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Ion-Pair Dissociation Dynamics of SO2 in the Photon Energy Range 14.87-15.15 eV Kai Liu,† Di Song,† Fan-ao Kong,*,† Juan Li,‡ and Yuxiang Mo*,‡ The State Key Laboratory of Molecular Reaction Dynamics, Institute of Chemistry, Chinese Academy of Science, Beijing 100190, China, and Department of Physics and Key Laboratory for Atomic and Molecular Nanosciences, Tsinghua UniVersity, Beijing, 100084, China ReceiVed: June 7, 2010; ReVised Manuscript ReceiVed: August 8, 2010
The ion-pair dissociation dynamics of SO2 f SO+ (X2Π,υ) + O- (2PJ) in the excitation energy range 14.87-15.15 eV has been studied using the tunable XUV laser and velocity map imaging method. The Oyield spectrum, the translational energy distributions, and the angular distributions of the photofragments have been measured. The electronic structures and selected cuts of potential energy surfaces for the ion-pair states have been calculated by employing the quantum chemistry calculation method at the CASSCF/6311++g** level. The equilibrium structures of the six ion-pair states all have linear geometries. An orbital correlation diagram was drawn to illustrate the ion-pair dissociation mechanism. Combining the experimental and theoretical results, it is concluded that the ion-pair dissociation takes place mainly via the predissociation of Rydberg states 1A1 [(C2B1)4db1] and 1A1 [(D2A1)4sa1]. The experimental results confirm the previous theoretical calculation results about the symmetry assignments for the energy sequence of SO2+ as C(2B1) < D(2A1). I. Introduction The photoionization and photodissociation dynamics of SO2 molecule have attracted great attention in the literature;1-7 however, most of the studies are in the energy region below the ionization energy (IE), and only a few studies have been performed to study the properties of SO2 above the IE, or the superexcited states of SO2. The superexcited molecule decays in various channels: autoionization, dissociative ionization, neutral dissociation, and ion-pair dissociation.8 The ion-pair dissociation usually occurs via the predissociation of Rydberg states; hence it carries rich information about the molecule superexcited states, and its mechanism has been studied in great detail in recent years.8-15 Kratzat and co-workers have studied the ion-pair dissociation of SO2 using the synchrotron radiation:16
SO2 + hV f SO+(X2Π,υ) + O-(2PJ)
(1)
They recorded the O- ion yield spectrum in the energy range 14-20 eV.16 The peaks in the spectrum were tentatively assigned to Rydberg states converging to the C, D, E, and F states of the SO2+ ion. The assignments were mainly based on the Rydberg formula
E(hV) ) IE(υ+) -
R (n - δ)2
(2)
where IE(υ+) is the ionization energy for a particular ionic state with vibrational quantum number υ+, n is the principal quantum number of the Rydberg state, δ is the quantum defect, and R is Rydberg constant for SO2. Since there are four cation states, C, * To whom correspondence should be addressed. E-mail: F.K.,
[email protected]; Y.M.,
[email protected]. † Chinese Academy of Science. ‡ Tsinghua University.
