doi.org/10.26434/chemrxiv.7665620.v1

Theoretical Investigations of Photoionization Efficiency of NaphthaleneChih-Hao Chin, Tong Zhu, John ZH Zhang

Submitted date: 02/02/2019 • Posted date: 04/02/2019Licence: CC BY-NC-ND 4.0Citation information: Chin, Chih-Hao; Zhu, Tong; Zhang, John ZH (2019): Theoretical Investigations ofPhotoionization Efficiency of Naphthalene. ChemRxiv. Preprint.

The equilibrium geometry and 48 vibrational normal-mode frequencies of the neutral and cationic ground stateand the cationic first excited states of naphthalene isomers were calculated and characterized in the adiabaticrepresentation by using the complete active space self-consistent field (CASSCF) and second orderperturbation theory (CASPT2). Photoionization-efficiency (PIE) spectrum of molecular beam conditions inenergy range 8 - 11 eV were determined by Kaiser et al. and they were analyzed using time-dependentdensity functional theory calculations (TDDFT). CASSCF calculations and PIE spectra simulations byone-photon excitation equations were used to optimize the cationic excited (D1) and neutral ground (S0) statestructures of naphthalene isomers. The photoionization-efficiency curve was attributed to the S0 D1electronic transition in naphthalene, and a curve origin was used at 8.14 eV. The ionization-induced geometrychanges of the bases are consistent with the shapes of the corresponding molecular orbitals. The displacedharmonic oscillator approximation and Franck-Condon approximation were used to simulate the PIE curve ofthe D1 S0 transition of naphthalene, and the main vibronic transitions were assigned for the ππ* state. Itshows that the vibronic structures were dominated by one of the xxx active totally symmetric modes, with v8being the most crucial. This indicates that the electronic transition of the D1 state calculated in the adiabaticrepresentation effectively includes a contribution from the adiabatic vibronic coupling through Franck-Condonfactors perturbed by harmonic oscillators. The present method can adequately reproduce experimental PIEcurve in the molecular beam condition.

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Theoretical investigations of photoionization efficiency of

naphthalene

Chih-Hao Chin1*, Tong Zhu1,2* and John Z.H. Zhang1,2,3

1School of Chemistry and Molecular Engineering, East China Normal University, Shanghai, 200062,

China 2NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai, 200062, China 3Department of Chemistry, New York University, New York 10003, United States

E-mail addresses: zhjin@chem.ecnu.edu.cn (C.-H. Chin), tzhu@lps.ecnu.edu.cn (T. Zhu)

ABSTRACT The equilibrium geometry and 48 vibrational normal-mode frequencies of the neutral and cationic ground state and the cationic first excited states of naphthalene isomers were calculated and characterized in the adiabatic representation by using the complete active space self-consistent field (CASSCF) and second order perturbation theory (CASPT2). Photoionization-efficiency (PIE) spectrum of molecular beam conditions in energy range 8 - 11 eV were determined by Kaiser et al. and they were analyzed using time-dependent density functional theory calculations (TDDFT). CASSCF calculations and PIE spectra simulations by one-photon excitation equations were used to optimize the cationic excited (D1) and neutral ground (S0) state structures of naphthalene isomers. The photoionization-efficiency curve was attributed to the S0 ® D1 electronic transition in naphthalene, and a curve origin was used at 8.14 eV. The ionization-induced geometry changes of the bases are consistent with the shapes of the corresponding molecular orbitals. The displaced harmonic oscillator approximation and Franck-Condon approximation were used to simulate the PIE curve of the D1 ¬ S0 transition of naphthalene, and the main vibronic transitions were assigned for the ππ* state. It shows that the vibronic structures were dominated by one of the xxx active totally symmetric modes, with v8 being the most crucial. This indicates that the electronic transition of the D1 state calculated in the adiabatic representation effectively includes a contribution from the adiabatic vibronic coupling through Franck-Condon factors perturbed by harmonic oscillators. The present method can adequately reproduce experimental PIE curve in the molecular beam condition.

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Introduction Polycyclic aromatic hydrocarbons (PAHs), organic molecules consisting of fused benzene rings, are known to be major air pollutants resulting from incomplete combustion of fossil fuels and also, together with their cations, have been proposed as possible carriers of the unidentified infrared emission bands form various interstellar objects.1,2 PAHs which are precursors to soot formation released into the atmosphere, their toxic and carcinogenic pose a risk to human health and play a significant role in degradation of air quality.3-7 PAHs are abundant in interstellar media and the low ionization energies of these species make them susceptiable to the photoelectronic effect upon absorption of a photon in the far-ultraviolet regin.8,9 Their planar structures allow photoelectrons to readily escape and contribute to the observed heating of interstellar cloud,10 which is contributed to by PAH clusters and early studies on single-photon photoionization of the PAHs such as pyrene and coronene were conducted over a broad photon energy range and aimed at facilitating estimations of interstellar gas heating as a results of photoionization.11 The formation mechanisms of the two-ring species naphthalene and indene were studied over temperature and pressure ranges that span the extreme environments relevant to many flames and interstellar media.12 In combustion chemistry research, the molecular-beam mass spectrometry (MBMS) using electron impact ionization (EI) or synchrotron-based photoionization (PI) for qualitative species may have advanced to be potentially the most often applied diagnostics for the characterization of the chemical reaction pathways, since an overview can be provided of basically all stable and short-lived transient species, such as radicals, occurring in the process. Such information is a prerequisite for the development and improvement of kinetic reaction mechanisms and thus extremely valuable especially for alternative fuels13 and novel operation conditions.14 Using PI-MBMS with tunable vacuum ultraviolet (VUV) radiation from synchrotrons has played a crucial role because of its capability of isomer identification, making use of the improved energy resolution with respect to electron impact sources and separation of different molecular structures from photoionization efficiency (PIE) curves. While immensely useful, PI-MBMS techniques are not without limitations, especially in situations where distinction is needed of isomers that show close-lying ionization energies and where vibrionic structure is needed for enhanced differentiation. Naphthalene which is one of the sixteen PAHs listed priority controlled by the US Environmental Protection Agency (EPA), is a highly carcinogenic environmental contaminant for human, it is easily produced during combustion of gasoline (such as benzene,15 toluene,16 ethylbenzene17) and has been observed by tunable synchrotron VUV photoionization technology.18 Parker et al. revealed that naphthalene can be

