Franck-condon simulation of photoelectron spectroscopy of DOO-：Including duschinsky effects

LI Ren-Zhong，ZHANG Huan-Huan，JING Jun-Feng，LI Peng-Fei ，LIANG Jun

（1．College of Electronic Information，Xi’an Polytechnic University，Xi’an 710048，China；

2．College of Physics and Electronic Information，Anhui Normal University，Wuhu 241000，China）

1 Introduction

The hydroperoxyl radical（HOO／DOO）is one of important combustion intermediate in the oxidation of fuels[1，2]，which has been the subject of many research group in the past several decades[3－22]．Among those works，a few theoretical and／or experimental studies about the structural parameters concerning the anion DOO-have been carried out[7，14，20]．Ramond reported the photoelectron spectroscopy（PES）on2A″and2A′of DOO-and obtained the electron affinity（EA）and vibrational frequencies of the neutral molecule[20]．Liang et al determined the geometries of the anion DOO-by applying Franck-Condon（FC）analyses to its photoelectron spectrum for2A″－1A′[14]．It is noted that the information about the spectroscopy and its structural parameters on the excited state（2A′）of DOO are fairly sparse．So a clear picture at molecular level for the excited state of DOO is necessary．

In this paper，we investigated the photoelectron spectrum of the DOO-（2A″－1A′and2A′－1A′transitions）theoretically by the combination of ab initio and Franck－Condon factors（FCF）calculations．Geometry optimization and harmonic vibrational frequency calculations were performed on the2A″and2A′states of DOO．Franck-Condon analyses and spectral simulation were carried out on the two PES bands of DOO-（2A″－1A′and2A′－1A′transition）．In addition，employing the iterative Franck-Condon analysis procedure in the spectral simulation，the equilibrium geometries of the state1A′of DOO-and the excited state2A′of DOO were derived in the spectral simulation．The position of origin peaks for2A″－1A′and2A′－1A′transitions were determined by the EA and T0values obtained at B3LYP，CCSD（T），QCISD（T）and CASSCF levels．

2 Theoretical method and computational detail

Geometry optimization and harmonic vibrational frequency calculations were carried out on the2A″of DOO and1A′of DOO-with B3LYP，QCISD（T）and CCSD（T）methods and 6-311＋（2df，2p）basis sets，as for the excited state2A′of the neutral molecule DOO，geometry optimization and harmonic vibrational frequency calculations were performed with the CASSCF and CIS methods．All these calculations were performed employing Gaussian03suits of programs[23]．

In our study，the computed FCFs were used to simulate the vibrational structure of the2A″－1A′and2A′－1A′photo-detachment spectra of DOO-，employing a Gaussian line-shape and a full-width-at-half-maximum （FWHM）of 300cm－1．In order to obtain a reasonable match between the simulated and observed spectra，the iterative Franck-Condon analysis （IFCA）procedure was also carried out，for the both2A″－1A′and2A′－1A′photo-detachment processes．Firstly，for the2A″－1A′photodetachment process，the ground state geometrical parameters of the DOO molecule were fixed to the experimental values，while the ground state geometrical parameters of DOO-were varied systematically until a best match between the simulated and observed spectra was obtained．Secondly，for the2A′－1A′photodetachment process，the ground state geometrical parameters of DOO-were fixed to the values obtained by the2A″－1A′photodetachment process，while the2A′state geometrical parameters of DOO were varied systematically until a best match between the simulated and observed spectra were obtained．

3 Results and discussion

3．1 Geometry optimization and frequency calculations

The optimized geometric parameters and computed vibrational frequencies for the2A″and2A′states of DOO，and1A′state of DOO-are listed in Tables 1～3．Some theoretical and／or experimental values published previously in literatures are also included for comparison．The bending vibration is denotedω2，according to the

convention for triatomic molecules．The other vibrational modes are listed in decreasing order of size，which designates the D－O stretch asω1and the O－O stretch asω3．

Table 1 Summary of some computed and experimental geometrical parameters and vibrational frequencies（cm－1）of the2 A″state of DOO obtained at different levels of calculation．

Table 1 Summary of some computed and experimental geometrical parameters and vibrational frequencies（cm－1）of the2 A″state of DOO obtained at different levels of calculation．

aRef．[14]；bRef．[27]；c Ref．[20]

