Theoretical study on the reaction of W+ with CO2 in the gas phase

Journal of Molecular Structure: THEOCHEM 807 (2007) 49–54 www.elsevier.com/locate/theochem

Theoretical study on the reaction of W+ with CO2 in the gas phase Xiao-Yan Yang a, Yong-Cheng Wang a

a,*

, Zhi-Yuan Geng a, Ze-Yu Liu a, Han-Qin Wang

b

Gansu Key Laboratory of Polymer Materials, College of Chemistry and Chemical Engineering, Northwest Normal University, LanZhou, Gansu 730070, People’s Republic of China b Institute of Chemistry and Physics, Chinese Academy of Sciences, LanZhou, Gansu 730070, People’s Republic of China Received 9 September 2006; received in revised form 3 December 2006; accepted 4 December 2006 Available online 20 Decemeber 2006

Abstract The reaction pathway and energies for the gas-phase CO2–CO conversion by W+ are discussed from density functional theory (DFT) UB3LYP calculation at the relativistic effective core potential (ECP) of Stuttgart basis sets with W+ and 6-311+G(2d) with CO2. The reaction mechanism between W+ and CO2 is an insertion–elimination mechanism. The W+ inserts with no energy barrier into a CO bond resulting in an OWCO+ insertion product. The intrinsic reaction coordinate for the insertion process has been defined and the reaction mechanism has been investigated by analyzing various structures along this path. Crossing points (CPs) are localized, and possible spin inversion processes are discussed by means of the intrinsic reaction coordinate (IRC) approach.  2007 Published by Elsevier B.V. Keywords: Two-state reactivity; Potential energy surfaces crossing points (CPs); Insertion–elimination mechanism; Endothermic process

1. Introduction Carbon dioxide is a very important natural source of carbon on our planet, and therefore the possibility of using it as a starting material for the synthesis of chemically useful compounds has received considerable attention [1–4]. Moreover, anthropogenic emissions of CO2 are known to contribute to the greenhouse effect. Thus, recycling CO2 through conversion to useful chemical compounds is also important from an environmental point of view. However, carbon dioxide is a thermodynamically very stable compound that needs to be activated for its utilization, for example through its interaction with transition metal complexes. For these reasons a good knowledge of the metal– CO2 interaction is important to understand the role of the metal in these processes. Recently, an experimental investigation was reported for transition metal cations with carbon dioxide in the gas phase by Bohme [5]. Carbon dioxide was found to react

*

Corresponding author. Tel.: +86 931 7970237; fax: +86 931 7971989. E-mail address: [email protected] (Y.-C. Wang).

0166-1280/$ - see front matter  2007 Published by Elsevier B.V. doi:10.1016/j.theochem.2006.12.017

in a bimolecular fashion by O atom transfer only with 9 early transition-metal cations: the group 3 cations Sc+, Y+, and La+, the group 4 cations Ti+, Zr+, and Hf+, the group 5 cations Nb+ and Ta+, and the group 6 cation W+. These systems exhibit complicated behavior because the ground states of the reactants and products have different spin states. The DFT calculation used in this paper is to study the reaction pathways of carbon dioxide with W+ including reliable structures of the reactants, products, intermediates, and transition states as well as their accurate energies. Meanwhile, the crossing between the two potential energy surfaces (PESs) of different spin states is discussed as well as the crossing points (CPs) is located and characterized. 2. Computational details In the present work, all molecular geometries (reactants, intermediates, transition states (TSs) and products) were fully optimized on three PESs. A spin-unrestricted hybrid functional of exact (Hartree–Fock) exchange with local and gradient-corrected exchange and correlation terms, as

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first suggested by Becke [6,7], was used in our calculations, which is commonly known as UB3LYP. We have chosen this method since recent calibration calculations on transition metal compounds have shown that this hybrid functional provides accurate results for the geometries and vibrational frequencies of systems containing transitional metal atoms [8–12]. Our previous investigations [13,14] also have underlined the reliability of the B3LYP functional for describing PESs, predicting electronic structures and calculating thermochemical properties for the systems containing a relatively large number of electrons. The basis set used consists of the relativistic effective core potential (ECP) of Stuttgart on W, the 5d and 6s in W are treated explicitly by a (8s7p6d) Gaussian basis set contracted to [6s5p3d]. For O and C, we use 6-311+G(2d) basis set. All stationary points are characterized by vibrational analysis and the zero-point energy (ZPE) corrections are included. The transition state structures all represent saddlepoints, characterized by one negative eigenvalue of the Hessian matrix. To ensure reliability of the reaction path, the pathways between the transition structures and their corresponding minima have been characterized by the internal reaction coordinate (IRC) calculations. All computations are carried out using the GAUSSIAN98 program package [15].

