Theoretical Views on Activation of Methane Catalyzed by Hf2+ and

Article pubs.acs.org/JPCA

Theoretical Views on Activation of Methane Catalyzed by Hf2+ and Oxidation of CO (x1Σ+) by N2O (x1Σ+) Catalyzed by HfO2+ and TaO2+ Jingyan Nian,† Lu Tie,† Ben Wang,†,‡ and Zhiguang Guo*,†,‡ †

State Key laboratory of Solid Lubrication, Lanzhou Institute of Chemical Physics, Chinese Academy of Sciences, Lanzhou 730000, China ‡ Ministry of Education Key Laboratory for the Green Preparation and Application of Functional Materials, Hubei University, Wuhan 430062, China S Supporting Information *

ABSTRACT: The mechanisms of activation of CH4 catalyzed by 1/3Hf2+ and oxidation of CO by N2O catalyzed by 1/3HfO2+ or 2/4TaO2+ have been investigated using the B3LYP level of theory. For the activation of methane, the TSR (two-state reactivity) mechanism has been certified through the spin−orbit coupling (SOC) calculation and the Landau− Zener-type model. In the vicinity of the minimum energy crossing point (MECP), SOC equals 900.23 cm−1 and the probability of intersystem crossing is approximately 0.62. Spin inversion makes the activation barrier decline from 1.63 to 0.57 eV. NBO analysis demonstrates that empty 6s and 5d orbitals of the Hf atom play the major role for the activation of C− H bonds. Finally, CH4 dehydrogenates to produce Hf−CH22+. For oxidation of CO by N2O catalyzed by HfO2+ or TaO2+, the covalent bonds between transition metal atoms and the oxygen atom restrict the freedom of valence electrons. Therefore, they are all SSR (single-state reactivity). The oxygen atom is directly extracted during the course of oxygen transfer, and its microscopic essence has been discussed. The detailed kinetic information of two catalytic cycles has been calculated by referencing the “energetic span (δE)” model. Finally, TOF(HfO2+)/TOF(TaO2+) = 2.7 at 298.15 K, which has a good consistency with the experimental result.

■

N2O( Σ+) + HfO2 + → N2(1Σ g ) + HfO2 2 +

Continued deterioration of environmental pollution and energy shortage will raise the potential global crisis. For the sustainable development of human society, environmental remediation and alternative clean energy development are an urgent task. Therefore, catalytic conversion between harmful gas and harmless gas and activation of methane to generate hydrogen energy will be of great significance. For catalytic activation of methane, the research mainly focused on the transition metal neutral atoms1−7 and transition metal monopositive cations.8−11 Meanwhile, transition metal monopositive cations12−14 and transition metal oxide monopositive cations15,16 have also been investigated for the catalytic conversion between N2O and CO to produce N2 and CO2. Recently, the Oliveira group reported their new findings.17,18 They found that the gas phase XO2+ (X = Hf, Ta) have a catalytic function for CO oxidation by N2O. Furthermore, Hf2+ can also make methane dehydrogenate and generate HfCH22+ and hydrogen.17 These new experimental results can be described as below. Hf

2+

1

+

1

INTRODUCTION

+ CH4(A1) → HfCH 2

2+

1

© 2013 American Chemical Society

+

1

HfO2 2 + + CO( Σ+) → HfO2 + + CO2 (1Σ g )

(R3)

+

1

N2O( Σ+) + TaO2 + → N2(1Σ g ) + TaO2 2 + 1

(R4)

+

TaO2 2 + + CO( Σ+) → TaO2 + + CO2 (1Σ g )

(R5)

In this paper, reaction R1 will be taken as the first research system. Reactions R2 and R3 will be termed as the second research system. The catalytic cycle of reactions R4 and R5 will be regarded as the third research system. As far as we know, for transition metal catalytic systems, most of them are typical “two-state reactivity”.19−21 Therefore, the detailed reaction pathways on different spin-state potential energy surfaces and the possible spin inversion process for three research systems will be investigated. For the possible potential energy surface crossing, it will be discussed by spin− Received: May 22, 2013 Revised: August 15, 2013 Published: August 15, 2013

+

+ H 2( Σg )

(R2)

(R1) 8843

dx.doi.org/10.1021/jp4050447 | J. Phys. Chem. A 2013, 117, 8843−8854

The Journal of Physical Chemistry A

Article

orbit coupling (SOC) calculation and the Landau−Zener-type model. Meanwhile, the activation mechanisms of the key bonds and kinetic information of the two catalytic cycles have not been revealed. Therefore, the activation mechanisms of chemical bonds will be elaborated using natural bond orbital (NBO) and molecular orbital theory. Finally, on the basis of the different spin-state potential energy surfaces and thermodynamic parameters obtained at the B3LYP level, the kinetic information of the two catalytic cycles will be calculated utilizing the formulas of the “energetic span” model established by Kozuch and Shaik. The catalytic performances of the two catalysts will be evaluated by the comparison of theoretical values of δE (apparent activation energy) and TOF (turnover frequency).

