Theoretical study of carbon dioxide-carbon monoxide conversion by La+, Hf+ and Ta+

Chemical Physics Letters 431 (2006) 39–44 www.elsevier.com/locate/cplett

Theoretical study of carbon dioxide-carbon monoxide conversion by La+, Hf+ and Ta+ Yong-Cheng Wang *, Xiao-yan Yang, Zhi-Yuan Geng, Ze-Yu Liu Gansu Key Laboratory of Polymer Materials, College of Chemistry and Chemical Engineering, Northwest Normal University, Lanzhou 730070, China Received 30 June 2006; in final form 24 August 2006 Available online 16 September 2006

Abstract The entire reaction mechanism for the gas-phase CO2–CO conversion by early transition metal ions, La+, Hf+, and Ta+, are studied using density functional theory (DFT). The results indicate that the lowest energy path corresponds to the g2-O coordination of CO2 followed by the insertion of M+ into the C–O bond. The reactions are all exothermic due to the participation of the metal ions, to be compared with the strong endothermic process of the unimolecular CO2 decomposition. Crossing points (CPs) are localized, and possible spin inversion processes are discussed by means of the intrinsic reaction coordinate (IRC) approach. Ó 2006 Published by Elsevier B.V.

1. Introduction Carbon dioxide is 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 metalCO2 interaction is important to understand the role of the metal in the catalytic processes. In 2006, the experimental investigation was reported for the transition metal cations with carbon dioxide in the gas phase by Koyanagi and Bohme [5]. Carbon dioxide was found to react in a bimolecular fashion by O atom transfer only with nine early transition-metal cations. These systems exhibit complicated behavior because the ground states of *

Corresponding author. Fax: +86 0931 7971989. E-mail address: [email protected] (Y.-C. Wang).

0009-2614/$ - see front matter Ó 2006 Published by Elsevier B.V. doi:10.1016/j.cplett.2006.09.035

the reactants and products have different spin states. The DFT calculation used in this Letter is to study the reaction pathways of carbon dioxide with La+, Hf+, and Ta+ 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. Theoretical methods The fully optimized geometries and the vibrational frequencies have been determined using the three-parameter hybrid [6] B3LYP density method [7]. 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]. The basis set used consists of the relativistic effective core potential (ECP) of Stuttgart on La, Hf, and Ta, the 5d and 6s in La, Hf, and Ta 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

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Y.-C. Wang et al. / Chemical Physics Letters 431 (2006) 39–44

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 [9]. 3. Results and discussion 3.1. Overview of the stationary points 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 [10–12]. However, cationic metals are bound to CO2 electrostatically, and since the leading term is charge-quadrupole and CO2 has a negative quadrupole moment, the linear g1-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 [13]. In this Letter, the g2-C,O modes is only found for La+ on the triplet PESs. Any attempt to optimize other structures for the third-row early transition metal ions 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 the g1-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 [13] (See Fig. 1). First considering the linear M+–OCO (IM1) systems, the first step of the reaction is the spontaneous formation of IM1 along both high- and low-spin PESs. Since the bonding is mainly electrostatic, the interaction between carbon dioxide and the metal cation produces only a small asymmetry in the two CO bond lengths; the CO bond ˚, length adjacent to the metal ion increases about 0.02 A ˚. while the other CO bond length decreases about 0.02 A This variation is very similar to the reaction of first transition-metal cations with CO2 [13], which indicates that no significant p back-donation from the metal ion to CO2 is present. In this reaction, the insertion of M+ into the CO bond can easily occur to form OMCO+(IM2) complex that is viewed as carbonyl complexes of diatomic MO+ species [14]. In order to explain the reason of forming the bent structure, we analyze the frontier molecular orbital of OTaCO+ as an example. The analysis of the a00 occupied orbitals in Fig. 3c and e show the mixture of Ta+ 5dxz and O 2pz orbitals. The other interaction of the a00 occupied orbitals in Fig. 3b and d is the bonding character between the Ta+ 5dyz and O 2pz orbitals. Because the 5dxz orbital is virtually orthogonal to the 5dyz orbital, OTaCO+ has a

