Experimental and theoretical investigations of ionization/dissociation
of cyclopentanone molecule in a femtosecond laser field
Qiaoqiao Wang,1Di Wu,1Mingxing Jin,1Fuchun Liu,1Feifei Hu,1Xihui Cheng,1 Hang Liu,1 Zhan Hu,1 Dajun Ding,1,a兲 H. Mineo,2 Y. A. Dyakov,3 A. M. Mebel,4,b兲 S. D. Chao,2and S. H. Lin3,5
1
Institute of Atomic and Molecular Physics, Jilin University, Changchun 130012, People’s Republic of China
2
Institute of Applied Mechanics, National Taiwan University, Taipei 106, Taiwan 3
Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan 4
Department of Chemistry and Biochemistry, Florida International University, 11200 SW 8th Street, Miami, Florida 33199, USA
5
Department of Applied Chemistry, National Chiao-Tung University, Hsin-Chu 300, Taiwan 共Received 25 June 2008; accepted 1 October 2008; published online 24 November 2008兲
The ionization/dissociation mechanism of cyclopentanone has been experimentally investigated in molecular beam by irradiating with intense 394 and 788 nm laser fields with pulse duration of 90 fs. The range of laser intensities varied from 3⫻1013 to 4⫻1014W/cm2. For both wavelengths, the singly charged parent ion is observable while the doubly charged one cannot be found easily, although the fragmentation pattern supports its presence. Meanwhile, the extent of fragmentation at 788 nm is less than that in the 394 nm case. We quantitatively analyze the ionization processes of cyclopentanone in intense femtosecond laser by comparing the calculation results of ionization rate constants obtained from Ammosov-Delone-Krainov, Keldysh, and Keldysh-Faisal-Reiss 共KFR兲 theories based on hydrogenlike atom model. We also compare the experimental and theoretical results; the generalized KFR theory is found to be useful in predicting the ionization yields of singly and doubly charged cyclopentanone ion. To interpret the dissociation patterns of the cyclopentanone ions, we have used the Rice-Ramsperger-Kassel-Marcus theory with the potential surfaces obtained from the ab initio quantum chemical calculations. © 2008 American Institute of Physics.
关DOI:10.1063/1.3006028兴
I. INTRODUCTION
The photoionization and dissociation processes of poly-atomic molecules induced by intense femtosecond laser pulses with an intensity range of 1013– 1016W/cm2 have been extensively reported recently.1–9 However, the photo-ionization mechanism of the molecules is still ambiguous, and the understanding of fragmentations of the molecules 共neutral or charged兲 is even less clear. Cycloketones are well known to have flexible structures with ring puckering or twisting motion,10 and their spectra have been investigated by numerous methods. Furuya et al.11 explored the triplet states of cyclopentanone and cyclohexanone using low-energy electron impact at electron low-energy of 5 eV and as-signed five triplet bands together with four singlet bands. Baba et al.12 reported the resonance enhanced multiphoton ionization 共REMPI兲 mass spectra of acetone and cycloke-tones by using UV excimer laser 共248 nm or 193 nm兲 with 10 ns pulse duration, which resonances with the intermediate state, 1共n,*兲 or 1共n,3s兲. They proposed that the fragment
ions of smaller ketones were originated from the sequential photoionization of the fragments containing carbonyl group after photodissociation. However, as the molecular size in-creased, the generation of fragment ions through direct
two-photon excitation became more important. Moreover, the two-photon excitations of the 3s, 3p, and 3d Rydberg transi-tions in these molecules were recorded by REMPI.10,13,14 Ac-cording to these studies, different vibronic modes have been identified and the photodissociation mechanism has been proposed. Recently, cycloketones including cyclopentanone were investigated by several groups making use of femtosec-ond pulsed laser. Zewail and co-workers15,16 extensively studied the molecular reaction dynamics of cycloketones ir-radiated by 60 fs pulsed laser, by using a 310 nm pump and 620 nm probe combined with a time-of-flight mass spec-trometer共TOF-MS兲. The evolutions of the reaction interme-diates involving diradicals provided a real-time picture of the nuclear motions and structural changes during the reaction. Wu et al.17 studied the dissociation dynamics of cyclopen-tanone and cyclohexanone by means of a femtosecond laser with 50 fs pulse duration and 800 nm wavelength. They con-cluded that the fragmentation of the parent ions increases with the laser intensity and molecular size. In our previous study,9we compared the experimental observations in a 90 fs laser at 394 or 788 nm with the time-dependent density func-tional theory calculated molecular absorption spectra, and illustrated that the yields of cycloketones molecular ions were affected by the characteristics of the cation absorption at the laser wavelength.
In this paper, we discuss the ionization/dissociation
pro-a兲Electronic mail: dajund@jlu.edu.cn. b兲Electronic mail: mebela@fiu.edu.
cesses of the cyclopentanone molecule in femtosecond in-tense laser field. Experimentally, we use 394 and 788 nm fs laser pulses to irradiate cyclopentanone, and observe the ion signals with TOF-MS. Theoretically, through a quantitative calculation of the ionization rate constants for the molecule, treating it as a hydrogenlike atom by different methods such
as Ammosov-Delone-Krainov 共ADK兲, Keldysh, and
Keldysh-Faisal-Reiss共KFR兲 theories, we point out that both ADK and Keldysh theories overestimate the rate constants. As for a real molecular system, the structural characteristics of the molecule, including its vibrational structure, should be considered; therefore, the generalized KFR theory combined with the molecular orbital共MO兲 theory is chosen to calculate the ionization rate constants of cyclopentanone. A consis-tency of the results between the experimental observations and the theoretical model calculation is achieved. A qualita-tive understanding of the femtosecond dissociation of cyclo-pentanone has been attempted by using Rice-Romsperger-Kassel-Marous 共RRKM兲 theory based on the ab initio calculations.
II. EXPERIMENTAL DETAILS A. Experimental setup
The experimental setup used for the femtosecond laser ionization/dissociation study has been described elsewhere.9,18 Briefly, a chirped pulse amplified Ti:sapphire laser共Spectra-Physics兲 is employed. This system produces a 90 fs, linearly polarized laser beam with a repetition rate of 10 Hz and wavelength centered at 788 nm. The laser beam is frequency doubled by a beta barium borate crystal to give a 394 nm linearly polarized laser beam. Variable attenuation of the beam intensity is achieved using a rotatable half-wave plate followed by a Glan-Taylor prism. This method can also ensure that the direction of laser polarization is parallel or perpendicular to the flight axis of the TOF always during changing the beam intensity. The laser beam enters the vacuum chamber through a quartz window and is focused by a quartz plano-convex lens 共f =350 mm兲 so as to achieve laser intensities in the range of 1013– 1014W/cm2, which are estimated by
I共W/cm2兲 = E共J兲
⌫共s兲A共cm2兲 共2.1兲
from the measured pulse energy E, the pulse width⌫, and the focus spot area A obtained from the radius r of this spot as the 1/e2 points of a Gaussian profile,
r =2f
D, 共2.2兲
where f is the mirror focal length, is the wavelength, and D is the prefocused beam diameter. In general, with a 350 mm focus lens, 90 fs pulse duration, 394 nm wavelength, and 1 mJ pulse energy, the beam intensity will be a few times of 1014W/cm2.
Commercial cyclopentanone sample 共Aldrich Co. Ltd., 99% purity兲 is used without further purification. It is ex-panded into a vacuum chamber in a background pressure of 10−7Torr through a pulsed valve with 400s duration. A
linear TOF-MS is operated on Wiley-McLaren focusing con-dition. The produced ions are introduced into a 90 cm field-free region after two-step acceleration and are detected by a pair of microchannel plates. A slit with 0.5 mm width is mounted in front of the flight tube for ensuring that only the ions produced in the center portion of the laser focus volume can enter the drift tube. By connecting the ion detector out-put through a fast preamplifier to a digital storage oscillo-scope共Tektronix TDS 3054B兲, mass spectra are accumulated and averaged over 512 laser shots normally and then trans-ferred into a computer. Typically, the mass resolution at
m/e=100 is M /⌬M =1000.
