calculation of the absolute photoionization cross-sections for ......further reliable quantitative...

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Calculation of the absolute photoionizationcross-sections for C1–C4 Criegeeintermediates and vinyl hydroperoxidesCite as: J. Chem. Phys. 150, 164305 (2019); https://doi.org/10.1063/1.5088408Submitted: 10 January 2019 . Accepted: 02 April 2019 . Published Online: 24 April 2019

Can Huang , Bin Yang , and Feng Zhang

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The Journalof Chemical Physics ARTICLE scitation.org/journal/jcp

Calculation of the absolute photoionizationcross-sections for C1–C4 Criegee intermediatesand vinyl hydroperoxides

Cite as: J. Chem. Phys. 150, 164305 (2019); doi: 10.1063/1.5088408Submitted: 10 January 2019 • Accepted: 2 April 2019 •Published Online: 24 April 2019

Can Huang,1,2 Bin Yang,1 and Feng Zhang2,a)

AFFILIATIONS1Center for Combustion Energy and Key Laboratory for Thermal Science and Power Engineering of MOE,Tsinghua University, Beijing 100084, People’s Republic of China

2National Synchrotron Radiation Laboratory, University of Science and Technology of China,Hefei, Anhui 230029, People’s Republic of China

a)Author to whom correspondence should be addressed: [email protected].

ABSTRACTCriegee Intermediates (CIs) and their isomer Vinyl Hydroperoxides (VHPs) are crucial intermediates in the ozonolysis of alkenes. To betterunderstand the underlying chemistry of CIs and VHPs, progress has been made to detect and identify them by photoionization mass spectro-metric experiments. Further reliable quantitative information about these elusive intermediates requires their photoionization cross sections.The present work systematically investigated the near-threshold absolute photoionization cross-sections for ten C1–C4 CIs and VHPs, i.e.,formaldehyde oxide (CH2OO), acetaldehyde oxide (syn-/anti-CH3CHOO), acetone oxide ((CH3)2COO), syn-CH3-anti-(cis-CH==CH2)COO,syn-CH3-anti-(trans-CH==CH2)COO and vinyl hydroperoxide (CH2CHOOH), 2-hydroperoxypropene (CH2==C(CH3)OOH),syn-CH2 = anti-(cis-CH==CH2)-COOH, syn-CH2 = anti-(trans-CH==CH2)COOH. The adiabatic ionization energies (AIEs) were cal-culated at the DLPNO-CCSD(T)/CBS level with uncertainties of less than 0.05 eV. The calculated AIEs for C1–C4 CIs and VHPs vary from8.75 to 10.0 eV with the AIEs decreasing as the substitutions increase. Franck-Condon factors were calculated with the double Duschinskyapproximation and the ionization spectra were obtained based on the calculated ionization energies. Pure electronic photoionization crosssections are calculated by the frozen-core Hartree–Fock (FCHF) approximation. The final determined absolute cross sections are around4.5–6 Mb for the first and second ionization of CIs and 15–25 Mb for VHPs. It is found that the addition of a methyl group or an unsaturatedvinyl substitution for the CIs does not substantially change the absolute value of their cross sections.

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I. INTRODUCTION

Ozonolysis of alkenes acts as a nonphotolytic source of theOH radical in the troposphere.1,2 The reaction mechanism of ozonewith the gas phase olefin is well established.3–6 Figure 1 illustratesthe general reaction path of ozone with typical C2–C5 alkenes.The addition of O3 to the double bond first forms a shallow vander Waals complex which quickly transforms to a primary ozonide(POZ). The POZ then undergo a concerted cyclization (with a bar-rier of ∼20 kcal/mol7,8) to produce two carbonyl species—a carbonyloxide (known as Criegee intermediate, CI) and a carbonyl coprod-uct. The alkyl-substituted Criegee intermediates are predicted to

undergo an intramolecular 1,4-hydrogen transfer to form isomericvinyl hydroperoxide (VHP) species, which break apart to release OHand vinoxy radicals.9 The CIs and VHPs are potentially importantin altering the oxidizing capacity of the Earth’s atmosphere and inchanging the rate of formation of secondary organic aerosol (SOA)through reaction with NOx, Sox, and water.10,11

