Velocity map imaging of the photolysis of n-C4H9Br in UV region

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Chemical Physics 340 (2007) 141–148 www.elsevier.com/locate/chemphys

Velocity map imaging of the photolysis of n-C4H9Br in UV region Pei-Jiao Liu c, Bifeng Tang b

a,b,*

, Bing Zhang

b

a Department of Physics, Xiaogan University, Xiaogan City, Hubei Province, Xiaogan 432100, PR China State Key Laboratory of Magnetic Resonance and Atomic Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, PR China c School of Science, Wuhan Institute of Technology, Wuhan 430074, PR China

Received 13 December 2006; accepted 15 August 2007 Available online 22 August 2007

Abstract Using velocity map ion imaging technique, the photodissociation of n-C4H9Br in the wavelength range 231–267 nm was studied. The results and our ab initio calculations indicated that the absorption of n-C4H9Br in the investigated region originated from the excitations to the lowest three repulsive states, as assigned as 1A00 , 2A 0 and 3A 0 in Cs symmetry. Dissociations occurred on the PES surfaces of the three states, terminating in C4H9+Br (2P3/2) or C4H9 + Br* (2P1/2) as two channels, and being impacted by an avoided crossing between the PES surfaces of the 2A 0 and 3A 0 states. The transition dipole to the 1A00 state was perpendicular to the symmetry plane, so perpendicular to the C–Br bond. The transitions to the 3A 0 state was polarized parallel to the symmetry plane, and also parallel to the C–Br bond. While the transition dipole to the 2A 0 state was in the symmetry plane, but formed an angle of about 53.1 with the C–Br bond. We have also determined the avoided crossing probabilities, which affected the relative fractions of the individual pathways, for the photolysis of n-C4H9Br near 234 nm and 267 nm.  2007 Elsevier B.V. All rights reserved. Keywords: Velocity map ion imaging; Photodissociation; n-Butyl bromide

1. Introduction Photodissociation of alkyl bromides has been a popular area of investigation, in view of their ozone depletion potential [1–4] and of the fundamental interest [5–12] in photodissociation dynamics. Methyl bromides, in particular, have been extensively studied at their first absorption A-band. The A-band of methyl bromides (centered near 200 nm) arises from an r* n transition localized on the C–Br bond, and consists of overlapping transitions to three excited states, 3Q1, 3Q0 and 1Q1, as denoted by Mulliken [13]. Excitation in the A-band leads to rapid C–Br bond breakage due to the repulsive nature of the excited states. The 3Q0 N transition is polarized parallel to C–Br bond * Corresponding author. Address: Department of Physics, Xiaogan University, Xiaogan City, Hubei Province, Xiaogan 432100, PR China. Tel.: +86 0712 2345587; fax: +86 0712 2345265. E-mail address: [email protected] (B. Tang).

0301-0104/$ - see front matter  2007 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2007.08.009

and has dual dissociation paths. The 3Q0 state is adiabatically correlated with the spin–orbit excited state Br (4p2 P1/2) (denoted Br*) by direct dissociation and also contributes to the formation of the ground state Br (4p2P3/2) (denoted Br) by nonadiabatic transition near the conical intersection of the 3Q0 and 1Q1 surfaces. The other states are correlated with the spin–orbit ground state Br, and the corresponding transitions to these states are polarized perpendicular to the bond axis. The theoretical interest for methyl bromides arises because of its C3v symmetry, which allows for an approximate treatment as linear pseudo-triatomics [14], and because of the strong spin–orbit coupling in the heavy halogen atom Br, which gives rise to the distinguishable reaction channels for Br* or Br. The asymptotic product states are correlated with several potential energy surfaces (PES) of the electronically excited parent molecule, a situation in which interesting coupling phenomena between interacting PES are to be expected. Thelen and Felder [15] and Kim

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et al. [16] have investigated photodissociation of CF3Br at 193 nm and at 234 nm, respectively. They proposed that during the photodissociation the molecular symmetry of CF3Br be reduced from C3v to Cs by zero-point motion along e-symmetry modes or the excitation of vibration. In going from C3v to Cs symmetry, the 3E(1Q1) state splits into the 4A 0 and 2A00 states, the 2E(3Q1) state splits into the 2A 0 and 1A00 states, and the 2A1(3Q0) state becomes the 3A 0 state [17]. The coupling between the A 0 states, which can be explained by the radial derivative terms in the Hamiltonian, causes an avoided crossing. The 4A 0 state is then adiabatically correlated with Br*, and the 3A 0 state with Br. In Cs symmetry, the transition dipoles to all the A00 states are perpendicular to the symmetry plane, and the transitions to all the A 0 states are polarized parallel to the plane. McGivern et al. [18] have studied the photodissociation dynamics of CH2BrCl, which is intrinsically Cs symmetry, in a wavelength range from 248 to 268 nm. Their ab initio calculations determined that the n ! r* (C–Br) orbits in CH2BrCl retained their local character. Then, they proposed that, for CH2BrCl, the transitions to the 2A 0 and 4A 0 states were polarized perpendicular to the C–Br bond but in the Cl–C–Br plane, whereas the dipole for the transition to the 3A 0 state was parallel to the bond axis in the symmetry plane. In comparison with the methyl bromides, the photodissociation dynamics of n-butyl bromide, with a comparatively long C–C chain, has not been studied in such detail. It is well known that n-butyl bromide has Cs molecular symmetry, but it is not clear whether there is avoided crossing between the excited state PESs of the compound. Also, there are few papers [19,20] reporting the photodissociation of n-butyl bromide at its A-band. n-Butyl bromide has a red-shifted A-band compared to that of methyl bromides. The photochemistry of n-butyl bromide in the A-band, where only a valence shell transition is possible, proceeds by cleavage to radical products via C–Br bond fission: n-C4 H9 Br þ hm ! C4 H9 þ Br 

