Theoretical Investigation for the Cycle Reaction of N2O (x1∑+) with

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Theoretical Investigation for the Cycle Reaction of N2O (x1∑+) with CO (1∑+) Catalyzed by IrOn+ (n = 1, 2) and Utilizing the Energy Span Model to Study Its Kinetic Information JingYan Nian, YongCheng Wang,* WeiPeng Ma, DaFang Ji, CuiLan Wang, and MaoJi La College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou, Gansu 730070, P. R. China

bS Supporting Information ABSTRACT: The mechanisms of the reactions between N2O and CO catalyzed by IrOn+ (n = 1, 2) have been investigated using B3LYP and CCSD(T) levels of theory. Spin inversion among three reaction profiles corresponding to the quintet, triplet, and singlet multiplicities was discussed by using spin
orbit coupling (SOC) calculations. The probability of electron hopping in the vicinity of the (MECP) has been calculated by the Landau
Zener-type model. The single P1ISC and double P2ISC passes estimated at MECP1# (SOC = 198.61 cm
1) are approximately 0.11 and 0.20, respectively. Important analysis and explanations were done using molecular orbital theory and natural bonding orbital (NBO). The energetic span (δE) model coined by Kozuch was applied in this cycle. The turnover frequency (TOF)-determining transition state (TDTS) and TDI (TOF-determining intermediate) were confirmed. Finally, TOF(IrO+)/TOF(IrO2+) = 0.38 at 298 K.

1. INTRODUCTION Carbon monoxide (CO) is a significantly toxic gas, combining with hemoglobin in the blood and preventing oxygen binding, leading to anoxemia.1 Nitrous oxide (N2O) is well-known as a greenhouse gas since it causes ozone depletion in the atmosphere.2 While the reaction of CO with N2O is quite exothermic, it does not occur directly to any measurable extent in the gas phase at either room or elevated temperature.3 Catalytic conversion of harmful gases, such as N2O and CO produced in fossil-fuel combustion, is of utmost importance, both environmentally and economically. How to reduce the harmful gases N2O and CO synchronously has been a hot subject for many experiments and theoretical calculations. Emission reduction of N2O and CO can be achieved by using heterogeneous catalysts often containing transition metal atoms or ions.4 Transition metal oxide cations also are of interest as intermediates in transition metal ion catalysis.5,6 The transition metal cations or transition metal oxide cations can provide fundamental information about catalytic action in different systems ranging from heterogeneous catalysis to homogeneous.7
15 Recent ICP/SIFT experiments have shown that a series of metal dioxide and higher metal oxide cations can be generated from N2O; several atomic ions form trioxides in sequential O-atom transfer processes, such as W+, Os+, and Ir+; and the higher oxides of Os+ and Ir+ have been treated with CO in some experiments, and these are sequentially reduced to the bare metal cation.3 The mechanisms for the IrOn+ (n = 1,2) catalyzed reduction of nitrous oxide combined with the oxidation of CO catalyzed by IrOn+ (n = 2,3) ions are also reported in the experiments.16

∑þ Þ þ COð1 ∑þ Þ f N2ð1∑gþ Þ þ þ CO2 ð1 ∑g Þ

N2 Oð1

r 2011 American Chemical Society

ð1Þ

Scheme 1. The Reactions of CO with N2O Catalyzed by Transition Metal Oxide Cation IrOn+ (n = 1, 2)

∑þ Þ f N2 ð1 ∑g þ Þ þ IrO2þ

ð2Þ

∑þ Þ f CO2 ð1∑gþ Þ þ IrOþ

ð3Þ

∑þ Þ f N2ð1 ∑g þÞ þ IrO3 þ

ð4Þ

∑þ Þ f CO2 ð1∑gþ Þ þ IrO2 þ

ð5Þ

IrOþ þ N2 Oð IrO2 þ þ COð

IrO2 þ þ N2 Oð IrO3 þ þ COð

These reactions can be described by Scheme 1. The mechanism for the reaction of N2O with CO catalyzed by an Ir+ ion has been investigated by Cheng et al.17 Their results clearly demonstrate that the mechanism corresponding to the O-atom transfer reaction appears to be an exothermic process with a reaction heat of 85.20 kcal/mol. Transition metal oxide cation IrOn+ (n = 1,2) has also been shown to catalyze the reaction between N2O and CO efficiently.18,19 To our knowledge, a detailed reaction path and a possible spin inversion process for reaction 1 catalyzed by IrO+ and IrO2+ have not been reported. Why does reaction 1 take place only in the presence of a catalyst? Why does carbon-end attacking appear rather Received: March 19, 2011 Revised: September 1, 2011 Published: September 01, 2011 11023

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The Journal of Physical Chemistry A than oxygen-end attacking during the course of oxidation of CO? What is the type of electron hopping among different orbits and should it be allowed? This paper will focus on the above problems and expound upon them. The turnover frequncey (TOF; E-representation) determining the efficiency of the catalyst will be applied in this cycle reaction as the newest notion. An energy landscape of the cycle reaction will be drawn in order to calculate TOF (E-representation). Intermediates and transition states will be researched in order to reveal their influences on the kinetics of the whole reaction. δE (given in Gibbs energies) serving as the apparent activation energy of the cycle reaction will be calculated.