To probe the underlying chemistry of these important reac-tions in the atmosphere, experimental tools are highly desiredfor the detection and quantification of CIs and VHPs. In recentyears, synchrotron-based, single-photon mass spectrometry hasshown to be a powerful method for analyzing these reac-tive Criegee intermediates.12–18 Vereecken et al.19 identified six

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FIG. 1. Reaction mechanism for the ozonolysis of C2–C5 alkenes. The corre-sponding Criegee intermediate produced from each alkene is also listed andshown in blue.

prototypical CIs—CIs produced through ozonolysis of ethylene,propene, isobutylene, and isoprene—that serve as the first steptoward a better understanding of the various CIs in the troposphere.Four of them—CH2OO, syn-CH3CHOO, anti-CH3CHOO, and(CH3)2COO (acetone oxide)—have been successfully detected bythe synchrotron-based tunable photoionization mass spectrome-try (PIMS).12–14,16,18 The smallest CI-CH2OO was identified byits mass to charge ratio (m/z) and from the agreement in theonset and shape of its photoionization spectrum with theoreti-cal predicted Frank-Condon spectrum by Taatjes et al.12,13 Withthe same methodology, the two distinct CH3CHOO conformers,syn- and anti-,14 and later the (CH3)2COO16,18 were detected bythe same group. In the previous PIMS experiments, the substi-tuted CIs and their isomers—VHPs—are distinguished by theirdifferent Franck-Condon spectra since they show similar ioniza-tion energies.12–14,16–18 The unsaturated C4 Criegee intermediates,syn-CH3–anti-(cis-CH==CH2)COO and syn-CH3–anti-(trans-CH==CH2)COO, are produced from ozonolysis of isoprene. These twospecies are of particular importance from the perspective of atmo-spheric chemistry4 because they will facilitate our understandingof the underlying chemistry of larger and more complicated CIs,especially biologically important species (e.g., isoprene and ter-penes) derived CIs. However, until now, very limited informationis obtained for the C4 CIs.20 Beyond detection and identification ofthe CIs and VHPs, the quantification requires knowledge of theirabsolute photoionization cross sections.

Measuring cross section requires special setups for detect-ing both the species under study and a reference compound.21–23The cross sections of stable species can be measured with highaccuracy, with an uncertainty factor ranging from 2% to 20% formolecules.21,24–31 For some radicals, the uncertainty factors can be20%–30%.23,32,33 Unfortunately, the experimental determination ofabsolute photoionization cross sections for highly reactive speciesremains a significant challenge. Due to the difficulty in quantita-tively produce these active species, the cross sections can only beestimated with large uncertainties.34,35 The development of the theo-retical methods shows great potential for obtaining cross sections of

those elusive species.33,36–38 Lucchese and McKoy used the frozen-core Hartree–Fock (FCHF) method39,40 to study the photoioniza-tion cross sections of a series of species including carbon dioxide,40methane,41 and acetylene.42 Stephens and McKoy43 calculated thecross section of hydroxyl radical with multiplet-specific Hartree-Fock potentials and numerical photoelectron continuum orbitalsobtained by the iterative Schwinger variational method. Veseth andKelly44 obtained the cross section of OH based on an integral equa-tion that relates the polarizability (calculated by many-body pertur-bation theory) on the imaginary frequency axis to the photoion-ization cross section. Recently, Moshammer et al.37 employed theFCHF method39,40 to calculate the photoionization cross section ofthe important intermediate—keto-hydroperoxide (KHP)—in com-bustion. Krylov et al.36 used the equation-of-motion coupled-clusterDyson orbitals and a Coulomb photoelectron wave function toobtain accurate cross sections of the radical species O and OH whichwere validated with PIMS experiments.33 Both the FCHF methodand the method that employs the Dyson orbital are proved to beaccurate in providing absolute cross sections. The average uncer-tainty is shown to be less than a factor of two.36,37,45 In this work,we use the FCHF method which is more efficient for large moleculesto obtain the near threshold cross sections for a series of CIs andVHPs.

This paper is organized as follows. We first obtain the accu-rate IEs and cross sections for these target species in a systematicmanner. Then, the calculated data are used to derive the isomericcomposition of CIs and VHPs in previous PIMS experiments. Also,by molecular orbital analysis, some general discussions regardingthe effect of substitution on the electronic transition moment willbe made.

