Journal of Molecular Spectroscopy 215, 312–316 (2002)
doi:10.1006/jmsp.2002.8647
Rotational Spectrum, Hyperfine Structure, and Internal
Rotation of Methyl Carbamate
B. Bakri,∗ J. Demaison,∗ I. Kleiner,† L. Margulès,∗ H. Møllendal,‡ D. Petitprez,∗ and G. Wlodarczak∗
∗ Laboratoire PhLAM, CERLA, UMR CNRS 8523, Université de Lille 1, 59655 Villeneuve d’Ascq, France; †Laboratoire de Photophysique Moléculaire,
UPR CNRS 3361, Université Paris-Sud, Bät. 350, 91405 Orsay Cedex, France; and ‡Department of Chemistry,
the University of Oslo, Sem Sælands vei 26, PO Box 1033, NO-0315 Oslo, Norway
Received May 29, 2002
Methyl carbamate, an isomer of glycine, is a possible candidate for interstellar detection. It might be more abundant than
glycine and its dipole moment is much larger. Furthermore, using high-level quantum chemical calculations, it is shown that
syn methyl carbamate has a lower energy than glycine. The quadrupole hyperfine structure due to 14 N has been measured using
microwave Fourier transform spectroscopy. The rotational spectrum of the ground vibrational state has been measured from 8
to 240 GHz and accurate spectroscopic constants have been determined for the A internal rotation components of the rotational
C 2002 Elsevier Science (USA)
lines. Finally, the internal rotation splittings have been analyzed. 1. INTRODUCTION
Amino acids are among the most fundamental biological compounds known and their detection in interstellar space would
have a great impact on interstellar chemistry and astrobiology.
A number of interstellar searches for glycine, H2 NCH2 COOH,
the simplest amino acid, have been reported but it seems that
its rotational lines are too weak to be detected unambiguosly
(1, and references therein). One obvious explanation is that the
most stable isomer of glycine, denoted Ip (one of the amino hydrogens forms a hydrogen bond with the carbonyl oxygen and the
heavy-atom skeleton is planar; the notation Ip was first proposed
by Császár (2)) has a small dipole moment: µa = 0.911 D and
µb = 0.607 D (3). Furthermore, glycine is the amino derivative
of acetic acid, CH3 COOH, which does not seem to be abundant
in interstellar space (4, 5). On the other hand, its isomer, methyl
formate (HCOOCH3 ) is much more abundant and ubiquitous
(4, 5). Thus, the search for its amino derivative, methyl carbamate (H2 NC(O)OCH3 ), might be more successful, all the more
as the µb component of its dipole moment, µb = 2.29 D, is much
larger than the components of glycine (6).
Methyl carbamate has a series of biological effects and there
are pharmaceutical applications of these (see Ref. (6) for a list
of pertinent references). Its microwave spectrum has already
been investigated (6). Only one conformer was found where the
methyl and carbonyl groups are in syn conformation. Approximate values of the barrier to internal rotation of the methyl group
and of the 14 N quadrupole coupling constants have been determined. The components of the dipole moment were measured
by Stark effect and the geometrical structure was calculated
2. AB INITIO CALCULATIONS
All the calculations were performed with the Gaussian 98
suite of programs (7). The energy difference between the syn
methyl carbamate and the most stable isomer of glycine was
calculated using different compound methods: Gaussian-2 (G2)
theory (8–10) and the Complete Basis Sets methods CBS-Q (11),
CBS-QB3 (12), and CBS-APNO (13). The G2, CBS-Q, CBSQB3, and CBS-APNO models are found to have mean absolute
deviations of 1.2, 1.0, 0.87, and 0.5 kcal/mol, respectively, for the
G2 test set (12). The results are given in Table 1. They all show
that the syn conformation of methyl carbamate is significantly
more stable than the most stable isomer (Ip ) of glycine. This
is one further argument in favor of the detection of interstellar
methyl carbamate.
