Chemical Physics Letters 384 (2004) 165–170 www.elsevier.com/locate/cplett
Matrix isolation infrared spectroscopic and theoretical study of the transition metal (Mn and Fe) dioxide–ethylene complexes Mohua Chen, Zhengguo Huang, Mingfei Zhou
*
Department of Chemistry and Laser Chemistry Institute, Shanghai Key Laboratory of Molecular Catalysts and Innovative Materials, Fudan University, No. 220, Handan Road, Shanghai 200433, PR China Received 16 October 2003; in final form 30 November 2003 Published online:
Abstract The transition metal dioxide–ethylene complexes (g2 -C2 H4 )MnO2 and (g2 -C2 H4 )FeO2 have been prepared by the reactions of transition metal dioxide molecules (MnO2 and FeO2 ) with ethylene in solid argon The metal dioxide molecules were prepared by the reactions of laser-ablated metal atoms with dioxygen. The (g2 -C2 H4 )MnO2 and (g2 -C2 H4 )FeO2 complexes were characterized by matrix isolation infrared absorption spectroscopy as well as density functional calculations. Both complexes were predicted to have low spin ground states, having C2v symmetry with the MC2 plane perpendicular to the MO2 plane. Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction The interactions of transition metal centers with olefins are of fundamental importance both in organometallic and coordination chemistry and in chemisorption studies of olefins on metal surfaces. Many studies have concentrated on the reactions between transition metal atoms and ethylene [1–8]. The spectra, structures and bonding of the transition metal–ethylene complexes have been investigated by matrix isolation infrared or ESR spectroscopy as well as theoretical calculations [1–12]. The activation of the C–H bond in ethylene by transition metal atoms has also been theoretically studied [13] and the inserted species such as HFeC2 H3 and HTiC2 H3 have been experimentally characterized in the cryogenic matrices [7,8]. In recent years, tremendous research efforts focused on the high-valence transition metal oxide additions across C@C bond of olefins, since there is considerable industrial interest in the activation of C@C double bonds by readily accessible metal oxides [14,15]. For example, permanganate serves to convert olefins to
*
Corresponding author. Fax: +86-21-65643532. E-mail address:
[email protected] (M. Zhou).
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2003.12.002
diols, ketones and carboxylic acids under mild condition [16]. Iron(IV)-oxo species are proposed to be the key reactive species that effect substrate oxidation in many heme and nonheme iron enzymes. In cytochrome P450, the iron(IV)-oxo moiety is used in conjunction with a porphyrin radical to effect hydroxylations of alkanes and arenes [17]. The C–H and C–C bond activation of olefins by bare transition metal monoxide and dioxide cations in the gas phase have been reported [16,18,19]. To our knowledge, the reactions of neutral transition metal oxide molecules with olefins such as ethylene have not been reported. In this Letter, we report a study of the reactions of neutral metal dioxides (MnO2 and FeO2 ) with ethylene molecules in solid argon. We will show that, the metal dioxide molecules form stable complexes with ethylene. These complexes are potential important intermediates in the transition metal oxide catalyzed C–C and C–H bond activation processes.
2. Experimental and theoretical methods The technique for matrix isolation infrared spectroscopic investigation has been described in detail previously [20]. Briefly, the Mn and Fe atoms were
M. Chen et al. / Chemical Physics Letters 384 (2004) 165–170
evaporated by the 1064 nm fundamental of a Nd:YAG laser (20 Hz repetition rate and 8 ns pulsed width) and co-deposited with molecular oxygen and ethylene mixtures in excess argon onto a 12 K CsI window for 1 h at a rate of 3–4 mmol/h. The stepwise broadband irradiation of the deposited sample using a high-pressure mercury lamp was carried out to enhance the yield of metal dioxide molecules. Infrared spectra were recorded on a Bruker IFS 113 V spectrometer at a 0.5 cm1 resolution using a DTGS detector. C2 H4 was subjected to several freeze–pump–thaw cycles before use. O2 (Shanghai BOC, 99.6%), 13 C2 H4 and C2 D4 (99%, Cambridge Isotope Laboratories) and 18 O2 (Isotec Inc., >97%) were used without further purification. Density functional calculations were performed using the GA U S S I A N 98 program [21]. The Becke three parameter hybrid functional with the Lee–Yang–Parr correlation corrections (B3LYP) was used [22,23]. Recent calculations have shown that, this hybrid functional can provide accurate results for the geometries and vibrational frequencies for transition metal containing compounds [24]. The 6-311++G** basis set was used for the H, C and O atoms, and the all electron basis set of Wachters–Hay as modified by Gaussian was used for the metal atoms [25,26]. Geometries were fully optimized. The vibrational frequencies were calculated with analytic second derivatives, and zero point vibrational energies (ZPVE) were derived. For comparison, single point CCSD(T)/6-31+G* calculations were carried out at the B3LYP/6-311++G** equilibrium geometries as well [27].