bent structure, which will reduce the repulsion between the MO+ and the CO orbitals. The HOMO of OTaCO+ in quintet state (Fig. 3a) is a 0 singly occupied orbital, which is bonding with respect to the Ta–C bond and antibonding for Ta–O bond. But in triplet state it is not this orbital. So in triplet state the Ta–O bond becomes shorter and Ta–C bond becomes longer than those of in quintet state. Comparison of the energy of IM2 in quintet and triplet -states also reveal that the dissociation of the CO from the insertion product is more feasible on the triplet surface. The experiment [5] was found that all of the nine observed O atom transfer reactions are exothermic. This is due to the fact that in OMCO+, La+, Hf+, and Ta+ form a strong metal oxide bond. In our calculation, the relative energies (relative to its corresponding high-spin state reactant) of IM2 in the low spin state are 232.64 kJ mol1 for La, 308.52 kJ mol1 for Hf, and 220.93 kJ mol1 for Ta, respectively. Compared with the frontier orbitals of IM2 in the low spin state, they have analogous structures and different energies. The energies of HOMO are 0.434 a.u. for La, 0.465 a.u. for Hf, and 0.323 a.u. for Ta, respectively. The variation of HOMO energies is agreed with the change course of the relative energy of IM2 in the low-spin state. So it can be presumed that the energy of HOMO is the mainly reason which makes the reaction exothermicity change. 3.2. Crossing point In the reactions, two electronic states are involved: the reactant, M+, which has a high spin multiplicity as ground state, while the product, MO+, which has a low spin multiplicity. Therefore, at least a crossing and spin inversion process must take place in the reaction pathway. For three metal ions, all the energies of IM1 in high spin state are more stable than those of in low spin state. But in TS12 it is reverse. So the crossing on the two-spin state PESs may occur between IM1 and TS12, which is a typical ‘two-state reactivity’ (TSR) reaction on the basis of Hammond postulate [15]. In order to search the CPs between the IM1 and TS12, we have carried out single-point energy calculations (in the low spin state) as a function of the structural change along the IRC of the high spin state [16,17]. 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 spin state IRC path. It can be seen in Fig. 4 that the crossing points in 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 obtained in this way could not be considered as the true minimal energy crossing points (MECPs) between two spin state PESs. 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

Y.-C. Wang et al. / Chemical Physics Letters 431 (2006) 39–44

2.3456

971

20

94 75

O

3

TSa (CS)

O

IM1′

74

12 48. O

3

(CS)

2.8

2

0 74 2

2

1. C 122 5 O

Hf 2

IM2 (CS)

2.3384

4

HfO (C∞V)

O

C O 1.1755

IM1 (CS)

2.2

95

4

C

104.55

O

4

176.48

1.1 2

61 O

Hf 4

IM2 (CS)

1.9725

O

Ta

O C 2.3271 1.1732

3

HfO (C ∞V)

9

C

1. 1

1.9927

12

176.49 19

Ta

1

3

IM2 (CS) C

O

O

1.1603

O

O C 2.3056 1.1756

5

TaO (C∞V)

1.1603

1.9603

Ta

1.6959

IM1 (CS)

O

3

IM1 (CS)

44

2. 3

.28 52

106 .

C

O

19

O C 1.1942

O

20 2.

Ta

Hf

O

6

Hf

O

3

LaO (C∞V)

176.42 1.7319

Ta

Ta

3

IM2 (CS)

O

2.288

C

TS12 (CS)

37 70 1. 103.99 O

2.1711

La

05

94.16

O

TS12 (CS)

1.1 16 C 3 O

Ta 94

O

4

2.3 4

4. 6 5

O

IM1 (C ∞ V)

3

. 65

3

Hf

O

9

O

TS12 (CS)

4

2.93 19

O C 2.6341 1.1752

3

LaO (C∞V)

La O

La

O

O

TS12 (CS)

Ta

99 5

1.9646

52

2. 30

0. 3

O C 1.2095

IM1 (CS)

Hf O

O

8

2

O C 2.2701 1.1797

1. 99 6

Hf

10

1

7

1.

