Energetics of the OH radical H-abstraction reactions from simple aldehydes and their geminal diol forms.

CONTEXT: Carbonyl compounds, especially aldehydes, emitted to the atmosphere, may suffer hydration in aerosols or water droplets in clouds. At the same time, they can react with hydroxyl radicals which may add or abstract hydrogen atoms from these species. The interplay between hydration and hydrogen abstraction is studied using density functional and quantum composite theoretical methods, both in the gas phase and in simulated bulk water. The H-abstraction from the aldehydic and geminal diol forms of formaldehyde, acetaldehyde, glycolaldehyde, glyoxal, methylglyoxal, and acrolein is studied to determine whether the substituent has any noticeable effect in the preference for the abstraction of one form or another. It is found that abstraction of the H-atom adjacent to the carbonyl group gives a more stable radical than same abstraction from the geminal diol in the case of formaldehyde, acetaldehyde, and glycolaldehyde. The presence of a delocalizing group in the Cα (a carbonyl group in glyoxal and methylglyoxal, and a vinyl group in acrolein), reverts this trend, and now the abstraction of the H-atom from the geminal diol gives more stable radicals. A further study was conducted abstracting hydrogen atoms from the other different positions in the species considered, both in the aldehydic and geminal diol forms. Only in the case of glycolaldehyde, the radical formed by H-abstraction from the -CH2OH group is more stable than any of the other radical species. Abstraction of the hydrogen atom in one of the hydroxyl groups in the geminal diol is equivalent to the addition of the •OH radical to the aldehyde. It leads, in some cases, to decomposition into a smaller radical and a neutral molecule. In these cases, some interesting theoretical differences are observed between the results in gas phase and (simulated) bulk solvent, as well as with respect to the method of calculation chosen. METHODS: DFT (M06-2X, B2PLYP, PW6B95), CCSD(T), and composite (CBS-QB3, jun-ChS, SCVECV-f12) methods using Dunning basis sets and extrapolation to the CBS limit were used to study the energetics of closed shell aldehydes in their keto and geminal-diol forms, as well as the radical derived from them by hydrogen abstraction. Both gas phase and simulated bulk solvent calculations were performed, in the last case using the Polarizable Continuum Model.

A new chapter in the never ending story of cycloadditions: The puzzling case of SO2 and acetylene.

A comprehensive study of the different classes of cycloaddition reactions ([3+2], [2+2], and [2+1]) of SO2 to acetylene and ethylene has been performed using density functional theory (DFT) and composite wavefunction methods. The [3+2] cycloaddition reaction, that was previously explored in the context of the cycloaddition of thioformaldehyde S-methylide (TSM) to ethylene and acetylene, proceeds in a concerted way to the formation of stable heterocycles. In this paper, we extend our study to the [2+2] and [2+1] cycloadditions of SO2 to acetylene, which would produce 1,1-oxathiete-2-oxide and thiirene-1,1-dioxide, respectively. One of the main conclusions is that cyclic 1,1-oxathiete-2-oxide can open through a relatively easy breaking of the SO single bond and rearrange toward sulfinyl acetaldehyde (SA). The SA molecule can easily undergo several internal rearrangements, which eventually lead to sulfenic acid and sulfoxide derivatives of ethenone, 1,2,3-dioxathiole, and CO plus sulfinylmethane. The most probable path, however, produces 2-thioxoacetic acid, whose derivatives (or those of the corresponding acetate) are usually obtained by Willgerodt-Kindler-type sulfuration of acetates. This product can in turn decompose, leading to the final products CO2 and H2CS. Comparison of this decomposition path with that of 2-amino-2-thioxoacetic acid shows that the process occurs through different H-transfer processes.

Toward Spectroscopic Accuracy for the Structures of Large Molecules at DFT Cost: Refinement and Extension of the Nano-LEGO Approach.

The SE100 database collecting accurate equilibrium geometries of medium size molecules obtained by the semiexperimental (SE) approach has been extended to species containing Br and I atoms. This has allowed the determination of accurate linear regressions between DFT and SE values for all the main bonds and angles involving H, B, C, N, O, F, P, S, Cl, Br, and I atoms. An improved Nano-LEGO tool has been developed, which is based on suitable hybrid and double hybrid functionals and combines in a fully coherent way the templating molecule and linear regression approaches. A number of case studies show that the new Nano LEGO tool provides geometrical parameters on par with state-of-the-art composite wave function methods, but can be routinely applied to medium- to large-size molecules. The accuracy reached for structural parameters is mirrored on rotational constants that can be predicted with an average error within 0.2%.