3. EXPERIMENTAL DETAILS
The sample utilized in this work was purchased from Aldrich
and used without further purification. The quadrupole hyperfine
Supplementary data for this article may be found on the journal home page.
0022-2852/02 $35.00
C 2002 Elsevier Science (USA)
All rights reserved.
ab initio. However, this work did not obtain accurate centrifugal
distortion constants, which are necessary for an accurate prediction of the rotational spectrum. Thus, before searching for
methyl carbamate, it would be desirable to improve the accuracy of the centrifugal distortion constants. This is one goal of
this work. We also accurately measured the hyperfine structure
of several low-J transitions by microwave Fourier transform
spectroscopy (MWFT), which could be useful for an interstellar
search in the microwave range. Finally, the energy difference
between syn methyl carbamate and the most stable isomer of
glycine (Ip ) was calculated ab initio.
312
313
ROTATIONAL SPECTRUM OF METHYL CARBAMATE
TABLE 1
Total Energy for the Most Stable Conformer (Ip ) of Glycine
and for syn Methyl Carbamate
Method
E I /EH
glycine Ip
E II /EH
methyl
carbamate
Kcal/mol
kJ/mol
G2
CBS-Q
CBS-QB3
CBS-APNO
−284.01176
−284.02286
−284.02577
−284.35154
−284.01914
−284.03038
−284.03322
−284.35848
4.63
4.72
4.68
4.35
19.38
19.75
19.58
18.20
E I − E II
structure of the spectrum was measured in the range 5–20 GHz
using the Lille pulsed-nozzle MWFT spectrometer described
in Ref. (14). µb -type and some µa -type lines were observed.
To polarize the methyl carbamate molecule, 2-µs microwave
pulses were used with power fields of 130 µW and 20 mW for
the µa - and µb -type transitions, respectively. The pulsed valve
was opened for 900 µs at a repetition rate of 2 Hz. Although
lines were observed with a sufficient S/N at room temperature,
the S/N ratio increased by one order of magnitude by heating
at a temperature of 45◦ C. The sample was introduced into the
controlled heated pulsed nozzle whose design is similar to the
one used by Suenram et al. (15). Neon, at a backing pressure
of 1 bar, was used as carrier gas. A total of 4096 data points
per free emission decay are collected at a 10-MHz sample rate
which gives, after Fourier transformation, a spectral resolution
of 2.4 kHz per point. The accuracy of frequency measurements
is estimated to be better than 3 kHz.
The microwave spectrum was measured in the range 13.5–
60.7 GHz using the Oslo spectrometer described in Ref. (16).
The spectrum was stored digitally using a program written by
Waal (17). The accuracy of the measurements is better than
100 kHz for isolated lines. The millimeterwave spectrum was
measured at Lille in the range 170–240 GHz using a video spectrometer with a phase-stablized backward wave oscillator as
source and a LHe-cooled bolometer as detector. The accuracy
of the measurements is about 100 kHz.
4. ANALYSIS OF THE HYPERFINE STRUCTURE
The hyperfine structure of the MWFT transitions was analyzed using Pickett’s program (18). Only the diagonal terms of
the nuclear quadrupole tensor could be determined (19). The
experimental frequencies are given in Tables 2 and 3 and the
results in Table 4. It is worth noting that, as far as the hyperfine structure is concerned, there is no difference between the
A and E internal rotation components of a line. For this reason,
only the parameters of the A-state are given in Table 4. A fit of
54 transitions gives a standard deviation of 3.3 kHz. It is worth
noting that the new quadrupole coupling constants are significantly different from the previous ones: χaa = 1.52(27) MHz,
and χbb = 3.51(20) MHz (6). This shows the importance of
fully resolving the hyperfine structure in order to get accurate
TABLE 2
Microwave Fourier Transform Measurements of the AComponents of syn Methyl Carbamate (obs. in MHz and o-c
in kHz)
J K a
K c
F
J K a
K c
F obs.
