Quantum-chemical calculations on the mechanisms of reactions of W and W+ with N2O

Chemical Physics Letters 470 (2009) 172–179

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Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett

Quantum-chemical calculations on the mechanisms of reactions of W and W+ with N2O Hsin-Tsung Chen a,*, Hui-Lung Chen b,*, Jee-Gong Chang a, Shin-Pon Ju c a

National Center for High-performance Computing, No. 28, Nan-Ke 3rd Rd., Hsin-Shi, Tainan 74147, Taiwan Department of Chemistry and Institute of Applied Chemistry, Chinese Culture University, Taipei 111, Taiwan c Department of Mechanical and Electro-Mechanical Engineering, Center for Nanoscience and Nanotechnology, National Sun-Yat-Sen University, Kaohsiung 804, Taiwan b

a r t i c l e

i n f o

Article history: Received 20 October 2008 In final form 16 January 2009 Available online 23 January 2009

a b s t r a c t The mechanisms of the reaction of W and W+ with the N2O were investigated at the CCSD(T)/[SDD+6311G(d)]//B3LYP/[SDD+6-31G(d)] level of theory. It was shown that the reaction of W(7S) + N2O(1R+) is a multi-state process, involves several lower-lying electronic   states of numerous intermediates and tranwith a negligible barrier and/or nitration, sition states, and leads to oxidation, WOð3 RÞ þ N2 1 Rþ g WN(4R) + NO(2P) with a barrier of 6.7 kcal/mol relative to reactants. The reaction of W+ with N2O, resemble its neutral analog, proceeds via the insertion and direct abstraction pathway, leads to oxidation and nitration of the W-center. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Reactions of transition metal systems with small nitrogen-containing molecules (such as NOx, N2, N2O, etc.) have attracted more attention due to designing novel and more efficient catalysts for important chemical processes, like the catalytic activation of the N–O bond, oxidation of transition metals, kinetics of corrosion, chemistry of the earth’s atmosphere and more. Such studies can provide vital information on the role of the nature of transition metals centers and their lower-lying electronic states in these reactions. In order to comprehend atomistic level of these reactions, the computational approaches along with gas-phase experiments have proved to be very useful [1–9]. In the literature, the interaction of N2O with alkaline-earth [10–13] and all 3d TMs [14–32] have been extensively studied using both theoretical and experimental methods. Three different mechanisms have been proposed to explain these observations. They are (i) the direct abstraction mechanism [14–16]: an oxygen atom is abstracted from the oxidant and metal oxide is formed, (ii) the insertion (electron transfer) mechanism [16,17,33]: an electron transfer from the metal to the N2O, (iii) the resonance interaction model [34–36]: the Arrhenius parameters and rate constants are evaluated by taking account of the ionization potential, the s–p excitation energies of the metal atoms, the electron affinity of N2O, and the bond energy in the MeO molecule in this model. It has been shown that the resonance interaction model performs well for alkali and alkaline-earth metals [34], but does not work * Corresponding authors. Fax: +886 2 28614212 (H.-L. Chen). E-mail addresses: [email protected] (H.-T. Chen), [email protected] (H.-L. Chen). 0009-2614/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2009.01.048

successfully for TM atoms [32] due to the neglect of the d electrons and electronic structures in the model. However, to our knowledge, theoretical studies on the reactions of W and W+ with N2O have not been investigated before. Since W and W+ chemistry involves several low-lying electronic states, we are including singlet, triplet, quintet and septet state surfaces for the reactions of W with N2O, and doublet, quartet, and sextet state surfaces in the case of W+. Such studies are very important and will provide vital information on the role of lower-lying electronic states of W atom and W+ cation for the understanding and explaining chemical reactivities and reaction mechanisms. 2. Computational procedures The geometries of reactants, intermediates, transition states and products of the reactions W/W+ + N2O in several low-lying electronic states of W and W+, as well as the potential energy surfaces (PESs) of these reactions were calculated at the B3LYP density functional level [37–41] using the GAUSSIAN03 program package [42]. In these calculations we used the Stuttgart/Dresden relativistic effective core potential (ECP) [43–45] and associated double-f SDD basis set for W/W+, and 6-31G(d) basis set for main group elements, expressed as B3LYP/[SDD+6-31G(d)]. The nature of all stationary points was confirmed by performing normal mode analysis and the calculated transition states were verified by the intrinsic reaction coordinate (IRC) approach. It has been demonstrated that B3LYP method with double-f plus polarization basis sets provides an excellent agreement with experiments for geometries of transition metal systems [46]. However, B3LYP-calculated energies could be off their most accurate values by several kcal/mol. In order to obtain more reliable values of energies, we carried out

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H.-T. Chen et al. / Chemical Physics Letters 470 (2009) 172–179

Table 1 The B3LYP and CCSD(T) calculated relative energies (in kcal/mol, relative to the ground-state reactants) of the intermediates, transition states and products of the reactions M(W/ W+) + N2O for several low-lying electronic states. Species

