Multireference Configuration Interaction Study of the Vibronic

Jul 12, 2010 - Present address: Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan. Phone: +81-29-282-1111 ...
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J. Phys. Chem. A 2010, 114, 7937–7944

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Multireference Configuration Interaction Study of the Vibronic Transitions and Photodissociation of Vinyl Bromide and Vinyl Chloride Radical Cations in the Second Excited State Makoto Yamaguchi* Institute of Research and InnoVation, 1201 Takada, Kashiwa, Chiba 277-0861, Japan ReceiVed: December 25, 2009; ReVised Manuscript ReceiVed: June 10, 2010

Recent development of techniques to obtain vibronically resolved spectra of radical cations of organic molecules provides detailed information regarding molecular structure and dynamics in the excited states that lead to photodissociation and/or ultrafast nonradiative decay through conical intersections. In this paper, the vibronic transitions and photodissociation of radical cations of vinyl bromide (CH2CHBr+) and vinyl chloride ˜ ) are studied by multireference configuration interaction calculations. (CH2CHCl+) in the second excited state (B ˜ -B˜ transitions are analyzed using Vibronically resolved photofragment yield spectra for the ground state X calculated Franck-Condon factors with optimized geometries and normal mode vectors for two states. The relevance of bond dissociation in the B˜ state to the experimental spectra and the dynamics of the C2H3+ fragment is explored using calculated potential energy curves for the lower electronic states. 1. Introduction Electronically excited states of radical cations of small organic molecules have been extensively studied in recent years as they provide typical examples of nonadiabatic dynamics leading to ultrafast nonradiative decay through conical intersections.1,2 X-ray and ultraviolet photoelectron spectroscopy (XPS and UPS, respectively) have been mainly employed for such studies because they can probe several ionized states.3-5 Nonadiabatic dynamics have been revealed by analyzing complex vibrational band structures with model Hamiltonians including vibronic couplings. However, the energy resolution of photoelectron spectra is limited and is often insufficient to derive vibrational frequencies. High resolution photoionization spectra in which vibrational states are resolved have become available by zero-kinetic energy electron (ZEKE) photoelectron spectroscopy6,7 and massanalyzed threshold ionization (MATI) spectroscopy.8 In these methods, either electrons (ZEKE) or molecular ions (MATI) are detected after ionization of molecules in Rydberg states by a pulsed electric field. Although multiphoton excitation by pulsed lasers via an intermediate excited state is currently the most typical method to generate molecules in Rydberg states, one-photon ionization with vacuum ultraviolet (VUV) radiation is advantageous as the intensities of vibronic bands can be compared with Franck-Condon factors (FCFs) between the neutral ground state and the ionized state.9 Recently Kim et al. developed VUV radiation sources of up to 12 eV by four-wave mixing of Hg,10 which was successfully applied to generate not only the ground but also the first excited ionized state of vinyl halides.11,12 Vibronic bands in MATI spectra of the ground and first excited states of radical cations were successfully analyzed using calculated FCFs. The MATI method has been extended to obtain not only the photoionization spectra of neutral molecules but also the * To whom correspondence should be addressed. Present address: Japan Atomic Energy Agency, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan. Phone: +81-29-282-1111 (ext.67810). Fax: +81-29-2821098. E-mail: [email protected].

electronic spectra of ionized molecules. Johnson et al. developed a technique called photoinduced Rydberg ionization (PIRI) to detect molecular ions by photoexcitation of neutral molecules in Rydberg states. Because the interaction between the core cation and Rydberg electrons is negligible, the action spectrum of the molecular ion yield can be regarded as a vibronic spectrum.13,14 This method has been successfully ˜ -B˜ transitions in applied for observation of forbidden X 15-18 benzene and halobenzenes. Kim et al. found that radical cations of vinyl halides generated by chemical exchange or electron impact are fairly long-lived,19 and they measured the kinetic energy released and angular distribution of the C2H3+ fragment from C2H3Cl+ at several excitation wavelengths.20 Recently, they developed a new technique called MATI photofragment yield (PFY) spectroscopy by scanning the excitation energy and detecting dissociated ions after photoexcitation of radical cations generated by the MATI method.21,22 Vinyl bromide and vinyl chloride were studied because their ground and first excited cationic states are stable ˜ -B˜ in the parent cationic form. The MATI-PFY spectra of X transitions were vibronically resolved by detection of the vinyl cation (C2H3+) and assignments were made by referring to vibrational analyses obtained from density functional theory (DFT) calculations. However, although the MATI spectra of ˜ and A ˜ states were successfully simulated radical cations in the X with FCFs calculated from vibrational analyses of neutral and ˜ -B˜ transitions have ionized states, the MATI-PFY spectra of X not yet been simulated. It was noted that the calculation of the excited states performed at the time-dependent DFT (TDDFT) level was not adequate for assignment of the MATI-PFY spectra.21 However, it is expected that spectroscopic data can provide a useful benchmark in developing reliable quantum chemical methods for excited state calculations. The radical cations of vinyl halides are isoelectronic with vinoxy-type radicals (CH2CHX: X ) O, S) and their electronic structures are expected to possess some similar characteristics. The low-lying electronic states of vinoxy-type radicals have been extensively studied by ab initio calculations.23-30 It has been