3. Results and discussions Recent investigations in our laboratory have shown that, laser-ablation combined with matrix isolation is a suitable technique in producing metal dioxide molecules for reaction study [28–30]. As has been mentioned, the primary products from co-deposition of some laserablated metal atoms with oxygen in excess argon are predominately metal dioxide molecules. Hence, the reactions of the primary formed metal dioxide molecules with other small molecules doped in the reagent gas have been reported. The present experiments employed relatively low ablation laser energy, typically, 5–10 mJ/ pulse laser power was used and focused into a spot of about 0.25 mm2 on the target. At such experimental conditions, the metal mole concentration is estimated to be 0.05–0.1%, less than the O2 and C2 H4 concentrations. Therefore, the possibility for the formation of multimetal clusters is rather small; no obvious multi-metal oxide absorptions were observed. Co-deposition of laser-ablated Fe or Mn atoms with molecular oxygen in excess argon at 12 K produced strong metal dioxide (FeO2 : 945.8 and 797.0 cm1 ,
1 MnO2 : 948.0 and 816.4 cm1 ) and O 4 (953.8 cm ) 1 absorptions with very weak O3 (1039.8 cm ) and other metal oxide absorptions (FeO: 872.8 cm1 , Fe(O2 ): 955.9 cm1 , MnO: 833.3 cm1 , MnO4 : 974.9 cm1 ) [31,32]. Subsequent 20 min broadband irradiation with highpressure mercury lamp destroyed the O 4 absorption and markedly increased the metal dioxide absorptions. Besides the above-mentioned metal oxide absorptions, new product absorptions were produced in the experiments when laser-ablated Fe or Mn atoms were deposited with mixed O2 /C2 H4 reagent gases in excess argon. The representative infrared spectra in selected region from co-deposition of laser-ablated iron atoms with O2 / C2 H4 (0.8% + 0.4%) mixtures in argon are shown in Fig. 1. Isotopic substituted O2 /C2 D4 , O2 /13 C2 H4 , O2 / C2 H4 + C2 D4 , 18 O2 /C2 H4 and 16 O2 + 16 O18 O + 18 O2 / C2 H4 samples were employed for product identification, and the infrared spectra are shown in Figs. 2 and 3, respectively. The 1022.8 cm1 band in the Fe + O2 /C2 H4 experiments increased on annealing and broadband irradiation. When an 18 O2 /C2 H4 sample was used, the band was observed at 986.2 cm1 . The 16 O/18 O isotopic frequency ratio of 1.0371 implies that this band is predominantly an antisymmetric OFeO stretching vibration. In the 16 O2 + 16 O18 O + 18 O2 /C2 H4 experiment (Fig. 2d), a triplet at 1022.8, 1008.1 and 986.2 cm1 was observed, indicating that two equivalent oxygen atoms are involved in this mode. The antisymmetric OFeO stretching mode of neutral FeO2 molecule was observed at 945.8 cm1 in solid argon with the 16 O/18 O isotopic frequency ratio of 1.0380 [32]. The 1022.8 cm1 band is 77 cm1 blue-shifted from the neutral FeO2 absorption. This band was observed only when C2 H4 was added in the reagent gas,
C2H4 0.15
Absorbance
166
(C2H4)FeO2 0.10
(d)
0.05
O3
(c) (b) (a)
0.00 1050
1000
950
Wavenumber (cm-1)
Fig. 1. Infrared spectra from co-deposition of laser-ablated iron atoms with 0.8% O2 + 0.4% C2 H4 in argon: (a) 1 h sample deposition followed by 20 min broadband irradiation; (b) 25 K annealing; (c) 20 min broadband irradiation; (d) 30 K annealing.