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synthesized via the reaction of the phenyl radical (C6H5) with vinylacetylene (C4H4) via the hydrogen abstraction-vinylacetylene addition (HAVA) reaction, this bimolecular reaction via an barrierless pathway leads to naphthalene (C10H8) plus atomic hydrogen at temperatures as low as 10 K.19, 20 Despite numerous studies on PAH ionization energies, photoionization quantum yields, and photodissociation rates, only a limited number of PAHs had their photoionization efficiency curve measured, calculated, or estimated over wide photon energy ranges. The photoelectron/photoionization spectroscopy provides additional distinctive capability by mass-resolved photoelectron spectra that show an individual electronic and vibrational fingerprint structure for each species and isomers. Combustion-related applications are comparatively recent with isomer-selective analysis of combustion-related gas samples by Bodi et al.21, the first demonstration of TPES in a flame by Obwald et al.22 and a very recent attempt to identify PAHs in a flame by Mercier et al.23. However, the lack of reference photoelectron/photoionization spectroscopy with a resolution suitable for the identification and reliable quantification of (isomeric) species is one of the factors that limit the application of this technique to more challenging situations in combustion chemistry. Our work aims at the unambiguous identification and qualitative amounts of three isomers of C10H8 species in molecular beam condition. Recently, PIE spectra of C10H8 in gas phase has been obtained using VUV photoionization spectroscopy.15, 24, 25 The AIE and relative intensities of the bands of these species are provided, and this information can be used as a starting point for gas phase measurements and for evaluating the combustion relevance of the species. Identification of different isomers is accomplished by comparing experimental PIE spectra with simulated curves based on calculated adiabatic ionization energies and Franck-Condon factor analysis. Theoretical studies focused on assigning different bands in the PIE spectra of naphthalene, knowledge of the geometric structure for the cationic states is desirable because normal-mode displacement, distortion, and mixing can noticeably affect the FCFs and hence the peak intensities of the spectra. The main objective of the current study was determined the geometry and vibrational frequencies of the cationic state of naphthalene through ab initio calculations and to use the obtained data for assigning and predicting the spectra and cationic state dynamics of naphthalene, respectively. Computational Methods The ground state geometry of naphthalene and its isomers was optimized using density functional theory (DFT) along with the B3LYP method which was used with the corresponding 6-311G(d,p) basis sets.26-28 Full geometry optimizations as well as

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frequency analysis were performed at this level of theory. Excitation energies and optimized geometries were computed by the CASSCF/CASPT2 method as implemented in the MOLPRO program with cc-pVTZ basis set. To obtain more accurate energies, we applied the G3(MP2,CC)//B3LYP modification29, 30 of the original Gaussian 3 (G3) scheme31 for high-level single-point energy calculations. The final energies at 0K were obtained using the B3LYP optimized geometries and zero-point energy (ZPE) corrections according to the following eqn (1):

E0[G3(MP2,CC)] = E[CCSD(T)/6-311G(d,p)] + DEMP2 + E(ZPE) (1) where DEMP2 = E[MP2/G3large] – E[MP2/6-311G(d,p)] is the basis set correction, and E(ZPE) is the zero-point energy. DE(SO), a spin-orbit correction, and DE(HLC), a higher level correction, from the original G3 scheme were not included in our calculations, as they are not expected to make significant contributions into relative energies. The AIE of naphthalene and its isomers can be calculated using the formula

AIE = E0,cation – E0,neutral (2) where E0 represents the zero-point energy corrected total electronic energy. As the process concerns ionization of the neutral closed-shell naphthalene monomer by removing one electron from the highest doubly occupied molecular orbital to form the C10H8+ cation, the spectrum was simulated considering the change of geometry/normal modes/frequencies between the neutral ground state and the low-energy final (ionized) state. Because radical cations are electron deficient, the wave functions are sufficiently compact at low excitation energies that interactions with Rydberg states are negligible. The complete active space self-consistent field (CASSCF) wave functions were obtained using the state averaging technique, all states of a given symmetry are described by a common set of molecular orbitals. The neutral ground state (S0) of naphthalene has been computed using CASSCF by 10 electrons distributed on 10 πorbitals (10e, 10o) and the cationic ground, first excited states (D1) have been computed by 9 electrons distributed on the 10 π orbitals (9e, 10o). CASSCF calculations were performed using both Gaussian without symmetry restrictions and MOLPRO with symmetry restrictions. Where symmetry-restricted calculations were carried out, these are the results quoted below for energy, geometry and gradient vectors. For each normal mode, the Huang–Rhys vibronic coupling parameter, which takes into account the difference in equilibrium geometry and evaluates overlaps of the vibrational wave functions of the two shifted harmonic potentials between the initial and final state were computed. We use the harmonic oscillator approximation, where each multidimensional

