Active Thermochemical Tables: The Partition Function of

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Active Thermochemical Tables: The Partition Function of Hydroxymethyl (CHOH) Revisited 2

David H. Bross, Hua-Gen Yu, Lawrence B Harding, and Branko Ruscic J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02295 • Publication Date (Web): 18 Apr 2019 Downloaded from http://pubs.acs.org on April 18, 2019

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The Journal of Physical Chemistry

Active Thermochemical Tables: The Partition Function of Hydroxymethyl (CH2OH) Revisited David H. Bross,*‡ Hua-Gen Yu,§ Lawrence B. Harding,‡ and Branko Ruscic*‡↨ ‡

Chemical Sciences and Engineering Division, Argonne National Laboratory, Lemont, Illinois 60439, United States §

Division of Chemistry, Department of Energy and Photon Sciences,

Brookhaven National Laboratory, Upton, New York 11973, United States ↨

Consortium for Advanced Science and Engineering, The University of Chicago, Chicago, Illinois 60637, United States

e-mail: [email protected] (BR), [email protected] (DHB)

The submitted manuscript has been created by UChicago Argonne, LLC, Operator of Argonne National Laboratory (“Argonne”). Argonne, a U.S. Department of Energy Office of Science laboratory, is operated under Contract No. DE-AC02-06CH11357. The U.S. Government retains for itself, and others acting on its behalf, a paid-up nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public, and perform publicly and display publicly, by or on behalf of the Government.

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Abstract The best currently available set of temperature-dependent non-rigid rotor anharmonic oscillator (NRRAO) thermochemical and thermophysical properties of hydroxymethyl radical is presented. The underlying partition function relies on a critically evaluated complement of accurate experimental and theoretical data, and is constructed using a two-pronged strategy that combines contributions from large amplitude motions obtained from direct counts, with contributions from the other internal modes of motion obtained from analytic NRRAO expressions. The contributions from the two strongly coupled large-amplitude motions of CH2OH, OH torsion and CH2 wag, are based on energy levels obtained by solving the appropriate two-dimensional projection of a fully-dimensional potential energy surface that was recently obtained at the CCSD(T)/cc-pVTZ level of theory. The contributions of the remaining seven, more rigid, vibrational modes and of the external rotations are captured by NRRAO corrections to the standard rigid rotor harmonic oscillator (RRHO) treatment, which include corrections for vibrational anharmonicities, rotation-vibration interaction, Coriolis effects, and low-temperature. The basic spectroscopic constants needed for the construction of the initial RRHO partition function rely on experimental ground-state rotational constants and the best available experimental fundamentals, additionally complemented by fundamentals obtained from the variational solution of the full-dimensional potential energy surface using a recently developed two-component multi-layer Lanczos algorithm. The higherorder spectroscopic constants necessary for the NRRAO corrections are extracted from a second-order variational perturbation treatment (VPT2) of the same potential energy surface. The Lanczos solutions of the fully dimensional surface are validated against available experimental data, and the VPT2 results and the solutions of the reduced dimensionality surface are validated both against the Lanczos solutions and available experiments. The NRRAO thermophysical and thermochemical properties, given both in tabular form and as 7- and 9coefficient NASA polynomials, are compared to previous results. In addition, the latest ATcT values for the enthalpy of formation of CH2OH at 298.15 K (0 K), -16.75 ± 0.27 kJ/mol (-10.54 ± 0.27 kJ/mol), and of other related CHnOm species (n = 0-4, m = 0,1) are reported, together with a plethora of related bond dissociation enthalpies (BDEs), such as the C-H, O-H, and C-O bond dissociation enthalpies of methanol, 402.16 ± 0.26 kJ/mol (395.61 ± 0.26 kJ/mol), 440.34 ± 0.26 kJ/mol (434.86 ± 0.26 kJ/mol), and 384.85 ± 0.15 kJ/mol (377.14 ± 0.15 kJ/mol), respectively, and analogous BDEs for hydroxymethyl, 343.67 ± 0.37 kJ/mol (339.16 ± 0.37 kJ/mol), 125.54 ± 0.28 kJ/mol (121.11 ± 0.28 kJ/mol), and 445.86 ± 0.29 kJ/mol (438.76 ± 0.29 kJ/mol), respectively. The reasons governing the alternation between strong and weak sequential Hatom BDEs of methanol are also discussed.


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I. Introduction Hydroxymethyl, CH2OH, the simplest -hydroxyalkyl radical, is an important intermediate in a variety of reactive chemical environments, ranging from the atmosphere and combustion to the interstellar medium. In the atmosphere, CH2OH is generated via a reaction of CH4 with O (1D), as well as via H-atom abstraction from methanol with OH or halogen (F, Cl) atoms, and is subsequently destructed by reaction with either O2 or O, producing HO2 or OH radicals.1-4 Hydroxymethyl is ubiquitous in combustion of oxygenated hydrocarbon fuels, particularly methanol, where it is the preferred product during the initial attack of O2 or O, and is profusely generated during later steps that involve H-atom abstraction by OH or HO2.5,6 Historically, astrochemistry focused its attention on homogeneous gas-phase ion-molecule reactions, and the cation, hydroxymethylium, CH2OH+, rather than its neutral counterpart, is one of the positively identified interstellar species.7 However, newer thoughts posit heterogeneous reactions involving neutral species, such as CH2OH, adsorbed on dust or ice grains, as possible routes to more complex biologically interesting molecules.8-11 Clearly, the availability of reliable and accurate thermochemistry is a sine qua non for the understanding and modeling of chemical reactions. Most chemists would promptly agree that for a given chemical species the central thermochemical quantity is its enthalpy of formation, fH°, by convention given at 298.15 K and/or 0 K. In practice, however, modeling also requires reliable values of temperature-dependent thermophysical properties that are derived directly from the partition function, Q°(T), such as the isobaric heat capacity, C°p(T), the entropy, S°(T), and enthalpy increment, [H°(T)-H°(0)]. The enthalpy increments are vital for correct conversion of the enthalpies of formation (and thus reaction exo-/endothermicity) between various temperatures, the entropies are needed for conversion of the latter to the corresponding ex/endergonicity (and hence the equilibrium constant) and vice versa, and the heat capacities are requisite for determining the temperature change of the system during a reaction. The overwhelming majority of available Q-derived thermophysical properties for polyatomic gas-phase species are based on the ubiquitous rigid rotor harmonic oscillator (RRHO) partition function. Within the RRHO model, the computations of Q-derived thermophysical properties are conveniently straightforward, involving simple analytical expressions12,13 and requiring only the knowledge of the most basic spectroscopic properties, such as the symmetry and multiplicity of the ground state, the vibrational fundamental frequencies i (rather than harmonic frequencies12,14), the ground-state rotational constants A0, B0, C0, and, if available, analogous spectroscopic properties of the excited electronic states and their term energies. Barring chemical species with prominent large-amplitude internal motions (i.e. non-rigid species), RRHO partition functions are usually assumed to be sufficiently accurate for an approximate conversion of enthalpies of reaction (or formation) from 0 K to room temperature and vice versa, if chemical accuracy (± 1 kcal/mol) is the target. However, RRHO partition functions are generally not accurate enough for thermochemical applications in extended temperature ranges or for applications demanding high accuracy.12 Given that the partition function is a Boltzmann-weighted count of accessible states, its accuracy (and consequently the accuracy of its derivative properties) evidently depends upon the fidelity by which the energies and degeneracies of the rovibronic levels have been



quantified. While the RRHO model generally tends to capture approximately correctly the properties of rovibrational levels at low internal energies, it does not include effects that are frequently collectively termed as anharmonic by thermodynamicists (though, alongside vibrational anharmonicities, these include effects such as rotation-vibration interactions, centrifugal stretching, vibrational resonances, etc.). All of these effects tend to progressively gain prominence as the internal excitation energies increase. The influence of higher rovibronic levels on the derived thermophysical properties grows as the temperature increases and enhances their Boltzmann weight in the partition sum. Consequently, at higher temperatures (such as those occurring in combustion), a simple RRHO partition function is generally not able to preserve the sub-kJ/mol accuracies of 0 K or room-temperature enthalpies of formation that have nowadays become available from state-of-the-art electronic structure methods, such as HEAT,15-18 W4,19,20 Feller-Peterson-Dixon (FPD),21-26 Focal-Point (FP),27-31 or ANL-n,32 or from novel thermochemical paradigms that derive the best current values by simultaneously considering all available experimental and theoretical thermochemically-relevant determinations, such as the Active Thermochemical Tables (ATcT) approach.33-35 In principle, if one had the luxury of knowing sufficiently accurately the energies and degeneracies of all rovibronic levels up to sufficiently high excitations, the best partition function would be obtained by direct count. While experimental sets of levels are seldom sufficiently complete for this purpose even at relatively modest internal excitation energies (with the exception of some atoms and diatomics), there are various theoretical techniques36-38 for calculating the rovibrational energy levels of general polyatomic molecules. Assuming that an adequately accurate potential energy surface is available or can be constructed, one possible choice are fully variational methods.36,39,40 Other possibilities include the vibrational selfconsistent field approach (VSCF),41,42 and its various vibrational correlation methods extensions, such as configuration interaction (VCI),43,44 coupled cluster (VCC),45,46 and perturbation theory (VMP2).47 One complication in the direct count approach is that, as a rule of thumb, reasonably accurate and complete sets of rovibronic states up to at least 30,000 - 35,000 cm−1 are needed in order to achieve good convergence of the thermophysical functions at temperatures relevant in combustion, and up to 40,000 cm−1 (and even beyond) if higher temperatures, such as those occurring in explosions, will be considered. This is a tall order both for experiment and theory. If computing the partition function via direct summation is frustrated by the unavailability of a comprehensive list of levels, the next best approach - partially systematized by McBride et al.48-50 and Gurvich et al.,51,52 and subsequently embraced by CODATA53 as a “gold standard” - is to compute non-rigid rotor anharmonic oscillator (NRRAO) corrections to the basic RRHO partition function. In addition to the basic spectroscopic constants needed for the RRHO approach, the relevant analytical expressions for the NRRAO corrections12,51,50,54-59 require the availability of higher-level spectroscopic constants, such as those arising from the RayleighSchrödinger second order perturbation theory,60-63 e.g. vibrational anharmonicities, xij, rotationvibration interaction constants, Ai, Bi, Ci, Nielsen centrifugal distortion constants DJ, DJK, DK, J, R5, and R6 (or, equivalently, Kivelson-Wilson ' constants), further augmented by other pertinent terms such as Fermi resonance constants W0 and/or Darling-Dennison resonance constants , and, if available, by higher-order vibrational anharmonicities, yijk, and rotationvibration interaction constants Aij, Bij, Cij.