M + NO

State

B3LYP DE + ZPE

CCSD(T) DE + ZPE

1

68.31 37.58 5.21 0.00 55.47 40.27 7.02 1.30 54.83 39.40 8.34 10.43 92.50 111.85 94.09 28.56 3.92 15.28 16.40 7.23 9.10 4.33 – – 13.27 19.39 6.90 – 7.41 24.45 58.76 54.20 68.80 46.59 7.45 – 107.49 112.83 113.49 56.63 93.74 113.01 95.30 29.66 15.67 26.10 44.46 76.14

71.47 45.08 4.61 0.00 63.24 27.90 3.41 0.28 64.06 8.57 7.98 16.13 98.29 121.62 99.83 35.42 8.84 12.58 4.66 2.28 14.68 2.98 – – 3.94 10.32 2.22 – 6.68 37.13 66.04 40.70 57.15 37.74 1.16 – 106.24 102.24 110.33 52.85 97.31 120.64 98.74 34.44 19.17 21.69 57.82 75.88

S P 5 D 7 S 1 0 A 3 00 A 5 0 A 7 0 A 1 0 A 3 00 A 5 0 A 7 0 A 1 A 3 A 5 A 7 A 1 0 A 3 00 A 5 0 A 7 0 A 1 A 3 00 A – – 3 00 A 5 0 A 7 0 A – 3 0 A 5 0 A 7 0 A 1 0 A 3 0 A 5 0 A 7 0 A – 1 0 A 3 00 A 5 0 A 7 0 A 3

M(g1-ONN)

TSO

MO  N2

M(g1-NNO)

TSN M(g2-ONN) M(g2-NNO)

TSNN

NM(g1-NO)

TSNO OM(g1-NN)

MO + N2

R+ R+ 5 + R 7 + R 2 R 4 R 6 R 8 R

1

3

MN + NO

W+

W 2

S

State

B3LYP DE + ZPE

CCSD(T) DE + ZPE

49.05 36.47 0.00

47.00 27.61 0.00

2

2.16 6.19 12 0.00 2.00 6.19 12.00 0.00 2.03 6.07 12.01 0.00 2.05 6.02 12.00 0.00 2.09 6.18 12.03 0.00 2.00 – – 2.09 6.04 12.02 – 2.14 6.20 12.32 0.00 2.02 6.03 12.01 – 0.00 2.04 6.02 12.02 0.00 2.05 6.02 12.00 0.76 3.81 8.78 15.75

P F 6 D – 2 00 A 4 00 A 6 0 A – 2 00 A 4 00 A 6 00 A – 2 A 4 A 6 00 A – 2 00 A 4 00 A 6 0 A – 2 A – 6 0 A 2 00 A 4 00 A – – 2 0 A 4 A 6 0 A – 2 0 A 4 00 A 6 0 A – 6 0 A 2 00 A 4 00 A 6 0 A – 4

2

R+ R+ 6 + R 4

– 1

R R 5 R 3

–

–

– 14.35 0.20 28.26

– 17.12 4.13 2.72 – 77.72 113.28 37.97 – 3.27 9.81 38.96 – 20.28 – 16.57 2.66 23.12 – – 15.42 11.96 42.55 – 64.02 54.72 5.52 – 15.99 116.09 129.56 52.69 – 78.89 114.47 22.75 – 31.71 7.84 30.64 –

2.59 4.34 26.78 – 15.81 6.21 4.93 – 112.77 116.78 39.90 – 57.24 1.13 30.82 – 4.09 – 4.44 11.73 10.75 – – 24.02 1.64 57.64 – 51.11 42.48 18.68 – 5.11 124.94 130.91 47.07 – 88.94 115.92 22.88 – 6.53 4.71 35.56 –

S2 0.89 3.82 8.75 – 1.76 3.76 8.75 – 1.73 3.83 8.76 – 0.76 3.75 8.76 – 1.76 3.77 8.77 – 1.67 – 8.78 0.77 3.80 – – 2.28 3.85 8.87 – 0.80 3.78 8.76 – 8.78 1.75 3.78 8.76 – 0.76 3.78 8.75 – 0.00 2.03 6.02 –

The S2 values of NO and N2 are 0.75 and 0.00, respectively.

the single point CCSD(T) calculations to improve the energy of the calculated structures at their B3LYP-optimized geometries. In the CCSD(T) calculations we extended the basis sets for main group elements from 6-31G(d) to 6-311G(d). Unscaled zero-point energy corrections (ZPC) estimated at the B3LYP level added to the final CCSD(T) energetics. The single determinant nature of wavefunction of all calculated structures was confirmed by performing T1 diagnostics (the T1 parameter for all structures is calculated to be within 0.02–0.06). We also checked the hS2i values to evaluate the spin contamination in these calculations. As shown from Table 1, in general, spin contamination in these calculations is not significant. As it will be discussed below, the PESs of several lower-lying electronic states of the studied reactions cross many times upon completion. Search for the exact location of seam of crossing of these PESs would require the use of computationally much more demanding methods and inclusion of the spin–orbit-coupling