B. TOF-MS observation of cyclopentanone
The mass spectra of cyclopentanone for two wave-lengths 共394 nm, 788 nm兲 are shown in Figs. 1 and 2, re-spectively. They are obtained under four different laser inten-sities, covering from 3⫻1013to 4⫻1014W/cm2. In the case of 788 nm irradiation with low laser intensities, the singly charged cyclopentanone parent ion is dominant, being ac-companied by weak fragment ions. For the 394 nm case, however, although singly charged parent ion is predominant at low laser intensities, the fragment ions are more abundant than at 788 nm. Moreover, with increasing laser intensity, smaller fragment ions appear and increase for both wave-lengths. It should be noted that in all mass spectra, the singly charged parent ion is clearly seen while the doubly charged parent ions cannot be assigned definitely because the peak at FIG. 1. Mass spectra of cyclopentanone interacted with 90 fs laser pulses at 394 nm for four different intensities: 共a兲 3.3⫻1013W/cm2, 共b兲 7.0
⫻1013W/cm2,共c兲 1.5⫻1014W/cm2, and共d兲 3.9⫻1014W/cm2. The
m/z=42 may be attributed to a fragment ion with the same
mass-to-charge ratio共such as C3H6+兲. This result is different from the observation of other aromatic molecules such as toluene and benzene under similar experimental conditions,19 in which for laser intensities I⬎2⫻1014W/cm2 further in-crease of fragment ions and multiply charged parent ions can be observed, and the molecular aromaticity favors generation of the multiply charged intact ion regardless of the nature of the highest occupied molecular orbital共HOMO兲.
The ion intensities of the parent ion and two fragment
ions, m/z=55 and m/z=42, as a function of laser intensity from 2⫻1013to 4⫻1014W/cm2are shown in Figs.3and4 for 394 and 788 nm, respectively, in a log-log form. With regard to each wavelength, this laser intensity dependence of the ion yield is determined by measuring the ion peak area under the curve in the mass spectrum. For cyclopentanone, since its ionization potential is 9.28 eV,20the minimum pho-ton number of 394 nm necessary for ionization is 3 while that of 788 nm is 6. It is noted that the measured dependence cannot be fitted well by only one straight line in a log-log scale for the whole laser intensity range used. Roughly, we can explain the experimental results within the frame of the MPI mechanism in a certain laser intensity range. At 394 nm with intensity from 4⫻1013to 1⫻1014W/cm2, the slope for the yield of the parent ion is 2.9, which is close to the photon number for ionization mentioned above. The m/z = 55 peak exhibits a photon number of 3.1, implying that the photodissociation of this fragment may be a rate-limiting共or bottleneck兲 process and the meaning of this slope also pre-sents the order of photoionization process. The yield of
m/z=42 ion has a slope of 4.2, suggesting that this ion is
produced through a process with a higher order. On the other hand, for 788 nm, the slope of the parent ion yields in the intensity region below 9⫻1013W/cm2is 6.2. Similar to the results obtained for 394 nm, the slope of m/z=55 fragment ion is the same as that of the parent ion. On the contrary, the slope of fragment ion with m/z=42 is less than that of the parent ion. This may be owing to some effects induced by intense femtosecond laser field such as so-called field assis-tant dissociation共FAD兲 and requires further investigation.
III. THEORETICAL TREATMENTS A. Theoretical model
There are many theoretical methods used to treat for the ionization processes of polyatomic molecules, such as ADK,21–23Keldysh,24–26KFR theory,24,27,28and so on. In the present work, we firstly use these theories to calculate ion-ization rate constants of cyclopentanone and cyclopentanone ion based on a hydrogenlike atom approach. By comparison, according to the rate limitation of ionized electron, we ob-FIG. 2. Mass spectra of cyclopentanone interacted with 90 fs laser pulses at
788 nm for four different intensities: 共a兲 3.4⫻1013W/cm2, 共b兲 7.0
⫻1013W/cm2,共c兲 1.5⫻1014W/cm2, and共d兲 4.0⫻1014W/cm2. The
aster-isk denotes the parent ion.
FIG. 3. Relative ion yields of parent and main fragments ions as a function of laser intensity. The wavelength is 394 nm. A linear fit through the data points is shown as the solid line. Notice the approach to saturation of the parent ion signal for intensities in the region of 1014W/cm2.
serve that ADK theory and Keldysh theory overestimate the rate constants in the intensity range of 1013– 1015W/cm2. Therefore, the generalized KFR theory is chosen finally.
In detail, generalized KFR theory29 is originally pro-posed by Faisal30 based on the Keldysh theory and devel-oped with the S-matrix formalism by Reiss31 by combining the MO theory and the Born-Oppenheimer共BO兲 approxima-tion. We assume that the ground electronic state of molecule 共or molecular cation兲 is well described in terms of molecular orbitals and obtained from ab initio calculation. For the ion-ized state, the ionion-ized electron wave function is described by the Volkov continuum state,
pជ共rជ,t兲 = exp
冋
i冉
pជ· rជ− 1 2me冕
−⬁ t dt⬘
共pជ− eAជ共t⬘
兲兲2冊
册
, 共3.1兲 where e共=−1兲 is the charge of electron, pជ is the momentum of the ionized electron, and under the dipole approximation the vector potential Aជ共t兲 is given by Aជ共t兲=−Fជsin共t兲/ for the linearly polarized laser field Fជ共t兲=Fជcos共t兲.Then, the total electronic wave function of the molecule 共or molecular cation兲 is expressed as
⌿M共rជ1, . . . ,rជNe,t兲 = ⌿g共rជ1, . . . ,rជNe,t兲
+
冕
d3p
共2兲3cpជ共t兲⌿l,pជ共rជ1, . . . ,rជNe,t兲,
共3.2兲 where Neis the number of electrons and
cpជ共t兲 = − i
冕
−⬁ t dt⬘
具⌿l,pជ共pជ1, . . . ,rជNe,t兲 ⫻兩VˆA共pˆ1, . . . , pˆNe,t兲兩⌿g共rជ1, . . . ,rជNe,t兲典, 共3.3兲 with VˆA共pˆ1, . . . , pˆNe,t兲 =兺
l=1 Ne冉
−epˆl· Aជ共t兲 me +e 2A共t兲2 2me冊
, 共3.4兲and pˆi= −iⵜជrជi 共i=1, ... ,Ne兲.
Therefore, by using similar treatments of Keldysh24,32 and KFR共Ref.33兲 and under the assumption that the
ioniza-tion only takes place from the HOMO, the photoionizaioniza-tion rate constant can be formulated as
k共Fជ兲 = 2S2
兺
j,j⬘=1 Ne cjc*j⬘冕
d2p 共2兲3ˆj共pជ兲ˆj*共pជ兲冉
p2 2me + I0冊
2冏
⫻JN冉
eFជ· pជ me2 , U 2冊
冏
2 cos共pជ·共Rជj− Rជj⬘兲兲 ⫻兺
N=−⬁ ⬁ ␦冉
I0+ U + p2 2me − N冊
=兺
N 2S2兺
j,j⬘=1 Ne cjcj*⬘冕
d3p 共2兲3ˆj ⫻共pជ兲ˆ*j共pជ兲冉
p 2 2me + I0冊
2冏
JN冉
eFជ· pជ me2 , U 2冊
冏
2 ⫻cos共pជ·共Rជj− Rជj⬘兲兲␦冉
I0+ U + p2 2me − N冊
⫻兺
N⬎共le+U兲/ kN, 共3.5兲where JNis the generalized Bessel function,31cjdenotes the
coefficients of the linear combination of atomic orbitals-molecular orbital, I0 is the ionization potential of molecule, U =共eF兲2/共4me2兲 is the ponderomotive potential associated
with the optical field, S =
冑
2 for the closed shell parent mol-ecule or molecular cation, and S = 1 for the open shell. In addition, for multi-ionization of molecules, we consider the following sequential ionization process:M ——→ k1 M+——→ k2 M2+. . . ——→ k3 Mn+, 共3.6兲
where ki is the photoionization rate constant of Mi+ cation.