2. CALCULATION METHODS All computations were carried out by manipulating the GAUSSIAN 03 program package.20 The fully optimized geometries and the vibration frequencies have been determined by using the spin-unrestricted three-parameter hybrid21B3LYP density method,22 which was adopted by its successful performance for many open-shell transition metal compounds.23,24 The standardized 6-311++G (3df, 3pd) basis sets were used for the carbon, oxygen, and nitrogen atoms.25In addition, high-level single-point energies for reactants, products, and transition states (TSs) were calculated using the coupled cluster with single, double, and perturbative triple excitations, CCSD(T), with the aug-cc-pVDZ basis set. The relativistic effective core potential (RECP) of Stuttgart was used for the transition metal atom. Harmonic vibration frequencies were computed to verify the minima (the number of imaginary frequencies NIMAG = 0) and transition state structures (NIMAG = 1). To ensure reliability on the reaction path, the connections between the transition state and the corresponding minima were verified using an intrinsic reaction coordinate (IRC) technique developed by Gonzalez and Schlegel26,27 in the mass-weighted internal coordinate system. It is well-known that transition metal-mediated reactions often occur on two or more potential energy surfaces (PESs).28
30 All coordinates were optimized in search of the crossing point (CP) between the two PESs. Thus, starting from the transition states closest to the crossing seams, the reaction pathway was traced down to the corresponding minimum. Thereafter, each optimized point along the IRC path was submitted to a single-point energy calculation with the other electronic state. For the sake of comparison, the minimum energy crossing points (MECPs) proposed by Harvey et al.31 have also been employed. A semiempirical procedure implemented by Koseki et al.32,33 relies on the one-electron part of the spin
orbit Hamiltonian, HSO in eq 1: ! ! α2 Zk α e2 Hso ¼ ð1Þ ∑ rik3 Si 3 Lik 2 ¼ 2m2e c2 2 ∑ i k Here Si and Lik are the orbital and spin angular momentum operators for an electron (i) in the framework of the nuclei, indexed by K. To account for the missing two-electron part of the Hamiltonian, the nuclear charge ZK is replaced by an effective parameter, Zk*, which can be taken as the screened nuclear charge.34 In the semiclassical picture based on PESs, the probability of intersystem crossing (ISC) for a molecule passing through a triplet
quintet crossing in a Landau
Zener-type model,35
37 is given by   π LZ ð2Þ P ¼ exp
ξ 4

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ξ¼

2 8HSOC h gBd B v NAV

ð3Þ

P1ISC ¼ 1
PLZ

ð4Þ

P2ISC ¼ PLZ ð1
PLZ Þ

ð5Þ

PISC ¼ P1ISC þ P2ISC ¼ ð1
PLZ Þð1 þ PLZ Þ

ð6Þ

Here, HSOC is the Hamiltonian matrix element between the two spin states, B g d is the gradient difference vector between the quintet and triplet states, and Bv is the velocity of the molecule at the MECP. A catalytic cycle is a wheel with many individual chemical steps spinning in a coordinated manner at a common “speed”. This “speed” is defined by the turnover frequency (TOF) of the cycle, given in eq 7 as the number of cycles (N) per catalyst concentration (C) per time (t): TOF ¼

N ½Ct

ð7Þ

It is well-known that computational chemistry produces an energy landscape of the reaction. Therefore, an energy representation (E-representation) TOF will be calculated. On the basis of Eyring’s transition state theory, an important formula, eq 8, was deduced by Kozuch for catalytic cycles of N steps. TOF ¼

kB T h

expð
ΔGr =RTÞ
1 N

∑

ij ¼ 1

with δG0ij ¼

(

ΔGr 0

exp½ðTi
Ij
δG0ij Þ=RT

if if

¼

Δ M

ð8Þ

i>j iej

Kozuch also linked eq 8 to Ohm’s law. The TOF is given as the forward chemical current of the reaction, determined by the potential divided by the resistance. The potential of the process is Δ, a function of the energy of the reaction (ΔGr), which is related to the thermodynamics. The “
1” term provides thermodynamic consistency for the case of ΔGr = 0, for which the TOF is zero, or in the case of an endothermic reaction where the current flows backward and the TOF is negative. The resistance to the chemical flow is given by M, corresponding to the sum of exponentials of Gibbs energy differences between all the combinations of intermediates (Ij) and transition states (Ti). M is closely related to the dynamic. For an exothermal reaction (ΔGr < 0), the “
1” term in the numerator can be neglected. More importantly, the denominator is usually (but not always) dominated by a single term of the summation. In these conditions, eq 8 is simplified to eq 9. TOF ¼

kB T
δE=RT e h

ð9Þ

δE, the energetic span, is defined as ( if TDTS appears after TDI TTDTS
ITDI δE ¼ TTDTS
ITDI þ ΔGr if TDTS appears before TDI ð10Þ 11024

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Table 1. The Calculated Bond Length (in Å) and Bond Angle (in degrees) for Important Species in the Reaction Catalyzed by IrOn+ (n = 1, 2), Which Was Calculated on the B3LYP/6-311+G (3df, 3pd) Levela catalyst IrO

dO1
Ir(Å)

species

+

5

1.767

4.394

1.151

1.126

180.00

3.004 2.205

1.189 1.216

1.126 1.108

69.99 131.81

1.689

1.872

1.529

1.100

121.88

IM3

1.680

1.680

3.092

1.093

111.66

IrO2+

1.684

1.684

1 1

1

— Ir
O2
C

109.03

1.685

1.685

3.007

1.114

1.665

1.817

1.584

1.323

72.21

1.641

2.051

1.188

1.131

179.72

IM5

species 1

dO1
Ir(Å)

dO2
Ir(Å)

d Ir
O3(Å)

dO3
N(Å)

d N
N(Å)

— Ir
O3
N 180.00

IM1

1.682

1.682

4.287

1.147

1.125

TS1
2

1.682

1.681

2.783

1.190

1.131

67.77

IM2

1.681

1.681

2.078

1.239

1.105

121.97

TS2
3

1

dO3
C(Å)

d C
O4(Å)

— Ir
O3
C

1.683

1.683

1.869

1.562

1.097

121.37

IM3

1.692

1.692

1.694

2.696

1.091

114.22

IrO3+

1.691

1.691

1.692

3

IM4

1.758

1.76

1.761

1.761

1.114

43.08

TS4
5 1 IM5

1.74 1.68

1.741 1.68

1.833 2.094

1.841 1.193

1.121 1.132

64.99 137.55

1 1

a

d C
O3(Å)

IM4

5

3

d O2
C(Å)

TS4
5

1

1

— Ir
O2
N

1.748 1.760

TS2
3

1

d N
N(Å)

IM1

3

IrO2+

dO2
N(Å)

TS1
2 5 IM2

5

catalyst

dIr
O2(Å)

O1, O2, and O3 indicate different oxygen atoms.