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TOF =

kT exp( −ΔGr /RT ) − 1 Δ = B · n n M h ∑i ∑ j exp[(Ti − Ij − ΔGij′)/RT ] (1)

⎧ ΔGr i > j ΔGij′ = ⎨ i≤j ⎩0 ⎪

⎪

(2)

Here, Δ is the difference between the positive and reverse reaction rate constant product. It has no relationships with the catalyst but could be related to the thermodynamics property of the reaction itself. In contrast, M is the sum of exponentials of Gibbs energy differences between all the combinations of intermediates Ij and transition states Ti. Ti and Ij in eq R1 indicate the Gibbs free energy of transition states and intermediates respectively. ΔGr is the Gibbs free energy difference of reaction. In a word, this formula is similar to Ohm’s law. Δ and M have the functions of voltage and resistors, respectively. According to the knowledge of statistical thermodynamics, the turnover frequency calculation formulas were simplified through a large number of mathematic deducing, that is33

COMPUTATIONAL DETAILS

Geometry Optimization of Reaction Species. All computations were carried out with the GAUSSIAN 03 program.22 The fully optimized geometries and vibration frequencies have been determined by using the spinunrestricted three-parameter hybrid B3LYP23 density functional method. Stationary points on different spin-state potential energy surfaces were fully optimized without the symmetry constraints, followed by evaluation of harmonic frequencies to characterize their nature as minima or first-order saddle points. The standard Stuttgart/Dresden effective core potential (ECP) SDD basis set24,25 was used for Hf and Ta, and the standardized 6-311++G(3df,3pd)26 diffuse and polarization basis set was used for carbon, hydrogen, nitrogen, and oxygen atoms. To ensure reliability of the reaction pathway, the connection between the transition state and corresponding minima was verified using the IRC (intrinsic reaction coordinate) technique27,28 in the mass-weighted internal coordinate system. For finding the regions of potential energy surface crossing, all coordinates were optimized in search of the crossing point (CP) between the two PESs (potential energy surfaces). Namely, starting from the transition state that is closest to the crossing seam, the reaction pathway was traced down to the corresponding minimum. Thereafter, each of the optimized points along the IRC path was submitted to a single-point energy calculation with other electronic state. Based on the foundation of CP, for the sake of comparison, the MECP (minimum energy crossing point) procedure proposed by Harvey’s group29 has also been employed. The energy of the MECP and the relative slope of different spin-state potential energy surfaces at the crossing seam were also obtained through this procedure. The natural bond orbital (NBO) analysis was carried out using the NBO 5.0 procedure.30 Gibbs free energy is the focus of our attention, because it is the foundation of the “energetic span” model. This model is the latest mathematical model to calculate the kinetic information for a catalytic cycle. Introduction of Energetic Span Model (δE). The steadystate method was first proposed by Christiansen31 to process the influences of the multistep reaction rate constant (k) for the total reaction rate. Kozuch and Shaik took the rate constant matrix M (k-index) of Christiansen as the foundation, and the Gibbs free energy index M matrix was deduced through the Eyring formula transformation. Therefore, the TOF (turnover frequency) calculation formula for a catalytic cycle can be written as below.32

TOF =

KBT −δE / RT e ≈ e−δE h

(for exothermic reaction)

TOF =

KBT δE / RT e ≈ − e−δE h

(for endothermic reaction)

(3)

(4)

δE, the energetic span, is defined as eq R5

33

⎧TTDTS − ITDI if TDTS appears after TDIS δE = ⎨ ⎩TTDTS − ITDI + ΔGr if TDTS appears before TDI ⎪

⎪

(5)

Here, the TDTS (TOF-determining transition state) and the TDI (TOF-determining intermediate), every of them is the special one that has the biggest value of the degree of TOF control in many transition states and intermediates. As shown in eqs R3 and R4, δE as the apparent activation energy can be used to evaluate the performance of a catalyst. Furthermore, on the basis of the “degree of rate control” of the Campbell group,34 Kozuch derived the notion of “degree of TOF control” for a catalytic cycle. It is indicated by XTOF, and the calculation formulas can be written explicitly in the Erepresentation as follows:35 X TOF, Ti =

X TOF, Ij =

∑j e(Ti − Ij −ΔGij′)/RT ∑ij e(Ti − Ij −ΔGij′)/RT

(6)

∑i e(Ti − Ij −ΔGij′)/RT ∑ij e(Ti − Ij −ΔGij′)/RT

(7)

The establishment of “energetic span model” could be applied to calculate the kinetic information for a catalytic cycle by using the Gibbs free energy of the transition states and intermediates included in the reaction. In this model, each of intermediates and transition states has different extent of influence for the catalytic cycle rate. Here, intermediates and transition states are respectively taken as the potential well and potential barrier to hinder the kinetic process of one catalytic cycle. The turnover frequency determined transition state (TDTS) and turnover frequency determined intermediate (TDI) are not necessarily adjacent. In contrast, the viewpoint 8844



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on the second pass is PLZ (1 − PLZ). Finally, the total probability of electronic hopping (Ph) is then

of classical theory is that the reaction rate is only determined by the activation energy of rate-limiting step. Therefore, this model has a great improvement compared with the viewpoint of classical rate-limiting step. The schematic diagram of “energetic span” mode is described as Figure 1. In this paper, the temperature is 298.15 K when the kinetic information calculation is carried out, and it is the same as the experimental temperature.