The rate equation can be solved if the photoionization rate constant is assumed to be independent of the laser time t during pulse duration.26,34This assumption has been checked FIG. 4. Relative ion yields of parent and main fragments ions as a function of laser intensity. The wavelength is 788 nm. In the same way, a linear fit through the data points is shown as the solid line. The saturation of the parent ion signal for intensities occurs in the same region of 1014W/cm2.
previously26,34 by taking into account the laser pulse of a Gaussian shape
Fជ共t兲cos共t兲 = Fជrexp共− 共4 ln 2兲t2/共⌬tF兲2兲cos共t兲
for the generalized Keldysh theory where Fជ0is the peak am-plitude, and⌬tFis the full width at half maximum. However,
it is also important to consider the spatial distribution of the laser pulse,35 and similar to the previous work,26we assume that the laser has a Gaussian shape of the spatial distribution with the width ⌬R, i.e., I共R兲=I0exp共−8R2/⌬R2兲. Then the ionization yield is dependent on time and R, i.e., Mi+共t,R兲,
and we define the spatial averaged ionization yield as
Mi+共t兲 = 4
冕
0 ⬁dRR2Mi+共t,R兲. 共3.7兲
B. Calculation results
The Keldysh or adiabatic parameter ␥=
冑
2mI0/共eF兲, which denotes the ratio of the tunneling time to the optical period, is frequently used to qualitatively identify the mecha-nism of ionization. In this expression, I0 denotes the ioniza-tion energy. If ␥Ⰷ1 the multiphoton ionization 共MPI兲 pro-cess dominates and if␥Ⰶ1 field ionization occurs.The calculated values of Keldysh parameter versus laser intensity are shown in Fig. 5 for both wavelengths. At 394 nm, when laser intensity is lower than 1014W/cm2, ␥ ⬎1 means MPI is dominant. As laser intensity increased, the value of ␥ tends to 1 and the effect of tunneling ionization cannot be neglected. On the contrary, the MPI is predomi-nant below 4⫻1013W/cm2 for 788 nm. Thus, it is reason-able to consider absorption photon numbers, namely, MPI mechanism, when laser intensity is below 1014W/cm2 for 394 nm and 4⫻1013W/cm2 for 788 nm, respectively.
For simplicity, we calculate the ionization rate constant with the hydrogenlike atom model. The HOMO of cyclopen-tanone mainly consists of the 2p atomic orbitals 共AOs兲. Therefore, we replace the photoionization rate constants of
Mn+ molecular cations by the one of the 2pz AO with the
same ionization potential, such as 9.28 eV for the M+ and 26.61 eV for the M2+. In Fig. 6, the photoionization rate
constants of a molecule using the model of hydrogenlike atom with 2pz orbital and the ionization potential of I1 = 9.28 eV are plotted as a function of the laser intensity for both wavelengths =394 nm 共a兲 and 788 nm 共b兲. Firstly, it should be noted that for both wavelengths, the ADK theory overestimates the rate constants for high laser intensity, es-pecially above 1014W/cm2, where the values of the rate constants go beyond 1017s−1. Secondly, the results obtained from the Keldysh theory also tend to overestimate the rate constants for the high intensity region, reaching k = 1016s−1 at I = 1015W/cm2. Furthermore, in the whole intensity region 共1013⬍I⬍1015W/cm2兲, the rate constants from the Keldysh theory and the KFR theory differ by a factor of 101– 103. This difference comes from the pole approximation where a contribution from a circle contour integral is neglected for the time integral in the Keldysh theory, while the time inte-gral in KFR theory is exactly performed. Moreover, we also illustrate the second ionization rate constants of cyclopen-tanone ion using the model of hydrogenlike atom with 2pz orbital and the ionization potential I2= 26.61 eV in Fig. 7: =394 nm 共a兲 and 788 nm 共b兲. The similar trends may point out that the results from the Keldysh theory are larger than those from the ADK and the KFR theory.
As mentioned above, the HOMO of a ketone molecule is a nonbonding orbital of the C–O group, which has the FIG. 5. Keldysh parameter as a function of laser intensity ranging from 1
⫻1013W/cm2to 1⫻1015W/cm2for 394 and 788 nm.
FIG. 6. 共Color online兲 Calculation results for first ionization rate constants of cyclopentanone by using various theories, where g-KFR represents the generalized KFR theory.共a兲 =394 nm; 共b兲 =788 nm.
FIG. 7. 共Color online兲 Calculation results for second ionization rate con-stants of cyclopentanone by using various theories, where g-KFR represents the generalized KFR theory.共a兲 =394 nm; 共b兲 =788 nm.
p-orbital character. For the purpose of comparing the
perfor-mance of the ADK, KFR, and Keldysh calculations, a 2p orbital has been used and the results are shown in Fig. 6. However, in the generalized KFR theory case, a realistic HOMO has been used in which the 2p orbital is mixed with a 3p orbital. For 394 nm, the results are shown in Figs.6共a兲 and 7共a兲. It is notable that the rate constants of the second ionization are much smaller than those of the first ionization, differ by a factor 104 at I = 1015 W/cm2and even larger for
I⬍1015W/cm2. In Fig. 8共a兲, the ion yields of cyclopen-tanone molecule with a single and double charge are illus-trated at 394 nm. Since the first and second ionization rate constants are quite different, the ion yield of singly charged cyclopentanone is quite larger than that of doubly charged one by a factor more than 103. Similarly, in Fig.8共b兲, we plot the ion yields of cyclopentanone molecule for the case of 788 nm as a function of laser intensity.
IV. DISCUSSION
A. Ionization rate constants
First, we compare our experimental results共Fig.1兲 with
the conventional mass spectrum of cyclopentanone provided by NIST共Ref. 36兲 共Fig.9兲. One can see that the peak
posi-tions of the two mass spectra are identical but the relative peak intensities differ. This is due to the fact that the energy
deposited in the parent ion depends on the experimental method, and variations in the available internal energy result in differences in the rate constants for decomposition of the ion. In this paper, these rate constants are obtained by em-ploying RRKM theory using ab initio potential surfaces.
We consider that ionization is followed by dissociation in our experiments because for neutral dissociation of a mol-ecule to take place, the molmol-ecule has to absorb energy from the laser first and then either predissociate or decompose after internal conversion. The decomposition products would ionize afterwards, and all these steps have to take place within the laser pulse duration of ⬃100 fs, making this sce-nario rather unlikely. Discussions of experimental data re-lated to this issue can be found in Refs.9,34, and 37.
Considering the larger difference between the ion yields for singly and doubly charged cyclopentanone, a factor more than 103, from the calculation results shown in Fig. 8, it should be hard to see the doubly charged molecular parent ion within the laser intensity used in the present experiment. This is confirmed by the experimental observations since there is no evidence for the doubly charged parent ions in all the measured mass spectra. For example, from Figs.
1共a兲–1共c兲, for 394 nm laser with the intensity below 2 ⫻1014W/cm2, only C
5H8O+ion together with the fragment ions resulted from its dissociation are produced. Actually, the ion peak at m/z=42 can be attributed to C3H6+from the dis-sociation other than the doubly charged parent ion. When increasing the laser intensity up to 3⫻1014W/cm2, C2+ions begin to be detectable, most probably from further ionization of the fragment C+in this 90 fs laser field. The similar trend can also be found in 788 nm case and, based on the calcula-tions mentioned above, the C5H8O++ion does not appear.
The wavelength dependence of the ionization can be ex-plained simply by the hydrogenlike theoretical model. From Fig. 6, we can also find a similar dependence of the wave-length based on the Keldysh theory and KFR theory. If the wavelength becomes shorter, both results become more flat keeping the asymptotic behavior for higher intensity around
I = 1015W/cm2 where the rate constants from the Keldysh 共KFR兲 theory seem to converge to a value of order 1016 共1014兲 s−1. Furthermore, by comparing the results for 394 and 788 nm with the same theoretical model in Fig.6, espe-cially for KFR theory, we observe that the first ionization rate constants for 394 nm are higher than those for 788 nm if laser intensity is below 1014W/cm2. According to the Keldysh parameter illustrated in Fig. 5, within this laser range, MPI mechanism may play an important role in the ionization process for both wavelengths. Thus, the ionization probability of cyclopentanone under the 394 nm irradiation is larger than that under the 788 nm irradiation. When laser intensity is increased to nearby 1014 W/cm2, the effect of field ionization cannot be neglected, particularly for the 788 nm irradiation; the laser field will then lead to nearly the same ionization probabilities for both wavelengths. As laser intensity continues to increase up to 1015W/cm2 or even higher, the ionization rate constants become independent of the wavelength.