The cycle reaction in this experiment is an exothermal reaction. Therefore, eq 9 as the simplest formula will be adopted to calculate the TOF. The TDTS (TOF-determining transition state) and the TDI (TOF-determining intermediate) are the transition state and the intermediate that maximize the energetic span within the cyclic constraints, and thereby gauge the kinetics of the cycle. The degree of rate control (Xrc) belongs to the family of structure
reactivity coefficients used in physical organic chemistry to describe the influence of various factors on rates. Campbell defined Xrc as the normalized influence of a certain rate constant on the overall rate of the reaction, where all the other rates and equilibrium constants are held constant. Thus,   ki ∂r  ∂ ln r  ¼ Xrc, i ¼   ð11Þ ∂ ln ki  r ∂ki  Km , kn6¼i,
i

Km , kn6¼i,
i

Knowing the connection between the k and E-representations, Kozuch derived the notion of “degree of rate control” in the catalytic cycle reaction using state energies, and termed it the degree of TOF control (XTOF):    1 ∂TOF   ð12Þ XTOF, i ¼   TOF ∂Ei  Here Ei can be a transition state or an intermediate Gibbs energy. The meaning of XTOF is simple: the bigger its value, the higher the influence of the corresponding state (TS or intermediate) on the TOF. Kozuch defined the TDI and TDTS as the states that have XTOF closest to 1, thus, the use of XTOF values is a quick method for identifying the TDTS and TDI and for deciding whether there are more states that determine the kinetics of the cycle. The degree of TOF control can be written

explicitly in the E-representation:

XTOF, Ti

∑j exp½ðTi
Ij
ΔG0ij Þ=RT ¼ ∑ij exp½ðTi
Ij
ΔG0ij Þ=RT

ð13Þ

XTOF, Tj

∑i exp½ðTi
Ij
ΔG0ij Þ=RT ¼ ∑ij exp½ðTi
Ij
ΔG0ij Þ=RT

ð14Þ

Here, Ij and Ti symbolize the standard-state Gibbs energies of the ith intermediate or transition state.38

3. RESULTS AND DISCUSSION For the reaction between N2O and CO catalyzed by IrOn+ (n = 1, 2), Table 1 shows the selected geometrical parameters of the reactant complexes, the intermediates, the transition states, and the product complexes along the reaction pathway corresponding to the quintet, triplet, and singlet states. The optimized geometries and detailed geometrical parameters of the reaction catalyzed by IrOn+ (n = 1, 2) can be obtained from Figures 1 and 2 of the Supporting Information. The total and relative energies of the stationary points calculated with the B3LYP and CCSD(T) methods on the three PESs are summarized in Tables 1 and 2 of the Supporting Information. The reaction pathways based on our B3LYP calculations are plotted in Figures 1 and 2. Imaginary frequencies, ν (in cm
1), of the TS were calculated by using the B3LYP/6-311+G (3df, 3pd) level of theory. They are summarized in Tables 2 and 3. In the following discussion, all the values of relative energy were obtained at the B3LYP (CCSD(T)) level of theory. 11025

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Figure 1. Potential energy diagrams of the reaction between N2O and CO catalyzed by IrO+ in the quintet, triplet, and singlet states.

3.1. The Reaction between N2O and CO Catalyzed by IrO+. After many explorations, the reaction mechanism of IrO+ with N2O was found to be that the O-atom is directly abstracted from N2O by IrO+. When we conducted a survey on reaction 3, it is found that carbon monoxide directly abstracts the O-atom from IrO2+. The whole cycle reaction is an oxygen atom extraction process.

3.1.1. The Reaction of IrO+ with N2O. For the reaction IrO+ + N2O f IrO2+ + N2, the ground electronic state of the IrO+ is calculated to be quintet state. As for the quintet surface, 5IM1 is initially formed when 5IrO+ collides with N2O. All atoms locate on the same plane instead of linear structure. The bond length of the Ir
N is 2.117 Å in the 5IM1; the bond length of the Ir
O is 1.767 Å and has some elongation compared with the bond length 11026

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Figure 2. Potential energy diagrams of the reaction between N2O and CO catalyzed by IrO2+ in the quintet, triplet, and singlet states.

of 5IrO+, which is 1.745 Å. The bond lengths of N
N and N
O are shortened compared with N2O. This phenomenon indicates that the interaction between 5IrO+ and N2O is electrostatic in nature. Electrostatic interaction can be explained from the knowledge of group theory. N2O has a C∞v molecular point

group. If one molecule belongs to molecular point group C∞v, it should be a polar molecule. From the 5IM1 to the 5IM2, the transformation proceeds through the transition state 5TS1
2, which has been confirmed by the IRC calculations. The5TS1
2 is located at 34.12 (31.69) kcal/mol above the complex 5IM1 at 11027

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Table 2. Imaginary Frequencies, ν (in cm
1), of the TS in the Cycle Reaction Catalyzed by IrO+, Which Was Calculated by Using the B3LYP/6-311+G (3df, 3pd) Level of Theory TS

ν (cm
1)

5

TS1
2

222.47i

5

826.53i

5

679.81i

3

207.21i

3

TS2
3 3 TS4
5

780.99i 549.86i

1

781.72i

1

781.72i

1

525.21i

TS2
3 TS4
5 TS1
2

TS1
2 TS2
3 TS4
5


1

Table 3. Imaginary Frequencies, ν (in cm ), of the TS in the Cycle Reaction Catalyzed by IrO2+, Which Was Calculated by Using the B3LYP/6-311+G (3df, 3pd) Level of Theory TS

ν (cm
1)

