Chemical Physics Letters 555 (2013) 31–37
Contents lists available at SciVerse ScienceDirect
Chemical Physics Letters
journal homepage: www.elsevier.com/locate/cplett
~ 2 A1 ) and its
The Fourier transform microwave spectrum of YC2 (X
isotopologues: Chemical insight into metal dicarbides
13
C
D.T. Halfen ⇑, J. Min, L.M. Ziurys
Department of Chemistry and Department of Astronomy, Arizona Radio Observatory, and Steward Observatory, University of Arizona, 933 N. Cherry Avenue, Tucson, AZ 85721, USA
a r t i c l e
i n f o
Article history:
Received 12 August 2012
In final form 22 October 2012
Available online 29 October 2012
a b s t r a c t
~ 2 A1 ) and its 13C isotopologues has been measured in
The Fourier transform microwave spectrum of YC2 (X
the 10–57 GHz range, the first FTMW study of a metal dicarbide species. The molecule was created from
yttrium vapor and CH4 in argon in a supersonic jet with a discharge-assisted laser ablation source
(DALAS). Rotational, fine structure, and Y and 13C hyperfine constants were determined for each isotopoð1Þ
logue. The calculated r m structure is r(Y–C) = 2.187(4) Å, r(C–C) = 1.270(4) Å, and h(C–Y–C) = 33.74(7)°.
The hyperfine parameters indicate that the unpaired electron resides principally in an sd hybridized orbital on the yttrium nucleus.
Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
Transition metal dicarbide species (MC2) play a prominent role
in chemistry. Since the discovery of metallo-carbohedrenes (metcars) in 1992, large metal–carbon clusters have been the subject
of intense study [1–3]. These clusters are thought to be produced
when MC2 units assemble in a cage structure [2]. Transition-metal
dicarbides have also been shown to be the starting point for singlewalled carbon nanotubes (SWNT) and carbon nanocapsules [4,5],
and may also be involved in the formation of endohedral metallofullerenes [6,7]. In addition, MC2 species are generated by H2 elimination in the reaction of metal atoms with acetylene; the metal
acetylide MCCH is the other main product when insertion occurs [8–10]. Understanding such simple C–H activation reactions
is fundamental in evaluating more complex organometallic
processes [8].
Depending on the relative degrees of ionic vs. covalent bonding,
monomeric metal dicarbide species in principle can have three
structures: linear MCC, bent MCC, and cyclic T-shaped MC2. Spectroscopic studies of nonmetal and metalloid CCX compounds, such
as CCN, CCS, CCP, and CCAs [11–14], have shown that these species
are linear, while SiC2, in contrast, is cyclic [15–17]. Theoretical
investigations of the metal dicarbides, both main group and transitions metals, suggest cyclic or T-shaped geometries [18,19]. Little
experimental work has been done on these molecules, however,
to verify such predictions, and current spectroscopy has been limited to YC2, AlC2, and most recently, ScC2 [20–24].
YC2 is of particular interest with regard to transition metal dicarbides [25]. Graphitic cages, as well as single-walled nanotubes,
⇑ Corresponding author. Fax: +1 520 621 5554.
E-mail address: [email protected] (D.T. Halfen).
0009-2614/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.cplett.2012.10.062
have been known to form around YC2 particles [4,5]. Yttrium also
forms some of the strongest bonds with carbon [25], and has a simple electron configuration, (core) 5s24d1, making YC2 an attractive
model system. Furthermore, it has been demonstrated that the
lowest energy pathway for the reaction of yttrium with acetylene
leads to yttrium dicarbide, YC2, while a higher energy pathway
produces YCCH [8–10].
There have been numerous theoretical studies of YC2, including
those of Roszak & Balasubramanian, Jackson et al. and Glendening,
using CASSCF/CI and DFT methods [6,9,26], as well as Puzzarini &
Peterson [27], employing MRCI and CCSD(T) techniques. These cal~ 2 A1
culations concur that the molecule is a radical species with a X
ground state and a cyclic T-shaped structure with a C–Y–C bond
angle near 33°. Spectroscopically, YC2 was first investigated by
Steimle et al. in 1997, who conducted medium-resolution laser-induced fluorescence (LIF) and dispersed LIF spectroscopy of the
~ 2 A1 –X
~ 2 A1 , 31 band [21]. This study was followed by that of BousA
0
quet & Steimle in 2001, who recorded optical Stark spectra and
determined the ground state dipole moment of YC2 to be
6.38(3) D [22]. Shortly thereafter, Steimle et al. in 2002 measured
high-resolution LIF spectra of the 000–000 and 310 bands of the
~ 2 A1 –X
~ 2 A1 transition of YC2 [23]. These authors also recorded rotaA
tional spectra of the NKa,Kc = 101
000 through 404
303 transitions of this radical with pump/probe microwave optical double
resonance (PPMODR) techniques, resolving the yttrium hyperfine
structure.
Here we present the first Fourier transform microwave (FTMW)
study of the pure rotational spectrum of YC2. This Letter extends
the past work of Steimle et al. in recording additional transitions
of the main isotopologue, as well as spectra of singly- and doubly-substituted carbon-13 species Y13CC and Y13C2, which have
not been observed previously. A new U-band (40–60 GHz) source
was employed for some of these measurements. Spectroscopic
32
D.T. Halfen et al. / Chemical Physics Letters 555 (2013) 31–37
constants were established from these data, including both 13C and
Y hyperfine parameters, and an improved molecular structure was
determined. Here we present these measurements, their analysis,
and the implications for the bonding in YC2.
