JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 17
1 NOVEMBER 2004
Characterizing the later 3 d cyanides: The submillimeter spectrum
of CoCN„ X 3 ⌽ i …
P. M. Sheridan, M. A. Flory, and L. M. Ziurysa)
Department of Chemistry, Department of Astronomy, and Steward Observatory, University of Arizona,
Tucson, Arizona 85721
共Received 14 June 2004; accepted 19 July 2004兲
The pure rotational spectrum of the CoCN radical has been recorded in the frequency range 350–
500 GHz using direct absorption techniques. This study is the first spectroscopic observation of this
molecule by any experimental technique. Spectra of Co 13CN have been measured as well. These
data indicate that this species is linear in its ground electronic state and has the cyanide, as opposed
to the isocyanide, geometry. The ground state term has been assigned as 3 ⌽ i , based on the
measurement of three spin components 共⍀⫽4, 3, and 2兲 and in analogy to other isovalent
cobalt-bearing species. Hyperfine splittings resulting from the 59Co nuclear spin of I⫽7/2 were
observed in every transition, each of which exhibited an octet pattern. For the lowest energy spin
component, ⍀⫽4, vibrational satellite features were also identified arising from the first quantum of
the Co-C ( v 1 ⫽1) stretch and the v 2 ⫽1 and v 2 ⫽2 quanta of the bending mode, which were split
by Renner-Teller interactions. The ground state measurements of CoCN were analyzed with a case
a ␤ Hamiltonian, establishing rotational, fine structure, and hyperfine parameters. The vibrational
and Co 13CN spectra for the ⍀⫽4 component were fit as well. An r 0 structure was also calculated,
providing estimates of the Co-C and C-N bond distances, based on the ⍀⫽4 transitions. CoCN is
the fourth molecule in the 3d transition metal series to exhibit the linear cyanide structure, along
with the Zn, Cu, and Ni analogs. The preference for this geometry, as opposed to the isocyanide
form, may indicate a greater degree of covalent bonding in these species. © 2004 American
Institute of Physics. 关DOI: 10.1063/1.1791091兴
be ZnCN(X 2 ⌺ ⫹ ) and CuCN(X 1 ⌺ ⫹ ), i.e., linear cyanides.
Laser-induced fluorescence studies of NiCN(X 2 ⌬ i ) by
Kingston, Merer, and Varberg showed that this radical in its
ground state also exhibited the linear cyanide geometry,13 as
confirmed by the measurement of the pure rotational
spectrum.14 Unfortunately, the remaining transition metal
cyanides/isocyanides have received almost no attention, either theoretically or experimentally. Cobalt cyanide, in particular, is of interest because it lies between NiCN, a cyanide,
and FeNC, an isocyanide; hence, its ground state structure is
highly speculative.
Unfortunately, most spectroscopic studies of cobaltbearing molecules have been limited to diatomic species.
Electronic spectra of CoH, CoO, CoC, CoF, and CoCl have
been recorded, for instance,15–20 and pure rotational measurements of these species have been conducted as well, using millimeter direct absorption methods21–24 and laser magnetic resonance.25 In many of these cases, large hyperfine
interactions due to the cobalt nuclear spin of I⫽7/2 were
observed. Also, assignment of the ground electronic state for
some species has been problematic because of the presence
of many close-lying terms 共e.g., see Ref. 24兲.
As part of an ongoing study of the 3d cyanide/
isocyanide series, we have recorded the pure rotational spectrum of CoCN. Based on the observation of three apparent
spin components, and in comparison with spectra of CoCl,24
the ground electronic state has been assigned as X 3 ⌽ i . In
I. INTRODUCTION
Triatomic molecules consisting of a metal atom and the
cyanide group exhibit an interesting range of geometries.
Three distinct structures have been observed for these species so far. The sodium and potassium cyanides, for example,
have a T-shaped geometry where the metal ion M ⫹ orbits the
CN⫺ moiety in a highly ionic, polytopic bond.1,2 In contrast,
lithium, the alkaline earth metals, and the IIIA Group 共aluminum, gallium, indium兲 are found to possess the linear isocyanide structure in which the metal forms a directional bond
with the nitrogen atom.3– 6 This structural change is thought
to arise from an increase in covalent character.7,8 The linear
cyanide geometry, where the metal bonds to the carbon end
of the CN group, has only been encountered as a higher
energy isomer9 until the very recent studies of the transition
metal analogs.
The first transition metal species of this class investigated by high-resolution gas-phase spectroscopy was
FeNC.10 Using laser-induced fluorescence, Lie and Dagdigian observed the ⍀ ⬘ ⫽7/2→X(⍀ ⬙ ⫽9/2) electronic transition of the main and 13C-substituted isotopomers. These authors concluded that FeNC was linear and an isocyanide.
Millimeter-wave investigations of the zinc and copper analogs followed shortly thereafter, conducted by our group. We
measured the pure rotational spectrum of both species11,12
and unambiguously established the ground state structures to
a兲
Fax: 1-520-621-1532. Electronic mail: [email protected]
0021-9606/2004/121(17)/8360/9/$22.00
8360
© 2004 American Institute of Physics
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J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
addition to the three spin sublevels 共⍀⫽4,3,2兲, rotational
transitions arising from several vibronic states were observed. Rotational lines of the Co 13CN isotopomer were also
recorded, which have enabled the ground-state geometry to
be established. In this paper we present these data and their
spectroscopic analysis, as well as discuss the structure and
bonding in CoCN relative to other 3d cyanides.
II. EXPERIMENT
The pure rotational spectrum of CoCN was recorded using the high temperature millimeter/submillimeter spectrometer of the Ziurys group.26 Briefly, this instrument consists of
a Gunn oscillator/Schottky-diode multiplier source 共65– 650
GHz兲, a water-cooled, steel reaction chamber containing a
Broida-type oven, and an InSb bolometer detector. Offset
ellipsoidal mirrors are used to direct the radiation through the
reaction cell, a double-pass system, and a pathlength modulator is employed for baseline stabilization. The radiation is
frequency modulated at 25 kHz and is detected at 2 f using a
lock-in amplifier.