! C4 H9 þ Br :

ð1Þ ð2Þ

In the present study, we investigated the photodissociation dynamics of n-butyl bromide in the range of 231– 267 nm, employing the two-dimensional photofragment velocity map ion imaging technique. The (2 + 1) resonance-enhanced multiphoton ionization (REMPI) scheme was used to ionize state-selectively Br and Br* generated after the photolysis of n-butyl bromide. The translational energy distribution and anisotropy parameter of the photoproducts (Br and Br*) were extracted from the ion image. The relative quantum yields and the anisotropy parameters of the photoproducts give insight into the photodissociation dynamics of n-butyl bromide, and helped to understand the character of the dissociative states and the interactions in the exit channels.

2. Experiment and calculation The experiments were performed using a modified timeof-flight (TOF) mass spectrometer equipped with an electrostatic ion lens similar to that reported by Eppink and Parker [21]. N-C4H9Br was purchased commercially with rated purity 99.9% and used without further purification. The sample seeded in He at about 1 atm was expanded through a pulsed nozzle with a 0.6 mm orifice into the vacuum. The pulsed nozzle was driven by a valve driver (General Valve, IOTA-1). The molecular beam was skimmed by a 1 mm skimmer mounted 6 cm downstream, and passed through a 5 mm hole in the repeller plate of the ion lens. The resulting gas pressure within the sample chamber was typically 1 · 104 Pa. In order to minimize cluster formation, photolysis was performed on the rising edge of the molecular beam pulse. The electrostatic ion lens consists of three 1 mm thick, 80 mm diameter stainless steel plates, the repeller, the extractor and ground electrodes, surrounded by a grounded cylindrate stainless steel shield. The repeller plate, with a 5-mm-hole, the extractor and ground plates, with 20-mm-hole, were mounted with aluminum oxide spaces of 20 mm length. The designs of the ion lens have been optimized for velocity mapping based on numerous simulations using the SIMION 3D software package (Scientific Instruments Services, version 7). Midway between the repeller and the extractor plates the molecular beam was intercepted by the laser beam, which was focused by using a 20 cm focal length lens. Laser pulses were generated by a pulsed dye laser (Lambda Physik Scanmate 2E OG) pumped by the third harmonic (355 nm) of a Nd:YAG laser (YG 981 E 10). The output of the dye laser was frequency-doubled by a BBO crystal. The exact wavelength of the laser was checked by resonantly ionizing Br or Br* through a know transition [10,11]. The UV laser power is typically 400 lJ per shot. The same laser pulse photodissociated the n-C4H9Br by single-photon absorption into the A-band and ionized the Br or Br* product by using (2 + 1) resonance-enhanced multiphoton ionization. Details about the photolysis wavelengths and the states involved in the REMPI detection are given in Table 1. Higher-order multiphoton processes, as well as saturation and space charge effects were minimized by reducing the laser intensity. Ionized fragments were extracted from the photolysis region through a 20 mm diameter aperture on the extractor and ground electrodes and accelerated by the extractor electric field into a 50 cm long time-of-flight tube. The masses of the charged photofragments were determined by their subsequent flight time to a 40 mm diameter two-dimensional position sensitive detector, which consists of a dual microchannel plate (MCP) coupled to a fast phosphor screen. To mass select a photofragment, the gain of the MCP was gated by applying a timed voltage pulse (AVRH-3-C, PULSE GENERATOR) on the front plate. The images of the mass-selected photofragment

P.-J. Liu et al. / Chemical Physics 340 (2007) 141–148

143

Table 1 The average translational energies, available energies, fT, the anisotropy parameters, the speed of Br fragments and the intermediate states involved in the REMPI detection of Br atom for photolysis of n-C4H9Br in the wavelength range of 231–267 nm Channel

k (nm)

Intermediate state

Speed (m/s)

