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The pure rotational spectrum of CrCN (X 6Σ+): an
unexpected geometry and unusual spin interactions
Online Publication Date: 01 March 2007
To cite this Article: Flory, M. A., Field, Robert. W. and Ziurys, L. M. (2007) 'The pure
rotational spectrum of CrCN (X 6Σ+): an unexpected geometry and unusual spin
interactions', Molecular Physics, 105:5, 585 - 597
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Molecular Physics, Vol. 105, Nos. 5–7, 10 March–10 April 2007, 585–597
The pure rotational spectrum of CrCN (X 6'1): an unexpected
geometry and unusual spin interactions
M. A. FLORYy, ROBERT. W. FIELDz and L. M. ZIURYS*y
yUniversity of Arizona, Tucson, AZ, USA
zMassachusetts Institute of Technology, Cambridge, MA, USA
(Received 16 October 2006; in final form 26 November 2006)
The pure rotational spectrum of CrCN (X 6þ) has been recorded in the frequency range
250–520 GHz using direct-absorption techniques. This is the first spectroscopic investigation
of the CrCN radical. This species was synthesized by reacting Cr vapour with (CN)2. Spectra
were obtained for the main isotopic species, the 53Cr and 13C isotopologues, and the heavy
atom stretch and several quanta of the bending vibration. The molecule was found to have a
linear cyanide geometry and a 6þ ground state. Rotational, fine structure, and l-type
doubling constants have been determined. The spin–spin parametre was found to be
small – a likely result of competing second-order spin–orbit contributions from excited 4,
4
, and 6 states. However, increased significantly in the bending mode, which may be
caused by a reduction of the 6þ4 interaction strength due to spin–orbit vibronic coupling.
In contrast, the value of , arising from interactions with a nearby 6state, was independent
of v2. The CrCN bond lengths were determined to be rCr–C ¼ 2.019 Å and rC–N ¼ 1.148 Å.
Delocalization of the 3d electrons into the CN 2 orbital, which is polarized towards the
carbon atom, may account for the CrCN structure.
1. Introduction
Molecules containing a metal–cyanide bond are found in
many areas of chemistry. There are multiple cases in
biochemistry, such as in enzymes, certain vitamins, and
poisons [1–3]. From the synthetic aspect, a cyanide or
isocyanide ligand often serves as a bridge between
metal centres [4]. Cyanides have also been the most
commonly-observed carriers of metals in interstellar
molecules [5].
Spectroscopic studies of simple metal cyanide species
are important because they elucidate bonding properties
of more complex systems. Three different geometries
have been observed in the gas phase for metal
monocyanides in their electronic ground states: linear
cyanides (M–CN), as in CuCN or ZnCN [6, 7], linear
isocyanides, as is the case of MgNC, AlNC, or GaNC
[8–10], or a bent T-shaped structure, as found for the
sodium and potassium analogues [11, 12]. It is believed
that the three structures arise from subtle differences in
covalent versus ionic character in the metal–CN
bond [13].
*Corresponding author. Email: [email protected]
The structures of transition metal cyanides have been
particularly difficult to predict. Ab initio studies have
suggested that the lowest energy isomer of both NiCN
and CuCN is the linear cyanide by at least 10 kcal/mol
[14, 15]. On the other hand, computations have shown
that FeNC, the iso-cyanide, is more stable than FeCN
by only 0.6 kcal/mol [13]. It is also thought that the
bending potential in FeNC is very shallow such that the
zero-point averaged structure is bent [16].
Millimetre-wave studies have shown that later 3d
metals (cobalt through zinc) have the linear cyanide
geometry in their ground electronic states [6, 7, 17, 18].
In contrast, iron takes on the FeNC structure, as
demonstrated by laser-induced fluorescence experiments
[19]. Therefore, the geometry appears to switch in the 3d
series at iron. Because calcium, a ‘pseudo’ 3d0 transition
metal, also has the MNC geometry [20, 21], it is
tempting to speculate that the early 3d transition
metals take on the isocyanide geometry as well.
However, these species have not been investigated
either theoretically or experimentally.
Here we present the first spectroscopic study of
an early 3d cyanide, CrCN. The pure rotational
spectrum of this radical has been measured at
Molecular Physics
ISSN 0026–8976 print/ISSN 1362–3028 online ß 2007 Taylor & Francis
http://www.tandf.co.uk/journals
DOI: 10.1080/00268970601146872
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586
M. A. Flory et al.
sub-millimetre wavelengths. From isotopic substitution,
the structure has been established to be the linear
cyanide in the electronic ground state, which is X 6þ.
The spectra have been analysed, and the fine structure
constants determined (which exhibit some unusual
properties) are interpreted. Differences in the bonding
between CrCN and the corresponding halides are also
discussed.
2. Experimental
The pure rotational spectrum of CrCN was recorded
using the high temperature direct absorption spectrometer of the Ziurys group. Details of this system are
described elsewhere [22]. Briefly, the radiation source is
a phase-locked Gunn oscillator, which is used to pump a
Schottky diode multiplier, providing frequency coverage
in the range 65–660 GHz. The millimetre/sub-millimetre
wave beam is propagated quasi-optically using
a polarizing grid, mirrors, and lenses into the
double-pass reaction chamber, a cooled, stainless steel
cell. The detector is an InSb, hot-electron bolometer.
Phase-sensitive detection is employed, using FM
modulation, and data are recorded at 2f.
Chromium cyanide was synthesized by reacting
chromium vapour with cyanogen gas. The metal
vapour was generated by subliming Cr pieces (99.5%
Alfa Aesar) in a Broida-type oven [23]. Approximately
4–7 mTorr of pure cyanogen gas were flowed over the
top of the oven crucible containing the metal. No carrier
gas was needed, and the CrCN molecules were readily
observed without a dc discharge. No chemiluminescence
was seen during the production process. In addition to
the main isotopologue (52CrCN), spectra of the 53Cr and
13
C isotopologues were also recorded. The 53CrCN
species was observed in its natural abundance (52Cr:
53
Cr ¼ 83.8: 9.5%). In the case of the 13C species, H13CN
was used as a precursor instead of cyanogen. This
compound was synthesized previously from Na13CN
and H2SO4 and was stored in liquid N2. Only 0.3 mTorr
of H13CN was used in the flow system in order to
conserve the reagent; in this case, a dc discharge was
necessary and was optimized to 10 V and 750 mA.
