JOURNAL OF CHEMICAL PHYSICS
VOLUME 117, NUMBER 10
8 SEPTEMBER 2002
Rotational spectroscopy of 3 d transition-metal cyanides: Millimeter-wave
studies of ZnCN „ X 2 ⌺ ¿ …
M. A. Brewster and L. M. Ziurysa)
Department of Astronomy, Department of Chemistry, and Steward Observatory, The University of Arizona,
Tucson, Arizona 85721
共Received 5 April 2002; accepted 13 June 2002兲
The pure rotational spectrum of the ZnCN radical in its X 2 ⌺ ⫹ ground electronic state has been
recorded using millimeter/sub-mm direct absorption techniques in the range 339–543 GHz. This
work is the first spectroscopic observation of this molecule, which was created by the reaction of
zinc vapor and cyanogen gas in a dc discharge. Twenty-one rotational transitions were recorded for
the main zinc isotopomer, 64ZnCN, in its ground vibrational state, as well as 8 –16 transitions for the
66
Zn, 68Zn, and 13C isotopomers. Data was also obtained for ZnCN in several quanta of its bending
mode and in the 共100兲 stretching vibration. These measurements indicate that the most stable form
of zinc and the cyanide moiety is the linear cyanide structure, as has also been found for copper and
nickel. In contrast, the linear isocyanide geometry is lowest in energy for gallium and aluminum. A
spectroscopic analysis has been carried out of the 共000兲 and excited vibrational data, establishing
(1)
兲 have
rotational, spin-rotation, and l-type doubling parameters. Several structures 共r 0 , r s , and r m
been determined for ZnCN as well, along with estimates of the heavy-atom stretch ( ␻ 1 ), and
bending ( ␻ 2 ) frequencies. These calculations suggest that the metal–carbon bond in ZnCN is
weaker than in CuCN or NiCN. The tendency of these metals to form the linear cyanide geometry,
as opposed to the linear isocyanide or T-shaped structures, is additionally discussed. © 2002
American Institute of Physics. 关DOI: 10.1063/1.1498466兴
I. INTRODUCTION
implications. Metal cyanide complexes are found in a variety
of environments, including biological systems at enzyme
sites,13 and in high-temperature superconductors.14 They also
play a role in metal extraction for mining techniques,15 and
in organic synthesis.16 Copper cyanide, for instance, is
widely used in the creation of carbon–carbon bonds. Such
varied use has inspired theoreticians to model the binding of
the CN moiety on metal surfaces,17,18 as well as perform ab
initio structural calculations of monomeric species.6 – 8
Transition metals are common in many of these environments. Yet, very little is known about the structures of monomeric transition metal cyanide/isocyanide complexes.
Only recently have any of these species been investigated
experimentally. Lie and Dagdigian, for example, have observed the FeNC molecule in the near UV by laser-induced
fluorescence.11 These authors established that this radical has
indeed the linear isocyanide structure in its most stable form.
LIF studies have also been done very recently of NiCN by
Merer and co-authors,19 who found that, in this case, the
linear cyanide form was the ground state structure. In our
group, we have measured the pure rotational spectrum of
CuCN (X 1 ⌺ ⫹ ) using millimeter/submillimeter methods. A
complete substitution structure was done on this molecule,
unambiguously demonstrating that the ground electronic
state has the linear cyanide geometry.20 Finally, we have also
recorded the pure rotational spectrum of NiCN (X 2 ⌬ i ), verifying the work of Merer et al. and establishing lambdadoubling parameters.21 It is interesting to note that iron prefers the isocyanide geometry, but for nickel and copper, the
cyanide species is the lower-energy configuration. At gal-
One of the more interesting chemical systems are the
metal–cyanide complexes. These species in their simplest,
monomeric form can exhibit three distinct geometries: a linear cyanide compound, a linear isocyanide, and a T-shaped,
quasistructureless molecule.1–5 As theorists have described,
the dominance of a particular geometry depends on the balance between columbic attraction and exchange repulsion,
and electronegativity of the metal involved.6 –9 In the alkali
group, the metal is thought to completely give its valence
electron to the cyanide moiety, generating an M⫹ CN⫺ structure in which the M⫹ ion orbits the CN⫺ group with no
preference for a particular bonding site.1,2,6 Hence, a
T-shaped structure is generated with a highly ionic bonding
scheme. The alkaline earth metals tend to form linear
isocyanides,3,9,10 where the metal atom is attached at the
negatively polarized nitrogen end of the CN group. There is
then a covalent contribution to the bonding. It is thought that
if covalent bonding dominates, then the linear cyanide species is expected, analogous to HCN.6 – 8 Therefore, for certain
metals, the cyanide form might be the lowest-energy structure. Until recently, experimental work has proved otherwise;
aluminum,4,5 iron,11 gallium,12 and even indium,12 for example, have all been shown to favor the isocyanide geometry
in their ground state. NaCN and KCN adopt the T-shaped
structure.1,2
Establishing the geometries of metal cyanide species,
particularly in their monomeric form, has many chemical
a兲
Electronic mail: [email protected]
0021-9606/2002/117(10)/4853/8/$19.00
4853
© 2002 American Institute of Physics
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4854
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
M. A. Brewster and L. M. Ziurys
lium, the linear isocyanide species is again favored.12
In order to further examine the trends in transition
metal/CN bonding, we have measured the pure rotational
spectrum of ZnCN. This study is the first spectroscopic observation of this molecule. A wide range of rotational transitions were recorded for the main isotopomer, 64ZnCN, as
well as for 66ZnCN, 68ZnCN, and 64Zn 13CN. Transitions
arising from several of the vibrationally excited states were
observed in the zinc isotopomers as well. This free radical
was also found to be linear and exists as a metal cyanide in
its lowest-energy configuration, with a 2 ⌺ ⫹ ground electronic state. Spectroscopic constants, vibrational frequencies,
and bond lengths have been established for ZnCN. Here we
present these results and discuss them in the context of metal
cyanide/isocyanide complexes.