Reliable Gas Phase Reaction Rates at Affordable Cost by Means of the Parameter-Free JunChS-F12 Model Chemistry.

A recently developed strategy for the computation at affordable cost of reliable barrier heights ruling reactions in the gas phase (junChS, [Barone, V.; J. Chem. Theory Comput. 2021, 17, 4913-4928]) has been extended to the employment of explicitly correlated (F12) methods. A thorough benchmark based on a wide range of prototypical reactions shows that the new model (referred to as junChS-F12), which employs cost-effective revDSD-PBEP86-D3(BJ) reference geometries, has an improved performance with respect to its conventional counterpart and outperforms the most well-known model chemistries without the need of any empirical parameter and at an affordable computational cost. Several benchmarks show that revDSD-PBEP86-D3(BJ) structures and force fields provide zero point energies and thermal contributions, which can be confidently used, together with junChS-F12 electronic energies, for obtaining accurate reaction rates in the framework of the master equation approach based on the ab initio transition-state theory.

Correcting the Experimental Enthalpies of Formation of Some Members of the Biologically Significant Sulfenic Acids Family.

Sulfenic acids are important intermediates in the oxidation of cysteine thiol groups in proteins by reactive oxygen species. The mechanism is influenced heavily by the presence of polar groups, other thiol groups, and solvent, all of which determines the need to compute precisely the energies involved in the process. Surprisingly, very scarce experimental information exists about a very basic property of sulfenic acids, the enthalpies of formation. In this Article, we use high level quantum chemical methods to derive the enthalpy of formation at 298.15 K of methane-, ethene-, ethyne-, and benzenesulfenic acids, the only ones for which some experimental information exists. The methods employed were tested against well-known experimental data of related species and extensive CCSD(T) calculations. Our best results consistently point out to a much lower enthalpy of formation of methanesulfenic acid, CH3SOH (ΔfH0(298.15K) = -35.1 ± 0.4 kcal mol-1), than the one reported in the NIST thermochemical data tables. The enthalpies of formation derived for ethynesulfenic acid, HC≡CSOH, +32.9 ± 1.0 kcal/mol, and benzenesulfenic acid, C6H5SOH, -2.6 ± 0.6 kcal mol-1, also differ markedly from the experimental values, while the enthalpy of formation of ethenesulfenic acid CH2CHSOH, not available experimentally, was calculated as -11.2 ± 0.7 kcal mol-1.

In Vitro and In Silico Vibrational-Rotational Spectroscopic Characterization of the Next-Generation Refrigerant HFO-1123.

Very short-lived substances have recently been proposed as replacements for hydrofluorocarbons (HFCs), in turn being used in place of ozone-depleting substances, in refrigerant applications. In this respect, hydro-fluoro-olefins (HFOs) are attracting particular interest because, due to their reduced global warming potential, they are supposed to be environmentally friendlier. Notwithstanding this feature, they represent a new class of compounds whose spectroscopic properties and reactivity need to be characterized to allow their atmospheric monitoring and to understand their environmental fate. In the present work, the structural, vibrational, and ro-vibrational properties of trifluorothene (HFO-1123, F2C = CHF) are studied by state-of-the-art quantum chemical calculations. The equilibrium molecular structure has an expected error within 2 mÅ and 0.2° for bond lengths and angles, respectively. This represents the first step toward the computation of highly accurate rotational constants for both the ground and first excited fundamental vibrational levels, which reproduce the available experimental data well within 0.1%. Centrifugal distortion parameters and vibrational-rotational coupling terms are computed as well and used to solve some conflicting experimental results. Simulation of the vibrational transition frequencies and intensities beyond the double harmonic approximation and up to three quanta of vibrational excitation provides insights into the couplings ruling the vibrational dynamics and guides the characterization of the gas-phase infrared spectrum experimentally recorded in the range of 200-5000 cm-1. The full characterization of the IR features is completed with the experimental determination of the absorption cross sections over the 400-5000 cm-1 region from which the radiative forcing and global warming potential of HFO-1123 are derived.

