Anchoring the Gas-Phase Acidity Scale from Hydrogen Sulfide to

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Anchoring the Gas-Phase Acidity Scale from Hydrogen Sulfide to Pyrrole. Experimental Bond Dissociation Energies of Nitromethane, Ethanethiol, and Cyclopentadiene Kent M. Ervin J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp510137g • Publication Date (Web): 29 Dec 2014 Downloaded from http://pubs.acs.org on January 2, 2015

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Anchoring the Gas-Phase Acidity Scale from Hydrogen Sulfide to Pyrrole. Experimental Bond Dissociation Energies of Nitromethane, Ethanethiol, and Cyclopentadiene

Journal:


Manuscript ID:

jp-2014-10137g.R1

Manuscript Type:

Special Issue Article

Date Submitted by the Author: Complete List of Authors:

19-Dec-2014 Ervin, Kent; University of Nevada, Reno, Department of Chemistry Nickel, Alex; University of Nevada, Reno, Chemistry Lanorio, Jerry; University of Nevada, Reno, Chemistry Ghale, Surja; University of Nevada, Reno, Chemistry

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[submitted to J. Phys. Chem. A, revised 12/18/2014] Anchoring the Gas-Phase Acidity Scale from Hydrogen Sulfide to Pyrrole. Experimental Bond Dissociation Energies of Nitromethane, Ethanethiol, and Cyclopentadiene Kent M. Ervin,* Alex A. Nickel, Jerry G. Lanorio, and Surja B. Ghale Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, 1664 N. Virginia St. MS 216, Reno, Nevada 89557-0216 Abstract: A meta-analysis of experimental information from a variety of sources is combined with statistical thermodynamics calculations to refine the gas-phase acidity scale from hydrogen sulfide to pyrrole. The absolute acidities of hydrogen sulfide, methanethiol, and pyrrole are evaluated from literature R–H bond energies and radical electron affinities to anchor the scale. Relative acidities from proton transfer equilibrium experiments are used in a local thermochemical network optimized by leastsquares analysis to obtain absolute acidities of 14 additional acids in the region. Thermal enthalpy and entropy corrections are applied using molecular parameters from density functional theory, with explicit calculation of hindered rotor energy levels for torsional modes. The analysis reduces the uncertainties of the absolute acidities of the 14 acids to within ±1.2 to ±3.3 kJ/mol, expressed as estimates of the 95% confidence level. The experimental gas phase acidities are compared with calculations, with generally good agreement. For nitromethane, ethanethiol, and cyclopentadiene, the refined acidities can be combined with electron affinities of the corresponding radicals from photoelectron spectroscopy to obtain improved values of the C–H or S–H bond dissociation energies, yielding D298(H–CH2NO2) = 423.5 ± 2.2 kJ mol−1, D298(C2H5S–H) = 364.7 ± 2.2 kJ mol−1, and D298(C5H5–H) = 347.4 ± 2.2 kJ mol−1. These values represent the best available experimental bond dissociation energies for these species. *Corresponding Author: Kent M. Ervin . E-mail: [email protected]. Telephone: 775-784-6041.

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INTRODUCTION The gas-phase negative ion thermochemical cycle, eq 1, D(R–H) = ∆acidH (R–H) + EA(R) – IE(H)

(1)

provides one of the most reliable ways of obtaining the R-H bond dissociation energy or enthalpy of molecules, D(R–H).1–3 The electron affinity of the radical, EA(R) corresponding to R− → R + e−, can be obtained by negative ion photoelectron spectroscopy,4,5 often to an accuracy of within 0.01 eV or 1 kJ/mol. The ionization energy of hydrogen atom, IE(H), is very precisely known, which leaves the gasphase acidity, ∆acidH (R–H) corresponding to RH → R− + H+, as limiting the precision of the dissociation energy. An extensive scale of relative gas-phase acidities has been established from mass spectrometric measurements of gas-phase proton transfer equilibria,6–10 bracketing experiments,11,12 and collisioninduced dissociation experiments using either the Cooks kinetic method13–15 or energy-resolved competitive threshold methods.16–20 Relative acidities from the proton transfer equilibrium experiments have been reported with uncertainties of typically ±0.8 kJ/mol (±0.2 kcal/mol), but the uncertainties of the absolute acidities are assigned as ±8 kJ/mol or larger because the relative acidities are anchored using eq 1 for a relatively few species for which the bond dissociation energy and electron affinity are known independently.21,22 For instance, the acidity of nitromethane in the NIST Chemistry Webbook database21 is tabulated as ∆acidH298(CH3NO2) = 1491 ± 9.2 kJ/mol and 1495 ± 12 kJ/mol based on two different equilibrium experiments.6,7 The electron affinity of the radical, EA(CH2NO2) = 2.475 ± 0.010 eV, is established from photoelectron spectroscopy by Metz et al.,23 who averaged the NIST acidity values to report D298(H– CH2NO2) = 420 ± 12 kJ/mol via eq 1. Nitromethyl radical (CH2NO2) is an intermediate of interest in combustion and atmospheric chemistry23 and therefore its thermochemistry is important in modeling the kinetics of those systems. However, there has apparently been no direct experimental measurement of the gas-phase CH bond dissociation energy of nitromethane. For kinetics modeling, the bond energies and 2 ACS Paragon Plus Environment