The CoCN radical was synthesized by the reaction of
cobalt vapor, produced in the Broida-type oven, with pure
cyanogen gas. Initially, 15–20 mTorr of (CN) 2 were passed
into the reaction chamber from underneath the oven. Unlike
our previous syntheses of transition metal cyanides 关see
Refs. 11 and 12兴, more intense signals were observed if the
reactant gas was introduced through a steel tube over the top
of the Broida oven. Neither a dc discharge nor a carrier gas
such as argon was needed, as they did not improve signal
strength. In order to produce the 13C isotopomer, H 13CN was
substituted for the cyanogen. This species had to be synthesized because it was not commercially available. H 13CN was
produced by reacting an aqueous solution of Na 13CN with
H2 SO4 . The resulting gaseous mixture was then distilled by
passing it through CaSO4 and P2 O5 drying traps, and the
H 13CN product collected in a liquid nitrogen-cooled flask.
To create Co 13CN, 10–15 mTorr of pure H 13CN was added
over the top of the oven, but a dc discharge of 0.2 A at 200 V
was required for the synthesis.
Final transition frequencies of CoCN and Co 13CN were
determined by averaging two scans, one in decreasing and
the other in increasing frequency, each 5 MHz in width. For
the weaker features, up to five such scan pairs were found to
be necessary for the measurements. Each line was fit with a
Gaussian profile in order to determine the center frequency.
Typical linewidths ranged from 800 kHz at 350 GHz to 1400
kHz at 500 GHz.
III. RESULTS
Because no previous spectroscopic information existed
for CoCN, an extensive search in frequency space 共of ⬃30
GHz in coverage兲 was conducted in order to locate rotational
transitions arising from this molecule. In the course of the
search, a weak octet was observed that suggested the presence of an open shell molecule containing cobalt (I⫽7/2).
Additional harmonically-related octets were then located
which required integer rotational quantum numbers, indicating an odd spin multiplicity of S⭓1. 共A state with S⫽0 was
Spectrum of CoCN
8361
not likely because it would not produce a pattern of eight
almost equally spaced lines.27兲 The B value 共⬃4 GHz兲 obtained for this set of octets was also found to be similar to
those of other transition metal cyanides. Therefore, these features were attributed to CoCN or CoNC. After 30 GHz of
searching, eight groups of harmonically related octets were
identified.
Based on similar cobalt radicals such as CoH(X 3 ⌽ i ),
CoF(X 3 ⌽ i ), and CoCl(X 3 ⌽ i ), 15–18,24 the ground state of
CoCN was likely to be 3 ⌽ i . In this term, three fine structure
components arise, labeled by quantum number ⍀, where
⍀⫽⌳⫹⌺. In an inverted state, the ⍀⫽4 sublevel lies lowest
in energy. Therefore, the most intense group of octets observed for CoCN was initially assigned as the ⍀⫽4 spin
component. The vibrational progression of this sublevel was
then identified. Based on our previous spectroscopic studies
of ZnCN, CuCN, and NiCN,11,12,14 the bending mode ( v 2 ) of
CoCN should lie quite low in energy 共⬃200–300 cm⫺1兲, and
thus vibrational satellite features arising from several quanta
should be observable. For a linear triatomic molecule in a 3 ⌽
state, the bending vibrational levels are subject to RennerTeller coupling,28,29 where the vibrational 共l兲 and electronic
orbital 共⌳兲 angular momenta add to form the total momentum K (l⫹⌳⫽K). Such vibronic components are labeled by
K P , where P⫽K⫹⌺. For the v 2 ⫽1 level in a 3 ⌽ term, two
Renner components result ( 3 ⌫ and 3 ⌬), and for the v 2 ⫽2
state, three arise ( 3 H, 3 ⌽, and 3 ⌸). This progression will
occur for each ⍀ sublevel. In addition to the bending mode,
rotational transitions arising from the metal-carbon stretch
may also be present, as has been observed in ZnCN 共Ref. 12兲
and NiCN.14
In the spectra, two octets of similar intensity were observed ⬇2 and 3 GHz to higher frequency of the ⍀⫽4 spinorbit component. In ZnCN, CuCN, and NiCN, satellite transitions arising from the v 2 ⫽1 state were found to be located
at a similar frequency spacing from the ground state.11,12,14
As a result, these octets were identified as the two Renner
components of the v 2 ⫽1 level of the ⍀⫽4 ladder. Furthermore, the two octets did not exhibit any evidence of P-type
doubling. This interaction usually is not found in ⌬ and ⌫
vibronic states, but is present in ⌸ states, such as the
2
⌸ 3/2 ( v 2 ⫽1) vibronic component in NiCN.14 The 3 ⌫ 5 and
3
⌬ 3 terms were then tentatively assigned based on the positions of these features in the spectrum. Two additional
weaker octets were observed ⬇5– 6 GHz higher in frequency
relative to the ⍀⫽4 line, which had to arise from the v 2
⫽2 vibronic level. They were given tentative assignments as
the 3 H6 and 3 ⌸ 2 Renner components. 共The ‘‘missing’’ component is most likely the 3 ⌽ 4 state, because it can be shifted
by Fermi resonance interactions with the v 1 ⫽1 state, the
metal-carbon stretch, which has the same P value.兲
The remaining three octets were located between the
⍀⫽4 spin component and the v 2 ⫽1 vibronic sublevels. One
of the three had an effective B value less than that of the
⍀⫽4 ladder of the ground state; however, at higher J, this
feature moves to the higher frequency side of the ⍀⫽4 spin
component because of its smaller centrifugal distortion constant. Furthermore, the hyperfine splitting in this octet was
very similar to the ⍀⫽4 lines, suggesting it arose from the
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8362
J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
FIG. 1. A stick spectrum of the J⫽45←44 rotational transition of
CoCN(X 3 ⌽ i ) near 380 GHz. For simplicity, each hyperfine octet is represented by a single feature with its approximate relative experimental intensity. Several obvious patterns emerge in this diagram: one is the progression
of the three spin components of the ground vibrational state, labeled by ⍀,
located at the low frequency end of the spectrum. Also visible is the vibrational progression of the v 2 bending mode. The v 2 ⫽1 lines and the v 2 ⫽2
features lie approximately 2.5 GHz and 5 GHz to higher frequency, respectively, of the ground state. These states are split into Renner components
共the vibronic assignments are tentative兲. Also present in the spectrum is a
line arising from the v 1 ⫽1 metal-carbon stretching mode, which lies close
to the ⍀⫽4, v ⫽0 transition and may be shifted by Fermi resonance interactions.