After transitions from 52Cr13CN were identified,
additional measurements could be conducted in the
natural 13C abundance using (CN)2.
Because there was no previous work on the chromium
cyanide species, rotational constants were estimated
from those of CrCl [24]. Initially, approximately 8B in
frequency were scanned to locate signals and identify
harmonic relationships. In the course of this search,
numerous sextets of transitions were observed,
each spanning about 180 MHz. The pattern indicated a
linear molecule, either CrCN or CrNC. After identifying
the two chromium isotopologues and several excited
vibrational features among the sextets, preliminary
rotational constants could be estimated, and additional
transitions were measured. The Cr13CN and CrN13C
rotational constants were then estimated and, after
additional scanning, only the 13C cyanide species was
found.
Frequencies were measured by fitting the observed
peaks to Gaussian profiles. The data used for these fits
typically were averaged from two scans, one taken at
increasing frequency and one at decreasing frequency.
For measurements of the 13C isotopologue in natural
abundance, up to 34 scans were necessary to achieve an
adequate signal to noise ratio. Each scan was 5 MHz in
width, and typical line widths in this experiment were
0.6–1.2 MHz over the range 250–522 GHz.
3. Results
Thirteen rotational transitions of CrCN were recorded
(main isotopologue) in its ground vibrational state in the
range 250–512 GHz. Because the ground state symmetry
is 6þ, each rotational level, labelled by N in a Hund’s
case (b) coupling scheme, is split into six fine structure
components, indicated by J, as shown in figure 1.
The splittings arise from spin–spin coupling, characterized by the constant , and spin–rotation interactions,
described by . The net result is that each rotational
transition (N ¼ þ 1) is potentially split into six
observable fine structure transitions for J ¼ N.
These six spectral components, which are separated
from each other by about 36 MHz, were measured
in virtually every transition. Hyperfine structure, arising
from the nitrogen nuclear spin, is possible but was
not observed, even at the lowest N values (N ¼ 31).
In addition to the ground state, transitions arising in the
excited bending mode up to v2 ¼ 5 were recorded in the
main isotopologue, as well as the (100) stretching
vibration; l-type splittings were observed in the v2 ¼ 1
and 2 states. For the two less abundant isotopologues,
53
CrCN and Cr13CN, nine and four transitions were
measured in the ground state, although not always the
complete sextet. No hyperfine splitting was observed
from the 53Cr nuclear spin, where the lowest N measured
was N ¼ 57. Finally, the v2 ¼ 1 l-type doublets were
recorded for the 53Cr species. A sample of transition
frequencies for CrCN, 53CrCN, and Cr13CN is presented
in table 1. The full set of transitions is available in the
journal’s supplementary information.
In figure 2, the general vibrational pattern for a given
rotational transition is shown as a stick diagram,
illustrated by the N ¼ 57 ! 58 transition near 456 GHz.
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The pure rotational spectrum of CrCN (X 6Sþ )
CrCN (X 6Σ+)
61.5
62.5
60.5
59.5
N = 60
58.5
57.5
∆N = ∆J = +1
60.5
61.5
59.5
58.5
N = 59
Hrot
Hss
Hsr
587
however, because the vibrational progression overlaps
with that of the adjacent rotational transition.
Figure 3 displays a sample spectrum of each
isotopologue measured in the ground vibrational state;
here the N ¼ 66 ! 67 transitions are shown. The fine
structure, labelled by J, is fairly evenly spaced at this
high N in all three species, reflecting the small
N-dependence of the spin–rotation interactions.
(The spin–spin coupling is fairly independent of N.)
The overall splitting, however, is less regular at lower N
(N 5 40).
Figure 4 shows the spectrum of the N ¼ 56 ! 57
transition of CrCN in the v2 ¼ 5 level near 456 GHz. As
this figure demonstrates, the fine structure pattern in the
v2 mode deviates from the regular sextet of the ground
state. Although the total width of the sextet remains
approximately 180 MHz, the spin components get
closer together at the higher frequency end.
This deviation is seen to a lesser degree in the v2 ¼ 1
lines and steadily increases with excitation of the v2
vibration.
57.5
4. Analysis
56.5
Each vibrational state of CrCN was analyzed separately
using an effective Hund’s case (b) Hamiltonian of the
form:
J
Figure 1. Qualitative energy level diagram of the
N ¼ 59 ! 60 rotational transition of CrCN, showing the fine
structure splittings that arise from spin–spin and spin–rotation
interactions. These splittings are exaggerated relative to the
pure rotational levels. The transitions observed for CrCN
(N ¼ J ¼ þ 1) are indicated by arrows, which produce a
sextet spectral pattern.
The fine structure sextets are not resolved on the scale of
the figure, and only approximate relative intensities are
shown. The v2 bending mode is seen progressing
regularly to higher frequency from the ground
state (000) line, for l ¼ v2. However, the (0200) state
experiences strong Fermi resonance with the (100) heavy
atom stretch, and both sets of lines are shifted from their
expected locations, as shown. In fact, the (0200) lines
occur in the centre of the (0110) l-doublet at the N
observed, a shift of over 2 GHz from the (0220) lines.
Furthermore, the (100) state, which should appear
at a lower frequency than the ground state for a
positive 1, appears at a slightly higher frequency.