3. Results and discussion 3.1. Overview of the stationary points The optimized geometries of various compounds in three different spin surfaces are collected in Fig. 1. Fig. 2 demonstrates computed potential energy diagrams in three spin states, the diagrams connecting the reaction intermediates (local minima) and the transition states (saddle points) on the PESs. Table 1 shows the total and relative energies for the optimized species which are calculated at UB3LYP level. Carbon dioxide can behave both as a bidentate ligand (g2-O,O or g2-C,O) or as a monodentate ligand (g1-O or g1-C) when interacting with neutral metal atom [16–18]. However, cationic metals are bound to CO2 electrostatically, and since the leading term is charge-quadrupole and CO2 has a negative quadrupole moment, the linearg1-O (end-on) coordination is the most favorable. Test calculations on reaction of the first-row transition metal cations with CO2 have confirmed this expectation [9]. In this paper, the g2-C,O mode is found on the doublet and quartet PESs. Moreover, their energies are all higher than the g1O one. Any attempt to optimize other structures for the W-metal ion in different electronic states collapse to the linear isomer. The reason is that the repulsion between the occupied d orbitals of the metal and CO2 is larger in those coordination modes than in theg1-O one, while the electrostatic stabilization is smaller. So the linear g1-O (end-on) coordination is the most favorable, which is similar to

the reaction of the first transition metal cations with CO2 [9]. First considering the linear W+–OCO (IM1) systems, the first step of the reaction is spontaneous formation of IM1 along three state spin PESs. All IM1 structures are planar. Since the bonding is mainly electrostatic, the interaction between carbon dioxide and metal cation produces only a small asymmetry in the two CO bond lengths; the CO bond length adjacent to the metal ion increases about ˚ , while the other CO bond length decreases about 0.02 A ˚ . This variation is very similar to the reaction of first 0.02 A transition-metal cations with CO2 [9], which indicates that no significant p back-donation from the metal ion to CO2 is present. In this reaction, the insertion of W+ into a CO bond can easily occur to form OWCO+ (IM3) complex that is viewed as carbonyl complexes of diatomic WO+ species [19]. The bond lengths of WO+ and CO in IM3 are shorter than those of IM1 and close to that in the free WO+ and CO. The relative energies of OWCO+ computed with respect to the ground state W++CO2 asymptote show that the insertion reaction is exothermic (except in sextet spin state). This is due to the fact that W+ form a strong metal oxide bond. In doublet state the WAO bond becomes shorter and WAC bond becomes longer than those of in quartet and sextet states. Comparison of the energy of IM3 in three spin states also reveals that the dissociation of CO from the insertion product is more feasible on the doublet surface (Table 1). In order to explain the reason of forming the bent structure, we analyze the frontier molecular orbital of OWCO+. The analysis of a00 occupied orbitals in Fig. 3b, d and f show the mixture of W+ 5dxz and O 2pz orbitals. The other interaction of a00 occupied orbitals in Fig. 3a, c and e is the bonding character between the W+ 5dyz and O 2pz orbitals. Because the 5dxz orbital is virtually orthogonal to the 5dyz orbital, OWCO+ has a bent structure, which will reduce the repulsion between the WO+ and CO orbitals. 3.2. Crossing point CPs and crossing seams are the subjects here. The potential energy surface (PES) of the system that consists of four atoms is a function of internal degree of freedom of dimension 6. The crossing seam between the two PESs is therefore a hyperline of dimension 5, and it is difficult to perform a detailed inspection of the crossing seam as a practical example. Thus to locate the crossing between the two PESs of different spin states, the procedure used by Yoshizawa et al. [20] has been selected. We have carried out single-point energy calculations (in the excited state) as a function of the structural change along the IRC of the ground state, and vice versa [21,22]. In this reaction, two electronic states are involved: the reactant, W+, which has a sextet spin multiplicity as ground state, while the product, WO+, which has a doublet spin multiplicity. Therefore, at least a crossing and spin inversion process must take place in the reaction

X.-Y. Yang et al. / Journal of Molecular Structure: THEOCHEM 807 (2007) 49–54

51

Fig. 1. UB3LYP structures of the reagents, the reaction products, the intermediates and the transition states on three PESs. (bond length in nm, bond angle in degree.)