Ph(E) = (1 − PLZ(E))(1 + PLZ(E))

In this formula, ΔF is the relative slope of the two potential energy surfaces at the crossing seam. H12 is the spin−orbit coupling-derived off-diagonal Hamiltonian matrix element between the two electronic states, and it was evaluated at the singlet−triplet-state-averaged complete active space self-consistent field [CASSCF(2,6)] wave function using the SOC−CI method.37 Here, 6-311G(d,p) basis set was used for H and C, and the SBK JC ECP basis set was used for Hf. Because the singlet and triplet states share a common set of frozen core orbitals to calculate the SOC matrix elements, we employed the wave function of the triplet state as a reference state for singlet CI wave function. All SOC calculations were carried out with the GAMESS program package.38 μ is the reduced mass of the system, EMECP is the relative energy of the MECP between potential energy surfaces corresponding to the different spin states, and E is the total internal energy.36 After calculation, ΔF = 0.053 hatree bohr−1, H1,2 = 900.23 cm−1, and PLZ = 0.62. The probability of electronic hopping on the first and second pass through the crossing region is 0.38 and 0.23, respectively. Finally, the probability of intersystems crossing Ph (H1,2 = 900.23 cm−1) is approximately 0.62. For the first hydrogen transfer course, a large SOC value and efficient intersystem crossing of the electron lead to the activation barrier declining from 1.63 to 0.57 eV. Therefore, the reaction speed is accelerated. Catalytic Mechanism Analysis. NBO analysis indicates that the status of electrons occupancy in 3Hf2+ is 5dyz (1.02) 6s (0.98). It clearly demonstrates that the 5d orbital and 6s orbital have lost one electron respectively during the forming course of 3 2+ Hf . Namely, there are four empty d orbitals and two single occupied valence orbitals in 3Hf2+. First, CH4 gets close to the 3Hf2+ to form the 3IM1 by electrostatic attraction because there is no bond between the Hf atom and C atom. Then, a spin-crossing phenomenon appears, which is attributed to the spin−orbital coupling and the electron hopping. It leads to the reaction occurring on the pathway of the singlet-state potential energy surface. Here, the electron hopping style is restricted by the zero integral rule. As we all know, the parities of s and d orbitals are all g. Meanwhile, the parity of the magnetic field is also g, and the direct product of three g equals g. It meets the selection rule of magnetic dipole hopping. Namely, the electronic hopping between the 6s orbital and 5d orbital in the style of magnetic dipole hopping is allowed. Electronic hopping leads to the 6s orbital being empty. In 1 TS1−2, the Hf−C σ bond appears and it is composed of the s (28.91%) p 0.01 (0.36%) d 2.45 (70.74%) hybrid orbital of Hf atom and the s (8.38%) p 10.88 (91.19%) d 0.05 (0.43%) hybrid orbital of C atom. The empty 6s orbital of Hf atom will be more favorable for the electrons transferring from the sp3 hybrid orbital of the C−H bond to the empty d orbitals of Hf2+. Therefore, the first C−H bond is activated. In 1IM2, the Hf−H bond consists of Hf s (34.37%) p 0.02 (0.66%) d 1.89 (64.96%) and H s (99.05%) p 0.01 (0.95%). This σ bond is mainly composed of sd hybrid orbitals of the Hf atom and the s orbital of the H atom. Then, the interaction between Hf and C becomes stronger and the Hf−H bond is weakened. These can be proven from the bond length of the Hf−C and Hf−H bonds in 1TS2−3. Empty s and other empty

Figure 1. “Energetic span model” schematic diagram.

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RESULTS AND DISCUSSION Activation of Methane Catalyzed by 1/3Hf2+. The geometries and its parameters of the stationary points on triplet and singlet states are depicted in Figure 2, and the calculated potential energy profiles are presented in Figure 3. The imaginary frequency of the transition states can be seen in Table SI 1 (Supporting Information). The Gibbs free energy and relative free energy of the stationary points located on triplet- and singlet-state PESs are shown in Table 1. The ground electronic state of Hf2+ was calculated to be triplet state. CH4 collides with 3Hf2+ to form 3IM1, which makes the system energy decline by 1.67 eV. In 3IM1, the interaction between the two reactants is electrostatic force because the natural charge on Hf and C are +1.81 and −1.03 au, respectively. 3IM2 is formed via the first H transfer transition state 3TS1−2 and the activation barrier is 1.64 eV. Subsequently, the second H transfer takes place from 3IM2 to 3 IM3 via transition state 3TS2−3 with an activation barrier of 0.52 eV. Compared with the activation of the first C−H bond, the activation of the second C−H bond is easier. The overall reaction on this pathway is endothermic by 0.30 eV. As for the singlet-state potential energy surface, the whole dynamic process is similar to that with triplet-state potential energy surface. The activation barriers corresponding to the first and second hydrogen transfer are 0.57 and 1 eV, respectively. Here, the activation of the second C−H bond is more difficult than the first C−H bond. The overall reaction on this pathway is exothermic by 2.82 eV. As shown in Figure 3, the crossing phenomenon appears between the triplet- and singlet-state potential energy surfaces. The crossing point locates before the transition state of the first hydrogen transfer. The confirmation of CP can be seen in Figure 4. This kind of system has been dealt with the Landau− Zener formula,36 and the PLZ is defined as follows: ⎛ −π 2H 2 12 pLZ (E) = exp⎜⎜ ⎝ hΔF

⎞ μ ⎟⎟ 2(E − EMECP) ⎠

(9)

(8)

Here, the probability of electronic hopping from one adiabatic state to the other on the first pass through the crossing region is (1 − PLZ). The probability of electronic hopping during a potential double pass is (1 − PLZ) times the probability of not hopping on the first pass. Namely, the probability of hopping 8845



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Figure 2. Optimized structures and parameters of transition states and intermediates corresponding to the low-energy pathway along the singlet and triplet surfaces of the Hf2+ + CH4 system calculated at the B3LYP/6-311++G(2df,2pd)+SDD level of theory (bond lengths in angstroms and bond angles in degrees).

the first hydrogen transfer, the valence electrons in 5d orbitals has increased to some extent and it will hinder the continuing transfer of the electrons in sp3 orbitals. As for the dehydrogenation course, the 6s orbital of Hf has the best symmetry matching with the 1s orbital of H. It should

d orbitals still have the capability to accept the electrons of the sp3 orbitals, leading to the activation of the second C−H bond. On the pathway of the singlet potential energy surface, the activation barrier of the second hydrogen transfer is higher than that of the first hydrogen transfer. It can be explained that, after 8846