This figure greatly simplifies the actual pattern,
ð4Þ
Heff ¼ Hrot þ Hsr þ Hð3Þ
sr þ Hss þ Hss þ Hld
ð1Þ
which accounts for rotation, spin–rotation, spin–spin
and l-type interactions (v2 6¼ 0 states only). Centrifugal
distortion terms associated with these parameters were
also included, as well as the fourth-order spin–spin and
third-order spin–rotation terms, when necessary. The
third-order spin–rotation interaction, which indirectly
arises from spin–orbit coupling, has the general form in
spherical tensor notation [25]:
10
3
2
3
Hð3Þ
sr ¼ pffiffiffi s T ðL , N Þ T ðS, S, S Þ
6
ð2Þ
This term was originally suggested by Hougen [26] and
developed by Brown and Milton [27]. It is thought to be
needed for states of quartet multiplicity and higher.
The fourth-order spin–spin coupling term, applicable
to states of quintet multiplicity and higher, is
described by
Hð4Þ
ss ¼
½35Sz4 30S 2 Sz2 þ 25Sz2 6S 2 þ 3S 4 12
ð3Þ
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588
M. A. Flory et al.
Table 1.
Selected Transition Frequencies of CrCN (X 6þ; v ¼ 0) in MHz.
52
Cr12CN
53
Nþ1
Jþ1
N
J
obs
obs–calc
32
29.5
30.5
31.5
32.5
33.5
34.5
56.5
57.5
58.5
59.5
60.5
61.5
57.5
58.5
59.5
60.5
61.5
62.5
61.5
62.5
63.5
64.5
65.5
66.5
62.5
63.5
64.5
65.5
66.5
67.5
64.5
65.5
66.5
67.5
68.5
69.5
31
28.5
29.5
30.5
31.5
32.5
33.5
55.5
56.5
57.5
58.5
59.5
60.5
56.5
57.5
58.5
59.5
60.5
61.5
60.5
61.5
62.5
63.5
64.5
65.5
61.5
62.5
63.5
64.5
65.5
66.5
63.5
64.5
65.5
66.5
67.5
68.5
249045.100
249082.562
249114.421
249146.254
249181.247
249221.081
458409.764
458444.425
458478.522
458513.391
458550.079
458589.289
466139.633
466174.210
466208.312
466243.247
466279.964
466319.226
497037.879
497072.193
497106.321
497141.372
497178.204
497217.482
504756.994
504791.243
504825.346
504860.415
504897.262
504936.558
0.045
0.150
0.268
0.214
0.156
0.011
0.039
0.023
0.027
0.003
0.027
0.059
0.050
0.013
0.015
0.012
0.000
0.112
0.016
0.030
0.004
0.025
0.022
0.013
0.026
0.060
0.016
0.048
0.001
0.072
59
60
64
65
67
58
59
63
64
66
Cr12CN
52
Cr13CN
obs
obs–calc
obs
obs–calc
455723.744
455758.091
455792.067
455826.844
455863.216
455902.245
463408.515
463442.775
463476.833
463511.588
463548.003
463587.034
494126.574
494160.714
494194.800
494229.577
494266.256
494305.268
501800.708
501834.764
501868.760
501903.669
501940.349
501979.408
517142.380
517176.198
517210.190
517245.117
517281.878
517321.009
0.061
0.023
0.058
0.001
a
0.001
0.056
a
a
a
a
0.012
0.059
0.026
0.064
0.042
0.069
0.024
0.065
a
0.047
0.049
0.028
0.035
0.053
0.003
0.034
0.067
0.024
0.005
461555.527
461589.693
461623.617
461658.253
461694.699
461733.529
492150.194
492184.062
492218.011
492252.846
492289.264
492328.211
499793.460
499827.269
499861.198
499896.107
499932.570
499971.497
515073.267
515106.978
515140.829
515175.759
515212.382
515251.235
0.077
0.002
0.012
0.078
0.075
0.095
0.011
a
0.004
a
0.045
a
0.008
0.016
a
0.039
a
a
0.047
0.065
0.025
0.021
0.023
0.104
a
Line blended with other features; not included in fit.
Again, this coupling term arises indirectly from
spin–orbit interactions with remote perturbers [25].
Centrifugal distortion corrections to this term, D and
H, were also found necessary in certain cases:
1 h ð4Þ ^ 2 i
1 h ð4Þ ^ 4 i
þ H
:
Hss = , N
Hss = ,N
Hð4Þ
sscd ¼ D
þ
þ
2
2
ð4Þ
The D term has been employed in previous analyses,
such as the X5 state of FeO [28], while this work
represents the first use of H.
The ground state of the main isotopologue of CrCN
was initially fit with the rotational constants,
spin–rotation constants (, D, and s) and spin–spin
parameters (, D, and ). However, the rms of the fit
was significantly larger than the estimated experimental
accuracy of 100 kHz. Therefore, D was added as a
fitting parameter, with noticeable improvement. The term in the final analysis had to be fixed to a constant
value, otherwise it was not defined. Use of s did not
affect the fit in any way, and thus the parameter was not
used. The rms of 65 kHz was finally achieved by using
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The pure rotational spectrum of CrCN (X 6Sþ )
Cr CN (X 6Σ+): N = 66 →67
CrCN (X6Σ+): N = 57 → 58
(000)
52Cr12CN,
J=
66.5 → 67.5
68.5 → 69.5
64.5 → 65.5
67.5 → 68.5
63.5 → 64.5
65.5 → 66.5
(0110)
Cr13CN
(000)
(0200)
53CrCN
(0110)
(0220)
(100)
520180
(0330)
53CrCN
(000)
447
589
(0440)
450
453
456
459
462
(0550)
520230
520280
520330
520380
517180
517230
517280
517330
53Cr12CN
465
Frequency (GHz)
Figure 2. Stick diagram of the N ¼ 57 ! 58 rotational
transition of CrCN and associated vibrational satellite
features, neglecting fine structure splittings. The vibrational
progression of the v2 bending mode is shown to the right of the
(000) line with satellite features up to v2 ¼ 5. The (0200) state
and the (100) stretch interact through Fermi resonance, and
hence are both shifted from predicted positions, as shown in
the diagram. Features due to 53CrCN and Cr 13CN are seen at
the left of the figure.
higher order centrifugal distortion corrections to the
spin–spin interaction, H and L. These results suggest
that most of the higher-order terms and their centrifugal
distortions are due to interactions with low-lying
electronic states, most likely 4 and/or 4. Note that
while D/B 3.7 105, D/ 4.7 107 and D/
1.3 105. For the carbon-13 and chromium-53
isotopologues, the range of transitions was not nearly
as large as the main isotope. Hence, only , , D, and
D were required to obtain an acceptable rms.