Dipolar 1,3-cycloaddition of thioformaldehyde S-methylide (CH2 SCH2 ) to ethylene and acetylene. A comparison with (valence) isoelectronic O3 , SO2 , CH2 OO and CH2 SO.

Methods rooted in the density functional theory and in the coupled cluster ansatz were employed to investigate the cycloaddition reactions to ethylene and acetylene of 1,3-dipolar species including ozone and the derivatives issued from replacement of the central oxygen atom by the valence-isoelectronic sulfur atom, and/or of one or both terminal oxygen atoms by the isoelectronic CH2 group. This gives rise to five different 1,3-dipolar compounds, namely ozone itself (O3 ), sulfur dioxide (SO2 ), the simplest Criegee intermediate (CH2 OO), sulfine (CH2 SO), and thioformaldehyde S-methylide (CH2 SCH2 , TSM). The experimental and accurate theoretical data available for some of those molecules were employed to assess the accuracy of two last-generation composite methods employing conventional or explicitly correlated post-Hartree-Fock contributions (jun-Cheap and SVECV-f12, respectively), which were then applied to investigate the reactivity of TSM. The energy barriers provided by both composite methods are very close (the average values for the two composite methods are 7.1 and 8.3 kcal mol-1 for the addition to ethylene and acetylene, respectively) and comparable to those ruling the corresponding additions of ozone (4.0 and 7.7 kcal mol-1 , respectively). These and other evidences strongly suggest that, at least in the case of cycloadditions, the reactivity of TSM is similar to that of O3 and very different from that of SO2 .

Gliding on Ice in Search of Accurate and Cost-Effective Computational Methods for Astrochemistry on Grains: The Puzzling Case of the HCN Isomerization.

The isomerization of hydrogen cyanide to hydrogen isocyanide on icy grain surfaces is investigated by an accurate composite method (jun-Cheap) rooted in the coupled cluster ansatz and by density functional approaches. After benchmarking density functional predictions of both geometries and reaction energies against jun-Cheap results for the relatively small model system HCN···(H2O)2, the best performing DFT methods are selected. A large cluster containing 20 water molecules is then employed within a QM/QM' approach to include a realistic environment mimicking the surface of icy grains. Our results indicate that four water molecules are directly involved in a proton relay mechanism, which strongly reduces the activation energy with respect to the direct hydrogen transfer occurring in the isolated molecule. Further extension of the size of the cluster up to 192 water molecules in the framework of a three-layer QM/QM'/MM model has a negligible effect on the energy barrier ruling the isomerization. Computation of reaction rates by the transition state theory indicates that on icy surfaces, the isomerization of HNC to HCN could occur quite easily even at low temperatures thanks to the reduced activation energy that can be effectively overcome by tunneling.

Accurate Quantum Chemical Spectroscopic Characterization of Glycolic Acid: A Route Toward its Astrophysical Detection.

The first step to shed light on the abiotic synthesis of biochemical building blocks, and their further evolution toward biological systems, is the detection of the relevant species in astronomical environments, including earthlike planets. To this end, the species of interest need to be accurately characterized from structural, energetic, and spectroscopic viewpoints. This task is particularly challenging when dealing with flexible systems, whose spectroscopic signature is ruled by the interplay of small- and large-amplitude motions (SAMs and LAMs, respectively) and is further tuned by the conformational equilibrium. In such instances, quantum chemical (QC) calculations represent an invaluable tool for assisting the interpretation of laboratory measurements or even observations. In the present work, the role of QC results is illustrated with reference to glycolic acid (CH2OHCOOH), a molecule involved in photosynthesis and plant respiration and a precursor of oxalate in humans, which has been detected in the Murchison meteorite but not yet in the interstellar medium or in planetary atmospheres. In particular, the equilibrium structure of the lowest-energy conformer is derived by employing the so-called semiexperimental approach. Then, accurate yet cost-effective QC calculations relying on composite post-Hartree-Fock schemes and hybrid coupled-cluster/density functional theory approaches are used to predict the structural and ro-vibrational spectroscopic properties of the different conformers within the framework of the second-order vibrational perturbation theory. A purposely tailored discrete variable representation anharmonic approach is used to treat the LAMs related to internal rotations. The computed spectroscopic data, particularly those in the infrared region, complement the available experimental investigations, thus enhancing the possibility of an astronomical detection of this molecule.

