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DFT study on the gas phase reaction of Ni+ with CS2
Chemical Physics Letters 458 (2008) 19–23
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
DFT study on the gas phase reaction of Ni+ with CS2 Tao Hong Li a,*, Chuan Ming Wang b, Xiang Yi Liu a, Xiao Guang Xie c a b c
Department of Chemistry, Southwest Forestry University, Kunming 650224, China Department of Biology, Honghe University, Menzi 661100, China Department of Chemistry, Yunnan University, Kunming 650091, China
a r t i c l e
i n f o
Article history: Received 9 February 2008 In final form 14 April 2008 Available online 9 May 2008
a b s t r a c t The reaction of Ni+ with CS2 has been investigated at B3LYP/TZVP and B3LYP/6-311 + G* levels of theory. The reaction mechanisms have been explored in detail on both doublet and quartet potential energy surfaces. The products observed in the experiment have been explained according to the cleavage of different bonds in the insertion intermediate S–Ni+–C–S. The product [Ni, C, S]+ observed in experiment was confirmed as Ni–CS+ (2R). The spin-forbidden reaction Ni+(2D) + CS2 ? NiS+(4R) + CS (1R) was found to proceed through a doublet–quartet surface crossing and the crossing seam was approximately calculated. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The chemistry of transition-metal sulfur systems has been an active area due to their significance in industrial catalysis, biology systems and material science [1–4]. In industrial areas, considerable attention has been focused on the role of sulfur transition-metal complexes in catalysis poisoning [1]. In many biological systems, it has been found that sulfur coordination is necessary for the functioning of numerous biological transition-metal centers [2,3]. CS2 and COS are important sulfur-transfer reagents, which have been considered as possible sulfur sources for preparing thin layers of semiconductor materials [4]. Schwarz’s and Armentrout’s research groups have reported a serial of studies on the reactions of the whole 3d metals with CS2 using Guided Ion Beam Mass Spectrometer (GIB), where the sulfur-metal bond energies were determined [5–9]. They found the dominant products are MS+ (M = Sc Zn) and [M, C, S]+ (which was safely assigned as the metal-thiocarbonyl cation, M–CS+, at the lowest energy). According to the experimental observations, they predicted that the S–M+– C–S species could be an intermediate in these reactions, and they proposed that these reactions could proceed in an insertion–elimination mechanism. The general reaction pathway could be described as M+ + CS2 ? S–M+–C–S ? MS+ + CS or [M, C, S]+ + S. The previous DFT theoretical studies on the reactions of V+ and Fe+ with CS2 have confirmed this mechanism, and the experimentally observed products have been rationalized [6,10]. However, due to the different electronic structures, the reactions of V+ and Fe+ are different in details including mechanism and potential energy surfaces (PES). It can be expected that the reactions of all 3d metal ions could be different from each other. For example, by comparing the thermochemical data of the reactions of different ions with CS2, * Corresponding author. E-mail address: [email protected] (T.H. Li). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.04.057
it was found that for Sc+ Co+ the formation of MS+ is always energetically favorable than that the formation of [M, C, S]+ [5–8], whereas for Ni+ the formation of the [Ni, C, S]+ species has a lower threshold energy than NiS+ [9]. What is the most stable structure for [Ni, C, S]+? Further, Ni+ has a doublet ground state of 2D (3d9), but the ground state of the product NiS+ is a quartet state 4R. Thus, the formation of ground state products from ground state reactants is formally spin-forbidden: Ni+(2D) + CS2(1R) ? NiS+(4R) + CS(1R). As a result, the intersystem crossing between the doublet and quartet potential energy surfaces occurs when the total energy of the system is close to the energy of the crossing point and this has been pointed out by Armentrout et al. as well. Is this true? And where is the crossing point located? Providing answers for these questions needs the theoretical studies to provide correct mechanism and accurate potential energy surfaces. As a supplement of experimental study, we present here a theoretical study of the reaction of the late 3d ion Ni+ with CS2 aiming to give a reasonable model that how Ni+ activates the C–S bond in CS2 and explaining the products observed in experiment. Further, in this study the reaction of Ni+ will be compared with those of V+ and Fe+. 2. Computational method All geometries (reactant, products, intermediates and transition states) were fully optimized by using density functional theory method B3LYP [11,12] with TZVP [13] basis set. Harmonic vibration frequencies were calculated at the same level to characterize the stationary points and to estimate the contributions of zero-point vibration to relative energies. The intrinsic reaction coordinate (IRC) method was used to track the reaction pathways from the transition states to the corresponding minimums. The choice of B3LYP method is motivated by its reliability and efficiency as a practical tool in transition-metal chemistry [14–20]. The quality of B3LYP/TZVP level has been tested in previous studies of transition-metal-containing sys-
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tems, and it has been shown to be computational efficiency to provide reasonable accurate geometries and energies [16–18]. To obtain more reliable potential energetic picture for the reaction, all energies of B3LYP/TZVP optimized geometries were recalculated by the conjunction of B3LYP with the larger standard basis set 6-311+G* [21,22]. To confirm that the lowest energy solution to SCF equations was found for each stationary point, the wave function stability was always tested. All calculations were carried out with GAUSSIAN 03 program package [23]. 3. Results and discussion
tion energy and bond dissociation energies of the reactant and products are compared in Table 1. The relevant energies are collected in Table 2. To evaluate the reliability of chosen method, we first calculated the excitation energy of Ni+ and the bond dissociation energies (BDE) of the ground state of CS2(1R), NiS+(4R) and NiCS+(2R) at different levels. By comparing the calculated values with experimental results, we found that the B3LYP/6-311+G* gave the smallest absolute errors and the results at this level are in good agreement with experimental findings. Unless otherwise specified, all energies discussed in the text refer to the results obtained at B3LYP/ 6-311+G* level.