From comparison of the theoretical and experimental re-sults as shown in Figs. 8共a兲 and 8共b兲, it is clear that the FIG. 8. 共Color online兲 Comparison of relative ion yields between
experi-mental and theoretical results.共a兲 =394 nm; 共b兲 =788 nm. The dot rep-resents experimental result of C5H8O+while the line corresponds to
theo-retical one. The dashed denotes the theotheo-retical prediction of the ion yield for C5H8O++.
FIG. 9. Conventional mass spectrum for cyclopentanone provided by the NIST Chemistry WebBook共Ref.36兲. The asterisk denotes the parent ion.
theoretical calculated ion yields of C5H8O+fit well with the experimental observations for the 394 nm case. From the calculated curve, a value of theoretical slope ranging from 2.9 to 3.4 for I =共5–7兲⫻1013W/cm2 is very close to the minimum number of photons required for MPI of the mol-ecule experimentally. Nevertheless, there exists an obvious difference at 788 nm for the high intensity region 共larger than 1014W/cm2兲. In Fig.8共b兲, the value of theoretical slope ranges from 5.5 to 6.3 for I =共1–3兲⫻1013W/cm2, which is close to the minimum number of photons required for MPI of the molecule experimentally. However, when laser inten-sity is up to 1014 W/cm2, the value of theoretical slope is smaller than 5, which is quite different from the experimental value of 6.2. From Fig.6, we can see that the ADK contri-bution to molecular ionization is not negligible even at I ⬃1013W/cm2; this indicates that the contribution from the tunneling ionization is not negligible in our laser intensity range. However, we feel that the resonance excitation pro-cesses of molecules do play a significant role in our obser-vations since the slopes equal roughly to the numbers of photons共N=3 or 6 for 394 or 788 nm, respectively兲 required for ionizing the ground state molecules. With increasing laser intensity at 788 nm, the calculated slope shifted from 6 to 5; this may be due to the contribution of the saturation effect involved in the ionization. In addition, the FAD 共Ref. 38兲
would play a non-negligible role in the fragmentation as well, which also affects the performance of the laser depen-dence. Namely, the fragmentation is higher now than that in the 394 nm case in the high intensity region. On the other hand, owing to the difference of the available internal energy for various wavelengths used here, compared with the shorter wavelength condition, the longer one may stimulate more dissociation channels, especially for the higher laser intensity region. However, in fact, we do not consider the influence of dissociation when using the generalized KFR theory for calculating the photoionization rate constants. Therefore, this calculation may lead to an obvious difference between the theoretical and experimental results in this high intensity region. It is clear that further investigation is re-quired both experimentally and theoretically.
B. Ab initio/RRKM calculations of the dissociation mechanism
The dissociation of molecular ions induced by an intense femtosecond laser can proceed in two ways. Within the laser-pulse duration and spatial distribution, the potential surfaces of molecular ions can be modified by the laser electric field, and if the laser intensity is strong enough, it can induce the ion dissociation during the laser duration. This type of ion dissociation is usually referred such as FAD 共Ref. 38兲 and
occurs in the femtosecond range. The second type of ion dissociation takes place outside the temporal and spatial in-fluence of the femtosecond laser pulse. In this case, the ions are hot and unstable and for reasonably large-sized ions, this type of ion dissociation can be treated by a statistical theory, for example, RRKM theory or quasiequilibrium theory. In this case, the rate constant of ion dissociation can be ex-pressed as k共E兲 =1 h· W*共E − E 0 *兲 共E兲 ,
where W⫽共E−E0⫽兲 and 共E兲 represent the total number of states of the activated complex with activation energy E0⫽ and the density of states of the reactant with energy E, respectively.
To study the dissociation mechanism of cyclopentanone ions, we here performed ab initio quantum chemical calcu-lations of potential energy surfaces 共PESs兲 for C5H8O+ and C5H8O++. The B3LYP/6-31G* method39 has been used to carry out geometry optimizations, and the energies of the ions have been refined by the G3共MP2,CCSD兲 ab initio calculations.40 The zero-point energy corrections to the total G3共MP2,CCSD兲 energies have been computed using B3LYP/6-31G*frequencies without scaling. The differences between B3LYP/6-31G** and G3共MP2,CCSD兲 relative en-ergies both for local minima and barrier heights did not ex-ceed 5 – 10 kcal/mol, within the regular accuracy expected from the B3LYP method, and therefore geometry optimiza-tion at a higher theoretical level is not required. Also, no significant spin contamination was detected for open shell systems including C5H8O+ and fragmentation products, as calculated具S2典 values were close to 0.75 and did not exceed 0.77. Connections between transition states and local minima were checked by intrinsic reaction coordinate共IRC兲 calcula-tions at the B3LYP/6-31G* level. Such calculations were
carried for all significant isomerization and decomposition channels, excluding only those contributing less than 0.1% to the overall product yield. For instance, for the monocation, we computed IRC pathways for all transition states corre-sponding to barriers below⬃70 kcal/mol. All ab initio cal-culations have been performed using theGAUSSIAN 03共Ref.
41兲 and MOLPRO 2002 packages.42 B3LYP/6-31G* frequen-cies for all intermediates and transition states have been used to perform the RRKM calculation.34
C. Dissociation of the C5H8O+monocation
The computed adiabatic ionization potential of C5H8O is 9.24 eV, in close agreement with the experimental value of 9.28 eV.20 The multistep dissociation scheme for the C5H8O+monocation is shown in Figs.10and11. The variety of possible photodissociation channels of C5H8O+is given in the following: C5H8O+→ C4H8++ CO, m/z = 56, C5H8O+→ C3H4O++ C2H4, m/z = 56, C5H8O+→ C3H3O++ C2H5, m/z = 55, C5H8O+→ C3H6 + + H2C2O, m/z = 42, C5H8O+→ C3H3O++ C2H3, m/z = 57, C5H8O+→ C5H7O++ H, m/z = 83, C5H8O+→ C5H6O++ H2, m/z = 82,
C5H8O+→ C5H6 +
+ H2O, m/z = 66.
Let us first consider the CO elimination mechanism 关Fig.
10共a兲兴. Ring opening in cyclopentanone monocation C5H8O+ 共i1兲 accompanied with 1,2-H shift gives an open-chain inter-mediate i2, CH3CHCH2CH2CO+, residing 12.6 kcal/mol above i1. This process requires a barrier of 42.2 kcal/mol. Next, i2 can lose the carbonyl group producing a chain C4H8+ structure, CH3CH2CHCH2+, overcoming a transition state 共TS兲 lying 30.5 kcal/mol above i1. The CO elimination pro-cess here goes together with H migration from CH2 to CH. The overall endothermicity of this i1→C4H8++ CO product channel is 23.7 kcal/mol. Another CO elimination pathway involves ring opening to produce a CH2CH2CH2CH2CO+ intermediate i3 via a barrier of 14.2 kcal/mol. The interme-diate is metastable as it resides only 0.2 kcal/mol lower in energy than the ring opening transition state. i3 can further decompose to C4H8+ 共2兲, which is essentially a complex of neutral ethylene and its cation, C2H4¯C2H4+. The C4H8+共2兲 + CO products reside 41.2 kcal/mol above i1 and the CO elimination TS is located 41.9 kcal/mol higher in energy than the initial cyclopentanone monocation. The C4H8+共2兲 + CO products can also be formed directly from i1 by pulling away the CO group via a barrier of 45.9 kcal/mol.
In summary, three reaction channels producing
C4H8 +
+ CO have been found: i1→CH3CHCH2CH2CO+i2 →CH3CH2CHCH2
+
+ CO, i1→CH2CH2CH2CH2CO+i3
→C4H8
+共2兲+CO, and one-step i1→C 4H8
+共2兲+CO, with the highest barriers of 42.2, 41.9, and 45.9 kcal/mol relative to i1, respectively.