M. Chen et al. / Chemical Physics Letters 384 (2004) 165–170
16
(C2H4)Fe O2
18
(C2H4)Fe O O
Absorbance
(C2H4)FeO2
1.587
128.9
Fe
Fe
2.071
2.037
(C2D4)FeO2
1.400
H H
(c) 0.10
1.549
137.4
(d)
0.15
O O
O O
18
16
(C2H4)Fe O2
0.20
167
13
( C2H4)FeO2
C
C
120.9
1.084
H H
H H
C 1.084
120.7
H H
(η 2−C2H 4)FeO 2 (3A 2)
(η 2− C2H 4)FeO 2 (1A 1)
(b)
C
1.393
(C2H4)FeO2
0.05
O O
O O (a)
1.568
133.2
0.00 1020
1000
Mn
Mn
980
1.609
121.7
2.314
2.063
-1
Wavenumber (cm )
Fig. 2. Infrared spectra in the 1030–980 cm1 region from co-deposition of laser-ablated iron atoms with different isotopic samples in excess argon. One hour sample deposition followed by 30 min broadband irradiation and 25 K annealing: (a) 0.8% O2 + 0.4% C2 H4 ; (b) 0.8% O2 + 0.4% 13 C2 H4 ; (c) 0.8% O2 + 0.4% (C2 H4 + C2 D4 ); (d) 0.8% (16 O2 + 16 O18 O+18 O2 ) + 0.4% C2 H4 .
H H
C
1.402
120.6
C 1.085
H H
(η2−C2H4)MnO 2 (2A 1)
H H
C
1.356
121.2
C 1.086
H H
(η2−C2H4)MnO 2 (4B 2)
), bond angle (°) of Fig. 4. Optimized structures (bond length (A (g2 -C2 H4 )MO2 (M@Mn and Fe) at the B3LYP/6-311++G** level.
0.16 16
Absorbance
0.12 (C2H4)MnO2
18
18
(C2H4)Mn O O
(C2H4)MnO2
(d)
(C2H4)Mn O2
(C2D4)MnO2
(c) 0.08
13
( C2H4)MnO2
(O2)MnO2
(b) 0.04
(a) 0.00 1020
1010
1000
990
980
970
Wavenumber (cm-1)
Fig. 3. Infrared spectra in the 1020–970 cm1 region from co-deposition of laser-ablated manganese atoms with different isotopic samples in excess argon. One hour sample deposition followed by 30 min broadband irradiation and 25 K annealing: (a) 0.8% O2 + 0.4% C2 H4 ; (b) 0.8% O2 + 0.4% 13 C2 H4 ; (c) 0.8% O2 + 0.4% (C2 H4 + C2 D4 ); (d) 0.8% (16 O2 + 16 O18 O + 18 O2 ) + 0.4% C2 H4 .
which suggests that the band is due to a FeO2 –C2 H4 complex. This band showed no carbon-13 isotopic shift with 13 C2 H4 but very small deuterium shift (0.9 cm1 ) with C2 D4 . In the O2 /C2 H4 + C2 D4 experiment (Fig. 2c), a doublet at 1022.8 and 1021.9 cm1 was observed, suggesting that only one C2 H4 subunit is involved in the molecule. To support the spectroscopic assignment of (g2 C2 H4 )FeO2 , we performed density functional calculations. We carried out geometry optimization and vibrational analysis for singlet and triplet spin states. The optimized structures are shown in Fig. 4 and the vibrational frequencies and intensities are listed in Table 1.
