Identification and Characterization of the HCl–DMS Gas Phase

Article pubs.acs.org/JPCA

Identification and Characterization of the HCl−DMS Gas Phase Molecular Complex via Infrared Spectroscopy and Electronic Structure Calculations Nicolai Bork,†,‡ Lin Du,† and Henrik G. Kjaergaard*,† †

Department of Chemistry, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark Department of Physics, University of Helsinki, FI-00014 Helsinki, Finland

‡

S Supporting Information *

ABSTRACT: Models of atmospheric aerosol formation are dependent on accurate Gibbs free binding energies (ΔG°) of gaseous acids and bases, but for most acid−base pairs, only ab initio data are available. We report a combined experimental and theoretical study of the gaseous molecular complex of dimethylsulfide (DMS) and HCl. On the basis of infrared spectroscopy and anharmonic local mode calculations, we determine ΔG°295K to be between 6.2 and 11.1 kJ mol−1. We test the performance of MP2 and five often used DFT functionals with respect to this result. M06-2X performs the best, but also the MP2 prediction is within the experimental range. We find that coupled cluster corrections to the electronic energy improves ΔG° estimates if and only if triple excitations are included. These estimates may be further improved by applying vibrational scaling factors to account for anharmonicity. Hereby, all but the PW91 based predictions are within the experimental range.

■

INTRODUCTION Some of the most significant uncertainties in weather and climate forecasts are related to cloud formation. Cloud droplets are known to form around aerosol particles of which a large amount has a purely gaseous origin.1 Aerosol growth is governed by the rate of sticking collisions between two species, given as ⎛ 8RT ⎞0.5 Z(T ) = spA pB πd ⎜ ⎟ ⎝ πμ ⎠

advances, significant uncertainties remain associated with ab initio based predictions of ΔG°, inducing large uncertainties in the nucleation models. Here, we present a project to shed light on these uncertainties by direct observations of the cluster and monomer pressures at thermal equilibrium. Hereby, ΔG° is determined via the equilibrium constant Keq =

2

(1)

(2)

where ΔG° is the Gibbs free binding energy of the dissociating gaseous species and C is the frequency along the dissociation mode.3 Although several of the parameters in eqs 1 and 2 are somewhat uncertain, the exponential dependence on ΔG° makes this parameter decisively important. However, for most of the molecular clusters responsible for atmospheric aerosol formation, i.e., clusters containing H2SO4 and various amines,4,5 no experimental data exist. Instead, cluster growth models are heavily reliant upon ab initio based data.6 Despite recent © 2014 American Chemical Society

(3)

The most widely used measurement techniques for identifying atmospheric molecular clusters are based on mass spectrometry (MS). However, MS subjects a sample to a high vacuum before detection, inducing significant cluster decomposition.7 Furthermore, since MS can only detect charged clusters, neutral clusters are first ionized, also inducing cluster decomposition. These effects prevent accurate determination of the cluster to monomer ratio, and hence Keq and ΔG, via MS. To avoid this problem we use infrared spectroscopy (IR) in situ. Determining ΔG° via IR spectroscopy has been achieved for several hydrogen bond clusters. Mainly simple alcohols and CHCl3 have been used as hydrogen donor, mainly coordinating to amines, NH3, and SO2.8−15 Because of the rapid cluster growth, the equilibrium concentrations of the most stable bimolecular clusters, e.g., HCl−NH3, are below the detection limits of our current setups. Instead, among several candidates,

where s is the sticking probability, pA and pB are the partial pressure of species A and B, respectively, d is the collision diameter, R is the gas constant, T is the absolute temperature, and μ is the reduced mass.2 Evaporation of the A·B molecular complex is most often assumed to proceed without a transition state and is hence governed by the detailed balance condition ⎛ −ΔG° ⎞ ⎟ revap = pAB C exp⎜ ⎝ RT ⎠