R（DO）（nm） R（OO）（nm） ∠（DOO）（o） ω1（D-O） ω2（bend） ω3（O-O）B3LYP／6-311＋G（2df，2p） 0．09757 0．1326 105．5222 2634．95 1183．51 1057．09 QCISD（T）／6-311＋G（2df，2p） 0．09718 0．13354 104．26 2680．69 1142．98 1054．56 CCSD（T）／6-311＋G（2df，2p） 0．09716 0．1332 104．373 2682．22 1159．35 1061．13 B3LYP／6-311＋G （d，p）a 0．09773 0．13282 105．8646 2630．4 1047．4 1169．6 QCISD／6-311＋G（d，p）a 0．09710 0．13346 104．7368 2712．4 1057．5 1127．2 QCISD（T）／6-311＋G（d，p）a 0．09738 0．13376 104．5313 2680．9 1044．4 1122．4 CCSD／6-311＋G（d，p）a 0．09705 0．13261 105．0097 2718．4 1074．3 1170．1 CCSD（T）／6-311＋G（d，p）a 0．09736 0．13347 104．6489 2683．2 1050．6 1138．8 Expt． 2529．2b 1027．3b 1112（7）c

Table 2 Summary of some computed and experimental geometrical parameters and vibrational frequencies（cm－1）of the2 A′state of DOO obtained at different levels of calculation．

Table 2 Summary of some computed and experimental geometrical parameters and vibrational frequencies（cm－1）of the2 A′state of DOO obtained at different levels of calculation．

aRef．[20]

R（DO）（nm） R（OO）（nm） ∠（DOO）（°） ω1（D-O） ω2（bend） ω3（O-O）CIS／6-311＋G（2df，2p）0．0947 0．1364 104．0234 2989．86 1052 1130 CIS／6-311＋G（d，p） 0．0948 0．1364 103．9271 2985．14 1122．98 1046．4 CASSCF／6-311＋G（2df，2p） 0．0947 0．1353 104．27 2969．32 1160．84 1020．94 CASSCF／6-311＋G（d，p） 0．0905 0．13524 104．21 2976．13 1145．75 1034．46 Expt 955（6）a

Table 3 Summary of some computed and experimental geometrical parameters and vibrational frequencies（cm－1）of the1 A′state of DOO-obtained at different levels of calculation

Table 3 Summary of some computed and experimental geometrical parameters and vibrational frequencies（cm－1）of the1 A′state of DOO-obtained at different levels of calculation

aRef．[14]，b Ref．[16]，c Ref．[28]，d Ref．[29]，e Ref．[7]

R（DO）（nm） R（OO）（nm） ∠（DOO）（°） ω1（D-O） ω2（bend） ω3（O-O）B3LYP／6-311＋G（2df，2p）0．9607 0．1511 99．4221 2768．88 862．55 777．50 QCISD（T）／6-311＋G（2df，2p 0．9596 0．15258 97．6038 2788．02 853．75 735．32 CCSD（T）／6-311＋G（2df，2p） 0．9593 0．15241 97．5841 2791．49 857．97 739．54 B3LYP／6-311＋G（d，p）a 0．09625 0．15219 99．3724 2765．1 754．4 843．4 QCISD／6-311＋G（d，p）a 0．09589 0．15139 99．0261 2814．9 754．6 852．1 QCISD（T）／6-311＋G（d，p）a 0．09617 0．15353 97．9083 2788．9 697．6 820．6 CCSD／6-311＋G（d，p）a 0．09585 0．15085 99．1571 2821．9 777．3 863．9 CCSD（T）／6-311＋G（d，p）a 0．09610 0．15338 97．9514 2792．5 701．1 823．7 QCISD（T）／6-311＋＋G（2df，pd）b 0．09619 0．15270 97．34 CCSD（T）／aug-cc-pVTZc 0．09593 0．15219 97．64 2776．0 740．3 843．4 CCSD（T）／aug-cc-pVQZd 0．09596 0．15204 97．77 2771．7 742．8 848．4 CCSD-T／aug-cc-pVQZd 0．09594 0．15200 97．79 2773．9 743．5 849．3 Expt． 900（250）e

It is noted thatthe calculated geometry parameters of1A′state DOO-and2A′state of DOO remain to be tested，since there is no complete experimental information yet on the structure of this system．In our present work，the more reliable bond length R（OO）is obtained by the iterative Franck-Condon analysis．