D, E, and F, several Rydberg states may appear at the same excitation energy. An unambiguous assignment of Rydberg states in the ion-pair yield spectrum could not be attained only based on eq 2. Recently, we found that the ion-pair dissociations occur via fast predissociation for a number of molecules, and the anisotropy parameters of the photofragments can be used to character the symmetries of the excited Rydberg states.9-15 The anisotropy parameter can be measured using the velocity map imaging method. In this work, we have performed such a study further on the ion-pair dissociation of SO2 using the velocity map imaging method and tunable XUV laser. An O- yield spectrum has been recorded, and two O- images corresponding to the peaks in the spectrum have been measured. The assignments about the state symmetries of SO2+ have been recently paid some attention due to the development of high level ab inito quantum chemistry calculation methods.17-21 For example, the C, D, and E states for SO2+ were assigned as C(2B2) < D(2A1) < E(2B1) in photoelectron spectroscopic studies;2,4 however, the theoretical calculations showed that the sequences should be C(2B1) < D(2A1) < E(2B2).17,18 The experimental results about the angular distribution of photofragments measured in this work provided the first experimental evidence confirming the theoretical results. To understand the dissociation mechanism, the equilibrium geometries and electronic structures of the ion-pair states have also been computed using ab initio quantum chemistry calculation method. It is found that all ion-pair states of SO2 have linear geometries. An orbital correlation diagram has been drawn to provide a picture about the change of electronic configurations in the ion-pair dissociation. II. Experimental Method and Theoretical Calculation (a) Experimental Method. The tunable XUV laser and velocity map imaging apparatus have been described in detail elsewhere;9-15 therefore, only a brief summary is given here. The coherent XUV radiation was generated using the resonance
10.1021/jp105206q 2010 American Chemical Society Published on Web 09/01/2010
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enhanced four-wave sum mixing (2ω1 + ω2) in a pulsed Kr jet. An Nd:YAG (YAG-yttrium aluminum garnet) (20 Hz) pumping two dye laser system was used in the experiments. One laser beam (ω1) was prepared by tripling of a dye laser, and the 2ω1 (98 855.1 cm-1) was fixed to match the resonance frequency of the Kr 4p5(2p1/2)5p[1/2]0 r (4p6)1S0. The other dye laser was tuned from 448 to 492 nm. The uncertainties of the XUV photon energies are (1 cm-1, and the resolution of the XUV laser is around 0.1 cm-1. The XUV light intensity was recorded for each laser pulse, and the ion-pair yield spectrum has been normalized by the XUV light intensity pulse by pulse. The velocity map imaging technique follows that of Parker and co-workers.22 The translational energies in the images were calibrated under the same experimental conditions using the F- images from the ion-pair dissociation of F2 f F+(3P2,1,0) + F-(1S0), in which the energy spacings among the three spin-orbit components F+(3P2,1,0) are well determined.10 The sample was a premixed gas of SO2 with He (SO2: 10% and He: 90%) with a stagnation pressure of ∼1000 Torr at room temperature. The pressures for the molecular beam source and ionization chamber were around 3 × 10-5 and 1 × 10-7 Torr, respectively. (b) Theoretical Calculation. Theoretical calculations have been performed to calculate the cuts of potential energy surfaces (PESs) correlating with the production of SO+ (X2Π,υ) + O(2PJ). The calculations employed the complete active space selfconsistent field (CASSCF) method using the MOLPRO software package.23 Around the energy region of the ion-pair states, a large number of excited valence states and Rydberg states coexist. The avoided crossings between the ion-pair states and other states with same symmetries occur, which makes the PESs with pure ion-pair electronic configurations difficult to find along the dissociation paths in the adiabatic picture. Therefore, we have limited possible excited configurations by including only the main electronic configurations of the ion-pair states in the calculation. It is known that the main electronic configuration for the ground state of SO2 is (core) (5a1)2 (3b2)2 (6a1)2 (4b2)2 (7a1)2 (2b1)2 (1a2)2 (5b2)2 (8a1)2 (C2V symmetry) or (core) (7a′)2 (8a′)2 (9a′)2 (10a′)2 (11a′)2 (2a′′)2 (3a′′)2 (12a′)2 (13a′)2 (Cs symmetry). Six active electrons and five active orbitals were employed in our calculation, i.e., (3a′′)2 (12a′)2 (13a′)2 (4a′′)0 (14a′)0 (Cs symmetry, bent). Small active space eliminates the mixing of ion-pair states with Rydberg states completely and some highly excited valence states. Any additional active orbital will result in a very large number of states that the calculations about ion-pair states become very difficult. The calculated electronic energies for the ion-pair states are expected to have large errors because the multireference configuration interaction (MRCI) method was not used in the present calculation; the number of active electronic orbitals and active electrons was also limited in the CASSCF calculations. However, it is expected that the calculated equilibrium geometries and the main characteristics of the PESs for ion pairs should not be greatly affected by our simplified calculations. III. Results and Discussion -
(a) O Yield Spectrum and Its Assignment. We have obtained the O- ion-pair yield spectrum from the ion-pair dissociation of SO2 in the energy range 14.87-15.15 eV (Figure 1). There are two very broad bands in the spectrum, which were assigned as vibrational excited Rydberg states converging to SO2+ ionic states C, D, and E on the basis of eq 2 in ref 16. In this work, the symmetries of the Rydberg states for the two bands were determined experimentally by utilizing the angular
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Figure 1. O- yield spectrum of SO2 + hV f SO+ (X2Π,υ) + O(2PJ) in the energy range 14.87-15.15 eV. The spectrum has been normalized to the XUV light intensity. The Rydberg state assignments for the two peaks are indicated in the figure. The vertical bars at the bottom represent the selected energy positions at which the velocity map images of O- have been measured.
