Journal of Molecular Spectroscopy 208, 92–100 (2001)
doi:10.1006/jmsp.2001.8366, available online at http://www.idealibrary.com on
The Submillimeter-Wave Spectrum and Quantum Chemical
Calculations of Glyoxylic Acid
B. Bakri,∗ J. Demaison,∗ L. Margulès,∗ and H. Møllendal†,1
∗ Laboratoire de Physique des Lasers, Atomes et Molécules, UMR CNRS 8523, Bât. P5, Université de Lille 1, FR-59655 Villeneuve d’Ascq,
France; and †Department of Chemistry, The University of Oslo, Sem Sælands vei 26, P. O. Box 1033, Blindern, NO-0315 Oslo, Norway
E-mail: demaison@pop.univ-lille1.fr, harald.mollendal@kjemi.uio.no
Received February 26, 2001; in revised form April 5, 2001
Glyoxylic acid is a possible candidate for interstellar detection. Many transitions of the submillimeter wave spectrum of the
ground vibrational state of its most stable conformer have been measured for the first time. These transitions have been used
together with microwave transitions measured previously to obtain accurate spectroscopic constants that should facilitate a search
for this compound in interstellar space. High-level quantum chemical calculations of the structure, quartic centrifugal distortion
constants, inertial defect, and energy difference between the two low-energy conformers of glyoxylic acid have also been made.
Accurate predictions of the equilibrium structures of the most stable forms of glyoxylic, as well as of formic acid, are reported.
°
C 2001 Academic Press
Key Words: glyoxylic acid; formic acid; interstellar molecule; submillimeter-wave spectrum; spectroscopic constants; quantum
chemical calculations; equilibrium structures.
other. The carboxyl group also has an anti-periplanar conformation with its hydrogen atom forming an intramolecular hydrogen
bond with the carbonyl group (Fig. 1). The dipole moments of
this conformer were determined to be µa = 1.85(3) D and µb =
0.20(10) D (6). A structure was calculated for this form from
several isotopomers (7). Later, van Eijck and van Duijneveldt (8)
assigned the microwave spectrum of the second planar form of
glyoxylic acid, denoted Trans 2 (Fig. 1). This conformer differs
from Trans 1 in having a “normal” (syn-periplanar) conformation of the carboxyl group. Trans 2 was found to be 5.0(20)
kJ/mol less stable than Trans 1. These authors (8) also made
ab initio calculations for the two conformers and derived an
improved substitution structure (9, 10) of the Trans 1 rotamer.
A new investigation of the infrared spectrum was made by
Redington and Liang in 1984 (11). Moreover, several theoretical
calculations at various levels of theory have been reported in the
past several years (8, 12–23).
Only a-type transitions were identified for the Trans 1 conformer in the old microwave work (2) because µb is so small (6).
Ten aR-branch lines with a maximum value of the quantum number J = 4 and forty aQ-branch lines with a maximum J = 61
were assigned for the ground vibrational state. Centrifugal distortion was found to be prominent. However, no accurate values
were obtained for the centrifugal distortion coefficients, mainly
because few aR-branch lines fall into the microwave region.
The aR-branch transitions are the strongest ones in this spectrum. Such lines with medium or high values of J are found in
the millimeter- and submillimeter-wave regions. Their frequencies could not be predicted accurately from the spectroscopic
1. INTRODUCTION
The identification of molecules, radicals, and cations in the
interstellar space has been a success story. In the last 30 years
about 120 different compounds consisting of up to 13 atoms
have been securely assigned largely by means of their rotational
spectra (1). About 1/3 of these species are inorganic. The rest
are organic, many of which are important in biology. Interstellar
organic molecules may well be incorporated into comets and
hence have been brought to early Earth. It is thus at least conceivable that such exogenous material may have played some
role in the origin of life (2, 3).
Glyoxylic acid, HCOCOOH, is the simplest α-oxoacid. It is
important in biology and is found in plants and in the metabolic
cycle of animals (4). This oxoacid consists of seven atoms. The
fact that as many as about 25 organic compounds with six to
eight atoms have been identified (1) shows that modern radio
astronomy should be capable of detecting this species if there is
a substantial amount of it. This study of glyoxylic acid has been
made to facilitate a search for it by this method.
The title compound has been subject to many studies, both experimental and theoretical, in recent years. The first gas-phase
study of glyoxylic acid was made by Fleury and Tabacik (5)
in 1971 using infrared spectroscopy. The microwave spectrum
of its most stable conformer, denoted Trans 1 (see Fig. 1), was
assigned two years later (6). This planar rotamer has the two
C==O groups in the anti-periplanar position (“trans”) to one an1
To whom correspondence should be addressed.