The optimized geometries are shown in Fig. 1, and the sketch of the PES is shown in Fig. 2. The calculated and experimental excita-
Fig. 1. Optimized geometries for the stationary points and the structure of the crossing point on the PESs of Ni+(2D, 4F) + CS2 reaction at B3LYP/TZVP level of theory (distances in Å and angles in degrees).
T.H. Li et al. / Chemical Physics Letters 458 (2008) 19–23
21
Fig. 2. Potential energy diagram for the Ni+(2D, 4F) + CS2 reaction at B3LYP/6-311+G* level of theory (relative energies in kJ/mol).
Table 1 The singlet–triplet splitting energy for Ni+ and the bond dissociation energies for NiS+ and NiCS+ (energies in kJ/mol)
4
DE (2D ? F) D0 (CS–S) D0 (Ni+–S) D0 (Ni+–CS) a
B3LYP/TZVP
B3LYP/6-311+G*
Experimentala
92.8 432.6 211.5 274.6
120.8 436.4 224.0 228.2
104.5 433.9 237.0 234.1
Excitation energies and BDEs taken from Ref. [9].
Table 2 Total energies (E, in hartree), zero-point energies (ZPE in kJ/mol), imaginary frequencies (IMG, cm1) and ZPE-corrected relative energies (Erel, in kJ/mol) B3LYP/6-311+G*
Species
B3LYP/TZVP E
ZPE
Ni+ + 1CS2 2 IM1 2 TS1 2 IM2 4 Ni+ + 1CS2 4 IM3 4 TS2 4 IM4 4 TS3 4 IM5 4 TS4 4 NiS+ + 1CS 2 NiS+ + 1CS 2 NiCS + 3S 4 NiCS + 3S
2342.570669 2342.628824 2342.566181 2342.574073 2342.535322 2342.573117 2342.558558 2342.565891 2342.549959 2342.577296 2342.517036 2342.492074 2342.476486 2342.509306 2342.434025
18.0 18.8 15.9 15.9 18.0 18.0 14.6 15.9 13.8 15.9 11.7 10.5 10.0 13.8 10.9
2
IMG
290
614 392 120
Erel
E
Erel
0.0 151.7 9.7 11.3 92.8 6.3 28.4 10.5 50.2 19.6 134.6 198.6 239.1 156.8 369.9
2342.512493 2342.56660 2342.502636 2342.510749 2342.466523 2342.507596 2342.489444 2342.501002 2342.485417 2342.513283 2342.444013 2342.428535 2342.417556 2342.431693 2342.364584
0.0 141.3 23.8 2.5 120.8 13.0 57.3 28.4 66.9 4.2 173.5 211.9 241.2 207.7 388.3
3.1. The doublet surface of the reaction of Ni+(2D) with CS2 The reaction of ground state of Ni+(2D, 3d9) with CS2 was found to be a typical insertion–elimination mechanism. As shown in Fig. 1, all the intermediates and transition state have the Cs symmetry and 2A00 electronic state, which means there must be a 2A0 surface as well. Considering this 2A0 surface may provide additional information for the C–S bond activation process, we have also located this surface. But it was found that this surface lies much higher above the 2A00 surface. Thus the reaction on this surface unlikely contributes to the formation of the products. Therefore this 2 0 A surface will not be discussed.