metal-carbon stretch, in analogy to CoCl.18,24 Also, the
stretching mode has 3 ⌽ 4 symmetry, and therefore can interact with the v 2 ⫽2 ( 3 ⌽ 4 ) component via Fermi resonance, as
has been observed in NiCN.13 Partial mixing of the rotational
constants of these two interacting states would then shift
lines originating from the stretching vibration closer in frequency to the ground state features, as is apparently observed.
The remaining two octets were assigned to be the ⍀⫽3
and ⍀⫽2 ladders of the ground vibrational state. They are
close to being regularly spaced in frequency relative to the
⍀⫽4 line, in an approximate case 共a兲 type pattern. Moreover,
their intensities relative to the ⍀⫽4 transitions are consistent
with a spin-orbit splitting of A⫽⫺4000 GHz 共⫺133 cm⫺1兲,
as is found for CoCl and CoH.24,25 The ⍀⫽3 lines, for example, are the second strongest octets in the data. Moreover,
in similar studies of molecules such as CoCl(X 3 ⌽ i ) 共Ref.
24兲 and FeCl(X 6 ⌬ i ), 30 all spin components were identified
in the rotational spectra; CoCN should be no different.
The spectrum of Co 13CN was located by scanning continuously over several gigahertz in frequency. The search
was carried out over a range that included the predicted frequencies of the ⍀⫽4 component of both Co 13CN and
CoN13C. Only one weak octet was detected over this region,
and then harmonically-related transitions were subsequently
found. The rotational constants obtained from this progression were consistent with a Co 13CN principal structure, not
CoN13C.
In Fig. 1, a stick figure of the features recorded for the
J⫽45←44 transition near 378 –383 GHz for CoCN is pre-
Sheridan, Flory, and Ziurys
FIG. 2. Spectrum of the three spin components of CoCN(X 3 ⌽ i ) in the J
⫽45←44 rotational transition near 378 GHz, each labeled by ⍀. There are
two frequency gaps in the spectrum with separations of ⬃500 MHz. Each
component is additionally split into eight hyperfine lines arising from the
59
Co nuclear spin (I⫽7/2). The splitting varies for the individual ⍀ components. Unidentified lines are marked by asterisks. The spectrum is a compilation of three scans, each 60 MHz wide and 1 min in duration.
sented. Each octet is indicated by a single line with its approximate relative intensity. The strongest feature naturally
belongs to the ⍀⫽4 spin-orbit component, located lowest in
frequency, followed by those of the ⍀⫽3 and ⍀⫽2 sublevels, which lie about 600 MHz and 1.2 GHz to higher frequency and uniformly decrease in intensity. The two Renner
components of the v 2 ⫽1 state, 3 ⌫ 5 and 3 ⌬ 3 , lie ⬃2 GHz
higher in frequency from the ground state line, and about 2
GHz from these features lie the v 2 ⫽2 octets. The weaker
line located ⬃100 MHz higher in frequency relative to the
⍀⫽4 component is the v 1 ⫽1 ( 3 ⌽ 4 ) stretch.
Representative spectra for CoCN are given in Figs. 2 and
3. In Fig. 2, the ⍀⫽4, 3, and 2 spin components of the J
⫽45←44 transitions near 378 GHz are shown. The distinct
octet pattern arising from the cobalt spin is clearly apparent
in each component. 共There are two, ⬃500 MHz, frequency
gaps in the spectrum such that all three spin components can
be shown with sufficient resolution.兲 Lines marked by asterisks are unidentified. The overall spacing within each octet
varies, with the ⍀⫽4 component having the largest splitting
and ⍀⫽3 the smallest. Given a spin-orbit constant of ⫺4000
GHz, or ⫺133 cm⫺1, the line intensities of the three sublevels suggest a rotational temperature of T rot⬇700 K. This
number is consistent with the melting temperature of cobalt
of 1768 K.
In Fig. 3, the ⍀⫽4 component of the J⫽48←47 transition of Co 13CN is shown. Although the signal-to-noise ratio
is rather low, eight lines comprising the cobalt h f octet are
clearly present. The line intensities of the 13C isotopomer are
not as good as the main isotopomer, probably because HCN
was the precursor. Cyanogen appears to be a more effective
reactant material for metal cyanide production.
The transition frequencies obtained for CoCN and
Co 13CN are presented in Tables I and II. As shown in Table
I, eleven, seven, and five rotational transitions were recorded
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J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
Spectrum of CoCN
FIG. 3. Spectrum of the ⍀⫽4 spin component of the J⫽48←47 rotational
transition of Co 13CN near 398.6 GHz. The eight hyperfine components that
comprise this transition are indicated in the spectrum. An unidentified line is
marked by an asterisk. The spectrum is an average of two 100 MHz scans,
each 1 min in duration.
for the ⍀⫽4, 3, and 2, respectively, of the main isotopomer.
Each transition is additionally split into a hyperfine octet, for
which eight individual frequencies were measured, as the
table shows. A total of 174 separate lines were recorded for
CoCN in its ground vibrational state. For Co 13CN, four transitions were observed for the ⍀⫽4 ladder only, but not every
hyperfine frequency was measured.