⎛ −ΔG° ⎞ ⎟ = exp⎜ ⎝ RT ⎠ pA pB pAB

Received: November 25, 2013 Revised: January 30, 2014 Published: February 18, 2014 1384

dx.doi.org/10.1021/jp411567x | J. Phys. Chem. A 2014, 118, 1384−1389

The Journal of Physical Chemistry A

Article

All DFT and MP2 calculations were performed using the Gaussian 09 program (revision B.01) (http://www.gaussian. com), and all coupled cluster calculations were performed using the Molpro program (version 2010.1) (http://www.molpro. net). Further details and references on each ab initio method and each basis set, as well as details on the optimization criteria are given as Supporting Information. The partial pressure of the molecular complex is calculated, following a procedure used in several similar studies.8−15 The integrated absorption coefficient, ( , depends on the length of the cell, l, and the partial pressure of the species of interest, p, as

the complex between dimethylsulfide (DMS) and HCl was chosen. Both DMS and HCl are found in quite high concentrations, especially in remote marine regions,16 and although atmospheric particle formation based on these two species alone is unlikely, they constitute a suitable model system. HCl−DMS complexes have previously been isolated in solid Ar matrices,17,18 but have, to the best of our knowledge, not been observed in the gas phase. As mentioned above, current models of aerosol formation and growth are largely reliant upon ab initio data.6 To assess the errors in using ab initio data to calculate ΔG° and Keq, we further conduct extensive ab initio benchmarking. Opposed to other, purely theoretical benchmarkings, we benchmark against an experimental value whereby the known problems of contributions of the harmonic oscillator and rigid rotor models used to determine the thermal corrections to ΔG° may be assessed.

(=

̃ ν̃ ∫ A(ν)d

(5)

where A(ν̃) is the frequency dependent absorbance and c is speed of light in vacuum.25 Further, ( can be expressed by the oscillator strength, f,

■

EXPERIMENTAL METHODS DMS (≥99%) and DMS-d6 (99 atom % D) were purchased from Sigma-Aldrich and purified with the freeze−pump−thaw method on a vacuum line. HCl (99.8%) was purchased from Air Liquide and used without any further purification. The IR spectra, in the range 1000 to 6500 cm−1, were recorded at 1.0 cm−1 resolution with a Vertex 70 FTIR spectrometer (Bruker) fitted with a CaF2 beam splitter, a liquid nitrogen cooled MCT detector, and a globar MIR light source. Via a vacuum line with a base pressure of 10−3 Torr, the vapors of the chemicals were loaded into a 20 cm glass cell equipped with KBr windows. Small amounts of HBr (less than 2% of pHCl), produced by reaction between HCl and the KBr windows, was observed but did not interfere significantly with the measurements. The uncertainties of the vacuum line pressure gauges (Varian PCG750), used for determining both base and experimental pressures, were less than 1%. All the measurements were carried out at room temperature (ca. 295 K).

(=f

NAe 2 4mecε0

(6)

where NA, e, me, and ε0 denotes Avogadro’s constant, the elementary charge, the electron mass, and the vacuum permittivity, respectively.2 The oscillator strength is given as f = 4.702 × 10−7[cm D−2 ]ν01 ̃ |μ01 ⃗ |2

(7)

where ν̃01 denotes the transition wavenumber of the active mode and μ̅01 = ⟨1|μ̅|0⟩ is the transition dipole moment matrix element.2,25 This matrix element is determined using the anharmonic oscillator local mode model25−27 via the expansion 6

⟨1|μ ⃗ |0⟩ =

∑ n=1

1 ∂μ ⃗ n ⟨1|qn|0⟩ n! ∂ nq

(8)

where q is the internal vibrational displacement coordinate, in this case the H−Cl bond. The potential energy and dipole moment are then calculated at varying displacements of the hydrogen atom around the ground state minimum along the H−Cl bond, from +0.20 to −0.20 Å in steps of 0.05 Å, while all other coordinates are fixed (Table S1, Supporting Information). An eighth order polynomial is fitted to these data to determine the dipole moment derivatives, and the local mode parameters are determined from the second, third, and fourth order derivatives of the potential energy (Table S2, Supporting Information).15,27,28 This approach has been found to yield oscillator strengths within ca. 20% of the experimental values for a range of molecules, provided a good ab initio method is used.28−30 However, for the water dimer complex this method yielded an oscillator strength a factor of ca. 2 larger than the experimental value.31