In addition，from the computed values（see Tables 1～3），we can see that the OD bond lengths and the D－O－O bond angles are almost unchanged，only small differences are predicted for2A″and2A′states of DOO and1A′state DOO-．This shows that the D－OO stretchω1and the bendingω2are negligibly small，not included in the assignment，only the DO－O stretchω3is active．

3．2 Electron affinity and term energy

The theoretical electron affinity （EA）and the term energy （T0）of DOO with different methods are listed in Table 4．For comparison，the theoretical and／or experimental values available in literatures are also included．From Table 4，the overall spread of these computed EA values of DOO is less than 0．24eV，suggesting that they should be highly reliable．It seems unlikely that any variations in the level of calculation would not change the computed EA values significantly．The EA （1．0637eV）of DOO on CCSD／6-311＋G（d，p）／／CCSD（T）／6-311＋G（d，p）level is in excellent agreement with the experimental value．As for the term energy，the computed value on CIS／6-311＋G（2df，2p）is close to the experimental value，we now suggest that the term energy of DOO is 0．8964eV，which agrees well with the experimental result．

Table 4 The computed electron affinity of DOO and term energy（2 A″－2 A′）obtained at different levels of calculation

Table 4 The computed electron affinity of DOO and term energy（2 A″－2 A′）obtained at different levels of calculation

eV References B3LYP／6-311＋G（d，p）Method EA／eV T0／1．0471 This work CCSD／6-311＋G（d，p）／／CCSD（T）／6-311＋G（d，p） 1．0637 This work QCISD／6-311＋G（d，p）／／QCISD（T）／6-311＋G（d，p） 1．0138 This work CCSD／6-311＋G（d，p）／／QCISD（T）／6-311＋G（d，p） 1．0895 This work B3LYP／6-311＋G（2df，2p） 0．9771 This work CCSD（T）／6-311＋G（2df，2p） 0．8557 This work QCISD（T）／6-311＋G（2df，2p） 0．8516 This work Expt． 1．089，1．077 [7，20]2 A′－1 A′CIS／6-311＋G（2df，2p）0．8964 This work CIS／6-311＋G（d，p） 0．7928 This work Expt． 0．874 [20]

3．3 Frank-Condon analyses and spectral simulations

The spectrum in Fig．1shows two different peak profiles，suggesting that transitions to two different electronic states of DOO．The simulated photoelectron spectrum of DOO-for2A″－1A′and2A′－1A′as generated is displayed in envelopes of Fig．1（b）．Vibrational assignments for stretchingω3mode of state2A″and2A′for the neutral molecule DOO are also provided，with the label（0，0，n－0，0，0）corresponding to（0，0，ω3－0，0，0）transition（see Fig．1（b））．The computed FCFs for the D－O stretchingω1and the D－O－O bendingω2modes are found to be negligibly small，therefore theω1andω2modes are not included in the assignment．

In spectral simulation，a FWHM of 300cm－1was utilized with Gaussian band envelopes．The relative intensities are chosen to match the vibronic profile in the experimental spectrum．

Fig．1 （a）The experimental photoelectron spectrum of DOO- （from [20]）and（b）the simulated spectrum invoking the experimental geometry for the～X 2 A″and～A2 A′states of DOO and the IFCA one for the～X 1 A′state of DOO-with vibrational assignments provided for the（～A2 A′－～X1 A′and～X 2 A″－～X1 A′）detachment process．The FWHM used for the components of the simulated spectra is 300cm－1

4 Conclusion

In the present study，we simulated the observed2A″－1A′and2A′－1A′detachment photoelectron spectra for DOO-，using a harmonic model including Duschinsky effects．The reliable geometrical parameters of the state2A″of DOO-and the excited state2A′of DOO were obtained through the Franck－Condon analysis．Based on the sensitivity of the relative intensities towards the variation of the bond length，the uncertainties are about±0．0005nm．The threshold behavior of the photodetachment cross section was modeled by using Franck-Condon analyses and obtained estimates of the electron affinity and the term energy of DOO，given in Table 4．On the basis of our high levelabinitiocalculations and Franck-Condon analysis of the photoelectron spectra，we obtained EA（DO2）＝1．0637eV andT0＝0．8964eV．

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