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vibrational wave function (initial/final) is expressed as a product of 3N-6 monodimensional wave functions to calculate the FC factors (only the zeroth order term corresponding to a static electronic transition dipole is considered) for excitation from the vibrational ground state of the neutral molecule to the various vibrational states of the ionized molecule.32-34 Each (3N-6) of the normal modes of the final state is projected onto the initial state (3N-6) normal modes in order to take into account that a mixing of the normal modes occurs during the transition between the initial neutral ground state and the ionized final state within the FC approximation. The geometries and harmonic frequencies of C10H8 isomers in its neutral electronic ground state and first cationic state have been calculated with a flexible large cc-pVTZ basis set at a DFT level of theory with the B3LYP. The basic theoretical approach used in the calculation of spectra is now presented

briefly. Let and represent the aforementioned vibronic states in the Born-

Oppenheimer approximation. We consider the energy level of initial (neutral) and finial (cationic) states with the molecular, which describes the coupling between the two

vibronic manifolds by ,

!"#$,&# = ("#$,&#) + ∑

,-.$,/."$ ,/.",1.

$

21.32/."4#" (3)

and

("#",4#") = 5y"#)6(7

)6y4#"8 = 9F"Q"#):(7):F4Q4#"; = 9Q"#):(7"4) :Q4#"; (4)

Here the electronic coupling matrix element is given by (7"4) = 9F":(7):F4; (5)

where denotes the electronic wave functions and represents the

vibrational wave function. In this study, we shall introduce the Placzek approximation, <&# − <4#" = <& − <4 (6) assuming that the electronic energy is much larger than the vibrational energy. Eq(3)

6

becomes

!"#$,&# = 9Q"#):("&) :Q&#; +>>

9Q"#$:("4) :Q4#";⟨Q4#"|(4&

) |Q&#⟩

<& − <4#"4

= BQ"#$C("&) + ∑

("4) (4&

)

<& − <44 CQ&#D = 9Q"#$:!E"&:Q&#;

(7)

!E"& = ("&) + ∑

,-/$ ,/1

$

2132/4 (8)

Although in principle, ab initio calculations of the intensities of the various peaks are possible, they can be performed after calculations of vibronic coupling between different electronic states have been completed. To analyze the spectra, the potential surfaces of the ground and ionic electronic states are required. Frequencies of these two states are nearly identical, the harmonic surfaces and the potential surfaces of the neutral state are different. When the intramolecular vibrational relaxation is not appreciable, the signal I can be expressed as I = kiv(A*)iv, where (A*)iv denotes the population of the vibronic state iv of the cationic naphthalene and kiv represents the ionization rate constant of the cationic naphthalene A* from the prepared ionic state. When the molecule is ionized by one-photon processes, the thermal rate coefficient W

for ground vibronic state g0 (i.e., g0 fv’). From the preceding discussion, it is clear

that the Franck-Condon factors are crucial for determining the intensities of vibronic bands by using W. Therefore, using the Condon approximation for non-adiabatic

transitions, the Franck-Condon factor should be calculated.

The PIE curve is simulated using the following analytical Franck-Condon formulation. Let us start with the thermal rate coefficient of the electronic transition from the ground adiabatic state i to f. We have the expression

W = GH

ħ:!"&:

G∑∑J&#:9Q"#$:Q&#;:

GK(<"#) − <&#) (9)

where J&# represents the Boltzmann distribution, is Planck’s constant, v and v’

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represent the vibrational quantum number in electronic states i and f, respectively,

associated with vibrational wave functions and for nuclear motion.

Furthermore, and are the energy level between the electronically ionic

vibrational state and the ground vibrational state. Using the integral representation for the delta function,

W = GH

ħ:!"&:

G∫ OPQ&RS-1T3T

∏ VW(P)W (10)

where

VW(P) = ∑ ∑ JX#Y 65c"#Y$ (ZW) )6c&#Y(ZW)86

G

Q&RSY$ (#Y$ [

\])

#Y$ Q3&RSY(#Y[

\])

#Y (11)

In the displaced harmonic approximation, we can derive the expression

^ =:_-1:

]

ħ]∫ OPexp[ePf"& − ∑ gh{j2lmh + 1o − jlmh + 1oQ

&RSp − lmhQ3&RSp}h ]

T3T (12)

where lmh = (QħSp s_⁄ − 1)3u is the average photon distribution, the parameter f"&

can be explicitly given by f"& =(2-321)

v where <"(<&) represents the minimum

energy for the equilibrium geometry of the electronic states f and i. The Huang-Rhys

factor gh is given as gh =Spwp

]

Għ where the displacement dj is simply defined as

Oh = Zh

) − Zh = ∑ xhs(ys) − ys)s (13)

