Spectroscopic and Computational Study of Acetic Acid and Its Cyclic

Article pubs.acs.org/JPCA

Spectroscopic and Computational Study of Acetic Acid and Its Cyclic Dimer in the Near-Infrared Region Krzysztof B. Beć,*,†,‡ Yoshisuke Futami,§ Marek J. Wójcik,*,∥ Takahito Nakajima,⊥ and Yukihiro Ozaki*,† †

Department of Chemistry, School of Science and Technology, Kwansei Gakuin University, Sanda, Hyogo 669-1337, Japan RIKEN, 519-1399 Aramaki-Aoba, Aoba-ku, Sendai, Miyagi 980-0845, Japan § Department of Biological and Chemical Systems Engineering, National Institute of Technology, Kumamoto College, Yatsushiro, Kumamoto 866-8501, Japan ∥ Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Kraków, Poland ⊥ RIKEN Advanced Institute for Computational Science, 7-1-26, Minatojima-minami-machi, Chuo-ku, Kobe, Hyogo 650-0047, Japan ‡

ABSTRACT: Anharmonic vibrational analysis of near-infrared (NIR) spectra of acetic acid was carried out by anharmonic quantum chemical calculation in a wide concentration range of its CCl4 solution. By predicting vibrational spectra of acetic acid for the first time over a wide NIR region, it was possible to elucidate the influence of the formation of acetic acid cyclic dimer on its NIR spectrum. Quantum chemical simulations were based on coupled cluster and density functional theory quantum methods. Additionally, Møller−Plesset perturbation theory was employed for the additional calculation of hydrogen bonding stabilization energies. An anharmonic vibrational analysis was performed with the use of generalized second-order vibrational perturbation theory (GVPT2). A hybrid approach was assumed, in which monomeric species was treated by CCSD(T)/aug-cc-pVDZ (harmonic approximation) and B3LYP/ SNSD (anharmonic approximation) methods. For the cyclic dimer, B3LYP and B2PLYP single and double hybrid functionals, paired with an SNSD basis set, were employed. DFT calculations were augmented with additional empirical dispersion correction. It was found that quantum chemically calculated vibrational modes in the NIR region are in a good agreement with experimental data. The results of anharmonic vibrational analysis were supported by a harmonic shift analysis, for elucidating the very strong anharmonic coupling observed between stretching modes of hydrogen bonded bridge in the cyclic dimer. However, the calculated wavenumbers for combination modes of double hydrogen bonded bridge in the cyclic dimer, which are very sensitive to the formation of hydrogen bonding, were found to be underestimated by quantum chemical methods. Therefore, by band fitting, the wavenumbers and shape parameters for these bands were found, and the modeled spectra were adjusted accordingly. A high accuracy of simulated spectra was achieved, and a detailed analysis of the experimental NIR spectra of acetic acid was possible, with successful identification of numerous experimental bands, including those which originate from concentration effects. It was also found that the main spectral features observed in the NIR spectra of carboxylic acid upon the formation of hydrogen bond should be accounted for combination modes of the stretching and bending vibrations of double hydrogen-bonded bridge in the cyclic dimers of acetic acid.

1. INTRODUCTION

assignments in the experimental spectra. The support coming from quantum chemical vibrational analysis, which has since long time been of great value for the IR and Raman spectroscopy,15,16 was not broadly available for NIR spectroscopy. In the past numerous attempts were made to incorporate anharmonicity of vibrational modes by employing approximations of anharmonic vibrational potential by Lennard-Jones or Morse functions and by solving one-dimensional vibrational Schrödinger equation;17−19 research papers involving these

Near-infrared (NIR) spectroscopy is a powerful tool for investigations of intermolecular interactions, hydrogen bonded systems in particular.1−3 The importance of NIR has been steadily growing since the nineties, witnessing both significant improvement in the instrumentation and also extensive developments of data analysis toolswith emerging powerful techniques such as quantum chemistry methods,3−5 twodimensional correlation analysis,6−10 and chemometrics.11−14 Yet, NIR spectra of organic molecules have often proved to be particularly difficult for detailed analysis, due to a high number of heavily overlapping bands.1−3 Also, spectral features observed in the NIR spectra mainly stem from combination modes, which demonstrate particular challenge for band © 2016 American Chemical Society

Received: May 3, 2016 Revised: June 17, 2016 Published: August 2, 2016 6170

DOI: 10.1021/acs.jpca.6b04470 J. Phys. Chem. A 2016, 120, 6170−6183

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The Journal of Physical Chemistry A

and many other chemical and physical properties as well. Acetic acid has often been of high interest to biochemical studies as well,44−46 in which it often assumes the role of a prototypic carboxylic acid, instead of less useful formic acid. Thus, its properties and chemistry of the fundamentally important acetyl group have often been investigated in detail. Significant role in the discovery of acetic acid properties was played by vibrational spectroscopy. Numerous studies have been reported in this field, incorporating IR47−49 and Raman spectroscopy;50−53 these studies were often supported by quantum chemical calculations.54,55 Recently, investigations of acetic acid have been carried out by powerful femtosecond laser pump−probe multidimensional IR and Raman spectroscopies.56−58 Vibrational and physicochemical properties of carboxylic acids in different phases were also subject of theoretical investigations.59,60,55 Such an extensive research interest put into an investigation of acetic acid highlights its scientific importance very well. Which may come as a surprise, NIR spectroscopydespite its intrinsic usefulness for the field of hydrogen bond research was not so widely utilized in the area of acetic acid research. Although there are investigations by NIR spectroscopy of other carboxylic acids including fatty acids,61,62 compared with IR and Raman investigations they are rather rare. This can be partially explained by complexity of the NIR spectrum of acetic acid and its derivatives, making it challenging in interpretation. Therefore, we feel that applying recent and powerful quantum chemistry methods, which will play the key role in the presented analysis of NIR spectra of acetic acids, may bring notable improvement for this area of research. In this work we aim at prediction and explanation of NIR vibrational modes of acetic acid and its derivatives, both in nonassociated and selfassociated forms, including prediction of the influence of formation of cyclic homo- and heterodimers on NIR vibrational modes of these molecules. We also aim at establishing a viable approach to quantum chemical prediction of spectral features in NIR region of hydrogen bonded systems, which have always been of particular interest in the NIR field of research.