Both the lowest singlet and triplet states have C2v symmetry with the FeC2 plane perpendicular to the FeO2 plane. The singlet and triplet spin states are very close in energy. At the B3LYP/6-311++G** level, the triplet state (3 A2 ) was predicted to be more stable than the singlet state (1 A1 ) by about 2.2 kcal/mol. In order to further ascertain the relative stability of the singlet and triplet states, high-level ab initio calculations were performed. We carried out single point calculations with the CCSD(T)/6-31+G* method at the optimized geometries of the B3LYP/6-311++G** calculations. The singlet state was calculated to be 7.3 kcal/mol lower in energy than the triplet state. We note that previous studies on FeO2 indicated that the B3LYP functional did not provide good energy predictions, whereas the CCSD(T) calculations predicted the appropriate ground state [32]. As listed in Table 1, the antisymmetric OFeO stretching frequencies of the singlet and triplet states (g2 C2 H4 )FeO2 were computed at 1096.0 and 1025.0 cm1 , respectively, which are 73.2 and 2.2 cm1 higher than the experimental value of 1022.8 cm1 . Due mainly to the neglect of anharmonicity, computed vibrational frequencies are generally higher than the experimental values. The calculated frequencies with B3LYP functional usually should be scaled by a factor of 0.95–0.99 to fit the experimental values [33]. It is difficult to predict the ground state based on the calculated frequencies. However, the calculated 16 O/18 O isotopic frequency ratio of singlet (1.0384) fits the experimental value (1.0371) better than that of triplet (1.0393). Therefore, we conclude that the ground state of (g2 -C2 H4 )FeO2 is the 1 A1 singlet. The DFT normal mode analysis indicated that the antisymmetric OFeO stretching mode shows no
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Table 1 Calculated vibrational frequencies (cm1 ) and intensities (km/mol) of (g2 -C2 H4 )MO2 (M@Mn and Fe) at the B3LYP/6-311++G** level (only the frequencies above 400 cm1 are listed) Frequency (intensity, mode) 2
2
(g -C2 H4 )MnO2 ( A1 )
(g2 -C2 H4 )MnO2 (4 B2 ) (g2 -C2 H4 )FeO2 (1 A1 )
(g2 -C2 H4 )FeO2 (3 A2 )
3223.0 (0, b1 ), 3208.5 (0, a2 ), 3132.1 (1, a1 ), 3128.2 (0, b2 ), 1532.5 (2, a1 ), 1457.4 (9, b2 ), 1239.6 (18, a1 ), 1224.9 (0, a2 ), 1076.6 (303, b1 ), 1017.2 (45, a1 ), 974.4 (20, b2 ), 958.6 (0, a1 ), 945.8 (0, a2 ), 815.9 (1, b1 ), 637.6 (5, b1 ), 461.4(2, b2 ), 411.1 (8, a1 ) 3230.7 (3, b2 ), 3207.6 (0, a2 ), 3128.7 (3, a1 ), 3123.7 (1, b1 ), 1612.9 (0.3, a1 ), 1469.3 (15, b1 ), 1342.2 (1, a1 ), 1241.4 (0, a2 ), 1052.4 (0, a2 ), 1022.5 (45, a1 ), 1000.2 (14, b1 ), 986.6 (288, b2 ), 953.0 (34, a1 ), 839.9 (1, b2 ) 3236.3 (0, b1 ), 3215.0 (0, a2 ), 3138.6 (0, a1 ), 3135.6 (0, b2 ), 1541.9 (1, a1 ), 1462.3 (10, b2 ), 1246.8 (11, a1 ), 1225.8 (0, a2 ), 1096.0 (287, b1 ), 1029.6 (32, a1 ), 986.6 (18, b2 ), 975.4 (0, a1 ), 951.2 (0, a2 ), 812.7 (1, b1 ), 637.3(4, b1 ), 462.0(0, b2 ), 428.7 (10, a1 ) 3238.6 (1, b2 ), 3217.1 (0, a2 ), 3136.7 (2, a1 ), 3133.3 (0, b1 ), 1544.7 (1, a1 ), 1460.8 (11, b1 ), 1259.5 (11, a1 ), 1227.7 (0, a2 ), 1025.0 (228, b2 ), 983.0 (25, b1 ), 980.3 (14, a1 ), 973.1 (0, a2 ), 953.8 (19, a1 ), 822.7 (1, b2 ), 605.3 (4, b2 ), 428.6 (1, b1 ),