II. METHODSA. Ionization energy

Previous calculations have confirmed that the dominant con-figuration of the Criegee intermediates is the singlet zwitterion.46Hence, single reference methods can sufficiently describe the elec-tronic structure of them.8,46,47 The geometries of both the neutralmolecules and the corresponding cations of the CIs and VHPs wereoptimized at the M06-2X/aug-cc-pVTZ level48 in this work. As sug-gested by Taatjes et al.,14,16 the first and second ionization ener-gies of the CIs are very close to each other [delta VIE = 0.096 eV,0.175 eV, and 0.18 eV for syn-CH3CHOO, anti-CH3CHOO, and(CH3)2COO, respectively]. Thus, the ionization to both A′ and A″cationic states was computed. As for the VHPs, the first excitedcationic state is roughly 2 eV higher in IE than the first ioniza-tion band to the 2A″ state.9,13,16 Therefore, the second ionizationband to the 2A′ cationic state for VHPs was not considered. Fre-quencies and zero point energies (ZPEs) were also calculated atthe M06-2X/aug-cc-pVTZ level.48 The ultrafine integration grid andvery tight SCF convergence criterion were used. A scale factor of0.97149 was employed for the ZPE correction. High-level energieswere obtained by the DLPNO-CCSD(T)50,51 method with the aug-cc-pVXZ, X = T and Q, basis sets.52 The 1/X3 extrapolation for-mula53,54 was used to obtain computed DLPNO-CCSD(T) ioniza-tion energies (IEs) at the complete basis set (CBS) limit. All den-sity functional theory (DFT) calculations were performed using the

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Gaussian 09 program.55 The DLPNO-CCSD(T) calculations wereperformed by the ORCA program package.56

B. Absolute cross sectionThe cross section is calculated as

σ(E) = S(E) ⋅D(E), (1)

where S(E) represents the Franck-Condon overlap envelope andD(E) is the transition moment. The transition moments were com-puted using the ePolyScat code of Lucchese et al.39 within the frozen-core Hartree–Fock approximation.57,58 The single-center expansiontechnique was used with lmax = 50. The molecular orbitals werecalculated from restricted Hartree–Fock wave functions with aug-cc-pVTZ basis set52 using the geometries optimized at the level ofM06-2X/aug-cc-pVTZ.48 The value of D(E) used in the calculationof the cross section is the average value of the length gauge and thevelocity gauge.37

Franck-Condon Factors (FCFs) were derived by using the equi-librium geometries and frequencies for the A″X and A′X statesobtained with M06-2X/aug-cc-pVTZ. For each molecule, the equi-librium geometry on the ground state was obtained at the same level.The FCFs were computed with the double-harmonic approxima-tion using the ezSpectrum code,59 and the Duschinsky rotation wasincluded within the framework of the harmonic oscillator model.For CH2CHOOH, the optimized geometry of the ground electronicstate has no symmetry, with the H atom of the OH group out ofthe CH2CHOO molecular plane. A planar CH2CHOOH structureof Cs symmetry is a first-order saddle point, with an imaginary fre-quency corresponding to the OH wagging mode. As suggested byTaatjes et al.,14 the planar Cs saddle point is only ca. 0.2 kcal/molabove the C1 true minimum at the level of UCCSD(T)-F12/VQZ-F12. Therefore, the OH wagging vibrational mode was treated as afree internal rotation,14 which was also adopted by this work. Thelowest electronic state of CH2CHOOH+ is a 2A″ state with a Cs pla-nar geometry. In FCF calculations, which are formulated within theharmonic oscillator model, it is inappropriate to include the inter-nal rotation mode. Consequently, the OH wagging mode has beenignored and the planar saddle point Cs structure of CH2CHOOHhas been used in the FCF calculation. Similar to CH2CHOOH,larger vinyl hydroperoxides also have loose OH wagging modes.Those modes were treated in the same way as in CH2CHOOH.The Lorentzian function was used for the line shape broadeningof the calculated Franck-Condon transitions. One thing to note isthat the Franck-Condon calculation assumes that the resonant statesdo not contribute to the ionization cross section. In the presentwork, autoionization and other complex nonradiative processes(e.g., photodissociation and internal conversion) have not beenincluded.