■

COMPUTATIONAL METHODS Numerous computational studies of the thermodynamics of molecular clustering, relevant for atmospheric nucleation, have been published. On the basis of a selection of these, we have chosen to use the MP2, B3LYP, CAM-B3LYP, PW91, M06-2X, and wB97XD ab initio methods combined with the 6-311+ +G(3df,3pd) and aug-cc-pV(T+d)Z [AV(T+d)Z] basis sets.5,6,14,19−24 Despite their fundamental differences, these methods and basis sets are of comparable computational expense and accuracy and are all suitable for both geometry optimizations and frequency calculations on clusters containing several dozens of atoms. See Supporting Information for further descriptions and references. It is well-known that DFT and MP2 based electronic energies may be significantly improved at moderate computational effort by single-point coupled cluster calculations. For this, we use the coupled cluster methods CC2, CCSD, and CCSD(T) with the same basis set as the optimization and CCSD(T)-F12b with the VTZ-F12 basis set on all geometries optimized with the AV(T+d)Z basis set. The coupled cluster corrected Gibbs free energies are thus obtained as * ° − ΔE DFT + ΔECC ΔG° = ΔG DFT

c ln(10) pl

■

RESULTS AND DISCUSSION IR spectra of seven gas mixtures were recorded with pHCl at 50, 100, 200, and 400 Torr and pDMS at 50 and 100 Torr. Reference DMS and HCl spectra were subtracted from the spectra of the mixtures, yielding the spectra shown in Figure 1. Although the resolution was too coarse for complete subtraction of the sharp HCl lines, a broad feature ranging from 2100 to 2800 cm−1 was clearly visible. In the feature, two distinct peaks and one shoulder were readily identified at 2450, 2585, and ca. 2320 cm−1, respectively. This is in accordance with matrix isolation spectra by Maes and Graindourze,17 reporting a weak peak at 2580 cm−1 and a double peak between 2432 and 2463 cm−1. In

(4)

where ΔE denotes the electronic energy and * denotes that the nuclear structure is not optimized at that level of theory. 1385

dx.doi.org/10.1021/jp411567x | J. Phys. Chem. A 2014, 118, 1384−1389

The Journal of Physical Chemistry A

Article

Figure 3. Structure of the HCl−DMS complex optimized at the CCSD(T)/AV(Q+d)Z level. See also Table S3, Supporting Information. This structure is used for assigning the main peak at 2450 cm−1 to the red-shifted H−Cl vibration and for determining the corresponding oscillator strength. Sulfur is yellow, chlorine is green, carbon is gray, and hydrogen is white.

Figure 1. Infrared spectra of the red-shifted HCl stretch frequency in the HCl−DMS complex at varying HCl and DMS partial pressures, in Torr. The spectrum with DMS-d6 is also shown (dashed line).

and DME−HCl.33−35 For each basis sets, the red-shifted H−Cl vibrational frequency and corresponding oscillator strength were determined via the anharmonic local mode model, as outlined in the Computational Methods. These results are summarized in Table 1, identifying the middle peak at 2450

all gas mixtures, the relative intensities of these three peaks were constant. Thus, they must originate from one or more complexes of identical chemical composition. By plotting the integrated absorption between 2100 and 2850 cm−1 as function of pDMS × pHCl, a straight line passing through (0,0) was found, proving that the complex contained exactly one HCl and one DMS, see Figure 2a. As seen in Figure 1, shifting to fully

Table 1. Calculated Absorption Wavenumbers, ν̃, Redshifts, Δν̃, and Oscillator Strengths, f, of the H−Cl Stretch Mode in the HCl−DMS Complex and in Molecular HCl from the Anharmonic Local Mode Model, Using CCSD(T) and the Indicated Basis Set HCl−DMS

a

HCl

basis set

ν̃ (cm−1)

f (×10−4)

ν̃ (cm−1)

f (×10−6)

Δν̃ (cm−1)

AV(D+d)Z AV(T+d)Z AV(Q+d)Z exptl

2543 2441 2411 2450

2.10 2.50 2.41

2922 2897 2895 2886

3.64 5.38 7.15 5.37a

379 456 484 436

Data from Rothman et al.36̀

cm−1 as the red-shifted H−Cl frequency. Although the calculated oscillator strengths of the HCl−DMS complex vary only a little, their accuracy remains uncertain. Comparing calculated and experimental oscillator strengths of the water dimer show that the anharmonic local mode approach seems to overestimate the experimental oscillator strength of the OH stretching vibration involved in hydrogen bonding by a factor of 2.31 This outcome is mainly due to neglecting coupling to the remaining modes of the cluster. We use this factor of 2 to give a lower limit of the oscillator strength and thus obtain a range of 1.2 × 10−4 to 2.4 × 10−4. Vibrational coupling is seen regularly in molecular complexes,15,37 resulting in two additional shoulders or peaks around a major peak. Often, these are split by the same low frequency mode and is thus located at ν̃1 ± ν̃2 where ν̃1 and ν̃2 denotes the major mode and the low-frequency mode, respectively. Here, we find a peak and a shoulder at 2585 and ca. 2320 cm−1, suggesting the existence of a low frequency mode at ca. 135 cm−1, similar to the mode at 119 cm−1 reported for the HCl−DME complex.35 Because of experimental constraints, this interpretation could not be confirmed spectroscopically. However, at the B3LYP/AV(T+d)Z level of theory, an intermolecular S−Cl stretch mode at 131 cm−1 was found, in accordance with the above considerations (Table S4, Supporting Information). The peak at 2585 cm−1 is unusually strong compared to the shoulder at 2320 cm−1 and compared to other molecular complexes.15 However, it could neither be assigned to any overtone nor to any frequency combination.

