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High-resolution FTIR spectroscopy of H13COOD: The ground state and v2 = 1 state rovibrational constants
Accepted Manuscript High-resolution FTIR spectroscopy of H13COOD: The ground state and v2 = 1 state rovibrational constants Rabia'tul A'dawiah, T.L. Tan, L.L. Ng PII: DOI: Reference:
S0022-2852(18)30271-6 https://doi.org/10.1016/j.jms.2018.09.008 YJMSP 11083
To appear in:
Journal of Molecular Spectroscopy
Received Date: Revised Date: Accepted Date:
16 August 2018 25 September 2018 26 September 2018
Please cite this article as: R. A'dawiah, T.L. Tan, L.L. Ng, High-resolution FTIR spectroscopy of H13COOD: The ground state and v2 = 1 state rovibrational constants, Journal of Molecular Spectroscopy (2018), doi: https://doi.org/ 10.1016/j.jms.2018.09.008
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High-resolution FTIR spectroscopy of H13COOD: the ground state and state rovibrational constants
Rabia’tul A’dawiah, T. L. Tan*, L.L. Ng Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
Date: 25 September 2018 No. of pages: 23 No. of tables: 2 No. of figures: 4 Running head: The 2 band of H13COOD *Corresponding author: T. L. Tan Tel: 65-67903837 E-mail address: [email protected] (T.L. Tan) Keywords: formic acid isotopologue; H13COOD; high-resolution FTIR spectroscopy; rovibrational constants; ground state constants Abstract The Fourier transform infrared (FTIR) rovibrational spectrum of the
band of the formic
acid isotopologue H13COOD was recorded in the 2550-2710 cm-1 region at an unapodized 1
resolution of 0.0063 cm-1. Rovibrational constants up to three quartic terms were derived for the first time with high precision for the
state through the fitting of 626 infrared
transitions using the Watson’s A-reduced Hamiltonian in the Ir representation with a rootmean-square (rms) deviation of 0.0023 cm-1. The rotational energy levels of the found to be perturbed by a nearby
band was
band. From the analysis, a- and b-Coriolis
resonance parameters from the interactions of the
band with
band were obtained
for the first time. The rotational constants A and B along with the band center of the band were also derived for the first time in this work. The band centers of the
and
bands of H13COOD were determined as 2631.13155(34) cm-1 and 2596.31(19) cm-1 respectively. The ground state constants of H13COOD were determined with higher precision than previously by fitting 301 ground state combination-differences (GSCDs) from the present work and 24 previous microwave measurements with rms deviation of 0.00073 cm-1. The equilibrium state rovibrational constants up to five quartic terms were derived from theoretical anharmonic calculations at four levels of theory: MP2/cc-pVTZ, B3LYP/ccpVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ using the principal axis coordinate system. These calculated constants agree with the ground state constants of H 13COOD derived from the current experimental GSCD combined with microwave transitions fit. In addition, all three rotational constants (A, B and C) of the ground state of H13COOD were obtained from anharmonic calculations using B3LYP and MP2 levels with the cc-pVTZ and cc-pVQZ basis sets. These rotational constants were found to agree with those derived experimentally with percentage
deviations
within
1.0%.
1. Introduction Formic acid (HCOOH) is the simplest organic acid with one carbon atom. The formic acid molecule and its isotopologues have been studied extensively by spectroscopists over the years due to their significant astrophysical, atmospheric and environmental relevance [1–5]. 2
Formic acid is among the most abundant pollutants in the atmosphere and has been constantly monitored in both remote and urban areas [4,5]. Formic acid has two isomeric configurations, trans-formic acid and cis-formic acid with a ratio of 726:1 at room temperature [6]. The higher stability of the trans-form of formic acid accounts for the larger amount of transformic acid present in the atmosphere. Therefore, many studies including this present study, were dedicated to the trans-conformer of formic acid. The nine fundamental vibrational bands of formic acid and its
13
C, D and
18
O
isotopically substituted species were studied by Redington [7] in 1977 using low-resolution infrared (IR) spectroscopy. Determining the equilibrium structure of formic acid molecule or any molecule is one of the major challenges of molecular spectroscopy. The precision and accuracy of molecular geometry obtained is dependent on the amount and accuracy of spectroscopic data available on the parent molecule as well its isotopologues since molecular geometry is essentially unchanged by isotopic substitution of the constituent atoms [8]. Thus, it is important to investigate the isotopic form of formic acid to determine its molecular structure. Another significant reason to study the high-resolution FTIR spectra of isotopologues of formic acid lies in the importance of understanding the complicated resonances among interacting vibrational levels which may change in isotopic substitution. The rovibrational structures derived from studying formic acid and its isotopic species at high-resolution, together with data on isotopic shifts, band centers and changes in the rovibrational constants, various interactions and coupling constants for the various vibrational states of formic acid can be accurately derived. Furthermore, the information obtained from the interaction studies can be used in testing ab initio calculations and aids in the accurate evaluation of the molecular structure of formic acid. Baskakov et al. [9] did a comprehensive study on the 41, 51, 61, 72, 81, 7191 and 92 interacting vibrational states of the HCOOH molecule. Accurate rotational constants (A, B 3
and C) of the
fundamental band of HCOOH and formic acid-d1 (HCOOD) have been
reported by Luo et al. [10] in 2017. In 2007, Demaison and co-workers [11] theoretically calculated the quadratic, cubic and semidiagonal quartic force fields of both cis- and transconformers of formic acid using three levels of theory. In their work, Demaison et al. [11] also reported the equilibrium rotational constants and the inertial defects of various isotopologues of formic acid except H13COOD. The rovibrational analyses of the various fundamental bands of the HCOOD isotopologue of formic acid have also been reported [6,10,12–21]. Most recently, A’dawiah et al. [18] did a rovibrational study on the
(O-D
stretch) band of HCOOD. In the study, A’dawiah et al. [18] reported on the rovibrational constants of the
state of HCOOD and observed a- and b-Coriolis interactions of the
band with
band of HCOOD. Furthermore, Goh et al. [22] did a high-resolution
FTIR study on the
(O-D) band of DCOOD. Some perturbations were also observed for this
band though they were not analyzed. The perturbations could be due to Fermi and c-Coriolis resonance with the
band or a- and b-Coriolis interactions with the
band.
Despite the numerous studies done on the fundamental bands of formic acid and its isotopologues, they are limited to wavenumbers below 1800 cm-1 [22]. To the authors’ present knowledge, no work has been done to investigate the upper state
of
H13COOD. In fact, the only high-resolution work reported on the H13COOD molecule was by Baskakov et al. [8]. In their study, Baskakov and his co-workers [8] measured microwave rotational transition frequencies of three isotopic forms of formic acid (i.e. H 13COOD, D13COOH and D13COOD). Baskakov et al. [8] mentioned difficulties in assigning these transitions as the samples were not enriched with
13
C but the
13
C were present as naturally-
abundant species in the samples of HCOOD, DCOOH and DCOOD, resulting in weaker transitions.
4
In this present investigation, the hybrid A/B-type
band of H13COOD was recorded
at an unapodized resolution of 0.0063 cm-1 using Fourier transform infrared (FTIR) spectroscopy in the 2550-2710 cm-1 wavenumber region. The predominantly B-type. By assigning 626 IR lines, accurate
band was found to be upper state rovibrational
constants and band center was derived in this work for the first time. The Coriolis resonances of the
and
states were also analyzed in this work yielding the a- and
b-Coriolis resonance parameters. The ground state rovibrational constants for H13COOD up to three sextic terms were also obtained with higher precision and accuracy by fitting the ground state combination-differences (GSCDs) derived from the present analysis of the band and the microwave measurements made by Baskakov et al. [8]. In addition, the equilibrium state rovibrational constants of H13COOD were calculated using four levels of theory (i.e. MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ). The ground state and upper state (
of H13COOD were also derived from the calculations.
