Fourier transform infrared isotopic study of the C12 chain trapped in solid Ar

Article abstract of DOI:10.1063/1.481067

A Fourier transform infrared investigation of the ¹³C isotopic spectrum of linear C₁₂ in solid Ar coupled with density functional theory calculations at the B3LYP/cc-pVDZ level has resulted in the identification of the v₈= 1997.2 and v₉ = 1818.0 cm^-1 stretching modes. Agreement between experimental measurements and theory is very good. The identification of a third mode v₇ =2140.6 cm^-1 is considered tentative.

Full text of DOI:10.1063/1.481067

Fourier transform infrared isotopic study of the C 12 chain trapped in solid Ar
X. D. Ding, S. L. Wang, C. M. L. Rittby, and W. R. M. Graham
Citation: The Journal of Chemical Physics 112, 5113 (2000); doi: 10.1063/1.481067
View online: http://dx.doi.org/10.1063/1.481067
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 112, NUMBER 11
15 MARCH 2000
Fourier transform infrared isotopic study of the C12 chain trapped
in solid Ar
X. D. Ding, S. L. Wang,a) C. M. L. Rittby,b) and W. R. M. Grahamb)
Department of Physics and Astronomy, Texas Christian University, Fort Worth, Texas 76129
͑Received 11 August 1999; accepted 14 December 1999͒
A Fourier transform infrared investigation of the 13C isotopic spectrum of linear C12 in solid Ar
coupled with density functional theory calculations at the B3LYP/cc-pVDZ level has resulted in the
identification of the ␯8ϭ1997.2 and ␯9ϭ1818.0 cmϪ1 stretching modes. Agreement between
experimental measurements and theory is very good. The identification of a third mode ␯
7
ϭ2140.6 cmϪ1 is considered tentative. © 2000 American Institute of Physics.
͓S0021-9606͑00͒00710-8͔
I. INTRODUCTION
͑Ref. 10͒ ͑local spin density͒ functionals, have indicated that
a ring structure (C6h) is more stable than the linear chain.
For this reason, predictions of harmonic vibrational frequen-
cies have focused on the cyclic structure.8,9
During previous FTIR ͑Fourier transform infrared͒ stud-
ies on cyclic C6,11 cyclic C8,12 and linear SiC9,13 formed by
trapping the products from the laser evaporation of graphite
and silicon rods in solid argon, we have noted that under
conditions when C3 is initially the dominant carbon molecule
produced with perhaps some C9, subsequent annealing of the
matrix to ϳ40 K preferentially produces carbon clusters with
multiples of the C3 unit, specifically linear C6,14 cyclic C6,11
and linear C9.15 In conjunction with this preference we have
Although the spectra of carbon chains formed by trap-
ping the products of the evaporation of graphite in matrices
were first reported in the pioneering work of Weltner and
McLeod1 35 years ago, experimental and theoretical work on
carbon clusters continue unabated. These efforts are inspired
by interest in understanding the structures and modes of for-
mation of clusters ranging in size and complexity from the
C4 chain and C6 ring (D3h) to the fullerene structures. Fur-
ther motivation is provided by the demonstrated role of car-
bon chains as interstellar and stellar molecular species and
by suggestions that they may be the carriers of the diffuse
interstellar bands.2,3 The spectroscopy of carbon clusters was
thoroughly reviewed by Weltner and Van Zee4 in 1989. Ref-
erences to that and subsequent work appear in the database
of vibrational and electronic energy level data compiled and
critically evaluated by Jacox.5
noted the growth of a strong absorption at 1818.0 cmϪ1
,
close to the 1819.3 cmϪ1 frequency Maier’s group7 attributed
to CϪ12 in a Ne matrix. These observations have prompted the
present matrix FTIR and theoretical investigation of 13C iso-
topic shifts for the carbon–carbon stretching fundamentals of
linear C12.
In the case of linear C12 Maier and co-workers6 tenta-
tively assigned frequencies at 2013.0 and 1819.5 cmϪ1
,
which appeared on trapping the mass selected products from
the laser evaporation of graphite in neon matrices and corre-
II. THEORY
Ϫ
3
Theoretical predictions for isotopic shifts of fundamental
vibrational frequencies can often be used successfully to aid
in the identification of new molecular species. Previously we
have also pointed out some of the problems of relying too
blindly on such an approach.12 In particular, for systems,
which exhibit several vibrational fundamentals close in fre-
quency, the perturbation introduced by the isotopic substitu-
tion may lead to strong interactions between these modes. In
the case of linear carbon chains this situation is inevitable as
the length of the chain increases. To further exacerbate ͑or
complicate͒ the situation only isotopomers that break the
Dϱh symmetry give rise to interactions between ␴ and ␴
lated with an absorption at 860.2 nm identified as the ⌺u
X 3⌺Ϫg electronic transition of C12. Later in a more exten-
sive report on the infrared vibrations of mass-selected neutral
and anion chains, they reported7 three bands of which they
assigned the two at 2012.6 and 1819.3 cmϪ1 to C1Ϫ2 . Their
revised assignments to the anion were based on a decrease in
the intensity of the two absorptions observed on irradiation
with light from a xenon arc lamp and on a correlation with
Ϫ
2
the ⌸u X 2⌸g electronic transition of C12 which they had
measured previously.6 In contrast, they reported that the third
band at 2002.9 cmϪ1 grew during photobleaching and thus
tentatively attributed it to neutral C12.