Eavl (kJ/mol)

hETi (kJ/mol)

fT

C4H9 + Br*

231.87 232.83 233.957 235.819 264.849 266.619

5p002 P03=2 7p4 P05=2 6p2 S01=2 5p02 P01=2 5p2 P03=2 5p4 S03=2

1157.5 897.3 895.9 886.9 842.1 827.3

181.5 179.4 176.9 172.9 117.3 114.3

128.4 77.2 76.9 75.4 69.5 65.6

0.71 0.43 0.43 0.44 0.59 0.57

1.98 ± 0.05 1.77 ± 0.06 1.58 ± 0.05 1.25 ± 0.07 0.87 ± 0.04 0.80 ± 0.04

C4H9 + Br

233.647 264.752 266.556

6p4 P03=2 5p4 D07=2 5p4 P03=2

931.4 886.8 878.0

221.6 161.5 158.4

83.1 75.4 73.9

0.38 0.47 0.47

0.63 ± 0.05 0.23 ± 0.03 0.16 ± 0.02

produced on the phosphor screen were optimized for size and sharpness by adjusting the repeller and extractor voltages (VR, VE). Optimal velocity mapping was obtained with VE/VR = 0.71 (VR  2200 V). Images of the signal on the phosphor screen were recorded using a CCD camera and accumulated in a computer for 30,000 laser shots. The data acquisition was controlled using a commercial ionimaging system(COD32/Video), which processed raw images and generated centroided images by comparing nonzero pixels with a number of near neighbors to determine the local maximum. The centroiding algorithm takes advantage of the finite size of an individual ion impact as it is seen by the camera. The laser, molecular beam, and detection system were run at 10 Hz. Timing was synchronized using a delay pulse generator (Stanford Research System, DG 535). The linearly polarized UV laser beam was vertically aligned using a half-wave retardation plate. During the accumulation of images, the laser wavelength was scanned over a range of ±0.4 cm1 to cover all ion velocity components. The velocity, and thus the kinetic energy, of the bromine ions was calibrated using images produced following the photodissociation of CH2BrCl [22]. A magnification factor N = 1.19 was derived from the Br or Br* image by using the expression R = Nvt, where R is the ring radius, v the fragment recoil speed, and t the ion time-of-flight. The velocity resolution of the imaging apparatus, understand as the peak full with at half maximum (FWHM) of a monoenergetic fragment, is about 30 m/s, and the energy resolution is 5% for a 80–120 kJ/mol kinetic energy release. To ensure a uniform and constant magnification factor, all apparatus parameters were held constant while recording images of CH2BrCl and n-C4H9Br. The REMPI time-of-flight mass spectra were acquired using a photomultiplier tube instead of CCD camera. We have calculated the geometries of the molecule nC4H9Br, in the ground and low-lying excited states, and also have calculated potential energy curves along the dissociation coordinate (C–Br bond distance) for these states. All calculations were performed by using the Gaussian 98 package [23]. The geometries of ground state and excited states were optimized with B3LYP/6-311++G(d, p) and

b

UTD/6-311++G(d, p), respectively, all under constraint of Cs symmetry. The potential energy curves along the C–Br bond distance were scanned, that means calculating the potential energy point by point, for the ground state at B3LYP/6-311++G(2d, 2p) level, for the excited states at UTD/6-311++G(2d, 2p) level. 3. Results Fig. 1 shows the raw images corresponding to Br [a, c] and Br* [b, d] generated after the photolysis of n-C4H9Br near 234 nm [a, b] and near 267 nm [c, d]. Each raw image is a two-dimensional projection of the three-dimensional speed and angular distributions with cylindrical symmetry around the polarization axis of the photolysis laser. The shape of an image is dependent on the speed and angular distribution patterns of the fragments.

Fig. 1. Raw ion images of Br and Br* fragments from the photolysis of nC4H9Br near 234 nm (a, b) and near 267 nm (c, d). The double arrow marks linear polarization vector of the photolysis laser.

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By performing an inverse Abel transformation, a threedimensional velocity distribution can be reconstructed from a raw image. The raw image was pre-smoothed, using a Gaussian filter with a 7 · 7 window and a standard deviation of 2 in pixel units, to reduce the noise effect, which is unavoidable with the present centroiding algorithm and event-counting and which will be amplified by the reconstruction procedure [24]. The cylindrical symmetry of the velocity distribution allows one to reconstruct a three-dimensional image from every planar slice containing the symmetry axis. The angular distribution, P(h), can be obtained by integrating the reconstructed three-dimensional speed distribution over a proper range of speed at each angle. The angular distribution can then be expressed in an expansion of orthogonal Legendre polynomials [25]: P ðhÞ ¼ 1 þ b2 P 2 ðcos hÞ þ b4 P 4 ðcos hÞ þ b6 P 6 ðcos hÞ:

ð3Þ

The parameter b2 contains information on photofragment density. The parameters b4 and b6 reflect the photofragment alignment. The detection scheme in our experiment, where the pump and probe laser were the same, and where (2 + 1) REMPI was used to ionize Br atoms, is not sensitive to the photofragment alignment, because a linearly polarized two-photon optical probe is capable of only photofragment density and quadrupolar alignment, which causes a neglectable modulation in the photofragment density [26,27]. Then, The parameters b4 and b6 in Eq. (3) vanish, and the spatial recoil distribution

of fragments can be described by the anisotropy parameter b, which reflects the dissociation dynamics and the symmetry of the potential energy surfaces involved. The parameter b is extracted by fitting P(h) with the standard formula P ðhÞ / 1 þ bP 2 ðcos hÞ;

ð4Þ

where h indicates the angle between the recoil velocity of photofragments and the polarization axis of the photolysis laser. P(h) and P2(cosh) denote the ion signal intensity and the second order Legendre polynomial, respectively. b varies from 2 (parallel transition) to 1 (perpendicular transition). The observed values are b(Br) = 0.63 ± 0.05 and b(Br*) = 1.58 ± 0.05 (Fig. 2a and b), indicating that two or more channels may be involved in the generation of Br and Br*, or the transition dipole moments of the transition from the ground state to the excited states are neither purely parallel nor perpendicular [25]. The speed distribution can be extracted by integrating the reconstructed three-dimensional speed distribution over all angles at each speed. The center-of-mass translational energy distribution, P(E), was obtained by converting the speed distribution using the equations P ðEÞ ¼ P ðV Þ

dV ; dE

1 mBr 2 ET ¼ ðmBr þ mC4 H9 Þ  V : 2 mC4 H9 Br

ð5Þ ð6Þ

The total translational energy distributions for Br and Br* are presented in Fig. 2c and d, respectively. In Fig. 2c, the small peak at about 30 kJ/mol kinetic energy is I+ from

Fig. 2. Fit for translational anisotropies (a, b) and translational energy distributions (c, d) of fragments Br and Br* from the photolysis near 234 nm.

P.-J. Liu et al. / Chemical Physics 340 (2007) 141–148

background gas. One of I atom’s REMPI wavelengths is about 233.6 nm, near Br’s REMPI wavelength of 233.647 nm, and 266.566 nm, so it is difficult to get rid of I+. Leaving this small peak out of account, each distribution is well characterized by a single Gaussian curve, implying that Br and Br* are generated as a result of direct dissociation via repulsive potential energy surfaces. The values of fT in Table 1 represent the ratio of the average translational energy, hETi, to the available energy, Eavl, fT ¼

hET i : Eavl

ð7Þ

The available energy is calculated by Eavl ¼ hm  D0  Eel þ EPint ; Eavl ¼ ET þ Eint ;

ð8Þ

where hm is the photon energy. The C–Br bond dissociation energy, D0, is 289.9 kJ/mol from the known thermochemical data [28–30]. Eel is the electronic energy level of the atomic halogen. A value of 0 kJ/mol is chosen for the ground state Br, and 44 kJ/mol [31] for the excited state Br*. EPint , the internal energy of n-C4H9Br, is estimated to be zero since the rotational and vibrational excitations are negligible in a supersonic molecular beam. ET is the total translational energy of the photoproducts. Eint is the internal energy of C4H9, including the rotational and vibrational energy. Using the same analysis method, the data for the photodissociation of n-C4H9Br at other wavelengths were also obtained. Our results on the photodissociation of nC4H9Br at each wavelength are listed in Table 1. 4. Analysis and discussion Before proceeding to discuss our experimental results, an overview of the results of our ab initio calculation is in order. As shown in Fig. 3, we have calculated cuts of

Fig. 3. Ab initio potential energy curves along the dissociation coordinate for the lower electronic states of n-C4H9Br.

145

Table 2 Excitation energies of the low-lying excited states of n-C4H9Br States

1A00

2A 0

3A 0

2A00

4A 0

Excitation energy (eV)

5.86

5.89

6.11

6.82

6.86

the potential energy surface along the C–Br intermolecular separation for the ground state and low-lying excited states of n-C4H9Br. As already pointed out, in Cs symmetry, the symmetry of n-C4H9Br, the 3E(1Q1) state splits into 4A 0 and 2A00 , the 2E(3Q1) state splits into 2A 0 and 1A00 , and the 2A1(3Q0) state becomes 3A 0 . As shown in Table 2, ab initio calculation at UTD/6-311++G(2d, 2p) level with the Gaussian 98 package has predicted the excitation energies of the five excited states. From Table 2, we find that the Jahn–Teller splits between 4A 0 and 2A00 , and between 2A 0 and 1A00 are so small that just three PES curves have been calculated out, corresponding to the five excited states. We denoted the three PES curves as 3Q1(1A00 , 2A 0 ), 3Q0(3A 0 ), and 1Q1(2A00 , 4A 0 ), respectively. Our calculation suggested that the excited states denoted by 1Q1(2A00 , 4A 0 ) curve were probably bound states. In order to explain this result, we briefly analyze the origination of A-band of the alkyl bromides. As first discussed by Mulliken [32], A-band of the alkyl bromides arises from an electronic excitation of r* n type. For n-C4H9Br ½r  ¼ Cð½rC4 H9  rBr Þ;