In the case of the v2 ¼ 1 and 2 states, additional terms
were needed to account for l-splitting and l-doubling
effects. For the v2 ¼ 1 state, only l-type doubling is
involved, and the data were readily fit with the constant
q and its centrifugal distortion correction, qD [29, 30].
In addition, a p term was included to compensate for
the parity dependence of the spin–rotation splitting of
the l-type doublets. This parameter has been used
previously to fit vibrational satellite lines of MgOH
and ZnCN [7, 30]. For the v2 ¼ 2 levels, l-type doubling
and l-type resonance occur such that a 3 3 matrix
involving all three states [(0200), (022e0), (022f0)] is
needed to model these effects. The difference in energy
between the (0200) and (0220) levels is necessary for this
representation, which is not known for CrCN.
Therefore, an effective l-doubling parametre, qeff, was
used to fit the (0220) data. In analogy to the (010) states,
517130
52Cr13CN
515060
515110
515160
515210
515260
Frequency (MHz)
Figure 3. Sample spectra showing the N ¼ 66 ! 67 transitions of the main isotopologue, 52CrCN, as well as the 53Cr
and 13C species. The 52CrCN and 53CrCN were observed in
natural abundance, while Cr13CN was produced using
isotopically enriched H13CN. An unidentified feature appears
at the left in the 53CrCN spectrum. Each transition exhibits
a regular sextet fine structure pattern, labelled by quantum
number J, indicating a good case (b) 6þ ground state for
CrCN. Each spectrum is composed of two scans, each
120 MHz wide and acquired in 60 seconds.
qeff defines the energy splitting, E(0220), between the
(022e0) and (022f0) levels [30, 31]:
Eð02 2 0Þ ¼
qeff
fðN½N þ 1 6Þ ðN½N þ 1 12Þg1=2
2
ð5Þ
A centrifugal distortion correction, qD,eff, was also
employed using the N^ 2 operator.
Analysis of the fine structure in the bending mode
revealed some surprises. As for the ground state of the
main isotopologue, , , , and their centrifugal
distortion corrections were used initially to fit the
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590
M. A. Flory et al.
CrCN (X 6Σ+) (0550): N = 56→57
J=
53.5→ 54.5
J=
54.5→55.5
J=
56.5→57.5
J=
55.5→56.5
J=
58.5 →59.5
J=
57.5 →58.5
*
456030
456080
456130
456180
456230
Frequency (MHz)
Figure 4. The N ¼ 56 ! 57 transition of CrCN in the v2 ¼ 5
level. An unidentified feature is marked by an asterisk. In this
v2 ¼ 5 level, the fine structure pattern has changed significantly
from the ground state data, as shown in figure 3. The sextet
is now irregularly spaced, with the individual components
moving closer together at higher frequency, indicating a large
change in . This figure is a composite of two scans, each
120 MHz wide and collected in 60 seconds.
data. However, at v2 ¼ 4, the value of increased by two
orders of magnitude, and the v2 ¼ 5 data would not fit to
an acceptable rms without s. Moreover, increased
steadily with v2 quantum number. The sudden excursions of these parametres near v2 ¼ 5 implies a perturber
near the energy of this state (1000 cm1). Interestingly,
D did not improve the fits for the v2 ¼ 4 and 5 data,
although it was used for all v2 3 states. However, in
these lower v2 cases, had to be fixed, in analogy to the
ground state. Without and D, the v2 3 analyses
resulted in rms values that were larger than the expected
experimental precision.
The resulting constants from fits of the (000) state of
the three isotopologues are presented in table 2, with the
parameters for the excited vibrational modes in table 3.
For the ground vibrational state of the main
isotopologue, 76 lines were fit from 13 rotational
transitions with an overall rms of 65 kHz. The rms
achieved was typically 40–80 kHz for the other data sets.
5. Discussion
5.1. Structure and geometry of chromium cyanide
Measurements of Cr13CN clearly indicate that the
structure of this species is the linear CrCN form.
From the rotational constants of the three isotopologues
studied, r0, rs, and rð1Þ
m bond lengths were calculated.
The r0 values were determined from a non-linear least
squares fit to the three moments of inertia. The rs
structure was calculated from Kraitchman’s equations
[32], invoking the centre of mass condition to solve the
geometry. The rð1Þ
m bond lengths were established from a
non-linear least squares fit using the method of Watson
[33]. This analysis partly compensates for zero-point
energy differences and is probably closest to the
equilibrium structure. The resulting bond lengths are
listed in table 4, as well as those of other 3d cyanides.
As shown in the table, the rð1Þ
m value for the Cr–C bond
distance is rCr–C ¼ 2.019 Å, which varies at most from
the other two structures by 0.004 Å. The C–N bond
length from the rð1Þ
m calculation is rC–N ¼ 1.148 Å, which
is slightly smaller than the values of the r0 and rs
structures. The metal–carbon bond distance in CrCN is
the largest of any 3d transition metal cyanide studied
thus far (see table 4). The others fall in the range
1.83–1.95 Å. This variation does not appear to reflect the
atomic or ionic radii. The C–N bond length for CrCN is
shorter than the re value of 1.153 Å for HCN [34] – a
property that is also apparent in NiCN, ZnCN, and
possibly CoCN. The unusually short CN bond lengths
found for the cyanides are thought to arise from
curvilinear bending and the projection of the bent CN
bond distance back onto the linear molecular axis [16].