2. Experimental
The microwave spectrum of YC2 and its carbon-13 isotopologues was measured using the Balle-Flygare-type FTMW spectrometer of the Ziurys group [28,29]. This machine is composed
of a large vacuum chamber with a background pressure near 108 Torr, evacuated with a cryopump. Inside the cell are two spherical
mirrors in a near confocal arrangement, forming a Fabry–Perot cavity. Two sets of mirrors are used to cover the 4–60 GHz range. Molecules are created in a supersonic jet expansion, using a pulsed
valve/laser ablation nozzle that lies at 40° relative to the optical
axis. Microwaves are pulsed into the cavity through either an antenna (4–40 GHz) or waveguide (40–60 GHz) imbedded in one
mirror. After interaction with the molecular beam, emission signals
are collected by an antenna or waveguide imbedded in the second
mirror and detected with a low noise amplifier (LNA). Time domain
signals are acquired at a rate of 10 Hz and are processed with an
FFT to produce spectra with 4 kHz resolution. The detected spectra
appear as Doppler doublets with a line width of 10 kHz per feature,
and the center frequency is taken as the average of the two Doppler
components. For more details, see Ref. [29,30].
Yttrium dicarbide was created from the reaction of Y vapor and
methane in the presence of a DC discharge using DALAS (Discharge-Assisted Laser Ablation Source) [31]. A Nd/YAG laser operating at 532 nm was used to ablate a yttrium rod, housed in a steel
ablation adapter that is attached to a Teflon discharge nozzle, i.e.
DALAS. Yttrium vapor was entrained in a mixture of 0.2–0.5%
CH4 and/or 13CH4 in Ar (200 psi), which was pulsed through the
nozzle with a backing pressure of 36 psi (248 kPa) and a flow of
50 sccm (standard cubic centimeters per minute). As the gas exited
the source and expanded into the chamber, a 800–1200 V DC dis-
charge was applied. More details on DALAS can be found in Ref.
[31]. The YC2 signals could also be produced with a 0.1% acetylene
(C2H2) in argon mixture, but the spectra were 5 times weaker in
intensity. Typically, 250–2000 pulsed averages were need for the
main isotopologue and 500–2000 for the 13C-substituted species.
Despite the presence of a l-metal shield, Zeeman doublets with
a separation of about 20–40 kHz were seen in several of the
DJ = DF = 0 components of the low N transitions. Transition frequencies were taken as the average of the observed components.
3. Results
YC2 has C2v symmetry with a large dipole moment of
la = 6.38(3) D [22], and follows the a-type selection rules DKa = 0,
DKc = ±1. The isotopologues Y12C2 and Y13C2 have equivalent nuclei, but this symmetry is broken in Y13CC, which is in the Cs point
group. In Y12C2, the two 12C nuclei are bosons, such that the total
wavefunction must be symmetric on exchange of these two nuclei.
For Y13C2, the total wavefunction must be antisymmetric with respect to particle exchange because carbon-13 is a fermion. A 2A1
ground state term in the v = 0 level has symmetric electronic and
vibrational wavefunctions with respect to particle exchange, such
that the overall symmetry is determined by pairing the rotational
wavefunction with the appropriate nuclear spin function. The spin
of 12C is I = 0, such that Itot = 0 and the spin function is always symmetric. In the case of Y13C2, the spin of 13C is I = 1/2 and Itot = 0, 1;
Itot = 0 is antisymmetric and Itot = 1 is symmetric. The symmetric
rotational wavefunctions for a-type transitions are those with
Ka,Kc = ee and eo, where e is even and o is odd, while those with
Ka,Kc = oo and oe are antisymmetric [32].
Pairing the appropriate nuclear spin and rotational wavefunctions has important consequences, as summarized in Figure 1,
which shows the energy level diagrams for YC2 and its 13C isotopologues for the N = 0 and 1 rotational levels. The spin-rotation fine
structure levels are indicated by quantum number J, and those
for hyperfine interactions by F. For Y12C2 (Itot = symm), only sym-
Energy Level Diagrams of YC2 Isotopologues
~
Y13CC (X2A )
~
YC2 (X2A1)
~
Y13C2 (X2A1)
110
110
110
111
111
111
3/2
101
1/2
1/2
000
NKa,Kc
J
F
2
1
1
0
101
1
0
000
NKa,Kc
5/2
3/2
3/2
1/2
3/2
1/2
1/2
3/2
1/2
1/2
J
F1
F
2
1
1
0
101
1
0
000
NKa,Kc
J
F1
F
Figure 1. Energy level diagrams of YC2 and its 13C isotopologues, illustrating the differences in level structure as a function of nuclear spin in 2A1 and 2A0 states. Rotational,
fine structure, and hyperfine levels are indicated by N, J, and F, as well as F1, when appropriate. The transitions observed in this Letter are marked by arrows. In YC2, Ka = odd
levels are not allowed by boson spin statistics of the 12C nuclei (I = 0), including the NKa,Kc = 110 and 111 levels, shaded in gray. YC2 has hyperfine splittings only from the 89Y
spin (I = 1/2). Y13CC does not have C2v symmetry and all Ka levels are allowed, and hyperfine interactions from both the Y and 13C (I = 1/2) are present. For Y13C2, fermion
statistics of the 13C nuclear spins pairs the Ka even levels with Itot = 0, and the Ka odd levels with Itot = 1. Therefore, the Ka = 0 levels do not have 13C hyperfine splitting, while
those with Ka = 1 do.