ð9Þ

where [r*] is a wave function of the molecular orbit corresponding to the antibonding, ½rC4 H9 and rBr are atomic orbits localized on C–Br bond. We assume that in 1Q1(2A00 , 4A 0 ) state the orbit of ½rC4 H9 be delocalized from C–Br bond to C–C–C–C chain. This change would result in the decrease of repulsive force originated from the antibonding orbit of r*, and then a combination of the bonding orbit of r and the antibonding orbit of r* may make the 1Q1(2A00 , 4A 0 ) state become a bound state. From Fig. 3, we find that the 1A00 and 2A 0 are adiabatically correlated with the spin–orbit ground state Br, and the 3A 0 with the spin–orbit excited state Br*. We know that the transition dipole to the 1A00 state is perpendicular to the symmetry plane, so perpendicular to the C–Br bond. The transitions to the 2A 0 and 3A 0 states are polarized parallel to the plane, but not certainly polarized parallel to the C– Br bond, now that our ab initio calculations show that the n ! r* (C-Br) orbits in n-C4H9Br have delocalized character. As shown in Table 1, the anisotropy parameter for Br* from the photodissociation of n-C4H9Br at 231.87 nm, b(Br*), is 1.98 ± 0.05. This indicates that the Br* almost all stemmed from the 3A 0 N transition, and we can choose the anisotropy parameter for the transition to 3A 0 state to be b(3A 0 ) = 2. So, we can determine that the transition to the 3A 0 state is polarized parallel to the C–Br bond. The anisotropy parameter b can be related to the lifetime s of the dissociative state and the angle v between

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P.-J. Liu et al. / Chemical Physics 340 (2007) 141–148

b ¼ 2P 2 ðcos vÞ

1 þ x2 s2 ; 1 þ 4x2 s2

ð10Þ

where x is the angular velocity of the parent molecule, P2(cosv) denotes the second order Legendre polynomial. From b(Br*) = 1.98 ± 0.05 at 231.87 nm, we also can tell that the lifetime s of the dissociative states of n-C4H9Br is extremely short compared with the rotational period of the parent molecular. For this reason, we can suggest that the anisotropy parameter for transition to 1A00 state, b(1A00 ), is 1, since v = 90 for the transition. As can be seen in Table 1, the anisotropy parameter for Br*, as well as for Br, is sensitive to the photolysis wavelength, indicating that there is coupling between the PES curves of the dissociative states. Based on the ab initio calculations, we proposed that there was an avoided crossing between the PES curves of the 2A 0 and 3A 0 states. So, the 1A00 and 2A 0 states are adiabatically correlated with the spin–orbit ground state Br, and the 2A 0 state is also nonadiabatically related with the spin–orbit excited state Br*, while the 3A 0 state adiabatically with Br*, non-adiabatically with Br. Then, the photofragments of Br* are originated adiabatically from the 3A 0 N transition, and non-adiabatically from the 2A 0 N transition via the avoided crossing. From Table 1, we can see that as the photolysis wavelength increases from 232 to 267 nm, though the change of the anisotropy parameter for Br has no monotonicity, the anisotropy parameter for Br*, b(Br*), monotonously declines from 1.98 to 0.80, indicating more and more Br* fragments coming from the 2A 0 N transition via the avoided crossing. As pointed out previously, for the photolysis of n-C4H9Br at 231.87 nm, the Br* photofragments almost all originated from the 3A 0 N transition. As the photolysis wavelength approached the red wing of the absorption A-band, there are comparatively more Br* photofragments coming from the 2A 0 N transition. We can expect that when photolysis wavelength change to some value at the red wing of the absorption A-band all the Br* photofragments would stem from the 2A 0 N transition, where the anisotropy parameter for Br* would be the anisotropy parameter for the transition to 2A 0 state.

β

the internuclear axis and the direction of the transition dipole moment for the final state via the relationship [33]

Fig. 4. Wavelength dependence of the anisotropy parameter b for Br*.