400

6

WO++CO 385.2

Relative energy / kJ.mol-1

2

300

+

W +CO2

6

302.9

TS13

265.4 2

200

4

W +CO2

178.9

2

IM1

155.6 4

IM1

100

179.7

CP2 2 IM2

4

TS12

4

107.7

108.3

2

+

99.7

TS12

4

157.9

IM2

6

IM3

TS23

220.4

206.1

CP1

4

WO++CO

TS23

119.8

158.9

CP3

2

WO++CO

107.6 6

0

W++CO2

4

IM3

0.0

6

-3.7

IM1

2

IM3

-53.2

-44.4

-100

Reaction Coordination

Fig. 2. Diagram for the reaction W+ with CO2 on three spin state PESs.

pathway. In Fig. 4, the solid lines are the IRC paths in high spin state, and the dotted lines are the single-point energy values in low spin state on the geometries of each optimized point along the high state IRC path. Fig. 4 points out the crossing point which the values of energy for both electronic states become equal for a determined geometry along the IRC path. It should be noted that

the CPs we obtained in this way cannot be considered as the true minimal energy crossing points (MECPs) between two spin state PESs. Three CPs are expected to occur according to the results of analysis described above: between 6IM1 and 4TS23 (CP1), between 6IM1 and 2TS23 (CP2), and between 4 TS23 and 2IM3 (CP3). In Fig. 2, the first crossing (CP1)

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X.-Y. Yang et al. / Journal of Molecular Structure: THEOCHEM 807 (2007) 49–54

Table 1 Total and relative energies for the optimized species are calculated at UB3LYP level Species

EC T =ða:u:)

ER/(kJ mol1)

Species

EC T =ða:u:)

ER/(kJ mol1)

Species

EC T =ða:u:)

ER/(kJ mol1)

6

W++CO2 IM1

252.837987 252.858251

0.0 53.2

4

252.736906 252.754038 252.691272

265.4 220.4 385.2

178.9 99.7 107.7 108.3 158.9 3.7 119.8

2

TS13 IM3 6 WO++CO

252.769848 252.800028 252.796966 252.796738 252.777429 252.839381 252.792358

252.722619 252.778722 252.769557 252.777846 252.759496 252.854906 252.797004

302.9 155.6 179.7 157.9 206.1 44.4 107.6

6

6 6

W++CO2 IM1 4 TS12 4 IM2 4 TS23 4 IM3 4 WO++CO 4

W++CO2 IM1 2 TS12 2 IM2 2 TS23 2 IM3 2 WO++CO 2

ETC , total energy; ER, relative energy.

Fig. 3. Diagram of the frontier molecular orbital of OWCO+ at three spin states.

on the sextet and quartet-spin state PESs exists in prior to 6 TS13, which is a typical ‘‘two-state reactivity’’ (TSR) reaction on the basis of Hammond postulate [23]. As shown in Fig. 4a, CP1 is located at s = 2.68 with a relative energy of 252.78 kJ/mol. The complex at this point has Cs geometry, in which the dissociating CAO bond distance is ˚ and the forming WAO bond distance is 2.2286 A ˚ 2.0509 A. The sextet and quartet PESs can begin to touch at this point because the IRC valley of the sextet state still lies below that of the quartet state in this region of reaction pathway. That is, after CP1, the quartet PES can provide a low-cost reaction pathway toward the product complex. As reaction system moves along one of the IRC valleys, the crossing seam looks like a ridge, the molecular system maybe change its spin multiplicity from the sextet to quartet state in this crossing region. In other words, intersystem crossing (ISC) maybe occurs if energy condition permits. Therefore the spin inversion acts as a mechanistic distributor and it is responsible for the reaction efficiency and reaction rates.

In Fig. 4c, we find CP3 after 4TS23 (s = 2.25), the relative energy being 252.81 kJ/mol. At CP3 the complex has also Cs structure, in which the WAC bond distance is ˚ and the forming WAO bond distance is 2.1608 A ˚ . However, since the CP3 is located at the exit of 1.8031 A the reaction channel, where the reaction have got over the barrier of corresponding TS, these crossing seam does not play a significant role in the reaction process [24]. Therefore, the molecular system would preferentially move on the quartet PES of reaction pathway. We have found additional CPs: CP2 (between sextet and doublet spin states), which do not have mechanistic significance. Considering the length of the manuscript, the detailed discussion about this point is ignored. When the reaction reaches the vicinity of CPs, the state of CPs in high spin state may mix with that in low spin state, which will decrease the activation barrier. For example, the frontier molecular orbital of CP1 is investigated in two spin states. In Fig. 5, the (a) orbital is the antibonding interaction between the W dxz and O pz orbitals, which is