u
g
modes. This makes it increasingly difficult to interpret a
spectrum including highly substituted isotopomers since
some isotopomers may remain unperturbed whereas others
may be coupled strongly to other modes. To illustrate this
situation and to aid in the identification of the vibrational
spectrum of linear C12 we have performed a series of density
functional calculations at the standard B3LYP/cc-pVDZ
level using the GAUSSIAN 94/DFT16 program suite.
In theoretical work, density functional theory ͑DFT͒ cal-
culations with both the BP ͑Ref. 8͒ ͑Becke–Perdew͒, B3LYP
͑Ref. 9͒ ͑Becke 3-parameter Lee–Yang–Parr͒, and LSD
a͒
Present address: Bruker Optics, 47697 Westinghouse Drive, Fremont,
CA 94539.
b͒
Authors to whom correspondence should be addressed. Electronic mail:
w.graham@tcu.edu and m.rittby@tcu.edu
0021-9606/2000/112(11)/5113/8/$17.00
5113
© 2000 American Institute of Physics
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5114
J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Ding et al.
To further analyze this situation we have previously in-
troduced a perturbative treatment of isotopic shifts.17 One
can show that, working within the harmonic approximation,
the first order singly substituted shift for a noninteracting
vibrational frequency is given by
␻
mi
mf
2
⌬1ϭ
1Ϫ
͉
u͉
2ϵ2␻␣
͉
u͉
,
͑1͒
ͩ
ͪ
2
where mi and mf are the initial and final isotopic masses,
respectively, ␻ the fundamental frequency, and u is the mass
weighted, zeroth-order normal mode coordinate for the iso-
topically substituted nucleus. To add the effects of interac-
tions with other modes one can consider a first-order effec-
tive Hamiltonian matrix ͑see e.g., Ref. 12͒ with elements
Heff͒rsϭ␻r␦rsϪ2 ␻ ␻s␣ur•us .
͑2͒
ͱ
͑
r
1
This introduces a mixing of vibrational modes provided the
scalar product between the atomic displacement vectors, ur
and us , is nonzero. For linear C12 this only introduces mix-
ing between stretching modes since they are all perpendicu-
lar to the bending vibrations. Upon diagonalization of the
matrix defined by Eq. ͑2͒, the frequencies obtained will ef-
fectively include higher-order contributions in the perturba-
tion series. The magnitude of these contributions depend on
the scalar product above as well as on the difference in fre-
quency between the zeroth order fundamental frequencies.
Since the isotopic shift can also be obtained to infinite order
by diagonalization of the appropriately mass weighted force
constant matrix one can easily get an estimate of the impor-
tance of higher-order contributions. We have previously
introduced12,15 a convenient measure of the relative impor-
tance, which we termed the isotopic sensitivity index, de-
fined by
FIG. 1. Vibrational stretching frequencies for linear carbon chains with odd
number of carbon atoms. Solid lines indicate ␴ modes, dotted lines indicate
u
␴
modes.
g
With an increasing number of carbons in a chain the
density of vibrational fundamentals at high frequency in-
creases. This is illustrated in Figs. 1 and 2 where the stretch-
ing fundamental frequencies obtained at the B3LYP/cc-
pVDZ level have been plotted as a function of the number of
carbon atoms for odd and even numbered clusters, respec-
tively. For shorter chains, the modes are well separated in
frequency with alternating ␴ and ␴ modes whereas for
u
g
longer chains the situation becomes more complicated, par-
ticularly in the high frequency domain. This general behavior
leads to some difficulties when trying to interpret the isotopic
spectra of long carbon chains.
⌬2ϩ⌬3ϩ¯
⌬
ϱ
␫ ϵ
s
ϭ 1Ϫ
,
͑3͒
ͯ
ͯ ͯ ͯ
⌬
⌬
1
1
where ⌬i denotes the isotopic shift to the ith order. A low
value of the sensitivity index would indicate that a first-order
treatment based on Eq. ͑1͒ should suffice for small mass
perturbations whereas a larger value would indicate a sub-
stantial admixture of other vibrational modes. In the latter
case calculated isotopic shifts would thus be more sensitive
to the exact behavior of all vibrational fundamentals.