Here, ys) (ys) and Zh)(Zh) are the mass-weighted Cartesian and vibrational normal-mode coordinates at the equilibrium geometry of the electronic state f(i), respectively. In this study, the transformation matrix L in eqn (12) and ys) (ys) were calculated using the Gaussian 0935 and Molpro36 program package. If kiv is identical for all vibrionic transitions, then the spectra will be proportional to the PIE spectra. In this case, eqn (12) can be used to evaluate the PIE spectra in terms of the Franck-Condon factors. We limited the calculation of the PIE spectra to the Franck-Condon region, 8 – 11 eV, as shown in Fig x. In this narrow energy region,

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vibrational amplitudes are not large, and the use of harmonic oscillator approximation is reasonable. Let !E"& denote the transition moment from the pumped neutral state to the ionized electronic state, evaluated at the equilibrium position (i.e., the Condon approximation). Then, using the aforementioned theoretical results, calculated adiabatic ionization energies (for the 0 – 0 transition; Table 2) and vibrational frequencies and normal modes (Table 4), we can calculate the PIE spectra of four isomers shown in Fig. 4. Because of the quality of the optimized structures used in the calculation, qualitative agreement is evident among Fig. 1, 3, and Table 1. We present a tentative assignment of the PIE spectra and these types of spectra are useful for discussing the vibronic level dependence of naphthalene. Results and Discussion Calculated structures and vibrational frequencies of different C10H8 isomers. The identification of novel reactive intermediates and radicals is revealed in flame, pulsed photolysis, and pyrolysis reactors, leading to the elucidation of spectroscopy, reaction mechanisms, and kinetics. Photoionization-efficiency measurements provide unprecedented access to vibrationally resolved spectra of free radicals, molecules, clusters, and their reaction products inform thermodynamics and spectroscopy present in high-temperature reactors.37–39 The natural choice of a computational tool for analyzing the electronic states of PAH cations is the CASSCF method because it fully accounts for configuration interactions in a π-electron system (orbital active space) and provides an accurate description of the rest of the molecule. To study the PIE curve of naphthalene is to simulate the photoionization process of naphthalene molecules with the conditions of molecular beam using quantum chemistry calculation. Hirata et al.40 and Malloci et al.41 conclusion about a series of PAHs and their ions in the interstellar clouds were made on the basis of their TD-B3LYP calculated the excitation energies and oscillator strengths. Srivastava et al.42 have been systematically analyzed using ab initio and B3LYP/6-311++G** method calculated the IR and vibrational spectra of naphthalene and its cation, and are found to be in better agreement with corresponding experimental values43, 44 in comparison to previous results.45, 46 Their experimental and theoretical studies of neutral and ionized naphthalene have revealed an unexpected effect of the ionization on the vibrational spectra that lead to a dramatic reduction in intensities of CH stretching modes and concurrently large increase in the intensities of ring CC stretching and CH bending vibrations. Bally et al.47 have calculated the excited state of the naphthalene cation electronic structure on the basis of ab initio CASSCF/CASPT2 method which yield a description in good accord with their

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photoelectron and electronic absorption spectra such as band positions and intensities. Eisfeld48 has used the multi-reference configuration interaction (MRCI) level of theory to calculate the vertical excitation energies of C3H3 isomers that play a major role in combustion chemistry and of fundamental interest in understanding photodissociation processes of hydrocarbons. Vertical and adiabatic ionization energies are calculated by coupled-cluster theory and CASPT2 method are suitable to aid the experimental detection of the different C3H3 isomers. Hall et al.49 have employed CASSCF/CASPT2 method to calculate the electronic structures of the ground and excited states potential energy surfaces on the naphthalene radical cation, they propose a mechanism for its ultrafast non-radiative relaxation from the second excited state (D2) down to the ground state (D0), which could explain the photophysics of matrix-isolated experiment50 observed photostability. Naphthalene cation is proposed as one of the species contributing to a series of diffuse infrared absorption bands originating from interstellar clouds, and understanding the mechanism for photostability in the gas phase has important consequences for astrophysics. Sánchez-Carrera et. al.51 have used the vibronic coupling in ground and excited states of naphthalene cation on the basis of a joint experimental and theoretical study of ionization spectra using high resolution gas phase photoelectron. Their theoretical and experimental results reveal the direct correlation between the nature of the vibronic interaction and the pattern of the electronic state structure. The CASSCF analysis of the neutral ground electronic state (S0), cationic ground (D0) and cationic first (D1) excited states of C10H8 (naphthalene, 1-buten-3-ynylbenzene, 3-buten-1-ynylbenzene) presented here demonstrates the practical application of the CASSCF method level by using the cc-pVTZ basis set, and it was performed with the aim of understanding the photoionization behavior of the system. To enhance the accuracy of the simulation results, benchmark CASSCF and CASPT2 calculations were also performed on the neutral ground electronic state (S0), cationic ground electronic state (D0), cationic first excited state (D1) using MOLPRO.36 All ground and excited states in the geometry optimization of the three C10H8 isomers have a Cs symmetry, except the ground state structure of naphthalene has D2h symmetry. The correlation-consistent basis set used was cc-pVTZ,52 in which 4s3p2d1f was for carbon and 3s2p1d was for hydrogen. Vibrational frequencies and normal modes of C10H8 isomers (S0, D0 and D1) were computed at the DFT and TDDFT levels with the cc-pVTZ basis set, respectively. A scaling factor of 0.965 was used for calculating the ground state frequencies, and the calculation of the excited state frequencies did not involve any scaling. Fig. 1 shows the optimized geometries and numbering scheme of C10H8, and three different isomers, corresponding to different carbon sites on the molecules, may be predicted for C10H8. Among the different isomers of C10H8, naphthalene, 1-buten-3-ynylbenzene, and 3-