The rotation–vibration dependence of the CrCN
rotational constant can be determined by fitting the
experimental data to the power series [35]:
1
Bv ¼ B~ e 1 v1 þ
2 ðv2 þ 1Þ þ 22 ðv2 þ 1Þ 2 þ ll l 2
2
ð6Þ
where B~ e ¼ Be – 3/2. The derived constants are given in
table 5. The value for 2, the rotation–vibration constant
of the bending mode, is negative, as is typically found
for linear triatomic species, and is roughly comparable
with those of the other 3d cyanides. The magnitudes of
22 and 11 are a factor of two larger than the
corresponding values in ZnCN [7], and would be
smaller if Fermi resonance were not present.
The rotation–vibration constant of the heavy atom
stretch has also been determined to be 1 ¼ –0.942 MHz.
The unusual negative value arises from the effects of the
Fermi resonance as well. Because the (100) and (0200)
states lie roughly at the same energy, they perturb each
other, which shifts the (100) features to higher frequency
and the (0200) lines to lower frequency. In a
Fermi-resonance pair, the rotational constants of the
interacting states are also perturbed, such that the trace
invariance rule is obeyed [36]:
B0100 þ B0020 0 ¼ B100 þ B020 0
ð7Þ
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The pure rotational spectrum of CrCN (X 6Sþ )
Table 2.
Ground state spectroscopic constants of CrCN (X 6þ) in MHz.a
52
Cr12CN
B
D
D
D
H
L
(1011)
D
H
(1018)
rms
591
3895.6410(10)
0.00144627(14)
36.427(71)
0.0000170(57)
640(20)
0.00845(94)
0.00000094(34)
8.4(3.9)
53
Cr12CN
3872.7636(21)
0.00143045(26)
36.21(15)
0.000016(12)
609(35)
0.004969(76)
52
Cr13CN
3857.3185(39)
0.00143023(47)
35.866(51)
560(63)
0.00495(14)
2.692551 2b
0.00084(25)
9.8(3.3)
0.065
0.051
0.053
a
Values in parentheses are 3 errors.
Held fixed to value determined in preliminary fit.
b
where B0 is the unperturbed, ‘true’ value of the
rotational constant and B is the observed value. If the
assumption is made that B0020 0 ¼ B02 2 0 ¼ 3941.2 MHz
(a shift of 19.1 MHz from the observed B value of the
(0200) state), then B0100 ¼ 3877.5 MHz, a value smaller
than the (000) rotational constant, which would result in
1 4 0. Table 3 shows that, in fact, several of the other
fitted constants appear to reflect mixing of the (100) and
(0200) states, including and D. Using the deperturbed
value of B0100 , 01 is approximately 18.1 MHz, and
B~ 0e 3878.06 MHz.
The vibrational frequencies of the heavy-atom stretch
and bending modes can be roughly estimated from the
molecular constants determined in this study. Assuming
that CrCN is a pseudo-diatomic species, with the CN
group behaving as a single atom, the stretching frequency
can pbe
calculated from the Kratzer relation,
ffiffiffiffiffiffiffiffiffiffiffiffiffiffi
!1 4B3e =D. The value for CrCN thus derived is
!1 423 cm1, consistent with those of other transition
metal cyanides, which fall in the range 418–491 cm1 (see
table 5). The bending frequency, !2, can be estimated
from the l-doubling term q via the equation [36]:
X 2!2 2B 2
2i 2
q e 1þ4
ð8Þ
i !2 !2
!2
i
2
The summation (4) is the Coriolis term, which is
usually approximately equal to 0.1–0.3 for triatomic
species [36, 37]. The bending frequency is thus calculated
to be !2 ¼ 201–235 cm1, again similar to other
cyanides. The heavy-atom stretch is therefore approximately twice the bending frequency, as the relative
intensities of the satellite lines suggest, consistent with
the Fermi resonance hypothesis.
5.2. Fine structure interactions and vibronic effects
The value of , the spin–spin parameter, is relatively
small in the ground vibrational state of CrCN – on the
order of 600 MHz for all isotopologues. However, in
the bending mode, the spin–spin constant steadily
increases with vibrational excitation, such that in v2 ¼ 5,
¼ 4070 MHz. The one exception is the (0200) state,
which interacts with the (100) state via Fermi resonance.
In these two cases, appears to be larger than expected in
the (100) state, and smaller than expected in the (0200)
level – indicative of mixing. In contrast, the spin–rotation
parametre appears to be fairly constant across all levels,
with 36 MHz. The effects can be understood in terms
of the second-order contributions of H^ so and H^ rot to the
fine structure interactions.
The value of the spin–spin parameter is determined
by first-order microscopic electronic effects and secondorder spin–orbit interactions with energetically remote
perturbing electronic states [38]. In heavy transition
metal compounds, it is usually assumed that the secondorder spin–orbit contribution is dominant [25]. This
contribution to is defined as [39]:
30ð2S 2Þ! X X
½3 2 SðS þ 1Þ
ð2Þ
n ¼
n0 0 0
ð2S þ 3Þ!
hn0 0 S0 0 jHso jnSi 2
ðEn En0 Þ
ð9Þ
where the summation is over all electronic states that can
interactP by the one-electron spin–orbit operator,
H^ so ¼ i ai l^i s^i . In this case, jn S 4 is the ground
electronic state, and jn0 0 S0 0 4 represents excited
0.057
5.541(11)
0.0000221(15)
0.238(88)
0.181
2.2753158b
6.8532258b
0.000114(77)
b
0.070
0.1493737b
0.101
0.7869009b
0.000111(92)
0.0974(79)
0.0000085(10)
(0220)
3941.1809(40)
0.00161247(52)
37.14(30)
0.000034(25)
1270(77)
0.0126(16)
0.00000146(20)
0.043
2.4701610b
0.000175(60)
(0330)
3964.7201(44)
0.00169913(63)
38.15(33)
0.000085(30)
2122(68)
0.0396(19)
0.00000408(27)
0.076
500(300)
(0440)
3 988.837 9(74)
0.0017917(10)
38.97(56)
0.000133(48)
3780(160)
0.143(57)
0.000027(16)
0.0000000018(15)
Spectroscopic constants of CrCN (X 6þ, v 4 0) in MHz.a
(0200)
3922.1406(78)
0.0020547(10)
37.08(65)
0.000078(55)
808(73)
0.00218(18)
Values in parentheses are 3 errors.
