Theoretical Investigation of the Reaction of Mn+ with Ethylene Oxide

ARTICLE pubs.acs.org/JPCA

Theoretical Investigation of the Reaction of Mn+ with Ethylene Oxide Yuanyuan Li,† Wenyue Guo,*,† Lianming Zhao,*,† Zhaochun Liu,† Xiaoqing Lu,† and Honghong Shan‡ † ‡

College of Science, China University of Petroleum Qingdao, Shandong 266555, P. R. China State Key Laboratory for Heavy Oil Processing, China University of Petroleum Qingdao, Shandong 266555, P. R. China

bS Supporting Information ABSTRACT: The potential energy surfaces of Mn+ reaction with ethylene oxide in both the septet and quintet states are investigated at the B3LYP/DZVP level of theory. The reaction paths leading to the products of MnO+, MnO, MnCH2+, MnCH3, and MnH+ are described in detail. Two types of encounter complexes of Mn+ with ethylene oxide are formed because of attachments of the metal at different sites of ethylene oxide, i.e., the O atom and the CC bond. Mn+ would insert into a C
O bond or the C
C bond of ethylene oxide to form two different intermediates prior to forming various products. MnO+/MnO and MnH+ are formed in the C
O activation mechanism, while both C
O and C
C activations account for the MnCH2+/MnCH3 formation. Products MnO+, MnCH2+, and MnH+ could be formed adiabatically on the quintet surface, while formation of MnO and MnCH3 is endothermic on the PESs with both spins. In agreement with the experimental observations, the excited state a5D is calculated to be more reactive than the ground state a7S. This theoretical work sheds new light on the experimental observations and provides fundamental understanding of the reaction mechanism of ethylene oxide with transition metal cations.

’ INTRODUCTION Chemistry of transition-metal complexes in the gas phase mainly concerns their structural properties,1 bond energies,2,3 and especially ion
molecule reactions.4
7 The importance of reactions of transition metal ions with small molecules containing prototypical bonds (e.g., C
H, C
C, C
O, O
H, and N
H) has promoted extensive studies aimed at elucidating the catalytic reactivity of transition metal ions occurring with strong dependence on the nature of the metals.8,9 The ability of the metal center to access multiple low-lying electronic states and to adapt to different bonding situations could enable the system to find low energy reaction paths for otherwise difficult processes.4,10 In other words, the reactivity of metals depends strongly on their electronic states. In order to comprehend these transition-metal involved reactions at the atomic level, it has been proven that computational approaches along with gas-phase experiments are very useful. Ethylene oxide (c-C2H4O) is a three-membered ring molecule with two carbon atoms and an oxygen atom bonded to each other via single bonds. Owning to its special structure, reactions could occur via ring-opening of the epoxide unit to form useful chemical products. Early experimental and theoretical studies have been carried out for the unimolecular isomerization and decomposition of ethylene oxide.11
14 In the industrial field, ethylene oxide is not only an important product but also a basic organic chemical intermediate that is widely used to produce ethylene glycol, nonionic surfactants, ethanolamine, pharmaceutical intermediates, and other fine chemicals.13
15 The gas-phase reaction of ethylene oxide with a series of transition metal ions (groups 6
11: Cr+,16 Mn+,17 Fe+,18 Co+,20,22 Ni+,21,22 and Cu+22) has been experimentally investigated, and different r 2011 American Chemical Society

products have been found for different metal ions. That is, in contrast to the relatively simple product pattern for the chemistry of Cu+, i.e., C2H3O+, CuCH2+, and CuCH2O+, the reactions with metal ions Cr+
Ni+ give extensive products (MCH2+, MC2H2+, MC2H4+, MO+, MCO+, and C2H4+), though not all products are seen for a specific metal. Armentrout et al.20
22 postulated that C
O and C
C insertion intermediates were involved in the reaction of M+ (M = Mn, Co, Ni, and Cu), and the possible mechanisms proposed for the production of these species included C
O, C
H, and/or C
C bond insertion, β-H shift, and α-hydride. Although the reaction intermediates are somewhat elusive, spectroscopic and/or crystallographic evidence do exist for some transient species. By using Fourier transform infrared matrix isolation spectroscopy, Kafafi et al.19 identified the existence of the metallacyclobutane C
O intermediate containing an iron atom, and found the newly formed metallacycle undergoes a metathesis reaction, in which two possible pathways are involved: (i) rupture of the Fe
O and C
C bonds and (ii) cleavage of the Fe
C and C
O bonds. In addition, a secondary reaction pathway involving the C
C bond activation of ethylene oxide was also proposed. What’s more, owing to the large number of unpaired electrons and complete half-filling of its valence shell in the high-spin state, the real multiplicities of Mn-containing species are hard to confirm. As a result, Mn-containing species are regarded as a challenge for theoretical computations, and properly accounting for the electron correlation is critically important.4,17 Nevertheless, to the best of our knowledge, so far, few quantum studies Received: July 19, 2011 Revised: December 6, 2011 Published: December 07, 2011 512