The frequencies measured for the v 2 ⫽1 and v 1 ⫽1 excited vibrational levels of CoCN can be found in EPAPS.31
For the v 2 ⫽1 state, nine transitions were recorded in the two
Renner components, 3 ⌫ 5 and 3 ⌬ 3 . For the v 1 ⫽1 mode, the
metal-carbon stretch, three rotational transitions were measured. Again, in most cases, eight hyperfine frequencies were
recorded per transition.
IV. ANALYSIS
The data for CoCN(X 3 ⌽ i ) were fit using a case a ␤ basis
with the following effective Hamiltonian:25,32
Ĥ eff⫽Ĥ Rot⫹Ĥ SO⫹Ĥ SS⫹Ĥ MHF ,
共1兲
which consists of rotational, electron spin-orbit, electron
spin-spin, and magnetic hyperfine terms and their centrifugal
distortion corrections. Initially, to fit the ground state data, all
the parameters were allowed to vary. However, because A,
the spin-orbit constant, and ␭, the spin-spin constant, are
highly correlated, large errors were associated with both parameters. Therefore, A was fixed to a range of values and all
other constants were allowed to float, until the best fit was
obtained. In the final analysis, both the rotational and spinorbit terms required several centrifugal distortion corrections. For the spin-spin interaction, in contrast, only ␭ H was
needed, not ␭ D . The hyperfine structure was analyzed with
a, (b⫹c), and a term for the ⍀⫽3 ladder only, h 3D . The
h 3D constant was introduced in the analysis of the pure rotational spectrum of CoH(X 3 ⌽ i ), obtained by laser magnetic
resonance spectroscopy, where it was employed to compen-
8363
sate for systematic errors in the ⍀⫽3 frequencies.25 An
analogous term for the ⍀⫽2 ladder, h 2D , was put in the fit
for CoCN but was not found necessary. The h 3D parameter
arises because the ⍀⫽3 sublevel selectively undergoes perturbations, as suggested by the spin-orbit pattern; this phenomenon will be discussed later. However, neither the b hyperfine term nor the eqQ parameter could be defined in the
analysis; hence, both were not used in the final fit. Based on
the analysis of CoCl,24 the F quantum numbers for the hyperfine structure were assigned in ascending order with decreasing frequency 共see Table I兲. Reversing the order of F
increased the rms of the fit to over 700 kHz, making this
assignment unlikely. The final set of constants for CoCN in
its ground vibrational state determined in this matter is presented in Table III. As shown, the rms of the fit is 286 kHz
for a fit to 174 individual spectral lines.
Aside from the global analysis of the v ⫽0 data, individual fits were carried out for the ⍀⫽4 sublevel of
Co 13CN, the 3 ⌬ 3 and 3 ⌫ 5 vibronic components of the v 2
⫽1 state, and the v 1 ⫽1 level. Here the spectra could only
be fit with rotational parameters and the h ⍀ and h ⍀D hyperfine constants. 共For the vibronic data, the value of P was
substituted for ⍀.兲 For comparison, the ⍀⫽4, 3, and 2 ladders of the ground vibrational state were also fit. These results are given in Table IV. For these data sets, the rms of
each fit is below 100 kHz, except for the ⍀⫽2 data. Also, the
h ⍀ parameter has a value between 1700–1800 MHz for all
the ⍀⫽4 related substates except 3 ⌬ 3 ( v 2 ⫽1), where it increases to 2645 MHz.
V. DISCUSSION
A. Ground state term and geometry
In analogy to CoH, CoF, and CoCl,23–25 the most likely
ground state for CoCN is 3 ⌽ i . Location of the three spin
components that comprise this term and successfully fitting
them in a global analysis are good evidences for this assignment. Moreover, lack of lambda or P-type doubling in any of
the observed transitions indicates a high angular momentum
value for the ground state. Other possible terms such as 3 ⌺
or 5 ⌺ 共Ref. 33兲 are not supported by the data. The electron
configuration for the 3 ⌽ i state is ␦ 3 ␲ 3 .
Based on the spectra from the two isotopomers, CoCN
has been found to have a linear cyanide structure in its
ground electronic state. Hence, this radical follows the trend
of the 3d transition metal cyanides of nickel, copper, and
zinc.11–14 In fact, the ratio of the rotational constants between
the main isotopomer and the 13C species is the same for all
four 3d cyanides. Iron appears to be the 3d element where
the geometry switches back to the isocyanide.10
Bond lengths have been determined for CoCN and are
shown in Table V. Other 3d metal cyanide structures are also
given. Because only rotational transitions arising from the
⍀⫽4 spin component were observed for Co 13CN, a structure could be established only for this sublevel. For the ⍀⫽4
ladder, the r 0 structure yields r M -C⫽1.8827(7) Å and r C-N
⫽1.1313(10) Å. The metal-carbon bond lengths for NiCN
and CuCN are roughly comparable 共1.8281 Å and 1.8323 Å;
see Table V兲, taking into account that the overall mechanical
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8364
J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
Sheridan, Flory, and Ziurys
TABLE I. Rotational transition frequencies of CoCN(X 3 ⌽ i ): v ⫽0 共in MHz兲.