(SOC) effect in the calculations. Because of technical limitations, in this Letter, we did not perform SOC calculations and did not search for the seam of crossing of PESs of the lower-lying electronic states of the studied reactions, simply following the previous computational methodology [9]. 3. Results and discussion The ground electronic state of the W atom is calculated to be a septet 7S state which is associated with the s1d5 electronic configuration, while the quintet 5D(s2d4) state is slightly, 4.6 kcal/mol, higher in energy at the CCSD(T) level of theory, which does not agree with the result of Campbell-Miller and Simard, who have reported the 5D ground electronic state for W atom [47]. This discrepancy may be due to the result of lack the comprehensive spin–orbit interaction in the calculations. However, our calculated

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H.-T. Chen et al. / Chemical Physics Letters 470 (2009) 172–179

value agrees well with its reported experimental value of 4.3 kcal/ mol [47]. The triplet 3P(s2d4) and singlet 1S(s2d4) states of W are calculated to be 45.1 and 71.5 kcal/mol higher in energy than the ground-state, respectively, at the CCSD(T)/[SDD+6-311G(d)] level of theory. For W+ atom, the ground electronic state is the sextet 6 D(s1d4) state: its quartet 4F(s1d4) and doublet 2P(s1d4) states are 27.6 and 47.0 kcal/mol higher in energies, which are in reasonable agreement with experimental values (24.9 and 55.5 kcal/mol, respectively) [48]. The ionization energy of W is calculated to be 171.0 kcal/mol, which is also in reasonable agreement with the experimental value of 181.344 ± 0.002 kcal/mol [47]. In addition, we compared the available experimental data  on the heats of the

reactions W 7 S þ N2 Oð1 Rþ Þ ! WO 3 R þ N2 1 Rþ g . The calculated value of 120.6 kcal/mol is quite well in agreement with the experimental value of 121.4 kcal/mol reported by Harter et al. [49]. In the next section, we present potential energy surfaces (PESs) of the reaction of N2O with the 7S, 5D, 3P and 1S spin states of the W atom, while the reaction of W+ + N2O is investigated for the 6D, 4F, and 2P states of W+. The calculated structures of intermediates, transition states and products of the reaction W + N2O are shown in Fig. 1, while their relative energetics are presented in Fig. 2. Those for the reaction W+ + N2O are depicted in Figs. 3 and 4, respectively. The calculated relative energies and hS2i values of

137.1 133.2 112.4 112.5

123.6 105.3 112.2 116.5

2.316 3.570 3.479 3.312

1.216 1.196 1.196 1.196

2.132 2.241 2.201 2.267

1.128 1.133 1.133 1.133

1.232 1.221 1.239 1.249

W( 1-ONN) 1

5

3

1.155 1.149

3.302 3.304 3.252 3.300

1.956 2.027 2.863 1.214 1.227 1.222 134.8 136.3 136.7

1.747 1.771 1.917 2.147 2

3

5

A/ A/ A/ A

1

A'/3A''/5A'/7A'

102.5 101.7 113.0 180.0

3

A'/5A'/7A'

1

178.6 178.5 178.1 136.1

1.138 1.141 1.133 1.130

WNN 1

1.194 1.193 1.199 1.193

NW( 1-NO)

TSNN

1.908 1.914 1.970 2.267

1.820 1.850 2.067 2.002

1.677 1.685 1.677 1.788

1.202 1.180 1.205

1.566 1.922 1.923

1.195 1.197 1.233 1.226

1.400 1.394 1.289 1.215

W( 1-NNO)

7

1.888 1.845 1.858

1.195 1.208 1.215 1.216

WNO 4 6 / A''/8A'' A''/ g

1.724 1.732 1.813 2.028

WO---N2 1

1.823 2.033 2.819

180.0 180.0 137.0 121.2

1.133 1.127 1.135 1.136

114.6 114.8 122.5 142.8

3.303 3.304 3.252 3.249 1.105 1.105 1.105 1.105

7

A''/5A'/7A'

OW( -NN) A'/3A''/5A'/7A'

5

3

A'/3A''

1

1.670 1.674 1.728 2.022

W( 2-NNO)