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have been found for Mn+-containing gas-phase reactions.4,23 Considering the report on the state-specific reaction of Mn+ with ethylene oxide as a function of translational energy in a guided ion beam (GIB) tandem mass spectrometer of Armentrout’s group, which has been confirmed to give multiple products of MnO+, MnO, MnCH2+, MnCH3, and MnH+, in this paper we present a theoretical investigation of the reaction mechanism of Mn+ with ethylene oxide, including geometries and energetics in both the high- and low-spin states, considering various possible transition states, intermediates, and products as a follow-up to the experimental results.

Table 1. Bond Dissociation Energies and Excitation Energies (kcal/mol) at 0 K Determined by Calculations and Experiments Mn+ (5Df7S) [Mn
O]

35.9(5.8)

41.7d

62.7(
3.0 ( 1.4)

65.7 ( 1.4

92.3(4.7 ( 4.6)

87.6 ( 4.6e

[Mn
CH2]

69.5(
1.1 ( 3.0)

70.6 ( 3.0

31.3(1.3) 50.0(
1.4 ( 2.3)

12.7 ( 3.9
30.0e 51.4 ( 2.3

+

6

5

+

7

[Mn
CH3] 6 [Mn+
CH3] [Mn+
H]

6

48.6(0.2 ( 3.5)

48.4 ( 3.5

7

36.1(5.9 ( 4.4)

30.2 ( 4.4

[Mn
H]

a

At the B3LYP/DZVP(d)(opt+3f):6-311++G(2d,2p) level. b Values in the parentheses are error bars for the calculated BDEs, obtained by subtracting the experimental values from the calculated BDEs. c From ref 17, except where noted. d Ref 38. e Ref 39.

α2 e2 h ¼ 4πm2e c2 2

ð2Þ

where Lik amd Si are the orbital and spin angular momentum operators, respectively, for electron i in the framework of nuclei indexed by k. The effective nuclear charge Zk* is an empirical parameter in the one-electron spin
orbit Hamiltonian. Z* is 3.9, 5.6, and 12.8 for carbon, oxygen, and manganese, respectively.36 The SOC value is the matrix element that expresses the coupling of the septet and quintet states by the operator of eq 3 ÆHSO æS, S0 ¼ Æ7 Ψ 1 ðMS ÞjHSO j5 Ψ 2 ðMS 0 Þæ

ð3Þ

where 7Ψ1(5Ψ2) is the MS(MS’) component of the many-body septet-state (quintet-state) wave function. Considering the generated spin sublevels MS, a reasonable measure of the SOCinduced sextet
quartet interaction is the root-mean-square coupling constant (SOCC) of eq 4

2

Fði, jÞ ε j
εi

exptc

[Mn
O]

5

2. COMPUTATIONAL DETAILS Our calculations were performed using the density functional B3LYP method24,25 in conjunction with the DZVP(d)(opt+3f) basis set26 for manganese and 6-311++G(2d,2p) basis set27 for the nonmetal atoms. The DZVP(d)(opt) set built up by Chiodo et al. has presented a good reliability in prediction of transition metal ion ground- and excited-state ordering and splitting.26,28 For each optimized stationary point, frequency analysis was performed to determine its minimum or saddle point character as well as to calculate zero-point energy (ZPE). Scaling factor for the ZPE was selected to be 0.961. The intrinsic reaction coordinate (IRC)29 was then calculated to track the minimum energy path from transition states to the corresponding minima and to check if the correct transition state was located. We also made use of the natural bond orbital (NBO) theory30 to give further insight into the bonding characters between different groups for some species involved. For each donor NBO (i) and acceptor NBO (j), the stabilization energy E(2) associated with delocalization (“2e-stabilization”) ifj is estimated as eq 130 Eð2Þ ¼ ΔEij ¼ qi

calcda,b

species

ð1Þ

where qi is the donor orbital occupancy, εi and εj are diagonal elements (orbital energies), and F(i, j) is the off-diagonal NBO Fock matrix element. To locate the minimum energy crossing point (MECP) between the septet and quintet surfaces for a considered step, single-point energies of both states were calculated at the B3LYP/DZVP(d)(opt+3f):6-311++G(2d,2p) level for the relevant IRC points along the quintet pathway until an equal energy was reached. All these calculations were performed using the Gaussian 03 package.31 Spin
orbit coupling (SOC) at the MECP was calculated with the GAMESS package.32 CASSCF calculations with both the DZVP(opt+3f) and SBKJC ECP basis sets (in order to be consistent with the Zeff parameter9,34,35) for Mn, and the 6-311G basis for the remaining atoms, were first performed for both states at the MECP to get the converged CASSCF wave functions; the SOC matrix elements were then computed using the SOC-CI method.35 Because the orbital sets of the two states must share a common set of frozen core orbitals in the SOC matrix elements calculations, the converged CASSCF quintet wave functions were employed as a reference state for both the septet and quintet CI wave functions. The one-electron effective spin
orbit operator was used as eq 237 ! α2 Zk  HSO ¼ Si 3 Lik rik3 2 i k