5

TS1
2

162.47i

5

888.02i

TS2
3

5

506.8i

3

160.94i

3

678.47i

3

TS4
5 1 TS1
2

512.94i 276.50i

1

689.04i

1

403.17i

TS4
5 TS1
2 TS2
3

TS2
3 TS4
5

the B3LYP (CCSD(T)) level of theory. After the intermediate 5 IM2, the reaction undergoes the important transition state 5 TS2
3, which is located at 32.05 (36.02) kcal/mol above the 5 IM2. Unlike the 5TS1
2, the structure changes are much bigger. The end nitrogen points toward the IrO+, the O
N
N angle is about 158.84 in the 5TS2
3, the corresponding bond length of O
N increases to 2.983 Å in 5IM3, while the bond length of O
N distance is 1.225 Å in the nitrogen molecule. As shown in Figure 1A, the energy of 5IM3 is 30.60 (42.23) kcal/mol lower than the ground-state reactants. The following step is that the IrO2+ and N2 are obtained by O
N bond activation of the 5IM3. The overall reaction on this PES is exothermic by 40.46 (40.04), which is favorable from thermodynamic viewpoints. Along the triplet state pathway, the analysis of geometry and molecular orbital interaction of the 3IM1 indicates that the interaction between 3IrO+ and N2O is also electrostatic in character. The reaction starts from the 3IM1 and goes through the transition state 3TS1
2 to reach the 3IM2 by overcoming an activation barrier of 32.76 (31.62) kcal/mol. The following step is associated with 3IrO+, which directly abstracts the O-atom from N2O and leads to the formation of the 3IM3. The corresponding transition state is 3TS2
3. The end nitrogen of N2O is bent outward away from the 3IrO+, the molecular point group changes from Cs to C1. The activation barrier is 15.31 (17.00) kcal/mol in this step. Finally, the Ir
N bond of the 3IM3 breaks, thus leading to the separate products. Analysis of the triplet potential energy profile shows that the reaction appears to be an exothermic process with a reaction heat of 40.20 (64.07) kcal/mol. As for the singlet state pathway, the reaction starts

Figure 3. Important orbits of the reaction between N2O and CO catalyzed by IrOn+ (n = 1, 2).

from the 1IM1 and goes through the transition state 1TS1
2 to reach the 1IM2 by overcoming an activation barrier of 36.20 (70.66) kcal/mol. The following step is associated with 1IrO+, which directly abstracts the O-atom from N2O and leads to the formation of the 1IM3. The corresponding transition state is 1 TS2
3. The activation barrier is 16.15 (53.15) kcal/mol during this step. Finally, the Ir
N of the 1IM3 breaks, leading to the separate products. Analysis of the singlet potential energy profile shows that the reaction appears to be an exothermic process with a reaction heat of 76.97 (85.03) kcal/mol, much bigger than the other two spin states. This powerfully proved that 1IrO2+ is the main product from the viewpoint of thermodynamics. 3.1.2. The Reaction between IrO2+ and CO. Examination of the stabilities of the spin state species of the iridium dioxide ions shows that 1IrO2+ is the ground-state, which was also concluded from Figure 3A. 1IrO2+ attacks CO, thus forming 1IM4 with a binding energy of 62.09 (62.68) kcal/mol. The reaction, via the transition state 1TS4
5, should undergo O-atom migration to form the stable intermediate 1IM5, surmounting an activation barrier of 34.78 (41.72) kcal/mol. From the 1TS4
5 to the 1IM5, the corresponding bond distance of C
O shortens to 1.193 Å, and the distance between the metal atom and the carbon atom elongates to 2.094 Å. We can also see the formation of 1IrO+ and CO2 along this pathway. As shown in Figure 1B, quintet and triplet PESs are similar to the singlet PES, both involving IrO2+ attacks on CO to form the corresponding initial complex IrO2
CO+. As for the triplet, the initial intermediate 3IM4 and the product complex 3 IM5 are connected by the transition state 3TS4
5. The energy of 3 TS4
5 exceeds 3IM4 by 25.92 (26.86) kcal/mol. In summary, the whole reaction is exothermic by 46.30 (20.40) kcal/mol on the triplet state PES. Finally, we came to investigate the quintet state, the initial intermediate 5IM4 surmounting an activation barrier of 30.68(33.38) kcal/mol to form 5IM5. As Figure 1B shows, the energy of 5IM5 is the lowest compared with the corresponding intermediates on the other two spin states, such as 3IM5 and 1IM5. Therefore, 5IM5 is a precursor of the final product IrO+ and CO2 3.2. The Reaction between N2O and CO Catalyzed by IrO2+. The overall reaction of IrO2 + with N2O and IrO3+ with CO is not an insertion mechanism. The reaction is a direct abstraction mechanism in which the IrO2+ directly abstracts the O-atom from N2O and the IrO3+ directly gives the O-atom to CO. The reaction mechanism is the same as the first cycle reaction. 3.2.1. The Reaction of IrO2+ with N2O. In reaction 4 catalyzed by IrO2+, the ground-state of IrO2+ is a singlet state. An initial molecular adduct is formed between N2O and 1IrO2+, and then 1 IM1 undergoes a rearrangement process to form the stable 11028