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corresponding radical enthalpies of formation need to be known to within “chemical accuracy” of 4 kJ/mol or better. As shown in this work, refining the gas-phase acidity scale can provide accurate bond energies with improved precision. We are also motivated to refine the acidities for use as additional reference acids in experimental determinations of acidities by threshold collision induced dissociation in our laboratory. This work aims to improve the acidity scale in the region from hydrogen sulfide (H2S) to pyrrole (C4H4NH). We first evaluate literature experimental determinations of the dissociation energies for hydrogen sulfide, pyrrole, and methanethiol (CH3SH) and the electron affinities of their radicals to reanchor the relative acidities in this region. To take advantage of all relevant experimental information, we employ a meta-analysis of various proton transfer equilibrium experiments.6–10 A local thermochemical network approach3,16,18,24 with least-squares optimization is used to obtain the absolute acidities and their uncertainties for 14 other gas-phase acids in this region of the scale. Of these, three species have accurately known radical electron affinities, allowing us to obtain improved bond dissociation energies for nitromethane, ethanethiol (C2H5SH), and cyclopentadiene (C5H6). COMPUTATIONAL METHODS Computational chemistry calculations using Gaussian 0925 are employed for comparison with experimental gas-phase acidities and for molecular parameters to obtain thermal enthalpy and entropy corrections. For molecular geometries and vibrational frequencies, we use density functional theory (DFT) at the B3LYP/6-311++G(2df, p) level,26 with calculated harmonic frequencies scaled by 0.9679 following the recommendation of Uvdal et al.27 For high-level calculation of gas-phase acidities for select species, we use coupled-cluster theory with single point energies at the CCSD(T)/aug-cc-pVQZ level using optimized geometries from CCSD/aug-cc-pVTZ calculations.28–30 The zero-point vibrational energy corrections are from the scaled B3LYP vibrational frequencies and torsional mode calculations described below. We also calculate gas-phase acidities using the W131,32 and Gaussian-433 composite methods.



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Equation (1) requires the energy or enthalpy of deprotonation at 0 K to combine with adiabatic electron affinities referenced to the zero-point energies. The Gibbs energy and enthalpy of deprotonation are related by eq 2, ∆acidGT(HA) = ∆acidHT(HA) + T ∆acidST(HA)

(2)

where ∆acidST(HA) is the entropy change for the deprotonation reaction HA → H+ + A− at the temperature of the equilibrium experiment. Because some of the acids have low-frequency torsional modes or change rotational symmetry upon deprotonation, calculation of accurate entropic and thermal corrections requires due care. Specifically, thermal enthalpy, HT − H0, and entropy, ST, corrections for the neutral acid (HA) and its conjugate base anion (A−) are needed to convert spectroscopic energies at 0 K to acidities at room temperature. Statistical mechanical calculation34 of these corrections requires the rotational constants and vibrational frequencies of both species and information about free or hindered internal rotations. We use the independent-oscillator approximation, neglecting coupling between vibrational modes. Thermodynamic functions are calculated using standard statistical mechanics formulas in the rigid-rotor harmonic-oscillator approximation with the high temperature limit for external rotations,34 except for lowfrequency torsional and inversion modes. While experimental spectroscopic frequencies and rotational constants are available for the smaller neutral acids, complete information for the anions is lacking. Calculated frequencies and rotational constants from density functional theory (DFT) are used here for both the neutral acid and the anion, taking advantage of potential cancellation of errors. Uncertainties in ∆HT−∆H0 and ∆GT−∆G0 are obtained by assuming systematic errors in frequencies and rotational constants of 5% and 2%, respectively, for each molecular species. Uvdal et al.27 found that more than 95% of scaled calculated frequencies are within 5% of the experimental fundamental frequencies in their data set. The resulting uncertainties in enthalpies and entropies are largest for molecules with lowfrequency vibrational modes, with partial cancelation of errors for GT − G0 = (HT−H0) – TST.