SOCC ¼ ½

ÆHSO æ2S, S 1=2 ∑ S, S 0

0

ð4Þ

A crude estimation of the crossing probability at the MECP was done using the Landau
Zener formula37 P ¼ 1
e
2δ δ¼

πjVij j2 πjSOCCj2 ¼ pνjΔgij j ð2minðSi , Sj Þ þ 1ÞpνjΔgij j

ð5Þ

where Vij is the matrix element of a diabatic operator (SOC in this case) coupling adiabatic states i and j, Δgij is the difference in the gradients of the two adiabatic states i and j, and v is the effective velocity with which the system is passing through the crossing point that can be calculated from the kinetic theory of gases at 298 K.

3. RESULTS AND DISCUSSION Considering the effects of high- and low-spin electronic states of the metal ion on the reactivity and the reaction pathways,9,10 we present a study of both the septet and quintet PESs of the Mn+/c-C2H4O systems. In the following sections, we first establish the accuracy that can be expected from the level of theory chosen for the Mn+/ethylene oxide system. Then, we

∑∑

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Table 2. Summary of all the Possible Products and the Relative Energies Es (in kcal/mol) Associated with the Reaction of Mn+ with Ethylene Oxide at the B3LYP/DZVP(d)(opt+3f):6-311++G(2d,2p) Levela Es productsa

septet

quintet

MnO + C2H4 (P1)

28.5

16.4

MnO + C2H4+ (P2)

51.9

79.1

MnCH2+ + CH2O (P3)

19.5

3.2

MnCH3 + CHO+ (P4)

44.3

39.7

+

Figure 1. Geometries and selected structural parameters for the Mn+(ethylene oxide) complexes optimized at the B3LYP/DZVP(d)(opt+3f):6-311++G(2d,2p) level. Bond lengths are in angstroms, and bond angles are in degrees.

examine the title reactions in detail, including geometries of various stationary points and PESs for all possible product channels. Last, we give the reaction mechanisms by comparing our theoretical results with the experimental findings.17 For simplicity, total energies (E) together with ZPE and ÆS2æ for these calculated species at B3LYP/DZVP(d)(opt+3f):6-311++G(2d,2p) level are listed in the Supporting Information Table S1. 3.1. Calibration. To confirm the accuracy of our theoretical values calculated at the B3LYP/DZVP(d)(opt+3f):6-311++G(2d,2p) level in the Mn+/c-C2H4O system, a comparison of the calculated values with experimental findings is needed. Table 1 lists the theoretically predicted bond dissociation energies (BDEs) and the reliable experimental data for some relevant species. The examined species are ground-state MnCH2+, MnO+, MnO, MnH+, MnH, MnCH3+, and MnCH3. Given in the parentheses are error bars for the calculated BDEs expected at the employed theoretical level, which are obtained from the subtraction of the calculated BDEs by the experimental values. As shown in Table 1, the agreement is excellent for Mn+
CH2 and Mn+
H, and good for Mn+
O and Mn+
CH3, but the calculated values for Mn
H and Mn
O are about 5.9 and 4.7 kcal/mol higher than the experimental values. As for Mn
CH3, the calculated bonding energy (31.3 kcal/mol) is close to the experimental upper limit (30.0 kcal/mol)17 and the previous theoretical value (30.0 kcal/mol).40 Therefore, despite a bit larger error of the parameters for Mn
O and Mn
H, the computational strategy should be satisfactory to describe the features of PES for the reaction of Mn+ with ethylene oxide. It is well-known that B3LYP tends to favor high-spin states over low-spin states, due to the HF exchange energy mixture. In order to clarify the effect of the HF exchange mixture, we choose species 2 (a metallacyclobutane, see Figure 2) as a model and perform calculations on it by using the pure GGA functionals (BP8624,41 and BLYP41,42) and the B3LYP functional with different quantities of HF exchange. The calculated results are given in Supporting Information (see Tables S2 and S3). It is found that the 25 f 27 energy gap using the BP86 method is almost the same as the B3LYP value (28.4 vs 28.0 kcal/mol), and the BLYP value is 24.4 kcal/mol. In addition, the value of 25 f 27 varies from 27.9 to 28.1 kcal/mol when the quantity of the HF exchange component changes from 15% to 25% using the B3LYP functional. These facts suggest that the HF exchange energy mixture has little effect on the Mn+/ethylene oxide system. 3.2. Encounter Complexes. The first step of Mn+ reaction with c-C2H4O is the exothermic formation of the ion
molecule complexes on both high- and low-spin PESs. As shown in Figure 1, two types of encounter complexes could be formed

a

MnCH3+ + CHO+ (P40 )