10.1021/jp9121722  2010 American Chemical Society Published on Web 07/12/2010

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pointed out that a multiconfigurational approach is essential to properly describe the electronic states, which are qualitatively represented as “resonance” between two canonical valence bond configurations of carbon-centered formylmethyl (•CH2-CHdO) and oxygen-centered vinyloxy (CH2dCH-O•) radicals. It has ˜ transition of already been shown that the energy of the B˜-X vinoxy radicals can be quantitatively reproduced by calculation at the completely active space self-consistent field (CASSCF) level.23-25 However, inclusion of dynamical correlation by using a multireference configuration interaction (MRCI) method quantitatively provided more satisfactory results for the spectroscopic properties and dynamics, for example, transition energies and optimized geometries, of the B˜ state of vinoxytype radicals.27 On the basis of the successful applications of a multiconfigurational approach for ab initio calculations of vinoxy-type radicals, it is expected that the method can be successfully applied to radical cations of vinyl halides. In this paper, MRCI calculations of the low-lying electronic states of CH2CHBr+ and CH2CHCl+ are performed. First, the vertical excitation energies of the ionic states of optimized geometries of the neutral molecules are calculated and compared with experimental values obtained from XPS spectra. Geometry optimization and vibra˜ and B˜ states are then performed and tional analysis of the X the calculated vibrational frequencies are compared with previously reported values. Rotational profiles of the 0-0 bands are simulated using calculated transition moments and rotational ˜ state to constants. FCFs from the vibrationless level of the X the B˜ state are calculated using normal mode vectors and optimized geometries. Potential energy curves for halogen atom dissociation are calculated and saddle points in the B˜ state and conical intersections between the B˜ and C˜ states are located. Features of the MATI-PFY spectra and photodissociation dynamics of CH2CHBr+ and CH2CHCl+ are discussed by referring to these calculated results. 2. Computational Method All of the MRCI calculations were performed using the latest release of the COLUMBUS program.31-34 The program can compute analytical gradients at the state-averaged complete active space self-consistent field (SA-CASSCF) MRCI level,35-38 and the method has been successfully applied to calculate optimized geometries and potential energy curves of valence and Rydberg excited states of polyatomic molecules.39,40 Dunning’s cc-pVDZ-type basis sets41-44 were used in this study. SA-CASSCF calculations were performed by averaging the ˜ ) and lowest three excited states (A ˜ , B˜, C˜) with equal ground (X weighting factors. Configuration state functions (CSFs) were generated by seven electrons in six molecular orbitals (σ(CX) n(X)(in plane) n(X)(out of plane) π(CC) π*(CC) σ*(CX)), among which the σ* orbital was regarded as an auxiliary orbital with a maximum occupation number that was restricted to one, resulting in 135 CSFs. In the MRCI calculations, CSFs were generated by single and double excitation from the reference configurations (denoted as MRCISD) while the 1s orbital of C, 1s, 2s, and 2p orbitals of Cl, and 1s, 2s, 2p, 3s, and 3p orbitals of Br were frozen cores. The number of generated CSFs was 6 355 779 with generalized interaction restriction. State energies after Davidson’s correction were calculated; these values are denoted as MRCISD+Q.45,46 Geometry optimization was performed using the GDIIS method47 until maximum and root-mean-square (rms) values of the relative changes of coordinates and forces became smaller than 10-3 for all of the natural internal coordinates. Hessians