A number of different product channels are also feasible, but they are preceded by various rearrangements of the cat-ion, which normally involve ring opening, H migrations, etc. 关see Fig.10共b兲兴. A 1,3-H shift between the two CH2 groups adjacent to CO accompanied with ring opening via the cleav-age of the C共O兲–CH2 bond leads to the intermediate i4, CH3CH2CH2CHCO+ 共5.9 kcal/mol above i1兲, via a barrier of 58.8 kcal/mol. This process is rather peculiar. According to IRC calculations ran from the transition state all the way down to i1 and i4, before the TS an H atom moves from a CH2group to the CO carbon atom while the bond connecting this atom with the other neighboring CH2 group elongates and starts to break. After the barrier is cleared, the moving H atom continues its motion, leaves the carbonyl carbon, and eventually forms a CH3 group while the C共O兲–CH2 bond cleavage completes. Meanwhile, there exists a three-step lower energy pathway from i1 to i4. At the first step, ring opening occurs along the CH2– CH2 bond opposite to the CO group. This process leads to the formation of CH2CH2¯C共O兲CH2CH2+i5 over a barrier of 39.9 kcal/mol. The intermediate i5 lying 37.0 kcal/mol higher in energy than i1 can undergo 1,4-H migration to a terminal CH2group to produce the intermediate i6, CH3CH2COCHCH2+, 18.5 kcal/mol above i1, via a TS positioned 50.1 kcal/mol higher in energy than i1. Next, i6 rearranges to i4 by a 1,3-FIG. 10. 共Color online兲 Major channels of the dissociation mechanism of
C5H8O+.
shift of the C2H5 moeity overcoming a barrier of 17.0 共35.2兲 kcal/mol relative to i6 共i1兲. One can see that the high-est barrier on the multistep i1→i5→i6→i4 pathway is 50.1 kcal/mol with respect to i1, significantly lower than 58.8 kcal/mol for the direct i1→i4 process. Finally, i4 can further isomerize to i2 by 1,3-H migration between the CH2 and CH groups via a TS lying 36.3 kcal/mol above i1.
In addition to C4H8++ CO, the intermediate i2 can give rise to the C3H6+ 共CH3CHCH2+兲+H2CvCvO products, which lie 47.1 kcal/mol higher in energy than i1 关Fig.10共c兲兴.
In this case, the cleavage of the CH2– CH2 bond nearest to the carbonyl group occurs without an exit barrier. Also, in principle, H migration between two CH2groups followed by the cleavage of the C–C bond connecting them could bring forward C3H7+ 共2-propyl cation兲+HCCO, but since these products lie 70.9 kcal/mol higher in energy than i1, we do not consider the details of this channel further. i4 can disso-ciate to three different product pairs, C3H3O++ C
2H5, 39.4 kcal/mol above i1, without an exit barrier; C4H5O+ + CH3, 30.4 kcal/mol higher in energy than i1, via a barrier of 62.6 kcal/mol relative to i1; and C3H6
+
+ H2CvCvO, 47.1 kcal/mol above i1, via a TS involving two simulta-neous 1,2-H shifts accompanying the C–C bond cleavage and residing 62.6 kcal/mol above the initial C5H8O+ mono-cation. i5 can easily lose the C2H4fragment with the forma-tion of the C3H4O+ 共CH
2CH2CO+兲 cation, where the C3H4O++ C
2H4 products lie 40.8 kcal/mol above the initial C5H8O+ monocation. Finally, structure i6 can eliminate ei-ther C2H5 or C2H3 groups producing C3H3O+and C3H5O+ with overall endothermicities of 39.4 and 47.8 kcal/mol rela-tive to i1, respecrela-tively, and without exit barriers. In terms of the activation energy required共the highest barrier on the re-action pathway or rere-action endothermicity in case of disso-ciation steps occurring without an exit barrier兲, the product channels described here can be ranked as follows: i1→i5
→C3H4O++ C2H4 共40.8 kcal/mol兲, i1→i2→C3H6 +
+ H2CvCvO 共47.1 kcal/mol兲, i1→i5→i6→i4
→C3H3O++ C2H5,¯i6→C3H3O++ C2H5, and ¯i6 →C3H5O++ C2H3 共all 50.1 kcal/mol兲, followed by much less favorable ¯i4→C3H6O++ H2CvCvO and ¯i4 →C4H5O++ CH3共both 62.6 kcal/mol兲.
Now we consider H and H2 elimination pathways 共Fig.
11兲. Starting from the cyclic structure i1, the H loss from the meta carbon共relative to the CO group兲 is accompanied with
ring opening to produce an open chain C5H7O+ isomer CH2CHCH2CH2CO+residing 46.5 kcal/mol above the reac-tant. However, the barrier for this process is rather high, 61.2 kcal/mol. A cyclic c-C5H7O+ product, residing 58.1 kcal/mol higher in energy than i1, can be formed by H elimination from the meta position but the barrier in this case is higher, 71.2 kcal/mol. The CH2CHCH2CH2CO+ product can be also formed by H elimination from the terminal CH3 group in i2 and from the next-to-terminal CH2 group in i3, with lower barriers of 47.6 and 51.8 kcal/mol relative to i1, respectively. The intermediate i2 can also eliminate a hydro-gen atom from two different CH2 group producing C5H7O+ 共2兲, CH3CHCHCH2CO+, and C5H7O+共3兲 featuring a three-member carbon ring. These processes are calculated to be endothermic by 44.8 and 44.6 kcal/mol with respect to i1
and the corresponding TSs lie 47.9 and 60.4 kcal/mol, re-spectively, above i1. Finally, H elimination from the central CH2group in i4 produces C5H7O+共4兲, CH
3CH2CHCHCO+, with the barrier and endothermicity of 42.0 and 40.8 kcal/mol relative to i1. In summary, the most favorable H loss channels共their highest activation barriers兲 are the fol-lowing: i1→i2→CH2CHCH2CH2CO+ 共47.6 kcal/mol兲, i1 →i2→CH3CHCHCH2CO+ 共47.9 kcal/mol兲, and i1→i5 →i6→i4→CH3CH2CHCHCO+共50.1 kcal/mol兲.
Molecular hydrogen elimination is less favorable than an H atom loss. For instance, the H2 splitting from the cyclic C5H8O+ structure i1 requires a 60.7 kcal/mol barrier and produces cyclic C5H6O+ with endothermicity of 33.0 kcal/mol. H2 loss from i2 forms a more stable chain C5H6O+ 共2兲 isomer, CH3CHCHCHCO+, 12.3 kcal/mol above i1, but the barrier is even higher, 76.7 kcal/mol. From i4, molecular hydrogen can be eliminated either directly, pro-ducing C5H6O+共3兲, CH
3CH2CHCCO+, via a higher barrier of 88.7 kcal/mol, or following H migration and giving rise to C5H6O+ 共4兲, CH3CCHCH2CO+, with a barrier of 74.9 kcal/mol for the final step. Because of such high barri-ers, we do not expect the H2loss to play any significant role. The cyclopentanone cation i1 can also eliminate a water molecule. All H2O loss pathways start from the cyclic inter-mediate i8 produced from i1 by the 1,3-H shift from an ortho CH2group to the oxygen atom via a barrier 51.6 kcal/mol. i8 is 10.7 kcal/mol more stable than i1 and features a hy-droxyl group attached to a cyclopentenelike ring. Next, an-other CH2 to OH 1,3-H shift, exhibiting a barrier of 56.4 kcal/mol relative to i1, produces the intermediate i9, in which an H2O group is attached to the ring. i9 loses molecu-lar water via a barrier of 45.7 kcal/mol with respect to i1 and the C5H6++ H2O products are 43.4 kcal/mol less stable than the initial reactant. The other H2O elimination channels fea-ture multiple hydrogen shifts around the ring prior the for-mation of the H2O group and its elimination. In the most favorable pathway, i8 rearranges to i10 by the CH2 to CH hydrogen migration, then i10 isomerizes to i11 by the CH2to C共OH兲 H shift, i11 converts to i12 by another 1,2-H shift from the C共OH兲 carbon to the oxygen atom, and finally H2is eliminated from i12 giving rise to the C5H6+共2兲+H2O prod-ucts lying 39.6 kcal/mol above i1. The highest barrier on this pathway, 46.6 kcal/mol higher in energy than i1, is found for the i11→i12 step. The remaining pathways initiate from i10 and involve at least one 1,3-H shift and hence ex-hibit higher barriers. Summarizing, the preferable H2O loss
channel is the following: i1→i8→i10→i11→i12
→C5H6+共2兲+H2O, with the rate-determining barrier of 51.6 kcal/mol at the first reaction step. Note that elimination of the OH group to produce C5H7+, which can occur directly from i8, is 88.2 kcal/mol endothermic with respect to i1 and thus unlikely to happen.