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The Journal of Physical Chemistry A intermediate 1IM2 by overcoming an activation barrier of 44.52 (43.30) kcal/mol. In the next step, the O-atom transfer leads to the 1IM3 from the complex 1IM2, via the transition state 1TS2
3 with a barrier of 13.76 (10.42) kcal/mol. We note that the overall reaction on this pathway is exothermic, 48.99 (67.21) kcal/mol. The quintet and triplet state PES can also be characterized by the O-atom transfer pathway. Based on the CCSD(T) method calculation, the energy of every intermediate and transition state on the quintet state PES is higher than the corresponding species on the single state and triplet state. However, based on the B3LYP method, the energy of every intermediate and transition state on the quintet state PES is higher than the corresponding species on the single state and triplet state with the exception of the initial complex (3IrO2++N2O). Both the quintet and triplet states are also exothermic. The quintet state PES can be described as the initial molecular adduct formed between N2O and 5IrO2+ on the quintet PES. The 5IM1 can undergo a rearrangement process to form the stable intermediate 5IM2 by overcoming an activation barrier of 18.85 (14.11) kcal/mol. The transition state is 5TS1
2. In the next step, the O-atom’s transfer leads to the 5IM3 from the complex 5IM2, via the transition state 5TS2
3 with a barrier of 18.29 (35.08) kcal/ mol. Finally, we analyze the triplet state in detail: 3IM1 and 3IM2 are connected through 3TS1
2, and the formation of 3IM2 should overcome a potential barrier of 35.82 (27.36) kcal/mol. The final oxygen transfer process surmounts a barrier of 13.62 (14.88) kcal/mol to form 3IM3. 3.2.2. The Reaction between IrO3+ and CO. From the 1IM4, the singlet reaction pathway is associated with an oxygen transfer process between 1IrO3+ and CO. It is necessary to surmount an activation barrier of 12.93 (22.91) kcal/mol resulting with the pathway going down to the complex 1IM5. This step is exothermic by 37.55 (6.68) kcal/mol. Finally, the product complex 1IM5 directly breaks, leading to the separate products. The 3IM5 is formed from the 3IM4 by overcoming an activation barrier of 15.28 (17.25) kcal/mol and the corresponding transition state 3 TS4
5. Overall, the whole reaction of IrO3+ with CO is exothermic by 45.93 (42.86) kcal/mol. The quintet state PES can be summed up as follows: the 5IM5 is formed from the 5IM4 by overcoming an activation barrier of 15.07 (62.25) kcal/mol. The whole reaction of IrO3+with CO is exothermic by 69.30 (87.98) kcal/mol. 3.3. Theory Analysis about Cycle Reaction Catalyzed by IrOn+ (n = 1, 2). Some important orbits were shown by Figure 3. It is well-known that matching of the reactant’s frontier molecular orbital is the first condition to be satisfied if an elementary reaction is to occur. This is the viewpoint of the frontier molecular orbital theory that was proposed by Kenichi Fukui. The matching of the orbital symmetry is very special; it not only requests symmetrical geometry but also a consistent plus or minus. It is well known that the highest occupied molecular orbital (HOMO) is the electron-donating orbital and the lowest unoccipied molecular orbital (LUMO) is the electron-accepting orbital at the beginning of a reaction. The reaction between nitrous-oxide and carbon monoxide wants to occur: either the HOMO of N2O and the LUMO of CO are matching, or the LUMO of N2O and the HOMO of CO are matching. As Figure 3 shows, the LUMO of N2O and the HOMO of CO are not symmetrically matching, but the HOMO of N2O and the LUMO of CO are symmetrically matching. However, reaction will not occur because the second condition of the frontier molecular orbital theory is not satisfied. The second condition of the

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frontier molecular orbital theory requires that the electron transfer from the molecule that has large electronegativity to another molecule that has smaller electronegativity. We know that electronegativity equals half of the HOMO and LUMO energy interval. Calculated results demonstrate that the electronegativity of carbon monoxide is larger than that of nitrous-oxide. Namely, it is still forbidden although geometrical symmetry is matching. Therefore, reaction 1 will occur only in the presence of a catalyst. The bond length of N
O has some elongation during the course of forming IrO2+, the activation of bond N
O can be elaborated from the viewpoint of molecular orbital. 5IrO+ has four single occupied orbitals, but here only dxz can contact with px of the oxygen atom, thus forming a π bond that can be confirmed by a character table. px and dxz belong to the same irreduable representation E1 of C∞v. As shown in Figure 3, the LUMO of N2O contains px of the oxygen atom; therefore, the symmetry of the LUMO of N2O and the dxz of 5IrO+ match. The electron of the dxz orbital transfers to the LUMO of N2O, which is a π* orbital and leads to the activation of the N
O bond and the eventual formation IrO2+. The oxygen atom is abstracted by carbon monoxide from the transition metal dioxide cation. According to conventional thinking, it should be the oxygen-end that attacks the transition metal from the knowledge points of electronegativity. However, calculation results tell us that is the carbon-end attacking. Reasons for that can be explained as follows: it is well-known that 2σg(HOMO) is greater than 1πu in a nitrogen molecule, and a similar situation arises in the carbon monoxide molecule due to the nitrogen molecule and carbon monoxide being isoelectronic species. Namely, the HOMO of carbon monoxide is a σ orbital. As Figure 3 shows, the electron density of the carbon atom is significantly greater than that of the oxygen atom. This is the exact reason for carbon-end attacking. The reasons why the oxygen atom is abstracted by carbon monoxide from IrO2+ can be explained as follows: First, the HOMO of CO contacts the LUMO of IrO2+, which is a σ* orbital, and then the electron’s delocalization leads to the activation of σ bond between O and Ir. Meanwhile, the HOMO of 1IrO2+ and the LUMO of CO are symmetrically matching, and they can form a π bond. The formation of this π bond advances the trend of abstracting the oxygen atom by carbon monoxide from IrO2+. Spin
orbit coupling (SOC) is the reason for the appearance of CP3# and CP4#, but it can be discussed from another perspective. The dxz of the Ir atom gives one electron to the px of the C atom. This leads to the d orbital of the Ir atom with one single electron and the px orbital of the C atom with one electron. Therefore, the spin multiplicity is triplet. However, Hand’s rule tells us that electrons should occupy all empty orbitals in the form of a spin parallel. Four single electrons will appear on the d orbital. In other words, the spin multiplicity is quintet. Here px and dxz belong to the irreduable representation E1 of C∞v and B1 of C2v, respectively. The process of IrO2+ abstracting the oxygen atom is similar to that of IrO+ and can be seen in Figure 2 of the Supporting Information. However, the reaction of IrO2+ abstracting the oxygen atom is a “single-state reaction”. The reason for this phenomenon can be explained as follows: There is a conjugate π orbital that makes a marked reduction in the energy of the system. The reaction prefers to occur on the minimum energy reaction path. The oxidation of carbon monoxide catalyzed by IrO3+ is a “two-state reaction” because the electrons’ transfer 11029