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For the vast majority of chemical species, even the most basic spectroscopic constants (rotational constants and vibrational fundamentals) that are needed for the computation of RRHO partition functions are not necessarily available from experiment as a complete set.64-66 This paucity becomes even more pronounced for higher-order spectroscopic constants, frustrating attempts to compute a NRRAO partition function from experimental data alone. Luckily, in many cases of interest the available experimental data can be complemented by theoretical values, obtained by a second-order perturbative evaluation of rovibrational parameters (VPT2),67-69 and, as of very recently, even using a fourth-order perturbative evaluation (VPT4).70 Conveniently, these approaches compute higher-order spectroscopic constants by probing the properties in the immediate vicinity of the equilibrium point of a chemical species, and thus in principle do not require a full potential energy surface. Incidentally, they also show promise for the calculation of anharmonic zero point energies, as was recently shown by Harding et al.71 through comparison of VPT2 to diffusion Monte Carlo techniques. One serious complication is that the NRRAO expressions12 are intended for computing contributions to the partition function for internal modes that occur in rigid molecules, but they are clearly not suitable for large amplitude motions. Namely, for vibrational contributions to thermophysical properties, on top of the RRHO contributions of the vibrational fundamentals, i, the existing NRRAO expressions include corrections for the effects of first-order anharmonic constants, xij, and can include second-order anharmonic constants, yijk, if these are available. In order for these corrections to be sufficient, the energies of vibrational levels have to be reasonably well reproduced by a low order (at most cubic) polynomial. While this is typically a sensible assumption for non-degenerate vibrational levels of rigid molecules, a cubic polynomial is patently insufficient to adequately reproduce the energy levels of such internal motions as inversions, soft bends, etc., not to mention hindered rotors. A tightly related problem is that, despite their advantages, one major drawback of perturbation theory approaches, such as VPT2 or VPT4, is that they assume that the harmonic approximation is a reasonable starting point and that the deviations from it are relatively minor. This is a particularly poor assumption for large amplitude motions. The above suggests a two-pronged strategy for computing a NRRAO partition function, which combines regular NRRAO expressions for rigid modes with a direct count for large amplitude motions, as explored for CH2OH in the present study. The necessary spectroscopic constants for the former portion will be obtained by complementing the best available experimental data with the results from VPT2 computations. The energy levels corresponding to large amplitude motions will be obtained by solving a lower-dimensionality potential energy surface. Both the VPT2 results and the solutions of the lower-dimensionality surface will be, in turn, crossvalidated by comparison with available experiments and by comparison with solutions from the full-dimensional potential energy surface, at least up to the energies available from the latter.

II. A Historical Overview of the Relevant Thermochemistry of CH2OH Both the enthalpy of formation of hydroxymethyl and its Q-derived thermophysical properties have a tumultuous history (see Table 1). As we shall see, depending on the source of data, the resulting enthalpy of formation appears to be tightly related to the Q-derived properties.



In their 1969 review, Golden and Benson72 recommended the C-H bond dissociation enthalpy of methanol, BDE298(H-CH2OH) = 94 ± 2 kcal/mol (393 ± 8 kJ/mol), as a via media between the manifestly inconsistent limits of  92 kcal/mol (bromination, Buckley and Whittle73) and  95.9 ± 1.5 kcal/mol (iodination, Cruickshank and Benson74). Though not given explicitly by Golden and Benson, the implied fH°298(CH2OH) = -26 ± 8 kJ/mol, became the reigning value for several decades. Interestingly, in a 1976 kinetic study of higher alcohols at NBS, Tsang75 inferred a significantly higher C-H BDE of methanol, 401.8 kJ/mol, from which he derived fH°300(CH2OH) = -17.6 kJ/mol. However, Tsang’s finding was entirely ignored in the 1982 review of McMillen and Golden,76 who (now explicitly) recommended fH°298(CH2OH) = -6.2 ± 1.5 kcal/mol (-25.9 ± 6 kJ/mol), citing Golden and Benson,72 but further tightening the error bar. In his 1987 review,77 Tsang counterpointed by recommending fH°300(CH2OH) = -17.5 kJ/mol, essentially identical to his earlier value.75 Importantly, the kinetic studies73-7475 underlying these early evaluations inferred the thermochemistry of CH2OH from forward activation energies alone, rather than from fully determined equilibrium constants. The two most popular tabulations from the 80s, the NBS Tables78 and JANAF,79 did not include CH2OH, though the 1988 NBS GIANT compilation of Lias et al.80 adopted the value of McMillen and Golden,76 rather than that of Tsang.77 The 1990 English edition of Gurvich et al. 81 did not shed new light on the issue, and repeated the value from the 1982 Russian original,82 fH°298(CH2OH) = -20 ± 10 kJ/mol, corresponding to BDE298(H-CH2OH) = 399 ± 10 kJ/mol. The value was a weighted average of seven widely differing determinations (ranging from -1 ± 35 to -70 ± 50 kJ/mol): the already mentioned bromination and iodination kinetic studies,73,74 an even earlier kinetic study of the decomposition of methanol,83 as well as several positive ion cycles, one of which was based on the electron impact appearance energy of CH3+ from ethanol,84 the others on electron impact85 and photon impact86-88 appearance energies of CH2OH+ from several alcohols. The latter ion cycles were closed by using the only ionization energy (EI) of CH2OH available at the time: 8.14 ± 0.20 eV, from electron impact mass spectrometry.84 The Russian tabulation81,82 also reported the first temperature-dependent set of heat capacities, entropies, and enthalpy increments for CH2OH, but, for lack of sufficient information allowing a more elaborate approach, the underlying partition function was RRHO-based, including the treatment of the OH torsion as a pseudo-vibration. The partition function used rotational constants from available theoretical geometries,89-91 fundamental vibrational frequencies from Jacox and Milligan92 (who measured 1, 4, and 9 by IR matrix spectroscopy, and estimated the rest by a force field analysis), and took into account the fact that the assumed C1 X 2A ground state has two enantiomeric isomers. With respect to EI(CH2OH), a subsequent photoelectron study by Dyke et al.93 produced 7.56 ± 0.01 eV, significantly lower than electron-impact. The EI was afterwards confirmed and refined to 7.549 ± 0.006 eV in photoionization mass-spectrometric (PIMS) studies by Ruscic and Berkowitz,94,95 who combined it with the best prior PIMS determination of the 0 K appearance energy of CH2OH+ from methanol87 (11.67 ± 0.03 eV), producing BDE298(H-CH2OH) = 403 ± 3 kJ/mol and fH°298(CH2OH) = -16 ± 3 kJ/mol (-3.9 ± 0.7 kcal/mol). This was the first entirely spectroscopic determination of these quantities. Intrigued by the new spectroscopic results, Seetula and Gutman96 embarked on determining


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the actual equilibrium constants for bromination and iodination of methanol by explicitly measuring the kinetic rates of the reverse reactions, and derived fH°298(CH2OH) = -8.9 ± 1.8 kJ/mol and BDE298(H-CH2OH) of 410 ± 2 kJ/mol, in serious disagreement97,98 with the spectroscopic result. Dóbé attempted to resolve this discrepancy, and in an initial note99 derived a joint 2nd and 3rd law average of fH°298(CH2OH) = -12 ± 4 kJ/mol from newly measured forward and reverse rate constants for chlorination and bromination of methanol, but, a year later, in a more detailed account that focused just on the chlorination equilibrium constant, Dóbé et al. 100 derived a higher value of -9 ± 6 kJ/mol, congruent with that of Seetula and Gutman.96 Examining the same discrepancy, Traeger and Holmes101 suggested that part of the problem may reside in the partition function-related data. Namely, in converting the measured equilibrium constants to a reaction enthalpy, Seetula and Gutman96 used the entropy of CH2OH given by Tsang,77 who treated the OH torsion in CH2OH as a free rotor. By treating it instead as a vibration (using 420 cm−1 from Jacox102), Traeger and Holmes101 obtained a lower entropy for CH2OH, and reinterpreted the data of Seetula and Gutman96 in terms of fH°298(CH2OH) = -14.7 ± 1.4 kJ/mol (bromination) and -15.8 ± 7.8 kJ/mol (iodination). While per se this appeared to alleviate the discrepancy, Traeger and Holmes101 also questioned the appearance energy of CH2OH+ from methanol by Refaey and Chupka,87 11.67 ± 0.03 eV at 0 K, which was used95 to complete the ion cycle. By linear extrapolation of their somewhat noisy low-resolution PIMS threshold, Traeger and Holmes101 obtained a lower appearance energy of 11.632 ± 0.007 eV at 0 K, from which, together with the EI(CH2OH) of Ruscic and Berkowitz, they derived an even lower fH°298(CH2OH) = -19 ± 1 kJ/mol, reinforcing the discrepancy. In response to these developments, Ruscic and Berkowitz103 independently remeasured the Refaey and Chupka87 appearance energy of CH2OH+ from methanol, and demonstrated that the PIMS threshold has decisive inward curvature, not discernible in the noisy spectrum of Traeger and Holmes,101 but vitiating their linear extrapolation. Using a novel fitting procedure that involved a non-linear kernel convoluted by the internal energy distribution of the parent, Ruscic and Berkowitz103 obtained a 0 K threshold of 11.649 ± 0.003 eV, in full accord with Refaey and Chupka,87 but an order of magnitude more accurate. When combined with IE(CH2OH), the refined threshold yielded BDE298(H-CH2OH) = 402.3 ± 0.6 kJ/mol and fH°298(CH2OH) = -16.6 ± 0.9 kJ/mol, fully confirming the earlier spectroscopic result. The IE was later104,105 slightly refined to 7.553 ± 0.006 eV, implying BDE298(H-CH2OH) = 401.9 ± 0.7 kJ/mol and fH°298(CH2OH) = -17.0 ± 0.9 kJ/mol. In order to address the disagreement with the kinetic determinations, Ruscic and Berkowitz103 posited that treating the torsion in CH2OH either as a free rotor (Tsang77) or as a torsional vibration (Traeger and Holmes,101 Russian tabulation51,82) are both oversimplifications - though at the opposite ends of the spectrum - and that a more appropriate approach should involve a hindered rotor. Using a torsional barrier estimate from the theoretical study of Saebø et al.,106 Ruscic and Berkowitz deduced from the bromination experiment of Seetula and Gutman96 a 298.15 K enthalpy of formation of hydroxymethyl of -12.2 ± 1.7 kJ/mol which was midway between the free rotor (-9.1 kJ/mol) and the torsional vibration (-14.7 kJ/mol) approaches. While this alleviated only partially the discrepancy, it reinforced the notion that a non-negligible



aspect of the problem resides in the complexities of the partition function of CH2OH. Indeed, using resonance-enhanced multiphoton ionization (REMPI) spectroscopy of CH2OH and its deuterated isotopomers, Johnson and Hudgens107 concluded that the OH torsion is strongly coupled to the CH2 wag. Combining available experimental vibrational fundamentals (four from Ar matrix isolation spectroscopy of Jacox102 and one from their own gas-phase measurements) with scaled (0.94) theoretical harmonic frequencies for the two unobserved fundamentals and with computed rotational constants, Johnson and Hudgens107 constructed a new RRHO partition function for CH2OH up to 2000 K, in which the contributions from the two coupled modes was calculated by direct count over the first 837 levels (up to 29410 cm−1), obtained by solving an approximate two-dimensional potential surface using the Fourier grid Hamiltonian method. All relevant computations, including the two-dimensional surface, were obtained at the MP2/6-311G(2df,2p) level of theory, with the inertial moments for the reduced dimensionality surface adjusted semi-empirically to reproduce their experimentally observed transitions. Using their new partition function, Johnson and Hudgens obtained the 3rd law values for fH°298(CH2OH) of -13 ± 5 kJ/mol (chlorination study of Dóbé et al.100), -13 ± 8 kJ/mol (by combining the forward rate of Cruickshank and Benson74 and the reverse rate of Seetula and Gutman96 for iodination), and -18.7 ± 2.1 kJ/mol (from the new bromination study by Dóbé et al.,108 vide infra), giving them an averaged kinetic value of -17.6 ± 1.9 kJ/mol, in excellent agreement with the value of Tsang.75,77 From a positive ion cycle based on an averaged adiabatic IE of CH2OH and its isotopomers (Dyke,93,109 Ruscic and Berkowitz,94,95,103 and Klemm et al.110,111) and an averaged photoionization appearance energy of CH2OH+ from methanol (Refaey and Chupka,87 Traeger and Holmes,101 and Ruscic and Berkowitz103), Johnson and Hudgens obtained a 298.15 K enthalpy of formation of CH2OH of -17.9 ± 1.9 kJ/mol, leading to their final value of fH°298(CH2OH) = -17.8 ± 1.3 kJ/mol. Appearing in the same journal issue back-to-back with the study of Johnson and Hudgens,107 the above-mentioned new study by Dóbé et al.108 combined their redetermination of the forward and reverse kinetic rates for bromination with the new partition function of Johnson and Hudgens (vide supra), producing fH°298(CH2OH) = -15.5 ± 1.6 kJ/mol (2nd law analysis) and -18.8 ± 2.1 kJ/mol (3rd law analysis), leading to a weighted average of -16.6 ± 1.3 kJ/mol, in superb accord with the positive ion result of Ruscic and Berkowitz.103 (Note that Johnson and Hudgens used only 3rd law values from kinetic studies to obtain their averaged value.) In 2005, the IUPAC Task Group on thermochemistry of radicals has examined all experimental and theoretical determinations available at the time, and recommended112 fH°298(CH2OH) = 17.0 ± 0.7 kJ/mol, corresponding to BDE298(H-CH2OH) = 402.0 ± 0.9 kJ/mol, and heat capacities, entropies, and enthalpy increments based on the partition function of Johnson and Hudgens.107 Not surprisingly, hydroxymethyl was a direct or indirect target of numerous theoretical studies.32,106,113-137 In the context of the current discussion, the work of Marenich and Boggs129,130 is of particular interest. These authors have treated CH2OH as a molecule with highly anharmonic vibrations, and developed a partition function that includes vibrational anharmonicity. To that end, vibrational levels up to 60,000 cm−1 were obtained by solving a surface computed at the CCSD(T)138-140 level using correlation consistent polarized valence basis sets of Dunning and coworkers141-143 of triple  quality. The vibrational problem was solved