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SUBMILLIMETER-WAVE SPECTRUM OF GLYOXYLIC ACID
FIG. 1. The two rotamers of glyoxylic acid that have been identified by
microwave spectroscopy. Trans 1 is the preferred form of the molecule.
constants obtained in the microwave work (6). The major goal
of this work has been to provide accurate spectroscopic constants
for the ground vibrational state so that the frequency of any atype rotational transition can be accurately predicted. Moreover,
quantum chemical calculations at considerably higher and/or
different levels of theory than previously reported have been
made in order to assist and supplement the experimental work.
These calculations allow an accurate estimate of the equilibrium structure both of the syn-periplanar conformer of formic
acid and of the Trans 1 conformer to be made.
2. EXPERIMENTAL
A commercial sample of glyoxylic acid monohydrate was
dried over phosphorus pentoxide for several months. The rest
of the water was removed by pumping for several weeks using
a diffusion pump. Transitions in the spectral intervals 345–385
and 430–470 GHz were measured in Lille at room temperature at
a pressure of a few pascal using phase-stabilized submillimeter
BWOs (Thomson-CSF) as sources and a He-cooled bolometer
as the detector. The accuracy of the measurements is better than
50 kHz.
3. SPECTRUM AND SPECTROSCOPIC CONSTANTS
Glyoxylic acid was first investigated in the range 345–
385 GHz, where a strong and dense spectrum was observed.
The a-type R-branch transitions with J between about 40 and
60 are the strongest ones in this region. Centrifugal distortion is
large for these lines. The quartic centrifugal distortion constants
obtained in the microwave work (6) only allowed predictions
with rather large (hundreds of MHz) uncertainties to be made.
Fortunately, the quantum chemical calculations described below
yielded much more accurate quartic centrifugal distortion constants than the experimental ones that were available when this
work was initiated (6). These theoretical quartic constants were
thus used to make predictions. The first aR transition was found
in this manner only some 20 MHz away from its predicted frequency. Further transitions were then gradually included in the
least squares fit using the program described in Ref. (24). The
spectroscopic constants obtained so far were next used to predict the aR transitions in the region 430–470 GHz. The aR lines
here were found to be close to their predicted frequencies. The
93
spectroscopic constants were now so accurate that a search for
the weak b-type R-branch transitions made sense. About 10 of
these relatively weak transitions were ultimately assigned. The
232 transitions listed in Table 1 were used to derive the spectroscopic constants ( A-reduction I r representation (25)) shown in
Table 2. The correlation matrix is given in Table 3.
It is seen in Table 1 that several transitions are assigned accuracies larger than 50 kHz in a manner which seems arbitrary. The
reason for this is that these transitions did not fit as well as expected to Watson’s Hamiltonian (25). This should not be surprising given the many overlaps that occur in this spectrum. Instead
of relegating lines that fitted poorly, they have been weighted
according to the inverse squares of the uncertainties shown in
Table 2. It is felt that this is a better way of utilizing experimental data than omitting them. The new spectroscopic constants
(Table 2) are much more accurate than the old ones (6).
4. AB INITIO CALCULATIONS
All the calculations were performed with the MOLPRO98 and
MOLPRO2000 (26, 27) or Gaussian 94 (28) programs. First, the
energy difference between the Trans 1 and Trans 2 forms (see
Fig. 1) was calculated in order to ensure that the Trans 1 form
was indeed the most stable form. To attempt to achieve a high
accuracy, two compound methods have been used: the Gaussian2 theory (29–31) and the Complete Basis Set (CBS-Q) method
(32–35). Both methods are known to give accurate energies (36)
and were used as implemented in the Gaussian 94 program. The
results are given in Table 4. They agree that the Trans 1 form is
indeed more stable.
The next step was to calculate the harmonic force field in
order to make an accurate prediction of the quartic centrifugal distortion constants, which is very helpful to assign the
submillimeter-wave spectrum. Density functional theory with
the hybrid functional B3LYP (Becke’s three-parameter functional employing the Lee, Yang, and Parr correlation functional)
(37) was used. This method was shown to be often in better
agreement with experiment than the MP2 method and at a lower
cost (36). Different basis sets were tried: 6-31G∗∗ , 6-311G(3df,
2pd), 6-311 + G(3df, 2pd), and aug‘-cc-pVQZ, where the’ on
aug indicates that the diffuse functions were only considered for
the heavy atoms C and O. The best results were found with the
6-311 + G(3df,2pd) basis set and are reported in Table 5.
The agreement between the experimental and ab initio constants is extremely good, the largest deviation being only 3.74%
for 1 K . For the inertial defect, the agreement is also satisfactory,
except for the first excited state of the C-C torsion, as expected
for a large amplitude motion.