Held fixed to value from preliminary fit.
c
For (0220), parametres are qeff and qD,eff. See text.
a
B
D
D
D
H
L
s
D
qc
qcD
p
rms
(0110)
3918.1273(56)
0.00152462(74)
36.811(84)
0.00003b
870(110)
0.00321(25)
Cr12CN
(100)
3896.5799(57)
0.00100070(79)
35.852(42)
0.0000212b
759(50)
0.00733(13)
52
Table 3.
0.108
0.105(21)
580(430)
(0550)
4 013.570(16)
0.0018909(24)
38.96(25)
0.000133b
4070(300)
0.1308(70)
0.0000134(10)
Cr12CN
5.471(41)
0.0000207(58)
0.22(11)
0.180
6.3442509b
(0110)
3895.109(20)
0.0015077(29)
36.58(10)
0.00003b
810(130)
0.00303(30)
53
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592
M. A. Flory et al.
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The pure rotational spectrum of CrCN (X 6Sþ )
electronic states. The spin–orbit operator connects states
via the selection rules S ¼ 0, 1, ¼ 0, and
¼ ¼ 0,
1. The excited states that therefore
are relevant for CrCN (X 6þ) are 4, 4, 6, 6, 8
and 8. The octet states and the 6 states require the
Table 4.
Molecule
CrCN
r0
rs
rð1Þ
m
CoCNa
r0 (¼4)
NiCNb
r0
r0 (¼5/2)
rs (¼5/2)
rð1Þ
m (¼5/2)
CuCNc
r0
rs
rð1Þ
m
ZnCNd
r0
rs
rð1Þ
m
Structures of 3d metal cyanides.
rMC (Å)
rCN (Å)
2.02317(83)
2.0216(22)
2.019e
1.1529(12)
1.1495(35)
1.148e
1.8827(7)
1.1313(10)
1.8281(6)
1.8293(1)
1.8292
1.8263(9)
1.1580(8)
1.1590(2)
1.1534
1.152(1)
1.83231(7)
1.83284(4)
1.8358
1.1576(1)
1.15669(3)
1.1573
1.9545
1.9525
1.9496
1.1464
1.1434
1.1417
a
Ref. [17].
Ref. [18].
c
Ref. [6].
d
Ref. [7].
e
For rð1Þ
m structure, cb ¼ 0.063.
b
Table 5.
a
3 868.516(35)
3 868.987(28)
0.942(20)d
31.139(22)
4.4737(58)
4.7517(44)
423
201235
Ref. [18].
Ref. [6].
c
Ref. [7].
d
(100) state perturbed by Fermi resonance: see text.
e ~0
Be ¼ Be (1 þ 3)/2.
f
From ab initio calculation [14].
b
excitation of core electrons, so they are likely to be very
high in energy. Furthermore, H^ so can only connect states
that differ by at most one spin–orbital. The nominal
molecular configuration of the X 6þ state is 22 1.
Based on rare earth monoxides and monohalides, the orbital is likely to be strongly 3d/4s hybridized.
Therefore, viewing chromium cyanide as CrþCN, the
electronic structure of Crþ is a mixture of d5 and d4s
atomic configurations. Consequently, the H^ so operator
can connect 6þ to four isoconfigurational 4 states,
eight 4 states, and a single 6 state. These states all
potentially can contribute to the value of (2). However,
the energies of these states are not known in CrCN,
although several are predicted to lie less than 15 000 cm1
in energy above the X 6þ ground states in CrF and CrCl
[40]. Nevertheless, the spin–orbit matrix elements of
equation (9) can be evaluated, establishing relative
contributions of the lowest-lying 4, 6, and 4 states.
For a 6þ term, jj takes on the values 5/2, 3/2, and
1/2. Via the ¼ 0 selection rule, interaction with the
4 states occurs for jj ¼ 3/2 and 1/2. For the 4 and
6
states, jj ¼ 5/2, 3/2 and 1/2 components are the
interacting partners. Therefore, the 4 states only
affect the jj ¼ 3/2 and 1/2 spin components of the
ground state, while the 4 and 6 states also influence
the ¼ 5/2 sub-state. (Note that jj ¼ jj þ and can be negative. The ¼ 0, 1 selection rule, however, eliminates interaction of the jj 5 0 sublevels
between the states concerned.) Consequently, an evaluation of the perturbation-induced shift of the ¼ 5/2 substate relative to the ¼ 3/2 sub-state should give an
indication of the respective contributions, noting that
Vibrational parameters of 3d cyanide species in MHz.
CrCN
B~ e
0
B~ e
1
2
22
ll
!1
(cm1)
!2
(cm1)
593
NiCNa
CuCNb
4 307.4626(12)e
4 203.283(32)
22.3746(5)
21.482(25)
0.2129(40)
491
478
241f
270
ZnCNc
3 840.505(50)
3 835.6644(12)e
9.681(21)
31.5974(6)
2.1778(4)
2.4029(10)
418
212
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594
M. A. Flory et al.
E5=2 E3=2 ¼ 8. Using second-order perturbation
theory:
8 ¼ E5=2 E3=2
(
)
XjHso j6 5=2 2 X0 jHso j6 3=2 2
X
¼
X,X0
E5=2 E0
E3=2 E0
ð10Þ
0
4
6
4
4
where X ¼ 3/2, 3/2 and 3/2, and X ¼ 5/2 and
6
5/2.