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variationally for a rotational angular momentum of N = 0, using a model Hamiltonian that separated the two out-of-plane large amplitude motions (8 and 9) from the remaining seven in-plane motions, and included coupling limits to reduce the number of basis functions to less than 13,500. The variationally-obtained fundamentals were compared to those obtained by second-order perturbation theory at the same level of theory, with good agreement for the seven in-plane modes, but poor agreement for the two out-of-plane modes. Marenich and Boggs130 also calculated the enthalpy of formation of CH2OH using the O-H bond dissociation energy computed at the CCSD(T) level within the frozen core electron approximation with augmented correlation-consistent polarized valence basis sets up to quintuple  quality, extrapolated to complete basis set limit, with corrections for core-valence and scalar relativistic effects, as well as zero-point-energy (zpe). From D0(CH2O-H) = 121.88 ± 0.23 kJ/mol, they obtained the 0 K enthalpy of formation of CH2OH of -10.6 ± 0.7 kJ/mol, which, with their new partition function, converted to fH°298(CH2OH) = -17.0 ± 0.7 kJ/mol. However, the claimed uncertainty of the enthalpy of formation of Marenich and Boggs (and, by implication, the accuracy of the computed vibrational levels and hence the resulting partition function) was subsequently questioned by Harding et al.,71 who determined from a CCSD(T)/ccpVTZ surface (using diffusion Monte Carlo techniques) a zpe for CH2OH that is higher by 110 cm−1 (or 1.3 kJ/mol) than that obtained by Marenich and Boggs. Last, but not least, it should be mentioned that Reisler’s group studied extensively a number of spectroscopic and dynamic properties of CH2OH by sophisticated experimental methods.144-156 In particular, in 2012, Ryazanov et al.153 determined by velocity map imaging the 0 K O-H bond dissociation energy of hydroxymethyl, D0(CH2O-H) = 10160 ± 70 cm−1 or 121.5 ± 0.8 kJ/mol (cf. to their concomitant theoretical value of 10,188 cm−1 obtained at the ROCCSD(T)/CBS//ROCCSD(T)/aug-cc-pVTZ level of theory with anharmonic zero-point-energy correction152) as well as D0 of two additional isotopomers. When combined with the ATcT 0 K enthalpies of formation157 of formaldehyde (-105.35 ± 0.10 kJ/mol) and H-atom (216.034 ± 0.001 kJ/mol), their experimental D0(CH2O-H) implies a 0 K enthalpy of formation for CH2OH of 10.9 ± 0.8 kJ/mol (equiv. to -17.2 ± 0.8 kJ/mol at 298.15 K), in superb agreement with the IUPAC recommendation and the earlier photoionization results. Reisler’s group148 also determined the three largest, previously not measured, gas phase fundamental frequencies of CH2OH, adding to the knowledge base inferred from previous studies.92,102,107 All three values have been quite recently confirmed and further improved upon by Nesbitt’s group158-161 using high-resolution NIR spectroscopy. Recently, the Active Thermochemical Tables (ATcT) study157 of sequential bond dissociation energies of methanol reported the most accurate enthalpy of formation of CH2OH available so far: fH°298(CH2OH) = -16.57 ± 0.33 kJ/mol (or -10.26 ± 0.33 kJ/mol at 0 K). The resulting C-H BDE of methanol is BDE298(H-CH2OH) = 402.14 ± 0.32 kJ/mol (395.60 ± 0.32 kJ/mol at 0 K). Notably, the partition function used in the ATcT study was that which was proposed by Johnson and Hudgens107 and subsequently recommended by IUPAC.112 Clearly, a key for successful use of the currently known thermochemistry of CH2OH (and other species) in combustion applications is a reliable high-temperature partition function. Evidently, the quality of the related high-temperature thermophysical properties relies not only on



including the best available fundamentals and rotational constants, but also on incorporating effects beyond the RRHO model, such as including the NRRAO corrections discussed earlier. However, as also discussed earlier, since NRRAO corrections are not applicable to large amplitude motions, their contributions are best computed by direct count of levels obtained as solutions from the appropriate lower-dimensionality potential energy surface. The inherent complication in obtaining a good partition function for CH2OH is that the OH torsion is strongly coupled to the CH2 wag, necessitating the count of levels obtained by solving a two-dimensional potential energy surface simultaneously describing both modes. Although it has not included the NRRAO corrections pertinent to the more rigid modes, the study of Johnson and Hudgens107 has demonstrated that a reduced dimensionality approach may be able to produce satisfactory results for these two modes. Taking CH2OH as an example, in this study we are exploring a generally applicable approach for obtaining partition functions for a wider class of radicals that undergo large amplitude motion, which includes NRRAO corrections for the rigid modes, combined with a separate account of the contributions from the coupled OH torsion and CH2 wag. The latter contribution is obtained by direct count of levels obtained by solving the pertinent two-dimensional (2D) projection of the potential energy surface using the basis-set agnostic discrete variable representation (DVR) introduced by Colbert and Miller.162 The 2D DVR solutions are validated by comparison with a rigorous full-dimensional solution for the low-lying states using recent advances for pentaatomic systems163 on the full-dimensional potential energy surface. The NRRAO corrections for the other modes of motion are based on experimental rotational constants and a set of vibrational fundamentals selected by combining the best available experimental values with variational solutions of a full-dimensional potential energy surface, complemented by higher-order spectroscopic constants obtained by the VPT2 approach.

III. Computational Methodology III a. Full-Dimensional Lanczos Calculations Rovibrational energies of CH2OH have been computed in their full dimensionality (15D) up to an excitation energy of 4,000 cm−1 using the recently developed real two-component multi-layer Lanczos algorithm.163,164 Calculations were performed with an exact quantum Hamiltonian in a set of orthogonal polyspherical coordinates. Similarly to the approach used earlier for vinyl radical CH2CH,165 the combined (2+1) Radau-Jacobi coordinate (i.e. Icd = 1 in Ref. 166) system was used, where two Radau vectors (r1 and r2) were selected to describe two CH stretches in CH2 and two Jacobi vectors (r3 and r4) were used for the O-H and CH2-OH stretches, respectively. It has been shown that this set of scattering coordinates can well describe the large amplitude motions of CH2OH. The CCSD(T)/cc-pVTZ potential energy surface of CH2OH of Harding et al.71 was used in the variational calculation. In the calculations, a group contracted basis approach was employed. Briefly, for a given total angular momentum J, the Lanczos vector |vl> is expressed as23 | vl   Ctl, m , a ,  | tR aQm  , t  r , i , (1) t , m, a ,


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where t (t=r, i) stands for the real and imaginary part of the vector. | R aQm   is a direct product basis function in three groups of coordinates: radial coordinates (R), internal angular variables (Q), and overall rotational angles. It can be written as (2) | R a Qm  | R a | Qm (Q | ; JM  , 4

where | ; JM  is an uncoupled overall rotational basis function.23 | R a   | rai  refers to i 1

the direct product (1D) PO-DVR (potential optimized-discrete variable representation) basis functions in R with a being a collective DVR index. | Qm (Q)  are the vibrationally diabatic basis functions in the internal angular coordinates Q, formed by the lowest eigenstates of a (5D) reduced dimensional Hamiltonian Hˆ Q0 (Q; R 0 , R V0 ) with a 5D reference potential V (Q, R V0 ) . The 5D potential has been partially optimized in the radial coordinates R V0 , but the radial references in the pre-factors of kinetic energy operator were fixed at R0. The diabatic functions were solved using the neural network iterative diagonalization method (NNiDM)167 in a full dimensional DVR basis set. The DVR basis set was contracted by discarding DVRs with potential energies larger than a threshold value of 3.0 eV. The permutation symmetry of the two hydrogen atoms in CH2 is treated explicitly in calculations. Since the 1,2-H shifting barrier height is large (~2.2 eV), the isomerization pathway is excluded in this work. The vibrational states were assigned using the perturbative Lanczos iteration method,165 modified from those of Gruebele168 and Hutson169 in terms of the Hellmann-Feynman theorem.170,171 In order to easily deal with the large amplitude torsion motion of OH in CH2OH, the sine functions in the azimuthal angles were employed in the normal mode analysis.165 The calculated energy levels were checked for convergence by varying the basis size, especially the size (Ndiab) of diabatic basis functions. A large number of diabatic functions was required because the torsion motion of CH2OH becomes a nearly free internal rotor at high vibrational energies. The results reported here were computed using a large basis set that is given in DVR DVR Table S1. N1D is the primitive Fourier (for the radial coordinates). N refers to the Q

contracted DVR basis size in the angular variables Q using a threshold potential of Vth. 840 PODVR (N ) diabatic functions were used in the calculations. Together with N R PODVRs in the diab

vib radial coordinates, the final basis size in the outer-loop Lanczos iterations is 5.18M ( N tot ) for the pure vibrational state calculations. For the rovibrational state calculations, the basis size is vib determined by (2 J  1) N tot for a given J. With this large basis set, the vibrational energies are

converged better than 0.05 cm-1 up to 3500 cm-1 relative to the vibrational ground state (GS).

III b. NRRAO Partition Function The partition function for CH2OH relies on experimental ground-state rotational constants172 and, with the exception of the two lowest-frequency modes, 8 and 9, which are treated separately as described below, on a set of vibrational fundamentals that was obtained by complementing the best available experimental values148,158-161,173 with fundamentals



computed using the full-dimensional Lanczos approach of the CCSD(T)/cc-pVTZ potential energy surface. The NRRAO corrections to the partition function and the resulting thermophysical properties have been computed using analytical expressions detailed elsewhere.12 The rotational contribution to the NRRAO partition function includes the effect of centrifugal distortion and a correction for low temperatures. The contributions of vibrational modes 1 - 7 to the NRRAO partition function include the effect of vibrational anharmonicity and vibrationrotation interaction, with the necessary higher-order spectroscopic constants computed using second-order vibrational perturbation theory (VPT2)174-176 at the CCSD(T)/cc-pVTZ level of theory using CFOUR.177,178 The contributions from 8 and 9 are based on direct count of levels obtained by solving a twodimensional potential that was projected out of the full-dimensional CCSD(T)/cc-pVTZ potential energy surface of Harding et al.71 by performing a relaxed scan of that surface along two selected dihedral angles, both of which were referenced to the plane that contains the C and O atoms and bisects the CH2 group. The angle controlling the wag was defined as the dihedral angle between the reference plane and the plane containing O, C, and one of the two CH2 hydrogen atoms, virtually coalescing them at the 0 and  extremes. The dihedral angle controlling the OH torsion was defined as the angle between the reference plane and the plane containing C, O, and the OH hydrogen atom, covering the range 0 - 2. The two-dimensional potential was solved using the universal (i.e. basis set agnostic) DVR procedure of Colbert and Miller,162 with the corresponding reduced masses adjusted such that the harmonic frequencies corresponding to the wag and the torsion, computed from the second derivatives at the minima of the two-dimensional surface, matched the corresponding harmonic vibrational frequencies computed from the full-dimensional potential. The state counts of the solutions of the 2D DVR include the effect of parity coupling with the levels of the external rotation.