All rovibrational constants derived in this high-resolution FTIR study agree well with the computed values. 2. Experimental and computational details The H13COOD vapor of relatively high purity was obtained by mixing H13COOH vapor with D2O vapor at equal pressures at room temperature (298 K) in a gas cell. The infrared spectrum in the 2550-2710 cm-1 wavenumber region was recorded using the Bruker IFS 125HR Michelson Fourier transform spectrometer in the Spectroscopy Laboratory of the National Institute of Education, Nanyang Technological University in Singapore with an unapodized resolution of 0.0063 cm-1. Spectral measurements were recorded at an ambient temperature of approximately 298 K with a multiple-pass absorption cell of total absorption length of 0.80 m, a globar infrared source, a liquid nitrogen-cooled Hg-Cd-Te detector and KBr beamsplitter. A total mean vapor pressure of 8.1 mbar in the gas cell was measured 5
using a capacitance pressure gauge. The interferogram was processed with the four-point apodization function with a zero filling factor of 8. The final sample spectrum was obtained from a co-addition of 3300 scans collected over a period of 55 hours. The full-width at halfmaximum (FWHM) of the infrared peaks of the final transmittance spectrum were measured to have an average value of 0.013 cm-1. A total of 32 unblended D2O absorption lines of sufficient intensities located in the 2500-3000 cm-1 spectral range were used to calibrate the infrared transition lines of the band of H13COOD. The selected absorption wavenumbers were calibrated against the infrared standards taken from the public-access database HITRAN (2016) [23]. The rootmean-square (rms) deviation of the calibrated wavenumbers after the fitting of 32 D 2O lines in the calibration was 0.00033 cm-1. The absolute precision of the measured H13COOD lines could then be approximated to be ± 0.0013 cm-1 (1/10th of the measured FWHM of 0.013 cm1
) after accounting for systematic errors in the experiments. Rotational and quartic centrifugal distortion constants for the equilibrium state,
rotational constants for the ground and
state of H13COOD were computed
theoretically with the GAUSSIAN09 [24] program using an anharmonic oscillator model at the B3LYP/cc-pVTZ, MP2/cc-pVTZ, B3LYP/cc-pVQZ and MP2/cc-pVQZ levels of theory. The computed values were compared with the experimental values derived from non-linear least-squares fitting of the assigned infrared transitions. 3. Rovibrational analysis H13COOD is a near-prolate asymmetric rotor belonging to the Cs point group with an asymmetry parameter
-0.935. The
band is ascribed to the in-plane O-D stretch having
an A′ symmetry according to the numbering of normal modes by Redington [7]. The fundamental band is expected to be an A/B hybrid type consisting of both a-type and b-type 6
transitions. A high-resolution compressed plot of the
spectrum of H13COOD in the region
2550-2710 cm-1 is shown in Fig. 1. The well-defined P and R contours and the absence of a prominent central Q branch illustrates the appearance of a typical b-type band. A-type transitions were too weak to be observed in the spectrum, hence, only b-type transitions were assigned and fitted. A’dawiah et al. [18] and Goh et al. [22] observed similar strong b-type with non-observable a-type transitions when analyzing the same band ( ) corresponding to the OD stretching mode of the isotopologues molecules HCOOD and DCOOD respectively. The following selection rules for b-type rovibrational transitions apply:
3.1 Assignment of the infrared transitions The bootstrap method was employed in the assignment of the transitions. Assignments were started with transitions of Ka′ = 7 and 8 in the P and R branches of the band, which were observed to be of higher intensity. A series of transitions of constant Ka″ were observed to be approximately 4.3 cm-1 (≈ 2A) apart. Subsequent lines in each Ka″ series belonging to J = Ka + 1, J = Ka + 2, … are separated by about 0.72 cm-1 (B + C). The initial fitting process of the
state of H13COOD started off by using the ground state constants
reported by Baskakov et al. [8]. A preliminary set of rovibrational constants for the state was obtained from the fitting of these lines using the non-linear least-squares fitting program developed by Maki [25]. This program uses the Watson’s A-reduced Hamiltonian [26] in the Ir representation. Assignments of the lines were expanded, aided by calculated unperturbed line positions using the set of preliminary rovibrational constants and crosschecked using ground state combination differences (GSCDs). The rovibrational constants for the upper state were progressively refined as the set of assignments in the P and R branches were expanded. This bootstrap process was repeated until no new lines could be
7
confidently assigned. Analyses of the Q-clusters in the P and R branches were made after the assignments of the P and R branches. The Q-clusters were found to be separated by , where
. However, most of the transitions in the Q-clusters could not be fitted
accurately due to the blending of the transition lines caused by the large line-widths of the IR lines (mainly due to pressure and Doppler broadenings). Fig. 2 shows some of the final b-type PP10 to PP13 (i.e. those transitions belonging to Ka″= 10-13 with J′ - J″ = -1 and Ka′ - Ka″ = -1) line assignments in the 2572-2576 cm-1 wavenumber region of the P branch. No asymmetric splitting could be observed for Ka″ ≥ 7 in the present analysis. In the nonlinear fitting process, each unblended infrared transition was weighted by the inverse square of the measured uncertainty of ± 0.0013 cm-1 while those belonging to blended or unresolved asymmetry doublets were assigned to uncertainties in multiples of ± 0.0013 cm-1. 3.2 Analysis of the Coriolis interactions between the
state and (
) states
Most of the transitions of Ka′ ≥ 1 were found to deviate from their calculated unperturbed positions and could not be fitted satisfactorily. These perturbations are likely to state located at approximately 2597 cm-1 after
be caused by the nearby (
studying the rotational energy levels of all possible nearby vibrational states. A’dawiah et al. [18] observed similar perturbation profile for the
state of HCOOD. As the 3
band is a C-type band (A″ symmetry), a- and b-type Coriolis resonances between the rotational energy levels of the | = odd, |ΔKc′ (= even, |ΔKc′ (=
-
-
and (
states with |ΔKa′ (=
| = odd for b-Coriolis and |ΔKa′ (=
-
|=
| = odd for a-Coriolis were expected.