distribution of the photofragments (see next section). On the basis of the determined symmetries and the calculated quantum defects using the reported ionization energies,2 the bands at 14.94 and 15.04 eV were assigned to Rydberg states 1A1[(D 2 A1)4sa1 (1,0,0)] and 1A1 [(C 2B1)4db1 (0,0,0)], respectively, as listed in Table 1. As shown in Figure 1, the assigned Rydberg bands are very broad. This suggests that the ion-pair dissociation of SO2 occurs via a fast predissociation process, which is similar to the dissociation of several other molecules we have studied.9-15 (b) Angular and Translational Energy Distributions of the O- Fragments. Panels a and b of Figure 2 show the experimental images of O- from the ion-pair dissociation of SO2 at 14.94 and 11.54 eV, respectively. Each image is actually a summation of several images at neighboring excitation energies, as shown by the vertical bars in Figure 1. In the experiments, several images with excitation energies around the top of two bands (14.94 and 15.04 eV) have been taken to study the changes of images with the excitation energies. It was found that the changes are small. To improve the signal-to-noise ratios, the neighboring images have been added together. Each image corresponds to an accumulation time of around 24 h with a 20 Hz repetition laser. The raw images were transformed into 2-D slice images (Figure 2 (c or d)) by the inverse Abel transform.9 The angular distributions of the photofragments O- were obtained by extracting the information in 2-D slice images, and shown in Figure 3. The anisotropy parameters β are thus obtained using the following equation to fit the experimentally measured angular distributions24
f(θ) ∝ 1 + βP2(cos θ)
(3)
where θ is the angle between the recoil velocity and the polarization direction of the XUV laser, and P2(cos θ) is the second-order Legendre polynomial. The determined β values for the two bands are listed in Table 1. β is related to the angle χ between the directions of the transition dipole moment and the recoil velocity:
β ) 〈2P2(cos χ)〉 ) 〈2(3/2cos2 χ - 1/2)〉
(4)
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TABLE 1: Assignments for Rydberg States at the Two Excitation Photon Energiesa ion core
Rydberg electron b
hν (eV)
symmetry
vibrational state
IP (eV)
14.94(1) 15.04(1)
D(2A1) C(2B1)
(100) (000)
16.452 15.902
symmetry
δc
Eavld (eV)
βe
4sa1 4db1
1.00(1) 0.02(1)
0.45(1) 0.55(1)
-0.27(2) 0.09(2)
a Numbers in parentheses represent the uncertainties in the last digits. b Ionization energies (IP) are taken from ref 2. c Quantum defects defined in eq 2. d Maximum available translational energies to the photofragments. e Anisotropy parameters for the photofragments determined from the imaging experiments.
TABLE 2: Dependence of Anisotropy Parameters β on the Geometrical Structure and the Direction of Transition Dipole Momenta direction symmetry symmetry of transition dipole θ χ β ) 〈2(3/2 cos2 of Rydberg of ion moment (deg) (deg) electron core χ - 1/2)〉 C(B1) D(A1) E(B2) C(B1) D(A1) E(B2) any
b1 a1 b2 a2 b2 a1 any
z z z y y y x
109.2 118.4 101.0 109.2 118.4 101.0 any
54.6 59.2 50.5 35.4 30.8 39.5 90.0
0.01 -0.21 0.21 0.99 1.21 0.79 -1.00
a The bond angles are from quantum chemical calculations at the CASPT2/ANO-L level reported by Li and Huang.17 The orientation of x, y, and z are defined in Figure 4.
Figure 2. O- images from the ion-pair dissociation of SO2 at excitation energies of (a) 14.94(1) eV and (b) 15.04(1) eV, and their corresponding 2-D slice images (c) and (d) from the inverse Abel transforms, respectively. Each image was a summation of several similar images at neighboring energy positions; see the vertical bars in Figure 1. The polarization of the XUV laser is indicated by the arrow on the right. Panels a and b were recorded with extraction electric field of 600 and 900 V/m, respectively. A logarithmic color scale is employed to make the weak signals in the outer rings seen more clearly.
