Chemical Physics Letters 393 (2004) 343–346

www.elsevier.com/locate/cplett

Analysis of the m11 band of ethylene-13C2 by high-resolutionFourier transform infrared spectroscopy

T.L. Tan a,*, L.L. Kang a, K.L. Goh a, H.H. Teo b

a Natural Sciences Academic Group, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk,

Singapore 637616, Singaporeb Department of Physics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260, Singapore

Received 18 May 2004; in final form 1 June 2004

Available online 2 July 2004

Abstract

The spectrum of the m11 band of ethylene–13C2 (13C2H4) was recorded with an resolution of 0.006 cm�1 in the 2910–3020 cm�1

region by Fourier transform infrared (FTIR) spectroscopy. Accurate rovibrational constants for the upper state (v11 ¼ 1) up to sextic

centrifugal distortion terms were derived for the first time by fitting 583 transitions using a Watson’s A-reduced Hamiltonian in the Ir

representation. The rms deviation of the fit was 0.00084 cm�1. The m11 band was centered at 2969.601695� 0.000099 cm�1. The

ground state constants were improved by fitting 1052 combination-differences from the present m11 measurements and those of m12.� 2004 Elsevier B.V. All rights reserved.

1. Introduction

The ethylene (C2H4) molecule and its isotopomers in

the past decades [1–6] have been of great interest to

spectroscopists in the understanding of the basic vibra-

tional structure of the molecules. In a conscientious ef-

fort to study the rovibrational structure and to derive

accurate rotational and higher order constants for these

molecules, numerous high-resolution infrared measure-

ments and analyses of the various bands were conducted[7–21]. For example, in one of the latest Fourier trans-

form infrared (FTIR) work on the m12 band of 12C2H4

[17], a total of 1387 infrared transitions was fitted to

derive up to five quartic and three sextic centrifugal

distortion terms with a rms deviation of 0.00033 cm�1.

However, infrared studies on ethylene–13C2 (13C2H4)

have been very few. Duncan et al. [1] in 1973, studied

carbon-13 frequency shifts for 12C2H4,12C2D4, and as –

12C2H2D2 in solid and gaseous states, and the vibra-

tional bands of 13C2H4 were also assigned with an

accuracy of 0.05 cm�1. So far, the only high resolution

* Corresponding author. Fax: +65-6896-9432.

E-mail address: tlatan@nie.edu.sg (T.L. Tan).

0009-2614/$ - see front matter � 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2004.06.060

FTIR measurement on 13C2H4 has been reported re-

cently on m12 band [22]. In this work, the rovibrationalconstants for the upper state (v12 ¼ 1) up to three sextic

constants were derived for the first time by fitting 1177

infrared transitions using a Watson’s A-reduced Ham-

iltonian with a rms deviation of 0.00045 cm�1.

To further improve on the understanding of the

molecular structure of 13C2H4, the present work reports

the results of the measurement and analysis of the m11band. The FTIR spectrum of m11 was measured with aresolution of 0.006 cm�1 in the 2910–3020 cm�1 wave-

number region. By fitting 583 assigned transitions for

the m11 band, the rovibrational constants of the v11 ¼ 1

state were obtained for the first time. All three rota-

tional, five quartic, and two sextic centrifugal distortion

constants were accurately derived to fit m12 transitions

with a rms deviation 0.00084 cm�1. The ground state

rovibrational constants for 13C2H4 up to 5 quartic termswere improved by fitting 1052 combination-differences

derived from the present infrared transitions and those

of m12 from previous work [22]. During the analysis, the

m11 level was found to be perturbed by some nearby

levels, possibly the m2 þ m12 band [23]. A perturbation

analysis is not possible at this stage because of the lack

of high-resolution spectral data on the m2 þ m12 band.

Fig. 1. A survey spectrum of the m11 band of 13C2H4.

344 T.L. Tan et al. / Chemical Physics Letters 393 (2004) 343–346

2. Experiment

The ethylene–13C (13C2H4) gas samples were supplied

by Cambridge Isotope Laboratories (Cambridge, MA).

The sample of 13C2H4 has a chemical purity better than99%. Pyrex glass, stainless steel, Viton O-rings, CaF2

infrared windows, and perfluorinated grease were used.