Watson’s Hamiltonian [26] in the Ir representation and A-reduction with the inclusion of the first and higher order a- and b-type Coriolis interaction terms were applied in the fit to 8
account for the large number of perturbed transitions. The matrix elements are given by the following expressions: (1) (2) (3) (4)
where
and
represent the
and
first-order b-Coriolis resonance parameter of the
states respectively, = 1 and (
are the higher-order b-Coriolis coupling constants,
= 3,
= 1) states,
is the and
is the constant associated with
ΔK = ± 2 a-type Coriolis interactions and 3.3 Ground state combination differences (GSCDs) analysis A total of 301 GSCDs from present analysis of the b-type transitions of the
band of
H13COOD and 24 microwave (MW) transitions from Ref. [8] were used to obtain a revised set of ground state rovibrational constants. GSCDs were added from the infrared measurements as they were assigned. The ground state constants were systematically refined as more newly assigned infrared transitions were included in the fitting. Each GSCD is weighted by the inverse square of the measure line uncertainty of ± 0.0018 cm-1, which is (1/10th of the measure line width of 0.0013 cm-1). The rms deviation of the combined GSCD and MW fit is 0.00073 cm-1. Table 1 gives the rovibrational ground state constants of H13COOD up to 3 sextic terms derived using the Watson’s A-reduced Hamiltonian in the Ir representation. The inertial defect of the molecule was calculated using the ground state rotational parameters in this work and compared to the inertial defect calculated from the ground state constants from Baskakov et al. [8] and those of computational calculations. The final ground state constants derived in this work were then fixed in the FTIR fit of the upper 9
state (
) transitions to derive final and precise rovibrational constants and band centers
of the
and
states with the inclusion of one a-Coriolis and three b-
Coriolis interaction parameters. 4. Results and discussion A precise set of ground state constants comprising of three rotational constants, five quartic and 3 sextic centrifugal distortion constants was derived from the fitting of 301 GSCDs and 24 microwave measurements (from Baskakov et al. [8]). Table 1 shows the equilibrium and ground state constants calculated using four theoretical levels: MP2/ccpVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ levels, using the Watson’s Areduced Hamiltonian in the Ir representation. The ground state rotational constants derived from this work are in close agreement with those in Ref. [8] as seen from Table 1. In general, most of the newly derived ground state constants are more precise than those obtained previously [8]. The ground state rovibrational constants derived in this work give a better representation of the ground state due to the larger data pool of GSCDs combined with microwave transitions being used. Additionally, the quartic centrifugal distortion constant,
K, that was not previously determined in Ref. [8] could be determined in this work. The calculated ground state inertial defect Δ using the new set of ground state rotational constants is 0.08263(13) uÅ2. This experimentally derived value is much closer to the theoretical inertial defect values calculated from the four levels of theory as opposed to the inertial defect value calculated from Ref. [8]. These inertial defect values are presented in Table 1 for comparison. The small positive inertial defect agrees well with the high planarity of H13COOD. The experimentally-derived ground state rotational constants in this work are also in good agreement with those calculated using the four levels of theory (all percentage
10
deviations are within 1.0%). The rotational constant A was best predicted by the MP2/ccpVTZ level of theory with a percentage deviation of approximately 0.09% followed by MP2/cc-pVQZ with a percentage deviation of 0.22%. The cc-pVQZ basis set (for both MP2 and B3LYP methods) has the closest prediction of the rotational constants B and C with percentage deviation between 0.4% to 0.6%. All equilibrium rotational constants derived from the theoretical calculations are larger than the experimentally determined ground state values, as expected, due to the longer bond lengths in the ground state, giving rise to larger moments of inertia. Overall, the MP2 method proves to be in better agreement with the experimental values than the B3LYP method for both cc-pVTZ and cc-pVQZ basis sets in calculating ground state rotational constants, with B3LYP/cc-pVQZ level of theory having the largest percentage deviation. A total of 626 perturbed and unperturbed IR absorption lines were fitted using the Watson’s Hamiltonian [26] with the inclusion of off-diagonal a-
[
and b-Coriolis interaction terms to derive rovibrational constants up to three quartic terms for state of H13COOD. These constants, together with the a- and b-Coriolis resonance
the
parameters, are derived for the first time in this work and presented in Table 2. A rms deviation of 0.0023 cm-1 for the 626 b-type IR transitions of
was achieved after
considering the a- and b-Coriolis terms. The quartic constants δJ and δK were not welldetermined and therefore, fixed to the ground state values. The alpha constants ( ) of the
,
and
state calculated from the differences in the rotational constants A, B and C
respectively, are presented in Table 2. state of H13COOD derived from this work are
The A, B and C constants of the
in good agreement with the calculated values using the B3LYP/cc-pVTZ, MP2/cc-pVTZ, B3LYP/cc-pVQZ and MP2/cc-pVQZ levels of theory as seen from Table 2 (all percentage deviations are less than 1.2%). The
and
values derived from this work, 0.014291(15) 11
cm-1 and -0.001099(40) cm-1 respectively, are close to the
and
values of 0.0152566(75)
cm-1 and -0.001279(15) cm-1 reported by A’dawiah et al. [18] for the However,
value of 0.001743(79) cm-1 for the
band of HCOOD.
state of H13COOD differs from the
value (0.000898(14) cm-1) of the
state of HCOOD [18]. This could be due to some
unaccounted b-Coriolis resonances. The
band center, 2631.13155(34) cm-1, derived from
this analysis agrees with the band center reported by Redington [7] in 1977 and the calculated value of 2632.186 cm-1 using the MP2/cc-pVQZ level of theory. Although the intensities of the absorption lines of the perturbing
band were
not observable, the rotational constants A and B together with the band center of the perturbing band could be determined for the first time with good precision from the analysis of its Coriolis interactions with the
state. All higher order centrifugal distortion
constants we fixed to the ground state values. The band center of the unobserved
of
H13COOD was found to be 2596.31(19) cm-1. This value is close to the sum of the frequencies of the
and
fundamental states observed by Redington [7]. The
band center of HCOOD located at 2601.13(14) cm-1 [18] is close to the band center value derived in this work. The red shift in the band center of work could be attributed to the heavier
13
band in this
C atom. The 12C-13C isotopic shift for the
band center of formic acid-d1 was found to be 4.82(33) cm-1 whereas the isotopic shift for the band is 0.50668(51) cm-1 [18]. The a- and b-Coriolis resonance parameters and
,
and
between
bands derived in this study account for most but not all of the perturbations in
the Ka′ = 8-13 sub-series. Fig. 3 and Fig. 4 show significant reduction in the deviations (observed-calculated) in cm-1 of the perturbed lines of Ka′ = 10-13 after perturbation treatment. However, these a- and b-Coriolis resonance parameters could not account for some
12
of the perturbations in the Ka′ < 7 and Ka′ > 13 sub-series. This indicates that two or more state of H13COOD. A more
bands are also responsible for the perturbations of the
complex and comprehensive resonance study including several nearby upper states may be crucial to provide an accurate depiction of the interactions occurring between the
and
states of H13COOD. Some of the possible interacting nearby rovibrational bands are the A/B-type
(A′ symmetry) with a band center located at approximately
2700 cm-1 and the C-type 2
(A″ symmetry) at 2588 cm-1.
The new rovibrational constants of the and b-Coriolis interaction parameters with the
fundamental band of H13COOD and the aband that are derived for the first
time in this study is useful for the evaluation of equilibrium structures [11,27] and refinement of the equilibrium structural parameters of formic acid molecule. Overall, the J′ and Ka′ values (shown in Table 2) included in this analysis cover the entire frequency range of 25502710 cm-1 of the
band of H13COOD.
The revised ground state rovibrational constants derived from the simultaneous fit of GSCDs and microwave measurements are provided in Supplementary Data 1. The result of the final FTIR fit of the 626 perturbed and unperturbed b-type transitions of the
band of
H13COOD is provided in Supplementary Data 2. The wavenumbers of all IR transitions that were included in the fit and their fitting errors are also listed. 5. Conclusion From the simultaneous fit of 301 GSCDs from the present analysis of the fundamental band and 24 microwave measurements made by Baskakov et al. [8], ground state constants of H13COOD were derived with higher precision. These ground state rotational constants are in close agreement with those from theoretically computed values using the cc-pVTZ and cc-pVQZ basis sets with MP2 and B3LYP methods. A total of 626 13
perturbed and unperturbed b-type IR transitions of the assigned and fitted to obtain accurate upper state (
band of H13COOD were measured, constants up to three quartic terms
for the first time. Furthermore, from the Coriolis interactions between the states, rotational constants A and B, the band center of the
and and the
a- and b-Coriolis resonance parameters were also derived for the first time. The results of this study will further enrich the understanding of the molecular properties of the formic acid (HCOOH) molecule and its isotopologues. Acknowledgements The authors acknowledge the support of this work by the National Institute of Education, Singapore under research grants RS 9/15 TTL, RS 12/17 TTL, RI 5/16 TTLA, RP 5/16 TTLA and RP 1/17 TTL. Appendix A. Supplementary Material The ground state rovibrational constants derived from 301 GSCDs combined with 24 MW transitions using Watson’s A-reduced Hamiltonian in the Ir representation is provided in Supplementary Data 1. The FTIR fit of 626 IR lines of the
band of H13COOD using the
Watson’s
Supplementary
A-reduced
Hamiltonian
is
provided
in
Data
2.
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O.I. Baskakov, I.A. Markov, E.A. Alekseev, R.A. Motiyenko, J. Lohilahti, V.-M. Horneman, B.P. Winnewisser, I.R. Medvedev, F.C. De Lucia, J. Mol. Struct. 795 (2006) 54–77.
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15
[20] L. Nemes, A.R.W. McKellar, J.W.C. Johns, JOSA B 4 (1987) 1165–1172. [21] O.I. Baskakov, J. Mol. Spectrosc. 208 (2001) 194–196. [22] K.L. Goh, P.P. Ong, H.H. Teo, T.L. Tan, Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 56 (2000) 991–1001. [23] I.E. Gordon, L.S. Rothman, C. Hill et al., J. Quant. Spectrosc. Radiat. Transf. 203 (2017) 3–69. [24] M.J. Frisch, G.W. Trucks, H.B. Schlegel et al., GAUSSIAN09, Gaussian Inc., Wallingford, CT, USA, 2009. [25] A.G. Maki, T.L. Tan, E.C. Looi, K.T. Lua, J.W.C. Johns, M. Noel, J. Mol. Spectrosc. 157 (1993) 248–253. [26] J.K.G. Watson, in:, J.R. Durig (Ed.), Vib. Spectra Struct. A Ser. Adv., Elsevier, New York, 1977. [27] I. Yokoyama, Y. Miwa, K. Machida, J. Am. Chem. Soc. 113 (1991) 6458–6464. FIGURE CAPTIONS Figure 1.