The Spectroscopic Characterization of Halogenated Pollutants through the Interplay between Theory and Experiment: Application to R1122.

In the last decade, halogenated ethenes have seen an increasing interest for different applications; in particular, in refrigeration, air-conditioning and heat pumping. At the same time, their adverse effects as atmospheric pollutants require environmental monitoring, especially by remote sensing spectroscopic techniques. For this purpose, an accurate characterization of the spectroscopic fingerprint-in particular, those of relevance for rotational-vibrational spectroscopy-of the target molecules is strongly needed. This work provides an integrated computational-theoretical investigation on R1122 (2-Chloro-1,1-difluoro-ethylene, ClHC=CF2), a compound widely employed as a key intermediate in different chemical processes. State-of-the-art quantum chemical calculations relying on CCSD(T)-based composite schemes and hybrid CCSD(T)/DFT approaches are used to obtain an accurate prediction of the structural, rotational and vibrational spectroscopic properties. In addition, the equilibrium geometry is obtained by exploiting the semi-experimental method. The theoretical predictions are used to guide the analysis of the experimentally recorded gas-phase infrared spectrum, which is assigned in the 400-6500 cm-1 region. Furthermore, absorption cross sections are accurately determined over the same spectral range. Finally, by using the obtained spectroscopic data, a first estimate of the global warming potential of R1122 vibrational spectra is obtained.

A Computational Journey across Nitroxide Radicals: From Structure to Spectroscopic Properties and Beyond.

Nitroxide radicals are characterized by a long-lived open-shell electronic ground state and are strongly sensitive to the chemical environment, thus representing ideal spin probes and spin labels for paramagnetic biomolecules and materials. However, the interpretation of spectroscopic parameters in structural and dynamic terms requires the aid of accurate quantum chemical computations. In this paper we validate a computational model rooted into double-hybrid functionals and second order vibrational perturbation theory. Then, we provide reference quantum chemical results for the structures, vibrational frequencies and other spectroscopic features of a large panel of nitroxides of current biological and/or technological interest.

Accurate Biomolecular Structures by the Nano-LEGO Approach: Pick the Bricks and Build Your Geometry.

The determination of accurate equilibrium molecular structures plays a fundamental role for understanding many physical-chemical properties of molecules, ranging from the precise evaluation of the electronic structure to the analysis of the role played by dynamical and environmental effects in tuning their overall behavior. For small semi-rigid systems in the gas phase, state-of-the-art quantum chemical computations rival the most sophisticated experimental (from, for example, high-resolution spectroscopy) results. For larger molecules, more effective computational approaches must be devised. To this end, we have further enlarged the compilation of available semi-experimental (SE) equilibrium structures, now covering the most important fragments containing H, B, C, N, O, F, P, S, and Cl atoms collected in the new SE100 database. Next, comparison with geometries optimized by methods rooted in the density functional theory showed that the already remarkable results delivered by PW6B95 and, especially, rev-DSDPBEP86 functionals can be further improved by a linear regression (LR) approach. Use of template fragments (taken from the SE100 library) together with LR estimates for the missing interfragment parameters paves the route toward accurate structures of large molecules, as witnessed by the very small deviations between computed and experimental rotational constants. The whole approach has been implemented in a user-friendly tool, termed nano-LEGO, and applied to a number of demanding case studies.

Development and Validation of a Parameter-Free Model Chemistry for the Computation of Reliable Reaction Rates.

A recently developed model chemistry (jun-Cheap) has been slightly modified and proposed as an effective, reliable, and parameter-free scheme for the computation of accurate reaction rates with special reference to astrochemical and atmospheric processes. Benchmarks with different sets of state-of-the-art energy barriers spanning a wide range of values show that, in the absence of strong multireference contributions, the proposed model outperforms the most well-known model chemistries, reaching a subchemical accuracy without any empirical parameter and with affordable computer times. Some test cases show that geometries, energy barriers, zero point energies, and thermal contributions computed at this level can be used in the framework of the master equation approach based on the ab initio transition-state theory for obtaining accurate reaction rates.

Looking for the Elusive Imine Tautomer of Creatinine: Different States of Aggregation Studied by Quantum Chemistry and Molecular Spectroscopy.