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Torsional modes with low barriers are treated separately as one-dimensional hindered internal rotors.35–38 The full torsional potential is obtained as a relaxed potential energy scan of the dihedral angle over 360º at the B3LYP/6-311++G(2df, p) level. That potential is fit by multiple regression to a Fourier series expression, V(θ) = V0 + ∑An·(1−cosnθ)/2 + ∑Bn·(sinnθ) with up to six n terms, which can account for all symmetric and asymmetric internal rotors. The Schrödinger equation is solved for the analytical torsional potential using the method of Spangler et al.35 for methyl rotors, modified to include both cosine and sine terms and periodicities other than 3-fold. The reduced moments of inertia are calculated from DFT geometries as described by East and Radom39 using their method I(2,1), which uses the rotor moments of inertia with respect to the bond axis at the minimum energy geometry. Finally, the thermodynamic functions are obtained by direct sums over the torsional energy levels. The RNH2 inversion modes of the anilines are treated following the method of Larsen et al.40 The detailed vibrational, rotational, and torsional parameters and thermochemical correction terms are provided in the Supporting Information. The HA and A− species are all ground-state singlets with no low-lying electron states. ABSOLUTE ACIDITY ANCHORS This section examines current literature values for bond dissociation energies and radical electron affinities for hydrogen sulfide, methanethiol, and pyrrole, which are then used in eq 1 to derive absolute acidities as reference anchors for the relative gas-phase acidity measurements. Conversions and standards. Literature thermochemical values are given in the units reported, then converted using 1 cal = 4.184 J; 1 cm−1 = 0.01196266 kJ/mol (hcNA); 1 eV = 96.4853 kJ/mol (eNA); and 1 Hartree = 2625.49965 kJ/mol (2R∞hcNA) from the 2010 CODATA recommendations.41 The ionization energy of atomic hydrogen is IE0(H) = 1312.0495 kJ/mol.42 Standard pressure is 1.000 bar and room temperature is 298.15 K. Because the experiments are mass spectrometric, all calculations involving mass or symmetry refer to the most abundant isotopomer, rather than natural isotopic abundance.



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Uncertainties for thermochemical quantities are expressed as an estimate of ±2uc, two combined standard uncertainties43 or approximately the 95% confidence level. Hydrogen sulfide. A precise laser photodetachment microscopy measurement44 on HS− yields the electron affinity of HS radical, EA0(H32S) = 18669.543 ± 0.012 cm−1 or 223.33733 ± 0.0014 kJ mol−1. The bond dissociation energy of H2S measured by photofragment translational spectroscopy (PTS)45 is D0(H–SH) = 31440 ± 40 cm−1 or 376.11 ± 0.48 kJ mol−1, which is consistent with a reinvestigation by the same group46 reporting the limiting value D0(H–SH) ≥ 31430±20 cm−1 = 375.99± 0.25 kJ/mol. For both these determinations the rotational energy of the precursor H2S under seeded supersonic beam conditions is neglected,45,46 possibly making the values too low by up to 3RT/2 or 0.012 kJ/mol per degree Kelvin of the uncertain rotational temperature of perhaps 10-20 K. Using eq 1, the latter value gives ∆acidH0(H2S) ≥ 1464.70 ± 0.24 kJ mol−1. Threshold ion pair photoionization spectroscopy (TIPPS) of H2S by Schiell et al.47 directly gives ∆acidH0(H2S) = 122458 ± 3 cm−1 = 1464.923±0.036 kJ mol−1. These independent values are in excellent agreement, especially considering the possible effect of rotational temperature in the PTS experiments. The more direct and precise measurement from TIPPS is adopted here. Methanethiol. The electron affinities of the CH3S radical measured by two negative ion photoelectron spectroscopy experiments with resolved origin transitions are 1.871 ± 0.012 eV48 and 1.867 ± 0.004 eV,49 both referring to the ground spin-orbit state of CH3S (2E3/2). These values are in very good agreement; the adopted uncertainty-weighted average50 value is EA0(CH3S) = 1.868±0.005 eV. There are two independent routes for obtaining the experimental bond dissociation energy, D(CH3S–H). A kinetics study51 of the Br + CH3SH → HBr + CH3S reaction, gives D0(CH3S–H) = 85.96 ± 0.68 kcal mol−1 = 359.7 ± 2.8 kJ mol−1. This value agrees with but is more precise than earlier kinetics studies, and as discussed by Ruscic and Berkowitz52 it is consistent with photoionization energies of CH3S and CH2SH and the relative CH and SH bond dissociation energies of CH3SH. Alternatively, photofragmentation translational spectroscopy (PTS)53 of CH3S obtained by photodetachment of CH3S− gives D0(CH3–S) = 3.045±0.015 eV = 293.8 ± 1.4 kJ mol−1. Combining this result with the enthalpies of formation of CH3, S, 6 ACS Paragon Plus Environment