For the spectral measurements at the ambient temper-

ature of about 296 K, a single pass absorption cell of

20 cm absorption path length was used. The vapor

pressure of about 5 Torr in the cell was monitored using

a capacitance pressure gauge. A spectrum of the evac-

uated cell, consisting of 200 scans recorded at a resolu-tion 0.1 cm�1, was also measured and transformed at

0.006 cm�1 with zero-filling in order to obtain a back-

ground spectrum. This spectrum was ratioed with the

sample spectrum of 13C2H4 to give a transmittance

spectrum with relatively smooth baseline.

The infrared spectra of the m11 band of 13C2H4 were

recorded using a Bomem DA3.002 Fourier transform

spectrophotometer [14–19], with a unapodized resolutionof 0.006 cm�1. A Globar infrared source, and a high sen-

sitivity liquid nitrogen cooled Hg–Cd–Te detector, and

KBr beam splitter were all used. The final spectrum was

produced by coadding four runs of 60 scans each with the

total scanning timeof about 23 h.The linewidth (FWHM)

in the spectrum was observed to be about 0.007 cm�1.

Calibration of the absorption lines of m11 of 13C2H4

was done using the strong and unblended 12C2H4 m11lines in the range of 2850–3250 cm�1. The 12C2H4 m11transitions were measured in a separate spectrum re-

corded immediately before the 13C2H4 spectrum was

recorded. Selected 12C2H4 m11 calibration frequencies

were taken from [24]. A correction factor of 1.000000205

was required to bring the observed wavenumbers into

agreement with the calibrated frequencies. From the line

fitting involving the standard frequency values, the rel-ative precision of the wavenumbers obtained was in the

order of 0.0006 cm�1. It is reasonable to estimate the

absolute accuracy of the measured 13C2H4 lines to be

approximately �0.0008 cm�1 including small systematic

errors in the experiments.

Fig. 2. A detailed section of the P branch region of m11 of 13C2H4.

3. Assignments and frequency analysis

The molecule of ethylene–13C (13C2H4) is a simple

asymmetric top planar of D2h symmetry with asymme-

try parameter j of about )0.92. The m11 band is infrared

active with B1u symmetry [5] and as one of the 12 fun-

damental modes of vibrations [3,5], it is ascribed to anti-

symmetric 13C–H stretching. A survey plot of m11spectrum in the 2920–3010 cm�1 region around the bandcentre, is shown in Fig. 1. It shows the presence of a

prominent strong central Q branch at about 2970 cm�1,

which is typically A-type. In the rotational analysis, the

band has been confirmed to be A-type, and no B-typetransitions were found.

Initially, in the high resolution spectrum, series of

strong absorption lines were easily observed with a

regular spacing of about 1.7 cm�1 which is about Bþ C.During the initial assignment of the P and R branches of

the band, the strongest of these lines was assigned as

J ¼ Kc and Ka ¼ 0 or 1 which were resolved with de-

creasing magnitude, up to J 0 ¼ 29 in the P and Rbranches. These transitions become unresolved doublets

for higher J 0 ¼ K 0c and Ka ¼ 0 or 1 values. Fig. 2 shows

the transitions in the J 0 ¼ 3 and 4 clusters in the Pbranch, which are typical of other clusters. Asymmetrysplittings for J 0 ¼ K 0

c ¼ 3, Ka ¼ 0, 1 and 2 transitions in

the J 0 ¼ 3 cluster in the P branch were observed as

shown in Fig. 2. Similar asymmetry splitting were also

observed for the transitions of the J 0 ¼ 4 cluster. Tran-

sitions of higher Ka in the clusters were not split and

Table 1

Ground state and upper state (v11 ¼ 1) constants (cm�1) for ethylene–13C2 (A-reduction, Ir representation)

Ground statea v11 ¼ 1

A 4.86510(38)b 4.8815745 (67)b

B 0.9506898 (36) 0.9522833 (24)

C 0.7932736 (33) 0.7897607 (24)

DJ � 105 0.13289 (23) 0.14104 (16)

DJK � 105 0.98123 (181) 0.8956 (27)

DK � 104 0.98 (22) 1.45596 (74)

dJ � 106 0.24228 (109) 0.2778 (43)

dK � 105 0.934 (30) 1.6119 (83)

HKJ � 108 0.0 0.419 (26)

HJ � 1010 0.0 0.107 (38)

m0 – 2969.601695 (99)

Number of infrared 1052 583

T.L. Tan et al. / Chemical Physics Letters 393 (2004) 343–346 345

therefore, they were unresolved doublets. As observed in

Fig. 2, the intensity of the transitions in the same J 0

cluster decreases for higher Ka values. As the J 0 valueincreases, the asymmetry splitting occurs for even higher

Ka values for both P and R branches. The rotationalstructure of the m11 band is similar to that of the A-typem12 of 13C2H4 as reported in [22].