II. EXPERIMENT
The measurements were made with one of the quasioptical millimeter/sub-mm spectrometer systems of the Ziurys
group. This instrument consists of a Gunn oscillator/varacter
multiplier source, a reaction chamber containing a Broidatype oven for metal vaporization, and an InSb hot electron
bolometer detector. The system is under computer control.
Phase-sensitive detection is achieved by FM modulation of
the Gunn oscillator. For more details, see Ref. 22.
ZnCN was produced in a dc glow discharge using a mixture of 25–30 mTorr argon, 3–5 mTorr cyanogen, and ⬍1
mTorr zinc vapor, produced from the Broida-type oven. A
similar synthetic technique was previously used in our studies of AlNC,4 MgCN,23 and CuCN.20 The reactant and carrier
gases were premixed and introduced from beneath the oven
to produce the molecule. Mossy zinc was found to be an
acceptable material to use for the purposes of this synthesis.
The typical discharge voltage used was 400 V, producing 90
mA of current through the reaction mixture. The discharged
gas typically was purple in color due to argon.
Three zinc isotopomers of ZnCN were observed in their
natural abundances ( 64Zn: 66Zn: 68Zn⫽48.9:27.8:18.6). The
signal-to-noise of the spectra, however, was insufficient to
record data for the 13C species in its natural abundance.
Therefore, H13CN was substituted for the cyanogen as the
precursor for Zn13CN. Typically 1–3 mTorr H13CN was used
in an effort to minimize the amount of starting material consumed. H13CN was synthesized for this purpose by the slow
addition of concentrated sulfuric acid to a concentrated aqueous solution of Na13CN 共Cambridge isotopes兲, under a continuous flow of helium, introduced to the reaction vessel
from beneath the surface of the solution. The stream of gas
was subsequently flowed through anhydrous calcium sulfate
and then over P2 O5 to dry it. Finally, the H13CN was collected in a liquid nitrogen-cooled glass bulb fitted with a
valve. Upon warming to room temperature the material was
ready for use.
Actual transition frequencies were measured from spectra that were an average of two scans. One scan was taken in
increasing frequency and the other in decreasing frequency
over the same range. Signals were found to be sufficiently
strong such that only one average was necessary for all mea-
FIG. 1. A stick figure illustrating the positions and approximate relative
intensities of the spectral lines observed in the N⫽59→60 rotational transition of ZnCN (X 2 ⌺ ⫹ ). The spin-rotation splitting has been neglected for
simplicity. Lines originating from the main zinc isotopomer, 64ZnCN, in
both its ground vibrational state 共000兲, several quanta of the v 2 bending
mode, and the v 1 ⫽1 stretching vibration, are present in the spectrum. Also
visible in the data are the 共000兲 and 共010兲 states of the less abundant zinc
isotopomers, 68ZnCN and 66ZnCN, and the ground vibrational state of the
13
C isotopomer. The v 2 vibrational satellite lines are all split by l-type effects of varying magnitude, as illustrated in the figure.
surements. Linewidths were typically 700–1200 kHz over
the range 330–544 GHz.