Figure 4. Orientation of x, y, and z axes defined in the discussion. The direction of the dipole moment is expressed by d. (a)-(c) show the angle χ in three different cases.
Figure 3. Angular distributions of O- fragments extracted from (c) and (d) in Figure 2. Black dots represent the experimental data, and the solid lines are obtained by least-squares fittings using eq 3. The data near 0° and 180° have been neglected in the fittings due to the large uncertainties caused by inverse Abel transform.
where 〈 〉 represents an average all possible χ in the dissociation process.24 Even for prompt dissociation, β may be any values between -2 and +1 for polyatomic molecules, which are different from those for diatomic molecules. The ion-pair dissociation of SO2 is a fast predissociation process, as indicated
by the broad bands in ion-pair yield spectrum; therefore, χ can be regarded as an angle between the direction of transition dipole moment and the bond of S-O in the excited Rydberg state. Since the excited Rydberg states converging to C, D, and E have C2V symmetries, and the direction of the transition dipole moment should be located at the symmetry axis of the molecule. With the fact of fast predissociation, the possible β values can be calculated according to the symmetries of the Rydberg states, as listed in Table 2. Figure 4 shows the coordinate system and the definition of θ and χ in the discussion. If the transition dipole moment is outside the molecular plane, as shown in column c of Figure 4, β is always -1. This is in contrast to the measured β values. Therefore, the direction of transition dipole moment can only be in the y or z direction, or with A1 or B2 symmetries, respectively. Table 2 lists symmetries of the Rydberg ionic core for C, D, and E states, their corresponding geometric structure parameters calculated at the level of CASPT2/ANO-L,17 and possible symmetries of Rydberg electrons. The dependence of β values on the direction of the transition dipole moments and the geometric structures of ionic cores of the Rydberg states can be clearly seen in Table 2. By comparison of the measured β with the calculation values in Table 2, it is clear that the first band at 14.94 eV should be assigned as a Rydberg state with ionic core D(2A1) and a
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Figure 5. Total center-of-mass translational energy distributions for SO2 f SO+ (X2Π,υ) + O- (2PJ). The vibrational assignments of SO+ (X2Π,υ) are indicated. It is seen that the vibrational population distributions are inverted.
Rydberg electron with symmetry a1, and the second band at 15.04 eV should be assigned as a Rydberg state with ionic core C(2B1) and a Rydberg electron with symmetry b1, respectively. It is noted that the total symmetry for both Rydberg states is found to be A1. If the SO2+(C) state had the symmetry of 2B2 as proposed by earlier publications,2 the β value would be either 0.21 or 0.79 depending on the symmetry of Rydberg electron, as seen in Table 2. This is in contradiction with the experimental data. Therefore, the experimental data in this work confirmed the assignment of energy sequence of C(2B1) < D(2A1) predicted by ab inito theoretical calculations.17,18 Figure 5 shows the total center-of-mass translational energy distributions of the photofragments determined from images c and d in Figure 2. The most obvious feature from Figure 2 is that the vibrational population distributions of SO+(X2Π,υ) are highly inverted. In fact, the height ratios in Figure 2 for vibrational states of υ ) 3, 2, 1, and 0 are approximately 7:3: 1:0. In Figure 5, we have neglected the signals with translational energies less than 80 cm-1, or the bright dots in the center of the images, which may result from the electric-field induced dissociation.12 (c) Ion-Pair Dissociation Mechanism and Orbital Correlation Diagram. The equilibrium geometries of the ion-pair states were found to be all linear using the calculations at the CASSCF/6-311++g** level. The main electronic configurations and the geometric parameters of the ion-pair states are listed in Table 3. The ionic bond lengths are around 2.5 Å that are much longer than the lengths of covalent bonds, as expected. Figure 6 shows the cuts through the PESs of the ion-pair states with the bond lengths of SO fixed approximately at the equilibrium bond length of the ion-pair state and the bond angles as the variables. The curves in Figure 6 illustrate that the ion-pair states have linear equilibrium geometries.
Figure 6. Cuts through the PESs of the ion-pair states, which clearly indicate that the equilibrium geometries of ion-pair states are all linear. The bond angles are the variables, and the two bond lengths of SO are fixed approximately to the equilibrium bond lengths of ion-pair states, i.e., 1.42 and 2.50 Å, respectively. The energies of the calculated PESs are shifted down 4.7 eV so that the threshold of the ion-pair dissociation is in accordance with the experimental value. The six ion-pair states converge to four states in the linear geometries. All calculations were performed at the CASSCF/6-311++g** level.