2 IM1 is the initial complex formed as Ni+ and CS2 approach with each other. In this C–S bridged complex the Ni+ ion coordinates to C–S side forming a triangular structure with the Ni+–C and Ni+–S distances of 2.088 and 2.234 Å, respectively. The bridged C–S bond was not broken although this bond is stretched to 1.630 Å. This complex is mainly resulted from the p-s interaction between the p (C–S) orbital and the empty 4s orbital of Ni+. As shown in Fig. 2 2 IM1 is more stable than the ground state reactants by 151.7 kJ/ mol and it is the global minimum on both doublet and quartet PESs. The structure of 2IM1 is basically similar to the species found in the V+ + CS2 [6] and Fe+ + CS2 [10] systems, but closer to the corresponding complex of V+ with CS2. The main difference is that the S–C–S angle in 2IM1 is only slightly bent (170.2°) whereas this angle is more bend (<140°) in the complexes of Fe+ with CS2. It should be pointed out that in the reaction of Fe+ with CS2, a sulfur-bound encounter complex was found to locate before the C–S bridged complex, and the two complexes are connected by a transition state with a structure similar to 2IM1. Although numerous trials were taken to search for an earlier possible sulfur-encounter complex and a transition state lying before 2IM1, no such stationary points were located. Thus we conclude that the 2IM1 is the initial complex in the reaction, and its formation is a barrierless process. Starting from 2IM1, Ni+ inserts into the activated C–S bond via a transition state 2TS1 which is 165.1 kJ/mol above 2IM1. The distance between C and S in 2TS1 is greatly elongated to 2.505 Å and the Ni–S and Ni–C distances are significantly shortened, which indicates the C–S bond is nearly broken and Ni–S and Ni–C bonds are forming. With the complete rupture of C–S bond, the insertion intermediate 2IM2 is finally formed and it is more stable than 2TS1 by only 21.3 kJ/mol and slightly above the ground state reactants. Amentrout and co-workers have proposed the existence of the insertion intermediate of S–Ni+–C–S [9]. This proposition has been confirmed by our calculations. The experimentally observed products can be explained by the cleavages of different bonds in this insertion species. The dissociation products of NiS+ and CS can be formed through the cleavage of Ni–C bond. As shown in Fig. 2, this reaction is endothermic by 241.2 kJ/mol. According to the rule of spin conservation, the product NiS+ should be in its doublet state since CS is in its singlet ground state. However, our calculation and previous studies indicate that the doublet state (2P) is the excited state of NiS+ whereas the high spin quartet state (4R) is the
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ground state [24,25]. Therefore, the formation of ground state product NiS+ from the ground state reactants should be resulted from the spin-forbidden reaction Ni + (2D) + CS2(1R) ? + 4 1 NiS ( R) + CS( R) through the doublet–quartet surface crossing. To confirm the above propositions, we also investigated the quartet surface of the reaction which will be discussed later. Another main product observed in experiment is the structurally un-determined [Ni, C, S]+ species [9]. This product can be explained by the cleavage of S–Ni bond in 2IM2 leading to the product NiCS+ and S. Then two product channels are possible: 2 NiCS+ + 3S and 4NiCS+ + 3S. Our calculation indicates that NiCS+ has a doublet ground state of 2R with linear structure, whereas the quartet NiCS+ with an electronic state of 4A00 and Cs symmetry was found to be 180.6 kJ/mol (Table 2) higher in energy. Thus the formation of 2NiCS+ is energetically more favorable. As shown in Fig. 2, this reaction is endothermic by 207.7 kJ/mol, close to the experimental result 199.4 ± 8.8 kJ/mol. Another possible structure for [Ni, C, S]+ is CNiS+ which corresponds to the cleavage of C–S bond in 2IM2. As shown in Fig. 1, the C–S bond in 2IM2 is even shorter than that of separate CS, which indicates that the cleavage of this bond must be very unfavorable in energy. As suggested by Zhang et al. in the reaction of Fe+ with CS2, the formations of ground state and excited state of CFeS+ are endothermic by 646.2 and 909.2 kJ/mol at B3LYP/6-311+G* level [10], respectively. Such processes are impossible at low energy condition. Despite this, we also investigated this process for the reaction of Ni+ with CS2, but we found that the CNiS+ spices does not exist on both doublet and quartet surfaces. Therefore, we conclude that the observed product [Ni, C, S]+ should be NiCS+ (2R), and this is in agreement with Armentrout et al.’s assignment of this species. 