The perturbative analysis presented above can now be
used as a guide when interpreting the isotopic spectrum of
linear C12. The optimized B3LYP/cc-pVDZ geometry pa-
Ϫ
3
rameters for the ⌺g linear ground state of C12 are given in
Table I. Although the cyclic isomer of C12 has been pre-
dicted to be the global ground state,8,9 the linear structure is
found to be a local minimum on the B3LYP/cc-pVDZ po-
tential energy surface. The harmonic stretching fundamentals
calculated at this level of theory, are given in Table II. We
note that the ␯7(␴u) mode is relatively close ͑Ͻ25 cmϪ1͒ in
frequency to the infrared inactive ␯1(␴g) mode ͑see also Fig.
2͒. From our perturbative analysis, one can thus expect the
calculated shifts, for this mode in particular, to display sub-
stantial errors as compared with experiment. Table III shows
a comparison of the isotopic sensitivity index for single 13C
FIG. 2. Vibrational stretching frequencies for linear carbon chains with even
number of carbon atoms. Solid lines indicate ␴ modes, dotted lines indicate
u
␴
modes.
substitution calculated with Eq. ͑3͒ for the five ␴ modes of
g
u
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J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Study of the C12 chain
TABLE I. B3LYP/cc-pVDZ optimized geometry parameters for C12. The
TABLE III. Comparison of the isotopic sensitivity index for single 13C
equilibrium rotational constant for this geometry is Beϭ0.178 GHz.
substitution for the ␴ modes of linear C12.
u
Parameter value
C12 Isotopomer
Bond
͑Å͒
C–C–C–C–C–C–¯
␯7(␴u) ␯8(␴u) ␯9(␴u)
␯
10(␴u)
␯
11(␴u)
C1–C2
C2–C3
C3–C4
C4–C5
C5–C6
C6–C7
1.300
1.299
1.280
1.289
1.282
1.288
13–12–12–12–12–12–¯ Ͻ0.01
0.06 Ͻ0.01
0.07
0.07
0.05
0.09
0.09
0.08
0.03
Ͻ0.01
0.10
0.07
Ͻ0.01
0.09
12–13–12–12–12–12–¯ Ͻ0.01
0.10
0.12
0.08
0.06
0.19
0.09
0.18
0.12
0.17
12–12–13–12–12–12–¯
0.26
12–12–12–13–12–12–¯ Ͻ0.01
12–12–12–12–13–12–¯
0.14
12–12–12–12–12–13–¯
0.51 Ͻ0.01
RMS
0.24 0.08
0.14
0.08
0.06
linear C12. The sensitivity index behaves as expected in that
it predicts a low sensitivity for the low frequency ␯11(␴u)
mode whereas it predicts a high sensitivity for the high fre-
quency ␯7(␴u) mode. Below we will link the behavior of the
isotopic sensitivity index to the behavior of the experimental
isotopic shifts.
cmϪ1 using a Bomem DA 3.16 Fourier transform spectrom-
eter equipped with a liquid nitrogen cooled MCT ͑Hg–Cd–
Te͒ detector and KBr beamsplitter. Details of the optical sys-
tem have been reported previously.18 The frequencies of all
bands reported were measured to Ϯ0.1 cmϪ1, unless unre-
solved because of overlapping absorptions.
III. EXPERIMENTAL PROCEDURE
IV. RESULTS AND DISCUSSION
Matrix samples were prepared by vaporizing the surface
of carbon rods using a slightly focused Nd:YAG ͑GCR-11,
Spectra-Physics͒ pulsed laser operating at 1064 nm. The
evaporated species were condensed in solid Ar ͑Matheson,
99.9995% purity͒ on a gold plated surface cooled to ϳ10 K
by a closed cycle refrigerator ͑APD Cryogenics, Displex͒ in
a vacuum of 10Ϫ7 torr or better during the experiment.
The carbon rods were fabricated by mixing carbon-12
͑Alfa, 99.9995% purity͒ and carbon-13 ͑Isotec, 99.3% pu-
rity͒ powder in various ratios and then pressing the mixtures
into rods. A degassing procedure was used to remove any
trapped gas by heating the rods to ϳ200 °C under vacuum
for 24 h.
During evaporation, a filter was used to prevent solid
particles sputtered off the rod surface from reaching the
deposition site. After the evaporation, thermally induced dif-
fusion in the matrix was used to enable the growth of large
clusters by warming the matrix to a specific temperature and
maintaining it there for ϳ10 min before cooling back to
ϳ10 K.
Figures 3 and 4 show the absorptions at 1818.0 and
1997.2 cmϪ1, which are observed to grow in together during
annealing for 10 min at 5 K increments from 20 to 35 K.