33
D.T. Halfen et al. / Chemical Physics Letters 555 (2013) 31–37
Table 1
~ 2 A1 ).a
Transition frequencies of YC2 and Y13C2 (X
J0 ? J00
F0 ? F00
YC2
mobs
mo–mc
mobs
mo–mc
101 ? 000
0.5 ? 0.5
1.5 ? 0.5
1.5 ? 0.5
1.5 ? 1.5
1.5 ? 0.5
1.5 ? 0.5
1.5 ? 0.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 2.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
3.5 ? 2.5
3.5 ? 2.5
3.5 ? 2.5
3.5 ? 2.5
4.5 ? 3.5
4.5 ? 3.5
4.5 ? 3.5
4.5 ? 3.5
5.5 ? 4.5
5.5 ? 4.5
1?1
1?0
2?1
2?2
1?1
1?0
2?1
2?1
3?2
3?3
2?2
2?1
3?2
3?2
4?3
3?2
4?3
4?3
5?4
4?3
5?4
5?4
6?5
11401.079
11502.587
11557.241
22788.819
22865.377
22896.346
22945.008
22997.137
23039.059
34153.235
34290.711
34370.313
34403.431
34476.306
34508.363
45818.826
45843.808
45933.423
45958.082
57239.820
57259.121
57362.305
57381.517
0.008
0.003
0.001
0.001
0.010
0.015
0.017
0.005
0.001
10701.292
10795.578
10847.636
0.000
0.007
0.001
21583.493
21624.051
0.006
0.002
32258.367
32290.941
32356.608
32388.115
0.000
0.000
0.002
0.001
202 ? 101
303 ? 202
404 ? 303
505 ? 404
a
b
Y13C2
NKa,Kc0 ? NKa,Kc00
b
0.007
0.005
0.003
0.004
0.001
0.000
0.004
0.000
0.001
0.002
0.002
0.001
0.001
In MHz.
Unresolved Zeeman splitting, not included in fit.
metric rotational levels exist (i.e. Ka = 0, 2, 4, etc. components); odd
Ka levels are not allowed, as Figure 1 shows. Because the spin function can be symmetric or antisymmetric for Y13C2, all Ka levels are
allowed, but the Ka = 0, 2, 4, etc. components are paired with
Itot = 0, and thus have no 13C hyperfine interactions. In contrast,
the Ka = 1, 3, 5, etc. levels have Itot = 1 and thus hyperfine structure
is possible. For Y13CC, there are no equivalent nuclei and each rotational level is split into Y and 13C hyperfine states, see Figure 1. The
coupling scheme for this species is best described as F1 = J + I1(Y),
F = F1 + I2(13C).
The measurements for YC2 were based on the work of Steimle
et al. First, spectra were recorded for the lines observed by these
authors in the NKa,Kc = 202 ? 101 transition near 22 GHz, and chemical conditions optimized. Weaker hyperfine lines were then located, and the NKa,Kc = 101 ? 000, 303 ? 202, and 404 ? 303
transitions were measured accordingly. Frequency predictions were
then made for the NKa,Kc = 505 ? 404 transition, based on a preliminary fit of the data, and additional lines recorded. The FTMW measurements were within ±50 kHz of the 11 lines recorded by
Steimle et al. The transition frequencies of the 13C isotopologues
were predicted by scaling the YC2 constants by the appropriate reduced mass. Locating spectra of these two species required more
extensive searches, covering 10–12 MHz in frequency.
The rotational frequencies measured for YC2 and Y13C2 in their
~ 2 A1 ground states are listed in Table 1. As is evident in the table,
X
only data for the Ka = 0 components were recorded. The Ka = 1 levels for Y13CC and Y13C2 and the Ka = 2 states for YC2 exist. The Ka = 1
components for the two isotopic species were searched for but
could not be identified in the data. The values of B and C given
by Steimle et al. for YC2 were 99% correlated [23]. Thus, the value
of (B–C), which is directly related to the frequency separation of
the Ka = 1 lines, has very high uncertainty, and our search may
not have covered a sufficient range to locate these components.
The Ka = 2 levels lie over 14 K in energy, and would not likely be
very populated in the jet expansion, where the rotational temperature is near 5 K. In the Ka = 0 components, each rotational transition N + 1 ? N is split into spin-rotation doublets, and additional
splittings are generated by the yttrium nuclear spin of I(89Y) = 1/
2. Twenty-three hyperfine lines were recorded for the main isotopologue over five rotational transitions, and nine for Y13C2 in three
transitions. One line for YC2 had unresolved Zeeman splitting and
was omitted from the fit, as indicated in the table. From this line,
the residual magnetic field in the chamber is estimated to be
30 mG [32], about 8% of the Earth’s magnetic field of 350 mG,
as measured in Tucson, Arizona.