⍀⫽4
⍀⫽3
J ⬘ ←J ⬙
F ⬘ ←F ⬙
v obs
v obs⫺ v calc
v obs
42←41
38.5←37.5
39.5←38.5
40.5←39.5
41.5←40.5
42.5←41.5
43.5←42.5
44.5←43.5
45.5←44.5
352 544.087
352 540.703
352 537.161
352 533.409
352 529.544
352 525.470
352 521.268
352 516.860
⫺0.159
⫺0.181
⫺0.186
⫺0.229
⫺0.214
⫺0.238
⫺0.223
⫺0.247
353 137.467
353 135.010
353 132.455
353 129.711
353 126.625
353 123.889
353 120.835
353 117.468
43←42
39.5←38.5
40.5←39.5
41.5←40.5
42.5←41.5
43.5←42.5
44.5←43.5
45.5←44.5
46.5←45.5
44←43
40.5←39.5
41.5←40.5
42.5←41.5
43.5←42.5
44.5←43.5
45.5←44.5
46.5←45.5
47.5←46.5
369 292.944
369 289.854
369 286.496
369 283.111
369 279.584
369 275.907
369 272.077
369 268.131
45←44
41.5←40.5
42.5←41.5
43.5←42.5
44.5←43.5
45.5←44.5
46.5←45.5
47.5←46.5
48.5←47.5
46←45
⍀⫽2
v obs⫺ v calc
v obs
v obs⫺ v calc
0.089
0.088
0.164
0.222
0.105
0.503
0.744
0.830
353 615.228
353 612.209
353 609.045
353 605.682
353 602.059
353 598.204
353 594.293
353 589.961
0.546
0.624
0.681
0.657
0.486
0.190
⫺0.061
⫺0.638
361 515.121
361 512.504
361 510.335
361 507.778
361 505.055
361 502.193
361 499.258
361 496.197
⫺0.067
⫺0.384
⫺0.090
⫺0.025
0.031
0.101
0.248
0.415
362 009.340
362 006.534
362 003.517
362 000.227
361 996.893
361 993.348
361 989.610
361 985.627
0.001
0.157
0.217
0.115
0.073
⫺0.079
⫺0.331
⫺0.739
0.012
0.006
⫺0.116
⫺0.116
⫺0.109
⫺0.104
⫺0.106
⫺0.080
369 890.716
369 888.309
369 885.979
369 883.590
369 881.158
369 878.432
369 875.608
369 872.734
⫺0.143
⫺0.395
⫺0.419
⫺0.354
⫺0.185
⫺0.168
⫺0.108
0.039
377 665.296
377 662.352
377 659.172
377 655.958
377 652.501
377 649.039
377 645.354
377 641.520
0.087
0.101
0.020
0.045
⫺0.033
0.021
⫺0.012
⫺0.058
378 264.251
378 262.089
378 259.865
378 257.587
378 255.167
378 252.409
378 249.863
378 247.097
⫺0.070
⫺0.214
⫺0.279
⫺0.259
⫺0.245
⫺0.435
⫺0.282
⫺0.221
378 792.706
378 790.129
378 787.525
378 784.768
378 781.733
378 778.519
378 775.310
378 771.813
⫺0.586
⫺0.446
⫺0.232
⫺0.076
⫺0.106
⫺0.228
⫺0.263
⫺0.508
42.5←41.5
43.5←42.5
44.5←43.5
45.5←44.5
46.5←45.5
47.5←46.5
48.5←47.5
49.5←48.5
386 036.199
386 033.330
386 030.293
386 027.388
386 023.957
386 020.713
386 017.119
386 013.470
0.158
0.128
0.062
0.260
0.061
0.179
0.074
0.041
386 633.546
386 631.520
386 629.173
386 626.782
386 624.393
386 622.010
⫺0.069
⫺0.074
⫺0.270
⫺0.382
⫺0.367
⫺0.223
387 181.599
387 179.317
387 176.997
387 174.311
⫺0.869
⫺0.545
⫺0.165
⫺0.061
47←46
43.5←42.5
44.5←43.5
45.5←44.5
46.5←45.5
47.5←46.5
48.5←47.5
49.5←48.5
50.5←49.5
394 405.513
394 402.848
394 399.913
394 396.945
394 393.861
394 390.630
394 387.389
394 383.756
0.137
0.200
0.116
0.121
0.133
0.119
0.214
0.037
395 004.754
395 002.705
395 000.745
394 998.547
394 996.370
394 994.111
394 991.628
394 989.202
0.415
0.135
0.066
⫺0.118
⫺0.162
⫺0.171
⫺0.288
⫺0.235
48←47
44.5←43.5
45.5←44.5
46.5←45.5
47.5←46.5
48.5←47.5
49.5←48.5
50.5←49.5
51.5←50.5
402 773.318
402 770.665
402 767.967
402 765.112
402 762.047
402 759.062
402 755.854
402 752.541
0.157
0.126
0.166
0.164
0.067
0.163
0.148
0.141
403 371.593
403 369.656
403 367.760
403 365.715
403 363.705
403 361.399
403 359.240
403 356.816
0.840
0.557
0.431
0.270
0.257
0.058
0.114
0.011
403 954.584
403 952.289
403 950.218
403 947.697
403 945.270
403 942.701
403 939.963
403 937.134
⫺0.328
⫺0.219
0.196
0.239
0.451
0.593
0.634
0.649
55←54
51.5←50.5
52.5←51.5
53.5←52.5
461 299.671
461 297.528
461 295.349
⫺0.011
⫺0.126
⫺0.200
Downloaded 25 Mar 2005 to 128.196.209.95. Redistribution subject to AIP license or copyright, see http://jcp.aip.org/jcp/copyright.jsp
J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
Spectrum of CoCN
8365
TABLE I. 共Continued.兲
⍀⫽4
J ⬘ ←J ⬙
⍀⫽3
F ⬘ ←F ⬙
v obs
v obs⫺ v calc
54.5
55.5
56.5
57.5
58.5
←
←
←
←
←
53.5
54.5
55.5
56.5
57.5
461 293.307
461 290.976
461 288.754
461 286.410
461 283.775
⫺0.061
⫺0.134
⫺0.024
0.040
⫺0.114
56 ← 55
52.5
53.5
54.5
55.5
56.5
57.5
58.5
59.5
←
←
←
←
←
←
←
←
51.5
52.5
53.5
54.5
55.5
56.5
57.5
58.5
469 652.998
469 650.875
469 648.942
469 646.848
469 644.723
469 642.484
469 640.237
469 637.788
⫺0.078
⫺0.242
⫺0.142
⫺0.131
⫺0.079
⫺0.070
0.002
⫺0.057
57 ← 56
53.5
54.5
55.5
56.5
57.5
58.5
59.5
60.5
←
←
←
←
←
←
←
←
52.5
53.5
54.5
55.5
56.5
57.5
58.5
59.5
478 004.367
478 002.351
478 000.399
477 998.480
⫺0.041
⫺0.162
⫺0.151
⫺0.037
58 ← 57
54.5
55.5
56.5
57.5
58.5
59.5
60.5
61.5
←
←
←
←
←
←
←
←
53.5
54.5
55.5
56.5
57.5
58.5
59.5
60.5
486 353.626
486 351.688
486 349.790
486 347.886
486 345.889
486 343.821
486 341.688
486 339.441
0.011
⫺0.094
⫺0.093
⫺0.034
⫺0.002
0.022
0.046
0.019
59 ← 58
55.5
56.5
57.5
58.5
59.5
60.5
61.5
62.5
←
←
←
←
←
←
←
←
54.5
55.5
56.5
57.5
58.5
59.5
60.5