One can see that many different C5H8O+decomposition channels are feasible with the rate-controlling barriers lying in the range of 41– 52 kcal/mol. To evaluate the contribution of various dissociation products to the total yield more quan-titatively, RRKM calculations of rate constants and product branching ratios are required. According to such calculations, the dissociation yields depend on the internal energy and the
initial intermediate from which the dissociation starts 共Fig.
12兲. One can see that if the initial energized intermediate is
the cyclic i1 structure 关Fig. 12共a兲兴, the dominant
reaction products 共80%–95%兲 are C4H8+ 共2兲
共the C2H4¯C2H4+complex兲+CO and the only other signifi-cant products 共20%–5%兲 are C3H4O++ C2H4. These results can account only for the m/z=56 peak in the spectra; the peaks at m/z=55, 28, and 27 also observed even at the low-est laser field intensity at=394 nm can be explained only if secondary dissociation is invoked共see below兲. Nevertheless, the higher intensity of the m/z=55 peak compared to that of
m/z=56 cannot be understood from these data. The
mono-cation formed after multiphoton ionization can, in principle, absorb more photons to populate excited states and, to un-derstand the mechanism of subsequent dissociation, we stud-ied the first excited PES of C5H8O+ in the vicinity of the equilibrium structure of the monocation using multireference configuration interaction calculations43 with 共11,11兲 active space and Dunning’s aug-cc-pVTZ basis set.44 As seen in Fig.13, although the vertical excitation energy of C5H8O+is rather high, 74.3 kcal/mol, as the ring starts to open, the energies of the ground and excited states approach each other and their surfaces are likely to cross in the energy range of
⬃35 kcal/mol. Although we have not optimized a conical intersection geometry, we found a structure in this vicinity, for which the energy difference between the ground and first excited states is less than 1 kcal/mol, strongly suggesting an existence of a crossing point. The possibility and importance of such surface crossing with formation of an open-chain diradical structure in the ground electronic state was ob-served by Pedersen et al. for neutral cyclopentanone.45 If such crossing does indeed occur and the internal conversion takes place at an open-chain rather than cyclic geometry, the initial energized intermediates in the ground electronic state may be not only i1, but also i5 and i6 i5 is separated from i1 by a very low barrier of 2.9 kcal/mol and so its dissociation pattern is not expected to be different from that for i1. For i6, we carried out RRKM calculations considering this interme-diate as the initial energized species and the resulting product branching ratios illustrated in Fig. 12共b兲 are rather distinct from those obtained for cyclic C5H8O+. The dominant disso-ciation channel at internal energies below 150 kcal/mol is C3H3O++ C2H5. The C3H5O++ C2H3 channel starts to con-tribute early, and at the higher energies the C3H6++ H2C2O and C5H7O++ H products also exhibit noticeable yields. This result can account for the high intensity of the observed
m/z=55 peak and also for the appearance of the m/z=42
peak at higher laser intensities. On the other hand, the peaks with m/z=57 and 83 are practically not present in the mass spectra indicating that apparently C3H5O+ and C5H7O+ do not survive secondary dissociation.
D. Secondary dissociation of primary monocation products
If the primary dissociation products possess enough in-ternal energy 共or if they themselves absorb additional laser photons and become vibrationally hot after internal conver-sion to the ground electronic state following the photon ab-sorption兲, they can undergo secondary decomposition. Here, FIG. 12. 共Color online兲 Calculated branching ratios in dissociation of
C5H8O+:共a兲 starting from i1; 共b兲 starting from i6.
FIG. 13. 共Color online兲 Mechanism of relaxation of C5H8O+from the first
we address the most important primary products, such as C4H8 + , C3H4O+, C5H7O+, C3H5O+, and C3H3O+. Dissocia-tion of C4H8 +
is described in the following关Fig.14共a兲兴, C4H8+→ C2H4++ C2H4, m/z = 28, C4H8+→ C3H5++ CH3, m/z = 41, C4H8 +→ C 2H3+ C2H5 + , m/z = 29, C4H8+→ C4H7++ H, m/z = 55, C4H8 +→ C 2H6 + + C2H2, m/z = 30.
H elimination from the central CH2 group of C4H8+ 共1兲, CH3CH2CHCH2+, gives C4H7+, CH3CHCHCH2+, with the en-ergy loss of 33.8 kcal/mol and without an exit barrier. Simi-larly, C4H8+ 共1兲 can lose the terminal CH3 group producing allyl radical cation C3H5+endothermic by 37.9 kcal/mol. The elimination of C2H3with the formation of C2H5+is much less favorable and requires 62.9 kcal/mol. Splitting the terminal CH2 group as a neutral species or a cation exhibits prohibi-tively high endothermicities of 106.9 and 111.1 kcal/mol, respectively, and is not likely to occur. The pathway to the C2H6++ C2H2 products, endothermic by 78.3 kcal/mol, in-volves flipping over the terminal C2H3 group with the for-mation of an intermediate in which C2H2 and C2H5 frag-ments are connected via a bridging proton, which eventually
moves to the CH2 group of C2H5 to form C2H6+. Finally, C4H8+共1兲 can rearrange to C4H8+共2兲, which is described as a C2H4¯C2H4+ complex, by rotation around the central C–C bond followed by H migration from CH3to CH. The highest barrier on this pathway, 29.2 kcal/mol, is for the hydrogen shift. C4H8+共2兲, residing 17.5 kcal/mol above C4H8+共1兲, eas-ily decomposes to C2H4
+
+ C2H4 with the energy loss of 24.1 kcal/mol. According to RRKM calculations, dissocia-tion of C4H8+共2兲 at relatively low internal energies is domi-nated by C3H5
+
+ CH3 and C2H4 +
+ C2H4, whereas at higher energies the C2H5++ C2H3 channel becomes important 共Fig. 15兲. The contribution of the H elimination channel, C4H7+ + H, remains rather small, 2%–3%, in the entire internal en-ergy range considered.
Ethylene cation can be also produced in secondary de-composition of another important primary dissociation prod-uct, C3H4O+共CH2CH2CO+兲, by elimination of the CO group endothermic by 24.5 kcal/mol 共Fig.10兲. Interestingly, both
for C3H4O+ and C4H8+ 共2兲, likely dissociation products are C2H4++ C2H4+ CO, but the eliminations of CO and C2H4take place in a different order共see Fig.10兲. Another feasible
de-composition channel of CH2CH2CO+is H elimination from the central CH2 group to produce C3H3O+ 共CH2CHCO+兲 with endothermicity of 32.1 kcal/mol. The C5H7O+共4兲 pri-mary product 共CH3CH2CHCHCO+兲, which may be formed if primary decomposition starts from the open-chain i6 inter-mediate, is most likely to dissociate to C3H5+ + H2CvCvO 关Fig. 14共b兲兴. The pathway to these products involves isomerization to C5H7O+ 共CH2CHCH2CH2CO+兲 via a barrier of 48.0 kcal/mol by two hydrogen shifts a CH3CHCH2CH2CO+ intermediate formed after the first H migration appeared to be metastable, as it exists only at the B3LYP level, but disappears at G3. Next, CH2CHCH2CH2CO+ decomposes without an exit barrier to form allyl cation and H2CvCvO. Overall, 55.3 kcal/mol are required to form these products from C5H7O+ 共4兲. The other dissociation channels, such as H and CH3 elimination, are much less favorable. C3H5O+ is likely to decompose to C2H5
++ CO with endothermicity of 38.8 kcal/mol 关Fig. FIG. 14. 共Color online兲 Secondary dissociation channels of C4H8+共a兲 and
C5H7O+共b兲.