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The Journal of Physical Chemistry A makes the appearance of a single electron. Therefore, it is extremely possible to appear as a different spin state because of the magnetic dipole transition of electrons. 3.4. CPs and MECPs. On the basis of the CCSD(T) calculation, the energy value of the 5IrO2+ is higher than that of 3IrO2+. However, the energy value of the 3IrO2+ is higher than that of the 5 IrO2+ based on the B3LYP calculation. There are six energy crossing phenomena on the potential energy profiles of reactions 2, 3, and 5 based on B3LYP and CCSD(T) method calculations. We can see this in Tables 1 and 2 of the Supporting Information. In this paper, potential energy diagrams along the reaction pathway are based on B3LYP calculation. The probability of spin inversion is moderate, allowing for an efficient conversion to the most favorable energetic surface along the reaction path. They are typical “two-state reactivity” (TSR) reactions on the basis of the Hammond postulate.30 In order to search the CP, an approach suggested by Yoshizawa39 for approximately locating the CP of two PESs with different multiplicities has been used. To characterize the MECP, we have also used the algorithm proposed by Harvey et al.31 Because of the MECP1# located at the entrance of the reaction channels, it plays a significant role in the reaction processes, which can decrease the activation barriers. However, the other MECPs either provide a lower-energy reaction path or decide the distribution of products that have different spin multiplicity. Taking MECP1# as an example, we have gained useful information about it from frontier molecular orbital interaction analysis in order to have a deeper understanding of the crossing and the spin inversion. In Figure 4, the (a) orbital is the dxz orbital of Ir, which is the HOMO in the quintet state, but is the LUMO in the triplet state. The (d) orbital is the lowest single occupied orbital (SOMO) composed of the dx2
y2 orbital of Ir, which is the SOMO in the quintet state, but is the highest double occupied orbital in the triplet state. In the present case, the α electron in the dxz orbital will undergo spin inversion, that is to say, the single electron leaps from the dxz orbital to the dx2
y2 orbital of Ir. This single electron in an atom transfer at a different orbital is allowed.40 The reasons for that can be explained as follows: it is well-known that there are two types of electron transition: electric dipole transition and magnetic dipole transition. Electronic spin is closely connected with magnetic dipole transition. Because the electronic spin produces a ring current that generates a magnetic field that is symmetrical, the parity of the magnetic dipole is g. Magnetic dipole transition on different orbitals must satisfy certain selection rules. Zero integral rules require the parity of wave functions to be identical. We also know that the parity of the orbital should be consistent with the parity of the angle quantum number. Here, the angle quantum number is 2, so the parity of dxz and dx2
y2 are both g. g X g X g = g, electron transition is allowed. Many theoretical investigations41,42 have manifested the principal mechanism that mixes the two spin states and provides the probability of the ISC being SOC. Ideally, large SOC occurs when the electronic transition that accompanies the spin flip creates orbital angular momentum. For MECP1#, the computed SOC constant is 198.61 cm
1, obtained by using the one-electron spin
orbit Hamiltonian in GAMESS.43 In some cases, however, even much larger values of SOC do not warrant spin crossing activation,44,45 which has been demonstrated by Cimas et al. Thus, an estimate of the probability of ISC from one state to another state can be obtained by using a semiclassical picture based on PESs, where the probability of surface hopping through the CP is given by the Landau
Zener-type model given in the Calculation Methods section. For the calculation of Bv ; it is assumed that the

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Figure 4. Frontier molecular orbital interaction analyses for MECP1#.

excess excitation energy is converted into kinetic energy, and the corresponding velocity vector is parallel to the gradient difference vector. Using this approximation, the calculated values for the B gd and Bv are 0.043852 hartree bohr
1 and 0.00098 bohr per atomic time unit, respectively. On the basis of the calculated SOC value and PESs, the probabilities of ISC, P1ISC and P2ISC, estimated at MECP1# are approximately 0.11 and 0.20, respectively. That demonstrates that a spin inversion from the quintet to the triplet state will occur in the vicinity of the crossing seam. An important consequence of this spin inversion is that the barrier height of TS2
3 decreases from 32.04 to 19.62 kcal/mol. Therefore, the effective spin inversion will make the reaction accessible to a lower energy pathway, leading to rate acceleration. We likewise calculated MECP3# (SOC = 219.12) and MECP4# (SOC =182.03). P1ISC and P2ISC of MECP3# are 0.15 and 0.25, and P1ISC and P2ISC of MECP4# are 0.17 and 0.28, respectively. 3.5. Analysis Using Natural Bond Orbital (NBO). We take the minimum energy reaction path as our main study object to analyze details about the interaction between different atoms. The bond order analysis using NBO5.0 shows that the hyperconjugative interaction (often called the “covalent component”) is very weak in the initial complexes 5IM1, corresponding to the results calculated: Ir
N (0.0032 covalent + 0.0373 ionic = 0.0405 total). The ionic component is much larger than that of the covalent one. The geometries and NBO data of complex 5 IM1 indicate that the interaction between IrO+ and N2O is an electrostatic interaction in nature. The subsequent reaction is the process of abstraction of oxygen rather than nitrogen, which can be explained from the perspective of the nature of the charge of natural population. We noted that the charge distribution on an oxygen atom and a nitrogen atom is
0.34 a.u and
0.07 a.u., respectively. Wherein charge distribution on an iridium atom is 1.27 au, electrostatic attractions between the iridium atom and the oxygen atom is much bigger than those of the nitrogen atom, which makes the oxygen atom approach the iridium atom easier. From 5IM2 to 5TS2
3, we found that the Ir atom and O atom electron population increased. It changed from1.24 a.u. to 1.41 a. u. on the Ir atom and from
0.48 a.u. to
0.55 a.u. on O atom. However, the electron population of the N atom decreased from 0.49 a.u. to 0.22 a.u. in the same process. The reason is attributed 11030

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Table 4. Free Energy of Species along with the Minimum Energy Pathway in the First Cycle species

IM1

TS1
2

IM2

TS2
3

T (Hartree)