61.5
494 700.833
494 698.801
494 697.062
494 695.208
494 693.316
494 691.242
494 689.289
494 687.014
0.200
⫺0.058
0.040
0.084
0.152
0.099
0.227
0.094
B value for CoCN derived from all three spin components is
larger 共see Tables III and IV兲. CoCN exhibits the shortest of
the C-N bonds of the 3d metal cyanides, with r C-N
⫽1.1313 Å; NiCN and CuCN have r 0 lengths of 1.1576 –
1.1580 Å, and for ZnCN, r 0 ⫽1.1464 Å. Considering the fact
that r C-N in HCN is 1.1540 Å,6 the C-N bond distances in
CoCN and ZnCN are both anomalously short. A similar situation was found for InCN, where the r 0 structure yielded
(2)
r C-N⫽1.1456(53) Å. 6 However, calculation of an r m
geometry for indium cyanide resulted in a longer C-N bond length
of 1.1587 Å—more reasonable. This difference is thought to
arise from zero-point vibrations, which are accounted for in
(2)
calculation. Unfortunately, such a structure cannot be
the r m
determined for CoCN because more isotopic substitutions
are required 共see Refs. 34 and 35兲. Zero-point anomalies may
also be producing the rather long Co-C bond length as well,
although this effect was not found in InCN.6
Considering simple molecular orbital arguments, the
Co-C bond length might be expected to decrease relative to
v obs
⍀⫽2
v obs⫺ v calc
v obs
v obs⫺ v calc
the metal-carbon bonds in NiCN and CuCN. While the cobalt compound has a ␦ 3 ␲ 3 configuration, nickel cyanide has
␦ 3 ␲ 4 . Hence, the bonding in NiCN involves the addition of
an electron to a ␲ orbital, which is thought to be chiefly
antibonding.14 In simple terms, the Ni-C bond should therefore lengthen relative to the Co-C bond. Interestingly, the
bond distance of CoC in its X 2 ⌺ ⫹ ground state is r 0
⫽1.5612—significantly shorter than in NiC(X 1 ⌺ ⫹ ), which
has r 0 ⫽1.6308 Å. 21 On the other hand, calculation of ␻ 1 ,
the metal-carbon stretching frequency, suggests that the
Co-C bond is weaker than that of nickel. Using the Kratzer
relationship35 and treating the CN moiety as a unit, ␻ 1
共CoCN兲 was found to be ⬃478 cm⫺1. In contrast, the values
for NiCN and CuCN are 491 cm⫺1 and 478 cm⫺1,
respectively.11,14 Obviously, the bonding in these species is
more complex than implied by simple electron configurations.
Cobalt cyanide may have the weakest metal-carbon bond
of the later 3d series because it has one less d electron. The
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8366
J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
TABLE II. Rotational transition frequencies of Co 13CN(X 3 ⌽ i ): ⍀⫽4 共in
MHz兲.
J⬘
F⬘
45
45
45
45
45
45
46
46
46
46
46
46
47
47
47
47
48
48
48
48
48
41.5
42.5
43.5
46.5
47.5
48.5
44.5
45.5
46.5
47.5
48.5
49.5
43.5
48.5
49.5
50.5
44.5
45.5
46.5
50.5
51.5
←
J⬙
F⬙
v obs
v obs⫺ v calc
44
44
44
44
44
44
45
45
45
45
45
45
46
46
46
46
47
47
47
47
47
40.5
41.5
42.5
45.5
46.5
47.5
43.5
44.5
45.5
46.5
47.5
48.5
42.5
47.5
48.5
49.5
43.5
44.5
45.5
49.5
50.5
373 820.243
373 817.186
373 814.177
373 803.804
373 799.936
373 796.283
382 100.249
382 097.095
382 093.825
382 090.407
382 086.974
382 083.326
390 390.843
390 375.662
390 372.278
390 368.833
398 673.624
398 670.931
398 668.080
398 655.919
398 652.460
0.033
⫺0.020
0.118
0.033
⫺0.127
0.064
⫺0.091
⫺0.094
⫺0.082
⫺0.088
0.021
0.043
0.116
0.031
0.034
0.097
0.020
⫺0.010
⫺0.080
0.042
⫺0.061
preference for cobalt to form the linear cyanide structure
suggests that the metal-ligand bond has significant covalent
character, as has been postulated for nickel, copper, and zinc
cyanides.11–14 Ab initio calculations for FeNC and FeCN also
indicate little electrostatic interaction in the formation of the
metal-carbon bond.36 The linear cyanide structure is believed
to occur for these species as a result of d- ␲ * backbonding
from the metal to the ligand. The bonding preference to the
carbon atom arises because the ␲* orbitals of CN have
slightly greater carbon character. The fact that the lower energy structure switches to the isocyanide for iron suggests
that cobalt has just enough d electrons for backbonding to
make the cyanide form more favorable energetically.
B. Fine structure perturbations
Although the spin-orbit pattern of CoCN appears to be
relatively close to the expected case 共a兲 pattern, the ⍀⫽3
component appears to be shifted to higher frequency relative
to the other two ⍀ ladders. This shift results in a positive
spin-spin constant, roughly of the order of A, the spin-orbit
parameter 共1.7 THz vs ⫺4 THz, see Table III兲, similar to
what has been found for FeC (X 3 ⌬ i ). 37 Hence, it appears
that the ⍀⫽3 sublevel alone is perturbed.