We depicted the wavelength dependence of the anisotropy parameter for Br* in Fig. 4, and fitted the experimental data with sigmoidal fit. Extrapolating the photolysis wavelength to the red wing of the absorption A-band, where only the 2A 0 N transition is possible, we obtained asymptotic value b = 0.80, so we chose b(2A 0 ) = 0.80 as the anisotropy parameter for the transition to 2A 0 state. Then, according to Eq. (10), we obtained the angle between C–Br bond and the direction of the transition dipole moment to the 2A 0 state, v = 53.1. In general, the relative fractions of the individual pathways can be determined from the relative quantum yields and anisotropy parameters using the following relationships: /Br ð3A0 Þbð3A0 Þ þ /Br ð2A0 Þbð2A0 Þ ¼ /Br bðBr Þ /Br ð3A0 Þbð3A0 Þ þ /Br ð2A0 Þbð2A0 Þ þ /Br ð1A00 Þbð1A00 Þ ¼ /Br bBr /Br ð3A0 Þ þ /Br ð2A0 Þ ¼ /Br /Br ð3A0 Þ þ /Br ð2A0 Þ þ /Br ð1A00 Þ ¼ /Br ; ð11Þ

where /F(S) (F = Br*, Br; S = 3A 0 , 2A 0 , 1A00 ) represents the relative quantum yields of photofragment F originated from S state, b(S) is the anisotropy parameter corresponding to excitation to S state, b(F) is the anisotropy parameter of photofragment F obtained in this experiment, and /F is the relative quantum yield of photofragments F. Our group has determined /Br and /Br for photolysis of n-C4H9Br near 234 nm and 267 nm [10], as listed in Table 3.

Table 3 The relative fractions of the individual pathways and the avoided crossing probabilities for photolysis of n-C4H9Br Channel

C4H9 +

Br*

C4H9 + Br

a

Pathway

Channel yielda

Pathway yield

Crossing probability

234 nm

267 nm

234 nm

267 nm

234 nm

267 nm

0

3A 2A 0

0.2791 0.1478

0 0.341

0.428

0.341

Pup = 0.425

Pup = 0.445

3A 0 2A 0 1A00

0.1911 0.1998 0.1814

0 0.425 0.234

0.572

0.659

Pdown = 0.406

Pdown

Values taken from Ref. [10].

P.-J. Liu et al. / Chemical Physics 340 (2007) 141–148

The avoided crossing probability from lower PES to upper PES and that from upper PES to lower PES are given by P up ¼ P down

/Br ð2A0 Þ ; /Br ð2A0 Þ þ /Br ð2A0 Þ /Br ð3A0 Þ ¼ : /Br ð3A0 Þ þ /Br ð3A0 Þ

ð12Þ ð13Þ

For the photolysis of n-C4H9Br near 267 nm, because both b(2A 0 ) and b(Br*) are equal 0.8, by assuming that /Br*(3A 0 ) and /Br(3A 0 ) equal zero, we easily obtained the other relative fractions of the individual pathways as shown in Table 3. In the case of the photolysis of n-C4H9Br near 234 nm, the equations set (11) as it stands cannot be solved because there are five variants but only four equations. If the Landau–Zener model [34] is valid for the photolysis of nC4H9Br near 234 nm, the avoided crossing probability from the 2A 0 to the 3A 0 PES is the same as its reverse from the 3A 0 to the 2A 0 PES. Adopting Pup = Pdown as one equation, now we can solve the equations set with MATLAB. The determined relative fractions of the individual pathways and the avoided crossing probabilities are listed in Table 3. As detailed in Table 3, the transition to 3A 0 state dominates the absorption at 234 nm, while the transition to 2A 0 state leading in the absorption at 267 nm, which is consistent with estimation from the absorption spectrum of nC4H9Br [35]. At 234 nm, 47% of the total absorption is assigned to 3A 0 N transition, while the relative quantum yield of Br* is only 0.43. The avoided crossing has reduced the relative quantum yield of Br*. At 267 nm, the fraction of 3A 0 N transition is almost zero, but Br* is still produced, the relative quantum yield is 0.34. It is obvious that the avoided crossing has markedly affected the relative quantum yield of Br* and Br. The avoided crossing probability at 267 nm is larger than that at 234 nm, qualitatively coinciding with the Landau–Zener model. Another notable result is that, though we let Pup = Pdown as one equation of the equations set in the computing, the calculated Pup was obviously bigger than the calculated Pdown. We were unable to tell whether this result derived from the limitations of the calculation, which employed an iterative algorithm, or it represented a fact that Pup was really larger than Pdown for the photodissociation of n-C4H9Br in the A-band, as reported by Park et al. [36] in the case of allyl bromide. Our group [37] has also found that the probability of curve crossing from 3Q0 to 1Q1 surface was much higher than that of the reverse process in the case of C2H5Br. This disagreement with the limit of the Landau–Zener model may have resulted from the difference between the shapes of the twodimensional potential surfaces of the involved states. Though the Landau–Zener model holds for diatomic molecules, it does not apply for polyatomic molecules because of its one-dimensional potential-surface model.