IV. Results and Discussion Once the non-feasible symmetry operations are excluded,179,180 the full permutation-inversion symmetry group of CH2OH reduces to the inversion group  = {E, E*}, isomorphic with the Cs point group. As discussed earlier,107,129,161 the potential energy surface of CH2OH has four equivalent minima, corresponding to two enantiomeric pairs of C1 symmetry. Interconversion between these minima can occur either along the CH2 wag, through a relatively low transition state corresponding to a planar CH2OH structure, or along the internal rotation of OH, through a higher Cs transition state containing a pyramidal CH2O moiety with the COH plane bisecting the CH2 group. On the current CCSD(T)/cc-pVTZ potential energy surface,71,181 the zpe-exclusive barrier for inversion is 139 cm−1 and that for torsion is 1670 cm−1, more than an order of magnitude higher. These barriers can be compared to those obtained by Johnson and Hudgens107 on their MP2/6-311G(2df,2p) surface (156 and 1643 cm−1, respectively), as well as to those reported by Marenich and Boggs129 (157, 147, and 140 cm−1 for the inversion at the MP2, MP4, and CCSD(T) level, respectively, using the cc-pVTZ basis set, and “about 20 kJ/mol” for the torsion). Table 2 lists a selection of experimentally observed vibrational fundamentals and overtones, compared to the corresponding values from a previous theoretical study employing VCI with 4mode coupling,150 and to values obtained from the theoretical approaches examined in this


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work. The assignments follow the standard spectroscopic notation, with 1 through 7 having a' symmetry, and 8 and 9, involving out-of-plane motions, having a" symmetry. Where specified, the symmetry of inversion-split (a.k.a. tunneling-split) levels is denoted as pts = ±. Within the current context, the purpose of Table 2 is twofold: to obtain a cursory fiduciary mark on the fidelity of the theoretical vibrational levels of CH2OH that were obtained in the present study, and to aid the selection of the best currently available vibrational fundamentals for the NRRAO partition function. Not all of the vibrational modes of CH2OH have been experimentally measured in gas phase: 4, 5, and 7 are known only from Ar or N2 matrix spectroscopy.92,102 Furthermore, as pointed out by Johnson and Hudgens,107 the gas-phase selection rules for 8 and 9 (v8 + v9 = 0, ±2, ±4) in CH2OH preclude direct experimental observation of the respective fundamentals, which are inferred from overtones and combination bands. Reisler’s group148 used double-resonant ionization detected IR spectroscopy to report the gasphase 1 (3674.9 cm−1), 2 (3161.5 cm−1), and 3 (3043.4 cm−1) fundamentals and the 21 overtone (7158.0 cm−1) with a rotational linewidth of 0.4 cm-1, but did not attempt to explicitly assign uncertainties for the determined fundamentals. The three fundamentals can be further validated by examining recent high-resolution NIR spectroscopy of CH2OH obtained in Nesbitt’s group. 158-160 For 1, the result of Feng et al.148 agrees within 0.8 cm-1 with the corresponding origin of the unsplit band of 1 (3674.1042 cm−1) reported by Wang et al.158 The value for the 2 fundamental148 can be corroborated by considering the 3164.138 cm-1 transition between v2=0, N=1, Ka=0, Kc=1 and v2=1, N=1, Ka=1, Kc=0 states and the excitation of 1.8608 cm-1 for 2=0, N=1, Ka=0, Kc=1, both obtained by Nesbitt and collaborators,158-160 combined with the difference of 7.3 cm-1 between 2=1, N=1, Ka=1, Kc=0 and 2=1, N=0, Ka=0, Kc=0 inferred from VPT2 CCSD(T)/cc-pVTZ anharmonic constants computed in the present work. This leads to an estimate for the 2 fundamental of 3158.7 cm-1, which agrees within 3 cm-1 with the result of Feng et al.148 For 3, Schuder et al.161 reported both inversion-split components (3041.7561 and 3041.2270 cm−1) with an estimated uncertainty of ± 0.0003 cm−1. Notably, the earlier unresolved result of Feng et al.148 agrees with the 3+/3- average within 2 cm-1. The first three fundamentals, for which there are experimental gas phase values with accuracies better than one cm−1, provide a very small, but highly accurate and unbiased benchmark for theoretical values. In particular, for these three fundamentals, the RMSD between experiment and previous VCI results,152 the current full-dimensional Lanczos calculations, and the current VPT2 results are 28.5, 28.2, and 5.0 cm-1, respectively. If the benchmark is further expanded to include the other, less accurate, experimental observations (4 - 9, 21, 28, 29), which are either from gas-phase studies that are accurate to no better than ± 5-10 cm-1, or from matrix studies and thus inherently somewhat shifted compared to gas phase, the RMSDs for the literature VCI result and the current full-dimensional Lanczos calculations do not change substantially, becoming 23.3 and 18.9 cm−1, respectively, while the RMSD for the VPT2 values nominally jumps to 162.6 cm-1, due to a (not entirely surprising) pathological VPT2 result for the anharmonic constants related to the two a" modes. However, as discussed earlier, the contemplated strategy for computing the NRRAO partition function does not envision using the VPT2 results for the large-amplitude modes; rather, the contributions of 8 and 9 are to be obtained separately from direct counts of the solutions to



the corresponding two-dimensional projection of the potential energy surface. Indeed, replacing the VPT2 results for the 8 and 9 fundamentals with fundamentals computed using the 2D DVR approach reduces the RMSD for the extended benchmark set to 12.4 cm-1, suggesting that the VPT2 anharmonic constants are a very reasonable choice for the NRRAO partition function for CH2OH, providing that the pathological anharmonic constants involving large amplitude motion modes 8 and 9 are not included in the computations of the NRRAO corrections and that these two modes are treated separately. Figure 1 shows a visual comparison of the vibrational states below 2200 cm-1 corresponding to the coupled motions involving CH2 wag and OH torsion (8 and 9), as obtained from the fulldimensional Lanczos approach and from the 2D DVR approach (see Supplementary Information for a list of relevant values). Overall, there is good agreement between the two methods, with an RMSD of 59.1 cm−1 over the whole set, or, if only levels below 1000 cm−1 are included in the comparison, 21.9 cm−1. Additional post-factum correction of the 2D DVR results by including the coupling of 8 and 9 modes with 1 through 7 via VPT2 anharmonic constants xi8 and xi9, i = 1-7, was also tested, and it was found that this does not improve the comparison, and, in fact, increases the RMSD to 140 cm-1 for levels up to 2200 cm−1, suggesting, on the one hand, that at least a portion of the coupling with the other modes has been implicitly included in the twodimensional projection by virtue of the fact that it corresponds to a fully relaxed scan through the other vibrational degrees of freedom, and, on the other hand, that perturbation theory appears to overestimate the anharmonic couplings between the large amplitude modes and the remaining vibrational modes. The observed overtones 28 and 29 from Johnson and Hudgens107 were reported as 846 and 616 cm−1, with an estimated accuracy of ± 6 cm-1. In the solutions obtained by the fulldimensional Lanczos approach, 28 is 10 cm−1 and 29 is 31 cm−1 lower than the experimental benchmark, while in the case of the 2D DVR results the two overtones are 25 cm−1 higher and 20 cm−1 lower, respectively. One additional relevant observation is that the vibrational manifold involving 8 and 9 has an energy spectrum that is consistently less dense than what would be produced by assuming two harmonic vibrators oscillating at the corresponding fundamental frequencies,182 which, as we shall see (vide infra), explains the principal difference between thermophysical properties obtained from partition functions that include the contribution from 8 and 9 by direct count vs. those obtained from their RRHO counterparts. Incidentally, the ground state splitting due to tunneling, obtained from the full-dimensional Lanczos approach is 0.0064 cm−1, and from the reduced two-dimensional surface is 0.0050 cm-1, both in very good agreement with the experimentally observed value of 0.00466 cm-1 obtained from the mm-wave studies.172 While this splitting is not particularly relevant for the partition function outside cryogenic temperatures, obtaining a reasonable theoretical value is a necessary (though not sufficient) requirement for validating the full-dimensional Lanczos and the reduced dimensionality DVR approaches. Similarly, the zpe obtained from Lanczos calculations, 8003 cm-1, is in very good agreement with the DMC value71 of 8010 cm-1 obtained from the same potential. These two values for the zpe are noticeably larger than 7900 ± 7 cm-1 obtained from the normal-mode based variational calculations of Marenich and Boggs.130 Assuming that their CCSD(T) potential energy surface


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was comparable to the one used in the present work, the significant difference in zpe is likely rooted in the adiabatic approximation used for 8 and 9 by Marenich and Boggs, as previously suggested by Harding et al.71 An accurate anharmonic zpe is obviously crucial in electronic structure approaches that aspire to deliver high-accuracy enthalpies of formation.183 The surprising underestimate of the CH2OH zpe by Marenich and Boggs130 by 1.3 kJ/mol calls into question not only the proposed accuracy (± 0.7 kJ/mol) of their computed enthalpy of formation, but also, by implication, their partition function. The computation of the NRRAO partition function (as well as the simpler RRHO partition function) requires, inter alia, a careful selection of basic spectroscopic constants. In the present study, accurate ground-state rotational constants (6.4891589, 0.99548995, 0.86548085 cm−1) were taken from experiment.172 The comparison of experimental data and computational results that was detailed above suggests the following selection of vibrational fundamentals (averaged, when necessary, over the inversion-split doublets184): validated experimental gasphase values148,158-161 for 1, 2, and 3 (3674.1042, 3158.7, and 3041.4916 cm-1), complemented by the results from the full-dimensional Lanczos approach for 4, 5, 6, and 7 (1467.1, 1336.0, 1179.7, and 1063.5 cm−1). The related vibrational anharmonic constants, vibration-rotation interaction constants, and centrifugal stretching constants were adopted from the VPT2 computations at the CCSD(T)/cc-pVTZ level of theory, and are given in the Supporting Information. The 8 and 9 contributions to the NRRAO partition function were computed by a state count over the DVR solutions of a two-dimensional potential (which are also given in the Supporting Information). For the purpose of additional comparison, a straightforward RRHO partition function that includes all vibrational modes was also computed, corresponding in spirit to the partition function originally given by Gurvich et al.,81 but using the same fundamentals and rotational constants as those used for the current NRRAO partition function, with the addition of the 8 and 9 fundamentals (430.4 and 239.3 cm−1) taken from the DVR solution of the two-dimensional reduced potential energy surface. Table 3 provides a JANAF-style tabulation of the thermodynamic functions of CH2OH obtained by the NRRAO treatment described above, and lists the isobaric heat capacity, Cp°, the entropy, S°, the enthalpy increment, [HT°- H0°], and the reduced Gibbs energy, R lnQ°, as well as the updated enthalpy of formation, fH°, and Gibbs energy of formation, fG°, obtained by employing the NRRAO partition function in conjunction with the latest version of the ATcT Thermochemical Network (vide infra). An expanded version of Table 3 is given in the Supplementary Information (Table S5). Since combustion modelers often use the representation of thermochemical properties in compact form,185,186 most frequently as NASA polynomials, the thermochemical properties of CH2OH that are given in Table 3 were fitted to such polynomials using the NASA PAC program187 and are also given in the Supplementary Information. Figure 2 depicts the behavior of several relevant Q-derived thermophysical properties (isobaric heat capacity, entropy, enthalpy increment, and the RT lnQ° = -[H° - TS°] term), in terms of differences between values given previously in the literature81,107,130 and those derived using the current NRRAO partition function. The figure also includes a comparison to RRHO thermophysical properties obtained using the same basic spectroscopic constants as the