Typically, spectra for these matrices initially show a strong
␯3ϭ2038.9 cmϪ1 band of C3 which slowly diminishes while
strong absorptions indicative of linear C6 (␯
4
ϭ1952.5 cmϪ1͒, cyclic C6 (␯3ϭ1694.9 cmϪ1͒, and linear C9
(␯6ϭ1998.0 cmϪ1͒ grow in, presumably formed by reactions
of the C3 units. The observed 1818.0 cmϪ1 absorption is
fortuitously close to the frequency of one of the stretching
modes ␯9ϭ1817.8 cmϪ1 of linear C12 predicted by B3LYP/
cc-pVDZ DFT calculations. A second absorption at 1997.2
cmϪ1, which grows in simultaneously, is not as close to the
frequency of 2112.3 cmϪ1 predicted for the ␯ mode, but is
9
nevertheless a reasonable candidate. A detailed analysis of
the 13C isotopic shifts supports this contention.
Figure 3 shows the isotopic shifts which are observed as
a result of the enrichment of the starting material for the
graphite rod with 8% 13C. This level of enrichment is typi-
cally chosen for our studies of isotopic shifts in larger carbon
clusters in order to limit isotopic substitutions to single car-
bon replacements only. This strategy reduces the number of
isotopic shifts and the consequent confusion and error caused
by matching a large number of closely packed and frequently
overlapping bands with numerous shifts predicted by theory
in a fairly confined frequency region. The smaller number of
shifts resulting from single substitutions then provides a
critical test for an unambiguous identification of the cluster
in question.15,19
In Fig. 3, four isotopomer shifts are readily observed to
the low frequency side of the 1818.0 cmϪ1 absorption, which
grow in together with the main band during annealing and,
consistent with the level of 13C enrichment, are ϳ8–10% as
intense. A fifth band at 1813.4 cmϪ1 with an integrated in-
tensity consistently twice that of the others is revealed under
the optimum conditions of Fig. 3 to actually consist of two
overlapping bands at 1813.3 and 1813.6 cmϪ1. The six shifts
FTIR absorption spectra of the matrix samples were re-
corded in the region of 550–3900 cmϪ1 at a resolution of 0.2
TABLE II. B3LYP/cc-pVDZ harmonic frequencies and infrared intensities
for all stretching modes of linear C12.
Vibrational
mode
Frequency
Infrared intensity
͑cmϪ1
͒
͑km/mol͒
␯1(␴g)
␯2(␴g)
␯3(␴g)
␯4(␴g)
␯5(␴g)
␯6(␴g)
␯7(␴u)
␯8(␴u)
␯9(␴u)
2213
2005
1985
1569
997
0
0
0
0
0
350
0
2189
2113
1815
1290
683
2406
4794
1191
121
1.2
␯
␯
10(␴u)
11(␴u)
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5116
J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Ding et al.
FIG. 3. FTIR spectra of the proposed
␯9(␴u) mode of C12 and its 13C isoto-
pic shifts produced by the laser evapo-
ration of a mixture of 8% 13C and 92%
12C. Spectra were recorded after trap-
ping the products in Ar at ϳ10 K and
following annealing at 20, 25, and 35
K. The letters correspond to the single
13C substituted isotopomers listed in
Table IV.
thus observed are consistent with a chain of 12 carbon atoms.
The specific single 13C isotopomers responsible for the ab-
sorptions are designated by the letters B–G in Fig. 3 and are
identified in Table IV.
As can be seen in Table IV, comparison of the observed
shifts with the scaled predictions of the B3LYP/cc-pVDZ
DFT calculations for single 13C substitutions for the ␯9(␴u)
mode of linear C12 shows reasonably good agreement with
all but one assignment showing a difference between theory
and experiment of Ͻ1 cmϪ1. It should be noted that the
assignment of the 1811.9 and 1813.3 cmϪ1 absorptions to the
B and G isotopomers, respectively, rather than the reverse, is
guided by the sensitivity indices shown in Table III. The
smallest discrepancy between experiment and theory in
Table IV ͑0.0 cmϪ1͒ occurs for the 1811.9 cmϪ1 band as-
signed to the B isotopomer and is consistent with the con-
clusion that because of the very small sensitivity index
͑Ͻ0.01͒ for this isotopomer in Table III, the theoretical pre-
diction should be reliable. The largest discrepancy of 2.0
cmϪ1, which is observed for the assignment of the 1813.3
cmϪ1 band to the G isotopomer, is consistent with its rela-
tively larger isotopic sensitivity index and the consequent
lower reliability of theory for this shift. Also contributing to
the discrepancy may be greater experimental uncertainty in
the frequency of the 1813.3 cmϪ1 band because of its overlap
with the 1813.6 cmϪ1 absorption.