It is also interesting to try to determine a structure as accurate
as possible. To obtain a reliable structure, it is recommended
that the coupled-cluster method be used with single and double
excitations (38) augmented by a perturbational estimate of the
effects of the connected triple excitations [CCSD(T)] (39) with a
correlation-consistent polarized core-valence basis set (40) of at
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TABLE 1
Microwave and Submillimeter-Wave Spectrum of Glyoxylic Acid
a
In MHz.
Observed-calculated in MHz.
c Accuracy in kHz.
b
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SUBMILLIMETER-WAVE SPECTRUM OF GLYOXYLIC ACID
TABLE 1—Continued
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BAKRI ET AL.
TABLE 1—Continued
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97
TABLE 1—Continued
least quadruple zeta quality. In most cases, the CCSD(T) method
is believed to yield results close to the exact n-particle solution
within the given basis set (41).
However, for a molecule of seven atoms such as glyoxylic
acid, a cc-pVQZ basis set is too large to be able to achieve the
calculations within a reasonable time (assuming that there is
enough memory available). Thus, smaller basis sets were used
and consequently, the calculated structure is affected by an error,
which is mainly systematic for each kind of bond. These errors
can be approximately corrected provided that the structure of
a structurally similar but well-known molecule is calculated at
the same level of theory. For this reason, we first calculated
TABLE 2
Spectroscopic Constants a,b of the
Ground Vibrational State of Glyoxylic
Acid
the structure of trans-formic acid, HCOOH, which is still small
enough to allow us to calculate its structure at a very high level.
The CCSD(T) method was used with the well-known
Dunning’s correlation consistent polarized valence basis sets,
cc-pVnZ (42), where n = D, T, Q. The frozen core approximation (fc) was used in these calculations (oxygen and carbon 1s
core molecular orbitals were required to remain doubly occupied). The results are reported in Table 6. The coupled cluster T1
diagnostic (43), which is 0.0160 at the CCSD(T)/cc-pVQZ level,
indicates that non-dynamical electron correlation is not important and that the CCSD(T) results should be reliable. Improving
the basis set from cc-pVTZ to cc-pVQZ shows that convergence
is almost achieved for the C–H and O–H bond lengths as well as
for the bond angles (except for the 6 (COH), which decreases as
much as 0.4◦ ). The C==O bond is slightly shortened (0.0027 Å)
TABLE 3
Correlation Matrix
a A-reduction I r-representation (25). The remaining sextic centrifugal distortion constants
have been fixed at zero.
b Uncertainties represent one standard deviation.
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TABLE 4
Energy of the Two trans Conformers of Glyoxylic Acid
and probably within less than 0.002 Å from the infinite basis set
limit. On the other hand, the C−O single bond is shortened by
0.0035 Å, which is almost as much as when going from cc-pVDZ
to cc-pVTZ (0.0056 Å). Thus, it seems that for the C−O bond,
convergence is not achieved at the quadruple zeta level and that
extrapolation to infinite basis size is dangerous, the convergence
being too slow. For this reason, we made a further calculation
using a mixed basis set composed of cc-pV5Z at C and O and
cc-pVQZ at other atoms. Suprisingly, it is in perfect agreement
with the cc-pVQZ result for the C−O bond.
Nevertheless, as the O atoms are electronegative, addition of
diffuse functions might be necessary (44). To estimate the correction due to the diffuse functions at the aug-cc-pVQZ level,
the second-order Møller–Plesset perturbation theory (MP2) (45)
was used. This significantly reduces the complexity of the calculations whereas it gives a correction nearly identical to the
CCSD(T) method (46). Taking diffuse functions into account
leads to almost negligible change in the structural parameters,
except for the C==O bond length, which is increased by 0.0011
Å at the quadruple zeta level. This confirms that convergence is
almost achieved at this level. It would be tempting to extrapolate
to an infinite basis set using an empirical extrapolation formula,
but this is not always possible because the convergence is sometimes almost linear. Furthermore, even when this is possible, the
TABLE 5
Comparison of ab Initio and Experimental Quartic
Centrifugal Distortion Constants (kHz) and Inertial
Defects (u Å2 )
B3LYP/6-311 + G(3df,2pd).
First excited C−C torsion
c First excited in-plane bend
a
b
extrapolation of the cc-pVnZ and aug-cc-pVnZ basis sets (n =
D, T, Q) gives results which are sometimes rather different. In the
present case, it may only be used to estimate the accuracy of the
results. As the value of the parameters decreases when the basis
set increases (except for 6 (COH)), as best estimate we choose
the smallest value given either by the cc-pVQZ or the aug-ccpVQZ basis set (for 6 (COH)), the maximum value was chosen).