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CH3SH, and H and thermal corrections described in the Supporting Information,24,54–57 the result is D0(CH3S–H) = 359.7 ± 1.7 kJ/mol, coincidently in exact agreement with the kinetics value. The enthalpy of formation of CH3SH relies on a single combustion calorimetry measurement,56 but the agreement with the kinetics result for the bond energy provides corroborating evidence. The combined value50 of the two bond energies is D0(CH3S–H) = 359.7 ± 1.5 kJ/mol. Equation 1 then yields ∆acidH0(CH3SH) = 1491.5 ± 1.5 kJ mol−1. Pyrrole. The electron affinity of pyrrolyl radical measured by photoelectron spectroscopy9 of C4H4N− is EA0(C4H4N) = 2.145 ± 0.010 eV = 207.0 ± 1.0 kJ/mol. The N–H bond dissociation energy of pyrrole measured by photofragmentation translational spectroscopy58 is D0(C4H4N–H) = 32850 ± 40 cm−1 = 392.97 ± 0.48 kJ/mol. Applying eq 1 with these values gives ∆acidH0(C4H4N–H) = 1498.1 ± 1.1 kJ/mol. Because there is only one reported high-resolution determination each of the electron affinity and bond energy, these values should ideally be subject to further experimental verification. Using proton transfer bracketing and photodetachment, Richardson et al.59 obtained D298(C4H4N–H) = 99 ± 6 kcal/mol = 414 ± 25 kJ/mol. Based on the acidity of pyrrole in DMSO, Bordwell et al.60 estimated D298(C4H4N–H) = 96.6 ± 3 kcal/mol = 404 ± 13 kJ/mol. These are much less precise but are in agreement with the PTS value. Table 1 summarizes the recommended gas-phase acidities of H2S, CH3SH, and C4H4NH at 0 K. Table 1 also presents values for ∆acidH298, ∆acidS298, and ∆acidG298, using the thermal enthalpy and entropy corrections described above and in the Supporting Information. For the three anchor acids, we calculated the gas-phase acidities at 0 K at the CCSD(T)/aug-cc-pVQZ//CCSD/aug-cc-pVTZ level with zero-point vibrational energy corrections from scaled27 B3LYP vibrational frequencies and the torsional mode calculations. Andersson and Uvdal27 reported a rms error of 0.36 kJ/mol for the scaled zero-point energies compared with experimental values for 40 species in the harmonic oscillator approximation. Irikura et al.61 found standard uncertainties in scaled B3LYP zero-point energies of about ±2%. That suggests an estimated 95%-confidence uncertainty to the theoretical values of ±0.9 to ±1.6 kJ/mol, in addition to any error in the electronic energy. This ZPE uncertainty estimate assumes completely correlated errors in the 7 ACS Paragon Plus Environment


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ZPEs for RH and R− so that the error only affects the difference in ZPEs (the estimated uncertainty would be up to ±22 kJ/mol with zero correlation, which is unlikely). The results for ∆acidH0 are compared with the experimental values in Table 1. The agreement among the three anchor acids is very good, with absolute errors (theory minus experiment) of +0.1 kJ/mol, −0.6 kJ/mol, and −1.3 kJ/mol for H2S, CH3SH, and C4H4NH, respectively. We also compare acidities from the high-level composite W1 method31,32 in Table 1. The standard implementation of the W1 method uses all harmonic frequencies for the zero-point energy correction, which is not accurate for low-frequency torsional modes. We therefore also calculate the W1 electronic energies with our DFT zero-point energies, including the torsional mode for CH3SH treated as a hindered rotor. These values are in excellent agreement with the evaluated acidities, within 0.4 kJ/mol. EXPERIMENTAL RELATIVE ACIDITIES Relative gas-phase acidities of acids in the range of H2S to pyrrole have been measured in proton transfer equilibrium measurements by several methods.7–10 These experiments provide the equilibrium constant and Gibbs energy of reaction for proton transfer reactions, eq 3, Ai− + HAj