As discussed for CoCl 共Ref. 24兲 and NbN,38 a likely
perturber of the middle spin component is the isoconfigurational singlet state, which is 1 ⌽ 3 for CoCN. The two electronic states interact via second-order spin-orbit coupling,
which follows the selection rule ⌬⍀⫽0.38 As outlined in Ref.
24, the spin-orbit energy matrix of the ground state includes
off-diagonal terms of the form 具 1 ⌽ 3 兩 Ĥ SO兩 3 ⌽ 3 典 . The value of
this matrix element can be calculated by assuming a single
electron configuration for both states. It equals (a ␦ ⫺a ␲ /2),
where a ␦ and a ␲ are ␦ and ␲ electron contributions to
the molecular spin-orbit interaction. The diagonal term
Sheridan, Flory, and Ziurys
具 3 ⌽ 4 兩 Ĥ SO兩 3 ⌽ 4 典 ⫽⫺ 具 3 ⌽ 2 兩 Ĥ SO兩 3 ⌽ 2 典 yields a ␦ ⫹a ␲ /2, which
must equal 3A, the unperturbed spin-orbit splitting.
This information can be used to construct a 2⫻2 matrix
for the 3 ⌽ 3 - 1 ⌽ 3 interaction, which in turn can be solved to
find the unperturbed energy of the excited singlet state. This
matrix is constructed under the assumption that the major
contributor to the spin-spin constant ␭ is the second-order
spin-orbit interaction. Then, the 1 ⌽ 3 - 3 ⌽ 3 perturbation raises
the energy of the singlet state by 2␭ relative to its unperturbed energy, while lowering that of the ⍀⫽3 component of
the ground state by the same amount. The unperturbed energy ⌬E of the 1 ⌽ 3 state can therefore be calculated by
‘‘undiagonalizing’’ this matrix, resulting in the equation24,38
⌬E⫽
1
2␭
冋冉
a ␦⫺
a␲
2
冊
2
册
⫺4␭ 2 .
共2兲
Because only cobalt has d orbitals in CoCN, the ␦ molecular
orbitals must be centered on this atom. Therefore, it is reasonable to assume 2a ␦ ⫽ ␨ 3dCo . 39,40 Because a ␦ ⫹a ␲ /2⫽3A
⫽⫺399 cm⫺1 , a ␲ /2⫽⫺131 cm⫺1 . Using these values of a ␦
and a ␲ /2 and that of ␭ from the CoCN fit, Eq. 共2兲 yields
⌬E⬇31 cm⫺1 for the unperturbed energy of the excited 1 ⌽ 3
state relative to the ⍀⫽3 level. Considering the second-order
perturbation of 2␭, the singlet state actually lies about 546
cm⫺1 above the lowest spin component 共⍀⫽4兲 of the X 3 ⌽ i
state. The ⍀⫽3 sublevel is pushed down in energy and hence
lies only 285 cm⫺1 above the ⍀⫽4 component, while the
⍀⫽2 level is located 6A higher in energy at 800 cm⫺1. This
ordering appears to be reflected in the relative intensities of
the three spin-orbit ladders. The ⍀⫽3 lines are somewhat
stronger than expected, given the ⍀⫽4 and 2 spectral intensities 共see Fig. 2兲.
This energy ordering is displayed in Fig. 4, which shows
the perturbed and unperturbed X 3 ⌽ 3 and 1 ⌽ 3 levels, as well
as those of ⍀⫽2 and 4 components of the ground state.
Based on our calculation, the excited 1 ⌽ state lies lower in
energy than the ⍀⫽2 spin component of the ground state.
There may be other excited states intermixed within the
X 3 ⌽ manifold, as well.
TABLE III. Spectroscopic constants for CoCN(X 3 ⌽ i ): v ⫽0 共in MHz兲.a
Parameter
B
D
H
A
AD
AH
␭
␭H
a
b⫹c
h 3D
rms of fit
a
Value
4208.827共23兲
0.001 451共10兲
⫺3.11(15)⫻10⫺8
⫺4 000 000a
⫺1.3010共37兲
6.540(81)⫻10⫺5
1 730 000共9400兲
0.000 2845共21兲
853共13兲
⫺805共40兲
0.394共25兲
0.286
Errors are 3␴ and apply to the last quoted places. Held fixed, see text.
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J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
Spectrum of CoCN
8367
TABLE IV. Spectroscopic constants of individual spin components of CoCN and Co 13CN(X 3 ⌽ i ) 共in MHz兲.a
Parameter
v ⫽0 ( 3 ⌽ 4 )
v ⫽0 ( 3 ⌽ 3 )
v ⫽0 ( 3 ⌽ 2 )
v 2 ⫽1 ( 3 ⌬ 3 )
v 2 ⫽1 ( 3 ⌫ 5 )
v 1 ⫽1 ( 3 ⌽ 4 )
Co 13CN( 3 ⌽ 4 )
B
D
H
L
h⍀
h ⍀D
rms of fit
4200.653共31兲
0.000 967共18兲
⫺5.37(46)⫻10⫺8
2.07(43)⫻10⫺12
1753.8共6.1兲
4211.0393共49兲
0.002 024 9共12兲
4215.387共19兲
0.001 653 6共48兲
4227.4184共17兲
0.001 638 03共29兲
4199.62共35兲
0.000 37共17兲
⫺8.0(2.6)⫻10⫺8
4157.68共31兲
0.000 90共14兲
⫺5.0(2.2)⫻10⫺8
1706共13兲
3390共92兲
1780共12兲
0.097
0.328
1706共36兲
0.052共14兲
0.095
1807.7共7.0兲
0.068
4237.207共78兲
0.000 601共43兲
⫺2.10(11)⫻10⫺7
1.270(96)⫻10⫺11
2645共61兲
0.094共26兲
0.076
0.047
0.080
a
Errors are 3␴ and apply to the last quoted places.