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buten-1-ynylbenzene are planar isomers; moreover, naphthalene is the most stable isomer, 1-buten-3-ynylbenzene (2.52 eV) and 3-buten-1-ynylbenzene (2.43 eV) have a considerably higher than naphthalene, respectively. Our calculated results are in accord with the values of Mebel et al.12 and Zhao et al.24 The bond length in italics in Table 1 are shown for comparison and are taken from the experimentally determined geometry56 in the case of the neutral species and from the CASSCF calculations of Hall et al.49 for the cation structures. From a comparison of the optimized geometrical parameters of the isomers with the corresponding values of the neutral molecule (presented in the ESI), ionization was predicted to lead to substantial changes in the bond lengths and bond angles. The change in the bond angles is minor; here, we describe only the change in the bond lengths. While all the equilibrium structures are almost planar, each state has a distinctive pattern of carbon-carbon bond length alternation. For naphthalene cation, the aromatic C–H covalent bonds were almost unchanged (1.082 Å) compared with the corresponding aromatic C–H bonds in a naphthalene molecule (1.083 Å). Ionization at the Ca position caused the Ca–Cβ and Cg–Cg’ distances to increase to 1.400 and 1.427 Å, which corresponds to the neutral naphthalene having lengths in the range of 1.370–1.410 Å. In 1-buten-3-ynylbenzene cation, the C1-C7 and C8-C9 bonds were slightly shorter (1.413 Å, 1.381 Å); the C7-C8 bond was elongated (1.389 Å) in the cationic species than compared with neutral species (1.460 Å, 1.414 Å, 1.344 Å), respectively. In 3-buten-1-ynylbenzene cation, the aromatic C–H covalent bonds were almost unchanged (1.081 Å) compared with the corresponding aromatic C–H bonds in a neutral molecule (1.081 Å). The C1-C7 and C8-C9 bonds in the cationic state were slightly shorter (1.381 Å, 1.361 Å) than in neutral state (1.421 Å, 1.415 Å), respectively. Vertical and adiabatic ionization energies for different C10H8 isomers. The vertical ionization energies (VIEs) which computed at the optimized geometry of neutral molecule neglect structural relaxation but include wave-functions relaxation following the removal of one electrons. Adiabatic ionization energies (AIEs) are evaluated as the difference between the total energies of the neutral and the corresponding cation in their stablest configurations. The PIE spectrum and adiabatic ionization energy (8.14 ± 0.02) eV of C10H8 is obtained with synchrotron vacuum ultraviolet photoionization mass spectrometry (SVUV-PIMS) in fuel-rich benzene-oxygen flame15, high-temperature chemical reactor18,24, and cyclopentene pyrolysis25. The computed gas-phase ionization energies (VIE and AIE) of the C10H8 are given in Table 2. Calculated adiabatic ionization energies for naphthalene (8.14 eV) with CASPT2 using cc-pVTZ are in excellent agreement with measurements.18,24,25 The AIE

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for 1-buten-3-ynylbenzene is calculated to be 8.28 eV and agrees reasonably well with Kaiser’s measured appearance energy of 8.25 eV�24 The discrepancy of 0.01 eV between theoretical and experimental values is likely to be due to favorable Franck−Condon factors (FCFs); similar magnitude difference between 0-0 transitions and the computed apparent PIE onset has been observed in a previous study of PIE curve of C3H2.53 The PIE shown in Figure 2 rises gradually up to 8.14 eV and continues rising up to 9.5 eV. Our calculated AIE of 8.15 eV suggests FCFs for ionization. Experimentally, this manifests as the broad onset in the PIE shape as opposed to a sharp step function. Attempts were made to calculate the FCFs envelope as a fitting function to estimate the adiabatic ionization energy of naphthalene from the experimental data24, which has been successfully applied to compare experimental and theoretical results for C3H2,53 HOOH,54 and some nucleic acid bases.55 The frontier molecular orbitals (MOs) participating in the D1 transition of neutral and cationic naphthalene are shown in Table 3. Analysis of the major configurations contributing to the excited state wavefunctions reveals that the two lowest lying states (S0 to D1) correspond primarily to the single occupation of the MO34 and MO33 bonding orbitals. According to CASSCF calculations, in both neutral and cationic naphthalene (the most stable isomer), the one-electron excitation that mainly contributes to the D1 state in the HOMO ¬ HOMO-1 transition. These computed CASPT2/cc-pVTZ ionization energies suggest that the second ionization onward will contribute to the rise of signal in the experimental curve only beyond 11 eV. Thus, these states will not be discussed further. The MO from which the first ionization occurs from the MO34 orbital has significant electron density around the Ca–Cβ bonds is decreased while the antibonding character in the Cβ–Cβ’ bonds is decreased; the Ca–Cβ bonds are longer and the Cβ–Cβ’ bonds shorter than in the neutral species. Thus, removing the electron from MO34 orbital results in weakening of the Ca–Cβ in the cationic species (1.400 Å versus 1.370 Å in the neutral). The distribution of spin-density conforms the conclusion that the hole is delocalized almost equally over Ca and Cβ. Further details of the structural changes of others cationic species are given in the Supporting Information. The first state of the cation corresponds to excitation of an electron from MO33 into MO34. The small energy gap (2.5 kcal/mol) between the D0 and D1�states at the D1 minimum suggests the existence of a nearby�state crossing. Vertical transition to the D1 state would cause the electron density to increase around the Ca–Cβ bonds and decrease around the Cg–Cg’ and Cβ–Cβ’ bonds, leading to relaxation to the minimum structure on this state involving compression of the Ca–Cβ bonds and elongation of the Cg–Cg’ and Cβ–Cβ’ bond lengths. To check the reliability of the CASSCF energies, higher level calculations were performed to assess the effect of dynamic correlation on