22.6

71.0

MnH+ + CH3CO (P5a)

58.8

10.3

MnH+ + CH2CHO (P5b)

61.1

12.6

Energies are relative to the total energy of Mn+(7S) and ethylene oxide.

because of attachment of Mn+ at different sites of ethylene oxide, i.e., the O atom (noted as 1a) and the CC bond (1b). For 1a, the ground septet state lies at 35.1 kcal/mol below the energetic zero (Mn+(7S) + c-C2H4O), and the quintet state is 12.5 kcal/mol higher in energy. This complex is formed with the Mn+
O distance at 2.099 (1.960) Å and the angle of Mn+O to the C1
O
C2 plane being 170.3 (153.6) in the septet (quintet) state. The attachment of Mn+ results in elongation of the C
O bond [bond length: 1.478 (1.466) vs 1.433 Å in the septet (quintet) state] as well as decrease in the — C
O
C angle [from 61.5 to 59.2 (60.1)]. NBO analysis shows that this C2H4O
Mn+ association is dominated by electrostatic interaction as well as donor
acceptor stabilization, in which electrons are mainly donated from the 2s2p(O) lone pair orbital into the unoccupied 3d4s(Mn+) orbital [ΔE(2) = 20.1 (34.0) kcal/mol in the septet (quintet)]. As shown in Figure 1, species 1b possesses the C2 symmetry with the Mn+
C distance of 2.708 (2.041) Å in the septet (quintet) state. The most obvious change in ethylene oxide is the stretch of the C
C bond from 1.465 to 1.521 (2.188) Å, which favors the rupture of the bond. This species is 28.2 (0.3) kcal/mol unstable with respect to 1a in its septet (quintet) state. However, the order of the high- and low-spin states in this case is reverse with respect to that of Mn+ and 1a; i.e., the quintet state of 1b is indeed the ground state, located 1.8 kcal/mol below the septet state. NBO analysis detects that the binding of Mn+ with cC2H4O in 71b is primarily electrostatic with a little electron donation from the σ(C
C) orbital to the 4s3d* (Mn+) orbitals (ΔE(2) = 5.75 kcal/mol). However, in 51b, Mn+ and c-C2H4O are covalently bound via the formation of two doubly occupied σ(Mn+
C) binding orbitals. Moreover, strong donations are found from σ(Mn+
C1) to σ*(Mn+
C2) (ΔE(2) = 20.43 kcal/ mol) and σ(Mn+
C2) to σ*(Mn+
C1) (ΔE(2) = 20.44 kcal/ mol). These facts are in line with the very large stretch of the C
C bond as shown in Figure 1 and explain the much higher stabilization of 51b. 3.3. Reaction Potential Energy Surfaces. In the GIB tandem mass spectrometer experiment, Armentrout’s group detected five ionic products corresponding to MnCH2+, MnO+, MnO, MnH+, and MnCH3 for the gas-phase reaction of Mn+ with ethylene oxide.17 Table 2 tabulates reaction energies for these products as well as some unobserved species for comparison. In the following, we shall present a systematic survey of the [Mn, C2, H4, O]+ 514

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Figure 2. Energy profile for the MnO+/MnO formation channel involved in the reaction of Mn+ with ethylene oxide. Numbers refer to the relative stabilities (in kcal/mol) with respect to the separated reactants of Mn+(a7S) + ethylene oxide evaluated at the B3LYP/DZVP(d)(opt+3f):6-311+ +G(2d,2p) level including ZPE corrections. Scaling factor for the ZPE is 0.961.