Yamaguchi were calculated numerically from analytical gradients at geometries slightly displaced from the optimized geometry along natural internal coordinates.48,49 The isotopes of chlorine and bromine atoms were assumed to be 35Cl and 79Br in the calculation of vibrational frequencies and rotational constants. Because no scaling factor for vibrational frequencies calculated by the MRCISD method has been reported, calculated vibrational frequencies were multiplied by a scale factor of 0.9538, which was recommended by Radom et al. for QCISD/6-31G(d) calculations.50 ˜ and B˜ states were Transition moments between the X calculated using molecular orbitals obtained from the SACASSCF calculation at the planar optimized geometries of the B˜ state. Rotational profiles of the 0-0 bands were simulated using the program SPECVIEW.51 Molecules were assumed to behave as asymmetric tops and spin rotation was not taken into account. ˜ and B˜ states were calculated with the FCFs between the X program MolFC.52,53 If an instantaneous geometry in Cartesian coordinates (x) is described as small displacements from equilibrium geometries (x0) by normal coordinates (Q) and normal mode vectors (L) in the ground (superscript G) and the excited (superscript E) states,

x ) xG0 + LGQG ) xE0 + LEQE

(1)

a relationship between the two sets of normal coordinates is obtained.

QE ) JQG + K

(2)

This equation was first proposed by Duschinsky.54 The rotation matrix (J) and shift vector (k) of normal modes were calculated with the reference geometries and normal mode vectors of two electronic states as follows:

J ) (LE)tLG

(3)

K ) (LE)t(xG0 - xE0 )

(4)

Planar optimized geometries with a principal axis of inertia in ˜ and B˜ states were used as reference geometries. Normal the X mode vectors obtained from vibrational analyses at planar optimized geometries were used in the FCF calculations. For the vibrational frequencies, calculated values were used except for ν8 and ν9 modes in the B˜ state, where experimental values derived from MATI-PFY spectra were used. 3. Results and Discussion A. Ionization energies. Tables 1 and 2 show the ionization energies for the ground and three lowest excited states of radical cations of vinyl bromide and vinyl chloride, respectively. Experimental values are vertical ionization energies obtained from He(I) photoelectron spectra55,56 and adiabatic ionization ˜ and A ˜ states energies were derived from MATI spectra for the X 21,22 ˜ Vertical ionization and MATI-PFY spectra for the B state. energies were calculated for optimized geometries of neutral CH2CHBr and CH2CHCl molecules obtained by MRCISD(8,5)/ cc-pVDZ calculation and their Cartesian coordinates are given in the Supporting Information. Although calculated vertical ionization energies are ∼0.4 eV smaller than the experimental

Vibronically Resolved Spectra of CH2CHBr+ and CH2CHCl+

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7939

TABLE 1: Ionization Energies of CH2CHBr exp. state ˜ X (2A′′) ˜ A (2A′) B˜ (2A′′) C˜ (2A′) a

IE

calc. ∆E

a

9.804 9.8171b 10.899a 10.9150b 12.27a 12.0749b 12.95a

IE

∆E

9.374 1.095a 1.0979b 2.47a 2.2578b 3.15a

10.387

1.013 1.208b 2.466 3.093b 3.197 3.523b

11.840 12.571

Reference 55. b Reference 21.

TABLE 2: Ionization Energies of CH2CHCl exp. state ˜ X (2A′′) ˜ A (2A′) B˜ (2A′′) C˜ (2A′) a

IE

calc. ∆E

a

10.005 10.0062b 11.664a 11.6667b 13.13a 12.7518b 13.56a

IE

∆E

9.631 1.659a 1.6605b 3.125a 2.7456b 3.56a

11.141 12.596 13.422

1.511 1.757b 2.965 3.714b 3.792 3.885b

Reference 56. b Reference 22.