FIG. 4. FTIR spectra of the proposed
␯g(␴u) mode of C12 and its 13C isoto-
pic shifts produced by the laser evapo-
ration of a mixture of 8% 13C and 92%
12C. Spectra were recorded after trap-
ping the products in Ar at ϳ 10 K and
following annealing at 20, 25, and 35
K. The letters correspond to the single
13C substituted isotopomers listed in
Table V. The spectra recorded on
deposition ͑ϳ 10 K͒ and after anneal-
ing to 20 and 25 K have been dis-
placed to higher frequency to facilitate
comparison.
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5117
J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Study of the C12 chain
TABLE IV. Comparison of observed vibrational frequencies ͑cmϪ1͒ of the
␯9(␴u) mode for single 13C-substituted isotopomers of C12 with the predic-
tions of B3LYP/cc-pVDZ calculations.
TABLE V. Comparison of observed vibrational frequencies ͑cmϪ1͒ of the
␯8(␴u) mode for single 13C-substituted isotopomers of C12 with the predic-
tions of B3LYP/cc-pVDZ calculations.
B3LYP/
B3LYP/
C12 Isotopomer
Observed cc-pVDZ Scaleda Difference
C12 Isotopomer
Observed cc-pVDZ Scaleda Difference
C–C–C–C–C–C–¯
␯
␯
␯
⌬␯
C–C–C–C–C–C–¯
␯
␯
␯
⌬␯
12–12–12–12–12–12–¯ ͑A͒ 1818.0
13–12–12–12–12–12–¯ ͑B͒ 1811.9
12–13–12–12–12–12–¯ ͑C͒ 1805.3
12–12–13–12–12–12–¯ ͑D͒ 1814.8
12–12–12–13–12–12–¯ ͑E͒ 1811.1
12–12–12–12–13–12–¯ ͑F͒ 1813.6
12–12–12–12–12–13–¯ ͑G͒ 1813.3
1815.1 1818.0
1809.0 1811.9
1803.3 1806.2
1812.3 1815.2
1807.8 1810.7
1809.8 1812.7
1808.4 1811.3
12–12–12–12–12–12–¯ ͑A͒ 1997.2
13–12–12–12–12–12–¯ ͑B͒ 1995.0
12–13–12–12–12–12–¯ ͑C͒ 1983.6
12–12–13–12–12–12–¯ ͑D͒ 1981.6
12–12–12–13–12–12–¯ ͑E͒ 1996.8
12–12–12–12–13–12–¯ ͑F͒ 1991.5
12–12–12–12–12–13–¯ ͑G͒ 1995.0
2112.9 1997.2
2110.6 1995.0
2098.8 1983.9
2096.7 1981.9
2112.5 1996.8
2107.1 1991.7
2110.5 1994.9
0.0
0.9
0.4
Ϫ0.4
Ϫ0.9
Ϫ2.0
0.0
0.3
0.3
0.0
0.2
Ϫ0.1
aResults of the B3LYP/cc-pVDZ calculation scaled by a factor of 1.0016.
aResults of the B3LYP/cc-pVDZ calculation scaled by a factor of 0.94523.
Figure 4 shows a band at 1997.2 cmϪ1, which as indi-
cated by comparison with Fig. 3 grows in with the ␯9(␴u)
mode at 1818.0 cmϪ1. This new band thus becomes a candi-
date for the second of the three intense stretching modes
predicted by DFT theory, ␯8(␴u) at 2112.9 cmϪ1. As indi-
cated in Fig. 4 the nearby ␯6(␴u) mode of C9 at 1998.0 cmϪ1
and its single 13C substituted isotopomer bands complicate
this region of the spectrum. However, as shown, when the C9
isotopomer bands15,20 are eliminated, another series of isoto-
pomer bands, which grow in with the 1997.2 cmϪ1 band, are
readily identified ͑features B–G in Fig. 4͒. The 1995 cmϪ1
absorption is twice as intense as the well-resolved C and F
isotopomer bands because it consists of overlapping shifts
for the B and G isotopomers. The 1996.8 cmϪ1 absorption,
which appears as a shoulder in the top spectrum in Fig. 4, is
in other spectra resolved as a separate band ͑see inset͒. It is
worth emphasizing that the 1997.2 cmϪ1 band and its isoto-
pic shifts increase in intensity as the ␯6(␴u) mode of C9
decreases during extreme annealing, presumably as some C9
participates in reactions to form C12. In contrast, the initial
deposition of low concentrations of C3 and C9 in the prean-
nealed sample, which by this argument would be expected to
reduce the production of C12, results in little or no absorption
at 1997.2 cmϪ1
.