III. RESULTS
ZnCN had not been observed previously by any other
experimental method; nor had any ab initio calculations been
performed for this molecule. It was consequently unclear at
the start of the study whether the species was bent or linear,
or whether the cyanide or isocyanide form would be the
dominant structure. To attempt to measure its spectrum, it
was assumed that the molecule was linear and had a 2 ⌺ ⫹
ground state. A rotational constant of ⬃4 GHz was then estimated by scaling from that of CaNC by mass. A spinrotation constant of ⬃100 MHz was also predicted based on
that of ZnCH3 24 and using the ratio of spin-rotation constants
of MgNC and MgCH3 as a scaling factor.3,25 A range of ⬃2B
共⬃8 –9 GHz兲 was then scanned in frequency space in 100
MHz sections. Doublets were found in these data with approximately the estimated fine structure splitting. Harmonic
relationships were then predicted and other matching transitions identified, in the process establishing the correct rotational quantum numbers. Effective rotational parameters
were then accurately determined for the three zinc isotopomers in their ground vibrational state and several excited
vibrational states, such that additional transitions could be
readily predicted and measured. It was obvious at this point
that the molecule was linear; measurements of transitions of
the 13C isotopomer established that the radical was ZnCN, as
opposed to ZnNC.
A stick figure of the rotational lines observed for ZnCN
within a given transition (N⫽59→60) with approximate
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Millimeter-wave studies of ZnCN
4855
TABLE I. Observed transition frequencies of ZnCN (X 2 ⌺ ⫹ :(000)).a
64
66
ZnCN
68
ZnCN
Zn13CN
ZnCN
N⬙
N⬘
J⬙
J⬘
␯ obs
␯ o–c
␯ obs
␯ o–c
␯ obs
␯ o–c
␯ obs
␯ o–c
43
44
44
45
45
46
46
47
47
48
48
49
49
50
50
51
51
52
56
57
57
58
58
59
59
60
60
61
61
62
62
63
63
64
64
65
65
66
66
67
67
68
68
69
69
70
70
71
42.5
43.5
43.5
44.5
44.5
45.5
45.5
46.5
46.5
47.5
47.5
48.5
48.5
49.5
49.5
50.5
50.5
51.5
55.5
56.5
56.5
57.5
57.5
58.5
58.5
59.5
59.5
60.5
60.5
61.5
61.5
62.5
62.5
63.5
63.5
64.5
64.5
65.5
65.5
66.5
66.5
67.5
67.5
68.5
68.5
69.5
69.5
70.5
43.5
44.5
44.5
45.5
45.5
46.5
46.5
47.5
47.5
48.5
48.5
49.5
49.5
50.5
50.5
51.5
51.5
52.5
56.5
57.5
57.5
58.5
58.5
59.5
59.5
60.5
60.5
61.5
61.5
62.5
62.5
63.5
63.5
64.5
64.5
65.5
65.5
66.5
66.5
67.5
67.5
68.5
68.5
69.5
69.5
70.5
70.5
71.5
339 574.263
339 676.998
347 269.472
347 372.165
354 963.088
355 065.693
362 655.044
362 757.618
¯
¯
378 034.006
378 136.433
385 720.899
385 823.277
393 406.033
393 508.324
401 089.364
401 191.591
439 477.758
439 579.613
447 149.540
447 251.322
454 819.279
454 920.965
462 486.908
462 588.545
470 152.450
470 254.001
477 815.820
477 917.286
485 477.020
485 578.382
493 135.982
493 237.264
500 792.687
500 893.882
508 447.086
508 548.198
516 099.167
516 200.176
523 748.885
523 849.809
531 396.212
531 497.058
¯
¯
¯
¯
0.032
0.022
0.037
0.045
0.039
0.020
0.005
0.019
¯
¯
0.005
0.001
⫺0.005
0.010
⫺0.007
⫺0.011
⫺0.010
⫺0.009
⫺0.025
⫺0.028
⫺0.025
⫺0.024
⫺0.019
⫺0.035
⫺0.039
⫺0.023
⫺0.026
⫺0.014
⫺0.029
⫺0.019
⫺0.013
⫺0.022
⫺0.008
⫺0.012
0.001
⫺0.003
0.000
0.001
0.012
0.001
0.030
0.024
0.058
0.067
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
397 818.102
397 919.492
¯
¯
443 504.282
443 605.196
451 111.756
451 212.632
458 717.232
458 818.019
466 320.574
466 421.312
473 921.825
474 022.476
481 520.905
481 621.481
489 117.800
489 218.296
496 712.510
496 812.883
504 304.903
504 405.216
511 895.043
511 995.256
519 482.828
519 582.968
527 068.260
527 168.283
534 651.296
534 751.233
542 231.866
542 331.735
