Article Cite This: J. Phys. Chem. A 2017, 121, 8799-8806
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Active Thermochemical Tables: The Adiabatic Ionization Energy of Hydrogen Peroxide P. Bryan Changala,† T. Lam Nguyen,‡ Joshua H. Baraban,¶ G. Barney Ellison,¶ John F. Stanton,*,‡ David H. Bross,§ and Branko Ruscic*,§,∥ †
JILA, National Institute of Standards and Technology and University of Colorado Boulder, Boulder, CO 80309, United States Quantum Theory Project, Departments of Chemistry and Physics, University of Florida, Gainesville, FL 32611, United States ¶ Department of Chemistry, University of Colorado, Boulder, CO 80302, United States § Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL 60439, United States ∥ Computation Institute, The University of Chicago, Chicago, IL 60637, United States ‡
ABSTRACT: The adiabatic ionization energy of hydrogen peroxide (HOOH) is investigated, both by means of theoretical calculations and theoretically assisted reanalysis of previous experimental data. Values obtained by three different approaches: 10.638 ± 0.012 eV (purely theoretical determination), 10.649 ± 0.005 eV (reanalysis of photoelectron spectrum), and 10.645 ± 0.010 eV (reanalysis of photoionization spectrum) are in excellent mutual agreement. Further refinement of the latter two values to account for asymmetry of the rotational profile of the photoionization origin band leads to a reduction of 0.007 ± 0.006 eV, which tends to bring them into even closer alignment with the purely theoretical value. Detailed analysis of this fundamental quantity by the Active Thermochemical Tables approach, using the present results and extant literature, gives a final estimate of 10.641 ± 0.006 eV.
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INTRODUCTION In the past decade, the accuracy of fundamental thermochemical quantities (such as bond energies and enthalpies of formation) for many molecules have increased by at least an order of magnitude relative to values found in 20th century data compilations. This dramatic advance is made possible by the concept of Active Thermochemical Tables (ATcT),1,2 which represents a departure from the sequential manner in which thermochemical data have traditionally been determined and updated. ATcT relies on the concept of a thermochemical network (TN), in which the interdependence of thermochemical quantities that can exist between very different molecules (e.g., the phenyl radical and ammonia)3 is made explicit. By design, ATcT automatically accounts for these dependencies and thus guarantees an internally consistent set of data. All available information (in practice, both experimental and theoretical) relevant to the species involved is contained in the TN, and this provides a set of conditional thermochemical constraints that must be satisfied. The TN is then statistically analyzed, iteratively corrected for possible inconsistencies, and solved to obtain the thermochemical parameters, a process that involves detailed consideration of the uncertainties associated with the input data and which has been discussed elsewhere in the literature.1,2,4−9 As indicated above, the use of thermochemical networks means that isolated experimental measurements impact not just the species that are being probed in the laboratory but potentially © 2017 American Chemical Society
many other similar as well as chemically unrelated molecules. This provides considerable motivation for highly accurate and precise determinations of fundamental quantities such as bond energies, adiabatic electron affinities, and adiabatic ionization energies; any improvement in such information will propagate through the network and potentially lead to refined values and error bounds for many other species in the network. In the course of developing ATcT to its current state, effort has also been made to reinvestigate and reanalyze extant data. An excellent example of this is the dissociation energy of carbon monoxide, which ultimately plays a role in determining the enthalpy of formation for the carbon atom, clearly a quantity of fundamental importance. It transpires that the long-quoted standard enthalpy of formation of the carbon atom (711.49 ± 0.45 kJ mol−1 at 0 K; 716.68 ± 0.45 kJ mol−1 at T = 298 K from the CODATA compilation10) relies solely on the bond dissociation energy of carbon monoxide (CO) (as well as the thermochemistry of COwhich was determined by considering experimental calorimetry,11−14 the study of high-temperature equilibrium of CO, CO2, and O2,15,16 as well as the Boudouard reaction involving the equilibrium of CO, CO2, and graphite15,17and that of the oxygen atom). The CODATA value for D0(CO) is taken from a Received: June 27, 2017 Revised: September 6, 2017 Published: September 7, 2017 8799
DOI: 10.1021/acs.jpca.7b06221 J. Phys. Chem. A 2017, 121, 8799−8806
Article