Comparison of the frequencies of the observed isotopic
shifts with the scaled predictions of the DFT calculations for
the ␯8(␴u) mode of C12 is shown in Table V. The agreement
with theory is very good, with all differences being р0.3
cmϪ1. The smaller discrepancies between theory and experi-
ment for ␯ compared to ␯ are consistent with the conclu-
8
9
sion drawn from Table III that, because of the smaller sen-
sitivity indices for the former mode, the predicted isotopic
shifts for it should be more reliable.
The third stretching vibration of C12 predicted to have
observable intensity is the ␯7(␴u) mode at 2189.1 cmϪ1
.
Figure 5 shows an absorption band at 2140.6 cmϪ1, which
grows in with the ␯ and ␯ modes of C12 already identified.
8
9
Also exhibited are four potential isotopomer shifts labeled
D–G. As can be seen in Table VI, the frequencies of these
four absorptions agree reasonably well with the predictions
of the DFT calculations for four of the singly substituted 13
C
isotopomers of C12. Several factors, however, tend to make
FIG. 5. FTIR spectra of the proposed
␯7(␴u) mode of C12 and its 13C isoto-
pic shifts produced by the laser evapo-
ration of a mixture of 8% 13C and 92%
12C. Spectra were recorded after trap-
ping the products in Ar at ϳ10 K and
following annealing at 20, 25, and 35
K. The letters correspond to the single
13C substituted isotopomers listed in
Table VI.
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J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Ding et al.
TABLE VI. Comparison of observed vibrational frequencies ͑cmϪ1͒ of the
␯7(␴u) mode for single 13C-substituted isotopomers of C12 with the predic-
tions of B3LYP/cc-pVDZ calculations.
B3LYP/
C12 Isotopomer
Observed cc-pVDZ Scaleda Difference
C–C–C–C–C–C–¯
␯
␯
␯
⌬␯
12–12–12–12–12–12–¯ ͑A͒ 2140.6
2189.1 2140.6
2189.1 2140.6
2189.0 2140.5
2182.6 2134.3
13–12–12–12–12–12–¯ ͑B͒
12–13–12–12–12–12–¯ ͑C͒
¯
¯
¯
¯
12–12–13–12–12–12–¯ ͑D͒ 2133.4
0.9
0.1
0.0
1.3
12–12–12–13–12–12–¯ ͑E͒ 2123.9b 2172.1 2124.0
12–12–12–12–13–12–¯ ͑F͒ 2126.4b 2174.6 2126.4
12–12–12–12–12–13–¯ ͑G͒ 2134.7
2184.4 2136.0
aResults of the B3LYP/cc-pVDZ calculation scaled by a factor of 0.97784.
bAssignments doubtful. See text for discussion.
the assignment of the 2140.6 cmϪ1 absorption to the ␯7(␴u)
mode somewhat uncertain. The isotopic shift data is limited
because the predicted shifts of 0.0 and 0.1 cmϪ1 for the two
other isotopomers ͓͑B͒ and ͑C͔͒ place them within the enve-
lope of the 2140.6 cmϪ1 main absorption, rendering them
unobservable. In addition, careful examination of the spectra
in Fig. 5 recorded as the sample was annealed indicates that
absorptions E and F appear to have grown more quickly than
the main band and the candidates for its isotopomer bands, D
and G. In the case of the F band this may in part be an effect
of overlap by the nearby ␯4(␴u) mode of C7 ͑Ref. 14͒ at
2127.9 cmϪ1 which also grows in on annealing. Similarly,
the E band already appears to be growing in after 20 K
annealing when the main band ͑A͒ is still very weak. How-
ever, the presence of another weak feature in the vicinity
after 25 K annealing may indicate that the anomalously high
intensity of E is again the result of overlap with an unrelated
feature. Further uncertainty in the assignment is contributed
by the conclusion from sensitivity indices in Table III that
the theoretical shifts are likely to be relatively less reliable
for this mode. In view of these reservations the assignment
of the 2140.6 cmϪ1 absorption to the ␯7(␴u) mode must be
considered tentative.
Based on the assignments of isotopic shifts presented in
Tables IV–VI we can now compare the absolute value of the
errors relative to the predicted shifts and the values for the
isotopic sensitivity index in Table III. Figure 6 shows the
expected increase in the scatter of errors with an increase in
the isotopic sensitivity index. The behavior shown in this
graph is consistent with our previous experience, where as a
rule of thumb an absolute error of р0.5 cmϪ1 can be ex-
pected for an isotopic sensitivity less than 0.1.
As can be seen from Table II, the DFT calculations pre-
dict relative intensities of 0.50, 1.00, and 0.25 for ␯7 , ␯8 ,
and ␯9 , respectively, compared with measured relative inten-
sities of 0.13, 1.00, and 0.57 for the proposed assignments
␯7ϭ2140.6, ␯8ϭ1997.2, and ␯9ϭ1818.0 cmϪ1. ͑It should
be noted that the spectra in Figs. 4–6 are all plotted to the
same scale to facilitate comparison of the band intensities.͒
FIG. 6. Absolute error between observed and calculated ͑B3LYP/-cc-
pVDZ͒ isotopic shifts for the ␯7(␴u), ␯8(␴u), and ␯9(␴u) modes of C12 as
a function of the isotopic sensitivity index.
sured values typically found for carbon chains.