The survey spectrum of the
band of H13COOD recorded at high-resolution
(0.0063 cm-1) in the 2550-2710 cm-1 region. The strong absorption lines scattered throughout the spectrum belong to D2O which was present in the mixing of H13COOH with D2O. Figure 2.
Detailed section of the high-resolution FTIR spectra in the P-branch regions
showing the assignments of the
band of H13COOD. *Transitions belong to H13COOH,
D2O and H2O present in the sample. Figure 3.
Deviations (obs.-calc.) in cm-1 of Ka′ = 10 and Ka′ = 11 in the P branch plotted
as a function of J′ of
band of H13COOD. 16
Figure 4.
Deviations (obs.-calc.) in cm-1 of Ka′ = 12 and Ka′ = 13 in the P branch plotted
as a function of J′ of
band of H13COOD. TABLE TITLES
Table 1.
Rovibrational constants (cm-1) for the equilibrium and ground states of
H13COOD (A-reduction in the Ir representation). Table 2.
Rovibrational constants (cm-1) for the
and
states of
H13COOD as determined for an A-reduction of the Ir representation. MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ calculations are based on the anharmonic oscillator model. Figure 1.
The survey spectrum of the
band of H13COOD recorded at high-resolution
(0.0063 cm-1) in the 2550-2710 cm-1 region. The strong absorption lines scattered throughout the spectrum belong to D2O which was present in the mixing of H13COOH with D2O.
17
Figure 2.
Detailed section of the high-resolution FTIR spectra in the P-branch regions
showing the assignments of the
band of H13COOD. *Transitions belong to H13COOH,
D2O and H2O present in the sample.
18
Figure 3.
Deviations (obs.-calc.) in cm-1 of Ka′ = 10 and Ka′ = 11 in the P branch plotted
as
function
a
of
J′
of
band
of
H13COOD.
19
Figure 4.
Deviations (obs.-calc.) in cm-1 of Ka′ = 12 and Ka′ = 13 in the P branch plotted
as
function
a
of
J′
of
band
of
H13COOD.
20
Table 1 Rovibrational constants (cm-1) for the equilibrium and ground states of H13COOD (A-reduction in the Ir representation). Theoretical cc-pVTZ basis set Theoretical cc-pVQZ basis set (anharmonic model) (anharmonic model) Equilibrium state Ground state Equilibrium state Ground state MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP A 2.1656351 2.1683009 2.1553500 2.1582680 2.1685718 2.1710910 2.1581040 2.1611160 B 0.39098063 0.39194619 0.38830100 0.38932000 0.39272263 0.39259678 0.39000600 0.38993500 C 0.33118403 0.33193907 0.32849100 0.32928500 0.33250220 0.33247108 0.32977500 0.32979200
Experimental ground state This work (IR, MW)a 2.1533059(58)c 0.39224030(41) 0.33126166(43)
Ref. [8] (MW)b 2.15054(98)d 0.3922067(87) 0.3312959(87)
J 106 JK 106 K 106 J 106 K 106
0.33136 -2.3490 32.956 0.07172 1.216
0.33491 -2.3735 33.491 0.07268 1.238
-
-
0.33572 -2.5725 33.081 0.07280 1.234
0.33658 -2.3699 33.581 0.07302 1.247
-
-
0.35452(47) -2.0815(23) 32.130(23) 0.08206(42) 3.296(39)
0.3382(81) -1.973(48) 34.087e 0.0550(67) 1.39(88)
J 10
-
-
-
-
-
-
-
-
0.04103(84) -0.2449(30) 4.635(58)
-0.036(23)f 0.22(13)f -0.38(11)f 4.1(25)f
0.08362
325 0.00073 0.08263(13)
24 0.0637(58)
9
JK 10
9
9 KJ 10 9 JK 10
No. of transitions rms deviation (cm-1) Δ (uÅ2)
0.08328
0.08374
0.08324
a
Experimental ground state constants were derived from the simultaneous fit of 301 GSCDs of present FTIR work and 24 microwave transitions. Experimental ground state constants were derived from 24 microwave transitions of Ref. [8]. c The uncertainty in the last digits (twice the estimated standard error) of this work is given in parentheses. d The uncertainty in the last digits are from Ref. [8]. e The marked parameter could not be determined in the fitting of the 24 microwave transitions and therefore were fixed to the calculated value in Ref. [8]. f Values are not well determined (uncertainties are larger than 20%). b
21
Table 2 Rovibrational constants (cm-1) for the and states of H13COOD as determined for an Ar reduction of the I representation. MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ calculations are based on the anharmonic oscillator model. constants using constants using cc-pVTZ basis set cc-pVQZ basis set ( (anharmonic) (anharmonic) MP2 B3LYP MP2 B3LYP (this work) (this work) A 2.1400080 2.1433870 2.1424890 2.1462240 2.1390144(92)a 2.1585(13)a B 0.388666 0.389665 0.390380 0.390274 0.390497(79) 0.39331(33) C 0.328424 0.329216 0.329706 0.329719 0.332360(40) [0.331262]
J 106 JK 106 K 106 J 106 K 106
-
-
-
-
0.4908(92) -9.93(60) 40.38(66) [0.08206]b [3.296]
[0.35452] [-2.0815] [32.130] [0.08206] [3.296]
J 10
-
-
-
-
[0.04103] [-0.2449] [4.635]
[0.04103] [-0.2449] [4.635]
2634.452
2599.039
2632.186
2602.978
2631.13155(34)
2596.31(19)
9
9 JK 10 9 JK 10
0.000435(55) -0.1926(65) 0.002679(88) -0.000585(35) 0.01534 -0.00037 0.00007
0.01488 -0.00035 0.00007
0.01561 -0.00037 0.00007
0.01489 -0.00034 0.00007
No. of IR transitions rms deviation (cm-1)
0.014291(15) 0.001743(79) -0.001099(40) 626 0.0023
Range of J′ fitted
3-35
Range of Ka′ fitted
0-16
No. of fitted transitions for P branch
293
No. of fitted transitions for Q branch
60
No. of fitted transitions for R branch
273
a b
The uncertainty in the last digits (twice the estimated standard error) in this work is given in parentheses. The values in the square brackets in the present work were fixed to the ground state values from this work.
22
Graphical abstract
23
Research Highlights
FTIR spectrum of the band of H13COOD was recorded at 0.0063 cm-1 resolution. Total of 626 perturbed and unperturbed IR transitions of the band were analyzed. The rovibrational constants for the state were determined for the first time. a- and b-Coriolis parameters were obtained from interaction with the band. 13 Improved ground state constants of H COOD.