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As shown in Table 1, with increasing UV laser wavelength, the available energy, Eavl, from the photodissociation process decreases, and the measured average translational energy, hETi, distributed to Br and Br* also decreases. Whereas, the ratio of the average translational energy to the available energy, fT, is almost equal in the small regions of wavelength, though the value of fT in one region of wavelength is different from that in another region. These results indicate that in some wavelength regions the vibrational excitation is relatively stronger than in other wavelength regions. The ratio of the translational energy to the available energy can be estimated by introducing two radical limits of the impulsive model, the rigid model and soft model. According to the rigid model, almost all of the available energy should be partitioned into the translational energy, the rigid radical limit, fTrigid ¼ 1, which ignores vibrational excitation, is quite higher than the measured fT, so that the rigid model is not suitable to describe the photodissociation of n-C4H9Br. While using the soft radical limit of the impulsive model, which accounts for vibrational excitation, value of fTsoft ¼ lBr–C = lBr–C4 H9 ¼ 0:31 was determined, where lBrC is the reduced mass of the carbon and bromine atom, and lBr–C4 H9 is the reduced mass of the C4H9 radical and bromine atom. In this case, the estimated fraction is a little lower than the observed values. Comparing with the results of C2H5Br [37], n-C3H7Br [38] and n-C7H15Br [39], we can find that the value of fT declines, in general, from 0.7 to 0.32 with the carbon chain increasing, getting closer to the soft radical limit. This indicates that the molecules become softer as the carbon chain increases. In Ref. [9], we calculated cuts of the potential energy surface along the C–Br intermolecular separation for the ground state and low-lying excited states of C2H5Br and n-C3H7Br. The calculation suggested that as the carbon chain lengthening from C2H5Br to n-C3H7Br the excited states denoted by 1Q1(2A00 , 4A 0 ) might change from repulsive states to bound states. In this work, our calculation also indicated that the excited states 1Q1(2A00 , 4A 0 ) of nC4H9Br were probably bound states. The experimental data of n-C4H9Br matched the calculated result well, though could not prove it. As can be seen in Table 1, at 231.87 nm, at which wavelength the excited states 1 Q1(2A00 , 4A 0 ) of n-C4H9Br must can be populated, the anisotropy parameter for Br* from the photodissociation of n-C4H9Br, b(Br*), is 1.98 ± 0.05, almost equal to 2. This indicates that the Br* almost all stemmed from the 3 Q0(3A 0 ) N transition, and there were nearly not Br* originated from 1Q1(2A00 , 4A 0 ) N transition. Otherwise, the anisotropy parameter b(Br*) would not be so close to 2. This gives us some hints about that the excited states 1 Q1(2A00 , 4A 0 ) of n-C4H9Br may be really bound states. But, the velocity map imaging investigations of n-C3H7Br [38] and n-C7H15Br [39] did not give much information about whether the 1Q1(2A00 , 4A 0 ) states of these molecules were repulsive states or bound states. Clearly, this question needs to be determined by further investigations.

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5. Summary Based on our experimental results and ab initio calculations, the following conclusions regarding the photochemistry of n-C4H9Br at 231–267 nm can be reached. (1) The absorption of n-C4H9Br in the investigated region originates from the excitations to the lowest three repulsive states, as assigned as 1A00 , 2A 0 and 3A 0 in Cs symmetry. Other two states, 2A00 and 4A 0 , are probably bound states according to our ab initio calculations. Dissociations occur on the PES surfaces of the three states, terminating in C4H9 + Br (2P3/2) or C4H9 + Br* (2P1/2) as two channels. The 3A 0 state is adiabatically correlated with the spin–orbit excited state Br*, and the 2A 0 and 1A00 states are adiabatically correlated with the spin–orbit ground state Br. Because there is an avoided crossing between the PES surfaces of the 2A 0 and 3A 0 states, the 2A 0 state is also non-adiabatically related with Br*, while the 3A 0 state non-adiabatically with Br. (2) The transition dipole to the 1A00 state is perpendicular to the symmetry plane, so perpendicular to the C–Br bond. The transitions to the 3A 0 state is polarized parallel to the symmetry plane, and also parallel to the C–Br bond. While the transition dipole to the 2A 0 state is in the symmetry plane, but form an angle of about 53.1 with the C–Br bond. We have also discussed the relative fractions of the individual pathways and the avoided crossing probabilities for the photolysis of n-C4H9Br near 234 nm and 267 nm. We found that the avoided crossing had markedly affected the relative quantum yield of Br* and Br. Acknowledgements This research was supported by National Natural Science Foundation of China, Natural Science Foundation of Hubei Province of China, and Science Foundation of the Education Department of Hubei Province of China. References [1] L.A. Barrie, J.W. Bottenheim, R.C. Schnell, P.J. Crutzen, R.A. Rasamussen, Nature (London) 334 (1988) 138. [2] J.G. Anderson, D.W. Toohey, W.H. Brune, Science 251 (1991) 39. [3] S.C. Wofsy, M.B. McElroy, Y.L. Yong, Geophys. Res. Lett. 2 (1975) 215.