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
0.033
0.040
¯
¯
0.023
⫺0.015
⫺0.011
⫺0.011
0.009
⫺0.002
⫺0.018
0.000
⫺0.015
⫺0.003
⫺0.026
⫺0.008
⫺0.031
⫺0.010
0.004
⫺0.013
⫺0.016
⫺0.009
0.006
0.000
0.003
0.012
0.012
⫺0.006
0.025
0.011
0.007
0.017
¯
¯
¯
¯
¯
¯
¯
¯
364 474.364
364 575.263
¯
¯
379 606.958
379 707.717
387 170.704
387 271.388
394 732.695
394 833.326
¯
¯
440 066.087
440 166.289
447 614.841
447 714.993
455 161.619
455 261.723
462 706.382
462 806.349
470 249.020
470 348.932
477 789.546
477 889.333
485 327.902
485 427.624
492 864.047
492 963.703
500 398.018
500 497.532
507 929.701
508 029.159
515 459.089
515 558.438
522 986.131
523 085.416
530 510.882
530 609.951
538 033.131
538 132.244
¯
¯
¯
¯
¯
¯
¯
¯
0.045
0.035
¯
¯
0.033
0.013
0.028
0.001
0.016
0.005
¯
¯
0.010
0.010
⫺0.046
⫺0.018
⫺0.056
0.004
⫺0.025
⫺0.021
⫺0.029
0.003
⫺0.019
⫺0.030
⫺0.021
⫺0.012
⫺0.041
⫺0.011
⫺0.007
⫺0.031
0.001
0.009
0.010
⫺0.001
0.004
0.020
0.071
⫺0.036
0.034
0.066
¯
¯
343 455.845
343 557.411
351 065.036
351 166.550
358 672.637
358 774.089
366 278.612
366 380.013
373 882.913
373 984.243
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
525 564.381
525 664.138
533 125.549
533 225.199
540 684.247
540 783.827
¯
¯
0.020
0.010
0.000
⫺0.002
⫺0.009
⫺0.010
⫺0.007
0.004
⫺0.008
⫺0.003
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
¯
0.006
0.007
0.012
⫺0.002
⫺0.014
⫺0.004
a
In MHz.
relative intensities is shown in Fig. 1. The splittings due to
fine structure are neglected. For the main isotopomer
( 64ZnCN), the ground vibrational state and lines originating
from the v 2 ⫽1, 2, and 3 quanta of the bending mode were
observed, as well as the first quantum of the heavy-atom
stretch 共100兲. The 共010兲 and 共020兲 levels show the effects of
l-type doubling and l-type resonance. Also present are the
共000兲 and 共010兲 vibrational states of the 66ZnCN and 68ZnCN
isotopomers, which are weaker in intensity. The weakest signal recorded arises from Zn13CN in its ground vibrational
state. The vibrational satellite pattern is typical for a linear,
reasonably rigid triatomic molecule. The (011 0), (022 0),
and (033 0) states are regularly spaced in frequency with respect to the 共000兲 state, with ␣ 2 ⬍0. Also, the (020 0) line has
not significantly shifted away from the (022 0) features, as
occurs when a molecule is quasilinear.26
Table I presents the transition frequencies of the four
isotopomers observed 共64ZnCN, 66ZnCN, 68ZnCN, and
64
Zn13CN兲 in their ground vibrational state. Between 8 and
21 transitions were recorded for each species. In every transition measured, the spin-rotation splitting was resolved,
which varies from about 98 to 103 MHz. Between 10–12
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4856
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
M. A. Brewster and L. M. Ziurys
FIG. 2. Spectrum of the N⫽48→49 rotational transition of 64ZnCN(X 2 ⌺ ⫹ )
near 378 GHz, observed in its ground vibrational state. The transition consists of doublets, labeled by quantum number J, which arise from spin–
rotation interactions and indicate that this molecule has a 2 ⌺ ⫹ ground state.
This spectrum is a composite of two single 100 MHz scans, each acquired in
approximately one minute.
FIG. 3. Observed spectrum of the N⫽51→52 rotational transition of the
68
ZnCN isotopomer near 395 GHz in its ground vibrational and electronic
states, measured in natural abundance ( 64Zn: 68Zn⫽48.9:18.6). The line
marked by an asterisk is an unidentified feature. The spin–rotation doublets,
labeled by the J quantum number, are clearly resolved in these data. This
spectrum is a composite of two single 100 MHz scans, each recorded in
about one minute.