1

105.2 119.6 139.8 177.7 1

1.954 2.028 2.028

1.304 1.265 1.231

TSN

1.977 2.076 2.114 2.046

As seen in Fig. 2, this reaction may proceed via two different pathways, called the direct abstraction and insertion pathways. The first step of both pathways is coordination of N2O to W. The resulting W(N2O) complex may have several isomers, W(g1ONN), W(g1-NNO), W(g2-ONN), and W(g2-NNO), presented in Chart 1. We are not able to locate the W(g2-ONN), which is expected to possess W+d–(N2O)d electronic structure with a bent N2O molecule. Calculations show that the W(g1-ONN), which has triplet 3A00 electronic ground-state is energetically the most favorable isomer, which lies 27.9 kcal/mol lower than the W(7S) + N2O(1R+) groundstate reactants. The energies for the 5A0 quintet and 7A0 septet states of W(g1-ONN) isomer are found to be 3.4 and 0.3 kcal/ mol, respectively, with respect to the ground-state reactants. Its 1 0 A singlet state is much higher in energy. The most stable electronic state of the of W(g1-NNO) is also the triplet state, which lies 12.6 kcal/mol lower than W(7S) + N2O(1R+) ground-state reactants, but is 15.3 kcal/mol higher than that of the ground-state W(g1ONN) isomer. Its singlet 1A0 , quintet 5A0 and septet 7A0 states are

A'/ A''/ A'/ A'

1.713 1.923

1.685 1.698 1.728 2.025

3

1

A'/ A''/ A'/ A'

1.710 1.686

167.9 174.0 169.5 157.0

3.1. Mechanisms for the reaction of W with N2O

TSO

7

114.2 112.2

1.134 1.130 1.127 1.154

the reactants, intermediates, transition states and products of the reactions W/W+ + N2O are given in Table 1.

A'/3A'/5A'/7A'

1.670 1.674 1.728 2.018

1.666 1.674 1.866 2.179

WO

WN

1 +3 +5 +7 +

/

/

/

2

/4 / 6 / 8

A'/3A'/5A'/7A'

Fig. 1. Optimized geometry of major intermediates, transition states and products of the reaction of W with the N2O molecule. Bond lengths are given in Å and angles in degrees.

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H.-T. Chen et al. / Chemical Physics Letters 470 (2009) 172–179

75.9

80.0

75.9

71.5 (1S)

66.0

70.0

64.1

63.2

60.0

57.8

50.0

37.1

57.8

(3P) 45.0

40.0 30.0 20.0

6.7 -1.2

10.0

4.6

3.9 2.2 -10.3

-19.2

(5D)

0.0 7 ( S)

-10.0

3.4

16.1 8.6 8.0

14.7 8.8 2.3

-0.3

-12.6

-20.0

-21.7 -34.4

-30.0

-37.7

3.0

-4.7

-35.4

-27.9

-19.2 -34.4

-21.7

-40.0

-40.7

-52.6

-50.0 -60.0

-57.2

-70.0 -80.0

-97.3 -98.7

-90.0

-102.2 -106.2

-120.6

-98.3 -110.0

-110.3 -120.0

WN + NO WO +N2 NW( 1-NO) TSNN W( 2-NNO) OW( 1-NN)

Insertion pathway

-97.3

-100.0

W( 1-ONN) W+N2O

TSO

-99.8

-98.7

-121.7

-120.6

WO----NN W( 1-NNO)

TSN WO +N2

WN + NO

Abstraction pathway

Fig. 2. The calculated potential energy surfaces for oxidation and nitration of W by N2O on several low-lying electronic states of the reactants. The relative energy is in kcal/ mol.

higher in energy by 7.9, 14.9 and 21.4 kcal/mol, respectively. This isomer is found to have a bent-fragment with a \NNO angle of 114.6–142.8° (in the ‘free’ N2O anion the \NNO angle is calculated to be 132.9°), which indicates that this structure belongs to W+–(N2O) complex. The calculated Mulliken charges and spin densities are corresponding to this assessment: about 0.33, 0.34, 0.49 and 0.39 |e| transfers from W center to the N2O fragment for singlet, triplet, quintet and septet electronic states of W(g1ONN), respectively. The W(g2-NNO) having ground quintet electronic state, is 10.3 kcal/mol lower than the ground reactants. It is noticeable that we are not able to locate the singlet state after extensive search. Triplet and septet states of W(g2-NNO) are nearly degenerate with 14.2 and 12.5 kcal/mol higher than its quintet state. It is found that about 0.46, 0.52 and 0.38 |e| transfers from W center to the N2O fragment and the \NNO angles are 134.8, 136.3 and 136.7° for triplet, quintet and septet electronic states of W(g2-NNO), respectively. According to the electronic structure, the W(g2-NNO) could be a W+d–(N2O)d complex. Although we have calculated reaction pathways starting from all the located isomers of W(N2O), below we limit our discussions mainly to the lower energy pathways. As mentioned above, the reaction may proceed via two different pathways: (a) direct abstraction, and (b) insertion mechanisms. (a) The direct abstraction mechanism. From the ground-state reactants, the direct abstraction reaction may proceed via two different channels: (1) oxidation of the W-center and formation of WO + N2 products, (2) nitration of the W-center and formation of WN + NO products. As shown in Fig. 2, the oxidation pathway leading to the WO + N2 products is energetically the most favorable channel, and has an 8.0 kcal/mol