Our proposed assignments for the ␯7 , ␯8 , and ␯ vibra-
9
tional modes for C12 trapped in an Ar matrix can be com-
pared with the previous assignments by Maier’s group6,7 for
C12 and C12 trapped in Ne. Almost certainly, our ␯
9
ϭ1818.0 cmϪ1 mode for C12 corresponds to their 1819.3
cmϪ1 band which they observed in Ne and tentatively as-
signed to CϪ12 on the basis of behavior in their photobleaching
experiment. It is also probable that our ␯8ϭ1997.2 cmϪ1
mode corresponds to their 2012.6 cmϪ1 absorption, which
they also tentatively assigned to the anion based on its simi-
lar behavior to their 1819.2 cmϪ1 absorption. We can find no
evidence, however, in our experiments for assigning the ␯
9
ϭ1818.0 and ␯8ϭ1997.2 cmϪ1 bands to C1Ϫ2 . It is also im-
portant to note the at least 100-fold increase in the intensity
of these bands typically observed on annealing ͑see Figs.
3–5͒. This behavior appears very unlikely if their carrier is
the anion. Certainly, our experiment was not designed with a
source of electrons to produce anions, and none of the vibra-
tions of other ions, such as CϪ3 and C6Ϫ which have been
previously identified and had their 13C shifts measured,7,21,22
appear in our spectra. A counter argument to this latter point
is that laser evaporation by itself has produced electrons and
hence ions in other systems, and that the higher electron
affinity for longer carbon chains, such as C12, may enable the
unanticipated formation of their anions. For this reason
therefore, we have further explored this possibility by com-
paring our experimental spectra with the predictions of DFT
calculations for CϪ12 .
Table VII shows B3LYP/cc-pVDZ harmonic frequen-
cies and infrared intensities for all the stretching modes of
the CϪ12 anion. It is worth noting that the frequencies of the
three CϪ12 anion modes predicted to be the most intense
␯7(␴u)ϭ2197, ␯8(␴u)ϭ2124, and ␯9(␴u)ϭ1902 cmϪ1 dif-
fer from the observed frequencies 2140.6, 1997.2, and
The ␯ mode is thus observed to be the most intense, in
8
agreement with theory; however, the discrepancy between
the relative intensities of the other two modes is well within
the differences between DFT intensity predictions and mea-
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5119
J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Study of the C12 chain
TABLE VII. B3LYP/cc-pVDZ harmonic frequencies and infrared intensi-
of linear CϪ12.
2
ties for all stretching modes of the
⌸
g
Vibrational
mode
Frequency
Infrared intensity
͑cmϪ1
͒
͑km/mol͒
␯1(␴g)
␯2(␴g)
␯3(␴g)
␯4(␴g)
␯5(␴g)
␯6(␴g)
␯7(␴u)
␯8(␴u)
␯9(␴u)
2216
2039
1990
1537
982
0
0
0
0
0
344
0
2197
2124
1902
1272
671
2985
3761
1346
12
␯
␯
10(␴u)
11(␴u)
53
1818.0 cmϪ1, by 56, 128, and 84 cmϪ1, respectively. By
comparison the differences between the observed frequencies
and those predicted for the neutral C12 modes, ␯7(␴u)
ϭ2189, ␯8(␴u)ϭ2113, and ␯9(␴u)ϭ1815 cmϪ1, are 48,
115, and ϳ0 cmϪ1, respectively. There is thus on this basis
no significantly better fit for one over the other. Empirically
an approximate linear relationship is found between experi-
mental frequencies and calculated harmonic stretching fre-
quencies for linear carbon chains. The scaling factors used to
bring calculated frequencies in line with experimental data
are thus found to fall within a relatively narrow range ͑e.g.,
for B3LYP/cc-pVDZ calculations the scaling factors fall
within 0.93–0.98 for previously identified linear carbon
chain stretching fundamentals͒. Such considerations are
helpful to find an expected range of experimental frequencies
FIG. 8. Comparison of observed FTIR spectrum ͑top͒ showing singly sub-
stituted isotopic shifts with the simulated spectrum of the ␯8(␴u) mode of
neutral C12 ͑middle͒ based on the B3LYP/cc-pVDZ calculation, and also
with the simulated spectrum of the ␯8(␴u) mode of anion CϪ12 ͑bottom͒
based on the B3LYP/cc-pVDZ calculation. The letters correspond to the
single 13C substituted isotopomers listed in Table V.
from given calculated harmonic values. However, it is likely
that as linear chains grow longer one will observe an increase
in the spread of such scaling factors due to the growing num-
ber of vibrational modes.