approaches have been published on a regular basis, and good agreement with experimental data has been reported.4,5 These attempts, however, cannot be easily adopted for a prediction of the entire NIR spectra or for treatment of vibrational modes of complex molecules. Introduction of the vibrational selfconsistent field (VSCF) and the vibrational configuration interaction (VCI) methods have allowed for more flexible approaches to the prediction of overtone and combination modes;20−23 for these, however, the complexity and computational time demands expand rapidly with an increasing size of the molecular system beyond simplest cases. Therefore, attempts were made to increase the affordability level of VSCF based approaches,24−27 including recent advances in the field of perturbation corrected VSCF.28,29 Also, perturbationcorrected VSCF (PT2-VSCF) approach was recently successfully applied to the anharmonic calculations in the role of support studies in the analytical studies of ethanol in gasoline by Lutz et al.30 The recent progress in the development of quantum chemical methods, in particular the development of secondorder vibrational perturbation theory (VPT2)31,32 and its subsequent implementation in Gaussian softwarein its generalized formalism (GVPT2)allows of incorporation of both mechanical and electrical anharmonicity in vibrational analysis with very good accuracy and at moderate computational cost.33−35 This has opened completely new possibilities for the field of NIR spectroscopy. So far, mainly applications of GVPT2 approach for fully anharmonic approximation of fundamental modes have been focused on. At the same time, GVPT2 based prediction of overtone and combination modes, which determine the vibrational spectrum of organic molecules throughout NIR region, so far has only been reported briefly.34,36 Therefore, in this work we incorporate GVPT2 approach, for the first time to simulate spectral features in the broad NIR region of acetic acid and its derivatives, including prediction of the influence of formation of cyclic dimer on NIR spectra of studied carboxylic acids. NIR spectroscopy plays an important role among other vibrational spectroscopies, due to its significant and unique properties.1−3 Its usefulness is particularly pronounced in the investigation of hydrogen bonded systems. Significant anharmonicity of all kinds of X−H vibrations (X = N, C, O) when coupled with the X−H stretching mode, which has typically very high fundamental frequency, results in a supremacy of bands originating from these functional groups (NH, OH, CH) in a NIR spectrum.1−3 These functional groups are obviously very often involved in hydrogen bonding. In addition, the usual band shifts and intensity changes typical for hydrogen bonding formation are most of the time even more pronounced in the NIR region, and an X−H stretching vibrations band arising from monomeric species often more strongly appear compared with those originating from polymeric species.8,37−39 On the other hand, the NIR region should be generally described as much more difficult for analysis, compared with fundamental region. These peculiarities of NIR spectroscopy highlight the possible benefits stemming from possible quantum chemical support.3 Acetic acid has always been a common subject for numerous physiochemical investigations focusing on the properties of hydrogen bonding.40−43 Its remarkable attributes incorporate high value of hydrogen bond stabilization energy, formation of cyclic dimer, appearance of solvent and concentration effects and their influence on the dimerization equilibrium constant,

2. COMPUTATIONAL METHODS The calculation of NIR spectra of the studied systems was carried out in Gaussian 09 Rev. D.01 quantum chemical software.63 For the structure optimization, calculation of hydrogen bonding stabilization energies and vibrational analysis, density functional theory (DFT) was employed. Additionally, Møller−Plesset second-order perturbation theory (MP2)64 was applied for calculation of hydrogen bonding stabilization energies as well. For the DFT computation, single hybrid B3LYP65,66 and double hybrid B2PLYP67 density functionals were applied. The double hybrid density functionals (DHDF), taking into account on-local perturbation correction for the correlation part, are highly regarded for their accuracy in vibrational analysis, especially when anharmonic corrections are taken into account35,68 However, given DHDF’s increased cost of computational time, roughly on par with MP2 method, we decided to follow a hybrid approach for vibrational analysis, with harmonic part being calculated on higher level and anharmonic part on lower level of theory. For monomeric species, we employed CCSD(T)/aug-cc-pVDZ and B3LYP/ SNSD methods. The calculation of dimeric species involved B3LYP on harmonic level, and anharmonic part on B2PLYP level of theory; both with SNSD basis set. This approach proved to be reliable in the past and offers a substantial increase 6171


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Figure 1. Experimental NIR spectra of acetic acid in very low concentration range (0.001, 0.0005, and 0.0001 M) compared with the calculated (CCSD(T)/aug-cc-pVDZ and B3LYP/SNSD) NIR spectra of acetic acid monomer.