24
S0022-2852(18)30271-6 https://doi.org/10.1016/j.jms.2018.09.008 YJMSP 11083
To appear in:
Journal of Molecular Spectroscopy
Received Date: Revised Date: Accepted Date:
16 August 2018 25 September 2018 26 September 2018
Please cite this article as: R. A'dawiah, T.L. Tan, L.L. Ng, High-resolution FTIR spectroscopy of H13COOD: The ground state and v2 = 1 state rovibrational constants, Journal of Molecular Spectroscopy (2018), doi: https://doi.org/ 10.1016/j.jms.2018.09.008
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High-resolution FTIR spectroscopy of H13COOD: the ground state and state rovibrational constants
Rabia’tul A’dawiah, T. L. Tan*, L.L. Ng Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University, 1 Nanyang Walk, Singapore 637616, Singapore
Date: 25 September 2018 No. of pages: 23 No. of tables: 2 No. of figures: 4 Running head: The 2 band of H13COOD *Corresponding author: T. L. Tan Tel: 65-67903837 E-mail address: [email protected] (T.L. Tan) Keywords: formic acid isotopologue; H13COOD; high-resolution FTIR spectroscopy; rovibrational constants; ground state constants Abstract The Fourier transform infrared (FTIR) rovibrational spectrum of the
band of the formic
acid isotopologue H13COOD was recorded in the 2550-2710 cm-1 region at an unapodized 1
resolution of 0.0063 cm-1. Rovibrational constants up to three quartic terms were derived for the first time with high precision for the
state through the fitting of 626 infrared
transitions using the Watson’s A-reduced Hamiltonian in the Ir representation with a rootmean-square (rms) deviation of 0.0023 cm-1. The rotational energy levels of the found to be perturbed by a nearby
band was
band. From the analysis, a- and b-Coriolis
resonance parameters from the interactions of the
band with
band were obtained
for the first time. The rotational constants A and B along with the band center of the band were also derived for the first time in this work. The band centers of the
and
bands of H13COOD were determined as 2631.13155(34) cm-1 and 2596.31(19) cm-1 respectively. The ground state constants of H13COOD were determined with higher precision than previously by fitting 301 ground state combination-differences (GSCDs) from the present work and 24 previous microwave measurements with rms deviation of 0.00073 cm-1. The equilibrium state rovibrational constants up to five quartic terms were derived from theoretical anharmonic calculations at four levels of theory: MP2/cc-pVTZ, B3LYP/ccpVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ using the principal axis coordinate system. These calculated constants agree with the ground state constants of H 13COOD derived from the current experimental GSCD combined with microwave transitions fit. In addition, all three rotational constants (A, B and C) of the ground state of H13COOD were obtained from anharmonic calculations using B3LYP and MP2 levels with the cc-pVTZ and cc-pVQZ basis sets. These rotational constants were found to agree with those derived experimentally with percentage
deviations
within
1.0%.
1. Introduction Formic acid (HCOOH) is the simplest organic acid with one carbon atom. The formic acid molecule and its isotopologues have been studied extensively by spectroscopists over the years due to their significant astrophysical, atmospheric and environmental relevance [1–5]. 2
Formic acid is among the most abundant pollutants in the atmosphere and has been constantly monitored in both remote and urban areas [4,5]. Formic acid has two isomeric configurations, trans-formic acid and cis-formic acid with a ratio of 726:1 at room temperature [6]. The higher stability of the trans-form of formic acid accounts for the larger amount of transformic acid present in the atmosphere. Therefore, many studies including this present study, were dedicated to the trans-conformer of formic acid. The nine fundamental vibrational bands of formic acid and its
13
C, D and
18
O
isotopically substituted species were studied by Redington [7] in 1977 using low-resolution infrared (IR) spectroscopy. Determining the equilibrium structure of formic acid molecule or any molecule is one of the major challenges of molecular spectroscopy. The precision and accuracy of molecular geometry obtained is dependent on the amount and accuracy of spectroscopic data available on the parent molecule as well its isotopologues since molecular geometry is essentially unchanged by isotopic substitution of the constituent atoms [8]. Thus, it is important to investigate the isotopic form of formic acid to determine its molecular structure. Another significant reason to study the high-resolution FTIR spectra of isotopologues of formic acid lies in the importance of understanding the complicated resonances among interacting vibrational levels which may change in isotopic substitution. The rovibrational structures derived from studying formic acid and its isotopic species at high-resolution, together with data on isotopic shifts, band centers and changes in the rovibrational constants, various interactions and coupling constants for the various vibrational states of formic acid can be accurately derived. Furthermore, the information obtained from the interaction studies can be used in testing ab initio calculations and aids in the accurate evaluation of the molecular structure of formic acid. Baskakov et al. [9] did a comprehensive study on the 41, 51, 61, 72, 81, 7191 and 92 interacting vibrational states of the HCOOH molecule. Accurate rotational constants (A, B 3
and C) of the
fundamental band of HCOOH and formic acid-d1 (HCOOD) have been
reported by Luo et al. [10] in 2017. In 2007, Demaison and co-workers [11] theoretically calculated the quadratic, cubic and semidiagonal quartic force fields of both cis- and transconformers of formic acid using three levels of theory. In their work, Demaison et al. [11] also reported the equilibrium rotational constants and the inertial defects of various isotopologues of formic acid except H13COOD. The rovibrational analyses of the various fundamental bands of the HCOOD isotopologue of formic acid have also been reported [6,10,12–21]. Most recently, A’dawiah et al. [18] did a rovibrational study on the
(O-D
stretch) band of HCOOD. In the study, A’dawiah et al. [18] reported on the rovibrational constants of the
state of HCOOD and observed a- and b-Coriolis interactions of the
band with
band of HCOOD. Furthermore, Goh et al. [22] did a high-resolution
FTIR study on the
(O-D) band of DCOOD. Some perturbations were also observed for this
band though they were not analyzed. The perturbations could be due to Fermi and c-Coriolis resonance with the
band or a- and b-Coriolis interactions with the
band.
Despite the numerous studies done on the fundamental bands of formic acid and its isotopologues, they are limited to wavenumbers below 1800 cm-1 [22]. To the authors’ present knowledge, no work has been done to investigate the upper state
of
H13COOD. In fact, the only high-resolution work reported on the H13COOD molecule was by Baskakov et al. [8]. In their study, Baskakov and his co-workers [8] measured microwave rotational transition frequencies of three isotopic forms of formic acid (i.e. H 13COOD, D13COOH and D13COOD). Baskakov et al. [8] mentioned difficulties in assigning these transitions as the samples were not enriched with
13
C but the
13
C were present as naturally-
abundant species in the samples of HCOOD, DCOOH and DCOOD, resulting in weaker transitions.
4
In this present investigation, the hybrid A/B-type
band of H13COOD was recorded
at an unapodized resolution of 0.0063 cm-1 using Fourier transform infrared (FTIR) spectroscopy in the 2550-2710 cm-1 wavenumber region. The predominantly B-type. By assigning 626 IR lines, accurate
band was found to be upper state rovibrational
constants and band center was derived in this work for the first time. The Coriolis resonances of the
and
states were also analyzed in this work yielding the a- and
b-Coriolis resonance parameters. The ground state rovibrational constants for H13COOD up to three sextic terms were also obtained with higher precision and accuracy by fitting the ground state combination-differences (GSCDs) derived from the present analysis of the band and the microwave measurements made by Baskakov et al. [8]. In addition, the equilibrium state rovibrational constants of H13COOD were calculated using four levels of theory (i.e. MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ). The ground state and upper state (
of H13COOD were also derived from the calculations.