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second hydrogen transfers, two hydrogen atoms will form a hydrogen molecule. Namely, molecular H2 should be formed in the style of breaking away from Hf atom. Reaction Between N2O and CO catalyzed by HfO2+. The geometries and parameters of the stationary points on singlet and triplet states are depicted in Figure 5 and Figure SI 1 (Supporting Information), respectively. Potential energy profiles of singlet and triplet states are presented in Figure 6. The imaginary frequency of transition states can be seen in Table SI 1 (Supporting Information). The Gibbs free energy and relative free energy of the stationary points located on triplet- and singlet-state PESs are summarized in Table 2. Reaction between 1/3HfO2+ and N2O. 1IM1 is initially formed when 1HfO2+ collides with N2O, and the interaction between 1HfO2+ and N2O is caused by electrostatic force in nature due to N2O is a polar molecule. From 1IM1 to 1IM2, the transformation should go through transition state 1TS1−2 and it locates above 1IM1 by 2.44 eV. The reaction followed transition state 1TS2−3 to form 1IM3, and 1TS2−3 is located at 2.79 eV above 1IM2. Finally, N2 and 1HfO22+ are formed through the cleavage of N−O bond. The overall reaction on this pathway is exothermic by 0.78 eV. As for triplet-state potential energy surface, the whole dynamic process is similar to that with the singlet-state potential energy surface. Transition states 3TS1−2 and 3 TS2−3 have activation barriers of 1.02 and 0.47 eV compared with the values for the intermediates before them. The overall reaction on this pathway is exothermic by 2.36 eV. Something needs to be noted that there is no potential energy surface crossing. It is a typical “single-state reaction”, and thus, the reaction pathway on singlet-state potential energy surface is the minimum energy reaction pathway. Catalytic Mechanism Analysis. For 1HfO2+, natural electron configuration on Hf and O atoms are [core] 6s (0.01) 5d (1.31) and [core] 2s (1.96) 2p (4.72) 3s (0.01) 3d (0.02), respectively. Namely, the 6s orbital is an empty orbital; the bonds between Hf and O make electrons delocalize from the d orbital of Hf to the p orbital of the O atom. As for the N2O, natural charges for N and O are −0.08 and −0.34 au, respectively. There is an interesting phenomenon that the initial attacking style is N-end rather than O-end, which can be attributed to the higher electronic density of the N atom compared to that of the O atom. The electronic density of N2O can be seen in Figure SI 3 (Supporting Information). There is also a σ bond between Hf and N in 1IM1, and it consists of s (34.23%) p 0.00 (0.10%) d 1.92 (65.66%) of the Hf atom and s (59.41%) p 0.68 (40.58%) d 0.00 (0.01%) of the N atom. However, the natural charge on the O atom is much larger than that on the N atom. The stronger electrostatic attraction between the Hf atom and O atom makes the O atom approach to Hf atom through 1TS1−2, thus forming 1IM2. In 1IM2, there are two Hf−O bonds. The first bond consists of s (20.29%) p 0.01 (0.19%) d 3.92 (79.52%) of the Hf atom and s (1.35%) p 72.95 (98.56%) d 0.06 (0.09%) of the O atom. The second bond consists of s (0%) p 1 (2.19%) d 44.66 (97.81%) of the Hf atom and s (0%) p1 (99.90%) d 0 (0.10%) of the O atom. It is obvious that one is a σ bond and the other is a π bond. The forming of two bonds between Hf and O promotes the cleavage of N−O bond. The catalytic mechanism can also be explained from another viewpoint. The LUMO of N2O is mainly composed of p orbitals of O and N atoms, which is also a conjugate π* orbital. The electron transfer from the d orbital of the Hf atom to the

Figure 3. Triplet- and singlet-state potential energy surfaces diagram of activation of methane catalyzed by Hf2+.

Table 1. Gibbs Free Energy and Relative Free Energy of the Stationary Points Locate on Triplet- and Singlet-State PESs for the Activation of Methane Catalyzed by Hf2+

species

Gibbs free energy (singlet) (au)

Gibbs free energy (triplet) (au)

relative free energy (singlet) (eV)

relative free energy (triplet) (eV)

CH4 + Hf2+ IM1 TS1−2 IM2 TS2−3 IM3 HfCH22+ + H2

−87.586383 −87.674274 −87.653267 −87.689956 −87.652929 −87.655000 −87.629631

−87.631835 −87.693283 −87.633171 −87.635261 −87.616296 −87.638384 −87.620757

0.000 −2.392 −1.820 −2.818 −1.811 −1.867 −1.177

−1.237 −2.909 −1.273 −1.330 −0.814 −1.415 −0.935

Figure 4. Diagram of potential energy surfaces crossing along the triplet-state IRC and the structures of CP and MECP.

have formed another Hf−H bond. However, the 6s orbital of 1 2+ Hf is impossible to form two Hf−H bonds. Therefore, on the condition of the best symmetry of two 1s orbitals, once the 8847



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Figure 5. Optimized structures and parameters of transition states and intermediates corresponding to the low-energy pathway along the singlet potential energy surfaces of oxidation of CO by N2O catalyzed by HfO2+ (bond lengths in angstroms and bond angles in degrees).