in the accuracy of the calculation without significant increase of the total computational time.69 Additionally, Grimme’s empirical dispersion correction GD370 was applied for DFT method. It has been also reported that the dispersion correction for DFT methods brings improved accuracy for description of hydrogen bonded systems of medium size.71−73 For DFT calculations we applied recently introduced SNSD double-ζ basis set, which allows for a good level of accuracy in vibrational analysis at moderate computational cost.74 For energy calculation on MP2 level of theory, Dunning’s aug-cc-pVTZ basis set was used. In this case, the counterpoise correction (CP) for basis set superposition error (BSSE) was employed as well. All calculations using MP2 and B2PLYP methods employed frozen core approach; in this approach the correlation of inner-shell electrons is excluded from the correlation calculation. The anharmonic wavenumbers and intensities of vibrational modes were obtained by applying generalized second-order vibrational perturbation theory (GVPT2).31 In the anharmonic part, tight convergence criteria and superfine integration grid were defined, to minimize the inaccuracies in determination of quartic and quadratic force constants. It is recommended, since quartic and quadratic force constants are obtained by numerical differentiation of Hessian, thus being more sensitive to “numerical noise” than cubic force constants, which are calculated analytically. For the detailed analysis of vibrational motion and band assignment procedure, normal coordinate analysis (NCA) and potential energy distribution (PED) calculations were carried out in VEDA software;75 natural coordinates were constructed in accordance with Pulay et al.76 The predicted wavenumbers and intensities of the vibrational modes in the near-infrared region were used to draw the theoretical spectra. In the process of NIR spectra simulation, the Cauchy−Gauss product function, eq 1, was applied as the band shape for simulated bands

A (ν ) =

a1 2

1 + a 2 (ν − a3)2

× exp( −a4 2(ν − a3)2 )

(1)

The a1 and a3 parameters in eq 1 are respectively band intensity and wavenumber, obtained in the quantum calculation. The remaining shape parameters in this work were assumed as follows: a2 = 0.055; a4 = 0.013. These values were chosen for the best agreement with experimental lineshapes. The broadened bands that were the subject of the band fitting procedure had these parameters set in an iterative optimization procedure.

3. EXPERIMENTAL SECTION Acetic acid, CH3COOH (Wako, min. 99.5%), deuterated acetic acid-d1, CH3COOD (Tokyo Chemical Industry, min. 98%) and trifluoroacetic acid, CF3COOH (Sigma-Aldrich, min. 98%) were purchased with the highest purity available from commercial suppliers. The chemicals were stored over molecular sieves and under nitrogen. The spectra of the studied systems were measured in a broad NIR region (10 000−3700 cm−1) on a PerkinElmer Spectrum One NTS FT-NIR/IR spectrometer in transmittance mode. The spectra were recorded for solution phase, in a broad concentration range (from 10−4 M to 1.0 M); the solvent used was carbon tetrachloride (Wako, super dehydrated min. 99%). The spectral resolution was 1 cm−1 and the number of scans accumulated for each spectrum was 256. Quartz cells with the thickness range of 4−100 mm were used, depending on the concentration chosen to obtain the best quantitative transmittance data. Each spectrum was measured at least three times to exclude a possibility of random drift. All spectra were acquired at controlled temperature of 298 K. The experimental spectra were subject of spectral pretreatment when necessary; the Savitzky−Golay smoothing algorithm based on 25 points was applied for the spectra of low concentration solutions (10−4− 6172


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Figure 2. Proposed band assignments in the NIR spectrum of a diluted solution (10−4 M) of acetic acid in CCl4. Modes (in order of decreasing wavenumbers): δipOH + νas′CH3; δoopOH + νOH; δipOH + νsCH3; δCOC + νOH; δoopOH + νOH; δrockCH3 + δasCH3; δrock′CH3 + νsCH3; δCCO + νOH; δrockCH3 + νsCH3.

10−3 M). For better clarity of the presented figures, baseline correction and intensity axis scale normalization were applied, when necessary.

(10−4 M) the agreement between the experimental spectrum and either of the calculated spectra presented is good. Basing on obtained results, successful band identification could be performed (Figure 2). With increasing the sample concentration, however, spectral changes due to concentration effect occur for as low concentration as 5 × 10−4 M (Figure 1). Relative intensity of the free ν02OH band, clearly visible for 5 × 10−4 M and 10−3 M concentrations, indicates that a considerable amount of monomeric species exists under these conditions. Therefore, the experimental NIR spectra of acetic acid (Figure 1) provide the evidence that over a wide range of concentration monomeric species (free OH stretching band) coexist with dimeric species (baseline increase). This observation will be discussed in detail in section 4.2. A short overview of the accuracy level of different quantum methods and basis sets in reproducing the experimental wavenumbers of acetic acid monomer will be provided here. We would like to discuss the advantages of hybrid approach, in which the harmonic and anharmonic calculation is being done on different levels of theory; the impact of basis set and the performance of fairly new SNS basis sets and the influence of CPCM solvent model. For the comparison purposes we focused on selected, nonoverlapping and well-defined bands observed in the experimental NIR spectrum of acetic acid monomer in CCl4 solution. As presented in Table 1, inclusion of conductor-like polarizable continuum model (PCM) of CCl4 leads to improvement of accuracy. The improvement is more pronounced for advanced methods. The fairly elementary B3LYP/6-31G(d,p) combination gives, as expected, the less accurate results, with RMSD of 54 cm−1, and does not benefit from CPCM model at all. We added B3LYP/6-31G(d,p) results only because a large number of spectroscopic studies took advantage of this method in the past. Going from the 6-