values, their differences agreed closely with the differences in the experimental vertical ionization energies between the ground and excited ionized states. Energy differences calculated using TDDFT in previous studies are also listed in the tables. Although ˜ state of CH2CHBr+ the excitation energies to the first excited A + and CH2CHCl calculated by TDDFT showed fairly good agreement with the experimental values, the excitation energies to the second excited state B˜ were significantly larger than the experimental values obtained using the MATI-PFY method.21,22 This large discrepancy may be due to multiconfigurational character of the B˜ state, which is qualitatively described as “resonance” of canonical valence bond structures of a carboncentered radical (•CH2-CHdX) and a halogen-centered radical (CH2dCH-X•). The TDDFT method with a single reference configuration seems insufficient for quantitative calculation of ˜ exhibits this electronic state. In contrast, the first excited state A 2 the lowest state of A′ symmetry with planar geometry. Therefore, removal of one electron from the in-plane nonbonding orbital of the halogen atom can be appropriately described by the TDDFT method. B. Optimized Geometries. Figure 1 shows geometrical parameters of the planar optimized geometries of CH2CHBr+ ˜ and B˜ states. Although no constraint and CH2CHCl+ in the X was imposed on the molecular shape in the geometry optimizations, both radical cations were planar in the ground state and geometrical parameters were similar to those from the previous DFT calculation.21,22 On the other hand, the optimized geometry of the B˜ state of CH2CHBr+ was slightly twisted around the C-C bond, although the extent of stabilization from the planar optimized geometry was very small (-57 cm-1). The calculated ˜ and B˜ states was difference in the total energies between the X 18 567 cm-1, which is very close to the excitation energy for the 0-0 band (18210 cm-1) observed in the MATI-PFY ˜ state of CH2CHCl+ spectrum.21 The optimized geometry of the B was planar and the calculated difference in the total energies of ˜ and B˜ states was 22 099 cm-1, which is again very close the X to the excitation energy for the 0-0 band (22144 cm-1) found in the MATI-PFY spectrum.22

Figure 1. Planar optimized geometries of (a) CH2CHBr+ and (b) CH2CHCl+. For each pair of structural parameters, the upper and ˜ and B˜ states, lower (italic) numbers correspond to values for the X respectively. Bond lengths are given in angstroms; angles in degrees.

In both radical cations, C-C bonds became slightly shorter and C-X (X ) Br, Cl) bonds lengthened significantly by 0.25-0.3 Å upon excitation. These changes are understood by ˜ and B˜ states are considering that electronic structures in X characterized as “resonance” between two canonical valence bond structures as described above. In contrast to the present calculation, the optimized geometries for the B˜ state calculated by the TDDFT method were twisted around the C-C bond.21,22 Furthermore, the C-C bond lengths are shorter (1.305 Å (CH2CHBr+); 1.316 Å (CH2CHCl+)) and C-X bond lengths are longer (2.176 Å (CH2CHBr+); 1.991 Å (CH2CHCl+)) than the corresponding values shown in Figure 1. C. Vibrational Frequencies. Table 3 shows vibrational ˜ and B˜ states. Calculated frequencies of CH2CHBr+ in the X ˜ state are in close agreement with frequencies of the X experimental values derived from the MATI spectrum.9 One of the vibrational frequencies of the a′′ mode was imaginary in the B˜ state with planar optimized geometry, indicating that the equilibrium geometry in the B˜ state is nonplanar. In contrast to ˜ state, the calculated frequencies differ significantly from the X the experimental values and the values calculated by Lee et al. using the TDDFT method.21 In the present calculation, vibrational frequencies of the ν8 mode (CBr stretching) in nonplanar and planar optimized geometries were 423 and 479 cm-1, respectively, and these values were larger than those of the ν9 mode (CCBr bend). In contrast, TDDFT calculated the vibrational frequency of the ν8 mode to be 237 cm-1 and it appeared at a lower frequency than the ν9 mode.21 The vibrational frequencies of CH2CHCl+ are summarized in Table 4. As for the ground state, Zhang et al. measured the ZEKE spectrum of the cation and derived fundamental vibrational frequencies, which were compared with vibrational frequencies calculated using Møller-Plesset perturbation theory

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Yamaguchi

TABLE 3: Vibrational Frequencies of CH2CHBr+ ˜ (2A′′) X symmetry a′

a′′

a

mode

character

calc. MRCI

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12

C1H1 str. C1H2 str. C2H3 str. C1H1H2 scis. C2H3 rock C1H1H2 rock C1C2 str. C2Br str. C1C2Br bend C2H3 wag C1C2 wag C1C2 torsion

3204 3142 3084 1474 1312 1243 1009 673 339 980 843 413

B˜(2A′′)

exp. MATI

a

calc. DFT

a

calc. MRCI

calc. MRCI

3198 3148 3076 1567 1365 1195 952 479 290 910 385 205i

3184 3142 3062 1504 1345 1163 946 423 259 907 617 340

3247 3196 3136 1511 1350 1289 1043 689 351 1036 853 397

1470 1309 1258 1037 700 348 1037 838 392

exp. PDYb

calc. TDDFTb

1427 1306 994 644 413 292 1014 854 557

3126 3197 2991 1481 1296 961 734 237 330 925 879 556

Reference 9. b Reference 21.