carbon involvement but couples slightly with the H atoms (1.2 cm1 deuterium shift), which are consistent with the experimental observations. This mode was predicted to have the largest IR intensity (287 km/mol). The other vibrational modes all have IR intensities less than 32 km/ mol and were not observed in the experiments. The band at 1013.7 cm1 in the Mn + O2 /C2 H4 experiments is assigned to the antisymmetric OMnO stretching vibration of (g2 -C2 H4 )MnO2 . This band increased on annealing and appeared only when C2 H4 is added in the reagent gas. Analogous to the 1022.8 cm1 band in the Fe + O2 /C2 H4 reaction, the 1013.7 cm1 band showed no carbon-13 isotopic shift with O2 / 13 C2 H4 , and exhibited very small (1.3 cm1 ) deuterium isotopic shift with O2 /C2 D4 . This band shifted to 977.6 cm1 when 18 O2 /C2 H4 sample was used. The 16 O/18 O isotopic frequency ratio of 1.0369 is very close to that of the antisymmetric stretching vibration of the MnO2 molecule in solid argon (1.0388). This indicates that the 1013.7 cm1 band is due to an antisymmetric OMnO stretching vibration. A triplet at 1013.7, 1000.0 and 977.6 cm1 in the 16 O2 + 16 O18 O + 18 O2 /C2 H4 experiment (Fig. 3d) indicates that two equivalent O atoms are involved in this mode. While the doublet feature in the O2 / C2 H4 + C2 D4 experiment (Fig. 3c) suggests the involvement of one C2 H4 subunit. The assignment is supported by density functional calculations. The ground state of (g2 -C2 H4 )MnO2 was found to be a doublet (2 A1 ). The lowest quartet state of (g2 -C2 H4 )MnO2 is 15.6 kcal/mol higher in energy than the doublet state. As shown in Fig. 4, both the 2 A1 and 4 B2 state structures have C2v symmetry with the MnC2 plane perpendicular to the MnO2 plane. The antisymmetric OMnO stretching vibration of the doublet state (g2 -C2 H4 )MnO2 complex was computed at 1076.6 cm1 . The harmonic frequency analysis indicated that this mode has the largest IR intensity (303 km/mol versus less than 45 km/mol for the other vibrational modes, see Table 1). The computed isotopic frequency ratios (12 C/13 C: 1.0000, H/D: 1.0016, 16 O/18 O: 1.0380)
are in good agreement with the experimental values (12 C/13 C: 1.0000, H/D: 1.0013, 16 O/18 O: 1.0369). In transition metal–ethylene complexes, the interactions between metal and ligand C2 H4 are dominated by the synergic donation of electrons in p HOMO of C2 H4 to an empty r orbital of the metal and the back donation of the metal p electrons to the C2 H4 p* orbital. Similarly, (g2 -C2 H4 )FeO2 and (g2 -C2 H4 )MnO2 are formed by the interactions of FeO2 and MnO2 with C2 H4 . The 1 A1 ground state (g2 -C2 H4 )FeO2 molecule can be viewed as the interaction of a C2 H4 subunit and a bent closed-shell FeO2 subunit with an (core) (b1 )2 (a1 )0 electronic configuration. The a1 orbital of FeO2 is primarily a hybrid of the Fe 4s and 3dz2 orbitals that is directed away from the O atoms and is largely nonbonding. This orbital is the primary acceptor orbital for donation from the filled p bonding orbital of C2 H4 . The b1 orbital is the p bonding orbital of FeO2 , and is the primary back donation orbital to the empty p* antibonding orbital of C2 H4 . The ground state of neutral FeO2 molecule was determined to be a 3 B1 state with an (core) (b1 )1 (a1 )1 electronic configuration [32]. Therefore, the bonding interaction between ground state FeO2 and C2 H4 requires a costly FeO2 3 B1 to 1 A1 promotion, which was predicted to be about 20.9 kcal/mol at B3LYP/6-311+G* level. This can be accomplished since the back donation can be made from a doubly occupied b1 orbital and therefore, is enhanced, while the r repulsion is reduced, as the a1 orbital is empty. The donation from the filled bonding p orbital of C2 H4 and the back donation to the antibonding p* orbital of C2 H4 decrease the C–C bond order in the C2 H4 subunit. Consistent with this notion, the calculated C–C bond , which is intermelength in (g2 -C2 H4 )FeO2 is 1.400 A diate between a typical C–C double bond and a C–C single bond. The C–C bond length of free C2 H4 was at the B3LYP/6-311++G** lepredicted to be 1.329 A vel. The promotion of one electron from the nonbonding a1 orbital to the b1 bonding p orbital in FeO2 serves to strengthen the Fe–O bonds, whereas the p back do-
M. Chen et al. / Chemical Physics Letters 384 (2004) 165–170