The Journal of Physical Chemistry A 1955 study of predissociation of CO (B1Σ+) by Douglas and Møller,18 which was originally intended to distinguish between the contending high (∼11 eV) or low (∼9 eV) estimates of the dissociation energy favored by, among others, Pauling19 and Herzberg20 (low values) as well as Kistiakowsky21 and Brewer22 (high values). Perhaps as a consequence of the motivation for that study, which was essentially qualitative in nature, the value was determined by a method of data analysis that was not particularly rigorous, using simple straight lines instead of the so-called limiting curves of dissociation. Nevertheless, this rather imprecisely determined value of Δf H(C(g)) attracted essentially no attention for 50 years. This, despite its considerable importance in computational chemistry, where thermochemical parameters are often determined by calculating the “total atomization energy” (the entire molecular binding energy with respect to constituent atoms in their ground state) and then determining Δf H of the target species by removing the contributions from the unbound atoms, which are based on literature values. Focusing on this issue, the ATcT project has motivated highly accurate calculations of this quantity (D0(CO))23,24 and a new photoionization study of CO in which the appearance energy of C+ was precisely determined.25 In addition, the original data from ref 18 were analyzed using limiting curves of dissociation, and the value of D0(CO) was revised upward by some 25 cm−1 (0.30 kJ mol−1). These recent estimates, along with other relevant data, have led to the current ATcT estimates of Δf H(C(g)) of 711.401 ± 0.050 (0 K) and 716.886 ± 0.050 (298.15 K) kJ mol−,19 which are consistent with, but nearly an order of magnitude more accurate than, those from the CODATA compilation. It is worthwhile to explicitly mention that the thermochemical networks in ATcT contain not just original experimental data but also high-quality (and calibrated to some degree) ab initio data that come from computational thermochemistry. The carbon atom example is a case in point: the quoted enthalpies of formation above come from the solution of a thermochemical network, and of the 10 most important determinations contributing to the provenance of Δf H(C(g)), four come from highlevel quantum chemical calculations. This combination of theoretical and experimental information is an important feature of ATcT; high-quality experiments and theory provide the raw materials that lead to accurate thermochemical parameters. Beyond this, and again exemplified by the example of C(g), ATcT sometimes also uses published data that has been reanalyzed with appropriate, and often sophisticated, techniques. The present paper is an example of such a contribution and focuses on the adiabatic ionization energy of hydrogen peroxide (HOOH). This quantity was measured by one of us (B.R.) using photoionization mass spectrometry (10.631 ± 0.007 eV),26 to obtain a value that is consistent with a previous determination of 10.62 ± 0.02 eV.27 The implied ATcT value,28 which is given by the difference in the ATcT Δf H values of the ion and neutral at 0 K, is 10.637 ± 0.006 eV. However, there is a recent study29 that reports an adiabatic ionization energy of 10.685 ± 0.005 eV, which is welloutside the range of values consistent with ATcT. Given the stoichiometry of this molecule, this fundamental quantitythe ionization energy of HOOHhas potentially significant impact on ions of compounds involved in hydrogen combustion and, via their ionization energies, several key chemical species. The authors of ref 29 investigated two plausible assignments for the origin band in the photoelectron spectrum: their preferred assignment (10.685 ± 0.005 eV) and one at a lower value of 10.649 ± 0.005 eV. The latter overlaps the ATcT error range, although just barely so, but is outside the ranges given by
refs 26 and 27. However, the authors of ref 29 state that their determination is far from certain and hope that their study will “stimulate ... interest in this problem to test the assignments presented and the derived AIE”. This work takes up that challenge. In the following, the ionization energy of HOOH is determined using three distinct approaches. First, we apply the HEAT approach from computational thermochemistry24,30,31 to this problem. In addition, we perform an elaborate temperaturedependent Franck−Condon simulation of the photoelectron spectrum, which is a nontrivial undertaking, since the electronic structure of the cation is complex and is further complicated by the large amplitude motion associated with the torsional mode in this molecule. Moreover, the dihedral angle differs by roughly π/2 in the two electronic states studied, so it is imperative to treat the large amplitude motion appropriately. This calculation allows us to make a direct comparison with the spectrum of ref 29, as well as to analyze the photoionization efficiency curve produced in ref 26. It will be shown conclusively that the alternate assignment by the authors of ref 29 was indeed the correct one, and that the three determinations: direct calculation and reanalysis of the experimental data from refs 26 and 29 are in mutual agreement. Finally, all of these results are added to the ATcT database, and a new value for the adiabatic ionization energy of HOOH is determined.