PES to find the gas-phase reaction mechanism associated with all these products. 3.3.1. Formation of MnO+/ MnO. It can be envisioned that this product channel should involve the more stable encounter complex 1a. Figure 2 shows the PES together with the schematic structures involved. Starting from 1a, species 2, a metallacyclobutane,17,22 is formed due to insertion of Mn+ into one of the C
O bonds in c-C2H4O, giving a planar four-member ring structure. NBO analysis shows that in the low-spin state of the new species the metal center forms two doubly occupied σ bonds and one β occupied π bond with O to form the perfect four-member ring structure, while in the septet state binding of Mn+ to O is primarily electrostatic accompanied by electron donation from the 2s2p(O) lone pair orbital to the 4s3d*(Mn+) orbitals (ΔE(2) = 20.1 kcal/mol). As a result, the quintet metallacyclobutane (Erel =
38.6 kcal/mol) is effectively stabilized and is located 28.0 kcal/mol below the septet. The septet transition state (7TS1a‑2) for this process appears “late” as mirrored by its structure and energy compared to those of its direct product 72. The quintet 5TS1a‑2 is located 9.7 and 25.7 kcal/mol above the connecting minima 51a and 52. From the viewpoints of structures and vibrations, 5TS1a‑2 is found to be the real C
O activation transition state that connects 51a and 52. This transition state has an imaginary frequency of 489.0i cm
1, and is confirmed by the vibration vector and IRC calculation. As shown in Figure 2, a septet-to-quintet crossing is expected to occur before saddle point TS1a‑2. At both the DZVP and SBKJC ECP levels, the intersystem crossing probability is estimated to be less than 1% at room temperature, suggesting that spin inversion indeed does not occur in this step. The organometallic ring species 2 could lead to a metathesis reaction.17,19,22 Two futures of this ethylene manganese monoxide π-complex 2 can be envisioned, i.e., rupture of the Mn+
C and C
O bonds to form MnO+ + C2H4 and MnO + C2H4+, and rupture of the Mn+
O and C
C bonds to form MnCH2+ and MnCH3. The latter channel will be discussed later in this article.

For the former, as shown in Figure 2, species 2 could convert into complex 3, lying at
11.4 (
22.8) kcal/mol in the septet (quintet) state. In both states, species 3 is indeed a complex of ethylene interacting through its π electron with the metal side of Mn+O, with the difference that Mn+O is directed along the C2 axis in the septet state (C2v), whereas in the quintet state it is perpendicular to C1
C2. A transition state involved in this possibility is energetically located at 2.7 (
22.4) kcal/mol relative to the energetic zero in the septet (quintet) state. Different dissociations of 3 would give products MnO + + C 2 H 4 (P 1 ) and MnO + C2 H4 + (P 2 ). For the MnO + formation, the overall energy of the separated products lies at 28.5 (16.4) kcal/mol relative to the energetic zero in the septet (quintet) state. Alternatively, appearance energy is very high for the production of MnO, lying at 51.9 (79.1) kcal/mol. The fact that 7 P2 is 35.5 kcal/mol higher in energy than 5P1 is in agreement with the energy difference of 41 kcal/mol estimated with the ionization potentials of MnO (∼8.7 eV)43 and C2H4 (∼10.5 eV).17 3.3.2. Formation of MnCH2+/MnCH3. Calculated PESs together with schematic structures involved in the product channel are given in Figure 3. We can find that the formation of MnCH2+/ MnCH3 could occur through two alternative mechanisms starting from encounter complexes 1a and 1b, respectively. As shown in Figure 3, following the 1a to 2 conversion, insertion of Mn+ into the C
C bond accounts for species 4, which is striking due to the nearly linear H2C
Mn+
O
CH2 chain structure (C2v) with the Mn+
O distance of 2.017 (2.028) Å in the septet (quintet) state. The long distance between Mn+ and O suggests that the Mn+
O chemical bond has already been broken. Energy barrier for the 2 f 4 conversion is 8.4 (25.9) kcal/mol in the septet (quintet) state. Once complex 4 is formed, two possible channels noticed as direct dissociation and aldehyde-H shift dissociation are followed. Direct dissociation of species 4 accounts for product 515

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Figure 3. Energy profile for the MnCH2+/MnCH3 formation channel involved in the reaction of Mn+ with ethylene oxide. Parameters follow the same notations as in Figure 2.

MnCH2+ + CH2O (P3), with the overall endothermicity of 19.5 (3.2) kcal/mol on the septet (quintet) PES. Alternatively, the aldehyde-H shift converts species 4 into 5 (H3C
Mn+
OCH), which is the precursor of MnCH3. Species 5 is nearly degenerated in the septet and quintet states (
26.7 and
28.0 kcal/mol), while the relevant transition state TS4
5 is located at 4.9 and
0.3 kcal/mol. Along the coordinate, direct dissociation of species 5 gives0 the metal
methyl products of MnCH3 (P4) and MnCH3+ (P4 ), which are calculated to be endothermic by 44.3 (39.7) and 22.6 (71.0) kcal/mol in the septet (quintet) state, respectively. The appearance energy of MnCH3+ + CHO in the 0 septet state (P4 ) is lower than that of MnCH3 + CHO+ (P4), but the ionic product MnCH3+ was not observed in the related experiment.17 It is interesting that both MnCH3+ + R and MnCH3 + R+ (R = CH3CO, 2-C3H7, t-C4H9) are observed in the Mn+/(CH3)2CO, Mn+/(CH3)3CH, and Mn+/(CH3)4C reactions from the GIB tandem mass spectrometer experiments, and the former product is favorable.17 The experimental findings of the Mn+/(CH3)2CO, Mn+/(CH3)3CH, and Mn+/(CH3)4C systems give good support to our calculated results, while they do not coincide well with the results in Mn+/C2H4O system. NBO analysis detects that in H3C
Mn+
OCH the binding between Mn+CH3 and OCH in both the septet and quintet states is from primarily strong donations from the O lone-pair orbital to σ*(C1
Mn), the values of which are close to each other (ΔE(2) = 20.1 and 22.6 kcal/mol for the septet and quintet association, respectively). When it goes to the dissociation products MnCH3, in the septet state only one β occupied σ(C1
Mn) bond is formed, and the quintet product is stabilized more largely by two doubly occupied σ(C1
Mn) bonds. The different bonding situations between the precursor and the product explain why the septet and quintet precursors H3C
Mn+
OCH are nearly degenerate, whereas the energy gap between the products is comparatively large. The other pathway to form species 4 involves ring-opening of ethylene oxide by initial C
C bond activation starting from encounter complex 1b, as shown in Figure 3. The C
C bond

