. We will also
consider all atoms to be, to some degree, sp-hybridized
along the z-axis. If a2s is the degree of s-character of
the bonding hybrid atomic orbital, then ð1 2 a2s Þ is
Fig. 3. A plot showing the potential energy and electron density at the Bi
nucleus with respect to the internuclear separation calculated using density
functional theory for BiN in the X1Sþ electronic state. r0 is set to
6
23
˚
2.728100 £ 10 A
.

S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
21
Table 8
Collected vibrational ground state quadrupole coupling constants, eQq; and extracted electric field gradientsa, q; for some related molecules
Molecule
Nucleus, X ¼
eQqðXÞ (MHz)
q (1022 V m22 a
)
Reference
BiN X1Sþ
Bi
N
894.5607(69)b
22.4512(65)
898.2172(46)
25.1416(5)
7.17(21)
This work
This work
This work
[15]
0.49596(59)
7.20(22)
BiP X1Sþ
PN X1Sþ
Bi
N
1.0403(14)
BiF X0þ
Bi
Bi
35Cl
Bi
I
21148.08(10)
21027.0(120)
234.5(28)
29.20(28)
28.23(35)
20.175(16)
27.29(23)
20.5796(95)
[19]
[20]
[20]
[23]
[23]
Bi35Cl X0þ
BiI X0þ
2909.5(20)
2995.0(20)
a
Where q is calculated from eQqðXÞ by q ¼ ð2½eQqðXÞꢀhÞ=eQ and Q is the nuclear quadrupole moment taken from Ref. [66].
b
Numbers in parentheses indicate one standard deviation in units of the least significant figure.
the corresponding expression for the non-bonding orbital. In
this case, nz ¼ ð1 2 a2s Þ þ 2as2 ¼ 1 þ a2s : Thus
correspond to half-filled valence p-orbitals in both N and Bi.
The symmetry of this orbital configuration results in a zero
electric field gradient at the respective nuclei. An increase in
the vibrational state and hence a step toward this asymptote
is therefore consistent with a decrease in the electric field
gradient, q; experienced at both the Bi and N nuclei as
indicated by the eQq constants.
eQq ¼ ½1 þ a2s 2 1ꢀeQqn10 ¼ as2eQqn10
ð13Þ
For Bi in both molecules, a2s ¼ 0:60; and for 14N in
BiN a2s ¼ 0:25: This would imply that the s-bonding
atomic orbital on Bi has mostly s-character, and that for
N, it has mostly p-character. This seems somewhat
counterintuitive, though it does depend on the assumption
of full covalency. Given that the electronegativities of Bi
and P are close [65], the assumption is perhaps
reasonable. These conclusions may possibly be confirmed
by ab initio calculations, but such calculations may be
difficult and complicated by the need to account for
relativistic effects on Bi.
6. Spin-rotation coupling constants
The determined values for CIðBiÞ; CIðNÞ and CIðPÞ are
given in Tables 3 and 4. The CI constant is proportional to
the rotational constant B: The ratio CIðBiÞ=B for BiN and
BiP agree to within <4% which as one would expect
indicates that the Bi atom is in a very similar environment in
both molecules and is consistent with the Bi quadrupole
coupling constants. In this regard, we may calculate the
molecular magnetic field at the N and P nuclei for the
different rotational states of BiN and BiP, respectively,
using the following relationship [65]:
We may fit the following expression to the eQqv values
obtained for BiN:
ꢀ
ꢁ
1
2
eQqv ¼ eQqe þ eQqI v þ
ð14Þ
the result is eQqeðBiÞ ¼ 905:066ð88Þ MHz, eQqIðBiÞ ¼
14
14
221:010ð14Þ MHz, eQqeð NÞ ¼ 22:468ð13Þ MHz and
CIðkHzÞI
1=2
kHJlðgaussÞ ¼ 1:311
½JðJ þ 1Þꢀ
ð15Þ
eQqIð NÞ ¼ 0:033ð13Þ MHz. The decrease in magnitude
mIðnmÞ
for the eQq values for both nuclei with increasing
vibrational state is consistent with trends observed pre-
viously in the bismuth halides [19,20] and in PN [15]. A
literature survey indicates that BiN may well be the first
multiply bound diatomic molecule where both atoms
possess nuclear spins I $ 1; and for which eQq constants
for both atoms have been determined in more than one
vibrational state. The interhalogen compounds such as IBr
offer singly bound analogs to this case. For these
compounds and equally for the alkali halides, the trend
displayed is that the magnitude of eQq increases with v for
the more electronegative atom and decreases with v for the
less electronegative atom [65]. On the other hand for BiN
both eQq values decrease in magnitude with increasing v:
From relativistic calculations on the potential curves for
BiN [27], the X1Sþ ground state is calculated as going to
the Bi(4S3/2) þ N(4S3/2) asymptote. These atomic states
Here mI is the nuclear magnetic moment and I the nuclear
spin. For 14N (mI ¼ 0:403761; I ¼ 1) in BiN we find that for
the rotational state J ¼ 1; the magnetic field at the N nucleus
is approximately 26.3 G. For P (mI ¼ 1:13160ð3Þ; I ¼ 1=2)
in BiP, for the same rotational state the magnetic field at the
P nucleus is approximately 14.8 G. The difference in
magnitude between these values correlates with the larger
internuclear separation in BiP compared to BiN.
7. Conclusions
The first reported pure rotational spectra of BiN and BiP
have been measured with a cavity pulsed jet FTMW
spectrometer. Previous studies have generally used a
microwave discharge in conjunction with an oven to

22
S.A. Cooke et al. / Journal of Molecular Structure 695–696 (2004) 13–22
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