NRRAO approach. Before proceeding with a brief discussion of the observed differences, one should parenthetically note here that Johnson and Hudgens107 reported the functions only up to 2000 K, and for the purpose of Figure 2, the values were extrapolated to higher temperatures (shown as a dashed line) using the corresponding NASA polynomial fit recommended by IUPAC.112 In addition, the partition function published by Marenich and Boggs130 used the long-outdated standard pressure of 1 atm (rather than 1 bar, as adopted by IUPAC188 in 1982). Since for gas-phase species the pressure affects just the translational contribution to the entropy,13 the tabulated data of Marenich and Boggs130 were converted to the current standard by adding R ln(1.01325) = 0.109 J/K/mol to each of their reported entropies. As expected, if the only concern were the thermochemical properties at 298.15 K, the differences between the various partition functions probed here are rather minor, even if one were to use the straightforward RRHO approach. For example, compared to the current NRRAO value for the enthalpy increment [H298° - H0°] = 11.791 kJ/mol, which is relevant for the conversion of the enthalpy of formation between 0 K and room temperature, the RRHO value obtained with the current selection of spectroscopic constants is larger by only 0.344 kJ/mol, and the corresponding value given by the RRHO function of Gurvich et al.,81 which is based on somewhat outdated spectroscopic constants, is smaller by only 0.595 kJ/mol. The 298.15 K enthalpy increment obtained by the elaborate approach of Marenich and Boggs130 is smaller by 0.098 kJ/mol than the current NRRAO value, and the value given by the more sophisticated approach of Johnson and Hudgens107 is smaller by only 0.010 kJ/mol. Clearly, in this particular case, if the accuracy goal were no tighter than the revered chemical accuracy, using any of these partition functions for conversion to/from 0 K would not impose a prohibitive additional error. However, if the goal is to try to preserve as much as possible the accuracy of the currently derived ATcT enthalpy of formation of CH2OH, which currently carries an uncertainty of ± 0.27 kJ/mol (vide infra), one evidently needs to go beyond the RRHO partition function. As opposed to room temperature thermophysical properties, the differences become more substantial at higher temperatures. With the exception of the isobaric heat capacity at T > 3500 K, the two RRHO approaches overestimate the thermophysical properties of CH2OH. This is not surprising. Namely, as mentioned earlier, treating 8 and 9 as harmonic vibrators tends to produce a larger density of states than warranted for these two modes, leading to a corresponding overestimate of the enthalpy increment. Notably, this is just the opposite of the primary effect that is expected as a result of ignoring anharmonicities for typical rigid modes, which in most cases have negative anharmonic constants (where the sign convention follows the usual notation for polyatomics,63 which happens to be the opposite of the convention usually used for diatomics). Generally speaking, negative vibrational anharmonicities tend to increase the density of bound states compared to the model that does not include them, causing the latter to systematically underestimate the enthalpy increment. Given that the two large amplitude motions are the two softest modes in CH2OH, one can expect that their inadequate treatment will be the dominant effect in the RRHO partition function, affecting the resulting values already at moderate temperatures. Indeed, the straightforward RRHO approach using the current spectroscopic constants produces enthalpy increments that are larger by 4.471 kJ/mol at 2000 K, 5.527 kJ/mol at 2500 K, 6.257 kJ/mol at 3000 K, etc.; all of


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these differences exceed the chemical accuracy threshold. Similarly, the enthalpy increments of the RRHO approach of Gurvich et al.81 are higher by 3.254 kJ/mol at 2000 K, 4.498 kJ/mol at 2500 K, 5.374 kJ/mol at 3000 K, etc. In contrast to both RRHO approaches, the corresponding enthalpy increments of Marenich and Boggs130 display the opposite tendency, and are lower by 4.406 kJ/mol at 2000 K, 5.712 kJ/mol at 2500 K, 7.154 kJ/mol at 3000 K, etc. For all three partition functions, the other thermophysical properties depicted in Figure 2 display similar tendencies: the differences are rather substantial at higher temperatures, with straightforward RRHO and the RRHO of Gurvich et al. appearing to roughly track each other, while the function of Marenich and Boggs appears to depart in the opposite direction. Not surprisingly, the partition function of Johnson and Hudgens,107 which includes the anharmonic effects implicit in the CH2 wag and OH torsion and their coupling, shows the best agreement with the current NRRAO function, the primary difference between the two being the inclusion of additional anharmonic effects (related to 1 through 7) in the current NRRAO function, but absent in the partition function of Johnson and Hudgens. The majority of vibrational anharmonic constants related to the seven rigid modes (given in the Supplementary Information) have negative values, implying that their exclusion will tend to produce an underestimate of the thermophysical properties. As seen in Figure 2, this certainly appears to be the case with the values obtained by Johnson and Hudgens.107 Thus, at 2000 K - the highest temperature reported by these authors - their values are lower by 2.943 J/K/mol for heat capacity, 1.082 J/K/mol for entropy, 1.758 kJ/mol for the enthalpy increment, and 0.406 kJ/mol for the RT lnQ° term. Assuming that the extrapolated functions112 of Johnson and Hudgens107 provide a reasonable prediction of the behavior at even higher temperatures, it appears that these differences continue to grow further as the temperature increases. The above analysis suggests that a proper description of large amplitude motions in the partition function is essential even at moderate temperatures. In case of CH2OH, this was not adequately captured by the RRHO partition function of Gurvich et al.,81 nor apparently by the more sophisticated function of Marenich and Boggs,130 but it seems to have been adequately captured by the function of Johnson and Hudgens.107 However, if the goal is to extend the thermochemical and thermophysical properties beyond moderate temperatures to temperatures relevant in combustion, while preserving to the maximum extent possible the accuracy of room temperature thermochemical properties, one evidently needs to also include the anharmonic effects of all the other modes of internal motion. The last previously reported ATcT enthalpy of formation of CH2OH,157 fH°298(CH2OH) = -16.57 ± 0.33 kJ/mol (-10.26 kJ/mol at 0 K) used the partition function of Johnson and Hudgens.107 Given that the relevant experimental kinetics-based determinations74,96,99,100,108 in the corresponding ATcT Thermochemical Network (TN)157,189 are all at quite moderate temperatures (ranging between 349 and 615 K), and that at these temperatures the partition function of Johnson and Hudgens does not differ very much from the present one, one should not expect that the insertion of the current partition function in ATcT will result in a significantly different enthalpy of formation of CH2OH at 298.15 K. Indeed, if the exact same earlier version of ATcT TN157,189 is reused, but the partition function of Johnson and Hudgens107 is replaced with the current



NRRAO partition function, it produces an enthalpy of formation of CH2OH that is less negative by no more than 0.01 kJ/mol, well within the uncertainty of the earlier value. However, it should be noted that the new partition function does produce a noticeable change when the results for CH2OH are applied to higher temperatures, relevant to combustion processes. Thus, for example, compared to the earlier partition function of Johnson and Hudgens107 recommended by IUPAC,112 the new partition function systematically lowers the free energy of formation of CH2OH at higher temperatures, correspondingly affecting the nominal temperature at which a reaction involving hydroxymethyl as a reactant or a product achieves a particular value for the equilibrium constant. Since ver. 1.122,157,189 the ATcT TN has gone through a number of additions and expansions,190-199 and the current version (1.122r) encompasses > 2,000 chemical species, interconnected by > 25,000 experimental and theoretical determinations. For the sake of completeness, we report here some of the relevant thermochemical quantities produced using the most current ATcT TN (see Table 4). Compared to the previously reported ATcT value,157,189 the enthalpy of formation of hydroxymethyl in the most current version of ATcT TN is slightly more negative (by 0.18 kJ/mol) and very slightly more accurate, fH°298(CH2OH) = -16.75 ± 0.27 kJ/mol (-10.45 kJ/mol at 0 K). The change is primarily due to a slight improvement in the gasphase enthalpy of formation of the parent methanol, fH°298(CH3OH) = -200.91 ± 0.15 kJ/mol or -190.03 kJ/mol at 0 K (more negative by 0.20 kJ/mol than previously reported157,189), reflecting a richer and denser TN surrounding this species. Since the change in the enthalpies of formation of CH2OH and CH3OH nearly completely track each other, the corresponding BDE298(H-CH2OH) = 402.16 ± 0.26 kJ/mol (395.61 kJ/mol at 0 K), though also now being slightly more accurate, is otherwise essentially the same as that reported earlier.157,189 Furthermore, since the enthalpy of formation of gas-phase formaldehyde, fH°298(CH2O) = -109.21 ± 0.10 kJ/mol (-105.38 kJ/mol at 0 K) is essentially the same as reported before,157,189 the current value of the O-H bond dissociation enthalpy of CH2OH, BDE298(CH2O-H) = 125.54 ± 0.28 kJ/mol (121.11 kJ/mol at 0 K), has slightly increased (by 0.16 kJ/mol) from the previously reported value.157,189 Qualitative physical organic chemistry often relies on the concept of average bond dissociation enthalpies, such as those extensively used by Pauling.200 Within that framework, the O-H BDE of hydroxymethyl (given above) appears to be surprisingly low. Indeed, the corresponding O-H BDE of methanol, usually taken as the canonical alcohol O-H bond strength - the current ATcT value of which is BDE298(CH3O-H) = 440.34 ± 0.26 kJ/mol (434.86 kJ/mol at 0 K) - is significantly stronger than the O-H BDE of hydroxymethyl, by 314.80 ± 0.39 kJ/mol at 298.15 K (313.75 kJ/mol at 0 K). Mutatis mutandis, the C-H BDE in methanol (also given above) is stronger (by exactly the same amount201) than the C-H BDE in methoxy, the current ATcT value of which is BDE298(H-CH2O) = 87.35 ± 0.28 kJ/mol (81.86 kJ/mol at 0 K). In analogy with the earlier discussion157 of the sequential BDEs of ethane, it can be shown that the expense of removing the O-H hydrogen in CH2OH is compensated by a concomitant strengthening of the skeletal C-O bond, from an essentially single bond in CH2OH, BDE298(H2COH) = 445.86 ± 0.29 kJ/mol (438.76 kJ/mol at 0 K) to a double bond in CH2O, BDE298(H2C-O) = 750.06 ± 0.13 kJ/mol (743.28 kJ/mol at 0 K).202 The same type of effect lowers the enthalpy of the hydrogen removal in CH3O, which is compensated by a concomitant strengthening of the