New spectroscopic experiments and state-of-the-art quantum-chemical computations of creatinine in different aggregation states unequivocally unveiled a significant tuning of tautomeric equilibrium by the environment: from the exclusive presence of the amine tautomer in the solid state and aqueous solution to a mixture of amine and imine tautomers in the gas phase. Quantum-chemical calculations predict the amine species as the most stable tautomer by about 30 kJ mol-1 in condensed phases. On the contrary, moving to the isolated forms, both Z and E imine isomers become more stable by about 7 kJ mol-1 . Since the imine isomers and one amine tautomer are separated by significant energy barriers, all of them should be present in the gas phase. This prediction has indeed been confirmed by high-resolution rotational spectroscopy, which provides the first experimental characterization of the elusive imine tautomer. The interpretation of the complicated hyperfine structure of the rotational spectrum, originated by three 14 N nuclei, makes it possible to use the spectral signatures as a sort of fingerprint for each individual tautomer in the complex sample.

A computational insight into the relationship between side chain IR line shapes and local environment in fibril-like structures.

Infrared spectroscopy is a widely used technique to characterize protein structures and protein mediated processes. While the amide I band provides information on proteins' secondary structure, amino acid side chains are used as infrared probes for the investigation of protein reactions and local properties. In this paper, we use a hybrid quantum mechanical/classical molecular dynamical approach based on the perturbed matrix method to compute the infrared band due to the C=O stretching mode of amide-containing side chains. We calculate, at first, the infrared band of zwitterionic glutamine in water and obtain results in very good agreement with the experimental data. Then, we compute the signal arising from glutamine side chains in a microcrystal of the yeast prion Sup35-derived peptide, GNNQQNY, with a fibrillar structure. The infrared bands obtained by selective isotopic labeling of the two glutamine residues, Q4 and Q5, of each peptide were experimentally used to investigate the local hydration in the fibrillar microcrystal. The experimental spectra of the two glutamine residues, which experience different hydration environments, feature different spectral signals that are well reproduced by the corresponding calculated spectra. In addition, the analysis of the simulated spectra clarifies the molecular origin of the experimentally observed spectroscopic differences that arise from the different local electric field experienced by the two glutamine residues, which is, in turn, determined by a different hydrogen bonding pattern.

Isomerization and Fragmentation Reactions on the [C2SH4] Potential Energy Surface: The Metastable Thione S-Methylide Isomer.

Thione S-methylide, parent species of the thiocarbonyl ylide family, is a 1,3-dipolar species on the [C2SH4] potential energy surface, not so much studied as its isomers, thiirane, vinyl thiol, and thioacetaldehyde. The conrotatory ring-closure reaction toward thiirane was studied in the 90s, but no complete analysis of the potential energy surface is available. In this paper, we report a computational study of the reaction scheme linking all species. We employed several computational methods (density functional theory, CCSD(T) composite schemes, and CASSCF/CASPT2 multireference procedures) to find the best description of thione S-methylide, its isomers, and transition states. The barrier from thiirane to thione S-methylide amounts to 52.2 kcal mol-1 (against 17.6 kcal mol-1 for the direct one), explaining why thiocarbonyl ylides cannot be prepared from thiiranes. Conversion of thiirane to vinyl thiol implies a large barrier, supporting why the reaction has been observed only at high temperatures. Fragmentations of thiirane to S(3P) or S(1D) and ethylene as well as decomposition to hydrogen sulfide plus acetylene were also explored. Triplet and singlet open-shell species were identified as intermediates in the fragmentations, with energies lower than the transition state between thiirane and vinyl thiol, explaining the preference of the latter at low temperatures.

Accuracy Meets Interpretability for Computational Spectroscopy by Means of Hybrid and Double-Hybrid Functionals.

Accuracy and interpretability are often seen as the devil and holy grail in computational spectroscopy and their reconciliation remains a primary research goal. In the last few decades, density functional theory has revolutionized the situation, paving the way to reliable yet effective models for medium size molecules, which could also be profitably used by non-specialists. In this contribution we will compare the results of some widely used hybrid and double hybrid functionals with the aim of defining the most suitable recipe for all the spectroscopic parameters of interest in rotational and vibrational spectroscopy, going beyond the rigid rotor/harmonic oscillator model. We will show that last-generation hybrid and double hybrid functionals in conjunction with partially augmented double- and triple-zeta basis sets can offer, in the framework of second order vibrational perturbation theory, a general, robust, and user-friendly tool with unprecedented accuracy for medium-size semi-rigid molecules.