—

I (Hartree)


363.9865


363.9371

—


363.9467

—


363.9780

—

IM3

IM4

TS4
5

IM5

—

—


367.8289

—


364.0567


367.8844

—


367.9008

IM4

TS4
5

IM5

Table 5. Free Energy of Species along with the Minimum Energy Pathway in the Second Cycle species

IM1

TS1
2

IM2

TS2
3

T (Hartree)

—

I (Hartree)


439.2365


439.1651

—


439.2020

—

—


443.0321

—

—


439.2241

—


439.2425


443.0572

—


443.1443

) )

to the CT from IrO+ to the N2O, which conforms to our analysis utilizing molecular orbital theory. The calculation results showed that 5IM2 needs to overcome a smaller barrier to 3TS2
3. Through the data we obtained from NBO5.0, we found (LP Ir f BD* O
N) that the strengths of these interactions are also estimated by second-order perturbation theory (ΔE(2) =
2 ^ σ*æ/εσ*
εLP). It is found that the interaction secondÆLP E order perturbation energies, ΔE(2), is 12.29 kcal/mol in the 3 TS2
3. Thus, this N
O bond is elongated and weakened. In the carbon monoxide oxidation process, in the order of CO f 5 IM4 f 5TS4
5, the natural electron configuration on the carbon atom is described as [core]2s(1.64)2p(1.83)3s(0.03) 3p(0.01)4d(0.01)f[core]2s(1.32)2p(2.16)3s(0.02)3p(0.02) 3d(0.01)f[core]2s(1.10)2p(2.28)3s(0.02)3p(0.03)3d(0.01). Furthermore, the natural electron configuration on the Ir atom is [core]6s(0.46)5d(7.13)6p(0.02)6d(0.01)f[core]6s(0.59)5d (7.06)6p(0.02)6d(0.01) during the course of 5IM4f5TS4
5. From the above data, it is clearly shown that the electrons on the s orbital of the carbon atom are decreasing, and the electrons on the p orbital are increasing. Electrons on the d orbital of the Ir atom have an extreme amount of reduction due to the feedback bond. 3.6. Kinetic Information Obtained from the Results of Calculations. The results from Table 4 were XTOF, TS1
2 = e12.05/RT/e12.05/RT + e15.94/RT + e4.40/RT, XTOF, TS2
3 = e15.94/RT/ e12.05/RT + e15.94/RT + e4.40/RT, XTOF, TS4
5 = e4.40/RT/e12.05/RT + e15.94/RT + e4.40/RT, XTOF, IM1 = e8.05/RT/e8.05/RT + e4.09/RT + e0.25/RT + e11.87/RT + e7.99/RT, XTOF,IM2 = e4.09/RT/e8.05/RT + e4.09/RT + e0.25/RT + e11.87/RT + e7.99/RT, XTOF,IM3 = e0.25/RT/ e8.05/RT + e4.09/RT + e0.25/RT + e11.87/RT + e7.99/RT, XTOF,IM4 = e11.87/RT/e8.05/RT + e4.09/RT + e0.25/RT + e11.87/RT + e7.99/RT, XTOF, IM5 = e7.99/RT/e8.05/RT + e4.09/RT + e0.25/RT + e11.87/RT + e7.99/RT when eqs 13 and 14 were applied. The results from Table 5 were XTOF, TS1
2 = e12.02/RT/e12.02/RT + e15.76/RT + e4.48/RT, XTOF, TS2
3 = e15.76/RT/e12.02/RT + e15.76/RT + e4.48/RT, XTOF, TS4
5 = e4.48/RT/e12.02/RT + e15.76/RT + e4.48/RT, XTOF, IM1 = e8.11/RT/e8.11/RT + e4.14/RT + e0.26/RT + e0.26/RT + e11.71/RT + e8.03/RT, XTOF,IM2 = e4.14/RT/e8.11/RT + e4.14/RT + e0.26/RT + e11.71/RT + e8.03/RT, XTOF,IM3 = e0.26/RT/e8.11/RT + e4.14/RT + e0.26/RT + e11.71/RT + e8.03/RT , X TOF,IM4 = e 11.71/RT /e 8.11/RT + e4.14/RT + e0.26/RT + e11.71/RT + e8.03/RT, XTOF,IM4 = e8.03/RT/ e8.11/RT + e4.14/RT + e0.26/RT + e11.71/RT + e8.03/RT. Surprisingly, TS2
3 as TDTS and IM4 as TDI were confirmed in both cycles, despite the fact that they have very different energy landscapes. From values of XTOF of other intermediate or transition states, we found that there are more states that determine the kinetics of the cycle. According to the second formula of eq 10, δE = 52.19 kcal/mol in the first cycle, and δE = 0.41 kcal/mol in the second cycle. Finally, TOF(IrO+)/ TOF(IrO2+) = 0.38 at 298 K.

IM3

4. CONCLUSION Reaction 1 catalyzed by IrOn+ (n = 1, 2) in the gas phase has been studied at the B3LYP/6-311++G (3df, 3pd) and CCSD(T) levels of theory. The conclusions of the present study can be summarized as follows: (1) The minimum energy reaction path found on the different PESs can be described as: 5 IrO+ + N2Of5IM1f5TS1
2f5IM2f3TS2
3f 1 IM3f1IrO2++N2 1 IrO 2 + +COf 1 IM4f 1 TS4
5f 5 IM5f 5 IrO + +CO 2 1 IrO 2 + +N 2 Of 1 IM1f 1 TS1
2f 1 IM2f 1 TS2
3f 1 IM3f 1 IrO 3 + +N 2 1 IrO 3 + +COf 3 IM4f 3 TS 4
5f 1 IM5f 1 IrO 2 + + CO 2 (2) The frontier orbital’s symmetry, matching or not, determines whether a reaction will occur and also has influence on the style of attacking. The cycle reactions catalyzed by IrO+ and IrO2+ have the same kinetic information. The mechanisms of reactions 2
5 are O-atom abstraction mechanisms. Reactions 2, 3, and 5 are typical TSR reactions. For the MECP1#, MECP3# and MECP4#, the computed SOC matrix elements are strong in these regions. The large value of the PISC pass shows that the ISC occurs with great probability. The reaction of IrO2+ with N2O is a “single-state reaction” due to the existence of a conjugated π orbital leading to a more stable system. (3) TDTS and TDI are TS2
3and IM4, respectively. δE (given in Gibbs energies) serves as the apparent activation energy of the cycle and is an approximation as a predictor. TOF(IrO+)/TOF(IrO2+) = 0.38 at 298 K. One transition state does not determine the kinetics of the cycle. The determining states are not necessarily the highest TS or the lowest intermediate; there are no rate-determining steps, but there are rate determining states. ’ ASSOCIATED CONTENT