In Table 2, the data recorded for Y13CC are presented. In this
case, 13C hyperfine structure was resolved, as expected, in addition
to that from yttrium, which creates doublets of doublets, as both
spins have I = 1/2. (Additional, weaker hyperfine components are
present where DF = 0). Quantum number F1 labels the splitting
due to the Y nucleus, as discussed, and those arising from 13C by
F. In total, 19 hyperfine lines from three rotational transitions were
observed for Y13CC (see Table 2). Only a-type transitions were
measured; no b-type lines were observed because the b-type
Table 2
~ 2A0 ).a
Transition frequencies of Y13CC (X
NKa,Kc0 ? NKa,Kc00
J0 ? J00
F 01 ? F 001
F0 ? F00
mobs
mo–mc
101 ? 000
0.5 ? 0.5
1.5 ? 0.5
1.5 ? 0.5
1.5 ? 0.5
1.5 ? 0.5
1.5 ? 0.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
2.5 ? 1.5
3.5 ? 2.5
3.5 ? 2.5
3.5 ? 2.5
3.5 ? 2.5
1?1
1?0
2?1
2?1
1?0
2?1
2?1
2?1
3?2
3?2
2?1
2?1
3?2
3?2
3?2
3?2
3?2
4?3
4?3
1.5 ? 1.5
1.5 ? 0.5
2.5 ? 1.5
1.5 ? 0.5
1.5 ? 0.5
2.5 ? 1.5
1.5 ? 0.5
2.5 ? 1.5
3.5 ? 2.5
2.5 ? 1.5
2.5 ? 1.5
1.5 ? 0.5
3.5 ? 2.5
2.5 ? 1.5
2.5 ? 2.5
2.5 ? 1.5
3.5 ? 2.5
4.5 ? 3.5
3.5 ? 2.5
11030.529
11135.697
11187.673
11191.572
22161.884
22209.210
22259.516
22261.951
22301.962
22302.991
33269.433
33270.039
33301.593
33304.640
33307.392
33371.227
33373.127
33403.947
33404.448
0.003
0.004
0.001
0.006
0.003
0.003
0.006
0.000
0.002
0.000
0.005
0.008
0.008
0.013
0.002
0.000
0.003
0.002
0.001
202 ? 101
303 ? 202
a
In MHz; the coupling scheme is F1 = J + I1(Y) and F = F1 + I2(13C).
34
D.T. Halfen et al. / Chemical Physics Letters 555 (2013) 31–37
~2
YC2 (X A1): NK ,K = 303
a
J = 2.5
J = 3.5
1.5
F=3
F=3
F=2
34370.1
~2
13
Y C2 (X A1): NK ,K = 303
202
c
a
2.5
F=4
J = 2.5
3
2
F=2
F=3
F=3
2
2.5
F=4
3
2
2
34403.5
34476.4
34508.4
32258.1
~2
YC2 (X A1): NK ,K = 505
a
J = 4.5
404
J = 5.5
3.5
F=5
c
F=5
4
4.5
F=6
5
4
3
57240.0
57259.2
57362.3
57381.5
Frequency (MHz)
Figure 2. FTMW spectra of the NKa,Kc = 303 ? 202 (upper panel) and 505 ? 404
~ 2 A1 ) near 34 and 57 GHz. Each
(lower panel) rotational transitions of YC2 (X
rotational transition consists of fine structure doublets, marked by J, each of which
is further split into two hyperfine components, labeled by F, due to the Y nuclear
spin. There are three frequency breaks in the data in order to show all four features.
Doppler doublets, indicated by brackets, are apparent in each line profile. The
NKa,Kc = 303 ? 202 and 505 ? 404 spectra were each created from four, 500 kHz-wide
scans, with 270–2500 and 1800–2000 pulse averages per scan, respectively.
dipole moment is estimated to be 0.1 D, based on that of 13CC
[33]. Therefore, the b-type transitions would be a factor of 64
times weaker than the a-type lines that were measured, and thus
not detectable given the noise levels.
Spectra of the NKa,Kc = 303 ? 202 (upper panel) and 505 ? 404
(lower panel) transitions of YC2 near 34 and 57 GHz are presented
in Figure 2. Each transition consists of a spin-rotation doublet,
labeled by J, which is further split into two hyperfine lines due to
the spin of the 89Y nucleus, and indicated by F. There are three
frequency breaks in each spectrum in order to show all four lines.
32258.5
32291.0
32356.6
32388.0
Frequency (MHz)
Frequency (MHz)
57239.6
J = 3.5
1.5
1
34370.5
F=4
1
202
c
~ 2 A1 ) near
Figure 3. FTMW spectrum of the NKa,Kc = 303 ? 202 transition of Y13C2 (X
32 GHz. The spectrum is very similar to that of YC2, with spin-rotation doublets,
indicated by J, which are further split into two yttrium hyperfine components,
labeled by F. Carbon-13 hyperfine structure is not present in the Ka = 0 component
of Y13C2 because of fermion statistics. There are three frequency breaks in the
spectrum to show the four components. Doppler doublets for each feature are
indicated by brackets. The spectrum was created from four, 500 kHz-wide scans
with 2000 shots each.
Each feature is also split into Doppler doublets, indicated by brackets, due to the orientation of the molecular jet relative to the electric field of the cavity.