As for triplet-state potential energy surface, the activation barrier of oxygen transfer is 1.55 eV, and this course is exothermic by 1.39 eV. Catalytic Mechanism Analysis. For 1HfO22+, the natural electron configuration on the Hf atom is [core] 6s (0.08) 5d (1.21). Both of the oxygen atoms have the same natural electron configuration of [core] 2s (1.91) 2p (4.43) 3d (0.02). The electron transfer from the d orbital of the Hf atom to the p orbital of the O atom can be clearly seen. The first Hf−O bond consists of s (0.00%) p 1.00 (0.84%) d 99.99 (99.16%) of the Hf atom and O s (0.00%) p 1.00 (99.72%) d 0.00 (0.28%) of the O atom. The second Hf−O bond consists of s (13.99%) p 0.01 (0.13%) d 6.14 (85.88%) of the Hf atom and s (7.94%) p 11.55 (91.69%) d 0.05 (0.37%) of the O atom. As for CO, the

LUMO of N2O will lead to the cleavage of the N−O bond. Furthermore, one d orbital of the Hf atom and one p orbital of the O atom will form a π bond. Finally, N2 and HfO22+ will be generated. Reaction between 1/3HfO22+ and CO. The singlet-state reaction pathway is associated with an oxygen transfer process between 1HfO22+ and CO. The ground electronic state of HfO22+ was calculated to be a singlet state. It is necessary to surmount an activation barrier of 1.55 eV, resulting in the formation of 1IM5. Finally, 1IM5 directly breaks, with the generation of CO2 and 1HfO2+. This reaction course is exothermic by 2.97 eV. 8848



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Figure 6. Triplet- and singlet-state potential energy surfaces diagram of oxidation of CO by N2O catalyzed by HfO2+: (a) reaction between HfO2+ and N2O; (b) reaction between HfO22+ and CO.

0 (0.18%). The forming of this σ bond will promote the cleavage of the Hf−C bond during the course of the Hf−O cleavage. Finally, the p orbital of the oxygen atom and the p orbital of the carbon atom can form a π bond, resulting in the formation of CO2. Kinetic Information of the First Catalytic Cycle. The kinetic information of this catalytic cycle has been calculated on the pathway of singlet- and triplet-state potential energy surfaces, respectively. Here, ΔGr = −88.02 kcal mol−1. TOF(singlet) = 1.69 × 10−48 s−1, XTOF,1TS2−3 = 0.34, XTOF,1TS,1−2 = 0.33, and XTOF,1P1 = 0.33. Thus, 1TS2−3 is TDTS. 1XTOF,IM4 = 1 and TDI is 1IM4. TOF(triplet) = 5.63 × 10−46 s−1, XTOF,3TS1−2 = 0.34, XTOF,3TS2−3 = 0.33, and XTOF,3P1 = 0.33. 3TS1−2 is TDTS, and TDI is 3IM4 because of XTOF,3IM4 = 1. Finally, TOF(singlet)/TOF(triplet) = 3.0 × 10−3.

natural charges for C and O are +0.49 au and −0.49 au, respectively. However, the initial attacking style is C-end attacking, which is attributed to the electronic density of C atom being larger than that of the O atom. Here, the electrostatic force could be ignored compared with the symmetry matching of the orbitals. In 1IM4, there is also an Hf −C σ bond composed of Hf s (44.75%) p 0 (0.20%) d 1.23 (55.05%) and C s (58.61%) p 0.71 (41.33%) d 0 (0.06%). The forming of the Hf−C bond induced the Hf−O bond to be weakened. Electrons in the s orbital of the C atom will transfer to the σ* and π* of the Hf−O bond, leading to the breaking of the Hf−O bond. Here, σ* and π* mainly consist of s and p orbitals of the O atom and the d orbital of the Hf atom. Then, In IM5, another O−C bond consists of O s (38.86%) p 1.57 (60.89%) d 0.01 (0.25%) and C s (48.60%) p 1.05 (51.22%) d 8849



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Here, it is noted that the step of forming products has been taken as a transition state and marked with P1. The minimum energy reaction pathway is the reaction pathway on the singletstate potential energy surface; the true value of TOF in this catalytic cycle is 1.69 × 10−48 s−1 and δE1 = 2497 kcal mol−1. Reaction between N2O and CO Catalyzed by TaO2+. The geometries and parameters of the stationary points on doublet and quartet states are depicted in Figure 7 and Figure SI 2 (Supporting Information). The calculated potential energy profiles of doublet and quartet states are presented in Figure 8. The imaginary frequency of the transition states can be seen in Table SI 1 (Supporting Information). The Gibbs free energy and relative free energy of the stationary points located on doublet and quartet PESs are summarized in Table 3. Reaction between 2/4TaO2+ and N2O. The ground electronic state of TaO2+ was calculated to be a doublet state. As for this potential energy surface, 2IM1 is initially formed when 2TaO2+ collides with N2O. The interaction between 2 TaO2+ and N2O is electrostatic force. From 2IM1 to 2IM2, one

Table 2. Gibbs Free Energy and Relative Free Energy of Stationary Points Locate on the Singlet- and Triplet-State PESs for the Oxidation of CO by N2O Catalyzed by HfO2+

species

Gibbs free energy (singlet) (au)

Gibbs free energy (triplet) (au)

relative free energy (singlet) (eV)

relative free energy (triplet) (eV)

HfO2+ + N2O IM1 TS1−2 IM2 TS2−3 IM3 HfO22+ + N2 HfO22+ + CO IM4 TS4−5 IM5 HfO2+ + CO2

−308.055279 −308.157609 −308.068099 −308.157460 −308.055090 −308.090677 −308.083942 −311.872473 −311.951661 −311.894750 −312.076712 −311.981564