All rovibrational constants derived in this high-resolution FTIR study agree well with the computed values. 2. Experimental and computational details The H13COOD vapor of relatively high purity was obtained by mixing H13COOH vapor with D2O vapor at equal pressures at room temperature (298 K) in a gas cell. The infrared spectrum in the 2550-2710 cm-1 wavenumber region was recorded using the Bruker IFS 125HR Michelson Fourier transform spectrometer in the Spectroscopy Laboratory of the National Institute of Education, Nanyang Technological University in Singapore with an unapodized resolution of 0.0063 cm-1. Spectral measurements were recorded at an ambient temperature of approximately 298 K with a multiple-pass absorption cell of total absorption length of 0.80 m, a globar infrared source, a liquid nitrogen-cooled Hg-Cd-Te detector and KBr beamsplitter. A total mean vapor pressure of 8.1 mbar in the gas cell was measured 5
using a capacitance pressure gauge. The interferogram was processed with the four-point apodization function with a zero filling factor of 8. The final sample spectrum was obtained from a co-addition of 3300 scans collected over a period of 55 hours. The full-width at halfmaximum (FWHM) of the infrared peaks of the final transmittance spectrum were measured to have an average value of 0.013 cm-1. A total of 32 unblended D2O absorption lines of sufficient intensities located in the 2500-3000 cm-1 spectral range were used to calibrate the infrared transition lines of the band of H13COOD. The selected absorption wavenumbers were calibrated against the infrared standards taken from the public-access database HITRAN (2016) [23]. The rootmean-square (rms) deviation of the calibrated wavenumbers after the fitting of 32 D 2O lines in the calibration was 0.00033 cm-1. The absolute precision of the measured H13COOD lines could then be approximated to be ± 0.0013 cm-1 (1/10th of the measured FWHM of 0.013 cm1
) after accounting for systematic errors in the experiments. Rotational and quartic centrifugal distortion constants for the equilibrium state,
rotational constants for the ground and
state of H13COOD were computed
theoretically with the GAUSSIAN09 [24] program using an anharmonic oscillator model at the B3LYP/cc-pVTZ, MP2/cc-pVTZ, B3LYP/cc-pVQZ and MP2/cc-pVQZ levels of theory. The computed values were compared with the experimental values derived from non-linear least-squares fitting of the assigned infrared transitions. 3. Rovibrational analysis H13COOD is a near-prolate asymmetric rotor belonging to the Cs point group with an asymmetry parameter
-0.935. The
band is ascribed to the in-plane O-D stretch having
an A′ symmetry according to the numbering of normal modes by Redington [7]. The fundamental band is expected to be an A/B hybrid type consisting of both a-type and b-type 6
transitions. A high-resolution compressed plot of the
spectrum of H13COOD in the region
2550-2710 cm-1 is shown in Fig. 1. The well-defined P and R contours and the absence of a prominent central Q branch illustrates the appearance of a typical b-type band. A-type transitions were too weak to be observed in the spectrum, hence, only b-type transitions were assigned and fitted. A’dawiah et al. [18] and Goh et al. [22] observed similar strong b-type with non-observable a-type transitions when analyzing the same band ( ) corresponding to the OD stretching mode of the isotopologues molecules HCOOD and DCOOD respectively. The following selection rules for b-type rovibrational transitions apply:
3.1 Assignment of the infrared transitions The bootstrap method was employed in the assignment of the transitions. Assignments were started with transitions of Ka′ = 7 and 8 in the P and R branches of the band, which were observed to be of higher intensity. A series of transitions of constant Ka″ were observed to be approximately 4.3 cm-1 (≈ 2A) apart. Subsequent lines in each Ka″ series belonging to J = Ka + 1, J = Ka + 2, … are separated by about 0.72 cm-1 (B + C). The initial fitting process of the
state of H13COOD started off by using the ground state constants
reported by Baskakov et al. [8]. A preliminary set of rovibrational constants for the state was obtained from the fitting of these lines using the non-linear least-squares fitting program developed by Maki [25]. This program uses the Watson’s A-reduced Hamiltonian [26] in the Ir representation. Assignments of the lines were expanded, aided by calculated unperturbed line positions using the set of preliminary rovibrational constants and crosschecked using ground state combination differences (GSCDs). The rovibrational constants for the upper state were progressively refined as the set of assignments in the P and R branches were expanded. This bootstrap process was repeated until no new lines could be
7
confidently assigned. Analyses of the Q-clusters in the P and R branches were made after the assignments of the P and R branches. The Q-clusters were found to be separated by , where
. However, most of the transitions in the Q-clusters could not be fitted
accurately due to the blending of the transition lines caused by the large line-widths of the IR lines (mainly due to pressure and Doppler broadenings). Fig. 2 shows some of the final b-type PP10 to PP13 (i.e. those transitions belonging to Ka″= 10-13 with J′ - J″ = -1 and Ka′ - Ka″ = -1) line assignments in the 2572-2576 cm-1 wavenumber region of the P branch. No asymmetric splitting could be observed for Ka″ ≥ 7 in the present analysis. In the nonlinear fitting process, each unblended infrared transition was weighted by the inverse square of the measured uncertainty of ± 0.0013 cm-1 while those belonging to blended or unresolved asymmetry doublets were assigned to uncertainties in multiples of ± 0.0013 cm-1. 3.2 Analysis of the Coriolis interactions between the
state and (
) states
Most of the transitions of Ka′ ≥ 1 were found to deviate from their calculated unperturbed positions and could not be fitted satisfactorily. These perturbations are likely to state located at approximately 2597 cm-1 after
be caused by the nearby (
studying the rotational energy levels of all possible nearby vibrational states. A’dawiah et al. [18] observed similar perturbation profile for the
state of HCOOD. As the 3
band is a C-type band (A″ symmetry), a- and b-type Coriolis resonances between the rotational energy levels of the | = odd, |ΔKc′ (= even, |ΔKc′ (=
-
-
and (
states with |ΔKa′ (=
| = odd for b-Coriolis and |ΔKa′ (=
-
|=
| = odd for a-Coriolis were expected.
Watson’s Hamiltonian [26] in the Ir representation and A-reduction with the inclusion of the first and higher order a- and b-type Coriolis interaction terms were applied in the fit to 8
account for the large number of perturbed transitions. The matrix elements are given by the following expressions: (1) (2) (3) (4)
where
and
represent the
and
first-order b-Coriolis resonance parameter of the
states respectively, = 1 and (
are the higher-order b-Coriolis coupling constants,
= 3,
= 1) states,
is the and
is the constant associated with
ΔK = ± 2 a-type Coriolis interactions and 3.3 Ground state combination differences (GSCDs) analysis A total of 301 GSCDs from present analysis of the b-type transitions of the
band of
H13COOD and 24 microwave (MW) transitions from Ref. [8] were used to obtain a revised set of ground state rovibrational constants. GSCDs were added from the infrared measurements as they were assigned. The ground state constants were systematically refined as more newly assigned infrared transitions were included in the fitting. Each GSCD is weighted by the inverse square of the measure line uncertainty of ± 0.0018 cm-1, which is (1/10th of the measure line width of 0.0013 cm-1). The rms deviation of the combined GSCD and MW fit is 0.00073 cm-1. Table 1 gives the rovibrational ground state constants of H13COOD up to 3 sextic terms derived using the Watson’s A-reduced Hamiltonian in the Ir representation. The inertial defect of the molecule was calculated using the ground state rotational parameters in this work and compared to the inertial defect calculated from the ground state constants from Baskakov et al. [8] and those of computational calculations. The final ground state constants derived in this work were then fixed in the FTIR fit of the upper 9
state (
) transitions to derive final and precise rovibrational constants and band centers
of the
and
states with the inclusion of one a-Coriolis and three b-
Coriolis interaction parameters. 4. Results and discussion A precise set of ground state constants comprising of three rotational constants, five quartic and 3 sextic centrifugal distortion constants was derived from the fitting of 301 GSCDs and 24 microwave measurements (from Baskakov et al. [8]). Table 1 shows the equilibrium and ground state constants calculated using four theoretical levels: MP2/ccpVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ levels, using the Watson’s Areduced Hamiltonian in the Ir representation. The ground state rotational constants derived from this work are in close agreement with those in Ref. [8] as seen from Table 1. In general, most of the newly derived ground state constants are more precise than those obtained previously [8]. The ground state rovibrational constants derived in this work give a better representation of the ground state due to the larger data pool of GSCDs combined with microwave transitions being used. Additionally, the quartic centrifugal distortion constant,
K, that was not previously determined in Ref. [8] could be determined in this work. The calculated ground state inertial defect Δ using the new set of ground state rotational constants is 0.08263(13) uÅ2. This experimentally derived value is much closer to the theoretical inertial defect values calculated from the four levels of theory as opposed to the inertial defect value calculated from Ref. [8]. These inertial defect values are presented in Table 1 for comparison. The small positive inertial defect agrees well with the high planarity of H13COOD. The experimentally-derived ground state rotational constants in this work are also in good agreement with those calculated using the four levels of theory (all percentage
10
deviations are within 1.0%). The rotational constant A was best predicted by the MP2/ccpVTZ level of theory with a percentage deviation of approximately 0.09% followed by MP2/cc-pVQZ with a percentage deviation of 0.22%. The cc-pVQZ basis set (for both MP2 and B3LYP methods) has the closest prediction of the rotational constants B and C with percentage deviation between 0.4% to 0.6%. All equilibrium rotational constants derived from the theoretical calculations are larger than the experimentally determined ground state values, as expected, due to the longer bond lengths in the ground state, giving rise to larger moments of inertia. Overall, the MP2 method proves to be in better agreement with the experimental values than the B3LYP method for both cc-pVTZ and cc-pVQZ basis sets in calculating ground state rotational constants, with B3LYP/cc-pVQZ level of theory having the largest percentage deviation. A total of 626 perturbed and unperturbed IR absorption lines were fitted using the Watson’s Hamiltonian [26] with the inclusion of off-diagonal a-
[
and b-Coriolis interaction terms to derive rovibrational constants up to three quartic terms for state of H13COOD. These constants, together with the a- and b-Coriolis resonance
the
parameters, are derived for the first time in this work and presented in Table 2. A rms deviation of 0.0023 cm-1 for the 626 b-type IR transitions of
was achieved after
considering the a- and b-Coriolis terms. The quartic constants δJ and δK were not welldetermined and therefore, fixed to the ground state values. The alpha constants ( ) of the
,
and
state calculated from the differences in the rotational constants A, B and C
respectively, are presented in Table 2. state of H13COOD derived from this work are
The A, B and C constants of the
in good agreement with the calculated values using the B3LYP/cc-pVTZ, MP2/cc-pVTZ, B3LYP/cc-pVQZ and MP2/cc-pVQZ levels of theory as seen from Table 2 (all percentage deviations are less than 1.2%). The
and
values derived from this work, 0.014291(15) 11
cm-1 and -0.001099(40) cm-1 respectively, are close to the
and
values of 0.0152566(75)
cm-1 and -0.001279(15) cm-1 reported by A’dawiah et al. [18] for the However,
value of 0.001743(79) cm-1 for the
band of HCOOD.