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the relative energies of the three states (S0, D0, D1). CASSCF is capable of describing the qualitative features of covalent excited states. However, for excited states displaying differences in charge separation, the contribution from dynamic correlation energy becomes very important and is not well described by the CASSCF wave function. A perturbation theory approach was therefore employed, allowing all single and double excitations out of the full CASSCF wave function� An analysis of the correlation energies at the CASPT2 level revealed that there is a greater correlation effect in the D0 state compared to the D1 state, explaining this relative difference from the CASSCF results, and perhaps suggesting some extra ionic character in these state. Experimentally, there are several PIE curves for Naphthalene cation that all assign the strongest ionization band to the 0-0 to D1. This is consistent with the small geometry changes calculated on going from S0 to D1 minima (Table 1). A gas phase photoionization spectrum exhibits the data over a range of photon energies from 8.0 to 9.5 eV along with the PIE curves of naphthalene, 1-buten-3-ynylbenzene, and 3-buten-1-ynylbenzene. These data document an excellent match of the experimentally recorded PIE curve at m/z = 128 with a linear combination of the reference curves of three C10H8 isomers. The branching ratios12 for naphthalene to 1-buten-3-ynylbenzene to 3-buten-1-ynylbenzene were calculated based on the overall fitting of the experimental PIE curve at m/z = 128. By linear fitting of these calibration PIE curves to the experimentally measured curve, the branching ratios were extracted to be 43.5 ± 9.0: 6.5 ± 1.0: 50.0 ± 10.0%, taking 20% uncertainty in the PIE curves into consideration. It should be noted that the two-ring C10H8 isomer azulene has an adiabatic ionization energy of 7.42 eV and therefore the absence of signal below 8.14 eV clearly indicates the absence of azulene as a reaction product. Their theoretical study12 described the PES for the reaction, structures, and molecular properties of all intermediates and transition states involved and temperature- and pressure-dependent rate constants in the phenylvinylacetylene system. It is important to note that the pathway to 1-buten-3-ynylbenzene is produced via the phenyl radical addition to the C4 acetylenic carbon atom occurring via a barrier of 5 kJ mol-1 followed by the atomic hydrogen loss from the attacked carbon atom; 3-buten-1-ynylbenzene is formed by phenyl addition to the C1 carbon atom of the vinyl moiety via a submerged barrier located 0.4 kJ mol-1; naphthalene proceeds through the same submerged barrier and involves two hydrogen shifts and ring closure prior to hydrogen atom elimination via the transition state is lower in energy than the barrier involved in the immediate hydrogen atom loss from the collision complex forming 3-buten-1-ynylbenzene. Franck-Condon factors and differentiated photoionization efficiency curves: theory and experiment

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Though the real focus of the study of Raiser24 was on measuring the photoionization spectrum of the C10H8 isomers prepared by high-temperature chemical reactor, they included a photoionization efficiency (PIE) curve of the parent naphthalene, prompted both by the absence of other photoionization studies and a relative paucity of photoelectron spectra of the same molecule. The ionization energy of naphthalene was estimated by using the standard approach of determining the lowest-energy step-structured feature. The shape of the photoionization efficiency spectrum of Fig. 4 is modeled by using a calculated Franck-Condon envelope as a fitting function to estimate the adiabatic ionization energy of naphthalene from the experimental data. The simulated envelope requires a calculation of Franck-Condon factors for ionization of naphthalene, 1-buten-3-ynylbenzene and 3-buten-1-ynylbenzene. Force constant matices, unscaled frequencies and normal mode displacements calculated at the B3LYP/cc-pVTZ level for the neutral and cation of naphthalene, 1-buten-3-ynylbenzene and 3-buten-1-ynylbenzene are used to generate the Franck-Condon factors and the evaluation of overlap integral is carried out in the harmonic approximation. The resulting Franck-Condon factors, including hot bands arising from thermal population at the assumed temperature, are integrated and convolved with Gaussian response function corresponding to the measured experimental photon energy resolution of 2.0 eV. The PIE curves of stable species, agree well with room temperature measurements, indicating that effective vibrational temperatures in the beam are near 300k and give satisfactory fits to the present experimental data. To present a general overview of the C10H8 PIE spectrum, we start by considering the isomeric vibronic structure of the S0 ® D1 electronic transition. As a quantitative measure of the overall geometry change upon, we consider the difference between the geometries of the neutral and the cation positioned such that their centers of mass coincide and their principal axes are optimally aligned. The Franck-Condon progression of relative band intensities in the displaced Harmonic oscillator approximation is described by the Franck-Condon factor

z#p$ ={p.p$

#p$!Q3{p (14)

where }h) denotes the vibrational quantum number of the jth normal mode describing the Franck-Condon progression and }h) is the Huang-Rhys factor. The ionization-induced geometry changes can be explained by the shapes of MOs. The distance between the atoms for which the bonding or antibonding overlap is present in the