barrier at the transition state TSO. At TSO, the activated N–O bond distances of singlet, triplet, quintet and septet states are 1.232, 1.221, 1.239 and 1.249 Å, respectively, which are slightly longer than that in N2O molecule (1.193 Å), indicating that it is an earlier transition state. The overall oxidation reaction (ground-state to ground-state) of W atom by N2O is W(7S) + N2O(1R+) ? W(g1-ONN)(3A0 0 ) ? WO  N2 complex ð3 AÞ ! WOð3 RÞ þ N2 ð1 Rþ g Þ, which is calculated to be highly exothermic by 120.6 kcal/mol. It is noticed that the WO  N2 complex is slightly lower (about 1.0 kcal/mol) than the products, indicating that the N2 and WO parts of the final complex are only weakly perturbed by the complex formation. The nitration pathway (ground-state to ground-state) leading to WN + NO formation via the process of W(7S) + N2O(1R+) ? W(g1-NNO)(3A0 0 ) ? WN(4R) + NO(2P) is calculated to be exothermic by 21.7 kcal/mol and needs to overcome a 3.0 kcal/mol barrier at the transition state TSN. In addition, another possible channels forming WON + N and WNN + O products by the N- and O-elimination from the W(g1-ONN)(3A00 ) and W(g1-NNO)(3A00 ) complexes were considered. These pathways are unlikely and can be neglected due to the highly endothermic (94.0 and 31.9 kcal/ mol, respectively, which are calculated from the groundstate products and reactants). (b) The insertion mechanism. As seen in Fig. 2, two different channels were considered: (1) the W metal insert into the N–N bond of N2O molecule and formation of NW(g1-NO) intermediate, (2) the metal insert into the N–O bond leading to OW(g1-NN) intermediate. The N–N bond insertion pathway starts from W(g2-NNO) intermediate. The W(g2NNO)(5A0 ) complex can rearrange to the energetically

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128.2 127.3 130.4

2.108 2.101 2.151

107.3 120.6 143.2

1.984 2.016 2.058

1.236 1.237 1.230

1.126 1.120 1.134

1.294 1.267 1.323

1.120 1.120 1.121

2

A''/4A''/6A'

1.114 2.434

1.962 1.995

A''

2

2

2.087 1.153

6

A'

TSNO

180.0 180.0 180.0

1.767 1.778 1.827

1.115 1.165 1.168 +

WNO 5 3 g / g/

2.249 2.332 2.091

1.546

W( 2-ONN)+

1 g

6

2

1.666 1.654 1.779

1.657 1.659 1.918

WN+

WO+

/3 /5

A'/4A''/6A' 177.9 178.1 177.6

1.109 1.107 1.115

2.015 1.977 2.044

OW( 1-NN)+ A'

1.147 1.158 1.162

90.9 99.9 137.4

2

A'/4A/6A'

128.4 134.4 130.3

1.173

1.875 2.016 2.022

NW( 1-NO)+

TSNN+

1.673 1.674 1.941

136.2

1.677 1.662 1.777

1.120 1.631 1.799

2.117

1.372

A''/4A''/6A'

1.174 1.166 1.168

A''/4A''

2.000

2

2.465 2.031 1.861

W( 2-NNO)+

1.173 1.168 1.171

W( 1-NNO)+

A/4A/6A''

2.005 1.789 2.194

1.353 135.4 1.330 135.2

TSN+

2.025

2

180.0 180.0 179.9

1.146 1.146 1.145

1.983 1.988 2.024

WO+---N2

1.183 1.189

1.665

1

1.105 1.105 1.105

A''/4A''/6A''

1.872 1.900

176.8 176.8 179.9

3.281 3.298 2.417

160.3 168.0 153.0

120.3

2

3.288 3.303 3.369

TSO+

W( 1-ONN)+ 2

1.657 1.659 1.896

A''/4A''/6A'

WNN

1.118 1.124 1.116 +

2

A'/4A'/ 6A'

2 +4 +6 +

/

/

Fig. 3. Optimized geometry of major intermediates, transition states and products of the reaction of W+ with the N2O molecule. Bond lengths are given in Å and angles in degrees.

favorable intermediate NW(g1-NO)(3A0 ) with 6.7 kcal/mol barrier at the transition state TSNN or by crossing the singlet and septet PESs. Then the NO-elimination from NW(g1NO)(3A0 ) proceeds and forms the WN(4R) + NO(2P) products. The entire reaction process (ground-state to ground-state), W(7S) + N2O(1R+) ? W(g2-NNO)(5A)0 ? NW(g1-NO)(3A0 ) ? WN(4R) + NO(2P), is calculated to be exothermic by 21.7 kcal/mol. As shown in Fig. 2, the N–O bond insertion takes place without any energy barrier producing OW(g1-NN) intermediate at each electronic state. In order to confirm this channel, we place W atom at a distance of 2.0 Å from both the O and N atoms of the N–O bond and lengthen the N–O bond from 1.2 to 3.9 Å for each increment of