[4] K.L. Foster, R.A. Plastridge, J.W. Bottenheim, P.B. Shepso, B.J. Finlayson-Pitts, C.W. Spicer, Science 291 (2001) 471. [5] K.Q. Lao, M.D. Person, P. Xayariboun, L.J. Butler, J. Chem. Phys. 92 (1990) 823. [6] T. Gougousi, P.C. Samartzis, T.N. Kitsopoulos, J. Chem. Phys. 108 (1998) 5742. [7] Y.J. Jung, M.S. Park, Y.S. Kim, K.H. Jung, J. Chem. Phys. 111 (1999) 4005. [8] B. Tang, R. Zhu, Y. Tang, L. Ji, B. Zhang, Chem. Phys. Lett. 381 (2003) 617. [9] B. Tang, R. Zhu, Y. Tang, L. Ji, B. Zhang, Chem. Phys. 303 (2004) 37. [10] R. Zhu, B. Tang, L. Ji, Y. Tang, S. Zhang, B. Zhang, Opt. Commun. 235 (2004) 325. [11] Y. Tang, L. Ji, B. Tang, R. Zhu, S. Zhang, B. Zhang, Chem. Phys. Lett. 392 (2004) 493. [12] R. Zhu, B. Tang, L. Ji, Y. Tang, S. Zhang, B. Zhang, Chem. Phys. Lett. 405 (2005) 58. [13] R.S. Mulliken, J. Chem. Phys. 3 (1935) 513. [14] M. Shapiro, R. Bersohn, J. Chem. Phys. 78 (1980) 3810. [15] M.A. Thelen, P. Felder, Chem. Phys. Lett. 204 (1996) 135. [16] T.K. Kim, M.S. Park, K.W. Lee, K.H. Jung, J. Chem. Phys. 115 (2001) 10745. [17] P. Felder, Chem. Phys. 155 (1991) 435. [18] W.S. McGivern, T. Li, P. Zou, S.W. North, J. Chem. Phys. 111 (1999) 5771. [19] G.R. Freeman, J.M. Fauadh, J. Chem. Phys. 43 (1965) 86. [20] Q-X. Xu, M.A. Quesada, K-H. Jung, R.S. Mackay, R.B. Bernstein, J. Chem. Phys. 91 (1989) 3477. [21] A.T.J.B. Eppink, D.H. Parker, Rev. Sci. Instrum. 68 (1997) 3477. [22] S-H. Lee, Y-J. Jung, K-H. Jung, Chem. Phys. 260 (2000) 143. [23] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, et al., Gaussian 98, Revision A.3, Gaussian, Inc., Pittsburgh PA, 1998. [24] E. Wrede, S. Laubach, S. Schulenburg, A. Brown, E.R. Wouters, A.J. Orr-Ewing, M.N.R. Ashfold, J. Chem. Phys. 114 (2001) 2629. [25] T.P. Rakitzis, Chem. Phys. Lett. 342 (2001) 121. [26] A.S. Bracker, E.R. Wouters, A.G. Suits, Y.T. Lee, O.S. Vasyutinskii, Phys. Rev. Lett. 80 (1998) 1626. [27] A.J. van dan Brom, T.P. Rakitzis, J. van Heyst, T.N. Kitsopoulos, S.R. Jezowski, M.H.M. Janssen, J. Chem. Phys. 117 (2002) 4256. [28] M.W.J. Chase, J. Phys. Chem. Ref. Data, Monograph 9 (1998) 1951. [29] L. Bjellerup, Acta Chem. Scand. 15 (1961) 231. [30] J.A. Kerr, Chem. Rev. 66 (1966) 465. [31] S. Arepalli, N. Presser, D. Robie, R.J. Gordon, Chem. Phys. Lett. 117 (1985) 649. [32] R.S. Mulliken, J. Chem. Phys. 8 (1940) 382. [33] R.K. Sander, K.R. Wilson, J. Chem. Phys. 63 (1975) 4242. [34] L.D. Landau, E.M. LifshitzQuantum Mechanics, vol. 3, Pergamon, New York, 1977. [35] S.N. Kozlov, V.L. Orkin, R.E. Huie, M.J. Kurylo, J. Phys. Chem. A 107 (2003) 1333. [36] M.S. Park, K.W. Lee, K-H. Jung, J. Chem. Phys. 114 (2001) 10368. [37] Y. Tang, L. Ji, R. Zhu, Z. Wei, B. Zhang, ChemPhysChem 6 (2005) 2137. [38] S. Zhang, Y. Wang, B. Tang, Q. Zheng, B. Zhang, Chem. Phys. Lett. 413 (2005) 129. [39] H. Qu, H. Li, F. Liang, B. Zhang, Chem. Phys. 330 (2006) 355.