3.2. The quartet surface of the reaction of Ni+(4F) with CS2 The reaction of the excited state of Ni+(4F, 3d84s1) with CS2 is more complex than that of ground state of Ni+ with CS2. Two possible pathways were identified for Ni+(4F) + CS2 reaction. The reaction pathways and the geometrical parameters of the stationary points on the surfaces have been demonstrated in Fig. 1. At the initial step of the first reaction pathway, an encounter complex 4IM3 was located. In this complex, Ni+ coordinates to the two S atoms in CS2 to form a quadrangular structure with C2v symmetry and 4B1 electronic state. This complex is more stable than the excited reactants by 107.8 kJ/mol. It should be noted that the intermediate like 4IM3 was not found in the reactions of V+ and Fe+ with CS2 [6,10]. 4IM3 can interconvert to 4IM4 via 4TS2 that is 44.3 kJ/mol above 4IM3. As shown in Fig. 1 4IM4 is also a C–S bridged complex which is analogous to 2IM1. Compared with 2 IM1, 4IM4 has a shorter C–Ni bond but a longer S–Ni bond. Further, the S–C–S angle is more bended in 4IM4. Calculations at both theoretical levels indicate that 4IM4 lies above its doublet counterpart 2IM1 by around 160 kJ/mol. Similar to the insertion process on the doublet surface, from 4 IM4, Ni inserts into the activated C–S bond via 4TS3 leading to the insertion intermediate 4IM5. The barrier of this step is 38.5 kJ/mol, much lower than that on doublet surface (165.1 kJ/ mol). 4 IM5 is structurally similar to its doublet counterpart 2IM2. Note that the calculations at both theoretical levels indicate that 4 IM5 is slightly more stable than 2IM2. This result can be understandable if the insertion intermediate is viewed as the complex of NiS+ and CS. Two results are possible when CS interacts with NiS+: (1) the SNi–C–S+ keeps its ground state as quartet, that is to say, the relatively weaker interaction between CS and NiS+ does not change the ground state configuration of NiS+ (1r22r21p41d43r12p2). (2) The stronger interaction between CS and NiS+ drives the 3r1 orbital up in energy such that the NiS+ con-
figuration within the SNi–CS+ changes to doublet state (1r22r21p41d43r02p3). But this moves the doublet state above the quartet state. The longer Ni+–C bond in 4IM5 than that in 2 IM1 may confirm the above analysis. The cleavages of C–Ni and S–Ni bonds in 4IM5 will lead to the ground state products of NiS+(4R) + CS(1R) and NiCS+(2R) + S(3P), respectively. As shown in Fig. 2, both of the two processes are endothermic by 91.1 and 86.9 kJ/mol, respectively. Although the reaction above is described as a two-step mechanism, we can not rule out the possibility that the C–S bridged complex 4IM4 can be initially formed as Ni+ and CS2 approach with each other. Starting from the quadrangular complex 4IM3, another reaction pathway was identified. As shown in Fig. 1, via 4TS4, one of the S atoms is abstracted by Ni+. IRC calculation confirmed that as the C–S bond was broken the Ni moved close to the C atom to form C–Ni bond. Finally, the insertion intermediate 4IM5 was formed. 4 TS4 is higher in energy than the excited reactants and lies above 4 TS2 and 4TS3 by 116.2 and 106.6 kJ/mol, respectively. But once the reaction energy reach the threshold energy of the products both the one-step and two-step mechanisms can make contributions, because the threshold energies of the products are higher than all the transition states. Interestingly, such an abstraction– insertion mechanism was not found in the reactions of Fe+ and V+ with CS2 [6,10]. 3.3. Doublet–quartet crossing As we mentioned above, the NiS+ has a quartet ground state 4R. Thus, the energetically favorable channel of the NiS+ formation from ground state reactants is: Ni+(2D) + CS2(1R) ? NiS+(4R) + CS(1R), but this channel is spin-forbidden and has to go through intersystem doublet–quartet crossing. From the calculations at B3LYP/TZVP and B3LYP/6-311+G*, we can acquire the following information: (1) the quartet insertion transition state 4TS3 lies above the doublet counterpart 2TS1 by around 40 kJ/mol and they are similar in structure. (2) The insertion intermediate 4IM5 is slightly more stable than its counterpart 2IM1 and they are strikingly similar in structure. (3) NiS+(4R) is