A more decisive test is provided by comparing the iso-
topic shifts predicted for the C12 neutral and for the anion
with our observed spectra. The results support the conclusion
that the observed absorptions belong to neutral C12. Figures
7–9 show simulated isotopic spectra for the three modes of
the CϪ12 anion along with the experimentally observed spec-
tra. Also shown for comparison are the corresponding simu-
FIG. 7. Comparison of observed FTIR spectrum ͑top͒ showing singly sub-
stituted isotopic shifts with the simulated spectrum of the ␯9(␴u) mode of
neutral C12 ͑middle͒ based on the B3LYP/cc-pVDZ calculation, and also
with the simulated spectrum of the ␯9(␴u) mode of anion CϪ12 ͑bottom͒
based on the B3LYP/cc-pVDZ calculation. The letters correspond to the
single 13C substituted isotopomers listed in Table IV.
FIG. 9. Comparison of observed FTIR spectrum ͑top͒ showing singly sub-
stituted isotopic shifts with the simulated spectrum of the ␯7(␴u) mode of
neutral C12 ͑middle͒ based on the B3LYP/cc-pVDZ calculation, and also
with the simulated spectrum of the ␯7(␴u) mode of anion CϪ12 ͑bottom͒
based on the B3LYP/cc-pVDZ calculation. The letters correspond to the
single 13C substituted isotopomers listed in Table VI.
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J. Chem. Phys., Vol. 112, No. 11, 15 March 2000
Ding et al.
lated isotopic spectra for the ␯7 , ␯8 , and ␯ modes of neutral
1 W. Weltner, Jr. and D. McLeod, Jr., J. Chem. Phys. 40, 1305 ͑1964͒.
9
2 A. E. Douglas, Nature ͑London͒ 269, 130 ͑1977͒.
C12. As discussed earlier in connection with Table IV, the fit
of the shifts predicted for the ␯9(␴u) mode of C12 with the
observed shifts for our 1818.2 cmϪ1 absorption is good ͑see
Fig. 7͒. The predicted pattern of isotopic absorptions for CϪ12 ,
is more widely dispersed than the observed spectrum, with
larger deviations from the observed frequencies, and there is
no suitable absorption for the ͑C͒ isotopomer. Similarly, in
Fig. 8 the simulated isotopic spectrum for the ␯8(␴u) mode
of C12 fits the observed spectrum for the 1997.2 cmϪ1 band
very well as could be expected from the excellent agreement
between observed and calculated shifts noted earlier in Table
V. The 2140.6 cmϪ1 band which we have tentatively as-
3 J. P. Maier, J. Phys. Chem. A 102, 3462 ͑1998͒.
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7
by Maier;6,7 however, this is probably explained by its being
the weakest of the three. As demonstrated by Fig. 9, how-
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V. CONCLUSION
16
GAUSSIAN 94, Revision E1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, P.
C–C stretching modes of linear C12 have been identified
using FTIR isotopic shift measurements on single 13C sub-
stituted isotopomers trapped in Ar matrices in conjunction
with DFT calculations at the B3LYP/cc-pVDZ level. Mea-
surements for the ␯ and ␯ modes at 1818.0 and 1997.2
M. W. Gill, B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith, G. A.
Petersson, J. A. Montgomery, K. Raghavachari, M. A. Al-Laham, V. G.
Zakrzewski, J. V. Ortiz, J. B. Foresman, J. Cioslowski, B. B. Stefanov, A.
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17 C. M. L. Rittby ͑unpublished͒.
9
8
cmϪ1 are consistent with the theoretical predictions. The ␯
7
mode has been tentatively identified at 2140.6 cmϪ1
.
18 L. N. Shen, T. J. Doyle, and W. R. M. Graham, J. Phys. Chem. 93, 1597
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ACKNOWLEDGMENTS
19 R. H. Kranze, C. M. L. Rittby, and W. R. M. Graham, J. Chem. Phys. 105,
5313 ͑1996͒.
Grants from the Welch Foundation ͑Graham, No.
P-0786; Rittby, No. P-1259͒ and the TCU Research and Cre-
ative Activities Fund in support of this research, and from
the W. M. Keck Foundation for the Bomem spectrometer,
are gratefully acknowledged.
20 X. D. Ding, S. L. Wang, and W. R. M. Graham ͑unpublished data͒.
21 J. Szczepanski, C. Wehlburg, and M. Vala, J. Phys. Chem. A 101, 7039
͑1997͒.
22 J. Szczepanski, E. Auerbach, and M. Vala, J. Phys. Chem. A 101, 9296
͑1997͒.
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