Figure 2. (a) Integrated absorption (in cm−1) between 2100 and 2850 cm−1 of the spectra shown in Figure 1 as function of pHCl × pDMS. The near perfect fit to a straight line through (0,0) is shown. (b) Determined values of ΔG°295K (in kJ mol−1) as function of pHCl × pDMS. Uncertainties are mainly from the calculated oscillator strength and spectral assignment.

deuterated DMS, we did not observe any effect on this part of the spectrum, indicating that the methyl groups are not participating in the complex formation. To complement the experimental study, several configurations of the HCl−DMS complex were optimized, initially using B3LYP/AV(T+d)Z, but refined using CCSD(T) and the AV(D+d)Z, AV(T+d)Z, and AV(Q+d)Z basis sets. The lowest energy structure is shown in Figure 3, with XYZ coordinates given in Table S3, Supporting Information. This optimized structure is similar to an early Hartree−Fock based optimization32 as well as structures of DMS−CO, DMS−OH, 1386

dx.doi.org/10.1021/jp411567x | J. Phys. Chem. A 2014, 118, 1384−1389

The Journal of Physical Chemistry A

Article

See the Supporting Information for additional discussion. We thus assign the shoulder at ca. 2320 cm−1 and the second peak at 2585 cm−1 to the subtractive and additive combination peaks of 2450 ± 135 cm−1. To determine the integrated absorption coefficient, ( from eq 5, the spectra were deconvoluted using four Lorentzian functions (Figure S1 and Table S5, Supporting Information), of which one contributed to the fundamental H−Cl peak at 2450 cm−1, two contributed to the peak at 2585 cm−1, and one contributed to the shoulder at 2320 cm−1. There are no simple means of determining whether ( corresponds to the fundamental H−Cl peak only or to the entire absorption from 2100 to 2850 cm−1. Clearly, the former approach is a lower limit to the true integrated absorption, while the latter is an upper limit. In most similar studies, the combination peaks are much smaller than the fundamental peak in which case this question is a minor issue.15 Here, however, the former approach yields a value of ca. 1/3 of the latter, and this uncertainty cannot be neglected. We will use the average of these two extrema with an uncertainty of ±50%. Hereby, the uncertainty spans the same range as the two extrema. We can now evaluate the Gibbs free binding energy from each gas mixture, obtaining values between 8.9 and 9.4 kJ mol−1, see Figure 2b, using f = 2.4 × 10−4. This range of ΔG295K ° corresponds to a range of Keq from 0.0265 to 0.0217 atm−1. Taking the sample with largest pressures as example, i.e., p(HCl) = 400 Torr and p(DMS) = 100 Torr, this implies a concentration of the HCl−DMS complex of ca. 1.3 Torr. ° Excluding the sample with the lowest pressures, ΔG295K obtained from the remaining samples are in excellent accord, differing less than 0.2 kJ mol−1. However, because of the possible systematic errors from the calculated oscillator strength and integrated absorption coefficients, the uncertainties are rather large, ranging from 6.2 and 11.1 kJ mol−1. The oscillator strength uncertainty contributes with ca. 1.7 kJ mol−1 in the negative direction, whereas the uncertainty related to the choice of bands included in the integrated absorption coefficient contributes with ca. 1.0 and 1.8 kJ mol−1 in the negative and positive direction, respectively. Finally, we tested the performance of some of the most popular ab initio methods and basis sets used to calculate ΔG° for clusters relevant for atmospheric nucleation. These are described and justified in the Computational Methods section and in the Supporting Information. In general, the differences between the two basis sets under consideration, 6-311+ +G(3df,3pd) and AV(T+d)Z, were much less significant than the differences between the various methods. For brevity, the present discussion will focus on the AV(T+d)Z results, which are summarized in Figure 4. All results are tabulated in the Supporting Information (Tables S7 and S8 and Figure S3). Presented in the first column of data points in Figure 4, the ΔG°295K values calculated by DFT are seen to vary greatly, from 4.4 kJ mol−1 using PW91 to 13.8 kJ mol−1 using B3LYP and with the MP2 results at 6.4 kJ mol−1. The M06-2X result is only 0.6 kJ mol−1 from the experimental result. The MP2 result is just inside the lower experimental limit, and the wB97XD result is just outside the upper experimental limit. Presented in the second and third columns of data points in Figure 4, we find that CC2 and CCSD electronic corrections according to eq 4, in general, do not improve DFT or MP2 results. CC2 corrected results generally underpredict ΔG°295K, ° . while CCSD corrected results consistently overpredict ΔG295K Presented in the fourth column of data points in Figure 4, the