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skeletal C-O bond from an essentially single bond in CH3O, BDE298(H3C-O) = 374.25 ± 0.28 kJ/mol (367.91 kJ/mol at 0 K) to the quoted double bond in CH2O.203 In fact, it can be easily shown that BDE(CH2O-H) = BDE(OH) - [BDE(H2C-O) - BDE(H2C-OH)], or that BDE(H-CH2O) = BDE(CH3) [BDE(H2C-O) - BDE(H3C-O)].204 The compensation effects that can be traced back to concomitant changes in the skeletal bonding lead to the strong-weak-strong-weak alternation of successive hydrogen abstractions in methanol, analogous to those observed for sequential hydrogen abstractions in CH3CH3 and SiH3SiH3.205,206 Figure 3 shows two such alternating sequences in methanol, which differ in whether the O-H dissociation is the first or the second dissociation in the sequence. The first two steps, corresponding to a high BDE of hydrogen removal in methanol, followed by a low BDE in the resulting radical, are as discussed above. Progressing further along the sequence of successive hydrogen abstractions, one finds that the C-H BDE of CH2O, BDE298(H-CHO) = 368.98 ± 0.01 kJ/mol (362.80 kJ/mol at 0 K), is significantly stronger than the C-H BDE of HCO, BDE298(H-CO) = 65.70 ± 0.10 kJ/mol (60.84 kJ/mol at 0 K), because the expense of the latter hydrogen removal is compensated by a concomitant strengthening of the C-O bond, from an essentially double bond in HCO, BDE298(HC-O) = 803.62 ± 0.13 kJ/mol (798.27 kJ/mol at 0 K), to a triple bond in carbon monoxide, BDE298(C-O) = 1076.64 ± 0.05 kJ/mol (1072.05 kJ/mol at 0 K), which is incidentally the strongest chemical bond known. This rationalizes why HCO is bound so weakly that it becomes the central precursor of ‘prompt’ carbon monoxide207 in chemical mechanisms describing combustion processes. The low BDEs of CH2OH, CH3O, and HCO are in turn responsible for the related dissociation processes becoming exergonic at relatively moderate temperatures (~1350, ~860, and ~720 K for, respectively), and their dissociation can be further accentuated once non-equilibrium processes are also included in combustion models.208 Evidently, in addition to the two sequences depicted in Figure 3, two more sequences are possible, in which the O-H dissociation occurs during the third or the fourth step. These sequences involve the less stable isomers of formaldehyde and formyl, hydroxymethylene, HCOH, and isoformyl, COH, and are not discussed here in detail, but the related thermochemistry is given in Table 4. Suffice it to say that while these two additional sequences display a progressive weakening of the sequential hydrogen abstraction enthalpies, rather than strong-weak-strong alternations, the successive weakening of H-atom dissociation enthalpies can also be entirely rationalized by the progressive concomitant strengthening of the skeletal C-O bonds. The strong-weak alternation of successive bond dissociations is ultimately enabled by the propensity of carbon (and neighboring elements in the periodic table) to form single, double, and triple bonds. The potential amplitudes of the variations along the sequences are on the other hand governed by the comparative strengths of the skeletal - and -bonds. Thus, if the skeleton of the species contains first-row atoms (where the - and -bonds are competitive) the strong-weak bond differences tend to be much more pronounced then in species containing second- (or higher) row atoms (where the -bond tends to be significantly weaker than the -bond), such as, for example, in successive H-abstraction BDEs in CH3CH3 vs. those in SiH3SiH3.157,205,206



In general, sequences of successive bond dissociations of species that contain skeletons with atoms capable of forming multiple bonds, will tend to encompass instances where the dissociation of some precursor species in the sequence leads to a daughter species that has a skeletal bonding pattern similar to that existing in the precursor, and the daughter product species can undergo a subsequent dissociation that forms a granddaughter species that contains a significantly stronger (or weaker) skeletal bond (or has, for example, experienced a ring closure or opening). Whenever this occurs, there will tend to be a strong-weak-strong alternation in the sequential BDEs: If the skeletal bonding of the granddaughter has bonds that are stronger than the daughter species (or contains new rings), the second dissociation will tend to be energetically much less expensive than the first, and vice versa. This observation can be further generalized by realizing that by their nature, dissociation sequences of such species frequently alternate between a relatively stable closed shell species and an open shell radical, and that the strong and weak successive bond dissociations have a propensity of coinciding with dissociations of stable species and radicals, respectively. As a consequence, many radicals relevant in combustion and atmospheric chemistry tend to have BDEs that are unusually low because the related dissociation process is compensated by a concomitant generation of a stronger skeletal bond in the product.

Conclusions In general, one could state that the primary complications in partition functions, which are not captured well by the ubiquitous RRHO approach, are caused by large amplitude motions, with additional complexities arising if two or more such modes are strongly coupled. Short of being able to perform a direct count over all rovibronic levels up to rather high energies (up to 40,000 cm−1 - or even higher - for obtaining full convergence at high temperatures12), it appears that the complications inherent in large amplitude motions can be alleviated by applying a more sophisticated treatment to such motions. In particular, it appears that replacing the contributions of such modes with direct counts over the levels obtained by solving the appropriate lower-dimensionality potential energy projection is a viable generic approach that can be applied to many chemical species. The remaining vibrational anharmonic effects, due to other (more rigid) internal motions, which tend to additionally affect the partition function at high temperatures, can then be captured by the usual expressions for NRRAO corrections,12 which also include other effects that are not accounted for in the RRHO approach, such as vibration-rotation interaction, non-rigidity of the rotor, low-temperature effects, vibrational resonances, etc. This strategy was applied to obtain a fully corrected NRRAO partition function of hydroxymethyl radical, CH2OH. The basic spectroscopic constants (ground-state rotational constants and vibrational fundamentals for 1 through 7) were selected by complementing accurate experimental data for ground-state rotational constants172 and vibrational fundamentals148,158161 for modes  through  with fundamentals for modes  through  extracted from a 1 3 4 7 solution of a full-dimensional (15D) potential energy surface previously computed71 at the CCSD(T)/cc-pVTZ level of theory, using a recently developed two-component multi-layer Lanczos algorithm.163-167 The Lanczos solutions of the full-dimensional surface have shown rather good agreement with the available experimental data.66,92.102,107,148,158-161 The full-


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dimensional CCSD(T)/cc-pVTZ surface was also used to obtain higher-level spectroscopic constants using the VPT2 approach. The VPT2 fundamentals agree rather well both with experiments and the Lanczos solutions for the more rigid modes 1 through 7, but not for modes 8 and 9. In a separate step, a reduced-dimensionality surface describing just the two highly coupled large amplitude motions 8 and 9 was projected out of the full-dimensional CCSD(T)/cc-pVTZ surface by a relaxed scan, and solved using a two-dimensional DVR approach.162 The latter solutions were compared both to the available experimental data and to the full-dimension Lanczos results. The various contributions to the new NRRAO partition function for CH2OH have been computed using available analytical expressions for anharmonic corrections to RRHO partition functions.12 The rotational contribution to the NRRAO partition function includes the effect of centrifugal distortion and a correction for low temperatures. The contributions of vibrational modes 1 - 7 to the NRRAO partition function include the effect of vibrational anharmonicity and vibrationrotation interaction, with the necessary higher spectroscopic constants taken from VPT2 computations. The contributions from the large-amplitude modes 8 and 9 to the NRRAO partition function were computed by direct count of levels obtained by solving the appropriate two-dimensional potential surface. The NRRAO partition function, given both in tabular form and as NASA polynomials, was compared to previous partition function for CH2OH and to a straightforward RRHO partition function that uses the same rotational constants and vibrational fundamentals. In addition, the latest ATcT values for the enthalpy of formation of CH2OH are reported, fH°298(CH2OH) = -16.75 ± 0.27 kJ/mol (-10.54 ± 0.27 kJ/mol at 0 K), together with enthalpies of formation of other related CHnOm species (n = 0-4, m = 0,1), as well as a plethora of related bond dissociation enthalpies, such as the C-H, O-H, and C-O bond dissociation enthalpies of methanol and hydroxymethyl: BDE298(H-CH2OH) = 402.16 ± 0.26 kJ/mol (395.61 kJ/mol at 0 K), BDE298(H-CHOH) = 343.67 ± 0.37 kJ/mol (339.16 kJ/mol at 0 K); BDE298(CH3O-H) = 440.34 ± 0.26 kJ/mol (434.86 kJ/mol at 0 K), BDE298(CH2O-H) = 125.54 ± 0.28 kJ/mol (121.11 kJ/mol at 0 K); BDE298(H3C-OH) = 384.85 ± 0.15 kJ/mol (377.14 kJ/mol at 0 K), BDE298(H2C-OH) = 445.86 ± 0.29 kJ/mol (438.76 kJ/mol at 0 K). The strong-weak-strong alternations of BDEs along sequential Hatom dissociations in methanol were rationalized in terms of concomitant changes in the skeletal C-O BDE.

Supplementary Information Parameters used in the multi-layer Lanczos calculations Energies, tunneling splitting, and rotational constants for select vibrational states of CH2OH, obtained by the Lanczos approach Spectroscopic constants used for the NNRAO and RRHO partition functions of CH2OH List of levels corresponding to CH2 wag and OH torsion, obtained from the 2D DVR approach Extended table of standard thermodynamic functions of CH2OH 7- and 9-Coefficient NASA Polynomials for CH2OH, CH3OH, and H

Acknowledgement



The work at Argonne National Laboratory (BR, LBH, and DHB) was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, under Contract No. DE-AC02-06CH11357, through the Gas-Phase Chemical Physics Program (BR, LBH) and the Computational Chemical Sciences Program (DHB). The work at Brookhaven National Laboratory (HGY) was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences, under Contract No. DE-AC02-98CH10886, through the Gas-Phase Chemical Physics Program, and it also used the resources at the National Energy Research Scientific Computing Center (NERSC) under Contract No. DE-AC02-05CH11231.


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Figure 1. A comparison of the vibrational states below 2200 cm-1 corresponding to the coupled motions involving CH2 wag (8) and OH torsion (9), as obtained from the fulldimensional Lanczos approach (red) and from the 2D DVR approach, without (blue) and with (green) the inclusion of the effect of anharmonic constants xi8 and xi9, i = 1-7.

+

2000

-

E (cm-1)

69

+

+

1500

+

-

+

1000 -

29

500 -

+

-

49

+

-

8 + 9 +

59

+

-

8 + 29

39 +

+

- 8 + 49

+

+

-

8 + 39 +

-

-

+

28 + 39 +

-

-

38

28 + 9 + 28

8

-


-

48

38 + 9

28 + 29 +

9

0

+

-

Lanczos 2D DVR 2D DVR + anh. coupling


Figure 2. Differences between Q-derived thermophysical quantities for CH2OH in extant literature and the current NRRAO treatment. Red: X(RRHO) - X(current); blue: X(Gurvich et al.51) - X(current), green: X(Johnson and Hudgens107) - X(current), purple: X(Marenich and Boggs130) - X(current). Top panel: differences in isobaric heat capacity, in J/K/mol; uppermiddle panel: differences in entropy, in J/K/mol; lower-middle panel: differences in enthalpy increment (a.k.a. integrated heat capacity) in kJ/mol; bottom panel: differences in the reduced Gibbs function, RT lnQ°, in kJ/mol, equivalent to differences in the -[H° - TS°] terms. 4

 Cp° (J/K/mol)

3 2 1 0 -1

0

1000

2000

3000

4000 T (K) 5000

0

1000

2000

3000

4000 T (K) 5000

0

1000

2000

3000

4000T (K) 5000

3000

4000 T (K) 5000

-2 -3 -4 8

 S° (J/K/mol)

6 4 2 0 -2 -4 -6

 HT°- H0°] (kJ/mol)

-8 4 0 -4 -8

-12

RRHO Gurvich et al. Johnson and Hudgens Marenich and Boggs

-16 22

 RT lnQ° (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

16 10 4 -2 -8

0

1000

2000

-14 -20 -26


Page 24 of 45

Page 25 of 45

Figure 3. Strong-weak-strong alternation of sequential hydrogen bond dissociation enthalpies -H

-H

-H

-H

(BDEs) of methanol. Red: CH 3OH  CH 3O  CH 2 O  HCO  CO sequence; blue: -H

-H

CH 3OH  CH 2 OH  CH 2 O sequence (after which it merges with the prior sequence).