X.-Y. Yang et al. / Journal of Molecular Structure: THEOCHEM 807 (2007) 49–54

53 sextet doublet

sextet quartet -252.74

-252.74

-252.77

CP2

-252.76

1.2286 1.151 9

-252.78

CP1

-252.79 -252.80 -252.81

-252.78 -252.80

2.1736

V / hartree

-252.76

86 .7 5

V / hartree

2.0509

-252.75

94

.1

-252.82

-252.82

2

1.1931

-252.83

1.1441

-252.84

-5

-4

-3

-2

-1

0

-5

Reaction coordination (amu1/2)

-4

-3

-2

-1

0

Reaction coordination (amu1/2) quartet doublet

-252.76 -252.77

1.8 0

-252.80

57.88

-252.81

2 1.1

-252.82

24

V / hartree

-252.79

8 60 2.1

31

-252.78

CP3

-252.83 -252.84 -252.85 -252.86 -252.87 -1

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14

Reaction coordination (amu1/2)

Fig. 4. Potential energies cure-crossing points diagram between two spin state PES.

(IM1) systems. Then, before reaching 6TS13, CP1 is met and a path can be taken on the quartet state PES. And before reaching 4IM3, CP3 is found. From this point onward, the reaction can be continued on the doublet spin state PES as a low-cost reaction pathway toward the product complex. 3.3. Calculation the O-atom affinities in different spin state

Fig. 5. Diagram of the frontier molecular orbital of CP1.

the highest single occupied orbital (HOMO) in sextet state, but is the lowest empty orbital (LUMO) in quartet state. The (b) orbital is the bonding interaction between the W dyz and O pz orbitals, which is the lowest single occupied orbital in sextet state, but is the highest double occupied orbital in quartet state. When the spin inversion process takes place in the reaction pathway from the sextet state to the quartet state at CP1, the a electron in the dxz orbital will occur spin inversion and pair with the single electron in the (b) orbital. Because this single electron in an atom transfer at different orbital is allowed [25], so spin inversion is efficient. The existence of CP opens the possibility for an intersystem crossing to take place from high spin state to low spin state. It is conceivable that first stage of the reaction corresponds to the approach of W metal ions toward CO2 in sextet spin state, with formation the linear W+–OCO

From the potential energy diagram for the W++CO2 reaction shown in Fig. 2, it can be concluded that re-forming of carbon dioxide to carbon monoxide can be greatly enhanced in the presence of metal ions. For instance, the unimolecular CO2 fi CO+O (3P) decomposition is strong endothermic by 125.7 kcal mol1 [26] and this spin-forbidden reaction overcomes a barrier of at least 131 kcal mol1 [26], which makes the cleavage of CAO bond very difficult. When the W+ participates in the reaction, the reaction changes into weak endothermic and the activation barrier is reduced. The interaction between metal ion and CO2 illustrates an important role played by metals. When a metal is bonded to a substrate, the energy required for the endothermic process of deformation or even decomposition of the substrate decreases due to the electrostatic interaction between the metal ion and substrate. At the next reaction step, the bond between metal and a fragment of the substrate (oxygen atom for the case of WOCO+) strengthens and the metal–substrate complex dissociates yielding two fragments of initial substrate (CO+O), one of those is bonded

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X.-Y. Yang et al. / Journal of Molecular Structure: THEOCHEM 807 (2007) 49–54

WO +

OA (W+)

IE (W)

-IE (WO) WO

W + +O

D298 (W-O)

W+O

Scheme 1.

to the metal. The reaction energy changing for the substrate (CO2) decomposition in the presence of metal ion is due to the energy income from the formation of electrostatic interaction between metal ion and substrate fragment (oxygen atom). Therefore, we may conclude that the role of metal ions in re-forming CO2 relates to its ability of O capture. To depict the ability of O capture, the O-atom affinities (OA) of W+ is defined as follows: OA(W+) = IE(W) + D298(WAO)  IE(WO), which consults the method in the Ion-molecule reactions of W+ and WO+ [27] in Scheme 1. The results in three spin states show in follow: OA (2W+) = 725.46 kJ mol1, OA (4W+) = 589.32 kJ mol1, OA (6W+) = 144.97 kJ mol1, and OA (CO) = 532.21 kJ mol1 [26]. Thus in sextet spin state OA (W+) is less than OA (CO), but in quartet and doublet spin states are more than OA (CO). Furthermore, the OA (W+) in doublet spin state is more than those of in quartet spin state. This shows that W+ can capture O from CO2 only in quartet and doublet spin states and in doublet spin state is easier. So the reaction thermodynamically allowed. The conclusion is in accord with the experiment finding [5].