To evaluate the matrix elements, it is assumed that ai in
1
for the states originatH^ so is equal to a(Crþ
3d ) ¼ 224 cm
5
ing from a d configuration. Using Slater determinantal
wavefunctions, the matrix elements can be evaluated:
2 2
6 þ
2
ðIÞjH
j
4j
¼
a ¼ 20 070 cm2
j54 so
3=2
3=2
5
8 2
6 þ
2
j5 4 ðIIÞjH
j
4j
¼
a ¼ 80 280 cm2
so
3=2
3=2
5
3 2
2
j5 4 II5=2 jHso j6 þ
>j
¼
a ¼ 75 260 cm2
5=2
2
9
2
j5 4 3=2 jHso j6 þ
4j
¼
a 2 ¼ 45 160 cm2
3=2
10
ð11Þ
Here, 4(I) and 4(II) indicate the 2(3)2(1þ)
and 2(1þ)2(3) arrangements of the d5 configuration. The matrix elements involving j5 6|Hsoj 6þ4j2
are not as easy to calculate because 6 arises partly from
a d4s1 configuration. They can, however, be left in the
form:
56 jHso j6 þ
4
6
and 4 states, while 4 gives a net negative
contribution. The end result is that is almost
completely cancelled in the ground state. This cancellation is accidental, certainly not a consequence of any
symmetry rule. In fact, is at least an order of
magnitude smaller than in CrH, CrF, or CrCl
(6980 MHz, 16160 MHz, and 7990 MHz, respectively)
[24, 41, 42].
The increase in with vibrational excitation must
result from reduced or increased interaction with one of
these three types of excited states. One possibility is that
the contribution of the 6 state increases, raising the
value of . This hypothesis can be tested by examining
the value of , the spin–rotation constant. In analogy
to , this parametre consists of a first-order true
spin–rotation interaction and a second-order effect,
which arises from cross terms between H^ rot and H^ so .
For heavier molecules, the second-order term dominates. In contrast to , only the 6 state can contribute
to because the operator H^ rot ¼ BL^ requires the
selection rule S ¼ 0. However, is small for CrCN and
does not appreciably change with vibrational excitation,
as previously mentioned. Therefore, perturbations of the
ground state by the 6 state cannot be increasing with
v2 quantum number, and the 6 term is an unlikely
culprit to explain the unusual behaviour of . Assuming
that the major contribution to is the second-order
spin–orbit coupling, the energy of the 6 state can be
estimated from the following expression [38]:
where Hso and Hrot simplify to AL–Sþ and BJ–Lþ.
Calculating the individual matrix elements and
rearranging this equation in terms of gives:
¼ 56 j½ALþ S j6 þ
4
6
6
ð2Þ ¼
þ
¼ ½5 jjALþ jj 4
B aðCrþ 3dÞ 0:271
E
ð14Þ
5S ¼ 5=2, ¼ 1jS jS ¼ 5=2, ¼ 4
¼ ½51=2 5 ¼ 1jalþ j ¼ 04
½35=4 ð 1Þ1=2 :
E
ð2Þ D6 þ 5=2 J S6 þ
3=2 ¼
2
ð12Þ
hD
6
6
þ
5=2 jHso j 5=2
ED
6
Assuming B B ¼ 0.132 cm1 and (2) ¼ obs ¼
0.0012 cm1, then E 6 500 cm1 – far larger than
the estimated 1000 cm1 of the proposed perturber.
E D
ED
Ei
6 þ
6
6
5=2 jHrot j6 þ
3=2 jHso j6 þ
3=2 þ 5=2 jHrot j 3=2
3=2
If the very rough approximation is made that the ¼ 0
orbitals in both the 6 and 6þ states are of the 4s/3d
hybridized form (i.e. j 4 ¼ 21/2[js 4 jd 4 ]),
then 5 65/2jHsoj 6þ5/2 4 ¼ 194 cm1. Assuming that
the remote perturbers of the X 6þ state lie at
approximately the same energy above the X 6þ state,
summing over these matrix elements results in an overall
positive contribution to (or E5=2 E3=2 ) from the
ð13Þ
E
Evaluation of matrix elements inP equation (13)
required the approximation of L ¼ i li in the Cr
atomic orbital basis set (j 4 ¼ 21/2[js 4 jd 4 ]).
This approximation is extremely
poor [43], in contrast
P
aðr
Þl
to the situation for the
i i spin–orbit matrix
i
elements. The a(ri) operator is sharply peaked at the Cr
nucleus, making it a good approximation to evaluate
spin–orbit matrix elements in the atomic orbital basis
[38]. The Hrot operator (which includes BJþli), on the
other hand, is defined with respect to a coordinate
system with origin at the molecular center of mass. For
CrCN, the molecular center of mass is far from the Cr
nucleus, grossly violating the pure precession hypothesis, which can only be expected to be valid for MH
molecules.
A contribution from the 4 state that decreases with
excited bending would also produce the observed result
in . This decrease could occur via a spin–orbit vibronic
coupling effect embodied in the h parametre described
for 2–2 systems by Mishra, Domcke and Poluyanov
[44]. The 6þ and 4 states in CrCN appear to be
relatively close in energy, even closer with increasing v2
quantum number, and could be relativistically coupled
by the degenerate bending mode. Furthermore, the h
parameter is second-order in the bending coordinate and
should increase linearly with vibrational excitation.
A v2-dependent pattern similar to that of is found in
the fourth-order spin–spin interaction term , although
this constant is not as nearly well-determined. In the
ground and lower vibrational states, is small, –6 to
2 MHz. This value of is comparable to values found
for CrH, CrF, and CrCl, which range from 2.3 to
4.8 MHz [42, 45]. However, for the v2 ¼ 4 and 5 states,
this constant increases suddenly to 600 MHz.
The term results from the fourth-rank
tensor operator T4(S4), which generates interactions
of the ground 6þ state with nearby 6 , 4 , and 4
states. The sudden ‘turn-on’ of at the v2 ¼ 4 and 5
states is probably due to a low-lying excited state,
which is nearly degenerate with the v2 ¼ 5 level.
This state may also be responsible for the
abrupt need for s, suggesting that the perturber is a
4 state.
5.3. Trends in 3d transition metal cyanides/isocyanides
Predicting the geometries of 3d metal cyanides and
isocyanides has been somewhat problematic for theory
(see [13, 16]). Thus far, all known species have had the
M–CN linear structure as the most stable isomer, with
the exception of iron, where optical data indicate that
the FeNC geometry is lower in energy. Some qualitative
predictions could be derived from comparison of the 3d
cyanides with the corresponding halides. To this end, the
M–C bond lengths of the cyanides have been plotted
along with those of the transition metal fluorides and
chlorides, as shown in figure 5. The r0 bond lengths are
used because of limited structural data for the cyanides.