TABLE 4: Vibrational Frequencies of CH2CHCl+ ˜ (2A′′) X symmetry a′

a′′

a

mode

character

calc. MRCI

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12

C1H1 str. C1H2 str. C2H3 str. C1H1H2 scis. C2H3 rock C1H1H2 rock C1C2 str. C2Cl str. C1C2Cl bend C2H3 wag C1C2 wag C1C2 torsion

3211 3134 3086 1476 1350 1242 1045 809 386 963 844 374

B˜ (2A′′)

exp. ZEKEa

calc. MP2a

calc. MRCI

1477 1367 1257 1067 834 394

3180 3082 3048 1476 1372 1249 1077 847 393 993 846 380

3198 3166 3077 1592 1357 1193 945 504 324 911 291 186

384

exp. PDYb

1421 1018 408 323 832 598

calc. TDDFTb 3173 3118 2991 1438 1303 1021 796 396 319 938 880 596

Reference 57. Calculated values in Table 1 of ref 57 were scaled by 0.96. b Reference 22.

TABLE 5: Rotational Constants of CH2CHBr+ and CH2CHCl+ a CH2CHBr+ 2 ˜ X( A′′) B˜(2A′′)

CH2CHCl+ 2 ˜ X( A′′) B˜(2A′′)

a

1.6922

1.6644

b

0.1443

0.1200

c

0.1329

0.1119

1.7820 (1.823)b 0.2074 (0.208)b 0.1858 (0.187)b

a

1.6724 0.1705 0.1547

Units in wavenumbers (cm-1). b Reference 22.

(MP2).57 The present calculation shows very good agreement with their experimental and calculated values. For the B˜ state, most of the calculated vibrational frequencies in the present study were 20% larger than the corresponding values published by Lee et al.22 They derived six vibrational frequencies from the MATI-PFY spectrum and their calculated values agreed closely with them. However, the number of vibronic bands observed in the MATI-PFY spectrum of CH2CHCl+ was limited and their assignments based solely on comparison with calculated vibrational frequencies is not conclusive. D. Rotational Profiles. Rotational profiles of the 0-0 bands in the MATI-PFY spectra of CH2CHBr+ and CH2CHCl+ were simulated using calculated values of rotational constants and transition moments. The rotational constants of the planar ˜ and B˜ states are summarized in optimized geometries of the X Table 5. Transition moments for ground state optimized geometries were 0.886 and 0.709 e Bohr for CH2CHBr+ and CH2CHCl+, respectively. The rotational temperature was set to 10 K to reproduce observed peak widths, because the parent

Figure 2. Simulated rotational profiles of the 0-0 band at 10 K for (a) CH2CHBr+ and (b) CH2CHCl+.

cations were generated using the MATI method from molecules cooled with a supersonic jet. Figure 2 shows simulated rotational profiles that are asymmetric. This is a feature of the a/b type transition that is expected from the rotational constants of

Vibronically Resolved Spectra of CH2CHBr+ and CH2CHCl+

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7941 ˜ TABLE 6: Shift Vectors of Normal Modes between the X and B˜ Statesa symmetry

mode

CH2CHBr+

CH2CHCl+

ν1 ν2 ν3 ν4 ν5 ν6 ν7 ν8 ν9 ν10 ν11 ν12

0.001 0.005 0 0.031 0.112 0.018 -0.123 -0.798 -0.738 0 0 0

0.001 -0.011 0.002 -0.114 0.240 0.046 0.317 -0.843 -0.506 -0.001 -0.001 0.005

a′

a′′

a

Figure 3. MATI-PFY spectrum (top) and calculated FCFs (bottom) ˜ and B˜ states of CH2CHBr+ between the X