450 400

BDE298(X-H) (kJ/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


350 300 250 200 150 100 50

CH3O-H H-CH2OH

CH2O-H H-CH2O

H-CHO


H-CO


Page 26 of 45

Table 1. A selection of literature values for the enthalpy of formation of hydroxymethyl, fH°298(CH2OH), and the corresponding C-H bond dissociation enthalpy of methanol, BDE298(HCH2OH), in kJ/mol

fH°298(CH2OH)

BDE298(H-CH2OH)

Reference

 -34

 385

 -18 ± 6

 401 ± 6

-26 ± 8

393 ± 8

-17.6

401.8

-25.9 ± 6

392.8 ± 6

McMillen and Golden (1982)e

-24 ± 13

395 ± 13

Dyke et al. (1984)f

-17.5

401.2

-25.9 ± 6

393.7 ± 6

Lias et al. (1988)h

-20 ± 10

399 ± 10

Gurvich et al. (1990)i

-16 ± 3

403 ± 3

Ruscic and Berkowitz (1991)j

-8.9 ± 1.8

410 ± 2

Seetula and Gutman (1992)k

-12 ± 4

407 ± 4

Dóbé (1992)l

-9 ± 6

410 ± 6

Dóbé et al. (1993)m

-19 ± 1

400 ± 1

Traeger and Holmes (1993)n

-16.6 ± 0.6

402.3 ± 0.6

Ruscic and Berkowitz (1993)o

-17.0 ± 0.9

401.9 ± 0.7

Litorja and Ruscic (1998)p

-17.8 ± 1.3

401.1 ± 1.3

Johnson and Hudgens (1996)q

-16.6 ± 1.3

402.3 ± 1.3

Dóbé et al. (1996)r

-17.0 ± 0.7

402.0 ± 0.9

Ruscic et al. (2005)s

-17.2 ± 0.8

401.7 ± 0.8

Ryazanov et al. (2012)t

-16.57 ± 0.33

402.14 ± 0.32

Ruscic (2015)u

-16.75 ± 0.27

402.16 ± 0.26

current study (2019)

Buckley and Whittle (1962)a Cruickshank and Benson (1969)b Golden and Benson (1969)c Tsang (1976)d

Tsang (1987)g


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ref. 73 ref. 74 c ref. 72 d ref. 75 e ref. 76 f ref. 93 g ref. 77 h ref. 80 i ref. 51 j refs. 94 and 95 k ref. 96 l ref. 99 m ref. 100 n ref. 101 o ref. 103 p refs. 104 and 105 q ref. 107 r ref. 108 s ref. 112 t refs. 153 u ref. 157 a

b



Page 28 of 45

Table 2. A selection of experimental and computed vibrational fundamentals and overtones of CH2OH, in cm−1.

State

Mode

1

OH str.

2

CH asym. str.

3 4 5 6 7

CH sym. str. CH2 sciss. HCOH inphase bend CO str. HCOH out-ofphase bend

TwoDim. DVRd

VCIa

Full-Dim. Lanczosb

VPT2c

3662

3711.3

3675.1

3116

3179.8

3151.9

3020

(+)3065.2 (-)3065.3

3036.4

1448

1467.1

1469.5

(1334)i,j

1336

1336.0

1342.1

1176k

1171

1179.7

1176.6

1032

1063.5

1042.3

468

414.6

343.7

430.4

244

222.6

231.6

239.3

Exp. 3674.9e 3674.1042f 3161.5e 3158.7g 3043.4e (+)3041.7561h (-)3041.2270h (1459)i

8

OH tors.

9

CH2 wag

(1048)i,j (1056)l (420)i,j (482)l (234)k

21

overtone

7158.0e

28

overtone

846k

835.7

656.2

871.2

29

overtone

616k

585.1

91.5

596.4

7171

7178.4

VCI calculations with 4-mode coupling from Ref. 152 b Current work. The average of the tunneling split fundamentals is reported, except for  , 3 where both fundamentals have been reported. The largest splitting in the other modes was 0.6 cm-1. c Current work; VPT2 calculations at the CCSD(T)/cc-pVTZ level of theory d Current work. Values were obtained by solving a projected two-dimensional potential energy surface using the DVR approach of Ref. 162 e Ref. 148 f Ref. 158 g Estimated from the transition of 3164.138 cm-1 between  =0, N=1, K =0, K =1 and  =1, N=1, 2 a c 2 -1 Ka=1, Kc=0 reported in Ref. 159, the excitation of 1.8608 cm of 2=0, N=1, Ka=0, Kc=1 above the ground state reported in Ref. 158, and the energy difference of 7.3 cm-1 between 2=1, a


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N=1, Ka=1, Kc=0 and 2=1, N=0, Ka=0, Kc=0, obtained from VPT2 anharmonic constants computed in this work at the CCSD(T)/cc-pVTZ level of theory. h Ref. 161 i Ar matrix, Ref. 102 j Ar matrix, Ref. 92 k Ref. 107 l N matrix, Ref. 92 2



Page 30 of 45

Table 3. Standard thermodynamic functionsa of CH2OH: isobaric heat capacity, Cp°, entropy, S°, enthalpy increment, [HT°- H0°], reduced Gibbs energy, R lnQ°, enthalpy of formation, fH°, and Gibbs energy of formation, fG° T K

Cp° J/K/mol

S° J/K/mol

[HT° - H0°] kJ/mol

R lnQ° J/K/mol

fH° kJ/mol

fG° kJ/mol

0 100 200 298.15 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 2200 2400 2600 2800 3000 3200 3400 3600 3800 4000 4500 5000 5500 6000

0.000 36.969 42.248 47.345 47.453 53.508 59.178 64.015 68.115 71.666 74.808 77.623 80.159 82.448 84.514 86.380 88.066 89.590 90.971 92.225 93.365 94.407 96.236 97.790 99.129 100.300 101.337 102.267 103.113 103.890 104.612 105.289 106.834 108.238 109.557 110.824

5.763 199.019 226.408 244.183 244.476 258.953 271.516 282.746 292.930 302.262 310.888 318.918 326.438 333.512 340.195 346.527 352.545 358.278 363.752 368.988 374.005 378.821 387.907 396.349 404.231 411.621 418.577 425.147 431.373 437.289 442.925 448.309 460.801 472.131 482.509 492.096

0.000 3.423 7.405 11.791 11.878 16.925 22.566 28.732 35.344 42.337 49.664 57.288 65.179 73.311 81.661 90.208 98.931 107.815 116.845 126.005 135.286 144.675 163.744 183.151 202.846 222.792 242.957 263.319 283.858 304.560 325.411 346.402 399.440 453.213 507.664 562.761

5.763 164.789 189.383 204.636 204.883 216.641 226.384 234.859 242.439 249.341 255.706 261.630 267.184 272.420 277.379 282.093 286.591 290.894 295.020 298.985 302.802 306.484 313.478 320.036 326.213 332.052 337.591 342.860 347.885 352.689 357.291 361.709 372.037 381.488 390.206 398.303

-10.451 -13.037 -14.878 -16.752 -16.788 -18.608 -20.207 -21.592 -22.788 -23.813 -24.686 -25.422 -26.038 -26.549 -26.972 -27.319 -27.603 -27.835 -28.025 -28.181 -28.311 -28.418 -28.592 -28.734 -28.868 -29.010 -29.174 -29.369 -29.602 -29.878 -30.204 -30.581 -31.769 -33.312 -35.161 -37.200

-10.451 -9.069 -4.370 1.182 1.293 7.600 14.343 21.386 28.647 36.066 43.604 51.233 58.929 66.677 74.463 82.280 90.119 97.974 105.843 113.724 121.610 129.504 145.305 161.119 176.945 192.784 208.633 224.491 240.364 256.252 272.158 288.081 327.980 368.035 408.252 448.654


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a

relative molecular mass Mr = 31.03392; standard pressure p° = 1 bar; entropy contribution of the total nuclear spin and the natural isotopic composition, by convention excluded in chemical applications,12 S°nucl = 18.048 J/K/mol; uncertainty in the 298.15 K enthalpy of formation, u95%(fH°298) = ± 0.27 kJ/mol.



Page 32 of 45

Table 4. Current ATcT values for thermochemical quantities relevant to the present study, in kJ/mola Quantity

0K

298.15 K

Uncertaintyb

fH°(CH3OH)

-190.03

-200.91

± 0.15

fH°(CH2OH)

-10.45

-16.75

± 0.27

fH°(CH3O)

28.80

21.43

± 0.28

fH°(CH2O)

-105.375

-109.214

± 0.096

fH°(HCOH)

112.68

108.92

± 0.27

fH°(HCO)

41.395

41.771

± 0.096

fH°(COH)

217.26

217.64

± 0.69

fH°(CO)

-113.804

-110.524

± 0.025

fH°(CH4)

-66.557

-74.526

± 0.050

fH°(CH3)

149.866

146.451

± 0.055

fH°(CH2)

391.059

391.616

± 0.097

fH°(CH)

592.824

596.158

± 0.098

fH°(H2O)

-238.928

-241.831

± 0.026

fH°(OH)

37.252

37.492

± 0.026

fH°(C)

711.397

716.882

± 0.046

fH°(O)

246.844

249.229

± 0.002

fH°(H)

216.034

217.998

± 0.001

BDE(H-CH2OH) BDE(CH3O-H) BDE(H3C-OH) BDE(CH2O-H) BDE(H-CHOH) BDE(H2C-OH) BDE(H-CH2O) BDE (H3C-O)

395.61 434.86 377.14 121.11 339.16 438.76 81.86 367.91 39.25

402.16 440.34 384.85 125.54 343.67 445.86 87.35 374.25 38.18

± 0.26 ± 0.26 ± 0.15 ± 0.28 ± 0.37 ± 0.29 ± 0.28 ± 0.28 ± 0.33

362.804 743.28 144.75 320.61 517.40 218.05

368.983 750.06 150.85 326.72 524.73 218.13

± 0.008 ± 0.13 ± 0.27 ± 0.73 ± 0.29 ± 0.27

60.835 798.27

65.703 803.62

± 0.096 ± 0.13

rH°(CH2OH  CH3O) BDE(H-CHO) BDE(H2C-O) BDE(HCO-H) BDE(H-COH) BDE(HC-OH) rH°(CH2O  HCOH) BDE(H-CO) BDE(HC-O)


Page 33 of 45 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


BDE(CO-H) BDE(C-OH) rH°(HCO  COH) BDE(C-O) BDE(H-CH3) BDE(H-CH2) BDE(H-CH) BDE(C-H) BDE(H-OH) BDE(O-H)

-115.03 531.39 175.86

-110.16 536.73 175.87

± 0.69 ± 0.69 ± 0.68

1072.045 432.457 457.227 417.80 334.607 492.215 425.625

1076.635 438.975 463.163 422.54 338.721 497.321 429.735

± 0.047 ± 0.026 ± 0.098 ± 0.11 ± 0.088 ± 0.002 ± 0.026

a

All values are from ATcT TN ver. 1.122r

b

The quoted uncertainties for ATcT BDEs are obtained by using the full covariance matrix and correspond to the nominal 95% confidence intervals that reflect the actual knowledge of the enthalpy of the corresponding reaction based on the current ATcT TN; consequently, some of the BDEs have uncertainties that are lower than what would be obtained by standard propagation in quadrature of the uncertainties of the constituent enthalpies of formation.209