In Figure 3, a spectrum of the NKa,Kc = 303 ? 202 transition of
Y13C2 is displayed near 32 GHz. The pattern is virtually identical
to that of the main isotopologue, with a ‘doublet of doublets’
resulting from spin-rotation and Y hyperfine interactions, labeled
by J and F. Again, there are three frequency breaks in the spectrum
in order to show all four lines, and the Doppler doublets are indicated by brackets.
Figure 4 shows lines arising from the NKa,Kc = 303 ? 202 transition for Y13CC near 33 GHz. There are multiple frequency breaks
in the spectrum in order to display six of the nine components
measured for this transition. The Doppler doublets present in each
feature are indicated by brackets. For this species, hyperfine coupling from the single 13C nucleus now splits each yttrium F1 hyperfine component into additional lines, labeled with F. The relative
contributions of the 89Y and 13C hyperfine interactions is illustrated
by the J = 3.5 ? 2.5 spin component, shown in the figure. Yttrium
generates the F1 = 4 ? 3 and 3 ? 2 splitting of about 30 MHz,
while that due to 13C is much smaller, less than 0.5 MHz for the
F = 4.5 ? 3.5 and 3.5 ? 2.5 lines, for example.
4. Analysis
The spectra of YC2 and its 13C isotopologues were individually
fit with an S-reduced asymmetric top Watson Hamiltonian that included rotation, centrifugal distortion, spin-rotation,and magnetic
hyperfine interactions [34]:
^ eff ¼ H
^ rot þ H
^ cd þ H
^ sr þ H
^ mhf :
H
ð1Þ
The spectroscopic constants were determined using the nonlinear least squares fitting program SPFIT [35], and are given in Table 3. In each fit, A and eaa, as well as the ratio of B to C, were
fixed to the values from Steimle et al. [23]. In addition, DNK was
35
D.T. Halfen et al. / Chemical Physics Letters 555 (2013) 31–37
~2
13 12
Y C C (X A'): NK ,K = 303
a
J = 2.5
c
J = 3.5
1.5
2.5
F = 3.5
2
33269.8
3
3.5
2
3.5
2
4
2.5
3
1.5
33371.2
33270.2 33301.5
2.5
2
2.5
0.5
3
3.5
2.5
1
1.5
4
4.5
3
F1 = 3
202
33373.2
33404.0
33404.5
Frequency (MHz)
~ 2 A0 ) near 33 GHz. The spectrum is more complex that those of YC2 and Y13C2 because of the
Figure 4. FTMW spectrum of the NKa,Kc = 303 ? 202 transition of Y13CC (XX
presence of both Y and 13C hyperfine structure. Each fine structure component, labeled by J, is first split into F1 components due to the yttrium nuclear spin, separated by
about 30 MHz. Additional, smaller splittings of order a few MHz or less, arising from the 13C nuclear spin of ½ and labeled by F, produce the observed spectrum. Each feature
exhibits Doppler doublets, indicated by brackets, and there are four frequency breaks in the data to display multiple lines. The spectrum is a composite of four, 500 kHz wide
scans, and 1 MHz-wide scan-composite of two 500 kHz-wide scans; each 500 kHz scan is 2000 pulse averages.
Table 3
~ 2A1), Y13CC (X
~ 2A0 ), and Y13C2 (X
~ 2A1).
Spectroscopic constants of YC2 (X
Parametera
MW
52 246c
6054.3651(25)d
5434.6584(23)d
5744.5117(17)
0.02 087(17)
1.537c
1.00(35) 106
eaa
2123c
ebb
103.6879(67)d
ecc
163.440(11)d
(ebb + ecc)/2 133.5637(62)
0.04 205(25)
DsN
aF (Y)
566.56(17)
Taa (Y)
44.340(36)
TaaD (Y)
0.0327(57)
aF (13C)
aFD (13C)
Taa (13C)
TaaD (13C)
rms
0.006
A
B
C
(B + C)/2
DN
DNK
HN
a
b
c
d
Y13CC
YC2
Y13C2
Opticalb
MW
MW
52 246(13)
6054.3(5.4)
5434.6(5.4)
5744.5(3.8)
0.0210(90)
52 246c
5860.7142(52)d
5260.8291(46)d
5560.7716(35)
0.03 447(26)
1.537c
52 246c
5682.651(12)d
5100.991(11)d
5391.8210(82)
0.04 920(58)
1.537c
2123(72)
265.6(2.7)
0c
132.8(1.3)
0.3127(45)
589.2(1.2)
45.0(6.3)
2123c
100.327(37)d
158.141(59)d
129.234(70)
0.0459(17)
565.25(25)
44.69(25)
0.032(11)
28.115(79)
0.0123(95)
3.40(12)
0.080(27)
0.005
2123c
97.334(79)d
153.42(12)d
125.379(74)
0.0455(34)
566.85(35)
43.70(49)
0.024(17)
0.003
In MHz; errors are 3r in the last quoted decimal places.
Ref. [23].
Held fixed.
Ratio held fixed, see text.
fixed to the value of DJK for SiC2 [16,17] and the ratio of ebb to ecc to
that calculated for AlC2 [36]. More rotational transitions and asymmetry components would be needed to determine more global
constants. Several higher-order distortion constants were also used
in the analysis: HN for the main isotopologue and TaaD for both Y
and 13C hyperfine interactions, as well as aFD for Y13CC (see Table 3).
These terms reflect the rather asymmetric nature of the molecule.