more stable than NiS+(2P) by around 40 kJ/mol. All these results suggest that the formation of NiS+(4R) + CS(1R) from Ni+(2D) + CS2(1R) involves a change of spin and must therefore proceed through a crossing of doublet surface to quartet surface with relative efficiency, while at higher energies the spin-allowed reaction Ni+(2D) + CS2(1R) ? NiS+(2P) + CS(1R) can occur. It should be mentioned here that the intersystem crossing in the reaction of Fe+ and V+ with CS2 was also suggested [6,10]. The aim of our following calculations is to determine the region where the spin inversion occurs, and to acquire the structure and energy of the crossing point. By analyzing the structural similarities of the insertion transition states and insertion intermediates on both surfaces (Fig. 1), we speculate that the crossing point should be located after both of the doublet and quartet insertion transition states. To locate this crossing point, we chose a simple approach suggested by Yoshzawa et al. [26], for approximately locating the crossing points of the two PESs of different multiplicities. The main idea of this approach is to perform a series of single point calculations of one spin state along the IRC of the other spin state and vice versa. Starting from the doublet insertion transition state, along the IRC of 4 TS3 ? 4IM5, a series of single point calculations were carried out with quartet multiplicities at B3LYP/TZVP level, we obtain the quartet potential energy surface (Fig. 3a). It was found that these two surfaces cross at IRC = 0.80 with relative energy of 22.6 kJ/mol. The structure of this crossing point (CP1) is collected in Fig. 1. Similarly, another crossing point along the IRC of 2 TS1 ? 2IM2 was located at IRC = 0.80 with relative energy of 0.8 kJ/mol. According to Yoshiza et al. [26], CP2 would be the
T.H. Li et al. / Chemical Physics Letters 458 (2008) 19–23
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Fig. 3. Doublet potential energy along the quartet IRC from 4TS3 ? 4IM5 (a) and quartet potential energy along the doublet IRC from 2TS1 ? 2IM2 (b) at the level of B3LYP/ TZVP. (Energies relative to the ground state reactants, kJ/mol).
energy-minimum crossing point, and CP1 would be the energymaximum crossing point between the doublet and quartet surfaces in the reaction pathway from the C–S bridged complex to the insertion intermediate. As the reaction goes on, the reaction system should change its spin multiplicity from doublet state to quartet state in this region and move to the quartet PES which provides a lower energy pathway to the insertion intermediate 4IM5. Thus, the favorable reaction pathway for the formation of ground state NiS+ could be described as Ni+(2D) + CS2(1R) ? 2IM1 ? 2TS1 ? CP ? 4IM5 ? NiS+(4R) + CS(1R). Our calculation indicates that this reaction is endothermic by 211.9 kJ/mol, which is in agreement with the experimental threshold energy for the formation of NiS+ + CS (211.9 ± 7.5 kJ/mol). And our calculations support the experimental result that the product NiS+ has a slightly higher threshold than NiCS+ [9] (207.7 kJ/mol calculated and 199.4±8.8 kJ/mol experimentally measured). 4. Conclusions The reaction of Ni+ with CS2 was investigated in details by using DFT method B3LYP with TZVP and 6-311+G* basis sets. The products observed in experiment have been rationalized. The main conclusions of this work can be drawn as following: 1. The spin-allowed reaction of ground state of Ni+(2D) with CS2 was found to proceed according to a typical insertion–elimination mechanism leading to the excited state product NiS+(2P) and the ground state product NiCS+(2R). Our calculation indicates that the CNiS+ species does not exist and NiCS+(2R) is the most stable structure for the [Ni, C, S]+ species in experiment. 2. Two possible reaction pathways have been identified for the reaction of excited state of Ni+(4F) with CS2. Both of them start from a quadrangular S-bound encounter complex, but one undergoes through a two-step insertion mechanism, whereas another undergoes through a one-step abstraction–insertion mechanism. 3. The spin-forbidden reaction Ni+(2D) + CS2 ? NiS+(4R) + CS(1R) was found to proceed through a doublet–quartet surface crossing. The crossing seam was approximately calculated.
4. The results of our calculations indicate that the product NiCS+ has slightly lower threshold energy than NiS+, which is in agreement with experimental measurement.