4. RESULTS AND DISCUSSION The vibrational properties of acetic acid and its deuterated derivatives, both as monomers and as self-associated species, have been studied extensively and are well-known for the fundamental region. Here, we will focus on the prediction of NIR spectra of these systems and on the correlation between their vibrational properties and spectral features observed in the NIR region. Depending on the solvent and concentration level, NIR spectra of carboxylic acids show a broad band below 6800 cm−1. Acetic acid yields a very prominent spectral feature in the NIR spectrum. The broad spectral features originate from associated species; in case of nonpolar solvent, cyclic dimer of acetic acid is stabilized and therefore exists with significant abundance throughout wide range of concentrations.60 However, under these conditions the spectral data consist of bands originating from monomeric species as well. 4.1. Experimental and Calculated NIR Spectra of the Acetic Acid Monomer. For CCl4 solutions, acetic acid monomer has a major contribution to the NIR spectrum only when the concentration is very low. Figure 1 shows a comparison of experimental NIR spectra of acetic acid in a concentration range 10−4−10−3 M and two kinds of calculated spectra of an acetic acid monomer by the B3LYP/SNSD method and hybrid approach (CCSD(T)/aug-cc-pVDZ method for harmonic calculation and B3LYP/SNSD for anharmonic calculation). Note that, in our computational study, we focused on the trans-conformer of acetic acid monomer. It is well-known that the cis-conformer is much less stable,77 and at room temperature and in a solution phase it is very unlikely to observe bands originating from the cis form. It can be seen from Figure 1, that for the lowest concentration 6173


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6909 6452 5810 5286 4859 4692 4434 6955 6518 5848 5364 4932 4716 4456 54

All values in cm−1. a

CCSD(T)/aVDZ + B3LYP/SNSD

6869 6452 5816 5286 4877 4679 4433 17 6913 6526 5866 5313 4926 4706 4465 46

B2PLYP/aVTZ + B3LYP/SNST B3LYP/SNST

6910 6479 5816 5293 4909 4687 4441 22 6956 6518 5848 5365 4932 4716 4456 54

B3LYP/6-31G(d,p) B2PLYP/aVTZ + B3LYP/SNST B3LYP/6-31G(d,p) mode

ν02OH νsCH3 + νOH νsCH3 + νas′CH3 νCO + νOH δsCH3 + νOH νC−O + νOH δasCH3 + νOH RMSD

B3LYP/SNST

6973 6517 5848 5345 4943 4721 4474 57

CPCM/CCl4 solvation model no solvation model

Table 1. Accuracy of Selected Methods in Reproducing Experimental Wavenumbers in the Case of Acetic Acid Monomera

31G(d,p) basis set to the triple-ζ SNST basis set improves the RMSD by 28 and 32 cm−1 for the standard approach and the one with added CPCM calculation, respectively. The hybrid approach, in which the harmonic part was calculated on B2PLYP/aug-cc-pVTZ level, and anharmonic correction on B3LYP/SNST level, is less accurate, with RMSD of 57 and 46 cm−1. This is likely due to not very accurate results with the use of B2PLYP double-hybrid functional coupled with correlationconsistent basis set, as it was presented before for VPT2 studies on NIR spectra of aliphatic alcohols.78 The best results were achieved with hybrid approach, in which the harmonic part was treated with CCSD(T)/aVDZ method, and anharmonic correction calculated on B3LYP/SNSD level; resulting RMSD equals to 17 cm−1. The coupled-cluster singles and doubles with iterative triples method, even paired with fairly elementary correlation-consistent augmented double-ζ basis set, seems to give much better harmonic frequencies than B2PLYP/aVTZ method. In this case we do not expect to improve the result much with changing the double-ζ SNSD basis set to triple-ζ SNST basis set. The quality of results obtained here is enough to fully explain the observed experimental spectrum. However, use of CCSD(T) with more advanced basis set, arguably tripleor quadruple-ζ (for harmonic part) and B3LYP/SNST (for anharmonic part), would likely bring the RMSD even further down. 4.2. Experimental and Calculated Spectra of Acetic Acid Solution in the Self-Association Concentration Range. 4.2.1. Calculated Spectrum of Acetic Acid Dimer. It is known, that, unlike in the neat liquid phase where associates of acetic acid include linear chains and higher polymer species,79,80 in aprotic, nonpolar solvents a well-defined cyclic dimer is formed.81 This stabilization effect of cyclic dimer by CCl4, in a wide concentration range, can be confirmed by the analysis of NIR spectrum. For very low concentration level of acetic acid, monomeric species has dominant concentration (section 4.1). However, as soon as the concentration level increases over ca. 10−3 M, the NIR spectrum reveals clear evidence of cyclic dimer primary existence (Figure 1). With a further increase of concentration no rapid change in spectra occurs though; the observed changes are gradual. Between medium and high concentrations, 0.1 and 1 M, overall only small differences can be noticed (Figure 5). The NIR spectra of acetic acid solutions in the concentration range of higher than 10−4 M contain mostly contribution from its associated species, as the very broad band at around 5000 cm−1 can be clearly seen for the higher concentrations. Overall, the spectra of solutions of medium and high concentrations exhibit very similar shape, including the very similar broad band (at 5000 cm−1). These features do not depend much on the concentration, even when comparing significantly different concentrations; 0.01 and 1 M (Figure 1 and Figure 5). This can be explained by the fact that cyclic dimer of acetic acid dominates in CCl4 solutions over a wide range of concentrations. This stabilization effect caused by nonpolar solvents is well-known in the literature.60 Exceptional stability of cyclic species in the liquid phase as well has been reported by Czarnecki in his two-dimensional correlation spectroscopy (2DCOS) studies in NIR region of octanoic acid.82 However, the concentration of monomeric species still decreases with increasing the concentration of acetic acid, as can be noticed by the decreasing intensity of the free OH stretching overtone band at 6909 cm−1 (Figure 1 and Figure 5). The decrease in the intensity of the free OH stretching overtone band is gradual with the increasing concentration.