−307.947307 −308.051663 −308.014271 −308.050850 −308.033401 −308.082629 −308.033985 −311.822516 −311.875615 −311.874550 −311.970865 −311.873592

0.000 −2.784 −0.349 −2.780 0.005 −0.963 −0.780 0.000 −2.155 −0.606 −5.558 −2.968

2.938 0.098 1.116 0.121 0.590 −0.744 0.579 1.359 −0.085 −0.057 −2.677 −0.030

Figure 7. Optimized structures and parameters of transition states and intermediates corresponding to the low-energy pathway along the doublet surfaces of oxidation of CO by N2O catalyzed by TaO2+ (bond lengths in angstroms and bond angles in degrees). 8850



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Figure 8. Doublet- and quartet-state potential energy surfaces diagram of oxidation of CO by N2O catalyzed by TaO2+: (a) reaction between TaO2+ and N2O; (b) reaction between TaO22+ and CO.

transformation should go through transition state 2TS1−2, which locates above the 2IM1 by 1.61 eV. After the intermediate 2IM2, the reaction undergoes a transition state 2 TS2−3 to form 2IM3. 2TS2−3 locates at 1.06 eV above 2IM2. Finally, generating the N2 and 2TaO22+, the whole course is exothermic by 3.32 eV. As for quartet-state potential energy surface, the whole dynamic process is similar to that with the doublet-state

potential energy surface. The transition states 4TS1−2 compared with the 4IM1 and 4TS2−3 compared with 4IM2 have two activation barriers of 0.48 and 0.17 eV, respectively. The whole course is exothermic by 3.38 eV. Catalytic Mechanism Analysis. As for 2TaO2+, the first Ta−O bond consists of O s (3.20%) p 30.28 (96.75%) d 0.02 (0.05%) and Ta 5s (25.69%) p 0.03 (0.72%) d 2.86 (73.59%), and it is a σ bond. The second Ta−O bond consists of O s 8851



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the step of forming products has been taken as a transition state and is marked with P2. The minimum energy reaction pathway is the reaction pathway on the doublet-state potential energy surface; the true value of TOF in this catalytic cycle is 6.21 × 10−49 s−1 and δE = 2558 kcal mol−1. Comparing with the TOF of HfO2+, TOF(TaO2+) equals 6.21 × 10−49 s−1 and TOF(HfO2+)/TOF(TaO2+) = 2.7 at 298.15 K. Meanwhile, the δE of the second catalytic cycle is higher than the first catalytic cycle. These results are enough to prove that HfO2+ has better catalytic performance for oxidization of CO by N2O.

Table 3. Gibbs Free Energy and Relative Free Energy of Stationary Points Locate on the Doublet- and Quartet-State PESs for the Oxidation of CO by N2O Catalyzed by TaO2+

species

Gibbs free energy (doublet) (au)

Gibbs free energy (quartet) (au)

relative free energy (doublet) (eV)

TaO2+ + N2O IM1 TS1−2 IM2 TS2−3 IM3 TaO22+ + N2 TaO22+ + CO IM4 TS4−5 IM5 TaO2+ + CO2

−316.868674 −316.986606 −316.927524 −316.982683 −316.967904 −317.006757 −316.990839 −320.780573 −320.864253 −320.808422 −320.918944 −320.816399

−316.737413 −316.890594 −316.873062 −316.880934 −316.874581 −316.920299 −316.861616 −320.651350 −320.733506 −320.725723 −320.800690 −320.686602

0.000 −3.209 −1.601 −3.102 −2.700 −3.757 −3.324 0.000 −2.277 −0.758 −3.765 −0.975

relative free energy (quartet) (eV) 3.572 −0.596 −0.119 −0.334 −0.161 −1.405 0.192 3.516 1.281 2.250 −0.547 2.557

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CONCLUSION For activation of methane, Hf2+ truly accomplishes the catalytic dehydrogenation. It is a typical “two-state reactivity” mechanism. There is a crossing phenomenon before the transition state of the first hydrogen transfer. At MECP, the value of SOC is 900.23 cm−1 and Ph = 0.62. These data indicate the intersystems crossing and spin inversion with a great probability. The activation barrier of the first hydrogen transfer declines by 1.06 eV, and thus reaction is accelerated. After the electron hopping from the 6s orbital to 5d, the empty 6s orbital will be more favorable to accept the electron of the sp3 orbital of the C−H bond through the Hf−C bond orbital and thus lead to the activation of two C−H bonds. No transition state that has the character of two hydrogen atoms getting close to each other in the style of vibration appears before the forming of the hydrogen molecule. The minimum energy reaction pathway can be confirmed between the two different spin-state potential energy surfaces according to the thermodynamic viewpoint. As for oxidization of CO by N2O catalyzed by two different catalysts, both of them are “single-state reactivity” mechanism. The bonds between transition metal atoms and the oxygen atom restrict the freedom of valence electrons and lead to the probability of electron hopping approximately equaling zero. As for CO oxidization by N2O catalyzed by HfO2+, electrons transferring from the d orbital of the Hf atom to the LUMO of N2O will lead to cleavage of the N−O bond. For oxidation of CO, forming the Hf−C σ bond in 1IM4 promotes the activation of the Hf−O bond. Namely, the electrons in the s and p orbitals of the C atom transfer to the σ* and π* orbitals of the Hf−O bond, leading to the break of the Hf−O bond. 1 TS2−3 is TDTS, XTOF,1TS2−3 = 0.34, XTOF,1TS 1−2 = 0.33, and XTOF,1P1 = 0.33. TDI is IM4, XTOF,1IM4 = 1. δE1 = 2497 kcal mol−1 and TOF = 1.69 × 10−48 s−1. As for the second catalytic cycle catalyzed by TaO2+, the HOMO of TaO2+ is only one of the d orbitals; the LUMO of N2O mainly consists of p orbitals of the N and O atoms and it is a π* orbital. The delocalization of electrons in the 5d orbitals leads to activation of the N−O bond. The forming of the Ta−C σ bond in 2IM4 promotes the activation of the Ta−O bond. Namely, the electrons of the s and p orbitals of the C atom delocalizes to the π* and σ* orbital of the Ta−O bond and thus leads to the activation of the Ta−O bond. 2TS1−2 is TDTS, XTOF,2TS1−2 = 0.35, XTOF,2TS2−3 = 0.33, and XTOF,2P2 = 0.32. TDI is 2IM4, XTOF,IM4 = 1. δE2= 2558 kcal mol−1 and TOF = 6.21 × 10−49 s−1. Experiment results have demonstrated that the second catalytic cycle is rather inefficient due to the electron transfer from N2O and CO to produce the inert monopositive oxides. Meanwhile, compared with D[Hf2+−O] = 686 ± 69 kJ mol−1 and D[OHf2+−O] = 186 ± 98 kJ mol−1, the lower bond