Figure 7. Cuts through the PESs of the ion-pair states and Rydberg states, which indicate the predissociation mechanism of the ion-pair dissociation. The bond angle is fixed to 119°, and one of the S-O bond lengths is fixed to 1.42 Å, respectively. The x-coordinate is the bond length of another S-O bond. The energies of the calculated PESs are shifted down 4.7 eV so that the threshold of the ion-pair dissociation is in accordance with the experimental value. The PESs for Rydberg states 1A1[(D2A1)4sa1] and 1A1[(C2B1)4db1] are obtained by shifting those of ionic states D2A1 and C2B1 to the experimentally determined Rydberg energy levels. Two horizon lines in the figure indicate the energy region where the experimental studies have been performed in this work. All calculations were performed at the CASSCF/6311++g** level.
TABLE 3: Equilibrium Geometries of the SO2 Ion-Pair States and the Corresponding Main Electronic Configurationsa equilibrium geometry Σ
ΣΠ ∆
electronic configurations near the crossing regionb
rSO (Å)
rSO (Å)
θOSO (deg)
1
1.41
2.53
180
15A′
(3a′′)2(12a′)2(13a′)1(4a′′)0(14a′)1 (3a′′)1(12a′)2(13a′)2(4a′′)1(14a′)0
(2π)4(3π)3(10σ)2(4π)1 (2π)4(3π)4(10σ)1(4π)1 (2π)4(3π)3(10σ)2(4π)1
1.41 1.39 1.42
2.58 2.43 2.45
180 180 180
14A′ 13A′
(3a′′)2(12a′)2(13a′)1(4a′′)0(14a′)1 (3a′′)1(12a′)2(13a′)2(4a′′)1(14a′)0
main configuration +
4
3
2
(2π) (3π) (10σ) (4π)
a Electronic configurations in ion-pair states of A′ symmetry with Cs geometry near the crossing region with Rydberg states. b The two SO bond lengths are 1.7 and 1.4 Å, and the bond angle is 119°, respectively. Only configurations that may interact with A′ symmetry Rydberg states are listed.
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Figure 8. Orbital correlation diagram indicating the ion-pair dissociation mechanism of SO2 f SO+ (X2Π) + O- (2Pj). Column a shows the main electronic configuration of the Rydberg state [(D1A1)4sa1], column b shows the main electronic configuration for the ion-pair state 1Σ+ and 1∆ in the linear equilibrium structure, and column c shows the electronic configurations of SO+ (X2Π) and O- (2PJ), respectively. It is seen that the configuration interaction between the Rydberg state and the ion-pair state can occur via the electrostatic interaction, and the ion-pair state is formed by exciting one electron in the occupied antibonding π-orbital (3π in linear, 12a′ or 3a′′ in Cs symmetry) or antibonding σ-orbital (10σ or 13a′) mainly consisting of the isolated electron in O atom to the antibonding π-orbital of SO+.