cleavage in 1b could carry the system into minimum 6, lying at
5.1 (2.0) kcal/mol relative to the energetic zero in its septet (quintet) state. This possibility involves a saddle point (TS1b‑6) on the septet (quintet) PES lying at 6.2 (22.9) kcal/mol above the energetic zero. As expected, the C
O activation in species 6 could carry the system into species 4 through transition state TS6
4. Energetically, TS6
4 is located 16.2 (10.4) kcal/mol above the energetic zero on the septet (quintet) PES. Different from the two directly connected transition states, species 76 is less stabilized than 56, and thus two crossings between the highand low-spin surfaces are expected to occur just before and after the intermediate. In summary, for the formation of MnCH2+/MnCH3, although two pathways starting, respectively, from complex 1a and 1b are identified, the former one is expected to be more favorable, and the latter is unlikely to be important due to the high energies of intermediates involved. 3.3.3. Formation of MnH+. Loss of MnH+ has two isomeric neutral products, i.e., acetyl radical CH3CO and vinyloxy radical CH2CHO. Both radicals are important intermediates in combustion and photochemical smog cycles and have been widely investigated in the gas-phase oxidation of unsaturated hydrocarbons.44
47 PESs together with schematic structures involved in the septet and quintet pathways for the MnH+ formation are shown in Figure 4. Formation of Acetyl Radical CH3CO. This channel involves the conversion of Mn+(ethylene oxide) (1a) to Mn+(acetaldehyde) (7). Different pathways of conversion are found on the high- and low-spin PESs. The difference mainly concerns the roles of Mn+ played in the activation of the C
O bond, that is, the assisting role of Mn+ in the C
O bond opening along the septet coordinate, and direct insertion of Mn+ into the C
O bond on the quintet PES. Along the septet coordinate, the direct C
O bond rupture assisted by Mn+ in 71a could carry the system into the Mn+(vinyl alcohol) adduct 720 , in which the metal ion attaches directly to the O atom of CH2CH2O. The transition state for this possibility (7TS1a‑20 ) can be described as a late 516

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Figure 4. Energy profile for the MnH+ formation channel involved in the reaction of Mn+ with ethylene oxide. Parameters follow the same notations as in Figure 2.

transition state, because its structure is quite similar to that of 20 and its energy is only 0.2 kcal/mol higher than species 20 (Erel =
20.9 kcal/mol). On the quintet PES, insertion of Mn+ into the C
O bond in 51a forms metallacyclobutane species 2, which has been discussed above. Once species 720 (52) is formed, a direct C1-to-C2 H-shift could carry the system into complex 7, the Mn+(acetaldehyde) association. The new species lies at
66.1 (
47.2) kcal/mol in its septet (quintet) state, constituting the deepest energy well on the whole PES. IRC calculations showed that transition state TS2
7 is directly connected to species 720 (52) in one direction and Mn+(acetaldehyde) 7 in the other direction in both septet and quintet states. For 77 and 57, the Mn+
acetaldehyde BDE is calculated to be 36.2 and 56.3 kcal/mol. A series of theoretical studies on the reactions of transition metal ions Ti+, Cr+, Fe+, Co+, and Ni+ with acetaldehyde have been carried out by our group.48
51 The results show that, owing to the strong binding ability of the metal ion to oxygen, Ti+ would undergo oxidation; decarbonylation is unique for Cr+, Fe+, and Ni+; and Co+ attacking the C
H bond would lead to products CoH+ and CoH besides the decarbonylation pathway to Co+CO. Similar to Co+, in this case the aldehyde C
H activation accounts for MnH+. The following step proceeds via transition state TS7
8, reaching the aldehyde C
H activation species 8 ((CH3CO)Mn+H) [Erel =
25.4 (
40.6) kcal/mol on the septet (quintet)], which serves as the direct precursor of MnH+. The saddle point TS7
8 is characterized by an imaginary frequency of 608.8 (704.1)i cm
1, and the transition vector clearly identifies the H abstraction. In this process, an activation barrier of 47.9 (19.0) kcal/mol in the septet (quintet) state is necessary to surmount. Direct dissociation of CH3CO
Mn+H accounts for MnH+ and acetyl radical (P5a) with the overall endothermicity of 58.5 (10.3) kcal/mol on the septet (quintet) PES. Formation of Vinyloxy Radical CH2CHO. Species 20 (2) could also transform into planar species 9 (CH2CHO
Mn+H) via a onestep H-shift, which stabilizes the system by 16.7 (0.9) kcal/mol on the septet (quintet) PES (see Figure 4). The relevant transition state (TS2
9) lies at
4.4 (
2.4) kcal/mol. Direct dissociation of 9 accounts for products MnH+ + CH2CHO (P5b), with the overall