state of H13COOD differs from the
value (0.000898(14) cm-1) of the
state of HCOOD [18]. This could be due to some
unaccounted b-Coriolis resonances. The
band center, 2631.13155(34) cm-1, derived from
this analysis agrees with the band center reported by Redington [7] in 1977 and the calculated value of 2632.186 cm-1 using the MP2/cc-pVQZ level of theory. Although the intensities of the absorption lines of the perturbing
band were
not observable, the rotational constants A and B together with the band center of the perturbing band could be determined for the first time with good precision from the analysis of its Coriolis interactions with the
state. All higher order centrifugal distortion
constants we fixed to the ground state values. The band center of the unobserved
of
H13COOD was found to be 2596.31(19) cm-1. This value is close to the sum of the frequencies of the
and
fundamental states observed by Redington [7]. The
band center of HCOOD located at 2601.13(14) cm-1 [18] is close to the band center value derived in this work. The red shift in the band center of work could be attributed to the heavier
13
band in this
C atom. The 12C-13C isotopic shift for the
band center of formic acid-d1 was found to be 4.82(33) cm-1 whereas the isotopic shift for the band is 0.50668(51) cm-1 [18]. The a- and b-Coriolis resonance parameters and
,
and
between
bands derived in this study account for most but not all of the perturbations in
the Ka′ = 8-13 sub-series. Fig. 3 and Fig. 4 show significant reduction in the deviations (observed-calculated) in cm-1 of the perturbed lines of Ka′ = 10-13 after perturbation treatment. However, these a- and b-Coriolis resonance parameters could not account for some
12
of the perturbations in the Ka′ < 7 and Ka′ > 13 sub-series. This indicates that two or more state of H13COOD. A more
bands are also responsible for the perturbations of the
complex and comprehensive resonance study including several nearby upper states may be crucial to provide an accurate depiction of the interactions occurring between the
and
states of H13COOD. Some of the possible interacting nearby rovibrational bands are the A/B-type
(A′ symmetry) with a band center located at approximately
2700 cm-1 and the C-type 2
(A″ symmetry) at 2588 cm-1.
The new rovibrational constants of the and b-Coriolis interaction parameters with the
fundamental band of H13COOD and the aband that are derived for the first
time in this study is useful for the evaluation of equilibrium structures [11,27] and refinement of the equilibrium structural parameters of formic acid molecule. Overall, the J′ and Ka′ values (shown in Table 2) included in this analysis cover the entire frequency range of 25502710 cm-1 of the
band of H13COOD.
The revised ground state rovibrational constants derived from the simultaneous fit of GSCDs and microwave measurements are provided in Supplementary Data 1. The result of the final FTIR fit of the 626 perturbed and unperturbed b-type transitions of the
band of
H13COOD is provided in Supplementary Data 2. The wavenumbers of all IR transitions that were included in the fit and their fitting errors are also listed. 5. Conclusion From the simultaneous fit of 301 GSCDs from the present analysis of the fundamental band and 24 microwave measurements made by Baskakov et al. [8], ground state constants of H13COOD were derived with higher precision. These ground state rotational constants are in close agreement with those from theoretically computed values using the cc-pVTZ and cc-pVQZ basis sets with MP2 and B3LYP methods. A total of 626 13
perturbed and unperturbed b-type IR transitions of the assigned and fitted to obtain accurate upper state (
band of H13COOD were measured, constants up to three quartic terms
for the first time. Furthermore, from the Coriolis interactions between the states, rotational constants A and B, the band center of the
and and the
a- and b-Coriolis resonance parameters were also derived for the first time. The results of this study will further enrich the understanding of the molecular properties of the formic acid (HCOOH) molecule and its isotopologues. Acknowledgements The authors acknowledge the support of this work by the National Institute of Education, Singapore under research grants RS 9/15 TTL, RS 12/17 TTL, RI 5/16 TTLA, RP 5/16 TTLA and RP 1/17 TTL. Appendix A. Supplementary Material The ground state rovibrational constants derived from 301 GSCDs combined with 24 MW transitions using Watson’s A-reduced Hamiltonian in the Ir representation is provided in Supplementary Data 1. The FTIR fit of 626 IR lines of the
band of H13COOD using the
Watson’s
Supplementary
A-reduced
Hamiltonian
is
provided
in
Data
2.
References [1]
A. Goldman, F.H. Murcray, D.G. Murcray, C.P. Rinsland, Geophys. Res. Lett. 11 (1984) 307–310.
[2]
P. Khare, N. Kumar, K.M. Kumari, S.S. Srivastava, Rev. Geophys. 37 (1999) 227– 248.
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S.-Y. Liu, D.M. Mehringer, L.E. Snyder, Astrophys. J. 552 (2001) 654–663.
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H.A. Khwaja, Atmos. Environ. 29 (1995) 127–139. 14
[5]
E.G. Chapman, D. V Kenny, K.M. Busness, J.M. Thorp, C.W. Spicer, Geophys. Res. Lett. 22 (1995) 405–408.
[6]
O.I. Baskakov, H. Bürger, W. Jerzembeck, J. Mol. Spectrosc. 193 (1999) 33–45.
[7]
R.L. Redington, J. Mol. Spectrosc. 65 (1977) 171–189.
[8]
O.I. Baskakov, S.F. Dyubko, S. V Sirota, J. Appl. Spectrosc. 54 (1991) 424–427.
[9]
O.I. Baskakov, I.A. Markov, E.A. Alekseev, R.A. Motiyenko, J. Lohilahti, V.-M. Horneman, B.P. Winnewisser, I.R. Medvedev, F.C. De Lucia, J. Mol. Struct. 795 (2006) 54–77.
[10] W. Luo, Y. Zhang, W. Li, C. Duan, J. Mol. Spectrosc. 334 (2017) 22–25. [11] J. Demaison, M. Herman, J. Liévin, J. Chem. Phys. 126,164305 (2007) 1–9. [12] O.I. Baskakov, Quantum Electron. 29 (1999) 226–228. [13] V. Lattanzi, A. Walters, B.J. Drouin, J.C. Pearson, Astrophys. J. Suppl. Ser. 176 (2008) 536–542. [14] K.L. Goh, P.P. Ong, H.H. Teo, T.L. Tan, J. Mol. Spectrosc. 197 (1999) 322–323. [15] K. Marushkevich, L. Khriachtchev, J. Lundell, A. V Domanskaya, M. Räsänen, J. Mol. Spectrosc. 259 (2010) 105–110. [16] K.L. Goh, P.P. Ong, T.L. Tan, H.H. Teo, W.F. Wang, J. Mol. Spectrosc. 191 (1998) 343–347. [17] T.L. Tan, K.L. Goh, P.P. Ong, H.H. Teo, J. Mol. Spectrosc. 198 (1999) 110–114. [18] R. A’dawiah, T.L. Tan, L.L. Ng, J. Mol. Spectrosc. 349 (2018) 43–48. [19] O.I. Baskakov, J. Mol. Spectrosc. 213 (2002) 1–7.