nation of electron density from the formally Fe–O bonding MO weakens the Fe–O bonds in (g2 C2 H4 )FeO2 . As a result, the Fe–O bonds in (g2 C2 H4 )FeO2 are strengthened and therefore, shortened relative to those of 3 B1 ground state FeO2 (The Fe–O bonds in 1 A1 (g2 -C2 H4 )FeO2 and 3 B1 FeO2 were cal, respectively). The culated to be 1.549 and 1.584 A strengthen of the Fe–O bonds also leads to a large blueshift of the predominantly antisymmetric OFeO stretching mode of (g2 -C2 H4 )FeO2 (1022.8 cm1 ) relative to that of the ground state FeO2 molecule (945.8 cm1 ). The binding energy of 1 A1 state (g2 -C2 H4 )FeO2 with respect to the ground state reagents: FeO2 (3 B1 ) + C2 H4 (1 Ag ) was predicted to be 24.6 kcal/mol at the B3LYP/6-311++G** level, after zero point energy corrections. The bonding mechanism in (g2 -C2 H4 )MnO2 is about the same as that in (g2 -C2 H4 )FeO2 . The neutral MnO2 molecule has a 4 B1 ground state with an (core) (a1 )1 (b1 )1 (a1 )1 electronic configuration, whereas the ground state of (g2 -C2 H4 )MnO2 was determined to be a 2 A1 state. The formation of 2 A1 state (g2 -C2 H4 )MnO2 from ground state MnO2 and C2 H4 involves MnO2 r (a1 ) to p (b1 ) promotion. This promotion increases the MnO2 – C2 H4 bonding by decreasing the r repulsion and increasing the MnO2 to C2 H4 p back donation. The binding energy of 2 A1 state (g2 -C2 H4 )MnO2 with respect to the ground state reagents: MnO2 (4 B1 ) + C2 H4 (1 Ag ) was predicted to be 28.0 kcal/mol at the B3LYP/ 6-311++G** level, after zero point energy corrections. The primary reaction products from co-deposition of laser-ablated iron and manganese atoms and O2 /C2 H4 mixtures in excess argon are metal dioxide molecules. The metal monoxides and O3 absorptions were hardly observed in the experiments. No obvious absorptions due to HOO, C2 H3 and C2 H2 were observed on sample deposition, indicating that the C2 H4 fragmentation during deposition is negligible. Broadband UV–Vis irradiation of the deposited sample markedly increases the metal dioxide absorptions. No manganese-ethylene reaction product was observed. While a weak absorption at 1696.6 cm1 was observed after broadband irradiation, which has been assigned to HFeC2 H3 formed from the reaction of Fe + C2 H4 [7]. Sample annealing allowed the ethylene molecules to diffuse and react with the metal dioxide molecules in solid argon: FeO2 ð3 B1 Þ þ C2 H4 ð1 Ag Þ ! ðg2 -C2 H4 ÞFeO2 ð1 A1 Þ DE ¼ 24:6 kcal=mol MnO2 ð4 B1 Þ þ C2 H4 ð1 Ag Þ ! ðg2 -C2 H4 ÞMnO2 ð2 A1 Þ DE ¼ 28:0 kcal=mol
ð1Þ
ð2Þ
These reactions were predicted to be exothermic and require negligible activation energy. The (g2 -C2 H4 )FeO2 and (g2 -C2 H4 )MnO2 complexes were stable upon UV–
169
Vis light irradiation and no other reaction product was observed.
4. Conclusions The reactions of transition metal dioxides (MnO2 and FeO2 ) with ethylene molecules have been studied using matrix isolation infrared absorption spectroscopy. The metal dioxide molecules were prepared by the reactions of laser-ablated metal atoms with dioxygen. In solid argon, the MnO2 and FeO2 molecules reacted with C2 H4 to form the (g2 -C2 H4 )MnO2 and (g2 -C2 H4 )FeO2 complexes spontaneously on annealing. Both complexes were predicted to have low spin ground states having C2v symmetry with the MC2 plane perpendicular to the MO2 plane. The binding energies with respect to the ground state reagents were predicted to be 28.0 and 24.6 kcal/mol, respectively at the B3LYP/6-311++G** level. The product absorptions were identified by isotopic substitutions and density functional calculations of isotopic frequencies.
Acknowledgements We greatly acknowledge financial support from NSFC (20203005 and 20125033) and the NKBRSF of China.
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