endothermicity of 61.1 (12.6) kcal/mol on the septet (quintet) PES. As the losses of CH2CHO and CH3CO have similar thermochemistry, they should be formed accompanied by MnH+. 3.4. Reaction Mechanisms. In this section, we summarize the mechanisms of Mn+ reaction with ethylene oxide by comparing our theoretical results with the findings from the GIB tandem mass spectrometry experiment.17 In ref 17, the data shown and analyzed involves the reaction of ethylene oxide with Mn+ in different electronic states produced in a surface ionization (SI) source and an electron impact (EI) source. In the SI source, 99.8% of the produced Mn+ is in the ground state at 2300 K and the populations of the SI produced ions can be described by a Maxwell
Boltzmann distribution, while EI produces a non-Boltzmann distribution of the electronic states with more excited ions, so that 22.4 ( 1.4% of Mn+ formed at 70 eV are in reactive excited states. The reaction should correspond to both ground and excited state chemistry, which gives MnO+, MnCH2+, MnO, MnCH3, and MnH+, as shown in the experiment: (i) the EI cross sections of all the products are larger than their corresponding SI cross sections; (ii) the SI and EI cross sections of MnO+, MnCH2+, and MnH+ are the largest among the overall products and the cross sections of MnO and MnCH3 come out to be the smallest; (iii) as the energy increases, the EI cross sections of MnO+, MnCH2+, and MnH+ decline to reach a minimum before increasing and the cross sections of MnO and MnCH3 are seen to increase monotonically with increasing energy.17 In the present theoretical study, all possible pathways of the products are searched for the reaction of Mn+ with ethylene oxide, and the state-specific reactivities of Mn+ toward c-C2H4O are analyzed by analyzing the PESs in detail. There are crossings between the septet and quintet PESs in the course of initial C
O insertion and C
C activation, which account for the MnO+/MnO (see Figure 2) and MnCH2+/MnCH3 (see Figure 3) formations. The crossing probability in the C
O activation process is calculated to be less than 1%, and this low efficiency of crossing possibility would decrease with the increasing temperature;10 hence, spin inversion should not occur in this process. 517

dx.doi.org/10.1021/jp206894y |J. Phys. Chem. A 2012, 116, 512–519

The Journal of Physical Chemistry A Because all the stationary points on the quintet surface lie far below the entrance channel (Mn+(5D) + c-C2H4O) and there is indeed no real energy barrier along the coordinate, the formation of MnO+ + C2H4 (P1) is favored adiabatically on the quintet surface, which is consistent with the declining feature of the EI cross section as well as the low energy feature of the SI cross section. Except for the reactants and encounter complex, stationary points on the septet surface are higher in energy than the respective quintet structures. Thus, the a7S state Mn+ only reacts more efficiently at much higher energies to form MnO+ + C2H4 (7P1) endothermically, as reflected in its increasing SI and EI cross sections at higher energies. The exothermic reaction of the excited state and endothermic reaction of the ground state of Mn+ explain the nonzero SI and EI cross sections at the lowest kinetic energy as well as the dramatic difference between SI and EI cross sections for the MnO+ formation process. Compared to MnO+, the endothermic feature of MnO formation is more obvious so that it is endothermic either on the septet or on the quintet surface to form product MnO + C2H4+ (P2). So the EI and SI cross sections are very small in magnitude and rise with energy monotonically. Furthermore, we can conclude from the energy profile (see Figure 2) that the quintet reaction to form MnO is more likely because it is less endothermic than the septet reaction, which is reflected in the larger maximum of the EI cross section. Although both C
O and C
C activation could result in the MnCH2+ formation (see Figure 3), the latter one is unlikely to be important on the basis of the following facts: (i) the transition state for initial C
C activation starting from 1a is higher than that for initial C
O activation by 32.2 (19.1) kcal/mol in the septet (quintet) state, and the involved transition states (7TS1b‑6, 7 TS6
4, and 5TS6
4) on the C
C activation PES are of higher energy; (ii) MnO+ and MnCH2+ are isoelectronic and have approximately the same values of the dissociation energies (62.7 kcal/mol for MnO+ and 69.5 kcal/mol for MnCH2+), and their cross sections are also similar in both energy dependence and magnitude (for both ground and excited states). As a result, formation of MnCH2+ should proceed through the same mechanism (C
O activation) as MnO+. Through the C
O activation mechanism, MnCH2+ is likely to be formed adiabatically on the quintet PES with a low C
O activation energy barrier, which is consistent with the declining feature of the SI and EI cross sections. Whereas products (MnCH2+ + CH2O) (7P3) forming on the septet PES is endothermic by 19.5 kcal/mol, the excited product 7P3 should become accessible with excess energies, as reflected by the increasing feature of the SI cross section at elevated energies. It can be found from Figure 3 that MnCH3 formation shares the former part of the coordinate with MnCH2+ in both C
O and C
C activation mechanisms. MnCH3 formation is not only endothermic on both the septet and quintet surfaces but also experiences an additional C2-to-C1 H-shift after the formation of MnCH2+
CH2O. We propose that it is the very strong endothermic feature and the more complex process that makes the SI and EI cross sections of MnCH3 much smaller than those of MnCH2+. However, the C
C activation channel is unimportant because of the high-energy barriers involved; MnCH3 formation is more likely to take place through the C
O activation mechanism. For MnH+, as shown in Figure 4, two candidates of the neutral products can be envisaged, i.e., acetyl radical CH3CO and vinyloxy radical CH2CHO. For both possibilities, all the stationary points lie below the entrance channel, and the MnH+ +