III. RESULTS AND DISCUSSIONA. Ionization energies for C1–C4 CIs and VHPs

Figure 2 shows the structures of the ten C1–C4 CIs and VHPsstudied in the present work. For simplicity, these species will bereferred to by the abbreviations shown in Table I. The computed

FIG. 2. Structures of the carbonyl oxide substitutions and the corresponding vinylhydroperoxides examined in this work.

adiabatic ionization energies (AIEs) and vertical ionization ener-gies (VIE) were summarized in Table I along with the experimentaland theoretical values in the literature for comparison. For C1–C3species for which high-level calculations are available, we comparewith those previous values mainly to validate our computed resultsand give the uncertainty of the current calculations. For the C4 CIsand VHPs, i.e., the intermediates produced in ozonolysis of iso-prene, one of the most abundant volatile organic compounds in theatmosphere, their ionization energies are calculated for the first timein this work.

Generally speaking, our calculations agree very well with theavailable measurements and calculations with a deviation of lessthan 0.05 eV. The separations between the first and second cationstates of all the Criegee intermediates are within 0.5 eV. For CH2OO,its first and second ionization states have almost identical energies assuggested by Nguyen et al.46 and Taatjes et al.12 Then, for the sub-stituted CIs, the computed ionization energy to the Ã2A′ states isalways slightly higher than that to the X̃2A″ states (the AIEs differby 0.043–0.34 eV). VHPs have very similar ionization energies withtheir corresponding CI isomers, differing from 0.01 to 0.1 eV. Thealmost negligible difference suggests that it will be very hard or evenimpossible to distinguish CIs from VHP experimentally by the ion-ization threshold alone. A full ionization spectrum is always neededto clearly interpret the experimental measurements, which will bepresented in Sec. III B.

B. Absolute cross sections1. Formaldehyde oxide (CH2OO)

Figure 3 illustrates the computed photoionization cross-sectionspectrum for the CH2COO ionization to the Ã2A′ and X̃2A″ states,and Fig. 4 shows the corresponding computed FCFs. For ionizationto the Ã2A′ state, the computed FCF gives a very strong adiabaticvibrational component. It indicates that the AIE and VIE positionsof the second ionization band of CH2COO coincide. This is in

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TABLE I. Calculated adiabatic ionization energy (AIE) and vertical ionization energy (VIE) of the C1–C4 Criegee intermediates and the vinyl hydroperoxides and values from theprevious literature (Unit: eV).

Theoretical ExperimentalMolecular Species Target AIE VIE AIE in the values in thestructure (abbreviation) states CBSa aVQZb CBSa literature literature

CH2OO (1CI) A′ 10.002 10.089 9.98c, 10.02d 9.85e, 10.0f

A″ 9.931 10.014 10.020

anti-CH3CHOO (2CI_a) A′ 9.275 9.402 9.331g

2A″ 9.113 9.243 9.271 9.156g

syn-CH3CHOO (2CI_s) A′ 9.421 9.550 9.474g

A″ 9.378 9.508 9.493 9.378g, 9.28h

CH2HOOH (2VHP) A″ 9.183 9.322 9.711 9.178g, 9.09h

(CH3)2COO (3CI) A′ 8.929 9.099 8.97i

A″ 8.743 8.918 8.936 8.79i

CH2==C(CH3)OOH (3VHP) A″ 8.755 8.936 9.369 8.75i

syn-CH3-anti-(cis-CH==CH2)COO (4CI_sac) A′ 8.839 9.026

A″ 8.499 8.694 8.697

syn-CH3-anti-(trans-CH==CH2)COO (4CI_sat) A′ 8.857 9.049

A″ 8.553 8.750 8.744

syn-CH2 = anti-(cis-CH==CH2)COOH (4VHP_sac) A″ 8.665 8.866 9.088

syn-CH2 = anti-(trans-CH==CH2)COOH (4VHP_sat) A″ 8.580 8.785 9.142

aDLPNO-CCSD(T)/CBS//M06-2X/aug-cc-pVTZ, CBS from aVTZ, aVQZ.bDLPNO-CCSD(T)/aug-cc-pVQZ//M06-2X/aug-cc-pVTZ.cCCSD(T)/CBS//CCSD(T)/aug-cc-pVTZ.46dCBS/QB3.12ePIMS experiment.12fPIMS experiment.13gAverage of the UCCSD(T)-F12a/CBS and UCCSD(T)/F12b/CBS based on geometry optimized by B3LYP/6–311++G∗∗ .14hCCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ.9iThe average of the F12a/CBS and F12b/CBS values based on geometry optimized by B3LYP/6–311++G∗∗ .16