molecules, which behave as prolate tops with transition moments almost parallel to the molecular axes. The simulated profiles agree well with those observed, particularly for CH2CHBr+. ˜ -B ˜ transiE. Franck-Condon factors. The FCFs of the X tion were calculated and compared with intensities of vibronic bands observed in the MATI-PFY spectra of the compounds. Figure 3 shows the MATI-PFY spectrum and calculated FCFs of CH2CHBr+. Although the optimized geometry in the B˜ state was slightly nonplanar, the energy difference between the planar and nonplanar optimized geometries was very small so the planar optimized geometry and normal mode vectors at this geometry were employed for the FCF calculation. The vibrational frequency of the ν12 mode was tentatively set to the value calculated for the nonplanar optimized geometry. The vibrational frequencies of the ν9 and ν8 modes were set to experimental values in the FCF calculation to facilitate comparison between the observed spectrum and the calculated FCFs. The MATIPFY spectrum showed strong vibronic bands that were assigned as combinations and overtones of ν9 and ν8 modes; most of these bands correlated with the calculated FCFs in the lower part of the spectrum. However, only ν9 and ν8 modes appeared in the calculated FCFs as expected from the shift vector shown in Table 6, whose elements other than those two modes are very small. Certain series of vibronic bands are absent in the calculated FCFs. For example, the progression in the MATIPFY spectrum starting at 557 cm-1, which has been assigned to 9n121, was missing in the calculated FCFs. In fact, all of the vibronic bands including nontotally symmetric modes are missing in the calculated FCFs. It should be noted that the intensities of the vibronic bands in the MATI-PFY spectrum are influenced by photodissociation yields so they are not directly proportional to the FCFs. The vibronic bands with nontotally symmetric modes may have larger photodissociation yields than the vibronic bands lacking nontotally symmetric modes. This is analogous to the case of the vinoxy radical in

Units in Å amu1/2.

˜ state that showed faster nonradiative decay from vibronic the B levels with nontotally symmetric modes.58 It should also be noted that potential energy curves along the nontotally symmetric modes are largely anharmonic as indicated by the slightly nonplanar optimized geometry, and it would be very difficult to accurately calculate the energy levels of nontotally symmetric modes. Another notable difference between the observed spectrum and calculated FCFs is the absence of the 8m9n progressions with m g 3 in the MATI-PFY spectrum while their calculated FCFs are still large (shown in the lower part of the spectrum). This may be due to large anharmonicity of the ν8 mode, which is almost parallel to the C-Br dissociation coordinate as discussed below. Figure 4 shows the measured MATI-PFY spectrum and calculated FCFs of CH2CHCl+. The calculated FCFs shown in the lower part of the figure are similar to the case of CH2CHBr+ in which FCFs for the ν9 and ν8 modes showed appreciable intensities. On the other hand, fewer vibronic bands are observed

Figure 4. MATI-PFY spectrum (top) and calculated FCFs (bottom) ˜ and B˜ states of CH2CHCl+ between the X

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in the MATI-PFY spectrum than in that of CH2CHBr+. Some of the vibronic bands are significantly broadened and no vibronic bands are discernible above 1500 cm-1 from the 0-0 band where the background signal increases continuously with the excitation energy. Close examination of the MATI-PFY spectrum reveals that peak broadening with increasing background signal caused by the 0-0 band of CH2CHBr+ is also present above ∼2000 cm-1, although this is not as prominent as found for CH2CHCl+. Progressions of the ν9 mode were assigned as 9n (323, 642, and 950 cm-1), 9n121 (598, 916, and 1230 cm-1), and 9n111 (832 and 1133 cm-1). No progression of the ν8 mode was observed other than the peak at 408 cm-1, possibly because of the low barrier height of the C-Cl dissociation reaction coordinate. Lee et al. assigned the vibronic bands at 1421 and 1018 cm-1 as the 41 and 61 modes, respectively, based on their excellent agreement with calculated vibrational frequencies (ν4 ) 1438 cm-1; ν8 ) 1021 cm-1). However, the calculated FCFs for those bands are very small, so their assignments as 92111 and 8192, respectively, are more likely to be correct. F. Potential Energy Curves. Potential energy curves along the C-X dissociation coordinates and optimized geometries of saddle points for both CH2CHBr+ and CH2CHCl+ were calculated to understand the difference in the MATI-PFY spectra and the dynamics of C2H3+ fragmentation in the radical cations. Energies for the three lowest electronic states obtained from the MRCISD+Q calculation relative to the ground state planar optimized geometries are shown in Figure 5. Geometrical parameters other than C-X bond lengths were fully optimized for each state by the MRCISD calculation where C-X bonds are shorter than 3.0 and 3.1 Å for CH2CHBr+ and CH2CHCl+, respectively. Because all three states converge to C2H3+ (1A′) + X(2P) at the dissociation limit, no geometry optimization was performed with C-X bonds longer than 3.2 Å (Br) and 3.3 Å (Cl). Also, state energies were calculated by changing C-X bond lengths whereas other geometrical parameters were fixed to the values of the ground state at 3.0 Å (Br) and 3.1 Å (Cl). The calculated C-X bond dissociation energies at 5.0 Å were 2.36 and 2.66 eV for CH2CHBr+ and CH2CHCl+, respectively. These values were larger than the measured values of 2.081 eV (CH2CHBr+) and 2.525 eV (CH2CHCl+).59,60 This may be partly due to the Y-shaped optimized geometry of C2H3+ at the dissociation limit, which was calculated to be less stable by about 0.2 eV than the nonclassical bridged structure of protonated acetylene.61 Recently Chang et al. calculated that potential energy curves of the second lowest B˜(2A′′) and third lowest C˜(2A′) states are correlated to C2H3(3A′′) + X(2P) and C2H3(1A′) + X(2P) at the dissociation limit and they cross at r(C-Cl) ) 2.2 Å with an ˜ excess energy of 0.34 V from the energy minimum in the B 62 state. Actually, the crossing of the potential energy curves in Cs symmetry form a symmetry-allowed conical intersection in C1 symmetry. In fact, the potential energy curves of the B˜ state of CH2CHBr+ and CH2CHCl+ are adiabatically correlated to C2H3(1A′) + X(2P) with barriers at around 2.4-2.5 Å as shown ˜ state in Figure 5. Barrier heights of the saddle points in the B -1 + were 2790 and 2370 cm for CH2CHBr and CH2CHCl+ according to MRCISD geometry optimization calculation and lowered to 1780 and 1400 cm-1 from the MRCISD+Q calculation. In Figure 5, points corresponding to conical intersections ˜ and C ˜ states are highlighted with asterisks. They between the B are located at significantly shorter C-X bond lengths than those of the saddle points and their relative energies are about 3500 cm-1 higher than the energy minima of the B˜ state.