ARTICLE

CH3CO (5P5a) formation has to undergo an additional C1-to-C2 H-shift to form the CH3CO
Mn+H adduct before the H-abstraction of the metal. Formation of MnH+ is exothermic by 25.6 and 23.3 kcal/mol on the quintet PES and is highly endothermic on the septet surface, so that MnH+ is favored to be formed adiabatically on the quintet surface. In summary, products MnO+, MnCH2+, and MnH+ from the reaction of Mn+ with ethylene oxide could be formed adiabatically on the quintet surface, while formation of MnO and MnCH3 is endothermic either on the septet or quintet surface. The large cross section of MnO+, MnCH2+, and MnH+ observed in the GIB tandem mass spectrometer experiment17 is consistent with the low C
O activation energy barrier as well as the singlestate reactivity paradigm on the quintet surface.

4. CONCLUSIONS The detailed mechanism for the reaction of Mn+/ethylene oxide has been investigated with the aid of DFT calculations. By analysis of the PES as well as comparison with the experimental findings, the following conclusions can be drawn out: (1) When Mn+ attacks ethylene oxide, two types of encounter complexes could be formed because of the attachment of Mn+ to different sites of ethylene oxide, i.e., the O atom and the CC bond. It is the O-attached complex that accounts for the products of Mn+ reaction with ethylene oxide. (2) MnO+/MnO and MnCH2+/MnCH3 are produced via C
O activation; although C
C activation could also contribute to the formation of MnCH2+/MnCH3, it is unlikely to be important. Two pathways are operative once the C
O insertion intermediate is formed: (i) rupture of the Mn+
O and C
C bonds and (ii) rupture of the Mn+
C and C
O bonds. MnO+/MnO are expected to be produced in the first case, and in the second case MnCH2+/MnCH3 are expected to be formed. MnH+ formation involves different mechanisms on the PESs of different spins. The difference lies in the role that Mn + played in the assistance of the ring-opening of ethylene oxide. (3) The a5D excited state is found to be more reactive than the a7S ground state; that is, the reactions of the groundstate Mn+ with ethylene oxide show no exothermic reactivity, while the excited state a5D involved reactions are all exothermic except the MnCH3 and MnO formation. The large cross section of MnO+, MnCH2+, and MnH+ observed in the GIB tandem mass spectrometer experiment17 is the result of the low C
O activation energy barrier as well as the single-state reactivity paradigm on the quintet surface. ’ ASSOCIATED CONTENT

bS

Supporting Information. Calculated energies, zeropoint energies, and ÆS2æ for all species involved in the Mn+ + ethylene oxide reaction. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected] (W.G.); [email protected] (L.Z.). 518

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The Journal of Physical Chemistry A

ARTICLE

’ ACKNOWLEDGMENT This work was supported by the Program for Changjiang Scholars and Innovative Research Team in University (IRT0759) of MOE, PRC, NSFC (21003158 and 10979077), State Key Basic Research Program of China (2006CB202505), CNPC Science & Technology Innovation Foundation (2009D5006-04-07), the Fundamental Research Funds for the Central Universities (09CX05002A), and the Graduate Innovative Foundation of the China University of Petroleum (CXYB11-11).

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