o-c
2
2
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
1
1
1
2
2
2
4
4
4
2
2
2
2
2
4
4
4
3
3
3
3
3
5
5
5
3
3
3
3
3
6
6
6
5
5
5
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
2
2
2
2
2
2
2
2
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
2
2
2
3
3
3
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
3
1
1
1
1
1
4
4
4
4
4
4
1
3
2
1
2
2
3
2
1
2
3
1
3
4
2
3
4
2
0
2
1
1
3
2
4
5
3
1
3
2
1
2
4
5
3
2
3
4
2
3
5
6
4
3
3
4
4
2
6
7
5
5
6
4
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
0
0
0
1
1
1
4
4
4
1
1
1
1
1
3
3
3
2
2
2
2
2
5
5
5
3
3
3
3
3
6
6
6
5
5
5
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
2
2
2
2
2
2
3
3
3
3
3
3
0
0
0
1
1
1
4
4
4
1
1
1
1
1
2
2
2
2
2
2
2
2
4
4
4
2
2
2
2
2
5
5
5
5
5
5
1
2
1
0
2
2
2
3
2
1
3
1
3
3
3
4
4
2
1
1
1
1
2
1
4
5
3
1
2
1
0
2
3
4
2
2
2
3
1
3
5
6
4
2
4
4
3
3
6
7
5
5
6
4
8 683.394
8 684.491
8 684.794
8 684.901
8 685.390
8 910.702
8 911.343
8 911.599
8 911.710
8 912.106
8 912.246
8 913.113
11 247.656
11 248.071
11 248.226
11 248.828
11 249.249
11 249.816
13 901.247
13 902.157
13 902.754
13 946.203
13 947.572
13 948.348
14 770.296
14 772.022
14 772.475
15 003.546
15 004.735
15 004.947
15 005.255
15 005.637
15 156.352
15 156.600
15 156.654
16 861.497
16 863.090
16 863.293
16 863.648
16 864.469
17 309.258
17 309.581
17 309.648
18 021.195
18 021.342
18 021.762
18 022.179
18 022.329
18 457.792
18 458.367
18 458.466
19 565.436
19 567.260
19 567.639
5.9
−1.7
3.5
3.4
−4.2
1.9
−4.1
−2.7
3.3
3.5
−2.6
4.0
0.6
−4.5
3.3
−5.1
−4.2
3.4
1.2
5.5
−1.3
3.6
1.7
0.6
−0.9
−5.6
3.0
−1.3
1.9
−2.6
−4.7
2.4
2.2
1.9
−7.8
−2.6
0.5
0.4
0.5
−1.3
−3.9
−5.0
−4.1
−1.2
−1.4
2.0
−1.1
3.0
3.0
2.5
4.3
0.5
−2.1
4.9
C 2002 Elsevier Science (USA)
314
BAKRI ET AL.
TABLE 3
Microwave Fourier Transform Measurements of the EComponents of syn Methyl Carbamate (obs. in MHz and o-c
in kHz)
J K a
K c
F
J K a
K c
F obs.