(0.00%) p 1.00 (99.93%) d 0.00 (0.07%) and Ta s (0.00%) p 1.00 (2.95%) d 32.86 (97.04%), and it is a π bond. The HOMO of TaO2+ is only a d orbital; the LUMO of N2O mainly consists of p orbitals of the N and O atoms and it is also a π*orbital. According to frontier molecular orbital theory, the delocalization of electrons in the d orbital will lead to the activation of the N−O bond. The frontier molecular orbitals are shown in Figure SI 3 (Supporting Information). Reaction between 2/4TaO22+ and CO. The doublet-state reaction pathway is associated with an oxygen transfer process between 2TaO22+ and CO. It is necessary to surmount an activation barrier of 1.52 eV, resulting in the formation of 2IM5. Finally, the product complex 2IM5 directly breaks, generating the products CO2 and 2TaO2+. This step is exothermic by 0.97 eV. As for triplet potential energy surface, an activation barrier of oxygen transfer is 0.97 eV, and this course is exothermic by 0.96 eV. Catalytic Mechanism Analysis. As for oxidization of carbon monoxide, in 2IM4, the first O−Ta consists of O s (3.20%) p 30.28 (96.75%) d 0.02 (0.05%) and Ta s (25.69%) p 0.03 (0.72%) d 2.86 (73.59%). The second O−Ta bond consists of O s (0.00%) p 1.00 (99.93%) d 0.00 (0.07%) and Ta s (0.00%) p 1.00 (2.95%) d 32.86 (97.04%). However, σ bond between Ta and C atoms has also been formed. This bond is composed of C s (58.00%) p 0.72 (41.93%) d 0.00 (0.07%) and Ta s (35.47%) p 0.00 (0.06%) d 1.82 (64.48%). The delocalization of electrons from s and p orbitals of C atom to π* and σ* orbital of Ta−O bond will lead to the activation of the Ta−O bond. In 4IM5, there is a new C−O bond that consists of O s (40.02%) p 1.49 (59.76%) d 0.01 (0.22%) and C s (48.21%) p 1.07 (51.61%) d 0.00 (0.19%), and it is also σ bond. Another π bond consisting of the p orbital of C and O atoms will be formed during the forming course of CO2. Kinetic Information of the Second Catalytic Cycle. The kinetic information of this catalytic cycle was calculated on doublet- and quartet-state potential energy surfaces, respectively. TOF(doublet) = 6.21 × 10−49 s−1, XTOF,2TS1−2 = 0.35, XTOF,2TS2−3 = 0.33, and XTOF,2P2 = 0.32. Thus, TS1−2 is TDTS. TDI is IM4 due to XTOF,IM4 = 1. TOF(quartet) = 1.52 × 10−46 s−1, XTOF,4TS1−2 = 0.33, XTOF,4TS2−3 = 0.33, and XTOF,4P2 = 0.34. Therefore, P1 is the TDTS. TDI is IM4. Finally, TOF(doublet)/TOF(quartet) = 4.09 × 10−3. Here, it is noted that 8852



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dissociation energy D[Ta2+−O] = 657 ± 58 kJ mol−1 and high bond dissociation energy D[OTa2+−O] = 500 ± 63 kJ mol−1 are also another reason for the low efficiency of TaO2+. Here, the calculated result shows TOF(HfO2+)/TOF(TaO2+) = 2.7 at 298.15 K, and δE1 = 2497 kcal mol−1 is lower than δE2 = 2558 kcal mol−1. These results are enough to prove the experimental conclusion from another perspective. Namely, HfO2+ is more efficient than TaO2+ to catalyze the oxidation of CO by N2O. Meanwhile, the turnover frequency of the catalyst on the pathway of the high-spin potential energy surface is mcuh larger than the reaction pathway on the low-spin potential energy surface. Here, TOF(3HfO2+)/TOF(1HfO2+) = 3.0 × 103 and TOF(4TaO2+)/TOF(2TaO2+) = 4.09 × 103.