2.2409

176.57

La

C

Hf

1.8865

1.

23 C O 1.2106

180.00

1.1 166 C O

IM2 (CS)

La

8 2.6

2.

2.4548

1

TS12 (CS)

27.86 O C 1.2536

.7 2

5 97

4 90.9

O

La

La

3

O

2. 9

52

1

IM1 (CS)

O C 1.1992

La

2.1788

1

O

1. 8

463

C 2.528 O 5 1.1806

2. 4

La

11 4 .7 7

2.1 7

La 166.57

41

2 .1 84

5

99.06

O

C

1.1 24 6

O

5

TS12 (CS)

O

5

IM2 (CS)

1.1257

C

C

O

180.00

5

TaO (C∞V)

1

CO2 (D∞h)

1

CO (C∞V)

Fig. 1. Gemetries of the critical on the potential energy surface bond length in nm, bond angle in degree.

example Hf+, the frontier molecular orbital of CP2 is investigated in the two spin states. In Fig. 5, the (A) orbital is the nonbonding dxz orbital of Hf, which is the highest single occupied orbital (HOMO) in quartet state, but is the lowest empty orbital (LUMO) in doublet state. The (B) orbital is the bonding interaction between the Hf dyz and the O pz orbitals, which is the lowest single occupied orbital in quartet state, but is the highest double occupied orbital in doublet state. When the spin inversion process takes place in the reaction pathway from the quartet state to the doublet state at CP2, 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 [18], so spin inversion is efficient. The existence of CP opens the possibility for an intersystem crossing to take place from the high spin state to low spin state. It is conceivable that the first stage of the reaction corresponds to the approach of transition metal ions toward the CO2 in high spin state, with formation the linear M+–OCO (IM1) systems. Then, before reaching TS12, CP is met. From this point onward, the reaction can be continued on the low spin state PES as a low-cost reaction pathway toward the product complex. Therefore the spin

42

Y.-C. Wang et al. / Chemical Physics Letters 431 (2006) 39–44

200

Relative energy / kJ.mol -1

3

LaO++CO

100

1

La++CO2

3

TS12

79.76 3

0

1

0.00

-29.42 3

IM1

3

TSa

64.11

1

TS12

CP1 3

IM1

-67.15

-100

IM2

76.58

La++CO2

112.27

3

-24.44

IM1¡ä

-62.75

-58.17 1

LaO++CO

-200

1

-187.31

IM2

-232.64

a

-300

300

5

TaO++CO 263.05

4

HfO++CO 134.62

100

4 2

+

Hf +CO2

CP2

11.43

0

2 IM1 Hf++CO2 -12.74 0.00

4

4

-100

TS12

44.92

4 2

TS12

IM2

8.22

-27.82

IM1

2

HfO++CO

-76.54

-105.04

-200

Relative energy / kJ.mol -1

Relative energy / kJ.mol -1

200 200 5 3

Ta ++CO2

100

3 3

IM1

0

46.39 CP3

5

Ta ++CO2

TS12

147.23

127.94

5

IM2

105.85

TS12

52.62

0.00

5

-100

IM1

3

TaO++CO

-84.83

-110.27

-200

3

IM2

-220.93

b

2

IM2

-300

-308.52

c

-300

Fig. 2. Diagram for the reaction La+, Hf+, and Ta+ with CO2 on both spin state PESs. (a) La++CO2, (b) Hf++CO2, (c) Ta++CO2.

a ′ , ε =-0.304 a.u.

a ′′ , ε =-0.326 a.u.

a

a ′′ , ε =-0.323 a.u.

a ′′ , ε =-0.409 a.u.

c

b

a ′′ , ε =-0.479 a.u.

d

e +

Fig. 3. Diagram of the frontier molecular orbital of OTaCO at two spin states. (a) 5OTaCO+, (b) 5OTaCO+, (c) 5OTaCO+, (d) 3OTaCO+, (e) 3OTaCO+.