Yamaguchi

Figure 5. Relative energies of low-lying electronic states along the C-X (X ) Br, Cl) bond for (a) CH2CHBr+ and (b) CH2CHCl+. Solid ˜ ) state; open squares: the first excited state (A ˜ ); squares: the ground (X solid circles: the second excited state (B˜). The asterisks correspond to the optimized geometries at the conical intersections between the B˜ and C˜ states.

Figure 6. Optimized geometries of saddle points in the B˜ state and conical intersections between the B˜ and C˜ states of CH2CHBr+ and CH2CHCl+.

Figure 6 shows optimized geometries of CH2CHBr+ and CH2CHCl+ at saddle points in C-X dissociation in the B˜ state and the conical intersections between the B˜ and C˜ states. At the saddle points, C-X bonds were elongated to r(C-Br) )

Vibronically Resolved Spectra of CH2CHBr+ and CH2CHCl+

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7943 TOF measurements were performed by excitation at 489 nm (+2240 cm-1) and 465 nm (+3295 cm-1) in the case of C2H3Br+.21 A small increase in the average KER indicates that the dissociation was statistical at these energies. The slightly anisotropic profile at 465 nm implies dissociation occurred faster than the rotational period. Because the dissociation lifetime estimated from RRKM theory (37 ps) was shorter than the rotational period (140 ps), Lee et al. rationalized that nonradiative decay to the ground state was rate determining at 465 nm. This means that the barrier height of C-Br bond dissocia˜ state is higher than 3295 cm-1. Although this value tion in the B is much larger than the calculated value of 1780 cm-1, the observed trend of the larger barrier for C2H3Br+ than C2H3Br+ was reproduced in the calculation.

Figure 7. Excitation energy dependence of average KERD (solid) and anisotropy (open) of C2H3+ from CH2CHBr+ (circles) and CH2CHCl+ (squares). Vertical lines in the upper part of the figure indicate calculated values for the relative energies of CH2CHBr+ (thick lines) and CH2CHCl+ (thin lines) at saddle points in the state and conical intersections (C.I.) between the B˜ and C˜ states.