TABLE II. Molecular constants for ZnCN (X 2 ⌺ ⫹ :( v 1 v 2 v 3 )). a
( v 1v 2v 3)
Parameter
共000兲
B
D
␥
␥D
B
D
H(109 )
␥
␥D
q
qD
p␲
B
D
H(109 )
␥
␥D
B
D
H(109 )
␥
␥D
q eff
q D eff(108 )
B
D
H(109 )
␥
␥D
q eff(109 )
B
D
H(109 )
␥
␥D
rms of fit
共010兲
(020 0)
(022 0)
(033 0)
共100兲
64
ZnCN
3865.08340 共86兲
0.001 472 52 共12兲
104.05 共18兲
⫺0.000 225 共17兲
3892.5528 共42兲
0.001 588 9 共12兲
0.63 共12兲
102.87 共17兲
⫺0.000 205 共15兲
⫺6.003 1 共16兲
0.000 032 21 共20兲
⫺0.482 共93兲
3910.857 共19兲
0.001 9750 共48兲
⫺0.75 共40兲
102.58 共47兲
⫺0.000 215 共41兲
3920.466 4 共43兲
0.001 685 0 共12兲
0.22 共11兲
100.98 共23兲
⫺0.000 147 共20兲
⫺0.000 052 02 共38兲
0.2141 共60兲
3948.8362 共58兲
0.001 817 0 共16兲
1.09 共14兲
98.52 共32兲
⫺0.000 063 共27兲
⫺0.1731 共78兲
3855.403 0 共76兲
0.001 265 4 共20兲
4.19 共17兲
103.43 共41兲
⫺0.000 229 共35兲
0.044
66
68
ZnCN
ZnCN
Zn13CN
3833.5004 共14兲
0.001 449 58 共18兲
103.15 共36兲
⫺0.000 217 共29兲
3860.7352 共47兲
0.001 564 4 共13兲
0.64 共11兲
102.06 共24兲
⫺0.000 205 共20兲
⫺5.905 9 共22兲
0.000 031 29 共26兲
⫺0.494 共93兲
3803.7148 共11兲
0.001 428 34 共13兲
102.45 共24兲
⫺0.000 223 共20兲
3830.7233 共76兲
0.001 540 9 共19兲
0.61 共16兲
101.39 共28兲
⫺0.000 209 共22兲
⫺5.814 0 共24兲
0.000 030 30 共28兲
⫺0.483 共95兲
3822.617 63 共99兲
0.001 451 24 共12兲
102.92 共20兲
⫺0.000 222 共19兲
0.034
0.030
0.009
In MHz; errors quoted are 3␴ and apply to the last quoted decimal places.
a
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
Millimeter-wave studies of ZnCN
TABLE III. Vibrational dependence of B v . a
ZnCN (X 2 ⌺ ⫹ )
Parameter
a
TABLE V. Bond lengths for transition metal cyanides.
CaOH (X 2 ⌺ ⫹ ) b
3835.6644共12兲
⫺31.5974 共6兲
⫺2.1778 共4兲
2.4029共10兲
B̃ e
␣2
␥ 22
␥u
4857
MgOH (X 2 ⌺ ⫹ ) b
¯
31.518共3兲
2.849共3兲
⫺3.361共1兲
14 911.76共10兲
110.47 共5兲
21.18 共3兲
18.27 共3兲
In MHz.
Reference 26.
b
Species
a
CuCN
ZnCN
GaCNb
rotational transitions were also recorded for 64ZnCN in its
(011c 0), (011d 0), (020 0), (022c 0), (022d 0), (033c 0),
(033d 0), and 共100兲 vibrational states, and for the 66Zn and
68
Zn isotopomers in their (011c 0) and (011d 0) levels. These
data are available via EPAPS.27 The l-type doubling in the
共010兲 state typically ranges from 550 to 800 MHz, while in
the 共020兲 state it is much smaller 共⬃20–50 MHz兲, as expected. In the 共030兲 level, the l-type splitting is collapsed at
the lower-N transitions observed, but is resolved at higher N,
where the separation between the c and d components is, at
most, 1–2 MHz.
Representative spectra of the ZnCN radical are shown in
Figs. 2 and 3. Figure 2 presents the N⫽48→49 rotational
transition in the 共000兲 vibrational mode of the main zinc
isotopomer, 64ZnCN, near 378 GHz. The spin–rotation doublets are clearly present in the spectrum, and are labeled by
quantum number J. Figure 3 shows the N⫽51→52 rotational transition of 68ZnCN in its ground vibrational mode
near 394 GHz, observed in the natural zinc abundance ratio
of 64Zn: 68Zn⫽48.9:18.6. An unidentified line in the data is
marked by an asterisk. Again, the fine structure doublets are
clearly visible in the spectrum. Curiously, the signal-to-noise
ratio in these data does not vary significantly from that of
64
ZnCN 共Fig. 2兲, although the zinc abundance differs by a
factor of 2.6. Such variations in signal are typical in this case
and reflect the fluctuations in molecule production of elusive
free radicals.
IV. ANALYSIS
The data for all isotopomers of ZnCN observed in their
ground vibrational state and the 共100兲 stretching mode were
analyzed using a simple Hamiltonian consisting of molecular
frame rotation and spin-rotation coupling, including their
centrifugal distortion corrections:
Ĥ eff⫽Ĥ rot⫹Ĥ sr .
共1兲
a
Structure
r0
rs
r m(1)
r0
rs
r m(1)
r0
rs
r m(1)
r M–C 共Å)
1.8323
1.8328
1.8358
1.9545
1.9525
1.9496
2.0616共4兲
2.059
2.058
r C–N 共Å)
1.1576
1.1567
1.1573
1.1464
1.1434
1.1417
1.1580共6兲
1.160
1.160
Reference 20.