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FIG. 3. The calculated absolute cross sections for photoionization of CH2OO tothe X̃2A″ and Ã2A′ states.

agreement with our calculated ionization energies, where the AIEto Ã2A′ state differs by only 0.018 eV from the vertical ionization.The photoionization cross section spectrum that results from thisdirect ionization process shows a sharp rise near threshold due tothe onset of vibrational transitions with significant transition prob-abilities. The AIE of CH2COO at ∼9.931 eV arises from a X̃2A″ ←X̃1A′ transition resulting in the ejection of an A″ electron in an

FIG. 4. The computed FCFs of the CH2OO ionization to (a) X̃2A″ and (b) Ã2A′

states.

antibonding π orbital around the COO moiety. The second largestionization is from the OOC bending mode at 10.157 eV. The ion-ization spectrum for the X̃2A″ state extends to a broader range thanthe Ã2A′ state and plateaus at around 10.5 eV. The absolute crosssections for the two states are at the level of 4–5 Mb at energieshigher than 10.3 eV, and the corresponding cross section for theX̃2A″ ← X̃1A′ transition is about 1.4 times as that of Ã2A′ ← X̃1A′transition.

Two experiments successfully captured the ionization spec-trum of CH2OO by using the chlorine atom-initiated oxidation ofdimethyl sulfoxide (DMSO)12 and the reaction of CH2I with O2,13respectively. Figure 5 shows the result of the ionization spectrumof CH2OO in previous experiments12,13 together with the weightedsum cross section of Ã2A′ and X̃2A″ states. The fitting was con-ducted by adjusting the relative ratio between the isomers. A ratioof Ã2A′; X̃2A″ = 3:4 will best fit the two experimental data.12,13The weighted sum value rises at an energy that is 0.08 eV largerthan the measurement in Ref. 12 and 0.05 eV smaller than that

FIG. 5. Photoionization efficiency spectrum of the Criegee intermediate CH2OO(formaldehyde oxide) from experiments of (a) Taatjes et al.12 and (b) Welz et al.13

together with our fitted values (red line) using the newly calculated cross sections.

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in Ref. 13. The second experiment13 is a direct measurement ofthe CH2OO signal, while the first12 is deduced from the differenceof two measurements. Our calculation is closer to the second. Ifadjusting our computed results by 0.05 eV [this is also the differ-ence between our calculated AIE and the CCSD(T)/CBS value fromRef. 46], our calculation will match with the experimental result verywell.

2. Acetaldehyde oxide (syn-/anti-CH3CHOO)and vinyl hydroperoxide (CH2CHOOH)

CH3CHOO is the smallest CI that has two conformers (anti-and syn-) and also the smallest to have a hydroperoxide isomer.Figure 6 presents the absolute cross sections of the CH3CHOOconformers (A′ and A″ states) and the vinyl hydroperoxide (A″state). The calculated FCFs for all the transitions are provided in thesupplementary material. From Fig. 6, we find that the transitionsfrom both anti- and syn-CH3CHOO to the A′ state are almostadiabatic ionization. The A″ spectrum instead spans a broader rangeand reaches a plateau at higher energies. The cross sections ofthe four transitions of CH3CHOO are around 2–4.5 Mb, with thecross section for the A″ states slightly larger (∼25%) than the A′states.