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(7) deAlmeida, K. J.; Cesar, A. Methane C-H Bond Activation by Neutral Lanthanide and Thorium Atoms in the Gas Phase: A Theoretical Prediction. Organometallics 2006, 25, 3407−3416. (8) Armentrout, P. B. Activation of CH4 by Gas-Phase Mo+, and the Thermochemistry of Mo-ligand Complexes. J. Phys. Chem. A 2006, 110, 8327−8338. (9) Santo, E. D.; Michelini, M. C.; Russo, N. Methane C-H Bond Activation by Gas-Phase Th+ and U+: Reaction Mechanisms and Bonding Analysis. Organometallics 2009, 28, 3716−3726. (10) Santo, E. D.; Santos, M.; Michelini, M. C.; Marc-alo, J.; Russo, N.; Gibson, J. K. Gas-Phase Reactions of the Bare Th2+ and U2+ Ions with Small Alkanes, CH4, C2H6, and C3H8: Experimental and Theoretical Study of Elementary Organactinide Chemistry. J. Am. Chem. Soc. 2011, 133, 1955−1970. (11) Lv, L. L.; Wang, Y. C.; Wang, Q.; Liu, H. W. Why Pt4+is the Least Efficient Cationic Cluster in Activating the C-H Bond in Methane? Two-State Reaction Computational Investigation. J. Phys. Chem. C 2010, 114, 17610−17620. (12) Blagojevic, V.; Orlova, G.; Bohme, D. K. O-Atom Transport Catalysis by Atomic Cations in the Gas Phase: Reduction of N2O by CO. J. Am. Chem. Soc. 2005, 127, 3545−3555. (13) Alikhani, M. E.; Michelini, M. C.; Russo, N.; Silvi, B. Topological Analysis of the Reaction of Uranium Ions (U+, U2+) with N2O in the Gas Phase. J. Phys. Chem. A 2008, 112, 12966−12974. (14) Chiodo, S.; Rondinelli, F.; Russo, N.; Toscano, M. On the Catalytic Role of Ge+ and Se+in the Oxygen Transport Activation of N2O by CO. J. Chem. Theory Comput. 2008, 4, 316−321. (15) Rondinelli, F.; Russo, N.; Toscano, M. On the Origin of the Different Performance of Iron and Manganese Monocations in Catalyzing the Nitrous Oxide Reduction by CarbonOxide. Inorg. Chem. 2007, 46, 7489−7493.8. (16) Nian, J. Y.; Wang, Y. C.; Ma, W. P.; Ji, D .F.; Wang, C. L .; La, M. J. Theoretical Investigation for the Cycle Reaction of N2O (x1Σ+) with CO(1Σ+) Catalyzed by IrOn+ (n = 1, 2) and Utilizing the Energy Span Model to Study Its Kinetic Information. J. Phys. Chem. A 2011, 115, 11023−11032. (17) Lourenço, C.; Michelini, M. C.; Marçalo, J.; Gibson, J. K.; Oliveira, M. C. Gas-Phase Reaction Studies of Dispositive Hafnium and Hafnium Oxide Ions: Generation of the Peroxide HfO22+. J. Phys. Chem. A 2012, 116, 12399−12405. (18) Santos, M.; Michelini, M. C.; Lourenço, C.; Marçalo, J.; Gibson, J. K.; Oliveira, M. C. Gas-Phase Oxidation Reactions of Ta2+: Synthesis and Properties of TaO2+ and TaO22+. J. Phys. Chem. A 2012, 116, 3534−3540. (19) Shaik, S.; Danovich, D.; Fiedler, A.; Schröder, D.; Schwarz, H. Two-State Reactivity in Organometallic Gas-Phase Ion Chemistry. Helv. Chem. Acta 1995, 78, 1393−1407. (20) Danovich, D.; Shaik, S. Spin−Orbit Coupling in the Oxidative Activation of H−H by FeO+. Selection Rules and Reactivity Effects. J. Am. Chem. Soc. 1997, 119, 1773−1786. (21) Filatov, M.; Shaik, S. Theoretical Investigation of Two-StateReactivity Pathways of H−H Activation by FeO+: Addition− Elimination, “Rebound”, and Oxene-Insertion Mechanisms. J. Phys. Chem. A 1998, 102, 3835−3846. (22) Frisch, M. J. et al. GAUSSIAN 03, revision E.01; Gaussian Inc: Pittsburgh, PA, 2003. (23) Becke, A. D. A New Mixing of Hartree−Fock and Local Density-Functional Theories. J. Chem. Phys. 1993, 98, 1372−1377. (24) Andrae, D.; Haeussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Energy-Adjusted Ab Initio Pseudopotentials for the Second and Third Row Transition Elements. Theor. Chim. Acta 1990, 77, 123−141. (25) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F., III, Ed.; New York, 1976. (26) McLean, A. D.; Chandler, G. S. Contracted Gaussian Basis Sets for Molecular Calculations. I. Second Row Atoms, Z = 11−18. J. Chem. Phys. 1980, 72, 5639−5648. (27) Gonzalez, C.; Schlegel, H. B. An Improved Algorithm for Reaction Path Following. J. Chem. Phys. 1989, 90, 2154−2161.

ASSOCIATED CONTENT

S Supporting Information *

Optimized structures of transition states and intermediates corresponding to the low-energy pathway along the spin-state potential energy surface, frontier molecular orbitals of the reactants, and the imaginary frequencies of all transition states. These material are available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Z. Guo: e-mail, [email protected]; tel, 0086-9314968105, fax, 0086-931-8277088. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Nature Science Foundation of China (Nos. 31070155, 11172301, and 21203217), the “Funds for Distinguished Young Scientists” of Hubei Province (2012FFA002), the cojoint scientific field project, the “Western Light Talent Culture” Project, and the “Top Hundred Talents” Program of Chinese Academy of Sciences. The authors thank Prof. Yongcheng Wang for his assistance in computation.

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REFERENCES

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Theoretical Views on Activation of Methane Catalyzed by Hf2+ and

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