6914 6482 5817 5321 4910 4699 4435 26

exp.


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Figure 3. Calculated NIR spectra of acetic acid. Spectrum of (A) monomer (CCSD(T)/aVDZ + B3LYP/SNSD) and (B) cyclic dimer (B2PLYP/ SNSD + B3LYP/SNSD).

Figure 4. Stretching and in-plane bending modes of the double hydrogen-bond bridge observed in acetic acid cyclic dimer: (A) symmetric (inphase) stretching; (B) antisymmetric (out-of-phase) stretching; (C) in plane bending.

with the medium to high concentration range, is significantly higher than the intensity of the free OH stretching band originating from the monomer. Such assumption is indeed very well reflected by quantum chemical calculation. The comparison of simulated NIR spectra of acetic acid monomer and dimer, C2h symmetry, (Figure 3) shows clearly that the intensity of the stretching overtone band of free OH group in the spectrum of monomer is much lower than the calculated intensity of the combination band of asymmetric and symmetric stretching modes of hydrogen bonded bridge of cyclic dimer (Figure 3). The high intensity of the combination modes involving both stretching modes of hydrogen bonded bridge in the cyclic dimer indicates that a very strong

However, evidence of monomeric species is still present in the spectrum of 1 M solution (Figure 5). At the same time, the increase in the baseline, caused by the increasing intensity and possibly FWHM (full width at half-maximum) parameter of the broad band at around 5000 cm−1, is significant (Figure 5). Therefore, the experimental data suggest that the spectral changes caused by the change of the concentration of acetic acid are not symmetric in such sense that the increase in the concentration of cyclic dimer influences spectral envelope much stronger than similar decrease in the concentration of monomer of acetic acid. The change of intensity of the broad band originating from the associated species and influencing the shape of the NIR spectrum of acetic acid in the CCl4 solutions 6175


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Figure 5. Experimental NIR spectra of acetic acid in CCl4 solutions with medium (0.1 M) and high (1.0 M) concentrations; and the difference spectrum (0.1−1 M), with the absorbance axis normalized.

Figure 6. Experimental NIR spectra of acetic acid (A, blue line), acetic acid-d1 (B, red line), and trifluoroacetic acid (C, green line) in CCl4 solution, 1.0 M concentration.

physicochemical and spectroscopic properties of carboxylic acids are similar, over a wide range of compounds from acetic acid to octanoic acid. The formation of acetic acid cyclic dimer has been studied in an IR region previously. The spectral changes induced by forming a cyclic dimer have been investigated in detail; for example experimentally by Maréchal83 and theoretically by Lewandowski et al.,54 by Emmeluth et al.,84 and by Dreyer.85 In these studies an analogous increase in the intensity of bands at experimental wavenumber of 3583/2965 cm−1 (for monomer/ dimer respectively), arising due to OH-stretching modes have been noted, upon the formation of cyclic dimer. Experimental data gathered for bands of acetic acid monomer and dimer in IR region indicates a factor of increase of over 20.83 No attempt

anharmonic coupling exists between these two fundamental modes. This very intense combination band appearing in the calculated NIR spectrum of cyclic dimer at 4899 cm−1, is very difficult to be observed directly in the experimental spectrum because of the significant broadening; its high intensity coupled with very high FWHM is the cause of the significant increase in the baseline, clearly observed in the experimental spectrum. The details on the experimental band originating from cyclic dimer in the octanoic acid could be successfully uncovered by two-dimensional correlations spectroscopy, as reported by Czarnecki.82 A very broad feature in the region of 5700 to 4700 cm−1, corresponding to the cyclic dimer, was reported there; the results of the discussed study82 are in good agreement with what we conclude here. This let us to expect that the 6176


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Figure 7. Experimental NIR spectrum of acetic acid solution of medium concentration (0.1 M) and predicted spectra modeled as a linear combination of the calculated spectra of monomer and cyclic dimer. Weight coefficients: (1) 0.5 and 0.5 (dashed line); (2) 0.1 and 0.9 (solid line); for monomer and dimer, respectively.

significant increase in the baseline of the NIR spectrum of acetic acid (Figure 4). However, in the case of experimental spectrum, these two bands are heavily red-shifted and broadened. Therefore, the raw calculated spectrum (Figure 7) needs to be adjusted for these effects to achieve even better agreement with the experimental data. It is noteworthy, that while the increase of the baseline is clear and very significant in NIR spectra of acetic acid and trifluoroacetic acid, it is missing in the NIR spectrum of acetic acid-d1, as expected (Figure 6). It is noteworthy that the calculation predicts very low intensity of the stretching overtone modes of hydrogen bonded bridge in the acetic acid dimer. This is expected, as the symmetry of the cyclic dimer induces inactivity of the overtones of overtones of both symmetric and asymmetric stretching modes of the hydrogen bonded bridge.86 However, combination bands involving these modes (of Ag and Au symmetries respectively) are both of Au symmetry, and are active modes. 4.2.2. Harmonic Shift Analysis. To explain the observed very high intensity of combination band of symmetric and antisymmetric stretching modes of the double hydrogen bonded bridge in acetic acid cyclic dimer, we performed a harmonic shift analysis.87 The calculations were performed on B3LYP/N07D level of theory. In a function of normal coordinate of symmetric stretching of the hydrogen bonded bridge (q40), we calculated the shift in harmonic frequencies of all the remaining modes, as presented in Figure 8A. The slope, or more precisely the curvature of the plotted functions can be interpreted as the strength of anharmonic couplings between mode ν40 and the remaining modes. It can be clearly seen, that the coupling between antisymmetric stretching mode (ν35) and the symmetric stretching mode (ν40) is the strongest one. It is by far the dominant for the most relevant low displacements from the equilibrium (Figure 8A). The only other examples of any meaningful coupling between mode ν40 and any other of the remaining 41 modes, are the low frequency intermolecular