The difference between this best estimate and the value extrapolated to an infinite basis set (when possible) is small, the largest
deviation being only 0.0016 Å for the two CO bond lengths. It
indicates that the accuracy of the bond lengths is likely to be
better than 0.0020 Å. For the angles, the accuracy is likely to be
better than 0.1◦ , except for 6 (COH), where the accuracy could
be a low as 0.3◦ . This is typical behavior for an angle composing
a floppy bond (47, 48).
Finally, it is worth noting that the variation from CCSD(T)/ccpVTZ to CCSD(T)/cc-pVQZ may be accurately predicted at the
MP2 level, as was found previously for the CC bond (49). This
will be used below to calculate the structure of glyoxylic acid.
In order to estimate the core and core-valence correlation
effects on the computed molecular geometry, the correlationconsistent polarized weighted core-valence quadruple-zeta (ccpwCVQZ) (40, 50) was employed. As for the diffuse functions,
to estimate this core correction it is enough to use the MP2
method (51). This correction leads to the expected shortening of
the X -H (0.001 Å) and CO (0.002 Å) bonds, whereas the angles
are only slightly affected (0.1◦ or less).
The final structure of trans-formic acid, corrected for the
effect of the core-correlation as described above, is given in
Table 6. It is compared to previous structure determinations.
The re structure of Davis et al. (52) is an extrapolation of the
electron diffraction rz structure. Therefore, it is not expected
to be very accurate. The re structure of van Dam and van Eijck
quoted in Ref. (53) was calculated from the experimental ground
state rotational constants and ab initio rovibrational α-constants.
There is no information of the basis set that was used and the
method, but, taking into account the time of the calculation (end
of the eighties), the result is likely not to be very accurate. The
last experimental structure, rmρ , is an approximation of the re
structure (54). This method is known to generally give accurate
results for a rigid molecule (55), but this conclusion is doubtful
for a molecule like HCOOH with a nonrigid O−H bond. There
is indeed rather fair agreement between the rmρ structure and the
re structures, except for the C−H and O−H bond lengths. Our
r (O−H) bond length is shorter than the previous re values, but
extrapolation to an infinite basis set should lead to a still shorter
value. Thus we believe that our value is more accurate than the
previous ones. The r (C–H) bond length may be estimated independently from the isolated stretching frequency (56), whose
value is 2931 cm−1 (57). It gives r (C−H) = 1.091(2) Å, in
fair agreement with our ab initio value. The small difference
may easily be explained by the fact that this vibrational frequency was only approximately corrected for a strong Fermi
resonance (57).
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SUBMILLIMETER-WAVE SPECTRUM OF GLYOXYLIC ACID
99
TABLE 6
Structure of trans-Formic Acid (Distances in Å, Angles in ◦ )
a
fc means frozen core approximation and ae that all electrons are correlated.
cc-pVnZ and aug-cc-pVnZ are denoted VnZ and AVnZ, respectively.
c CCSD(T)/VQZ + MP2/AVQZ-MP2/VQZ
d CCSD(T)/VQZ or CCSD(T)/AVQZ + core correlation, see text.
b
The structure of glyoxylic acid was calculated in the same
way, but the expensive calculation at the CCSD(T)/cc-pVQZ
level was replaced, as discussed above, by simpler calculations
using the following approximation formula:
CCSD(T)/cc-pVQZ ≈ CCSD(T)/cc-pVTZ
+ MP2/cc-pVQZ-MP2/cc-pVTZ.
(49)
TABLE 7
Structure of Glyoxylic Acid (Distances in Å, Angles in ◦ )
The best estimate of the equilibrium structure was obtained from
the CCSD(T)/cc-pVQZ values corrected for a small offset which
was estimated from trans-formic acid (Table 6), except for the
CC bond length, which was taken from Ref. (49) and whose
value is −0.0032 Å. The results are reported in Table 7 together
with the experimental substitution structure of van Eijck and
van Duijneveldt (8). The agreement between the ab initio and
experimental structures is outstanding, except for the r (O−H)
bond length, which is not surprising because the substitution
method is quite poor at determining r (X −H) bond lengths (56).
However, we believe that our ab initio structure is significantly
more accurate than the experimental one, e.g., about 0.002–
0.003 Å for the bond lengths and 0.2◦ for the angles. It is worth
noting that the structures of the acid moieties of formic and
glyoxylic acids are quite similar.
ACKNOWLEDGMENTS
J.-M. Colmont is thanked for help with the experiments. Anne Horn is thanked
for the art and assistance. Financial support from the Aurora Programme (Collaboration Research Project between France and Norway) to J. D. and H. M.
made this study possible.
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