Figure 4. Ab initio based ΔG295K ° predictions, using the AV(T+d)Z ° is calculated using eq 4 with ΔE calculated by the basis set. ΔG295K method given on the x-axis and the thermal correction with the method given by the color code.

CCSD(T)-F12b electronic energies are consistently improving CCSD predictions by about 2−3 kJ mol−1, while CCSD(T), presented in the fifth column of data points in Figure 4, consistently improves CCSD(T)-F12b predictions by about 1 kJ mol−1. Hereby, the M06-2X, B3LYP and CAM-B3LYP based, and CCSD(T) corrected predictions are well within the experimental range. The decreasing energy differences from CCSD over CCSD(T)-F12b to CCSD(T) suggest that the CCSD(T) results are close to the limit of full configuration interaction (full CI). However, as apparent from the scatter of the CCSD(T) corrected results, the harmonic oscillator and rigid rotor approximations used by the DFT and MP2 methods induce errors in the thermal correction and zero-point vibrational energy (ZPVE) terms. Several approaches exist for accounting for anharmonicity, e.g., ab initio molecular dynamics38 and vibrational second order perturbation theory (VPT2).39 See e.g. Temelso and Shields40 for a recent review. These methods are readily applicable for small molecular clusters, but due to computational scaling, these are, in practice, unavailable for clusters of relevance for atmospheric nucleation. A much simpler approach is based on vibrational scaling factors, which have been developed for a range of systems and methods, including hydrogen bound water clusters.40−42 Temelso et al.42 found that scaling ZPVE by 0.976 and the vibrational frequencies by 0.868 and 0.844 when entering the vibrational enthalpy and entropy terms, respectively, yielded results consistent with fully anharmonic calculations at the MP2/AVTZ level of theory. For the HCl−DMS cluster, this approach reduces ΔZPVE by ca. 0.3 kJ mol−1 and increases vibrational entropy by ca. 6.0 J mol−1 K−1. In total, the Gibbs free binding energies are reduced by ca. 2.0 kJ mol−1 by this procedure in accordance with similar approaches for small water clusters.42,43 When added to the CCSD(T) corrected ΔG°295K predictions, this brings all but the PW91 based result within the experimental range.

■

CONCLUSIONS Motivated by improving the current estimates of atmospheric nucleation rates, we have studied the molecular complex of DMS and HCl. Using infrared spectroscopy, we have identified the 1:1 complex via its red-shifted H−Cl vibration. After 1387