Reference 12.
b
For the excited bending states, however, the effects of l-type
doubling and l-type resonance had to be considered. As discussed in Apponi, Anderson, and Ziurys,26 these interactions
are quite simple for the 共010兲 state because they only involve
l-type doubling and an energy term in q, the l-type doubling
constant. For the higher quanta of the bending mode, on the
other hand, the l-type interactions include off-diagonal terms
varying by l⫾4 as well as l⫾2, and hence require matrix
representation. In the construction of these matrices, a
knowledge of the energy separation between the l subcomponents of a given v 2 level is additionally needed. This information is not presently available for ZnCN, and therefore
the l-type interactions in the v 2 ⫽2 and 3 states could only be
modeled using an effective term with a corresponding constant, q eff . 共For exact energy expressions, see Ref. 26.兲 Finally, a p ␲ term was found necessary for the 共010兲 state
analysis to account for differences in spin-rotation splittings
between the l-type doublets, c and d. This correction has the
same functional form as the lambda-doubling constant p in ⌸
states.26
The molecular constants determined for the four isotopomers of zinc cyanide, 64ZnCN, 66ZnCN, 68ZnCN, and
64
Zn13CN, are listed in Table II. This table also includes the
parameters established for the 共010兲, (020 0), (022 0),
(033 0), and 共100兲 vibrational states. As is evident in the
table, centrifugal distortion corrections to ␥ and q 共␥ D , q D ,
and q Deff兲 were found necessary in most of the analyses.
共One most global fit was done for all data for each isotopomer.兲 All resulting constants were well determined, and
the individual rms of each data was better than 45 kHz 共see
Table II兲.
V. DISCUSSION
A. Structural properties of ZnCN „ X 2 ⌺ ¿ …
TABLE IV. Derived vibrational frequencies of transition metal cyanides.a
␻ 1 (expt.)
NiCN
CuCN
ZnCN
GaCN
In cm⫺1
Reference 21.
c
Reference 20.
a
b
b
496
478c
418
348e
␻ 1 共ab initio兲
␻ 2 (expt.)
␻ 2 共ab initio兲
¯
453d
¯
339f
¯
270c
212
¯
¯
225d
¯
112f
d
Reference 32.
Reference 12.
f
Reference 31.
e
This study has shown that the most stable form of zinc
and the cyanide moiety is the linear cyanide structure, ZnCN.
Hence, zinc behaves similarly to the other later 3d transition
metals that have been investigated, copper and nickel.19–21
For gallium, the next element after zinc, the favored geometry is linear GaNC. The isocyanide structure is also found
for iron. This structural alternation will be discussed later.
Not only does zinc bond to the carbon as opposed to the
nitrogen in CN, but it forms a relatively rigid, linear structure
as well. Evidence for rigidity is found in the vibrational pro-
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4858
J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
M. A. Brewster and L. M. Ziurys
gression, as already discussed and shown in Fig. 1. Quantitatively, this vibrational sequence can be modeled using an
expression for the dependence of B v on v 2 , the bending
mode quantum number:26
B v ⫽B̃ e ⫺ ␣ 2 共 v 2 ⫹1 兲 ⫹ ␥ 22共 v 2 ⫹1 兲 2 ⫹ ␥ ll ,
共2兲
where B̃ e ⫽B e ⫺ 12 ( ␣ 1 ⫹ ␣ 3 ). Using the 共000兲, (011 0),
(022 0), (020 2), and (033 0) data, the four constants in Eq.
共2兲 have been determined for ZnCN and are presented in
Table III. Also listed in this table are a similar set of constants derived for rigid, linear CaOH, and quasilinear
MgOH.26 As this comparison demonstrates, the ␥ 22 and ␥ ll
constants that reflect the deviations from linearity, are very
similar in magnitude for ZnCN and CaOH, although the
signs change. In contrast, those of MgOH are about a factor
of 10 larger. ZnCN consequently does not appear to show
much evidence for quasilinear behavior.
CuCN also appears to be fairly rigid, as suggested by its
regular vibrational progression.20 GaNC, in contrast, exhibits
large-amplitude bending motions, which indicate a flat bending potential.12 Evidence for such a potential is found in the
unusually short N–C bond distances for GaNC 关r 0
⫽1.1494(46) Å and r s ⫽1.1419(80) Å兴. The value in HNC
(2)
is closer to 1.16 –1.17 Å. The calculation of an r m
structure
for GaNC, which takes into account zero-point vibrations,28
appears to correct this anomalously short bond length, yielding r N–C⫽1.1629 共1兲 Å—more in the range of usual
values.12 InCN also appears to exhibit a very short N–C
bond length and an even flatter bending potential.12
Although the geometry of ZnCN is linear, it does not
appear to be as strongly bonded as its copper or nickel analogs. This characteristic is apparent in calculated vibrational
frequencies for the metal–carbon stretch ( ␻ 1 ) and the bend
( ␻ 2 ) in these molecules. The heavy atom stretching frequency can be estimated by treating the CN moiety as a unit
and using the approximate relationship for diatomic
molecules:29
␻ 1⬇
冑
4B 30
D0
共3兲
.