The asymmetry parameter for YC2 is j = 0.974 [32]. This value
indicates more asymmetry than for the near-prolate asymmetric
top SrSH (j = 0.999), for example, and is closer to the values
found for T-shaped species NaCN and KCN (j = 0.957 and
0.985) [37–39]. The rms values of the fits are between 3 and
6 kHz, in good agreement with the experimental uncertainty of
±4 kHz.
Given the differences in the data sets, the parameters determined from the microwave data for YC2 agree well with those from
the optical work of Steimle et al. [23], in particular (B + C)/2 and DN.
For the spin-rotation constants, Steimle et al. could not independently determine ecc and therefore fixed it to 0. In our fit, both
ebb and ecc were fitted but their ratio was held fixed; however,
the average spin-rotation parameter (ebb + ecc)/2 for our work
agrees with that of Steimle et al. to within the uncertainties. The
dipolar term Taa is in excellent agreement with c, as given by the
Steimle et al. paper, recognizing that Taa = 23 c [23]. On the other
hand, the aF and DsN constants are smaller than those reported by
Steimle et al., most likely a reflection of the low N microwave data
set. When their PPMODR data is analyzed alone, aF and DsN reflect
our values. Combining the LIF and PPMODR data apparently has
a significant effect on these parameters.
5. Discussion
Assuming the molecule has C2v symmetry and a T-shaped
geometry, as established by Steimle et al. [23], the structure of
YC2 was determined by a nonlinear least-squares analysis in the
STRFIT code [40]. An r0 structure was first established using the
sum of the rotational constants (B + C) of all three isotopologues.
ð1Þ
In addition, an r m geometry was calculated using the (B + C) values
and the A constant from Steimle et al. [23]. This structure partially
takes into account the effects of zero-point vibrations by modeling
the mass dependence of the moment of inertia, bringing it closer to
the equilibrium geometry [41]. The structural parameters for YC2,
as well as the r0 values from Steimle et al. and the theoretical
geometry from Puzzarini & Peterson, are listed in Table 4 [23,27].
ð1Þ
From the r m analysis, the bond lengths and angle were established
to be r(Y–C) = 2.187(4) Å, r(C–C) = 1.270(4) Å, and h(C–Y–
C) = 33.74(7)°. These parameters agree with the theoretical values
and with those from Steimle et al. to within 0.01 Å and 0.02°
[23,27].
36
D.T. Halfen et al. / Chemical Physics Letters 555 (2013) 31–37
Table 4
Structural parameters of YC2 and related molecules.
Molecule
r(MC) (Å)
r(CC) (Å)
h(CMC)
(deg.)
Method
Ref.
YC2
2.194(2)
1.264(2)
33.5(1)
r0a
2.187(4)
1.270(4)
33.74(7)
rm
2.1946
2.1998
1.2697
1.2690
33.63
33.53
1.83 232(58)
1.26 855(36)
1.2425
1.3391(13)
1.20 241(9)
40.505(25)
r0
re, CCSD(T)/
CBS + CV + SO
rs
re, Optical
rz, MW
re, Infrared,
Raman
This
Letter
This
Letter
[23]
[27]
SiC2
C2
CH2@CH2
HC„CH
a
b
ð1Þ b
[17]
[45]
[43]
[42]
Fitted with (B + C) of isotopologues from this Letter.
Additionally fitted with A of Y12C2 from Ref. [23]; cb = 0.116(68).
The C–C bond length of YC2 (1.270 Å) lies between that of acetylene (1.202 Å) and ethylene (1.339 Å) [42,43]. This result suggests
that the C–C bond is a mixture of a double and triple bond, with a
bond order of about 2.5. The Y–C bond length, in comparison with
theoretical work [9], is indicative of a single bond. The perpendicular distance from the Y nucleus to the C–C moiety was calculated
to be 2.093 Å, larger than the Y atomic radius of 1.80 Å [44].
Table 4 also lists geometries of related species. As the table
show, the bond length of the C2 (X1 Rþ
g ) molecule is 1.2425 Å
[45], a triple bond, and thus slightly shorter than the C–C bond
in YC2. The electron density contributed by the Y atom appears
to increase the distance between the C atoms. In SiC2, the only
other T-shaped dicarbide molecule with an accurate experimental
structure, the geometry changes relative to YC2. The C–Si–C angle
in this molecule is larger (40.5° vs 33.7°), and the heteroatom-carbon bond length is shorter (1.8323(6) Å as opposed to 2.187(4) Å).
The C–C bond length in SiC2 (1.2685(4) Å) [17], in contrast, is almost identical to that of YC2. These findings suggest that the C–C
bond in the triangular dicarbide species does not change significantly on substitution of Y for Si, and that the C–M–C angle is a
function of the perpendicular distance between the heteroatom
and the C2 group. A larger heteroatom lengthens the distance to
the C2 moiety and decreases the angle. Further studies of dicarbide
species are certainly needed to verify this simple picture.