bS

Supporting Information. The optimized geometries and detailed geometrical parameters, and total and relative energy of stationary points calculated with B3LYP and CCSD(T) methods on the three potential energy surfaces. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Fax: 86-0931-7971989. E-mail: [email protected]. 11031

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’ ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Grant 20873102). Additionally, we wish to thank Vickie Wen for her assistance in English writing. ’ REFERENCES (1) Wang, Y. C.; Wang, Q.; Geng, Z. Y.; Lv, L. L.; Wang, X. B.; Liu, H. W.; Wang, Q.; Cui, D. D. Chem. Phys. Lett. 2010, 498, 245– 252. (2) Kapteijn, F.; Rodiguez-Mirasol, J.; Moulijn, J. A. Appl. Catal., B 1996, 9, 25–64. (3) Bohme, D. K.; Schwarz, H. Angew. Chem., Int. Ed. 2005, 44, 2336–2354. (4) Danderkar, A.; Vannice, M. A. Appl. Catal., B 1999, 22, 179–200. (5) Blagojevic, V.; Jarvis, M. J. Y.; Flaim, E.; Koyanagi, G. K.; Lavrov, V. V.; Bohme, D. K. Angew. Chem., Int. Ed. 2003, 42, 4923–4927. (6) Blagojevic, V.; Orlova, G.; Bohme, D. K. J. Am. Chem. Soc. 2005, 127, 3545–3555. (7) Honma, K.; Nakamura, M.; Clemmer, D. E.; Koyano, I. J. Phys. Chem. 1994, 98, 13286–13293. (8) Ritter, D.; Carrol, J. J.; Weisshaar, J. C. J. Phys. Chem. 1992, 96, 10636–10645. (9) Campbell, M. L.; K€osch, E. J.; Hooper, K. L. J. Phys. Chem. A 2000, 104, 11147–11153. (10) Tishchenko, O.; Vinckier, C.; Ceulemans, A.; Nguyen, M. T. J. Phys. Chem. A 2005, 109, 6099–6103. (11) Bauschlicher, C. W.; Zhou, M.; Andrews, L.; Johnson, J. R. T.; Panas, I.; Snis, A.; Roos, B. O. J. Phys. Chem. A 1999, 103, 5463–5467. (12) Rodgers, M. T.; Walker, B.; Armentrout, P. B. Int. J. Mass Spectrosc. 1999, 182, 99–120. (13) Wang, Y. C.; Zhang, J. H.; Geng, Z. Y.; Chen, D. P.; Liu, Z. Y.; Yang, X. Y. Chem. Phys. Lett. 2007, 446, 8–13. (14) Zhang, J. H.; Wang, Y. C.; Geng, Z. Y.; Liu, H. W.; Chen, X. X. J. Mol. Struct. (THEOCHEM) 2008, 869, 89–93. (15) Lv, L. L.; Liu, X. W.; Wang, Y. C.; Wang, H. Q. J. Mol. Struct. (THEOCHEM) 2006, 774, 59–65. (16) Lavrov, V. V.; Blagojevic, V.; Koyanagi, G. K.; Orlova, G.; Bohme, D. K. J. Phys. Chem. A 2004, 108, 5610–5624. (17) Cheng, X.; Zhao, Y.; Tang, K.; Wang, J. J. Mol. Struct. (THEOCHEM) 2010, 945, 53–56. (18) Blagojevic, V.; Jarvis, M. J. Y.; Flaim, E.; Koyanagi, G. K.; Lavrov, V. V.; Bohme, D. K. Angew. Chem., Int. Ed. 2003, 42, 4923–4927. (19) Balaj, O. P.; Balteanu, I.; Rossteuscher, T. T. J.; Beyer, M. K.; Bondybey, V. E. Angew. Chem., Int. Ed. 2004, 43, 6519–6522. (20) Frisch, M. J. et al. GAUSSIAN 03, revision E.01; Gaussian Inc.: Pittsburgh, PA, 2003. (21) Becke, A. D. J. Chem. Phys. 1993, 98, 1372–1377. (22) Stephens, P. J.; Devlin, F. J.; Chablowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994, 98, 11623–11627. (23) Davidson, E. R. Chem. Rev. 2000, 100, 351–352. (24) Pavlov, M.; Siegbahn, P. E. M.; Sandstrom, M. J. Phys. Chem. A 1998, 102, 219–228. (25) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639– 5648. (26) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154– 2161. (27) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1990, 94, 5523– 5527. (28) Wang, Y. C.; Gao, L. G.; Geng, Z. Y.; Chen, X. X.; Lv, L. L.; Dai, G. L.; Wang, D. M. Acta. Phys. Chim. Sin. 2005, 63, 1489–1494. (29) Gao, L. G.; Wang, Y. C.; Geng, Z. Y.; Chen, X. X.; Lv, L. L.; Dai, G. L.; Wang, D. M. Acta. Phys. Chim. Sin. 2005, 21, 1102–1107. (30) Schr€oer, D.; Shaik, S.; Schwarz, H. Acc. Chem. Res. 2000, 33, 139–145. (31) Harvey, J. N.; Aschi, M.; Schwarz, H.; Koch, W. Theor. Chem. Acc. 1998, 99, 95–99.

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