for a similar investigation in an NIR region have yet been made though. It seems that the increase observed by us in the NIR region between OH stretching overtone in monomer, and the combination band of stretching modes of the hydrogen bonded bridge in cyclic dimer, is lower. However, for the NIR region, it is typical for the free OH stretching overtone band to have a particularly high intensity.1,2 When we assume coexistence of the monomer and cyclic dimer, a good agreement is possible between the experimental and calculated NIR spectrum of acetic acid, for medium concentration range (0.1−1.0 M). A spectrum modeled as a linear combination of calculated spectra of acetic acid: (1) monomer and (2) dimer resembles experimental NIR spectrum of medium concentration much better (Figure 7). The weight coefficients in those linear combinations were chosen arbitrarily; following the best agreement with experimental line shape. Different weight coefficients can be considered for monomer and dimer; Figure 7 presents two boundary values, 0.5/0.5 and 0.1/0.9, for monomer and dimer, respectively. Estimating by the intensity of major bands in the calculated spectrum of monomer and comparing these with experimental bands, we conclude that the abundance of monomer is low for this concentration range (0.1 M) and is probably close to 20%. It is noteworthy that the influence of monomeric species can be still seen in the case of solution with the higher concentration (1.0 M), as evidenced by the overtone band of the free OH group stretching mode (Figure 5). Therefore, for further discussions and analysis we choose the following weight coefficients: 0.2/0/8 for monomer and dimer, respectively. Note that the bands at 4991 cm−1 (combination mode of a symmetric stretching and antisymmetric stretching modes of double hydrogen bonded O−H···O bridge) and at 4282 cm−1 (combination mode of a symmetric stretching mode of double hydrogen bonded O−H···O bridge and in-plane deformation mode involving the same moieties) contribute mainly to the 6177


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modes, which obviously are affected by the change in the strength and geometry of the hydrogen bonded bridge upon displacement of coordinate q40. The experimentally observed very high intensity of the combination band ν35 + ν40 is well reflected by the very high change of dipole moment of symmetric stretching mode, as presented in Figure 8B (the zcomponent, which is parallel to the displacement) and the significant change in the intensity of antisymmetric stretching mode (ν35) upon displacement of coordinate q40 (Figure 8C). Therefore, harmonic shift analysis fully supports the results obtained in the VPT2 approach. Very strong anharmonic coupling leads to domination of ν35 + ν40 combination band of cyclic dimer in the experimental NIR spectrum of acetic acid. 4.2.3. Approximation of the Observed Broadening of Combination Bands by Band Fitting Procedure. The broadening effect of the two prominent combination bands, involving vibrational modes of the hydrogen bonded bridge of cyclic dimer, is also accompanied by significant redshift, and the resulting wavenumbers are lower than the calculated ones. The exact positions of these two peaks in the experimental spectrum are difficult to estimate. However, the position and shape parameters of these bands seem to be similar in a wide range of concentrations; experimental spectra between 1.0 and 0.1 M (Figure 5) and even, to a degree, 0.001 M (Figure 1) exhibit similar baseline shapes, heavily affected by the two discussed bands. The raw calculated NIR spectrum of acetic acid, obtained as a combined monomer−dimer spectrum (Figure 7), needs to be adjusted for the broadening effect to obtain a good agreement with the experimental spectrum. To achieve this and to elucidate the details of these broadened bands, we employed a band fitting algorithm, developed in MATLAB software, to achieve a better agreement between modeled and experimental spectra. The results of the fitting procedure (Cauchy−Gauss band shape function, least-squares minimization and Powell gradientless optimization algorithm) are presented in Figure 9 and in Table 2. In the fitting procedure, only parameters of the two discussed combination bands were optimized. Parameters of all other model bands were not changed. The experimental spectrum used in this case was of 0.1 M solution in CCl4. This concentration value was chosen, as it offers the most typical and representative spectral features; both lower and higher concentrations give similar spectra. Therefore, the conclusions drawn should be applicable to self-associated acetic acid in general. The incorporation of the broadening and wavenumber shift for the two combination bands allowed to achieve a much better agreement between the model and experimental spectra of 0.1 M acetic acid solution in CCl4 (Figure 9). The spectra in Figure 9 and in Table 2 also show a significant redshift for both discussed bands. It would be interesting to see if the observed very strong effects of hydrogen bonding, are comparably well reflected in the calculated spectral data. From the calculated data, the complexation energy for cyclic dimer is as high as 16.78 kcal/mol (MP2/aug-cc-pVTZ); DFT methods used in our study indicate higher values (19.05 kcal/mol from B3LYP/SNSD calculation). The difference in the raw calculated and fitted wavenumber, in case of the stronger band (combination of antisymmetric and symmetric stretching modes of the hydrogen bonded bridge) is almost 700 cm−1; for the other band we found a still significant value of 400 cm−1. At the same time the resolved FWHM parameters are over 2300 and 550 cm−1. These values should be considered as rough

Figure 8. Harmonic shift analysis for acetic acid dimer performed on B3LYP/N07D level of theory. (A) Frequency shift of vibrational modes of acetic acid dimer as a function of normal coordinate of mode 40 (symmetric stretching of double hydrogen bonded bridge). (B) Change of x-, y-, and z-components of the total dipole moment of acetic acid cyclic dimer as a function of normal coordinate of mode 40. (C) change of the intensity of mode 35 (antisymmetric stretching of double hydrogen bonded bridge) as a function of normal coordinate of mode 40. 6178


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Figure 9. Band fitting results for the two combination bands of vibrational modes of hydrogen bond bridge of acetic acid cyclic dimer: (1) combination band of symmetric and antisymmetric stretching modes of hydrogen bonded bridge; (2) combination band of antisymmetric stretching and in-plane bending modes of hydrogen bonded bridge. Experimental spectrum: 0.1 M solution in CCl4 (red line). Modeled spectrum: combined calculated monomer and dimer (Figure 7); 0.2 and 0.8 weight coefficients for monomer and dimer, respectively (blue line); band fitting results for Cauchy−Gauss model bands representing contributions of (1) combination band (green line) and (2) combination band (black line).