Y.-C. Wang et al. / Chemical Physics Letters 431 (2006) 39–44

triplet singlet

1.

1.2194

-219.92

15 24

-219.93 -219.94

1.17 51

1.2899

-234.15 -234.16 -234.17

CP2

-234.18

-219.95

CP1

-234.19

-219.96

a

92 .42

-234.14

V / hartree

V/ hartree

-219.91

-234.12 234.13 -

92 .4 2

quartet doublet

-234.11 2.1901

-219.90

2.1901

-219.89

43

-234.20 -6

-5

-4

-3

-2

-1

0

Reaction coordition (amu1/2)

-10

b

V/ hartree

-4

-2

0

1/2

quintet triplet 2.0759

-242.80

-6

Reaction coordition (amu )

-242.78 -242.79

-8

-242.81

87 .7 1

1.15 43

1.2439

-242.82 -242.83 -242.84

CP3

-242.85 -242.86

c

-10

-8 -6 -4 -2 Reaction coordition (amu1/2)

0

Fig. 4. Potential energies cure-crossing points diagram between two spin state PES. (a) La; (b) Hf; (c) Ta.

a ( ε = -0.265 a.u.)

b ( ε =-0.433 a.u.)

Fig. 5. Diagram of the frontier molecular orbital of CP2 (Hf+).

inversion acts as a mechanistic distributor and it is responsible for the reaction efficiency and reaction rates. 3.3. Calculation the O-atom affinities in different spin state From the potential energy diagram for the M++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 ! CO + O (3P) decomposition is endothermic by 125.7 kcal mol1[19] and this spin-forbidden reaction overcomes a barrier of at least 131 kcal mol1 [19], which makes the cleavage of C–O bond very difficult. When the La+, Hf+, or Ta+ participates in the reaction, the reaction change into exothermic and the activation barrier are 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 MOCO+) strengthens and the metal-substrate complex dissociates yielding two fragments of initial substrate (CO+O), one of those is bonded 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 the 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 M+ is defined as follow: OA(M+) = IE(M) + D298(W– O) – IE(MO), which consults the method in the Ion-molecule reactions of W+ and WO+ [20] in Scheme 1: W O

O A (W

+

+

)

+

+O IE (W )

-IE (W O ) W O

W

D

298(W

-O )

Scheme 1.

W +O

44

Y.-C. Wang et al. / Chemical Physics Letters 431 (2006) 39–44

The results in two spin states show in follow: OA (1La+) = 797.28 kJ mol1, OA (2Hf+) = 646.69 kJ mol1, OA (3Ta+) = 768.43 kJ mol1, OA (3La+) = 417.95 kJ mol1, OA (4Hf+) = 395.59 kJ mol1, OA (5Ta+) = 267.17 kJ mol1, and OA (CO) = 532.21 kJ mol1. Thus in high spin state OA (M+) is less than OA (CO), but in low spin state is more than OA (CO). This shows that La+, Hf+, and Ta+ can capture O from CO2 only in low spin state and the reaction thermodynamically allowed. The conclusion is in accord with the experiment finding [5]. 4. Conclusion The reactions of the third-row early transition metal ions (La+, Hf+, and Ta+) with CO2 in two spin states have been studied at the DFT-UB3LYP level. The first step of the reaction corresponds to the approach of transition metal ion toward CO2 in high spin state, with formation the linear M+–OCO (IM1) systems which are bound to CO2 electrostatically. Then the M+ inserts into the C–O bond to form a bending structure OMCO+ in the low spin state, and OMCO+ easily dissociates into MO+ and CO product. The reactions are all exothermic due to the participation of the metal ions, 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 ions (La+, Hf+, and Ta+) with CO2. It is a typical TSR reaction as well as the CP occurs between IM1 and TS12 in the entrance channel.

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