The computed cross section for vinyl hydroperoxide is quitedifferent from those of CIs in both the magnitude and shape. TheFranck-Condon spectrum of 2VHP [see Fig. S1(e)] has several tran-sition bands that have large transition probabilities. Except for the 0-0 transition, the vibrational mode of C–C bond stretching at 9.38 eVand CO and OO bond stretching at 9.30 and 9.34 eV as well as theircombination modes are the principal contributors to the Franck-Condon spectrum. The ionization spectrum of 2VHP starts from9.183 eV and increases continuously to 9.8 eV. The final deter-mined absolute cross section of 2VHP is about 14 Mb at 9.8 eV,3 times larger than the cross sections of the four transitions fromCH3CHOO.

Using the calculated absolute cross sections, we obtained thecomposition of CH3CHOO and VHP in the experiment of Taat-jes et al.,14 as illustrated in Fig. 7. To reproduce the experimentaldata, 2VHP is unlikely to have substantial proportion because itscross section shows an abrupt increase above its threshold (AIE

FIG. 6. The calculated absolute cross sections for photoionization of syn- and anti-CH3CHOO to the X̃2A″ and Ã2A′ states and for CH2CHOOH.

FIG. 7. Photoionization efficiency spectrum of the m/z = 60 signal from experi-ments of Taatjes et al.14 together with our fitted values (red line) using the newlycalculated cross sections.

= 9.18 eV), while the ion signal in Fig. 7 is almost flat from 9.18 to9.25 eV. As a result, the ratio for the four CI states is deduced as2CI_a(A′)/2CI_a(A″)/2CI_s(A′)/2CI_s(A″) = 5:1:30:50. If VHP isto be included, the ratio of VHP/2CI_a(A′)/2CI_a(A″)/2CI_s(A′)/2CI_s(A″) will be 5:5:1:15:50 to match the signal at 9.5–9.9 eV,but the weighted-sum will be larger than the measurement at 9.37–9.47 eV. Hence, our final determined isomeric composition doesnot include VHP, which is in agreement with the results of Taat-jes et al.14 Despite the uncertainty in the calculation, it is importantto note that the syn-CH3CHOO must constitute a large propor-tion of the CIs to reproduce the measurement. Due to the differentreactivity of the syn- and anti-conformers,11,19,60 the relative ratio isan important factor to properly predict their atmospheric impacts.As suggested by Taatjes et al.,14 assuming the same transitionmoment of all CIs will result in an overall production (90%)of the more stable syn-conformer (3.6 kcal/mol lower than anti-CH3CHOO61). Our calculation confirmed their assumption andgives a ratio of 93/7 for syn-CH3CHOO/anti-CH3CHOO.

3. Acetone oxide [(CH3)2COO]and 2-hydroperoxypropene [CH2==C(CH3)OOH]

As the substitution increases, the ionization energies of CIsand VHPs decrease. As shown in Fig. 8, the first ionization bandof (CH3)2COO to the X̃2A″ state starts from 8.74 eV, 0.37, and0.64 eV smaller than anti- and syn-CH3CHOO, respectively. The2-hydroperoxypropene (3VHP) has almost the same AIE as that of(CH3)2COO to the X̃2A″ state. The two spectra overlap through theionization band, and it is not easy to distinguish between them bythe ionization onset alone. The ionization to the Ã2A′ state has avery strong adiabatic vibrational component; therefore, the ioniza-tion rises sharply at 8.93 eV and soon becomes flat. The ionizationsto Ã2A′ states all show strong adiabatic transitions while ionizationsto X̃2A″ states span about 0.4 eV above the threshold. The VHPshave more complicated Franck-Condon spectra [see Fig. S2(c) ofthe supplementary material], which lead to curved ionization spec-tra. The plateaus can only be reached at ∼1.0 eV above the thresholdenergies. More comparison and discussion about the CIs and VHPsregarding the effect of substitution will be presented in Sec. III C.

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FIG. 8. The calculated absolute cross sections for photoionization of (CH3)2COOto the X̃2A″ and Ã2A′ states and for CH2==C(CH3)OOH.

We applied the above calculated cross sections into two PIMS exper-iments16,18 that have detected (CH3)2COO. The results are shownin Fig. 9. The two experiments are reproduced very well at energieslower than 9.5 eV. At energies higher than 9.7 eV, the signal cor-responds to the ionization of hydroxyacetone [CH3C(O)CH2OH].Different from the case in experiments of CH3CHOO,14 here, the

FIG. 9. Photoionization efficiency spectrum of the m/z = 74 signal from experimentsof (a) Taatjes et al.16 and (b) Chhantyal-Pun et al.18 together with our fitted values(red line) using the newly calculated cross sections.