dx.doi.org/10.1021/jp411567x | J. Phys. Chem. A 2014, 118, 1384−1389

The Journal of Physical Chemistry A

Article

(2) Atkins, P. W.; de Paula, J. Physical Chemistry; Oxford University Press: Oxford, U.K., 2006. (3) Vehkamäki, H. Classical Nucleation Theory in Multicomponent Systems; Springer: Berlin, Germany, 2006. (4) Kirkby, J.; Curtius, J.; Almeida, J.; Dunne, E.; Duplissy, J.; Ehrhart, S.; Franchin, A.; Gagné, S.; Ickes, L.; Kürten, A.; et al. Role of Sulphuric Acid, Ammonia and Galactic Cosmic Rays in Atmospheric Aerosol Nucleation. Nature 2011, 476, 429−435. (5) Kurtén, T.; Loukonen, V.; Vehkamäki, H.; Kulmala, M. Amines are Likely to Enhance Neutral and Ion-Induced Sulfuric Acid−Water Nucleation in the Atmosphere More Effectively Than Ammonia. Atmos. Chem. Phys. 2008, 8, 4095−4103. (6) Ortega, I.; Kupiainen, O.; Kurtén, T.; Olenius, T.; Wilkman, O.; McGrath, M.; Loukonen, V.; Vehkamäki, H. From Quantum Chemical Formation Free Energies to Evaporation Rates. Atmos. Chem. Phys 2012, 12, 225−235. (7) Jokinen, T.; Sipilä, M.; Junninen, H.; Ehn, M.; Lönn, G.; Hakala, J.; Petäjä, T.; Mauldin, R., III; Kulmala, M.; Worsnop, D. Atmospheric Sulphuric Acid and Neutral Cluster Measurements Using CI-APiTOF. Atmos. Chem. Phys 2012, 12, 4117−4125. (8) Chung, S.; Hippler, M. Infrared Spectroscopy of HydrogenBonded CHCl3−SO2 in the Gas Phase. J. Chem. Phys. 2006, 124, 214316. (9) Hippler, M. Quantum Chemical Study and Infrared Spectroscopy of Hydrogen-Bonded CHCl3−NH3 in the Gas Phase. J. Chem. Phys. 2007, 127, 084306. (10) Hippler, M.; Hesse, S.; Suhm, M. A. Quantum-Chemical Study and FTIR Jet Spectroscopy of CHCl3−NH3 Association in the Gas Phase. Phys. Chem. Chem. Phys. 2010, 12, 13555−13565. (11) Howard, D. L.; Kjaergaard, H. G. Vapor Phase near Infrared Spectroscopy of the Hydrogen Bonded Methanol-Trimethylamine Complex. J. Phys. Chem. A 2006, 110, 9597−9601. (12) Howard, D. L.; Kjaergaard, H. G. Hydrogen Bonding to Divalent Sulfur. Phys. Chem. Chem. Phys. 2008, 10, 4113−4118. (13) Du, L.; Kjaergaard, H. G. Fourier Transform Infrared Spectroscopy and Theoretical Study of Dimethylamine Dimer in the Gas Phase. J. Phys. Chem. A 2011, 115, 12097−12104. (14) Du, L.; Lane, J. R.; Kjaergaard, H. G. Identification of the Dimethylamine−Trimethylamine Complex in the Gas Phase. J. Chem. Phys. 2012, 136, 184305. (15) Du, L.; Mackeprang, K.; Kjaergaard, H. G. Fundamental and Overtone Vibrational Spectroscopy, Enthalpy of Hydrogen Bond Formation and Equilibrium Constant Determination of the Methanol−Dimethylamine Complex. Phys. Chem. Chem. Phys. 2013, 15, 10194−10206. (16) Seinfeld, J. H.; Pandis, S. N. From Air Pollution to Climate Change. Atmospheric Chemistry and Physics; John Wiley & Sons: New York, 1998; p1326. (17) Maes, G.; Graindourze, M. Matrix Isolation Vibrational Spectra of Alkyl Chalcogenides Complexed with HCl: Structure of Alkyl Sulfide and Alkyl Selenide Complexes with Hydrochloric Acid in Ar Matrices from Infrared Spectra. J. Mol. Spectrosc. 1985, 113, 410−425. (18) Maes, G. Perturbation of the Internal Vibrations of (CH3)2S and (CH3)2Se in Matrix-Isolated Complexes with H2O and HCl: Indirect Evidence for the Trans Lone Pair Effect in (CH3)2X Molecules. J. Mol. Spectrosc. 1985, 114, 289−297. (19) Ianni, J. C.; Bandy, A. R. A Density Functional Theory Study of the Hydrates of NH3−H2SO4 and Its Implications for the Formation of New Atmospheric Particles. J. Phys. Chem. A 1999, 103, 2801−2811. (20) Herb, J.; Xu, Y.; Yu, F.; Nadykto, A. Large Hydrogen-Bonded Pre-Nucleation (HSO4−)(H2SO4)m(H2O)k and (HSO4−)(NH3)(H2SO4)m(H2O)k Clusters in the Earth’s Atmosphere. J. Phys. Chem. A 2012, 117, 133−152. (21) Bork, N.; Kurtén, T.; Enghoff, M. B.; Pedersen, J. O. P.; Mikkelsen, K. V.; Svensmark, H. Ab Initio Studies of O3−(H2O)n and O2−(H2O)n Anionic Molecular Clusters, n ≥ 12. Atmos. Chem. Phys. 2011, 11, 13947−13973. (22) Bork, N.; Kurtén, T.; Enghoff, M.; Pedersen, J. O. P.; Mikkelsen, K. V.; Svensmark, H. Structures and Reaction Rates of the Gaseous