The electron configuration for YC2 is proposed to be (core)
12a1213a125b1214a11. The 12a1, 13a1, and 5b1 orbitals are principally associated with the C2 moiety; the 14a1 orbital is thought
to be composed mainly of the 5s orbital of Y. The contribution of
the 5s orbital to the 14a1 orbital can be evaluated by comparing
the Y atomic Fermi contact term with the molecular constant aF,
which is defined as [32]:
aF ¼
8p
g l g l hjWð0Þj2 i:
3 s B N N
ð2Þ
Comparison of the yttrium atomic Fermi contact term
(1189 MHz [46]) to that of YC2 shows that the 5s contribution to
the 14a1 orbital is 48%. This value is considerably different from that
calculated by Glendening, who suggested that the orbital had 87%
5s character [9]. The remaining 52% contribution to the 14a1 orbital
is probably due to the 4dr orbital of Y. This result indicates that the
14a1 orbital of YC2 has substantial sd hybridization. Therefore, YC2
appears to be more covalent than previously thought.
The dipolar constant Taa is defined as [23]:
T aa
3 cos2 h 1
¼ g s lB g N lN
:
r3
ð3Þ
Assuming that the 4dr orbital makes the major angular contribution to the 14a1 orbital, and thus to Taa, the expectation value of
hr13 i for YC2 can be calculated. The result is hr13 i = 2.0 1025 cm3 or
2.94 a03, using the angular expectation value of 4/7 for the dr
orbital. The hr13 i parameter for the Y+ ion (5s14d1) is 1.6 1025
cm3 or 2.373 a03 [47], and that for the neutral atom (5s24d1) is
1.711 a03 [48]. The values of hr13 i in the neutral Y atom and Y+ reflects the size of the 4d orbital, which becomes more contracted for
the ion. This calculation would infer that the unpaired electron in
YC2 also lies in a more contracted orbital, perhaps resulting from
sd hybridization and also from carrying a more electropositive
charge. Glendening suggests a charge of +1.21 on the Y atom but
with 87% 5s character of the 14a1 orbital, clearly too large. The
effective charge on Y must be smaller, perhaps +0.6.
The 13C hyperfine constants of YC2 have been measured here for
the first time, providing additional insight into bonding. The value
of aF(13C) for Y13CC is 28.115(79) MHz, much smaller (<1%) than
the atomic parameter of 3777 MHz [47]. In addition, the dipolar
term Taa(13C) is only 3.40(12) MHz. These numbers clearly show
that little unpaired electron density exists on the carbon atoms
in YC2. The unpaired electron must reside principally on the Y nucleus in an orbital that is sd hybridized.
The bonding in YC2 has previously been described as highly ionic with a stoichiometry of Y2þ C2
2 [9]. In the ionic scheme, the two
electrons from the Y nucleus are completely transferred to the C2
moiety, with the remaining unpaired electron residing in the 5s
(now 14a1) orbital. The data presented here, however, suggest that
this model is oversimplified, for various reasons. First, the C2
2 moiety has a triple carbon–carbon bond, where as YC2 does not. Secondly, the 14a1 orbital is not primarily 5s, but has a major
contribution from the 4dr orbital. Hence, there is significant covalent character to the Y–C2 bond. This bonding is created when the
2pp a1 orbital of the C2 moiety, which is in the plane of the molecule, interacts with the Y 5s/4dr a1 hybrid orbital, which has electron density pointed perpendicular to the C–C axis. The two
electrons, which in the ionic scheme would reside on the C2 moiety, are actually shared with the Y atom, reducing the C–C bond order from 3 (triple bond) to 2.5. The remaining unpaired electron
resides in the corresponding ‘anti-bonding’ orbital with sd hybridization, which is localized near the Y nucleus.
6. Conclusion
This work is the first FTMW study of a metal dicarbide, in this
case YC2. Through measurements of the 13C isotopologues, which
had not been previously studied, a more accurate structure has
been determined for this interesting species. In addition, 13C
hyperfine splittings in Y13CC were observed for the first time, providing further insight into the bonding in the molecule. The C–C
bond in YC2 appears to be intermediate between a double and triple bond, with the C–M–C bond angle related to the size of the heteroatom. The unpaired electron resides in an sd hybridized orbital,
with more covalent character than predicted theoretically. In addition, the sharing of electron density between the metal atom and
the C–C moiety to some extent destabilizes the molecule relative
to the C2 species, activating the C–C bond. This effect could explain
the tendency for MC2 units to form clusters. In this case, the metal
atom would take the role of the activating group. Additional spectroscopic studies of metal dicarbide species would be very useful in
further elucidating their chemical and physical properties.
Acknowledgment
This research is supported by NSF Grant CHE-1057924.
References
[1] B.C. Guo, K.P. Kerns, A.W. Castleman Jr., Science 255 (1992) 1411.
[2] S. Wei, B.C. Guo, J. Purnell, S. Buzza, A.W. Castleman Jr., J. Phys. Chem. 96
(1992) 4166.
D.T. Halfen et al. / Chemical Physics Letters 555 (2013) 31–37
[3] M.-M. Rohmer, M. Bénard, J.-M. Poblet, Chem. Rev. 100 (2000) 495.
[4] D. Zhou, S. Seraphin, S. Wang, Appl. Phys. Lett. 65 (1994) 1593.
[5] Y. Saito, T. Yoshikawa, M. Okuda, M. Ohkohchi, Y. Ando, A. Kasuya, Y. Nishina,
Chem. Phys. Lett. 209 (1993) 72.
[6] P. Jackson, G.E. Gadd, D.W. Mackey, H. van der Wall, G.D. Willet, J. Phys. Chem.