VHP also contributes to the total ionization spectrum. The ratiofor 3CI(A′)/3CI(A″)/3VHP obtained by fitting the two experimentalsignals is 5/1/2. A larger proportion of 3VHP will result in a betterprediction at high energies (9.2–9.4 eV), while a worse performanceat low energies (8.9–9.2 eV).

4. syn-CH3-anti-(cis-CH==CH2)COO,syn-CH3-anti-(trans-CH==CH2)COO,syn-CH2 = anti-(cis-CH==CH2)-COOH,and syn-CH2 = anti-(trans-CH==CH2)COOH

The C4 CIs are the ozonolysis products of isoprene (the mostabundant biogenic volatile organic compound);4,19 thus, their com-position in the atmosphere as well as their reaction kinetics willhave a crucial impact on the atmospheric chemistry.4,19 The above-mentioned small CIs and VHPs serve as a prototype to understandthe CI chemistry; however, until now, very limited information isobtained for the C4 CIs. Here, we present the calculated cross sec-tions for the C4 CIs and VHPs for the first time, which will ben-efit their identification and quantification in future experimentalstudies.

The 4CI_sac and 4CI_sat differ only in the stereochemistryabout the C==C double bond. Their transitions to the A′ states haveAIEs of 8.839 and 8.857 eV, respectively. The computed FCFs (seeFig. S3 of the supplementary material) give very similar adiabatictransition bands. Consequently, as illustrated by Fig. 10, the two ion-ization spectra (red solid line and yellow dashed-dotted line) coin-cide with each other with the almost identical transition moment(2.4 Mb at 9.2 eV). The X̃2A″ ← X̃1A′ transitions of 4CIs have largergeometry change in the ionization process compared with the tran-sitions to the Ã2A′ state. For X̃2A″ ← X̃1A′ transitions of 4CI_sac(blue long-dash line), the computed FCFs suggest that besides the 0-0 transition, six or more vibrational components of this progressionhave appreciable intensities. The ionization band ends at ∼8.9 eVwith an absolute cross section of 10 Mb. For 4CI_sat (green shortdash line), the ionization to the X̃2A″ state has an onset at 8.55 eV.The modes that substantially contribute to the FCFs are the bend-ing and stretching modes of the C==C moiety and the bending modeover the CCCC skeleton. This ionization band plateaus at ∼9.0 eV,

FIG. 10. The calculated absolute cross sections for photoionization of C4 CIs andVHP.

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and the absolute value is ∼4 Mb. The two VHP isomers have ioniza-tion energies between the lowest and the highest ionization energiesof 4CIs, which means that it will be difficult to distinguish themapart. The VHPs generally have large transition moment, 11 Mband 18 Mb, respectively, for 4VHP_sac and 4VHP_sat at 9.2 eV.As suggested by Vereecken et al.,19 the facile H-migration of the4CI_sac leads to the vinyl hydroperoxide which will rapidly produceOH. Thus, it should be a more important OH source comparing to4CI_sat. The absolute cross sections provided here will enable quan-tification of these illusive species and improve our understanding oftheir contribution in the atmosphere.

C. The effect of substitution on the electronictransition moment

The total absolute cross section σ of a species consists of twoparts: the electronic transition moment D and the Franck-Condonenvelop S. While the Franck-Condon factor varies as the substitu-tion changes since it is strongly structure dependent, the electronictransition moment that reflects the full contribution of the relevantmolecular orbital of the neutral might not vary significantly. There-fore, it is reasonable to analyze the transition moment—the onethat determines the magnitude of the absolute cross section sepa-rately and obtain some general observations that can help to esti-mate the cross section of an unknown species. The similar protocolhas been used by Xu and Pratt,62 in which the experimentally mea-sured cross section of propargyl is compared with those that havesimilar orbitals at photon energies above the full Franck−Condonenvelope. The idea is later confirmed by Dodson et al.23 who inves-tigated the cross sections of HO2 and H2O2 that exhibit very similarHOMOs. In this section, we will follow the protocol introduced byXu and Pratt62 and focus on the transition moment itself as a wayto understand the cross sections of the CIs and VHPs studied in thiswork.