C. The hyperfine structure
The hyperfine structure appears to be relatively regular,
except for the ⍀⫽3 levels. These transitions had to be fit
with an additional hyperfine term h 3D indicating that they are
slightly perturbed. Again, the second-order spin-orbit interaction can generate off-diagonal matrix elements for the
Fermi contact and dipolar terms.38 The 1 ⌽- 3 ⌽ interaction
would only affect the ⍀⫽3 sublevel, as appears to be the
case. Additional evidence for perturbations is suggested in
the individual h constants determined for each ⍀ ladder. For
an isolated, unperturbed 3 ⌽ state, h ⍀⫽3 should be the average of h ⍀⫽2 and h ⍀⫽4 . 38 For CoCN, this relationship does
not hold, as h ⍀⫽3 ⫽1706 MHz, while (h ⍀⫽2 ⫹h ⍀⫽4 )/2
⫽2572 MHz 共see Table IV兲.
The hyperfine interactions appear to arise primarily from
the cobalt nuclear spin, as indicated by the octet pattern.
Nitrogen also has a spin of I⫽1, but interactions arising
from this nucleus were not apparent in these data. Additional
transitions recorded at much lower J did show evidence of
nitrogen hyperfine interactions, with each line in the usual
octets starting to split into triplets. These data will be a subject of a later paper. Because the electron configuration is
␲ 3 ␦ 3 , cobalt is expected to play a major role in generating
the hyperfine structure. The unpaired ␦ electron must be located on the cobalt nucleus in a nonbonding orbital, although
the ␲ electron is located in an antibonding orbital that has
both cobalt and cyanide contributions.
The h f parameters determined for CoCN from the global
fit are a and (b⫹c). The a parameter, the Î"L̂ term, has a
rather large value of 853共13兲 MHz for CoCN. In contrast, the
a constant for the 59Co nucleus is 621.01共21兲 MHz in CoH
共Ref. 25兲 and 512共45兲 MHz in CoCl.24 For the cobalt atom,
this constant has the value of 617.9 MHz for the 3d 8 4s 1
configuration and 702.8 MHz for 3d 7 4s 2 . 41 The a constant is
directly proportional to 具 1/r 3i 典 av , where r i is the distance of
the unpaired electrons from the nucleus, namely,27
a⫽
冓冔
2 ␮ 1␮ B 1
I
r 3i
.
共3兲
av
Therefore, 具 1/r 3i 典 av⫽4.58⫻1031 m⫺3 for CoCN, but 4.5
⫻1031 m⫺3 for the cobalt atom, 2.7⫻1031 m⫺3 for CoCl,24
and 3.3⫻1031 m⫺3 for CoH.25 The unpaired electrons in
CoCN are thus closer on average to the cobalt nucleus than
in the other species, including the atom. This difference may
indicate that the unpaired ␲ electron lies in an orbital that
actually participates in some bonding, perhaps ␲* backbonding, as previously suggested. Hence, it remains closer to the
internuclear axis. Such ␲ backbonding is not possible in the
other cobalt species.
TABLE V. Bond lengths for transition metal cyanides.
Molecule
Structure
r 0(⍀⫽4)
1.8827共7兲
1.1313共10兲
NiCN
r0
r 0(⍀⫽5/2)
r s(⍀⫽5/2)
r m(1) (⍀⫽5/2)
1.8281共6兲
1.8293共1兲
1.8292
1.8263共9兲
1.1580共8兲
1.1590共2兲
1.1534
1.152共1兲
CuCNc
r0
rs
r m(1)
1.832 31共7兲
1.832 84共4兲
1.8358
1.1576共1兲
1.156 69共3兲
1.1573
ZnCNd
r0
rs
r m(1)
1.9545
1.9525
1.9496
1.1464
1.1434
1.1417
Calculated from ⍀⫽4 data only.
Reference 14.
c
Reference 11.
d
Reference 12.
b
r C-N (Å)
b
CoCN
a
r M -C (Å)
a
FIG. 4. An energy level diagram of the three spin components of the X 3 ⌽ i
ground state of CoCN, and a possible nearby 1 ⌽ excited state. The 3 ⌽ 3 and
1
⌽ 3 states perturb each other via second-order spin-orbit coupling, which
lowers the energy of the ⍀⫽3 component of the ground state but raises that
of the singlet state, as shown, by the approximate amount 2␭. The 1 ⌽ 3 state
may be responsible for observed fine and hyperfine perturbations in the
⍀⫽3 ladder of CoCN.
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8368
J. Chem. Phys., Vol. 121, No. 17, 1 November 2004
VI. CONCLUSION
The measurement of the pure rotational spectra of cobalt
cyanide and its 13C isotopomer has shown that this molecule
is most stable in its linear cyanide form, a trend that has
already been observed for Ni through Zn. However, the Co-C
bond appears to be somewhat weaker than the Ni-C or Cu-C
bonds, perhaps a result of fewer 3d electrons that can participate in ␲ backbonding. For the next 3d metal, iron, the
isocyanide form is lower in energy. The ground electronic
state of CoCN appears to be 3 ⌽ i , as supported by measurement of rotational lines from all three spin ladders. Perturbations are evident in both the spin and hyperfine structure for
the ⍀⫽3 component, indicating a close-lying 1 ⌽ 3 excited
state, perhaps only ⬃550 cm⫺1 above ground state. The
electron-orbital nuclear spin hyperfine constant a is significantly larger than those measured for similar cobalt-bearing
species, suggesting a subtle change in bonding between the
molecules. Greater covalent character may be present in
CoCN as opposed to CoF or CoCl, as indicated by theory.
ACKNOWLEDGMENTS
This research was supported by NSF Grant Nos. CHE98-17707 and AST-02-04913. The authors would like to
thank Dr. J. M. Brown for use of his Hamiltonian code. This
work was also supported in part by a fellowship from Merck
Research Laboratories.
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