The Role of State-of-the-Art Quantum-Chemical Calculations in Astrochemistry: Formation Route and Spectroscopy of Ethanimine as a Paradigmatic Case.

The gas-phase formation and spectroscopic characteristics of ethanimine have been re-investigated as a paradigmatic case illustrating the accuracy of state-of-the-art quantum-chemical (QC) methodologies in the field of astrochemistry. According to our computations, the reaction between the amidogen, NH, and ethyl, C2H5, radicals is very fast, close to the gas-kinetics limit. Although the main reaction channel under conditions typical of the interstellar medium leads to methanimine and the methyl radical, the predicted amount of the two E,Z stereoisomers of ethanimine is around 10%. State-of-the-art QC and kinetic models lead to a [E-CH3CHNH]/[Z-CH3CHNH] ratio of ca. 1.4, slightly higher than the previous computations, but still far from the value determined from astronomical observations (ca. 3). An accurate computational characterization of the molecular structure, energetics, and spectroscopic properties of the E and Z isomers of ethanimine combined with millimeter-wave measurements up to 300 GHz, allows for predicting the rotational spectrum of both isomers up to 500 GHz, thus opening the way toward new astronomical observations.

Reinvestigation of the Deceptively Simple Reaction of Toluene with OH and the Fate of the Benzyl Radical: The "Hidden" Routes to Cresols and Benzaldehyde.

In a previous work, we have investigated the initial steps of the reaction of toluene with the hydroxyl radical using several quantum chemical approaches including density functional and composite post-Hartree-Fock models. Comparison of H-abstraction from the methyl group and additions at different positions of the phenyl ring showed that the former reaction channel is favored at room temperature. This conclusion appears at first sight incompatible with the experimental observation of a lower abundance of the product obtained from abstraction (benzaldehyde) with respect to those originating from addition (cresols). Further reactions of the intermediate radicals with oxygen, water, and additional OH radicals are explored in this paper through theoretical calculations on more than 120 species on the corresponding potential energy surface. The study of the addition reactions, to obtain the cresols through hydroxy methylcyclodienyl intermediate radicals, showed that only in the case of o-cresol the reaction proceeds by addition of O2 to the ring, internal H-transfer, and hydroperoxyl abstraction and not through direct H-abstraction. For both p- and m-cresol, instead, the reaction occurs through a higher-energy direct H-abstraction, thus explaining in part the observed larger concentration of the ortho isomer in the final products. It was also found that the benzyl radical, formed by H-abstraction from the methyl group, is able to react further if additional OH is present. Two reaction paths leading to o-cresol, two leading to p-cresol, and one leading to m-cresol were determined. Moreover, in this situation, the benzyl radical is predicted to produce benzyl alcohol, as was found in some experiments. The commonly accepted route to benzaldehyde was found to be not the energetically favored one. Instead, a route leading to the benzoyl radical (and ultimately to benzoic acid) with the participation of one water molecule was clearly more favorable, both thermodynamically and kinetically.

Modeling amino-acid side chain infrared spectra: the case of carboxylic residues.

Infrared (IR) spectroscopy is commonly utilized for the investigation of protein structures and protein-mediated processes. While the amide I band provides information on protein secondary structures, amino acid side chains are used as IR probes for the investigation of protein reactions, such as proton pumping in rhodopsins. In this work, we calculate the IR spectra of the solvated aspartic acid, with both zwitterionic and protonated backbones, and of a capped form, i.e. mimicking the aspartic acid residue in proteins, by means of molecular dynamics (MD) simulations and the perturbed matrix method (PMM). This methodology has already proved its good modeling capabilities for the amide I mode and is here extended to the treatment of protein side chains. The computed side chain vibrational signal is in very good agreement with the experimental one, well reproducing both the peak frequency position and the bandwidth. In addition, the MD-PMM approach proposed here is able to reproduce the small frequency shift (5-10 cm-1) experimentally observed between the protonated and zwitterionic forms, showing that such a shift depends on the excitonic coupling between the modes localized on the side chain and on the backbone in the protonated form. The spectrum of the capped form, in which the amide I band is also calculated, agrees well with the corresponding experimental spectrum. The reliable calculation of the vibrational bands of carboxyl-containing side chains provides a useful tool for the interpretation of experimental spectra.