4. Conclusion The reaction of W+ with CO2 in three spin states has been studied at the DFT-UB3LYP level. The first step of this reaction corresponds to the approach of W+ toward CO2 in sextet spin state, with formation the linear M+–OCO (IM1) system that is bound to CO2 electrostatically. Then the W+ inserts into a CAO bond to form a bending structure OWCO+ in doublet spin state, and OWCO+ easily dissociates into WO+ and CO product. The reaction is weak endothermic due to the participation of the metal ion, to be compared with the strong endothermic process of the unimolecular CO2 decomposition. The calculation results imply that changes in spin multiplicity take place during the third-row early transition metal ion W+ with CO2. It is a typical TSR reaction as well as the CP1 occurs between 6IM1 and 4TS23 in the entrance channel.

References [1] A. Behr, Carbon Dioxide Activation by Metal Complexes;, VCH Publishers, New York, 1988. [2] D.A. Palmer, R. van Eldik, Chem. Rev. 83 (1983) 651. [3] D.H. Gibson, Chem. Rev. 96 (1996) 2063. [4] F.J. Solymosi, Mol. Catal. 65 (1991) 337. [5] G.K. Koyanagi, D.K. Bohme, J. Phys. Chem. A. 110 (2006) 1232. [6] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [7] P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 (1994) 11623. [8] See for example: C.W. Bauschlicher, A. Ricca, H. Partridge, S.R. Langhoff, in: D.P. Chong (Ed.), Recent Advances in Density Functional Theory, World Scientific Publishing Co., Singapore, 1997, Part II. [9] M. Sodupe, V. Branchadell, M. Rosi, C.W. Bauschlicher, J. Phys. Chem. A. 101 (1997) 7854. [10] M. Aschi, M. Bronstrup, M. Diefenbach, J.N. Harvey, D. Schroder, H. Schwarz, Angew. Chem., Int. Ed. 37 (1998) 829. [11] S. S Yi, M.R.A. Blomberg, P.E.M. Siegbahn, J.C. Weisshaar, J. Phys. Chem. B 102 (1998) 395. [12] D.J. Zhang, C.B. Liu, S.W. Bi, S.L. Yuan, Eur. Chem. J. 9 (2003) 484. [13] Y.C. Wang, X.Y. Yang, Z.Y. Geng, Z.Y. Liu, Chem. Phys. Lett. 431 (2006) 39. [14] X.Y. Yang, Y.C. Wang, Z.Y. Geng, Z.Y. Liu, Chem. Phys. Lett. 430 (2006) 265. [15] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M.Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, C. Gonzalez, M. Challacombe, P.M.W. Gill, B.G. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian, Inc., Pittsburgh, PA, 1998. [16] G.H. Jeung, Chem. Phys. Lett. 232 (1995) 319. [17] M. Sodupe, V. Branchadell, A. Oliva, J. Phys. Chem. 99 (1995) 8567. [18] I. Pa´pai, J. Mascetti, R. Fournier, J. Phys. Chem. A. 101 (1997) 4465. [19] I. Pa´pai, G. Schubert, Y. Hannachi, J. Phys. Chem. A 106 (2002) 9551. [20] K. Yoshizawa, Y. Shiota, T. Yamabe, J. Chem. Phys. 111 (1999) 538. [21] L. Gracia, L.R. Sambrano, V.S. Safont, M. Calatayud, A. Beltra´n, J. Andre´s, J. Phys. Chem. A 107 (2003) 3107. [22] L. Gracia, J. Andre´s, V.S. Safont, A. Beltra´n, Organometallics 23 (2004) 730. [23] D. Schro¨der, S. Shaik, H. Schwarz, Acc. Chem. Res. 33 (2000) 139. [24] M. Sodupe, V. Branchadell, M. Rosi, C.W. Bauschlicher, J. Phys. Chem. A. 101 (1997) 7854. [25] N.J. Turro, Modern Molecular Photochemistry, Science Press, Beijing, 1987, pp.183  184.(in Chinese). [26] A.M. Mebel, K. Morokuma, M.C. Lin, J. Chem. Phys. 103 (1995) 7414. [27] V. Blagojevic, G.K. Koyanagi, V.V. Lavrov, G. Orlova, D.K. Bohme, Chem. Phys. Lett. 389 (2004) 303.