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RESULTS Quantum Chemical Determination. The 1A electronic ground state of HOOH and the ground 2Bg state of its cation were treated with the composite thermochemical methods known as HEAT-345(Q) and HEAT-456QP,24 albeit with modifications motivated by both practical and necessary considerations. First, the equilibrium geometries of the two species (which have C2 and C2h symmetry, respectively) were optimized at the CCSD(T)33 level of theory in the frozen core (fc) approximation using a triple-ζ atomic natural orbital basis designated as ANO1.34,35 The standard HEAT protocol, which has been extensively benchmarked,24,30,31 is based on geometries calculated at the CCSD(T) level of theory, but with the correlation-consistent cc-pVQZ basis36 in an all-electron (ae) calculation.30 The choice of the ANO1 basis is perhaps preferable for two reasons: the geometry optimization andespecially the evaluation of the zero-point energy are significantly less expensive, and the ANO1 basis has been shown to provide excellent estimates of the positions of vibrational fundamentals35 (and therefore, logically, the zero-point energy) when used in conjunction with CCSD(T). The effect on the energy of using the different geometry (fc-ANO1 vs ae-cc-pVQZ) is likely to be negligible, as was discussed in ref 24. At the fc-CCSD(T)/ANO1 geometries, the electronic energy contributions to HEAT were evaluated according to the standard protocols of the HEAT-345(Q) and HEAT-456QP approaches. That is, the total electronic energy is partitioned as follows: Eelec = ESCF + ECCSD(T) + E T − (T) + E HLC + EREL + ESO + EDBOC
(1)
where ESCF and ECCSD(T) are obtained from ae calculations using the aug-cc-pCVXZ basis sets (X = T, Q and 5 or Q, 5 and 6, for the two methods, respectively) and extrapolating both results to the basis set limit according to the prescriptions given in ref 30. ET−(T) and EHLC (high-level correction) are intended to remedy remaining deficiencies of the CCSD(T) treatment of correlation; the first accounts for the difference between a full treatment of 8800
DOI: 10.1021/acs.jpca.7b06221 J. Phys. Chem. A 2017, 121, 8799−8806
Article
The Journal of Physical Chemistry A Table 1. Contributionsa to the Adiabatic Ionization Energy of the Electronic Ground State of HOOH (in eV) HEAT-345(Q) UHF-based SCF CCSD(T) T-(T) HLC REL ZPE SO DBOC
HEAT-456QP ROHF-based
UHF-based
ROHF-based
increment
total
increment
total
increment
total
increment
total
9.645 1.000 −0.003 −0.009 −0.004 0.015 0 −0.001
9.645 10.644 10.641 10.632 10.627 10.642 10.642 10.641
9.962 0.682 −0.000 −0.011 −0.004 0.015 0 −0.001
9.962 10.643 10.643 10.632 10.628 10.642 10.642 10.641
9.644 0.998 −0.003 −0.010 −0.004 0.015 0 −0.001
9.644 10.642 10.638 10.629 10.624 10.639 10.639 10.638
9.961 0.680 −0.000 −0.011 −0.004 0.015 0 −0.001
9.961 10.641 10.641 10.630 10.625 10.640 10.640 10.638
a
As calculated by the modified HEAT protocols described in the text. The value determined from each component of the HEAT energy is given, along with running totals, for both calculations based on both unrestricted and restricted open-shell reference functions for the ground state of the cation. The derived ionization energy, with a plausible 2σ error range, is 10.638 ± 0.012 eV (see text).