The bending mode vibration can be derived from the l-type
doubling constant q via the relationship:30
q⫽
⫺2B 2e
␻2
冉
1⫹4
2
␰ 2i
␻ 22
兺i ␻ 2i ⫺ ␻ 22
冊
.
共4兲
The last term in this equation, the Coriolis term, is usually
near 0.3, so the above expression simplifies to30
q⬇
2.6B 2e
␻2
.
共5兲
In the case of CuCN and ZnCN, B e itself could not be derived, so B̃ e was used instead.
The resulting vibrational frequencies calculated for
ZnCN are listed in Table IV, along with those derived for
CuCN,20 NiCN,21 and GaCN,12 if available. 共Ab initio values
have also been computed for two of these molecules31,32 and
are given in Table IV as well. They are in good agreement
with those derived from experimental data and the above
approximations.兲 As shown, the metal–carbon stretch for
ZnCN was found to be ␻ 1 ⬇418 cm⫺1 as opposed to 478 and
496 cm⫺1 for CuCN and NiCN, respectively. Hence, the
stretching frequency decreases considerably in going from
CuCN to ZnCN, indicating a weakening of the metal–carbon
bond. Such an effect might be expected, because CuCN is
closed shell (X 1 ⌺ ⫹ ) while ZnCN is a radical (X 2 ⌺ ⫹ ). On
the other hand, NiCN is a radical as well, with a 2 ⌬ i ground
state, yet the metal–carbon stretching frequency is comparable to that of CuCN. The Ga–C stretch is lower in energy
than that of ZnCN, with ␻ 1 ⬇348 cm⫺1 , suggesting an even
weaker bond. Given that GaNC is the more stable geometry,
this decrease is not unexpected.
Experimentally derived bending mode frequencies are
only available for CuCN and ZnCN. Again, the bending frequency decreases in going from copper ( ␻ 2 ⬇270 cm⫺1 ) to
zinc ( ␻ 2 ⬇212 cm⫺1 )—another indication that ZnCN is not
as strongly bound as CuCN. A theoretical calculation of ␻ 2
is available from the literature for GaCN,31 and this value
共112 cm⫺1兲 is almost half that of ZnCN. 共An ab initio estimate has also been obtained for CuCN: ␻ 2 ⬇225 cm⫺1 , fairly
close to the experimental value of 270 cm⫺1.32兲
Because isotopic substitutions were carried out for the
(1)
structures
zinc and carbon atoms on ZnCN, r 0 , r s , and r m
can be calculated. These results are given in Table V, along
with those derived for GaCN and CuCN. The r 0 and r s geometries are determined, respectively, by a least-squares fit
to the moments of inertia (r 0 ) and to Kraitchman’s equations
(1)
structure was derived using the method
(r s ), 33 while the r m
employed by Watson.28 In the latter case, the experimentally
determined moments of inertia were fit to the expression
I 0 ⫽I m ⫹c 冑I m ,
共6兲
where I m are the rigid, mass-dependent moments of inertia
and c is a constant. The second term in the above equation is
thought to, in part, correct for zero-point vibrations; hence,
(1)
structure is thought to be superior to both r 0 and r s
an r m
(2)
geometries. 共The derivation of an r m
structure would have
been preferable because it is thought to be closest to the
equilibrium geometry.28 This calculation was not possible
because it requires the substitution of all atoms, which was
not done for ZnCN.兲
As shown in Table V, the zinc–carbon bond length is r
(1)
⫽1.9496 Å).
⬇1.95 Å, as indicated by all structures (r m
The C–N bond distance varies over the range 1.1417 Å
(1)
) to 1.1464 Å (r 0 ). The metal–carbon bond length in
(r m
ZnCN is intermediate in value between that of CuCN
共1.8358 Å兲 and GaCN 共2.058 Å兲, as might be expected. In
contrast, the C–N bond distance in ZnCN appears to be
anomalously short—both bond lengths in CuCN and GaCN
are significantly longer 共1.157–1.160 Å兲, and are comparable
to that in HCN 共1.1540 Å12兲.