2.565 Å and r(C-Cl) ) 2.382 Å, whereas C-C bonds were shortened to 1.297 and 1.302 Å, for CH2CHBr+ and CH2CHCl+, respectively. Large C1-C2-H3 angles indicate that the molecules behave as a loose complex of a Y-shaped vinyl cation and a halogen atom. It should also be mentioned that the optimized geometries are nonplanar as indicated by torsion angles of 111.6° (CH2CHBr+) and 107.4° (CH2CHCl+), which were calculated as half of the total of all of the dihedral angles around the C-C bond. Optimized geometries at the conical intersections between the B˜ and C˜ states are shown in the lower part of Figure 6. In contrast to the saddle point geometries, the molecules are almost planar with torsion angles of 178.5° (CH2CHBr+) and 184.2° (CH2CHCl+). Their geometrical parameters fall between those of the planar optimized geometries (Figure 1) and the saddle points in the B˜ state. G. Dissociation Dynamics. Lee et al. measured time-of-flight (TOF) profiles of the C2H3+ fragment after photoexcitation of CH2CHBr+ and CH2CHCl+ by changing the laser polarization angle, obtaining kinetic energy release distribution (KERD) and anisotropy data.21,22 Figure 7 shows average values of kinetic energy release (KER) and anisotropy plotted against the relative energy of the 0-0 band. Values at four different excitation energies are plotted for CH2CHCl+.22 The average KER value was small with statistical distribution and dissociation was isotropic at 445.1 nm (+323 cm-1 from the 0-0 band), indicating dissociation in the ground state after internal conversion. Slightly nonstatistical KERD with anisotropy was observed by excitation at 433.6 nm (+918 cm-1), although the estimated dissociation lifetime of 590 ps from Rice-RamspergerKassel-Marcus (RRKM) theory was longer than the rotational period. At this excitation energy in the MATI-PFY spectrum, peak broadening and the rise of the background signal toward higher excitation energy has begun, as shown in Figure 5. Thus, it is ˜ state has occurred at this supposed that dissociation in the B excitation energy. Both the average values of kinetic energy release and anisotropy increase almost linearly at the higher excitation energies of 405.8 nm (+2498 cm-1) and 357 nm (+5867 cm-1), indicating dissociation in the excited state. From these observations the onset of dissociation in the excited state is thought to be located at around 900 cm-1 above the vibrationless level of the planar ˜ state. This value is in fairly good agreement geometry of the B with the calculated barrier height of 1400 cm-1 for the B˜ state regarding C-Cl bond dissociation, which is indicated by a vertical line in the upper part of the figure.

4. Conclusion Lower electronic states of CH2CHBr+ and CH2CHCl+ were successfully calculated by the SA-CASSCF-MRCISD method. Calculated excitation energies and vibrational frequencies showed better agreement with measured values than those calculated previously, mainly because the nature of the excited states requires a multiconfigurational approach. The feature of the MATI-PFY spectra that the vibronic bands are dominated by the ν8 (CX stretch) and ν9 (CCX bend) modes was successfully reproduced by FCF calculations. The large intensities observed for vibronic bands in the MATI-PFY spectra including nontotally symmetric modes were attributed to larger photodissociation yields induced by the nontotally symmetric vibrations. Potential energy curves of the lower electronic states were calculated along the dissociation coordinates of the C-X bond and saddle points were located in the B˜ state. Optimized geometries at the saddle points showed twisting around the C-C bond, whereas conical intersections between the B˜ and C˜ states showed planar geometries. Dissociation dynamics probed by KERD and anisotropy parameters of fragment ions after photoexcitation were discussed in relation to the calculated profiles of the potential energy curves along the C-X dissociation coordinates. The present study has shown that radical cations of vinyl bromide and vinyl chloride can be regarded as vinoxy-type radicals for which a multiconfigurational approach is essential to calculate the lower electronic states. The MRCISD method was successful at calculating results that are helpful to analyze experimental results, such as rotational profiles and dominant vibrational modes in the vibronic bands in the MATI-PFY spectra. However, there are certain features that could not be captured by FCF calculation within harmonic approximation, such as intensities of vibronic bands with nontotally symmetric modes or the spectral broadening and background signal found in the MATI-PFY spectra, especially in the case of CH2CHCl+. Further studies on nonadiabatic dynamics along potential energy surfaces calculated with larger basis sets are expected to clarify these issues. Supporting Information Available: Optimized geometries in Cartesian coordinates and Duschinsky rotation matrices. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Ko¨ppel, H.; Domcke, W.; Cederbaum, L. S. AdV. Chem. Phys. 1984, 57, 59. (2) Ko¨ppel, H.; Domcke, W.; Cederbaum, L. S. In Conical Intersections; Domcke, W.; Yarkony, D. R.; Ko¨ppel, H., Eds.; World Scientific: NJ, 2004; p 323.

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