Early assignment of the transitions could be efficiently

made using accurate ground state rotational constants

for 13C2H4 which were available from our previous work

on m12 [22]. After these assignments were initially made

for the transitions with low J values, they were fit to get

preliminary constants which were then used to predictthe higher J transitions. These transitions were then as-

signed and the process repeated to extend the assign-

ments to even higher J , Kc, and Ka quantum numbers.

This bootstrap procedure allowed us to assign all the

transitions accurately. Accurate rovibrational constants

up to two sextic terms obtained from the fitting of the

P - and R-branch transitions were finally used to calculate

the Q-branch transitions with high precision. In the finalfit, a total of 76 well-resolved Q-branch transitions were

confidently assigned and used. The strongest lines were

all doublets with two possible values of Kc. TheQ-branchregion of m11 consists of well-defined clusters with the

same K 0a values. For each K 0

a cluster, the line intensity is

maximum for J 0 ¼ K 0a and K 0

c ¼ 0 or 1, and the intensity

decreases as J 0 increases. There were sufficient unblended

lines in the strong Q branch to ensure the accuracy of thepresent assignments.

During the analysis, some transitions in P - and R-branches were found to be shifted from the calculated

positions with deviations more than the estimated

measured uncertainty of �0.0008 cm�1. These perturbed

transitions include J 0 from 12 to 16 for K 0a ¼ 6–8. The

other transitions in the band except for these could be

accurately fitted with a deviation close to the estimatedmeasured uncertainty of �0.0008 cm�1. The nearby

band, m2 þ m12 at 3051 cm�1 is a possible perturber of the

m11 band at 2970 cm�1 through Fermi resonance as re-

ported by Van Lerberghe et al. [23]. Attempts were

made to record the spectrum of the m2 þ m12 band at high

resolution but they were too weak to be observed. Since

the transitions of the m2 þ m12 band were not available, a

quantitative treatment of the resonance is not possible atthis stage. The transitions of m11 band which were

identified to be perturbed were not included in the final

fit in deriving precise v11 ¼ 1 state constants.

transitions

rms Deviation

(cm�1)

0.00076 0.00084

D11 (u�A2) 0.05372 (43) 0.189593 (96)

a The ground state constants were derived from 1052 ground state

combination differences of the m11 and m12 [22] bands.b The uncertainty in the last digits (twice the estimated standard

error) is given in parenthesis.

4. Results and discussion

For fitting of the assigned transitions of m11 of13C2H4, the nonlinear least-squares program which was

previously used for m12 bands of 12C2H4 [17] and of13C2H4 [22] was used. This program for fitting asym-

metric rotor spectra uses a Watson Hamiltonian [25]

with an I r representation in an A-reduction.Given that the ground state constants of 13C2H4 were

available from our previous work on m12 band [22], we

have used them as initial values for the fit. In the presentanalysis to improve the ground state constants, we add

combination-differences from the present infrared mea-

surements as they were assigned. The improved ground

state constants were then fixed in the fitting program to

fit the upper state (v11 ¼ 1) constants. The ground state

constants were systematically refined and included those

of higher orders, as more newly assigned infrared tran-

sitions were gradually included in the fitting procedure.Most accurate ground state constants were required

because they are fixed in the analyses of the m11 band and

other fundamental bands of 13C2H4. A total of 1052

ground state combination-differences (GSCD) from the

present infrared transitions of m11 band and those of m12[22] of 13C2H4 was eventually used in the final refine-

ment to obtain the ground state constants. By using

combination-differences to fit the ground state constantsseparately from the upper state constants, any known or

unknown perturbation of the upper states will not affect

the ground state constants. The rovibrational ground

state constants consisting of 3 rotational and 5 quartic

constants presented in Table 1 were accurately derived

from this work. Inclusion of sextic constants did not

improve the accuracy of the ground state fit and are thus

fixed at zero. The rms deviation of the combination-difference fit to obtain the final set of ground state

constants is 0.00076 cm�1. This value is comparable to

the experimental precision of 0.0008 cm�1.