15
[20] L. Nemes, A.R.W. McKellar, J.W.C. Johns, JOSA B 4 (1987) 1165–1172. [21] O.I. Baskakov, J. Mol. Spectrosc. 208 (2001) 194–196. [22] K.L. Goh, P.P. Ong, H.H. Teo, T.L. Tan, Spectrochim. Acta Part A Mol. Biomol. Spectrosc. 56 (2000) 991–1001. [23] I.E. Gordon, L.S. Rothman, C. Hill et al., J. Quant. Spectrosc. Radiat. Transf. 203 (2017) 3–69. [24] M.J. Frisch, G.W. Trucks, H.B. Schlegel et al., GAUSSIAN09, Gaussian Inc., Wallingford, CT, USA, 2009. [25] A.G. Maki, T.L. Tan, E.C. Looi, K.T. Lua, J.W.C. Johns, M. Noel, J. Mol. Spectrosc. 157 (1993) 248–253. [26] J.K.G. Watson, in:, J.R. Durig (Ed.), Vib. Spectra Struct. A Ser. Adv., Elsevier, New York, 1977. [27] I. Yokoyama, Y. Miwa, K. Machida, J. Am. Chem. Soc. 113 (1991) 6458–6464. FIGURE CAPTIONS Figure 1.
The survey spectrum of the
band of H13COOD recorded at high-resolution
(0.0063 cm-1) in the 2550-2710 cm-1 region. The strong absorption lines scattered throughout the spectrum belong to D2O which was present in the mixing of H13COOH with D2O. Figure 2.
Detailed section of the high-resolution FTIR spectra in the P-branch regions
showing the assignments of the
band of H13COOD. *Transitions belong to H13COOH,
D2O and H2O present in the sample. Figure 3.
Deviations (obs.-calc.) in cm-1 of Ka′ = 10 and Ka′ = 11 in the P branch plotted
as a function of J′ of
band of H13COOD. 16
Figure 4.
Deviations (obs.-calc.) in cm-1 of Ka′ = 12 and Ka′ = 13 in the P branch plotted
as a function of J′ of
band of H13COOD. TABLE TITLES
Table 1.
Rovibrational constants (cm-1) for the equilibrium and ground states of
H13COOD (A-reduction in the Ir representation). Table 2.
Rovibrational constants (cm-1) for the
and
states of
H13COOD as determined for an A-reduction of the Ir representation. MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ calculations are based on the anharmonic oscillator model. Figure 1.
The survey spectrum of the
band of H13COOD recorded at high-resolution
(0.0063 cm-1) in the 2550-2710 cm-1 region. The strong absorption lines scattered throughout the spectrum belong to D2O which was present in the mixing of H13COOH with D2O.
17
Figure 2.
Detailed section of the high-resolution FTIR spectra in the P-branch regions
showing the assignments of the
band of H13COOD. *Transitions belong to H13COOH,
D2O and H2O present in the sample.
18
Figure 3.
Deviations (obs.-calc.) in cm-1 of Ka′ = 10 and Ka′ = 11 in the P branch plotted
as
function
a
of
J′
of
band
of
H13COOD.
19
Figure 4.
Deviations (obs.-calc.) in cm-1 of Ka′ = 12 and Ka′ = 13 in the P branch plotted
as
function
a
of
J′
of
band
of
H13COOD.
20
Table 1 Rovibrational constants (cm-1) for the equilibrium and ground states of H13COOD (A-reduction in the Ir representation). Theoretical cc-pVTZ basis set Theoretical cc-pVQZ basis set (anharmonic model) (anharmonic model) Equilibrium state Ground state Equilibrium state Ground state MP2 B3LYP MP2 B3LYP MP2 B3LYP MP2 B3LYP A 2.1656351 2.1683009 2.1553500 2.1582680 2.1685718 2.1710910 2.1581040 2.1611160 B 0.39098063 0.39194619 0.38830100 0.38932000 0.39272263 0.39259678 0.39000600 0.38993500 C 0.33118403 0.33193907 0.32849100 0.32928500 0.33250220 0.33247108 0.32977500 0.32979200
Experimental ground state This work (IR, MW)a 2.1533059(58)c 0.39224030(41) 0.33126166(43)
Ref. [8] (MW)b 2.15054(98)d 0.3922067(87) 0.3312959(87)
J 106 JK 106 K 106 J 106 K 106
0.33136 -2.3490 32.956 0.07172 1.216
0.33491 -2.3735 33.491 0.07268 1.238
-
-
0.33572 -2.5725 33.081 0.07280 1.234
0.33658 -2.3699 33.581 0.07302 1.247
-
-
0.35452(47) -2.0815(23) 32.130(23) 0.08206(42) 3.296(39)
0.3382(81) -1.973(48) 34.087e 0.0550(67) 1.39(88)
J 10
-
-
-
-
-
-
-
-
0.04103(84) -0.2449(30) 4.635(58)
-0.036(23)f 0.22(13)f -0.38(11)f 4.1(25)f
0.08362
325 0.00073 0.08263(13)
24 0.0637(58)
9
JK 10
9
9 KJ 10 9 JK 10
No. of transitions rms deviation (cm-1) Δ (uÅ2)
0.08328
0.08374
0.08324
a
Experimental ground state constants were derived from the simultaneous fit of 301 GSCDs of present FTIR work and 24 microwave transitions. Experimental ground state constants were derived from 24 microwave transitions of Ref. [8]. c The uncertainty in the last digits (twice the estimated standard error) of this work is given in parentheses. d The uncertainty in the last digits are from Ref. [8]. e The marked parameter could not be determined in the fitting of the 24 microwave transitions and therefore were fixed to the calculated value in Ref. [8]. f Values are not well determined (uncertainties are larger than 20%). b
21
Table 2 Rovibrational constants (cm-1) for the and states of H13COOD as determined for an Ar reduction of the I representation. MP2/cc-pVTZ, B3LYP/cc-pVTZ, MP2/cc-pVQZ and B3LYP/cc-pVQZ calculations are based on the anharmonic oscillator model. constants using constants using cc-pVTZ basis set cc-pVQZ basis set ( (anharmonic) (anharmonic) MP2 B3LYP MP2 B3LYP (this work) (this work) A 2.1400080 2.1433870 2.1424890 2.1462240 2.1390144(92)a 2.1585(13)a B 0.388666 0.389665 0.390380 0.390274 0.390497(79) 0.39331(33) C 0.328424 0.329216 0.329706 0.329719 0.332360(40) [0.331262]
J 106 JK 106 K 106 J 106 K 106
-
-
-
-
0.4908(92) -9.93(60) 40.38(66) [0.08206]b [3.296]
[0.35452] [-2.0815] [32.130] [0.08206] [3.296]
J 10
-
-
-
-
[0.04103] [-0.2449] [4.635]
[0.04103] [-0.2449] [4.635]
2634.452
2599.039
2632.186
2602.978
2631.13155(34)
2596.31(19)
9
9 JK 10 9 JK 10
0.000435(55) -0.1926(65) 0.002679(88) -0.000585(35) 0.01534 -0.00037 0.00007
0.01488 -0.00035 0.00007
0.01561 -0.00037 0.00007
0.01489 -0.00034 0.00007
No. of IR transitions rms deviation (cm-1)
0.014291(15) 0.001743(79) -0.001099(40) 626 0.0023
Range of J′ fitted
3-35
Range of Ka′ fitted
0-16
No. of fitted transitions for P branch
293
No. of fitted transitions for Q branch
60
No. of fitted transitions for R branch
273
a b
The uncertainty in the last digits (twice the estimated standard error) in this work is given in parentheses. The values in the square brackets in the present work were fixed to the ground state values from this work.
22
Graphical abstract
23
Research Highlights
FTIR spectrum of the band of H13COOD was recorded at 0.0063 cm-1 resolution. Total of 626 perturbed and unperturbed IR transitions of the band were analyzed. The rovibrational constants for the state were determined for the first time. a- and b-Coriolis parameters were obtained from interaction with the band. 13 Improved ground state constants of H COOD.
24