0.1 Å to calculate the relative energies at B3LYP/[SDD+6-31G(d)] level of theory. The results were depicted in Fig. 5. In all electronic states, the geometry optimizations yielded smooth curves and no energy barrier. Although we can not find a transition state for N– O bond insertion reaction, we cannot exclude the possibility that there is a barrier on these curves. Its energy barrier should be less than 4.6 kcal/mol required for a quintet-septet seam of crossing. We also tracked the Mulliken charge change of the N–O bond insertion, it was clearly shown that about 0.36, 0.31, 0.55 and 0.19 e transfers from W center to the N2O fragment for singlet, triplet, quintet and septet electronic states during the insertion, respectively. The ground electronic state of the energetically most favorable OW(g1-NN) isomer is the quintet (5A0 ) state, which lies 110.3 kcal/mol lower than the ground-state reactants. The final

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80.0 70.0 60.0 50.0 47.0 2P

57.6

35.6 4F

24.0

18.7

35.6

20.0 10.0

11.7

6.5

4.3

15.8 6.2

-4.4 0.0 -10.0

2.6

-4.9

-20.0

-26.8

6D

1.6

-4.7

40.0 27.6 30.0

-5.1 -10.8

-22.9

4.1 6.5 -4.7 -1.1 -22.9

-30.0 -42.5

-30.8

-40.0

-47.1

-39.9

-50.0

-51.1

-57.2

-60.0 -70.0 -80.0

-88.9

-88.9

-112.8

-90.0 -100.0

-115.9 -124.9

-115.9

-116.8

-110.0 -120.0 -130.0 -130.9 WN+ + NO NW( 1-NO)+ WO+ +N2

OW( 1-NN)+

W(

2-ONN)+

W++N

W( 2-NNO)+

TSNN+

Insertion pathway

TSNO+

W( 1-ONN)+ TSO+ WO+----NN WO+ +N2 W( 1-NNO)+ TSN+ WN+ + NO 2O

Abstraction pathway

Fig. 4. The calculated potential energy surfaces for oxidation and nitration of W+ by N2O on several low-lying electronic states of the reactants. The relative energy is in kcal/ mol.

M M

M

M O O

N 1

N

M( -ONN)

N

N

M( 1-NNO)

N

N

O 2

M( -ONN)

N O

N 2

M( -NNO)

Chart 1. Possible isomers of the M(N2O) complex.

stage of the reaction is the N2-ligand dissociation leading to the WO + N2 products. The overall ‘ground-state to ground-state’ 7 1 þ 1 5 0 insertion reaction   is Wð SÞ þ N2 Oð R Þ ! OWðg -NNÞð A Þ ! 1 þ 3 WOð RÞ þ N2 Rg . Another possible channels forming WNO + N and WNN + O products by the N- and O-elimination from the NW(g1-NO)(3A0 ) and OW(g1-NN)(5A0 ) complexes were also considered. These pathways are unlikely and can be neglected due to the highly endothermic (49.1 and 31.9 kcal/mol, respectively, which are calculated from the ground-state products and reactants). In summary, the above presented data clearly show that in the gas-phase the reaction W(7S) + N2O(1R+) proceeds with no (or small) barrier required for the N–O bond activation and leads to OW(g1-NN) intermediate. Thus, in the gas-phase the oxidation process of W with N2O via N–O bond insertion mechanism, Wð7 SÞ þ N2 Oð1 Rþ Þ ! OWðg1 -NNÞð5 A0 Þ ! WOð3 RÞ þ N2 ð1 Rgþ Þ is the energetically and kinetically most favorable process and involves several lower-lying electronic states of the reactants and intermediates. However, we also show the reaction pathway of the nitration is followed by N–N bond insertion mechanism, W(7S) + N2O(1R+) ? (see W(g2-NNO)(5A0 ) ? NW(g1-NO)(3A0 ) ? WN(4R) + NO(2P)

Fig. 2). Our calculations show that the W nitration by N2O is 21.7 kcal/mol exothermic, which is much smaller than that of oxidation, 120.6 kcal/mol. The most stable intermediates on the PES of the reaction W(7S) + NO2(2A1) are WO  N2(3A), OW(g1-NN) 5 0 A ), and NW(g2-NO)(3A0 ), which lie 121.6, 110.3, and 57.2 kcal/ mol lower than ground-state reactants. Incidentally, we also compare the potential-energy surfaces with that of the relevant study by Michelini et al. [50] in which they concluded that the major pathway of Mo + N2O is to form the product of MoO + N2. Similar to our calculated result, they demonstrated that the septet state plays an important role along the whole of pathway. In their study, however, the energetic and topological evolution of the Mo–N2O interaction showed that the N2 formation does not occur easily since the spin-forbidden states could be considered as a major constraint. 3.2. Mechanisms of the reaction of W+ with N2O Similarly, the first intermediate for the W+ with N2O reaction is found to be W(N2O)+ complex. In contrast to the neutral complex, where the most stable isomer has a W(g1-ONN) structure, for the

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and W(g1-NNO)+(2A0 0 ) complexes are unlikely and can be neglected due to the highly endothermic (110.9 and 58.1 kcal/mol, respectively, with respect to the W(g1ONN)+ 6A0 ) and W(g1-NNO)+(2A00 ).