An unusually short C–N bond of 1.143–1.146 Å has
(1)
structures. In
also been found in InCN,12 based on r s and r m
(2)
structhis case, all atoms were substituted such that an r m
ture could also be derived, which resulted in a more ‘‘normal’’ bond length of r C–N⫽1.1587 Å. The differences between the various structures are attributed to the presence of
a flat bending potential in InCN. The same situation could
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J. Chem. Phys., Vol. 117, No. 10, 8 September 2002
(2)
apply to ZnCN as well, in that the calculation of an r m
geometry could yield a more typical C–N bond distance.
However, this result would also imply a flat bending potential in ZnCN. An analysis of the vibrational structure suggests otherwise, as discussed. The shorter C–N bond distance may be a real effect.
B. Preference for a linear cyanide structure
The existence of a T-shaped geometry for NaCN and
KCN has been explained by simple electronegativity arguments 共e.g., Refs. 6 – 8兲. Sodium and potassium donate their
valence electron to the CN moiety, and an M⫹ CN⫺ polytopic structure results. More electronegative metals will have
the tendency to keep their electrons and form more covalent
linear isocyanide structures, and, at the far extreme, the most
covalently bonded species will be the linear cyanides.
For the 3d transition metal cyanides and their IIIA counterparts, such electronegativity arguments do not apply. Although copper and nickel are the most electronegative elements of this group, with values of 1.90 and 1.91,
respectively,34 the next most electronegative element is gallium 共1.81兲. Zinc is considerably less electronegative than
the others, with a value of 1.65—quite comparable to that of
aluminum with 1.61. Yet, the most stable form of zinc, copper, and nickel is the linear cyanide species, while gallium
and aluminum favor the isocyanide geometry.
The explanation likely lies in how these elements bond
to the CN group. Based on their electronic ground states
(ZnCN:X 2 ⌺ ⫹ ;CuCN:X 1 ⌺ ⫹ ;NiCN:X 2 ⌬ i ), the bond to the
CN moiety for these molecules is made through the ␴ (4s)
orbital from the metal. A full 3d shell (3d 10) is still present
on copper and zinc, and a 3d 8 shell on nickel. The 3d and 4s
shells are still relatively close in energy.35 Hence, there is a
possibility of metal– ␲* backbonding of the 3d electrons into
the empty ␲* orbital on the CN moiety. The ␲* orbital is
composed predominantly of contributions from the p orbitals
of the carbon atom, and consequently the metal forms the
bond to this site, as opposed to nitrogen, creating the cyanide
species.
In both aluminum and gallium, the bond to the CN group
occurs via a 3p or 4p 共␴兲 orbital. Aluminum has no 3d
electrons for backbonding; the 3d orbitals on gallium have
dropped considerably in energy relative to the 4p orbital, as
opposed to the 4s, making backbonding to the CN group
very unlikely. Because of the lack of ␲* backbonding, there
is no reason for gallium or aluminum to bond to the carbon.
The more electropositive metal would rather bond to the
more electronegative nitrogen atom of the C␦ ⫹ N␦ ⫺ functional group.
It should also be mentioned that iron is most stable in the
isocyanide form, FeNC.11 Iron has a 3d 6 configuration—two
d electrons less than nickel. It may be that there is some
critical number of d electrons that must participate in backbonding to produce the cyanide structure, as opposed to the
isocyanide. Spectroscopy of such molecules as MnNC/
MnCN, CrNC/CrCN, etc., would certainly verify this hypothesis. It would also be of interest to establish the preferred structure of cobalt and the cyanide group.
Millimeter-wave studies of ZnCN
4859
VI. CONCLUSION
The measurement of the pure rotational spectrum of
ZnCN and several of its isotopomers has demonstrated that
the radical has a 2 ⌺ ⫹ ground electronic state 共a linear structure兲, and that there is a preference for zinc to bond to the
carbon as opposed to the nitrogen atom. Therefore, zinc has
similar bonding properties to other late 3d transition metals
such as copper and nickel. Analysis of the vibrational satellite lines of the main isotopomer, 64ZnCN, indicate that the
molecule is fairly rigid, and does not appear to undergo
large-amplitude bending motions. However, estimates of the
bending and heavy atom-stretching mode frequencies, relative to those of CuCN and NiCN, suggest it is not as tightly
bound as these latter species. The metal–carbon bond length
successively increases in going from CuCN to ZnCN to
GaCN; the C–N bond distance, on the other hand, appears
anomalously short 共⬃1.14 Å兲 in zinc cyanide, relative to the
other two species, but is comparable to that found in InCN,
(1)
structure calculation. The formation of ZnCN, as
using a r m
opposed to ZnNC, can be attributed to metal– ␲* backbonding of the 3d electrons. This bonding scheme is also possible
for copper and nickel, but not for aluminum and gallium,
which both favor the isocyanide geometry.
ACKNOWLEDGMENTS
This research is supported by National Science Foundation 共NSF兲 Grant Nos. CHE 98-17707 and AST 98-20576
and NASA Grant No. NAG5-10333.
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