triple excitations (CCSDT37−39) and the perturbative treatment of CCSD(T), while EHLC endeavors to account for remaining “high-level” correlation effects. The triples correction involves basis set extrapolation from fc calculations done with the cc-pVTZ and cc-pVQZ basis sets, and the final correction is obtained (again in the fc approximation) with CCSDT(Q)40 (HEAT-345(Q)) or CCSDTQP (HEAT-456QP)41 with the economical cc-pVDZ basis. The remaining corrections for relativistic, spin−orbit, and the diagonal Born−Oppenheimer term (the adiabatic correction) are calculated according to the prescriptions given in refs 30 and 31. The spin−orbit term does not enter into the current calculations; HEAT treats these interactions only to leading order, which vanishes for nondegenerate electronic states. The remaining contribution to the HEAT energy is the zeropoint vibrational correction (EZPE), specifically E HEAT = Eelec + EZPE
constants necessary for VPT2 necessarily requires calculations to be done at lower-symmetry geometries. Moreover, unphysical harmonic frequencies are obtained for this species, for reasons that are well-known and discussed, for example, in refs 46 and 47. To obtain a suitable potential energy surface for calculations, we used EOMIP-CCSD(T)(a),48 which is free of artifacts from symmetry breaking.47 At the fc-EOMIP-CCSD/ANO0 level used to construct the potential energy surface used for the simulation described in the next subsection, variational and VPT2 calculations gave essentially identical zero-point energies (within 3 cm−1), so the strategy taken here was to evaluate the ZPE of the ion using VPT2. Accordingly, the final cation ZPE of 5844 cm−1 was obtained at the fc-EOMIP-CCSD(T)(a)/ cc-pVQZ level of theory with VPT2, the basis set chosen to be consistent with the surface used in the variational calculation for the neutral species. Despite the issues described above, we are confident that the differential zero-point energy between the neutral and the cation (118 cm−1) is in error by no more than 40 cm−1 (0.005 eV). The HEAT-345(Q) and HEAT-456QP determinations of the ionization energy are fully documented in Table 1. Given the fairly significant spin contamination of the cation unrestricted wave function, it was deemed worthwhile to perform calculations with both unrestricted Hartree−Fock (UHF, which is the standard approach for HEAT-based treatments of open-shell systems) and restricted open-shell Hartree−Fock (ROHF) reference functions. While significant differences are indeed seen at the SCF level, the characteristic near-invariance of coupledcluster energies obtained with methods that include single excitations is apparent: the corresponding ionization energies differ by less than 1 meV. When all contributions are included, ionization energies obtained from HEAT-345(Q) and HEAT456QP are 10.641 and 10.638 eV, respectively. Because of the difficulties associated with zero-point energies described in detail above, it is wise to be somewhat conservative in evaluating the magnitude of the uncertainty. While the standard HEAT protocols have errors that would suggest conservative (2σ) error bars somewhat less than 0.01 eV in this case, we will err on the side of caution and recommend an adiabatic ionization energy of 10.638 ± 0.012 eV. Note that the present determination is in fact very close to an ab initio calculation documented in ref 29. On the basis of the UCCSD(T*)-F12 approach, these workers obtained a best estimate adiabatic ionization energy of 10.66 eV, which is in good agreement with the present calculation. Attention is now turned toward reanalysis of the experimental determinations.
(2)
a matter that is deserving of special attention. Most of the molecules in the standard HEAT calibration set (in which the accuracy obtained for enthalpies of formation with HEAT345(Q) and HEAT-456QP is better than 0.5 kJ mol−1) are relatively rigid systems, and the treatment of anharmonicity provided by second-order vibrational perturbation theory (VPT2)42 is both appropriate and adequate. However, in HOOH, there is a large-amplitude torsional motion in the ground state with a relatively small barrier to interconversion of the two enantiomers and a sizable (11 cm−1) tunneling splitting of the ground vibrational state; the propriety of VPT2 can certainly be questioned here. Thus, the determination of the ZPE used in the original benchmark calculations (done with ae-CCSD(T)/cc-pVQZ) will be abandoned here. For HOOH, we chose to use a variational zero-point energy of 5726 cm−1 obtained with the fc-CCSD(T)/cc-pVQZ potential energy surface of Koput et al.,43 a result that was calculated with the NITROGEN program44 as part of the present research. Although this value compares favorably with the fc-CCSD(T)/ ANO1 VPT2 determination (which of course neglects the tunneling splitting) that gives 5711 cm−1, it behooves us to use the variational result that more properly treats the largeamplitude motion. For the cation, which is a considerably less problematic case in terms of nuclear motion, other issues arise due to artifactual symmetry breaking of the wave function. While the use of analytic second derivatives45 provides a means to obtain the harmonic zero-point energy without interference from symmetry breaking, the evaluation of cubic and quartic force 8801
DOI: 10.1021/acs.jpca.7b06221 J. Phys. Chem. A 2017, 121, 8799−8806
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The Journal of Physical Chemistry A Franck−Condon Analysis of Photoelectron Spectrum. Because of the presence of large-amplitude nuclear motion in the HOOH neutral and the stark geometry change that accompanies ionization, a simple harmonic Franck−Condon simulation is not appropriate. The more elaborate approach taken here is to use the global potential of ref 43 for the neutral (vide supra) and a semiglobal upper state potential that was constructed for the cation in the course of this research. The latter is based on fc-EOMIP-CCSD49 calculations using the ANO035 basis set. Energies for the cation were evaluated over a grid of 372 400 points that sample the entire range of torsional motion, and selected points from this set were fit to a function that is polynomial in the stretching and bending coordinates (through fourth degree in the stretches and sixth degree in the bends). The torsion was fit to a cosine series that terminated with cos(2τ); this 708 term function (for which the root-mean-square (RMS) of the fit potential energies was