60 singlet

40

triplet quintet

20

(b) The insertion mechanism. As seen in Fig. 4, two different pathways were considered, similar to the neutral W + N2O reaction. The N–N bond insertion pathway starts from W(g2-NNO)+(4A00 ) intermediate; then it can rearrange to the energetically intermediate NW(g1-NO)+(2A0 ) with 4 1.6 kcal/mol barrier at the transition state TSþ NN ( A). The 1 + 2 0 NO-elimination from NW(g -NO) ( A ) proceeds and forms WN+(4R+) + NO(2P) products. The entire reaction ‘groundstate to ground-state’ process W+(6D) + N2O(1R+) ? W(g2is NNO)+(4A00 ) ? NW(g1-NO)+(2A0 ) ? WN+(4R+) + NO(2P) calculated to be slightly exothermic by 4.7 kcal/mol.

Relative energy (kcal/mol)

septet 0 -20 -40 -60 -80 -100 -120 -140 1

1.5

2

2.5

3

3.5

4

4.5

Distance of N-O (A) Fig. 5. Reaction energy curve for W + N2O reaction on several low-lying electronic states of the reactants.

cationic complex the energetically most stable isomer is found to be a W(g1-NNO)+ structure. The neutral complex W(g1-NNO) belongs to W+d–(N2O)d complex, while the cationic complex W(g1-NNO)+ is a linear W–(N2O) complex. The difference in energies of the W(g1-NNO) and W(g1-NNO)+ complexes may be due to different electronic structures. The ground electronic state of the W(g1-NNO)+ and W(g1-ONN)+ complexes are found to be the doublet (2A00 ) and sextet (6A0 ) states, which are 57.2 and 26.8 kcal/mol below the ground-state reactants W+(6D) + N2O(1R+), respectively. The other two isomers: W(g2-NNO)+ and W(g2-ONN)+ (see Fig. 4) belong to W+d–(N2O)d complex. In the sextet state of the W(g2ONN)+ and the doublet and quartet states of the W(g2-NNO)+, it is found that the structures are not stable. The ground states of both isomers are calculated to be sextet 6A0 -state and quartet 4 00 A -state, respectively, which lie 4.4 and 10.8 kcal/mol lower than ground-state reactants. As seen as Fig. 4, the reaction of W+ + N2O, in general, may proceed via two different ways: (a) direct abstraction, and (b) insertion mechanisms. (a) The direct abstraction mechanism. W+(6D) + N2O(1R+) may proceed via two different channels, similar to the neutral W + N2O reaction discussed above. The first of them is an oxidation pathway leading to the WO+ + N2 products, via W(g1-ONN)+ intermediate, then passing a transition state þ TSþ O . At TSO , the activated N–O bond distances of doublet, quartet and sextet states are 1.294, 1.267 and 1.323 Å, respectively, which are slightly longer than that in N2O molecule (1.193 Å), indicating that it is an earlier TS. The overall ‘ground-state to ground-state’ oxidation reaction of W+ atom by N2O is W+(6D) + N2O(1R+) ? W(g1-ONN)+(6A0 ) ? WO+   N2 complex ð4 AÞ ! WOþ ð4 Rþ Þ þ N2 ð1 Rþ g Þ, which is a barrierless process with highly exothermic by 115.9 kcal/mol. The second is a nitration pathway, leading to the WN+ + NO formation, via the process of W+(6D) + N2O(1R+) ? W(g1NNO)+(2A00 ) ? WN+(4R+) + NO(2P), which is calculated to be only exothermic by 4.7 kcal/mol and needs to overcome a 4.1 kcal/mol barrier at the transition state TSþ N . Another possible channels forming WON+ + N and WNN+ + O products by the N- and O-elimination from the W(g1-ONN)+(6A0 )

In contrast to neutral W + N2O reaction, the N–O bond insertion takes place from the W(g2-ONN)+(6A0 ) isomer via the N–O bond activation transition state TSNO(6A0 ), leading to the formation of the OW(g1-NN)+(4A00 ). The calculated barrier is very small around 0.7 kcal/mol, and the ground electronic state of the energetically most favorable OW(g1-NN)+ isomer is the quartet (4A0 0 ) state, which lies 130.9 kcal/mol lower than the ground-state reactants. The final stage of the reaction is the N2-ligand dissociation leading to the WO+ + N2 produces. The overall ‘ground-state to groundstate’ insertion reaction is Wþ ð6 DÞ þ N2 Oð1 Rþ Þ ! Wðg2 -ONNÞþ  