calculating the corresponding oscillator strength, we determine the partial pressure of the molecular complex and calculate its Gibbs free binding energy at 295 K to between 6.2 and 11.1 kJ mol−1. Further, we have calculated ΔG°295K using MP2 and five of the most popular DFT functionals. The M06-2X prediction is closest to the experimental result, while most other predictions fall outside the experimental uncertainty. Correcting the electronic energies by CC2 or CCSD, in general, does not improve ΔG°295K predictions. Only when triple excitations are included in the coupled cluster scheme, either by CCSD(T)F12b or CCSD(T), are the results substantially improved. For systems relevant for atmospheric nucleation, applying simple, yet unphysical, scaling factors is a viable approach for addressing errors from the harmonic oscillator and rigid rotor approximations. Here, following the procedure of Temelso et al.42 reduced the Gibbs free binding energies by ca. 2.0 kJ mol−1. Utilizing both CCSD(T) electronic energy corrections and vibrational scaling factors, all but the PW91 based predictions are within the experimental range. As such, this approach illustrates a path for calculating the thermodynamics of hydrogen bound molecular complexes as accurate as the present experiments.

■

ASSOCIATED CONTENT

S Supporting Information *

Descriptions and references to all ab initio methods used in this study; potential energies and dipole moments used in the local mode model; Morse parameters for the local mode calculations; XYZ coordinates of the HCl−DMS molecular cluster optimized using CCSD(T)/AV(Q+d)Z; harmonic frequencies of HCl, DMS, and HCl−DMS calculated by B3LYP/AV(T+d)Z; a discussion of the possible combination peaks contributing to the spectra shown in Figure 1; representative deconvolutions of the spectra; tables of electronic and Gibbs free energies from all ab initio methods; a figure presenting data obtained using the 6-311++G(3df,3pd) basis set. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*(H.G.K.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We are grateful to Kasper Mackeprang for assistance in obtaining the oscillator strengths, Ville Loukonen for scientific discussions, and Daryl Howard for his ″Keq″ programme. Further, we acknowledge the Villum foundation and the Danish Council for Independent Research−Natural Sciences for funding and CSC-IT Center for Science Ltd. and the Danish Center for Scientific Computing for allocation of computational resources.

■

REFERENCES

(1) Kazil, J.; Stier, P.; Zhang, K.; Quaas, J.; Kinne, S.; O’Donnell, D.; Rast, S.; Esch, M.; Ferrachat, S.; Lohmann, U.; et al. Aerosol Nucleation and Its Role for Clouds and Earth’s Radiative Forcing in the Aerosol-Climate Model ECHAM5-HAM. Atmos. Chem. Phys 2010, 10, 10733−10752. 1388