Figure 11 illustrates the calculated transition moments of theten CIs and VHPs together with the molecular orbital of the ejectedelectron for selected states. The value given here is the average valueof the calculated transition moment over the range of the ioniza-tion threshold to 1.6 eV higher than that. The average transitionmoments of C1–C4 Criegee intermediates to the Ã2A′ state are closeto each other in the range of 2.7–4.1 Mb. As shown in Fig. 11(a), theorbitals of these six CIs are basically the same, belonging to the norbital of the OO group. Similarly, the ionizations of the CIs to theX̃2A″ state are in the same magnitude (around 5 Mb). The ejectedelectrons are from the π∗ orbitals of the COO moiety. One excep-tion is from the 4CI_sac which has an average transition momentof 9 Mb. The average transition moments of VHPs are from 13 Mbto 28 Mb, which are much larger than that of CIs. The scatteringamong the VHPs is because as the substitution increase from -CH3to -CH==CH2, the HOMOs of VHPs change gradually (see Fig. S4of the supplementary material). In conclusion, for CIs, the HOMOsof the species almost stay the same, resulting in similar transitionmoments. On the contrary, for the VHPs, the HOMOs change withsubstitutions, and thus, the transition moment of each moleculevaries considerably. Our results support the method proposed by Xuand Pratt62 from the theoretical perspective to reasonably estimatethe cross section by molecular orbital analysis.

FIG. 11. The calculated average electronic transition moments of the CIs andVHPs. The average value was calculated in the range from the ionization thresh-old to 1.6 eV above the ionization threshold. The molecular orbitals of theejected electrons from the (a) Ã2A′ state and (b) X̃2A″ state are shown forcomparison.

IV. CONCLUSIONThe absolute photoionization cross-sections for ten C1–C4

Criegee intermediates and vinyl hydroperoxides have been system-atically investigated using theoretical methods. The photoionizationenergies were calculated at the level of DLPNO-CCSD(T)/CBS. Thegap between the first and second ionization energies for CIs is verysmall with a magnitude of ∼0.2 eV. The photoionization energiesof CIs are found to be similar to their corresponding VHP isomers.Using the calculated vertical ionization energies, the near thresholdabsolute photoionization cross sections have been computed by theFCHF method with inclusion of the Frank-Condon spectrum. Thecross sections of the studied CIs are around 5 Mb, while those ofVHPs are in the range of 15–25 Mb. Based on the calculated crosssections, we derived the relative composition of the CIs in previ-ous experiments. Moreover, by comparing the average transitionmoments combined with the molecular orbital analysis, we found

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that our calculations for the CIs are consistent with the estima-tion method proposed by Xu and Pratt.62 The electronic transitionmoment near threshold is similar for species that have similar orbitalfor the ejected electron. Thus, the total cross section can be evalu-ated by using the value of the species with similar orbital and theninclude the vibrational part (the Frank-Condon factor) if measure-ment or detailed calculation is not available. Our data for C1–C4Criegee intermediates and vinyl hydroperoxides will be valuable toquantify these crucial species and ultimately enable capture of theirfascinating chemistry.

SUPPLEMENTARY MATERIAL

See supplementary material for the calculated Franck-Condonfactors of the ionization from C2–C4 species, the molecular orbitalsof the ejected electrons from the X̃2A″ states of the C1–C4 VHPs.

ACKNOWLEDGMENTSThis work was supported by the National Key Research and

Development Program of China (Grant No. 2016YFC0202600) andthe Joint Fund of the National Natural Science Foundation of Chinaand the Chinese Academy of Sciences (Grant No. U1832192). Thiswork was also supported by the Natural Science Foundation ofChina (Grant Nos. 51876199 and 91541112). The quantum chemi-cal calculations have been carried out on the supercomputing systemin the Supercomputing Center of University of Science and Tech-nology of China. We are grateful to Professor Robert R. Lucchesefor kindly providing us the ePolyScat code. We thank ProfessorGuangjun Tian for the helpful discussion on the calculation of theFrank-Condon factors.

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calculation of the absolute photoionization cross-sections for ......further reliable quantitative...

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