14

HOMO should increase or decrease, respectively. Using eqn (14), we have z~p$/zÄp$ =

0.0647, zuGp$/zÄp$ = 0.1120, zGÅp$ /zÄp$ = 0.0688, zG~p$/zÄp$ = 0.0773, zÇ~p$ /zÄp$ =

0.0532, etc. We can see that Huang-Rhys factors smaller than 0.01 can be neglected. We used the equilibrium geometries of the S0 and D1 states calculated to estimate the Huang-Rhys factors, and then used the Huang-Rhys factors to simulate the PIE spectra by using eqn (12). The Huang-Rhys factors are given in Table 4, the xxx modes (v12), yyy modes (v28), zzz modes (v24), aaa modes (v8) and bbb modes (v38) have Hung-Rhys factors (0.1120, 0.0773, 0.0688, 0.0647 and 0.0532). Conclusions With the analysis of combustion intermediates featuring in flames of different fuels, the discriminative capacity of photoionization efficiency spectroscopy have been examined under isomer-rich, chemically complex conditions. The photoionization mass spectrometry using tunable vacuum ultraviolet synchrotron radiation that profits from the unambiguous fingerprint of species of naphthalene, 4-phenylvinylacetylene and trans-1-phenylvinylacetylene were applied to high-temperature reactor to provide specific information about the chemical composition at a given mass. The technique had already been proven advantageous over more widely used photoionization molecular-beam mass spectrometry measurements that can only identify the contribution of several isomers if their ionization energies are not too close and the corresponding slopes of the PIE efficiency curves can each be assigned to a single species. The PIE curve of the naphthalene molecule was obtained from Franck-Condon simulations on the basis of high-level quantum chemistry calculations and suggests the presence of ethynyl and isoprene reaction. We demonstrated that tautomerization affects IEs, relative order, and the characters of ionized states. Analysis of ionization-induced geometry changes reveals correlation between the magnitude of the geometry changes and relaxation energy for most of the hydrocarbons. We obtained the PIE curve of a small-sized PAH and found that the vibrational normal mode (v8) is the most influential vibrational mode of naphthalene. The structural differences between the neutrals and the cations give rise to Franck-Condon progressions. The shape of the computed S0-D1 band follows a similar pattern in all three C10H8 isomers; the maxima of the spectra are » 1.5 eV higher than the 0-0 transition. The maximum corresponds to the coupled stretching and bending motions that are strongly affected by the radical’s relaxation. For symmetric molecular such as naphthalene, local vibration modes between carbon and hydrogen atoms must be

15

addressed; therefore, a damping parameter and multiple Huang–Rhys factors should be introduced to simulate the PIE curve. Spectral robustness was thoroughly investigated according to the Huang–Rhys factors by systematically performing simulations through the CASSCF(10,10) methods. It confirmed that one of the six active normal modes (vxx) was mainly responsible for the PIE spectra. It should be emphasized that the Huang–Rhys factors for the C–C and C–H local modes slightly rotate the normal modes. In the displaced oscillator calculations, the rotation and small changes in the frequencies were identical for both the ground and excited states; the rotation of the normal modes resulting from a change in the mass/locate mode factors tended to be small. Moreover, the Duschinsky rotation effects are negligible, but this should be confirmed by further studies. We calculated the Franck–Condon factors from a harmonic oscillator to determine the PIE spectra of small-sized polycyclic aromatic hydrocarbons, and the present method can be used to detect spectral changes and produce vibronic spectra for small PAH by adjusting the Huang–Rhys factors in the gas phase. Reanalysis of literature electron ionization measurements in the light of the present IE determination suggests that the C10H8 composition in several other flames is also a mixture of isomers. Franck-Condon analysis, based on ab initio calculations of frequencies and force constants, allows the determination of the ionization energy of naphthalene as 8.14 eV. The firm assignment of the majority of the observed intramolecular vibrational modes was proposed on the basis of harmonic frequency calculations. Reanalysis of literature electron ionization measurements in the light of the present IE determination suggests that the C10H8 composition in several other flames is also a mixture of isomers. Acknowledgments This work was supported by the National Natural Science Foundation of China (No.91641116), Innovation Program of Shanghai Municipal Education Commission (201701070005E00020) and NYU Global Seed Grant. We thank the Supercomputer Center of East China Normal University for providing us computer time.

16

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Table 1 Optimized geometry parameters of C10H8. Calculated values were obtained by the CASPT2(10,10)/cc-pVTZ methods for the neutral, cationic ground state and first cationic excited states, respectively.