Figure 10. Band assignment in the experimental NIR spectrum of acetic acid in a CCl4 solution of medium concentration (0.1 M) (see Table 2). Numbers over bands correspond to row numbers in Table 3. (A) Experimental NIR spectrum of acetic acid (0.1 M/CCl4). (B) Calculated NIR spectrum. (C) Contribution of bands calculated for the cyclic dimer. (D) Contribution of bands calculated for the monomer. The spectra have been artificially separated on the absorbance axis for a better view of details.

Final band assignments in the NIR spectrum of acetic acid in CCl4 solution of medium concentration, where a significant amount of self-association occurs, are presented in Table 3 and Figure 10. As can be seen, the spectrum is mainly influenced by combination modes originating from cyclic dimer. As it was stated before, the most prominent bands involve the vibrational modes of the double hydrogen bonded bridge of the cyclic dimer. The bands due to monomeric species are rather less significant in this concentration range. However, these bands can be still noticed, with a clearly visible band originating from the overtone of free OH group stretching mode, at 6908 cm−1. Two less significant bands stemming from the monomeric species can be noticed at 5301 and 4743 cm−1. Figure 10 shows contributions of the NIR spectrum stemming from individual bands of the monomer and cyclic dimer of acetic acid. It is noteworthy that the extremely strong integral intensity of the two prominent combination bands, involving vibrational modes of the hydrogen bonded bridge of cyclic dimer, can be noticed in the NIR spectra of acetic acid following concentration change. With increasing concentration, starting from as low as 5 × 10−3 M, a noticeable increase in the baseline can be noticed (Figure 1). However, other bands originating from cyclic dimer are not so strongly pronounced, and the spectra still contain bands mainly due to the monomeric species of acetic acid. Therefore, the two combination bands of acetic acid cyclic dimer, which were investigated in detail in this work, can be considered a very sensitive probe for the self-association level of acetic acid, and possibly other carboxylic acids.

Table 2. Band Fitting Results for the Two Strong Combination Bands of the Double Hydrogen-Bonded Bridge of Acetic Acid Cyclic Dimer (0.1 M Solution in CCl4)a band parameter band assignment νsHB(bridge) + νasHB(bridge) νasHB(bridge) + δipHB(bridge) a

raw calculated

final (fitted)

difference

resolved FWHM

4991

4298

693

2387

4282

3881

401

555

All values in cm−1.

estimates, as the band fitting procedure is sensitive to a number of factors. However, the significance of broadening and shifting can be expected, since the strength of the hydrogen bonding in the cyclic dimer of acetic acid is considerable. The final modeled NIR spectrum of acetic acid solution in CCl4, in the concentration range involving significant amount of self-association (around 0.1 M and higher) shows a much better agreement with experimental spectrum (Figure 9 and Figure 10), than a raw calculated spectrum, even when both monomer and cyclic dimer are taken into account (Figure 7). The redshift of the discussed combination modes due to formation of double hydrogen bonded bridge in acetic acid dimer, is therefore underestimated in the quantum chemical calculated data. This could be also accounted for the increased anharmonicity of OH stretching modes in the acetic acid cyclic dimer, as described by Nibbering et al.88 The strong redshift of the spectrum of acetic acid in solution phase versus the gas phase has been reported earlier for IR region as well.85 However, the final accuracy of predicted NIR spectra of acetic acid, following our fitting procedure, should be noted as very good, and therefore we conclude that assumed approach and the resulting band assignments are reliable.

5. CONCLUSIONS AND SUMMARY In this work, vibrational analysis of acetic acid in nonassociated and self-associated forms was carried out by using NIR spectroscopy and anharmonic quantum chemical calculation. NIR spectra of the studied systems were investigated in CCl4 solutions over a wide concentration range (0.0001−1 M). The spectrum of nonassociated acetic acid, observed at ∼10−4 M concentration level, was accurately reproduced. It was achieved by employing hybrid approach, in which harmonic vibrational analysis was treated by CCSD(T)/aug-cc-pVDZ method, and 6179


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Table 3. Band Assignments in the NIR Spectrum of Acetic Acid in a CCl4 Solution with Medium to High Concentrationsa ν [cm−1]

major contributions

assignment

exp.

calc.

typeb

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

6908 ∼5996 5949 5808 ∼5690 ∼5658 5301 ∼4743 4691 4654 4433 ∼4376 4336 4275 4224 ∼4070 4035 3978 3888 3836