TOC Graphic BDE298

fH°

fG° Cp° [H °- H °] T 0 S° R lnQ°


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Jasper, A. W.; Gruey, Z. B.; Harding, L. B.; Georgievskii, Y.; Klippenstein, S. J.; Wagner, A. F. Anharmonic Rovibrational Partition Functions for Fluxional Species at High Temperatures via Monte Carlo Phase Space Integrals, J. Phys. Chem. A 2018, 122, 1727−1740. 182 For example, the frequencies of the first overtones, 2 and 2 , are larger than twice the corresponding 8 9 fundamentals (by 6 and 140 cm−1, respectively, in the Lanczos solutions, or 10 and 118 cm−1 in the 2D DVR solutions), the second overtones, 38 and 39, are larger than three times the corresponding fundamentals (by 89 and 283 cm−1, respectively, in the Lanczos solutions, or 109 and 248 cm−1 in the 2D DVR solutions), the 8 + 9, 8 + 29, and 28 + 9 combinations are larger than the corresponding sums of the fundamentals (by 83, 202, and 130 cm−1, respectively, in the Lanczos solutions, or 81, 188, and 127 cm−1 in the 2D DVR solutions), etc. 183 Karton, A.; Ruscic, B.; Martin, J. M. L. Benchmark Atomization Energy of Ethane: Importance of Accurate ZeroPoint Vibrational Energies and Diagonal Born–Oppenheimer Corrections for a ‘Simple’ Organic Molecule. J. Mol. Struct. TheoChem 2007, 811, 345-353. 184 The  fundamental used to compute the partition function is taken as the average of the experimental 3 inversion-split fundamentals of Schuder et al. (Ref. 161). Similarly, the 4, 5, 6, and 7 fundamentals were taken as the averages of the two respective inversion-split fundamentals calculated using full-dimensional Lanczos approach in the present work. The largest splitting in these modes was 0.6 cm-1. 185 Burcat, A.; Ruscic, B. Third Millennium Ideal Gas and Condensed Phase Thermochemical Database for Combustion with Updates from Active Thermochemical Tables. Joint Report: ANL-05/20, Argonne National Laboratory, Argonne, IL, USA, and TAE 960, Technion - Israel Institute of Technology, Haifa, Israel (2005) 186 Goos, E.; Burcat, A.; Ruscic, B. Extended Third Millennium Ideal Gas Thermochemical Database with Updates from Active Thermochemical Tables, available at https://burcat.technion.ac.il/dir and mirrored at https://garfield.chem.elte.hu/Burcat/burcat.html 187 McBride, B. J.; Gordon, S. Properties and Coefficients: Computer Program for Calculating and Fitting Thermodynamic Functions, National Aeronautics and Space Administration: Washington, DC 1999 188 Cox, J. D. Notation for States and Processes, Significance of the Word Standard in Chemical Thermodynamics, and Remarks on Commonly Tabulated Forms of Thermodynamic Functions. Pure Appl. Chem. 1982, 54, 1239-1250. 189 Ruscic, B.; Bross, D. H. Active Thermochemical Tables (ATcT) Values Based on Ver. 1.122 of the Thermochemical Network, 2016; available at https://ATcT.anl.gov/ 190 Nguyen, T. L.; Baraban, J. H.; Ruscic, B.; Stanton, J. F. On the HCN-HNC Energy Difference. J. Phys. Chem. A 2015, 119, 10929-10934. 191 Chang, Y. C.; Xiong, B.; Bross, D. H.; Ruscic, B.; Ng, C. Y. A Vacuum Ultraviolet Laser Pulsed Field IonizationPhotoion Study of Methane (CH4): Determination of the Appearance Energy of Methylium from Methane with Unprecedented Precision and the Resulting Impact on the Bond Dissociation Energies of CH4 and CH4+. Phys. Chem. Chem. Phys. 2017, 19, 9592-9605. 192 Cheng, L.; Gauss, J.; Ruscic, B.; Armentrout, P. B.; Stanton, J. F. Bond Dissociation Energies for Diatomic Molecules Containing 3d Transition Metals: Benchmark Scalar-Relativistic Coupled-Cluster Calculations for 20 Molecules. J. Chem. Theor. Computat. 2017, 13, 1044-1056. 193 Porterfield, J. P.; Bross, D. H.; Ruscic, B.; Thorpe, J.; Nguyen, T. L.; Baraban, J. H.; Stanton, J. F.; Daily, J. W.; Ellison, G. B. Thermal Decomposition of Potential Ester Biofuels Part I: Methyl Acetate and Methyl Butanoate. J. Phys. Chem. A 2017, 121, 4658-4677. 194 Feller, D.; Bross, D. H.; Ruscic, B. Enthalpy of Formation of N H (Hydrazine) Revisited. J. Phys. Chem. A 2017, 2 4 121, 6187-6198. 195 Changala, P. B.; Nguyen, T. L.; Baraban, J. H.; Ellison, G. B.; Stanton, J. F.; Bross, D. H.; Ruscic, B. Active Thermochemical Tables: The Adiabatic Ionization Energy of Hydrogen Peroxide. J. Phys. Chem. A 2017, 121, 8799-8806. 196 Zaleski, D. P.; Harding, L. B.; Klippenstein, S. J.; Ruscic, B,; Prozument, K. Time-Resolved Kinetic Chirped-Pulse Rotational Spectroscopy in a Room-Temperature Flow Reactor. J. Phys. Chem. Lett. 2017, 8, 6180–6188. 181



Pratihar, S.; Ma, X.; Xie, J.; Scott, R.; Gao, E.; Ruscic, B.; Aquino, A. J. A.; Setser, D. W.; Hase, W. L. Post-Transition State Dynamics and Product Energy Partitioning Following Thermal Excitation of the F⋯HCH2CN Transition State: Disagreement with Experiment. J. Chem. Phys. 2017, 147, 144301/1-144301/15. 198 Nguyen, T. L.; Thorpe, J. H.; Bross, D. H.; Ruscic, B.; Stanton, J. F. Unimolecular Reaction of Methyl Isocyanide to Acetonitrile: A High-Level Theoretical Study. J. Phys. Chem. Lett. 2018, 9, 2532–2538. 199 Feller, D.; Bross, D. H.; Ruscic, B. Enthalpy of Formation of C H O (Oxalic Acid) from High-Level Calculations and 2 2 4 the Active Thermochemical Tables Approach. J. Phys. Chem. A 2019, in press; DOI: 10.1021/acs.jpca.8b12329. 200 Pauling, L. The Nature of the Chemical Bond, 3rd ed.; Cornell University Press: Ithaca, NY, 1960. 201 BDE(CH O-H) corresponds to the enthalpy of the reaction CH OH  CH O + H, and BDE(CH O-H) to CH OH  3 3 3 2 2 CH2O + H. In terms of reactions, the difference BDE(CH3O-H) - BDE(CH2O-H) then formally corresponds to the enthalpy of CH3OH + CH2O  CH3O + CH2OH. At the same time, BDE(H-CH2OH) and BDE(H-CH2O) correspond to the enthalpies of reactions CH3OH  CH2OH + H and CH3O  CH2O + H, respectively. Evidently, the difference BDE(H-CH2OH) - BDE(H-CH2O) corresponds to the enthalpy of the same formal reaction as BDE(CH3O-H) BDE(CH2O-H). 202 As discussed in Ref. 157 in some detail for the sequential BDEs of ethane, this is perhaps best explained by employing a gedanken experiment involving a Maxwell’s Demon, who is able to perform the hydrogen abstraction as a two-step process: during the first step, the hydrogen is removed without changing the skeletal C-O bond, and during the second step the skeletal bond is relaxed to its proper value for the dissociated product. Thus, BDE298(CH2O-H) = 125.54 ± 0.28 kJ/mol denotes the summary expense of both steps. The difference of 304.20 ± 0.28 kJ/mol between the larger C-O BDEs in the product, BDE298(H2C-O) = 750.06 ± 0.13 kJ/mol, and the smaller C-O BDE in the reactant, BDE298(H2C-OH) = 445.86 ± 0.29 kJ/mol, defines how much the Demon gains back during the second step. This suggests that the Demon would need to initially invest 429.74 ± 0.03 kJ/mol during the first step, which corresponds exactly to the current ATcT bond dissociation enthalpy of hydroxyl radical, BDE298(O-H) = 429.735 ± 0.026 kJ/mol. By analogy, the canonical O-H bond dissociation enthalpy in methanol, BDE298(CH3O-H) = 440.34 ± 0.26 kJ/mol denotes the summary expense of removing the OH hydrogen. The difference between the C-O BDE in the methoxy radical product, BDE298(H3C-O) = 374.25 ± 0.28 kJ/mol and the C-O BDE in the methanol reactant, BDE298(H3C-OH) = 384.85 ± 0.15 kJ/mol, corresponding in this particular case to a slight weakening of the skeletal bond during the OH hydrogen removal, implies that the Demon will incur during the second step an additional expense of 10.60 ± 0.26 kJ/mol. Consequently, the expense of the first step alone would have been 429.74 ± 0.03 kJ/mol, again corresponding - as expected exactly to the current ATcT BDE(OH). 203 Similarly, from BDE 298(H-CH2O) = 87.35 ± 0.28 kJ/mol and the difference between BDE298(H2C-O) = 750.06 ± 0.13 kJ/mol and BDE298(H3C-O) = 374.25 ± 0.28 kJ/mol (which indicates that Maxwell’s Demon receives a ‘rebate’ of 375.81 ± 0.29 kJ/mol during the second step), one obtains that during the first step the Demon would therefore need to expend 463.16 ± 0.10 kJ/mol, which corresponds exactly to the current ATcT bond dissociation enthalpy of methyl, BDE298(H-CH2) = 463.163 ± 0.098 kJ/mol. Finally, for BDE298(H-CO) = 65.70 ± 0.10 kJ/mol, the difference between BDE298(C-O) = 1076.635 ± 0.047 kJ/mol and BDE298(HC-O) = 803.62 ± 0.13 kJ/mol (273.02 ± 0.13 kJ/mol), suggest that during the first step the Demon would need 338.72 ± 0.09 kJ/mol, which corresponds exactly to current ATcT bond dissociation enthalpy of methylidyne, BDE298(C-H) = 338.721 ± 0.087 kJ/mol. 204 BDE(O-H) corresponds to the enthalpy of the reaction OH  O + H, BDE(H C-OH) to the enthalpy of CH OH  2 2 CH2 + OH, and BDE(H2C-O) to CH2O  CH2 + O. Summing up the first two reactions and subtracting the third produces the net reaction CH2OH  CH2O + H, the enthalpy of which corresponds to BDE(CH2O-H). Thus, BDE(CH2O-H) = BDE(O-H) - [BDE(H2C-O) - BDE(H2C-OH)]. Similarly, one can show that BDE(CH3O-H) = BDE(O-H) [BDE(H3C-O) - BDE(H3C-OH)]. This in turn means that [BDE(CH3O-H) - BDE(CH2O-H)] = [BDE(H3C-OH) - BDE(H2COH)] - [BDE(H3C-O) - BDE(H2C-O)], i.e. that the difference in O-H BDEs in CH3OH and CH2OH can be quantitatively rationalized entirely on the base of changes in the strengths of the skeletal C-O bonds during the two OH hydrogen dissociation processes. 205 Ruscic, B.; Berkowitz, J. Photoionization Mass Spectrometric Study of Si H . J. Chem. Phys. 1991, 95, 2407−2415. 2 6 206 Ruscic, B. Photoionization Mass Spectroscopic Studies of Free Radicals in Gas Phase: Why and How. Res. Adv. Phys. Chem. 2000, 1, 39−75. 197


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Labbe, N. J.; Sivaramakrishnan, R.; Goldsmith, C. F.; Georgievskii, Y.; Miller, J. A.; Klippenstein, S. J. Weakly Bound Free Radicals in Combustion: “Prompt” Dissociation of Formyl Radicals and Its Effect on Laminar Flame Speeds. J. Phys. Chem. Lett. 2016, 7, 85–89. 208 Labbe, N. J.; Sivaramakrishnan, R.; Goldsmith, C. F.; Georgievskii, Y.; Miller, J. A.; Klippenstein, S. J. Ramifications of Including Non-Equilibrium Effects for HCO in Flame Chemistry. Proc. Combust. Inst. 2017, 36, 525-532. 209 Note that the standard error propagation in quadrature simply sums up the variances and does not capture the possibility that the summands can be correlated. The correct uncertainty for a reaction enthalpy is in ATcT recovered by using the full covariance matrix. As a consequence of non-zero covariances, the various BDEs are occasionally known to higher accuracy than the constituent enthalpies of formation. Similarly, sums or differences of BDEs are occasionally known to higher accuracy than the individual BDEs. 207


Active Thermochemical Tables: The Partition Function of

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