(Note that r0 of CoCN is r0(¼4) and thus is slightly
longer than the true r0.) For FeNC, the experimentally
determined Fe–N bond distance is plotted, as well as the
2.3
2.2
Bondlength (Å)
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The pure rotational spectrum of CrCN (X 6Sþ )
1Σ
4Φ
595
5∆
6Σ
6∆
Chlorides
3Φ
2.1
2.0
7Σ
FeCN
( )
Cyanides
2Σ
2Π
1Σ
FeNC
1.9
1.8
Fluorides
1.7
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Cu
Zn
Figure 5. The metal–carbon bond lengths of 3d transition
metal cyanides (r0) plotted with those of the chloride and
fluoride analogues (r0). For iron, both the experimentally
measured Fe–N bond distance for FeNC and the calculated re
(Fe–C) for FeCN are shown on the graph. (The r0 bond
distance for CoCN is based only on ¼ 4, and is therefore
longer than the true r0.) Despite an incomplete data set, a trend
in bond distance exhibited for the cyanides is similar to that
seen in the halide species. There are subtle differences,
however, because in the cyanides, the metal d electrons can
interact with the CN empty antibonding orbitals – a feature
unavailable in the halides.
theoretical Fe–C bond length of FeCN [13, 19]. To a
first order approximation, the behaviour of the metal–
carbon bond length for the cyanides across the 3d row
appears to follow that of the halides. This property
suggests some similarity in the bonding of these types of
species.
On the other hand, the metal cyanide species do differ
from the analogous halides. Calculations of crude
orbital energies, based on observed ionization potentials, suggest that the 2 and 6 orbitals in CN lie
approximately 72 000 cm1 and 65 000 cm1 below the
ionization limit, respectively. These orbitals are antibonding in CN and are polarized towards the carbon
atom. The 3d and 4s orbitals on chromium lie about
67 000 cm1 and 55 000 cm1 below the ionization limit.
Because of the relatively close energies, a -bonding
interaction could occur between the Cr(3d) and
CN(2) orbitals that stabilizes the 3d relative to the
3d and 3d orbitals. The 3d electrons become
delocalized into the CN 2 orbital, thus increasing the
bonding interactions between the carbon and chromium
atoms. The additional metal-carbon bonding may
explain why the linear CrCN structure is preferred.
The 3d2 interaction should destabilize the C–N
bond, while stabilizing the Cr–C bond. As a result, the
C–N bond distance should lengthen and the Cr–C bond
should shorten. Yet, it appears that the opposite is
occurring: the C–N bond is anomalously short, while the
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596
M. A. Flory et al.
Cr–C bond appears to be unusually long. As mentioned,
the C–N bond appears to be unexpectedly short in
several cyanide species, probably as a result of large
amplitude bending motions within a very shallow
potential well [16]. As discussed by Hirano et al. [16]
for FeNC, the CN moiety ‘wags’ about the linear
molecular axis relative to a centroid located roughly at
the CN centre of mass. This motion also causes
the effective Fe–N bond distance to lengthen, or in
CrCN, the Cr–C bond. Hence, the actual bond
lengths may be consistent with the proposed bonding
picture.
Stabilization of the 3d and 3d orbitals through
delocalization into empty or ligand orbitals cannot
occur in CrF or CrH. Such stabilization could account
for what appear to be low-lying 4 and 4 states
in CrCN. In CrF, the lowest lying 4 state is
located 12 000 cm1 in energy above the ground state
[40] – considerably higher than the energy estimated
for the perturbers in CrCN (1000 cm1).
Genuine insight into the bonding in chromium
cyanide clearly requires additional information, which
can be obtained through ab initio calculations and
further experimental measurements. In particular, low N
microwave data would be useful because they would
enable resolution of 53Cr, 13C, and 14N hyperfine
interactions. Such interactions cannot be seen at high
N, where J~ and F~ are nearly parallel, and the selection
rule J ¼ F ¼ N ¼ þ 1 dictates the strongest
transitions. From the hyperfine structure, orbital
compositions for all three atoms could be established.
For example, the 4s character of the chromium atom
could be evaluated, indicating the degree of s d
hybridization. From the dipolar constant for 13C, the
3d–2 interaction could be quantified. In addition,
measurements of electronic transitions would provide
information on the excited state manifold and possible
perturbing states.
6. Conclusions
This study of the CrCN radical has demonstrated that
the linear cyanide structure is the lowest energy isomer,
and that the ground state is X 6þ. The cyanide
geometry thus appears in at least one of the earlier,
more electropositive 3d metal monocyanides.
The preference for the cyanide structure may result
from increased stability from delocalization of the 3d
orbitals into to the empty CN antibonding orbital,
which is primarily carbon in nature. The spin–spin
interaction in the ground vibrational state of CrCN
appears to be small, although the fourth-order spin–spin
coupling term was clearly needed to fit the data.
The second-order spin–orbit contributions from excited
and 4 states appear to cancel each other, resulting
in a small value for . In the excited vibrational states of
the bending mode, increases with v2 quantum number.
This effect is likely due to decreased second-order
spin–orbit interactions with the 4 state, perhaps
attributable to relativistic spin–orbit vibronic coupling
via the degenerate bending mode. The spin–rotation
coupling, on the other hand, is small and does not
appreciably change with vibrational excitation, suggesting minimal interactions with a 6 state that lies
higher than 6 500 cm1 in energy. The appearance
of low-lying perturber states may result from
stabilization of the 3d orbitals, an option not available
for CrF or CrH.
4
Acknowledgements
The authors wish to thank J. M. Brown for use of his
Hund’s case (b) fitting program. This work was funded
by NSF Grants CHE-04-11551 and AST-06-07803
(LMZ) and CHE-04-050876 (RWF).
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[3] D. Shriver and P. Atkins, Inorganic Chemistry, 3rd edn
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