FIG. 15.共Color online兲 Calculated branching ratios in dissociation of C4H8+
10共b兲兴. C3H3O+is more stable with respect to secondary de-composition and needs 56.3 kcal/mol of internal energy to dissociate to C2H3++ CO关Fig.10共c兲兴.
We can see that the secondary dissociation channels can account for the m/z=55 共C4H7+兲, 41 共C3H5+兲, 28 共C2H4+兲, and 29 共C2H5+兲 peaks. On the other hand, the nonappearance of the m/z=83 and 57 peaks in the spectra is likely due to instability of C5H7O+and C3H5O+ with respect to their de-composition to C3H5++ H2CvCvO and C2H5++ CO, respec-tively, which means that these primary products, if formed, possess internal energies of at least 55.3 and 38.8 kcal/mol, respectively.
E. Dissociation of the C5H8O++dication
A main drawback of the dissociation scheme originated from C5H8O+is that it cannot explain the production of H+ and CH3+and that the signal of m/z=42 may also be due to the production of C5H8O++. In general, the appearance of a proton peak in mass spectra is a sign of the production of ions with a charge higher than 1. For monocations, dissocia-tion channels giving H+ are energetically unfavorable as compared to other channels due to the very high ionization energy of a hydrogen atom, 13.6 eV. The vertical double ionization potential of cyclopentanone is computed to 26.58 eV. However, the cyclic structure of the dication is not a local minimum and, upon geometry optimization, under-goes spontaneous ring opening accompanied by H migration to the terminal CH2group to form CH3CHCH2CH2CO++in singlet electronic state. Considering this C5H8O++ isomer, the adiabatic double ionization energy of cyclopentanone is 21.63 eV. In Fig.16, we present the dissociation mechanism of C5H8O++; the main dissociation channels are shown in the following: C5H8O++→ C 4H5O++ CH3+, m/z = 69/15, C5H8O++→ C3H5O++ C2H3 + , m/z = 57/27, C5H8O++→ C3H3O++ C2H5, m/z = 55/29, C5H8O++→ C4H7 + + HCC+, m/z = 55/29, C5H8O++→ C5H7O++ H+, m/z = 83/1.
The most favorable channel for CH3+elimination involves the 1,2-H shift from CH2 to CH, which is followed by 1,2-migration of the CH3group after the transition state, to form a branched CH3C共H兲共CH2兲CH2CO+ intermediate residing 9.8 kcal/mol higher in energy than the initial dication. The barrier for this process is calculated to be 23.0 kcal/mol. The branched intermediate loses CH3+ via a barrier of 33.6 kcal/mol relative to the CH3CHCH2CH2CO++reactant producing C4H5O+ 共2兲, CH2CHCH2CO+, with overall exo-thermicity of 23.9 kcal/mol. The C4H5O+共2兲 cation is rela-tively unstable and needs only 24.2 kcal/mol of internal en-ergy to give the C3H5++ CO products. Other pathways leading to the CH3+ elimination involve the formation of a five-member C4O ring from the initial dication, with the CH3 group attached, followed by its loss either immediately or
after a number of hydrogen shifts and producing various cy-clic C4H5O+isomers. However, these channels are controlled by the initial ring closure step, which exhibits a high barrier of 73.1 kcal/mol, effectively rendering this mechanism non-competitive.
The C5H8O++dication can also decompose in one step to C3H5O++ C 2H3 +, C 3H3O++ C2H5 +, and C 4H7
++ HCO+via bar-riers of 41.4, 49.2, and 53.5 kcal/mol, respectively. Interest-ingly, in all of these processes, a bond cleavage goes together with a hydrogen atom migration. H+ elimination can take place from different positions in C5H8O++ to form C5H7O+ 共CH2CHCH2CH2CO+兲, C5H7O+ 共2兲 共CH3CHCHCH2CO+兲, and three-member ring C5H7O+共3兲 overcoming rather high barriers of 83.9, 88.2, and 94.7 kcal/mol, respectively. Fi-nally, splitting a neutral H2 molecule gives a C5H6O++ dica-tion 共CH2CCH2CH2CO++兲, but the barrier is also high, 94.0 kcal/mol. The calculated branching ratios are shown in Fig. 17. The C4H5O+共2兲+CH3+ channel appears to be most important up to internal energies higher than 200 kcal/mol. As mentioned above, C4H5O+共2兲 is likely to decompose to C3H5++ CO if it possesses internal energy higher than 24.2 kcal/mol. The second significant product channel is C3H5O++ C2H3+ with its branching ratio peaking at ⬃225 kcal/mol. The C3H5O+ product will not survive and will further dissociate to C2H5++ CO if its internal energy is higher than 38.8 kcal/mol. The third channel, which be-comes the most important above 200 kcal/mol is C4H7+ + HCO+. Finally, the H+elimination starts to play some no-ticeable role only at high internal energies. Interestingly, the C3H3O++ C2H5+ channel does not exhibit any significant
yield despite of a relatively low barrier of 49.2 kcal/mol, which is caused by a very tight character of the correspond-ing transition state resultcorrespond-ing in a low rate constant.
Considering the dication dissociation mechanism, we can now account for the m/z=15 peak 共CH3+兲 and the group of peaks down to m/z=12, which can be produced by se-quential H losses from CH3+to C+, m/z=41 共C3H5+formed by secondary decomposition of C4H5O+ or C5H7O+兲, m/z=27 and 26 共C2H3+ and C2H2+ produced by H loss from the former兲, m/z=29 共HCO+and C
2H5+from secondary dissocia-tion of C3H5O+, m/z=55 共C
4H7
+兲, and m/z=1 共H+兲. TableI summarizes our assignment of the origin of various peaks observed the mass spectra.
Only few spectral features remain unexplained at this stage, a small peak at m/z=32, a relatively high intensity of the proton peak, and a significantly higher intensity of m/z = 39 compared to that of m/z=40. The 32 peak might be due to methanol cation, CH3OH+, however, despite a careful search we failed to find any pathway to this product either on the monocation or dication PES. We speculate that this peak could originate from small O2impurity, if a small amount of oxygen molecules present undergo multiphoton ionization in intense laser field.
The H+peak growing with the laser field intensity might be due to decomposition of cyclopentanone trication. Indeed, our ab initio/RRKM calculations for C5H8O+++show that its major dissociation channels are expected to be C3H4O++ + C2H4+and C5H7O+++ H+, which require barriers of only 3.1 and 25.1 kcal/mol, respectively. However, since no evidence of the trication formation is found either in experiment or in theoretical calculations of ionization rate constants, we do not consider the C5H8O+++ PES in detail here. Another pos-sibility to produce H+, which should increase with the laser field intensity, is further ionization of the primary cationic products to form dications, which should be able to eliminate H+ more easily than their single-charged counterparts. This hypothesis is also supported by the absence of the m/z=83 共C5H7O+兲 and 41.5 共C5H7O++兲 peaks in the spectra.
Concerning the series of peaks at m/z=42–39, C3H6 + 共42兲 is a possible minor primary product 关Fig.12共b兲兴, C3H5+
共41兲 can be formed by H loss from C3H6
+and also is likely to be produced from C4H8+, C5H7O+, and from the C
4H5O+共2兲 primary product of dication dissociation. Next, C3H4+ 共40兲 and C3H3+共39兲 can be produced by sequential H losses from C3H5+. The fact that the 39 peak is significantly more intense than 40 can be attributed to different stabilities of the C3Hn+
ions with respect to the hydrogen atom elimination. In par-ticular, the endothermicities of the C3H5+→C3H4++ H, C3H4+ →C3H3++ H, and C3H3+→C3H2++ H reactions are calculated to be 91.7, 38.7, and 122.4 kcal/mol, respectively, which means that C3H3+is the most stable ion in the series, whereas C3H4+ is the least stable one and thus is most likely to de-compose. The higher stability of C3H3+owes to aromatic sta-bilization of its cyclic structure.
FIG. 17. 共Color online兲 Calculated branching ratios in dissociation of C5H8O++.