346 T.L. Tan et al. / Chemical Physics Letters 393 (2004) 343–346

The ground state constants in the rotational analysis

were fixed to determine the upper state (v11 ¼ 1) constants

of 13C2H4 up to 2 sextic terms (HKJ and hJ ). Inclusion of

more sextic constants did not improve the accuracy of the

fit. A total of 583 unperturbed infrared transitions wasfinally assigned and fitted in the determination of the

v11 ¼ 1 rovibrational constants as given in Table 1. The

m11 band is found to be centred at 2969.601 695� 0.000099

cm�1. This value is significantly smaller than that of

3016 cm�1 calculated byDuncan et al. [1], in 1973, in their

study of 13C frequency shifts in ethylene. However, this

presently measured band centre is in better agreement

with the value of 2970.553 cm�1 observed by Van Ler-berghe et al. [23]. The differences in band centre values

were explained by Van Lerberghe et al. [23] in term of a

strong Fermi resonance between m11 and m2 þ m12 bands.The fitting program, though written in terms of prolate

matrix elements, presented no difficulty in rapidly con-

verging to the correct solution after several iterations. In

the least square analysis, the infrared measurements were

weighted by the inverse square of the estimated uncer-tainty. The infrared transitions were given an uncertainty

of 0.0008 cm�1 which is close to the absolute accuracy of

the measured line. The rms deviation of the fit with all

weighted lines was 0.00084 cm�1. The transitions include

values of Ka ranging from 0 to 12. For the P and R bran-

ches, we have J 0 andK 0c ranging from0 to 29. The values of

J and Kc range from 2 to 15 and 0–8, respectively, for the

Q branch. The wide ranging values of J 0, K 0a and K 0

c usedin the analysis effectively cover the whole frequency

range of 2917–3013 cm�1 for the m11 band of 13C2H4.

The inertial defect D11 of 0.189593(96) u�A2 of 13C2H4

derived from the present analysis, as given in Table 1 is

larger than the value of 0.1212(4) u�A2 of 12C2H4 cal-

culated from [26]. The upper state rotational constant

A ¼ 4:8815745ð67Þ cm�1 of m11 of 13C2H4 is found to be

larger than A ¼ 4:85795ð13Þ cm�1 [23] and ofA ¼ 4:857087ð33Þ cm�1 [26] of m11 of 12C2H4. The con-

stant A which corresponds to the molecular axis which

lies along the C@C bond is expected to be very similar

for both 12C2H4 and13C2H4. In fact, similar values for A

were obtained for m12 of both isotopic molecules [22]. As

reported in [23] in their analysis, the value of constant Aand other constants of m11 of 12C2H4 contain contribu-

tions from the corresponding constants of m2 þ m12through Fermi resonance. This would explain the ob-

served discrepancy in constant A for m11 of 12C2H4 and

of 13C2H4. The ground state constants of 13C2H4 from

the present work are in good agreement with those from

our previous work [22] on m12 of 13C2H4. The upper state

rotational constants B and C of m11 of 13C2H4 (given in

Table 1) are found to be smaller than those m11 of12C2H4 [26] in a similar trend as in m12 [22]. The sign ofall three rotational (A, B, and C) and three quartic (DJ ,

DJK , and DK) upper state constants of m11 of 13C2H4 (as

shown in Table 1) agree with those of m11 of 12C2H4 [26].

Table 1 shows that the ground state constants A and

particularly DK of 13C2H4 are less well determined in

comparison to the other ground state parameters. This

is because only a-type transitions are available from m11and m12 bands in the present GSCD analysis. Furtherstudies with the addition of b- or c-type transitions in the

GSCD fit would improve the precision of A and DK .

In conclusion, the present investigation provides nu-

merous infrared transitions of the m11 band of 13C2H4

which were measured, assigned and fitted for the first

time to give accurate upper state (v11 ¼ 1) constants.

Furthermore the ground state constants of 13C2H4 were

improved using a fit of combination-differences frominfrared measurements. These results would add to the

present spectral data which are useful for understanding

the structure of the ethylene molecule.

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