o-c
2
2
2
2
2
2
2
2
3
3
3
1
1
1
4
4
4
4
4
4
3
3
3
3
3
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
2
2
2
2
2
1
1
1
2
2
2
1
1
1
3
3
3
3
3
3
3
3
3
3
3
1
3
2
1
2
2
3
1
3
4
2
0
2
1
4
5
3
4
5
3
2
3
4
2
3
1
1
1
1
1
2
2
2
3
3
3
0
0
0
4
4
4
3
3
3
2
2
2
2
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
3
3
3
0
0
0
4
4
4
2
2
2
2
2
2
2
2
1
2
1
0
2
2
3
1
3
4
2
1
1
1
4
5
3
3
4
2
2
2
3
1
3
8 691.104
8 692.202
8 692.505
8 692.601
8 693.099
8 905.392
8 906.935
8 907.802
11 241.909
11 243.503
11 244.070
13 892.922
13 893.827
13 894.421
14 764.358
14 766.085
14 766.539
15 186.007
15 186.249
15 186.301
16 866.962
16 868.556
16 868.757
16 869.113
16 869.933
4.9
0.3
1.1
−0.5
−5.8
0.2
−3.8
3.6
−0.8
−3.6
4.4
−0.1
3.5
−3.4
−1.8
−4.0
5.8
2.9
3.5
−6.4
−1.6
−2.1
1.7
5.4
−3.4
parameters. The out-of-plane component, χcc = −4.30 MHz, is
rather close to the value found for acetamide, −3.95 MHz (20),
indicating that the nitrogen has a similar electronic environment
in both molecules.
TABLE 4
Rotational, Centrifugal Distortion, and Nuclear
Electric Quadrupole Constants of the A-Species of syn
Methyl Carbamate
Parameter
Unit
Value
A
B
C
J
J K
K
δJ
δK
J
J K
K
ϕJ
ϕK
χaa
χbb
χcc
MHz
MHz
MHz
Hz
kHz
kHz
Hz
kHz
mHz
mHz
Hz
mHz
mHz
MHz
MHz
MHz
10719.3715 (15)
4399.14788 (66)
3182.88655 (68)
779.44 (65)
4.5326 (29)
8.9474 (22)
216.42 (34)
2.4033 (33)
3.8 (29)
86.1 (21)
2.3355 (13)
2.36 (13)
847 (17)
2.28325 (71)
2.01283 (75)
−4.29609 (75)
5. CENTRIFUGAL DISTORTION ANALYSIS
The spectrum is crowded even in the microwave range because
the rotational constants are small, the dipole moment is large,
and there are several low-lying vibrational states. Furthermore,
the lines are split by internal rotation and most of them are broadened by the unresolved quadrupole hyperfine structure. First, the
A-components of the rotational spectrum, which depend only on
even-order terms of the angular momentum operator, were fitted
to a Watson’s Hamiltonian using the A-reduction in I r representation (21). In order to obtain reliable centrifugal distortion
constants, a robust regression, the iteratively reweighted least
squares (IRLS) method (22), was used. This method is more
efficient than the ordinary least squares method when the distribution is heavy-tailed (i.e., there are more large residuals than
predicted by the normal law) which is probably the case here.
Furthermore, it automatically drops most of the misassigned
lines. This method is briefly described in the Appendix.
The 415 experimental frequencies (corrected for the quadrupole contribution), as well as the observed-minus-calculated
values, are given in the supplementary material. The fitted
parameters are given in Table 4 together with their standard
deviations. Their correlation matrix is given as supplementary
material. The least-well-determined parameter is the sextic centrifugal distortion constant J , nevertheless its value is 13 times
larger than its standard deviation. The condition number of the
fit is only κ = 123, indicating that there is no very strong dependency. The most correlated parameters are ϕ K and J . It is
possible to free more parameters, such as ϕ J K , for instance, but
it does not significantly decrease the standard deviation of the
fit and, furthermore, it is not well determined.
It has to be noted that the residuals of the fit (σ = 30 kHz
for the MWFT measurements and σ = 110 kHz for the other
lines) are slightly larger than the stated experimental accuracy.
Furthermore, many high-J lines had to be excluded from the fit
because their residuals were too large. A first explanation is that
many lines are broadened by the unresolved hyperfine structure.
Although this is true for a few lines, a calculation of the hyperfine
structure of all lines shows that this effect is smaller than 50 kHz
for most lines. Another explanation is that the spectrum is very
dense and that many lines are actually superpositions of several
lines. This is indeed true for some lines but the most likely
explanation is that, when the effect of the internal rotation is
treated as an additional centrifugal distortion, the convergence of
the Hamiltonian becomes extremely slow and this leads to larger
standard deviations than expected. There is much documented
evidence for this effect (23, 24).