dx.doi.org/10.1021/jp411567x | J. Phys. Chem. A 2014, 118, 1384−1389

The Journal of Physical Chemistry A

Article

Oxidation of SO2 by an O3−(H2O)0−5 Cluster: A Density Functional Theory Investigation. Atmos. Chem. Phys. 2012, 12, 3639−3652. (23) Elm, J.; Bilde, M.; Mikkelsen, K. V. Assessment of Density Functional Theory in Predicting Structures and Free Energies of Reaction of Atmospheric Prenucleation Clusters. J. Chem. Theory Comput. 2012, 8, 2071−2077. (24) Elm, J.; Bilde, M.; Mikkelsen, K. V. Influence of Nucleation Precursors on the Reaction Kinetics of Methanol with the OH Radical. J. Phys. Chem. A 2013, 117, 6695−6701. (25) Kjaergaard, H. G.; Yu, H.; Schattka, B. J.; Henry, B. R.; Tarr, A. W. Intensities in Local Mode Overtone Spectra: Propane. J. Chem. Phys. 1990, 93, 6239−6248. (26) Henry, B. R.; Kjaergaard, H. G. Local Modes. Can. J. Chem. 2002, 80, 1635−1642. (27) Howard, D. L.; Jørgensen, P.; Kjaergaard, H. G. Weak Intramolecular Interactions in Ethylene Glycol Identified by Vapor Phase OH-Stretching Overtone Spectroscopy. J. Am. Chem. Soc. 2005, 127, 17096−17103. (28) Lane, J. R.; Kjaergaard, H. G. XH-Stretching Overtone Transitions Calculated Using Explicitly Correlated Coupled Cluster Methods. J. Chem. Phys. 2010, 132, 174304. (29) Miller, B. J.; Du, L.; Steel, T. J.; Paul, A. J.; Södergren, A. H.; Lane, J. R.; Henry, B. R.; Kjaergaard, H. G. Absolute Intensities of NHStretching Transitions in Dimethylamine and Pyrrole. J. Phys. Chem. A 2012, 116, 290−296. (30) Lane, J. R.; Kjaergaard, H. G.; Plath, K. L.; Vaida, V. Overtone Spectroscopy of Sulfonic Acid Derivatives. J. Phys. Chem A 2007, 111, 5434−5440. (31) Kjaergaard, H. G.; Garden, A. L.; Chaban, G. M.; Gerber, R. B.; Matthews, D. A.; Stanton, J. F. Calculation of Vibrational Transition Frequencies and Intensities in Water Dimer: Comparison of Different Vibrational Approaches. J. Phys. Chem. A 2008, 112, 4324−4335. (32) Ohsaku, M. Molecular Structure and Vibrational Treatment of Dimethyl Sulphide and Ethyl Methyl Sulphide in Complexes with HCl: A Theoretical Study. J. Mol. Struct. 1989, 204, 57−66. (33) Sato, A.; Kawashima, Y.; Hirota, E. Fourier Transform Microwave Spectrum of the CO−Dimethyl Sulfide Complex. J. Mol. Spectrosc. 2010, 263, 135−141. (34) Jørgensen, S.; Kjaergaard, H. Effect of Hydration on the Hydrogen Abstraction Reaction by HO in DMS and Its Oxidation Products. J. Phys. Chem. A 2010, 114, 4857−4863. (35) Bertie, J. E.; Victor Falk, M. The Infrared Spectrum of the Hydrogen-Bonded Molecule Dimethyl Ether···Hydrogen Chloride in the Gas Phase. Can. J. Chem. 1973, 51, 1713−1720. (36) Rothman, L. S.; Gordon, I. E.; Barbe, A.; Benner, D. C.; Bernath, P. F.; Birk, M.; Boudon, V.; Brown, L. R.; Campargue, A.; Champion, J.-P.; et al. The HITRAN 2008 Molecular Spectroscopic Database. J. Quant. Spectrosc. Radiat. 2009, 110, 533−572. (37) Millen, D.; Zabicky, J. Hydrogen Bonding in Gaseous Mixtures. Part V. Infrared Spectra of Amine−Alcohol Systems. J. Chem. Soc. 1965, 3080−3085. (38) Thomas, M.; Brehm, M.; Fligg, R.; Vohringer, P.; Kirchner, B. Computing Vibrational Spectra from ab Initio Molecular Dynamics. Phys. Chem. Chem. Phys. 2013, 15, 6608−6622. (39) Bégué, D.; Baraille, I.; Garrain, P.; Dargelos, A.; Tassaing, T. Calculation of IR Frequencies and Intensities in Electrical and Mechanical Anharmonicity Approximations: Application to Small Water Clusters. J. Chem. Phys. 2010, 133, 034102. (40) Temelso, B.; Shields, G. C. The Role of Anharmonicity in Hydrogen-Bonded Systems: The Case of Water Clusters. J. Chem. Theory Comput. 2011, 7, 2804−2817. (41) Dunn, M. E.; Evans, T. M.; Kirschner, K. N.; Shields, G. C. Prediction of Accurate Anharmonic Experimental Vibrational Frequencies for Water Clusters, (H2O)n, n = 2−5. J. Phys. Chem A 2006, 110, 303−309. (42) Temelso, B.; Archer, K. A.; Shields, G. C. Benchmark Structures and Binding Energies of Small Water Clusters With Anharmonicity Corrections. J. Phys. Chem. A 2011, 115, 12034−12046.

(43) Kjaergaard, H. G.; Robinson, T. W.; Howard, D. L.; Daniel, J. S.; Headrick, J. E.; Vaida, V. Complexes of Importance to the Absorption of Solar Radiation. J. Phys. Chem. A 2003, 107, 10680−10686.

1389

dx.doi.org/10.1021/jp411567x | J. Phys. Chem. A 2014, 118, 1384−1389