The interaction between ion-pair states and Rydberg states can occur via various perturbations, for example, electrostatic coupling, vibronic coupling, spin-orbit coupling, and even rotational coupling. Except for the electrostatic coupling, the other couplings require that the electronic configurations describing the ion-pair states and the Rydberg states can differ by no more than one orbital; however, for electrostatic interaction the electronic configurations for the interacting states can differ by two orbitals.25 The ion-pair states often differ by two orbitals with the interacting Rydberg states. Therefore, the electrostatic interaction often plays the main role in the interaction between the ion-pair states and Rydberg states, as in the case of SO2. The electrostatic perturbation requires the interacting states have the same symmetry. Since the observed Rydberg states have 1A1 symmetries, the predissociating ionpair states in Cs geometry should have A′ symmetries. In Table 3, we list the electronic configurations for ion-pair states with A′ symmetries in the crossing region between the ion-pair states and Rydberg states, where the electronic configurations are very rich because of the strong state mixings. For ion-pair states in linear equilibrium structure, the electronic configurations are mainly (2π)4(3π)3(10σ)2(4π)1, which forms the ion-pair states with Σ-, ∆, and Σ+ symmetries, and (2π)4(3π)4(10σ)1(4π)1, which forms the ion-pair state with Π symmetry. To examine the predissociation mechanism, cuts through the PESs with one of the SO bond lengths as variable and the other SO bond and the bond angle fixed at the equilibrium geometry of SO2 have been calculated for ion-pair states and Rydberg
states converging to SO2+(C2B1, D2A1). The cuts of PESs for ion-pair states have shifted down 4.7 eV so that the calculated threshold has the same value as that of the experimental data. As we mentioned, at the level of the present calculations such errors were expected. The cuts of PESs for Rydberg states [(D2A1)4sa1] and [(C2B1)4db1] were obtained by moving the cuts of PESs curves of SO2+(C2B1, D2A1) to the energy position of Rydberg states, respectively. Figure 7 indicates that the ionpair dissociation could only occur via the predissociation mechanism since the Franck-Condon region is far from the equilibrium region of ion-pair states, and the direct excitation to the ion-pair state is difficult. To examine the changes of electronic configurations from the Rydberg states f linear ion-pair states f ion-pair dissociation limit, we have drawn an orbital correlation diagram based on the CASSCF calculation (Figure 8), which is in some way similar to the Walsh molecular orbital diagram, as described in a number of textbooks for molecular spectroscopy.26 Figure 8 provides a picture about the ion-pair dissociation mechanism. Column a shows the main electronic configuration of the Rydberg state [(D1A1)4sa1], column b shows the main electronic configuration for the ion-pair state 1Σ+ and 1∆ in the linear equilibrium structure, and column c shows the electronic configurations of SO+ (X2Π) and O- (2PJ), respectively. It is clear that the orbitals (12a′) and (3a′′), (4a′′) and (14a′) in the bent geometry correlate with the orbitals (3π) and (4π) in linear geometry, respectively, and correspondingly, (13a′)
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correlates with (10σ). The interaction matrix between the ionpair state and the Rydberg state is
calculation results about the symmetry assignments for the energy sequence of SO2+ as C(2B1) < D(2A1).17,18
〈
Acknowledgment. This work is funded by Projects 20773076 and 10734040 supported by the National Science Foundation of China, and Projects 2007CB815200s and 2010CB922900 supported by NKBRSF of China.
| |
〉
1 (2π)(4π) (12a′)(4sa1) rij
or
〈
(2π)(4π)
| r1 |(3a′′)(4db )〉 1
ij
From the correlations between columns b and c, it is seen that the orbitals (3π) and (10σ) in the ion-pair state correlate with (2px)(2py)(2pz) in the O- atom, and (8σ) correlates with the (2s) orbital in the O- atom, respectively. The (4π) orbital in ion-pair state correlates with the orbital (3π) in SO+ (X2Π). All other orbitals in linear geometry correlate with the orbitals in SO+ (X2Π). Basically, the ion-pair state is formed by exciting one electron in antibonding π-orbital (3π) or antibonding σ-orbital (10σ) mainly consisting of the isolated electron in O atom to the antibonding π-orbital in SO+. It is noted that this orbital correlation diagram could also be used to understand the ion-pair dissociation mechanism of other triatomic molecules. For example, it can be applied straightforwardly to explain the ion-pair dissociation mechanism of N2O.12 IV. Summary We have studied the ion-pair dissociation mechanism of SO2 + 14.87 - 15.15 eV f SO2** f SO+ (X2Π,υ) + O- (2PJ) using the velocity map imaging method and tunable XUV laser. In this energy region, the ion-pair yield spectrum has two very broad bands that indicate a fast predissociation process, which were assigned as Rydberg states converging to 1A1[(D2A1)4sa1] and 1A1[(C2B1)4db1], respectively. The translational energy distribution of the photofragments illustrates that the vibrational population of SO+ (X2Π,υ) is highly reverted. To understand the properties of the ion-pair states, ab initio quantum chemistry calculations were also performed. The results show that the equilibrium geometric structures of the ion-pair states are all linear. An orbital correlation diagram that correlates orbitals from Rydberg state to linear ion-pair states, and from the linear ion-pair states to the dissociation limit was drawn. The formation of the ion-pair states is by electron migration from the isolated electron in O atom to the antibonding π orbital of the SO bond. The experimental results confirm the previous theoretical
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