6. INTERNAL ROTATION ANALYSIS
Many splittings due to the internal rotation of the methyl group
were observed and some of them could be assigned without ambiguity. The splittings were fitted using Woods’ program (25),
which is based on the internal axis method (IAM). The values
C 2002 Elsevier Science (USA)
315
ROTATIONAL SPECTRUM OF METHYL CARBAMATE
TABLE 5
Internal Rotation Parameters of the Ground
Vibrational State of syn Methyl Carbamate
the population standard deviation which is a scale estimate is
estimated,
s = MAD/0.6745;
Parameter
Unit
Value
Iα
θ
V3
σa
u Å2
degree
J/mol
MHz
3.2195 (22)
23.985 (42)
4213.1 (33)
0.147
a
the residuals are scaled by dividing them by a scale estimate (s),
u i = |ei |/s;
of Iα , moment of inertia of the methyl group, V3 , hindering potential, and θ , angle between the symmetry axis of the methyl
group and the a-principal axis, could be determined. The 98
fitted splittings are given in the supplementary material and the
derived parameters in Table 5. All three internal rotation parameters could be determined from the fit. Iα = 3.220(2) u Å2 has the
expected order of magnitude (26). The potential, V3 = 4213(3) J/
mol, is not far from the previous value, V3 = 4236(7) J/mol (6).
The small difference is mainly due to the fact that the latter value
was obtained with Iα was fixed at 3.20 u Å2 . The small value
of the barrier has already been discussed in (6). The internal
rotation angle, θ = (i, a) = 23.99◦ , gives a direction cosine of
λa = 0.9137, which is also in fair agreement with the previous
value, λa = 0.911. Although these results seem satisfactory, the
standard deviation of the internal rotation fit is larger than the
experimental accuracy. Furthermore, many high-J transitions
had to be excluded from the fit. It might be explained by the
approximations made in the Woods program, but using an IAM
program which does not use these approximations (27) does not
improve the fit very much. It seems that the coupling between the
internal rotation and the centrifugal distortion should be taken
into account (28).
APPENDIX: ITERATIVELY REWEIGHTED LEAST
SQUARES (IRLS) METHOD
If the starting equation of the linear least-squares method is
defined as (29)
y = Xβ + ε,
[A2]
The method involves the following steps:
Step 0. Initial residuals ei and leverages h i are calculated
using the nonweighted least-squares method.
Step 1. The median absolute deviation (MAD) of the residuals ei is calculated,
[A3]
wi = wiH [1 − (u i /4.685)2 ]2
if u i ≤ 4.685
[A6a]
wi = 0
if u i > 4.685,
[A6b]
where
wiH = 1
if h i ≤ 0.3
[A7a]
wiH = (0.3/ h i )2
if h i > 0.3.
[A7b]
The leverage-based weights wiH are introduced to reduce the
influence of leverage points. One measurement is a leverage
point when one parameter is predominantly determined by this
datum.
Step 2. The weighted least-squares method is used with these
weights to obtain a new set of regression parameters and new
residuals.
Step 3. Step 1 and 2 are repeated until there is negligible
change from one iteration to the next.
In the IRLS, weights are a random variable and, for this reason, the standard errors cannot be calculated in the usual way.
A procedure to calculate robust standard errors is described in
Ref. (22) but, in our case, it leads to a small increase of the
standard deviations (less than 10%), which may be considered
as negligible.
ACKNOWLEDGMENT
The IDRIS (CNRS) is thanked for a grant of computer time.
[A1]
the leverages h i are the diagonal terms of the H matrix
MAD = median|ei − median(ei )|;
[A5]
and the weights are calculated by applying a biweight function,
Standard deviation of the fit.
H = X(X̃X)−1 X̃.
[A4]
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