Napthalene Neutral Cation

Exp56 6-31G*

/6-11++G**

DFT

/CAS(1010)

6-31G*

/6-311++G**

D1 (Cs)

/CAS(9,10)

Distances (Å)

Cg-Cg’ 1.412/1.421 1.409/1.410 1.428/1.411 1.422/1.430 1.427/1.427

Cb-Cb’ 1.417/1.410 1.417/1.410 1.428/1.418 1.378/1.380 1.386/1.383

Cα-Cg 1.422/1.420 1.421/1.420 1.416/1.423 1.402/1.410 1.408/1.404

Cα-Cb 1.381/1.377 1.358/1.360 1.370/1.367 1.400/1.400 1.400/1.402

Cα-H 1.092/1.095 1.076/1.075 1.083/1.074 1.075/1.083 1.082/1.073

Cb-H 1.092/1.098 1.075/1.075 1.082/1.073 1.073/1.083 1.081/1.071

Cα-Cg-Cg’ 119.5/119.0 119.0/119.0 118.8/119.0 119.1/118.8 119.0/119.1

Cb-Cα-Cg - 120.8/ 120.9/120.8 120.6/ 120.8/120.8

Cα-Cb-Cb’ /120.5 120.3/120.2 120.3/120.2 120.3/120.2 120.2/120.2

H-Cα-Cg - 118.8/ 118.8/118.9 119.7/ 119.4/119.5

H-Cb-Cb’ - 120.3/ 120.1/120.2 119.5/ 119.6/120.3

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Table 2 VIEs and AIEs for different isomers of C10H8 (in eV) computed at the B3LYP and G3(CC,MP2) levels with cc-pVTZ basis set.

species VIE AIE Exp56

Naphthalene 8.14

B3LYP/cc-pVTZ 8.26 8.15

G3(CC,MP2) 7.92 7.88

(E)-PVA

B3LYP/cc-pVTZ 8.42 8.26

G3(CC,MP2) 7.29 7.26

(Z)-PVA

B3LYP/cc-pVTZ

G3(CC,MP2) 7.41 7.35

PVA

B3LYP/cc-pVTZ 8.43 8.28

G3(CC,MP2) 7.39 7.37

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Table 3 Molecular orbitals defining the active space (10, 10) of our calculation. MO 38 π*

MO 39 π*

MO 36 π*

MO 37 π*

MO 34 π (HOMO)

(Au)

MO 35 π* (LUMO)

MO 32 π (B3g)

MO 33 π (B1u)

MO 27 π (Au)

MO 31 π (B2g)

24

Table 4 Experimental frequency (in cm-1), and calculated vibrational normal mode frequencies and Huang-Rhys factors of S0 and D1 states of C10H8 isomers calculated at B3LYP/cc-pVTZ and CASSCF(10,10)/cc-pVTZ level.

Naphthalene Mode Expt.57 S0 D1 S v9 (Ag) ring deformation 512 521 516 0.0647 v8 (Ag) ring deformation 758 775 777 0.1120 v7 (Ag) ring breathing 1020 1048 1068 0.0688 v6 (Ag) C-H bend 1163 1188 1208 0.0773 v4 (Ag) C-C stretch 1460 1497 1507 0.0178 v3 (Ag) C-C stretch 1577 1614 1553 0.0532

4-phenyl-1-butene-3-yne ((E)-PVA) Mode Expt S0 D1 S v32 X-sens (�-CH=CH-Cº) 231 238 233 0.1764 v31 X-sens (αC-C-C) 373 379 382 0.0661 v29 αC-C-C - 634 629 0.0500 v27 β CºC-H - 676 691 0.0794 v17 β vinyl C-H 1315 1333 1350 0.0956 v16 ring C-C stretch 1349 1352 1371 0.0372 v15 aryl βCH 1372 1371 1389 0.0382 v14 ring C-C stretch 1477 1487 1474 0.0997 v11 ring C-C stretch - 1641 1572 0.0518 v10 C=C stretch - 1668 1642 0.0406 v3 ring CH stretch - 3186 3211 0.0933

3-buten-1-ynylbenzene Mode Expt. S0 D1 S v32 C(α)-C(β) bend 192 202 193 0.0972 v31 X-sens ring puckering 366 375 383 0.2315 v27 vinyl + aryl gCH 706 719 719 0.0474 v11 C(α)=C(β) stretch - 2298 2209 0.0723 v4 ring CH stretch - 3186 3205 0.0353 v1 vinyl CH stretch - 3238 3259 0.0417

25

Fig. 1 Zero-point corrected ground state energies (kcal mol-1) of isomers of C10H8 at the CASPT2/cc-pVTZ level of theory and numbering pattern of the neutral ground state (S0), cationic ground state (D0) and the first cationic excited state (D1): (a) naphthalene; (b) E-4-phenylvinylacetylene (E-PVA); (c) Z-4-phenylvinylacetylene (Z-PVA); (d) trans-1-phenylvinylacetylene (PVA). Bond lengths are given in angstroms.

26

Fig. 2 Experimental PIE curves for species at m/z = 128 in the phenyl-vinylacetylene system. The black line refers to the normalized experimental data; the green, orange, and blue lines show the isomer PIE curves generated by linear fit with measured references PIE curves of naphthalene, 1-buten-3-ynylbenzene, and 3-buten-1-ynylbenzene, respectively. The red line reveals the overall fit via a linear combination of the reference curves.24

27

Fig. 3 Normal modes of the naphthalene with larger Huang-Rhys factors in the neutral state (in parentheses) and responsible for the false origins in the photoionization efficiency spectrum.

28

Fig. 4 S0 ® D1 photoionization-efficiency spectrum for three naphthalene isomers from the Franck–Condon calculations. Some of the important vibronic lines are assigned tentatively.

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