A 102 (1998) 8941.
[7] H. Shinohara, Rep. Prog. Phys. 63 (2000) 843.
[8] H.U. Stauffer, R.Z. Hinrichs, P.A. Willis, H.F. Davis, J. Chem. Phys. 111 (1999)
4101.
[9] E.D. Glendening, J. Phys. Chem. A 108 (2004) 10165.
[10] P.E.M. Siegbahn, Theor. Chim. Acta 87 (1994) 277.
[11] Y. Ohshima, Y. Endo, J. Mol. Spectrosc. 172 (1995) 225.
[12] S. Saito, K. Kawaguchi, S. Yamamoto, M. Ohishi, H. Suzuki, N. Kaifu, Astrophys.
J. 317 (1987) L115.
[13] D.T. Halfen, M. Sun, D.J. Clouthier, L.M. Ziurys, J. Chem. Phys. 130 (2009)
014305.
[14] M. Sun, D.J. Clouthier, L.M. Ziurys, J. Chem. Phys. 131 (2009) 224317.
[15] P. Thaddeus, S.E. Cummins, R.A. Linke, Astrophys. J. 283 (1984) L45.
[16] C.A. Gottlieb, J.M. Vrtílek, P. Thaddeus, Astrophys. J. 343 (1989) L29.
[17] J. Cernicharo, M. Guélin, C. Kahane, M. Bogey, C. Demuynck, J.L. Destombes,
Astron. Astrophys. 246 (1991) 213.
[18] P. Largo, C. Redondo, J. Barrientos, Am. Chem. Soc. 126 (2004) 14611.
[19] V.M. Rayon, P. Redondo, C. Barrientos, A. Largo, Chem. Eur. J. 12 (2006) 6963.
[20] J. Yang, R.H. Judge, D.J. Clouthier, J. Chem. Phys. 135 (2011) 124302.
[21] T.C. Steimle, A.J. Marr, J. Xin, A.J. Merer, A. Athenassenas, D. Gillet, J. Chem.
Phys. 106 (1997) 2060.
[22] R.R. Bousquet, T.C. Steimle, J. Chem. Phys. 114 (2001) 1306.
[23] T.C. Steimle, R.R. Bousquet, K.C. Namiki, A.J. Merer, J. Mol. Spectrosc. 215
(2002) 10.
[24] J. Min, D.T. Halfen, L.M. Ziurys, Int. Sym. Mol. Spectrosc. (2012) FC12.
[25] P.E.M. Siegbahn, J. Phys. Chem. 99 (1995) 12723.
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
37
S. Roszak, K. Balasubramanian, Chem. Phys. Lett. 246 (1995) 20.
C. Puzzarini, K.A. Peterson, J. Chem. Phys. 122 (2005) 084323.
T.J. Balle, W.H. Flygare, Rev. Sci. Instrum. 52 (1981) 33.
M. Sun, A.J. Apponi, L.M. Ziurys, J. Chem. Phys. 130 (2009) 034309.
D.T. Halfen, J. Min, A.J. Apponi, L.M. Ziurys, in preparation.
M. Sun, D.T. Halfen, J. Min, B. Harris, D.J. Clouthier, L.M. Ziurys, J. Chem. Phys.
133 (2010) 174301.
C.H. Townes, A.L. Schawlow, Microwave Spectroscopy, Dover, New York, 1975.
R.B. Bernstein, P.R. Certain, Comments At. Mol. Phys. 5 (1975) 27.
J.K.G. Watson, Aspects of Quartic and Sextic Centrifugal Effects on Rotational
Energy Levels, Vibrational Spectra and Structure, vol. 6, Elsevier, Amsterdam,
1977. pp. 1–89.
H.M. Pickett, J. Mol. Spectrosc. 148 (1991) 371.
D.J. Clouthier, private communication.
D.T. Halfen, A.J. Apponi, J.M. Thompsen, L.M. Ziurys, J. Chem. Phys. 115 (2001)
11131.
H.S.P. Müller, D.T. Halfen, L.M. Ziurys, J. Mol. Spectrosc. 272 (2012) 23.
T. Törring, J.P. Bekooy, W.L. Meerts, J. Hoeft, E. Tiemann, A. Dymanus, J. Chem.
Phys. 73 (1980) 4875.
Z. Kisiel, J. Mol. Spectrosc. 218 (2003) 58.
J.K.G. Watson, A. Roytburg, W. Ulrich, J. Mol. Spectrosc. 196 (1999) 102.
E. Kostyk, H.L. Welsh, Can. J. Phys. 58 (1980) 912.
E. Hirota, Y. Endo, S. Saito, K. Yoshida, I. Yamaguchi, K. Machida, J. Mol.
Spectrosc. 89 (1981) 223.
J.C. Slater, J. Chem. Phys. 41 (1964) 3199.
D.L. Kokkin, G.B. Bacskay, T.W. Schmidt, J. Chem. Phys. 126 (2007) 084302.
J.R. Persson, Z. Phys. D 42 (1997) 259.
J.R. Morton, K.F. Preston, J. Magn. Reson. 30 (1978) 577.
J.B. Mann, Atomic Structure Calculations II. Hartree–Fock Wave Functions and
Radial Expectation Values: Hydrogen to Lawrencium, Los Alamos Scientific
Laboratory Reports, USA, 1968.