→ ←

HAi + Aj−

(3)

where HAi and HAj are two gas-phase acids. The Gibbs energy change for the proton transfer reaction is related to the two gas-phase acidities by eq 4. ∆3GT = −RT lnK3 = δ∆acidGT = ∆acidGT(HAj) − ∆acidGT(HAi)

(4)

Cumming and Kebarle6 used high pressure mass spectrometry (HPMS) techniques to measure equilibrium constants for reaction 3 of a variety of nitroalkanes along with hydrogen sulfide and pyrrole. Bartmess et al.7 used ion cyclotron resonance (ICR) measurements of the equilibrium constants to measure relative acidities of alkanethiols, nitroalkanes, pyrrole, and substituted anilines. Bierbaum and coworkers8,9 measured the Gibbs acidity differences of a variety of alkanethiols and pyrrole using selected ion flow


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tube (SIFT) experiments, in which the forward and reverse rate constants for reaction 3 are used to find the equilibrium constant. All three of these groups included hydrogen sulfide in their measurements. Mackay and Bohme10 reported a single flow tube measurement for reaction 3 with methanethiol and nitromethane. Taken together, these experiments provide 52 independent measurements of relative acidities for 42 unique proton transfer reactions, as listed in Table 2, in the acidity range including hydrogen sulfide, methanethiol, and pyrrole. The proton transfer reactions in Table 2 are all written in the direction with δ∆acidG > 0 and K3 < 1. The measured relative acidities range from near-isergonic to δ∆acidG = 24 kJ/mol, corresponding to equilibrium constants from unity to K3 = 10−5, limited by the dynamic range of the ion abundance measurements6,7 or of the forward and reverse rate constant measurements.8–10 For the high-pressure mass spectrometry experiments,6 δ∆acidG values were reported at 500 K or 600 K. These are corrected here to room temperature using calculated molecular constants from density functional theory, including treatment of the torsional modes as hindered rotors, as given in detail in the Supporting Information. The ion cyclotron resonance studies7 were conducted in the range of 320±5 K ICR cell temperatures but corrected by the authors using an approximate method and reported at 298 K. We have “uncorrected” those values back to 320 K using the entropies given by Bartmess et al.7 and recorrected them using our calculated Gibbs-energy corrections. This neglects the actual variation of temperature for the individual measurements by Bartmess et al.,7 but this temperature correction has only very minor effects anyway. The flow-tube rate constants measurements8–10 were performed at or near room temperature and are used without temperature correction. Table 2 gives the originally reported values as well as our adjusted 298 K values. GAS-PHASE ACIDITY THERMOCHEMICAL NETWORK



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A local thermochemical network3,16,24 is used to refine the gas-phase acidity ladder of relative acidities at 298 K using least-squares optimization. The goodness of fit criterion is the weighted sum of squared residuals,62 chi-square or χ2, defined by eq 5, = ∑ − ∆acid (HA ) + ∆acid ( )

(5)

where yij = δ∆acidGij is the measured relative acidity, i.e., the free energy change for the proton transfer reaction (3), and ∆acid (HA ) and ∆acid (HA ) are the absolute acidities for acids HAj and HAi. The residuals are weighted and summed over the N measured relative acidities. The weighting factors are wij = 1/sn2 with the standard deviation sn given by eq 6, sn = [ sij2 + si2 + sj2]1/2

(6)

where n labels the relative acidity measurement, sij is the estimated standard deviation of the measured relative acidity (yij), si or sj are the estimated standard uncertainties for the reference anchor acids with fixed acidities, and si = sj = 0 for acidities to be optimized. The anchor acidity uncertainties are included to account for the precision of the reference values. The “unknown” acidities are optimized by minimization of χ2, i.e., by solving M simultaneous equations of the form of eq 7,

∆acid !(HA" )]

= 0 = −2 ∑ &', − ∆acid (HA ) + ∆acid (HA ) +

2 ∑&', − ∆acid (HA ) + ∆acid (HA )

(7)

where m labels one of the M = 14 optimized acidities and the sums are over the subset of proton transfer reactions where that acid appears as either HAi or HAj. This is a linear system of M equations which we solve numerically using an iterative grid search algorithm.62 The quality of the fit is given by the estimated standard error, sy, and uncertainty interval, uy, defined by eq 8, )* = ±,-* = ±,./ 0

∑91*23 4∆acid !(HA3 )5∆acid !(672 )8 :4;

=/

Anchoring the Gas-Phase Acidity Scale from Hydrogen Sulfide to

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