6869 ∼6000 5972 5907 5850 5658 5286 4797 4756 4672 4436 4416 4342 4272 4248 ∼4125 4099 4029 ∼3975 3841

m d d d d d m m d m/d d d d d d d d d d d

ν02OH νas′CH3 + νasCH3 νasCH3(1) + νasCH3(2) νas′CH3(1) + νas′CH3(2) νsCH3(1) + νsCH3(2) νasHB(bridge) + νasCH3 νCO + νOH δCHO + νOH νCO + νasCH3 (d)δCHO + νasCH3 δasCH3 + νasCH3 δas′CH3 + νas′CH3 νCO + νasHB(bridge) (νC−O,δipOH) + νas′CH3 (νC−O,δipOH) + νsCH3 νC−O + νsHB(bridge) δipOH + νasHB(bridge) δipOH + δsCH3 δrock′CH3 + νsCH3 δoopOH + νsHB(bridge)

νas′CH3 + νasCH3

νsHB(bridge) + νasCH3

(d)νCO + νsCH3 δasCH3 + νasCH3 δas′CH3 + νas′CH3 (νC−O,δipOH) + νasCH3 νC−O + νas′CH3 νC−O + νsCH3

δrockCH3 + νasCH3 δrock′CH3 + νsCH3

(m) δipOH + νOH

δrock′CH3 + νasCH3

δrockCH3 + νasCH3

a Only major bands are presented here. Calculated wavenumbers correspond to the final modeled spectral envelope (Figure 10). Vibrational analysis based on CCSD(T)/avDZ + B3LYP/SNSD methods (monomer) and B3LYP/SNSD method (cyclic dimer). bKey: m, monomer; d, cyclic dimer.

The two-dimensional correlation spectroscopy (2DCOS) analysis of octanoic acid82 shows the broad spectral feature, which was attributed to cyclic dimer. On the basis of our quantum chemical calculation for acetic acid, we can fully support this conclusion. Our results correspond well with the experimental data collected for far more complex carboxylic acid, like octanoic acid. This shows clearly, that the main factors determining the physical chemistry and spectroscopic properties remain similar between acetic acid and octanoic acid. Following conclusions stems from these observations. First, quantum chemical methods are currently capable of reproducing spectral complex patterns, which previously required powerful experimental techniques, like 2DCOS analysis, to provide explanation of observed spectral features. This makes theoretical studies a very promising emerging method for analysis and explanation of NIR spectra. Second, the physical chemistry of carboxylic acids, in particular their intermolecular interaction patterns, equilibria between monomeric and dimeric species, remain similar between acetic acid and octanoic acid. This allows to conclude, that the results obtained in our work are meaningful for a wider range of carboxylic acids and therefore can be substantial advance in our knowledge about carboxylic acids. In summary, by modeling vibrational spectra of acetic acid for the first time over a broad NIR region, it was possible to elucidate the influence of formation of acetic acid cyclic dimer on its NIR spectra. In particular, major factors influencing spectral changes in the NIR region of acetic acid due to formation of hydrogen bond were observed and discussed. It was also found that the main spectral feature observed in the NIR spectra of carboxylic acid upon the formation of hydrogen bond should be accounted for combination mode of the stretching vibrations of double hydrogen bonded bridge in dimers of acetic acids. A deep analysis of the experimental and calculated NIR spectra of acetic acids was presented with successful band assignments of numerous experimental bands,

the following anharmonic correction, based on generalized second-order vibrational perturbation theory (GVPT2) formalism, was calculated on B3LYP/SNSD level of theory. This hybrid approach, allowing to augment anharmonic study with harmonic foundation calculated on a higher level of theory, has been deemed fully useful for the needs of anharmonic vibrational analysis in the NIR region. A high level of agreement between theoretical and experimental spectra was achieved, and subsequent thorough explanation of NIR spectrum of acetic acid monomer was presented. Subsequently, the formation of hydrogen bonding in cyclic dimeric species was examined, and the differences in the NIR spectra of the studied system, caused by the formation of cyclic dimer, were explained on the basis of quantum chemical predicted NIR spectra. For the purpose of NIR vibrational analysis of cyclic dimer, hybrid approach was applied again, with the use of B2PLYP (for harmonic part) and B3LYP (for anharmonic part), both coupled with SNSD basis set. It was found that calculated wavenumbers of combination modes of the stretching and bending vibrations of the double hydrogen bonded bridge of cyclic dimer are underestimated. The strong coupling of the stretching modes of hydrogen-bonded bridge was examined in a harmonic shift analysis; the results fully supported the data obtained through VPT2 approach. Also, the bands originating from these modes are strongly red-shifted and broadened in the experimental NIR spectrum of acetic acid. Therefore, a band fitting algorithm was employed to elucidate a more reliable data on the position and shape parameters of these bands. It was found, that these bands have a very high integral intensity and heavily influence the experimental spectrum over wide range of concentrations. Following the obtained data, adjustments were made to the predicted spectrum, which resulted in a high level of agreement between theoretical and experimental NIR spectrum of self-associated acetic acid. 6180


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originating from monomeric and cyclic dimeric species. These observations and conclusions are in good agreement with the previous experimental reports. Moreover, spectral patterns of not only acetic acid but more complex carboxylic acids like octanoic acids could be explained as well. These results should form a basis for further studies of carboxylic acids in the NIR region. Additionally, the conclusions presented in this work show that the currently available quantum chemical approaches have achieved the level of accuracy and reliability which enable them for successful use as general methods of NIR vibrational analysis of at least simple molecules.

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AUTHOR INFORMATION

Corresponding Authors

*Telephone: +81-79-565-8349. E-mail: [email protected] (K.B.B.). *Telephone: +81-79-565-8349. E-mail: [email protected] (Y.O.). *Telephone: +48-12-663-2913. E-mail: [email protected]. pl (M.J.W.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge the RIKEN Advanced Center for Computing and Communication for access to their computational resourcesquantum chemical calculations were performed on the HOKUSAI GreatWave supercomputer.

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REFERENCES

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