TABLE I. Assignment of the observed peaks in the experimental mass spectra due to ionization/dissociation of cyclopentanone in a femtosecond laser field. m/z Species Origin 84 C5H8O+ Parent monocation 56 C4H8+ Primary dissociation of C5H8O+ C3H4O+ Primary dissociation of C 5H8O+
55 C3H3O+ Primary dissociation of C5H8O+initiated from
CH3CH2COCHCH2共i6兲 Secondary dissociation of C3H4O+ C4H7 + Secondary dissociation of C 4H8 + 42 C5H8O++ Parent dication C3H6 + Primary dissociation of C 5H8O+initiated from i6 41 C3H5+ Secondary dissociation of C4H8+ H loss from C3H6 +
Secondary dissociation of C4H5O+, a major product of
dication dissociation
Secondary dissociation of C5H7O+, a minor product of
dication dissociation 40 C3H4+ H loss from C3H5+ 39 C3H3+ H loss from C 3H4+ 32 O2+ Ionization of O 2impurity 29 C2H5+ Secondary dissociation of C 4H8+
Secondary dissociation of C3H5O+, a minor product from
i6 or dication
HCO+ Primary dissociation of dication
28 C2H4 + Secondary dissociation of C 4H8 + Secondary dissociation of C3H4O+ H loss from C2H5 +
Primary dissociation of C5H8O+++共if the trication can be
produced兲
C3H4O++ Primary dissociation of C5H8O+++共if the trication can be
produced兲
C5H8O+++ Parent trication共unlikely to be produced兲
27 C2H3+ Dissociation of C 3H3O+
Primary dissociation of dication H loss from C2H4+
26 C2H2
+ H loss from C 2H3
+
15 CH3+ Primary dissociation of dication
14 CH2+ H loss from CH3+
13 CH+ H loss from CH
2 +
12 C+ H loss from CH+
1 H+ Primary dissociation of dication共a minor product兲
Primary dissociation of C5H8O+++共if the trication can be
produced兲
Dissociation of dications produced by ionizing primary products
The present results on cyclopentanone ionization/ dissociation in intense femtosecond laser field in general show similarity with the previous experimental studies of laser induced ionization/dissociation of this molecule.10,12 Meanwhile, due to much higher laser intensity, significantly deeper dissociation patterns have been observed, which owe to higher available internal energies due to absorption of a large number photons. Several mass spectral features can be attributed to the formation of cyclopentanone dication fol-lowed by its decomposition. It should be also noted that the experimental measurements and theoretical calculations here are highly complementary to each other. Experimental mass spectra does not allow unique assignment of the observed peaks to particular fragments because different species can have the same mass 共e.g., C4H8
+
and C3H4O+兲 and because dications can be potentially formed with the same m/z ratio as monocations, such as C5H8O++and C3H6
+
. The experimen-tal mass spectra also cannot distinguish between different isomers of the same species. On the other hand, theoretical
ab initio/RRKM calculations assume statistical character of
dissociation after intramolecular vibrational redistribution is completed the assumption which may not be valid at high available internal energies. Also, under conditions of multi-photon ionization/dissociation, unlike in photodissociation upon absorption of a single photon of a fixed wavelength, the parent ions and their primary fragments may acquire differ-ent amounts of internal energy, which complicates the theo-retical analysis. In addition, field assisted dissociation may also play a significant role. Nevertheless, the combined experimental/theoretical study has allowed us to unravel the ionization/dissociation mechanism of cyclopentanone at least qualitatively and to positively assign all observed peaks in the mass spectra.
V. CONCLUSIONS
In conclusion, in this paper, we studied the ionization processes of cyclopentanone under 90 fs intense laser field irradiation for 394 or 788 nm wavelengths and the intensities varying from 3⫻1013to 4⫻1014W/cm2. Rescattering pro-cesses are important only under very strong laser field con-ditions, typically above 1014W/cm2; however, in our work, the laser intensity covers 1013– 1014W/cm2 and the field may not be high enough for the rescattering contribution to become important. More experimental and theoretical work needs to be done in future to address the role of rescattering at a stronger laser field regime.
The laser dependence of parent ion and the main frag-ment ions for both wavelengths has been demonstrated. We have calculated the ionization rate constants by using ADK, Keldysh, and KFR theories based on a hydrogenlike atom. We believe that the generalized KFR theory, which is based on the original KFR theory combined with MO theory and the BO approximation, is the best choice for calculating the ionization rate constants for cyclopentanone. According to the calculated results, in our laser-intensity range, the doubly charged parent ion may not be found due to much lower rate of second ionization process compared with first ionization. Furthermore, we compare the experimental ion yields with
theoretical results. In the lower intensity region, experimen-tal results for both wavelength cases show a good agreement with theoretical ones. However, in the higher intensity range, there exists a difference between experimental and calculated results for the 788 nm case. An important feature of the mass spectra obtained from the high power laser ionization/ dissociation of molecules is that due to the non-negligible contribution from the tunneling ionization, the internal en-ergy deposited in the parent ion forms a distribution function which is to be determined. It should be noted that the de-tailed analysis of the Keldysh theory can provide the infor-mation of the most probable multiphoton process involved in high-power laser ionization of molecules. In other words, it is possible to estimate the distribution function of internal energy kN/兺N⬁⬎N0kN with N0=共I0+ U兲/ from Eq. 共3.5兲, which is a function of photon numbers N
kN=
兺
N 2S2兺
j,j⬘=1 Ne cjcj ⬘ *冕
d3p 共2兲3ˆj共pជ兲ˆ*j共pជ兲 ⫻冉
p2 2me + Ie冊
2冏
JN冉
eFជ· pជ me2 , U 2冊
冏
2 ⫻cos共pជ·共Rជj− Rជj⬘兲兲␦冉
I0+ U + p2 2me − N冊
.Furthermore, in the case of high-power laser ionization/ dissociation, there might be some contribution from the so-called FAD of the parent ion which will further complicate the decomposition processes of the parent ion. From the the-oretical point of view, FAD processes will need to be ad-dressed by calculations of PES and reaction dynamics in the presence of a strong laser field. At this point, a qualitative understanding of the femtosecond ionization/dissociation mechanisms of cyclopentanone has been achieved by using the RRKM theory based on the ab initio surfaces.
ACKNOWLEDGMENTS
Support by the National Science Foundation of China 共NSFC兲 under Grant Nos. 10534010 and 10374036 are ac-knowledged. A.M.M. thanks the US Department of Energy-Basic Energy Sciences 共Grant No. DE-FG02-04ER15570兲 for partial support of this work.
1H. Harada, S. Shimizu, T. Yatsuhashi, S. Sakabe, Y. Izawa, and N.
Na-kashima,Chem. Phys. Lett. 342, 563共2001兲.
2L. Hongtao, Y. Zheng, G. Zhen, and T. Zichao,J. Chem. Phys. 126,
044316共2007兲.
3K. W. D. Ledingham, R. P. Singhal, D. J. Smith, T. McCanny, P. Graham,
H. S. Kilic, W. X. Peng, S. L. Wang, A. J. Langley, P. F. Taday, and C. Kosmidis,J. Phys. Chem. A 102, 3002共1998兲.
4R. Ma, C. Wu, N. Xu, J. Huang, H. Yang, and Q. Gong,Chem. Phys.
Lett. 415, 58共2005兲.
5N. Nakashima, S. Shimizu, T. Yatsuhashi, S. Sakabe, and Y. Izawa,J.
Photochem. Photobiol. C 1, 131共2000兲.
6S. Shimizu, V. Zhakhovskii, F. Sato, S. Okihara, S. Sakabe, K. Nishihara,
Y. Izawa, T. Yatsuhashi, and N. Nakashima,J. Chem. Phys. 117, 3180 共2002兲.
7M. Tanaka, M. Murakami, T. Yatsuhashi, and N. Nakashima,J. Chem.
Phys. 127, 104314共2007兲.
8S. A. Trushin, W. Fuß, and W. E. Schmid,J. Phys. B 37, 3987共2004兲. 9D. Wu, Q. Q. Wang, X. H. Cheng, M. X. Jin, X. Y. Li, Z. Hu, and D.