6 0 A ! OWðg1 -NNÞþ 4 A00 ! WOþ 4 Rþ þ N2 1 Rþ g , which is calculated to be highly exothermic by 115.9 kcal/mol. Another possible channels forming WNO+ + N and WNN+ + O products by the N- and O-elimination from the NW(g1-NO)+(2A0 ) and OW(g1-NN)+(4A00 ) complexes are found to be highly endo- thermic, 100.8 and 132.8 kcal/mol, with respect to the NW(g1-NO)+(2A0 ) and OW(g1-NN)+(4A00 ), respectively. Therefore, these pathways are unlikely to compete with the oxidation process. In summary, our above presented finding show that the oxidation of W+(6D) + N2O(1R+) reaction can proceed via both N–O bond insertion and oxygen abstraction mechanisms which are the energetically more accessible and feasible (barrierless) pathways. However, the reaction pathway of the nitration followed by N–N bond insertion (see Fig. 4) is only 4.7 kcal/mol exothermic, which is much smaller than that of oxidation, 115.9 kcal/mol and requires a small barrier (1.6 kcal/mol).

4. Conclusions From the above presented discussion we draw the following conclusions: (1) The oxidation reaction W(7S) + N2O(1R+) could proceed via two distinct mechanisms: direct abstraction and insertion. The calculations reveal that the insertion mechanism governed by electron transfer is dominant in the oxidation reaction. At the beginning, this reaction requires less than 4.6 kcal/mol energy for W(7S ? 5D) promotion (or for septet-to-quitet potential energy crossing). The oxidation reaction Wð7 SÞ þ N2 Oð1 Rþ Þ ! WOð3 RÞ þ N2 ð1 Rþ g Þ is calculated to be 120.6 kcal/mol exothermic. However, we cannot completely exclude the nitration pathway leading to WN(4R+) + NO(2P). It starts from the W(g2-NNO)(5A0 ) intermediate, requiring ca 6.7 kcal/mol energy barrier by the insertion mechanism or from W(g1-NNO)(3A00 ) intermediate, requiring ca 3.0 kcal/mol energy barrier by the direct abstraction mechanism, which is 98.9 kcal/mol less

H.-T. Chen et al. / Chemical Physics Letters 470 (2009) 172–179

exothermic than oxidation process; nevertheless it could be feasible in gas-phase due to low energy barrier. (2) The oxidation reaction of W+ with N2O may proceed via both insertion and direct abstraction mechanisms due to low þ transition states ðTSþ NO and TSO Þ, below the reactants. One may expect that the oxidation of W+ by N2O is a barrierless process in the gas-phase and is highly exothermic by 115.9 kcal/mol. However, the nitration of W+ by N2O is only 4.7 kcal/mol exothermic and it is an energetically less favorable pathway.

Acknowledgements We are grateful to (1) National Science Council, Republic of China, under Grant Number NSC-096-2628-E-110-005-MY2, NSC 96-2221-E-492-008 and NSC 97-2113-M-492-001-MY2 for the financial support, (2) the financial support provided to this study by the Department of Chemistry and Institute of Applied Chemistry, Chinese Culture University, and (3) National Center for Highperformance Computing, Taiwan, for the computer time and facilities. References [1] M.C. Michelini, N. Russo, E. Sicilia, J. Phys. Chem. A 106 (2002) 8937. [2] E. Sicilia, N. Russo, J. Am. Chem. Soc. 124 (2002) 1471. [3] M.C. Michelini, E. Sicilia, N. Russo, M.E. Alikhani, B. Silvi, J. Phys. Chem. A 107 (2003) 4862. [4] M.C. Michelini, N. Russo, E. Sicilia, Inorg. Chem. 43 (2004) 4944. [5] S. Chiodo, O. Kondakova, M.C. Michelini, N. Russo, E. Sicilia, A. Irigoras, J.M. Ugalde, J. Phys. Chem. A 108 (2004) 1069. [6] J.E. Bushnell, P.R. Kemper, P. Maitre, M.T. Bowers, J. Am. Chem. Soc. 116 (1994) 9710. [7] D. Schroder, H. Schwarz, Angew. Chem. Int. Ed. English 34 (1995) 1973. [8] Y.M. Chen, P.B. Armentrout, J. Phys. Chem. 99 (1995) 10775. [9] H.T. Chen, D.G. Musaev, S. Irle, M.C. Lin, J. Phys. Chem. A 111 (2007) 982. [10] C. Naulin, M. Costes, Z. Moudden, G. Dorthe, J. Phys. Chem. 95 (1991) 8244. [11] J.M.C. Plane, C.F. Nien, J. Phys. Chem. 94 (1990) 5255.

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