Acknowledgements This work is supported by National Natural Science Foundation of China (20563005) and the Science Foundation of Southwest Forestry University (200612M). References [1] J.A. Rodriguez, M. Kuhn, J. HrBek, J. Phys. Chem. 100 (1996) 15494. [2] R.H. Holm, Chem. Rev. 96 (1996) 2237. [3] W. Kaim, B. Schwederski, Bioinorganic Chemistry: Inorganic Elements in the Chemistry of Life, Wiley, NY, 1994. [4] M. Almond, B. Cockayne, S.A. Cooke, D.A. Pice, P.C. Smith, P.J. Wright, J. Mater. Chem. 6 (1996) 1693. [5] I. Kretzschmar, D. Schröder, H. Schwarz, C. Rue, P.B. Armentrout, J. Phys. Chem. 104 (2000) 5046. [6] C. Rue, P.B. Armentrout, I. Kretzschmar, D. Schröder, J.N. Harvey, H. Schwarz, J. Chem. Phys. 110 (1999) 7858. [7] C. Rue, P.B. Armentrout, I. Kretzschmar, D. Schröder, H. Schwarz, Int. J. Mass Spectrom. 210/211 (2001) 283. [8] C. Rue, P.B. Armentrout, I. Kretzschmar, D. Schröder, H. Schwarz, J. Phys. Chem. A 105 (2001) 8458. [9] C. Rue, P.B. Armentrout, I. Kretzschmar, D. Schröder, H. Schwarz, J. Phys. Chem. A 106 (2002) 9788. [10] N. Jiang, D.J. Zhang, Chem. Phys. Lett. 366 (2002) 253. [11] A.D. Becke, J. Chem. Phys. 98 (1993) 1372. [12] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [13] A. Schaefer, C. Huber, R. Ahlrichs, J. Chem. Phys. 100 (1994) 5829. [14] M.C. Holthausen, W. Koch, J. Am. Chem. Soc. 188 (1996) 9932. [15] M.C. Holthausen, A. Fiedler, H. Schwarz, W. Koch, J. Phys. Chem. 100 (1996) 6236. [16] X.L. Gao, J.L. Xu, X.G. Xie, J. Mol. Struct. (Theochem) 724 (2005) 9. [17] G. Xie, X.L. Gao, J.L. Xu, X. J. Mol. Struct. (Theochem) 715 (2005) 65. [18] A. Irigoras, O. Elizalde, I. Silanes, J.E. Fowler, J.M. Ugalde, J. Am. Chem. Soc. 122 (2000) 114. [19] N. Russo, E. Sicilia, J. Am. Chem. Soc. 123 (2001) 2588. [20] N. Russo, E. Sicilia, J. Am. Chem. Soc. 124 (2002) 1471. [21] A.D. Mclean, G.S. Chandler, J. Chem. Phys. 72 (1980) 5639. [22] P.J. Hay, J. Chem. Phys. 66 (1977) 4377. [23] M.J. Frisch et al., Gaussian Inc., Pittsburgh, PA, 2003. [24] A. Fiedler, J. Hrušák, W. Koch, H. Schwarz, Chem. Phys. Lett. 211 (1993) 242. [25] A. Fiedler, D. Schröder, S. Shaik, H. Schwarz, J. Am. Chem. Soc. 116 (1994) 10734. [26] K. Yoshizawa, Y. Shiota, T. Yamabe, J. Chem. Phys. 111 (1999) 538.
Contents lists available at ScienceDirect
Chemical Physics Letters journal homepage: www.elsevier.com/locate/cplett
DFT study on the gas phase reaction of Ni+ with CS2 Tao Hong Li a,*, Chuan Ming Wang b, Xiang Yi Liu a, Xiao Guang Xie c a b c
Department of Chemistry, Southwest Forestry University, Kunming 650224, China Department of Biology, Honghe University, Menzi 661100, China Department of Chemistry, Yunnan University, Kunming 650091, China
a r t i c l e
i n f o
Article history: Received 9 February 2008 In final form 14 April 2008 Available online 9 May 2008
a b s t r a c t The reaction of Ni+ with CS2 has been investigated at B3LYP/TZVP and B3LYP/6-311 + G* levels of theory. The reaction mechanisms have been explored in detail on both doublet and quartet potential energy surfaces. The products observed in the experiment have been explained according to the cleavage of different bonds in the insertion intermediate S–Ni+–C–S. The product [Ni, C, S]+ observed in experiment was confirmed as Ni–CS+ (2R). The spin-forbidden reaction Ni+(2D) + CS2 ? NiS+(4R) + CS (1R) was found to proceed through a doublet–quartet surface crossing and the crossing seam was approximately calculated. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction The chemistry of transition-metal sulfur systems has been an active area due to their significance in industrial catalysis, biology systems and material science [1–4]. In industrial areas, considerable attention has been focused on the role of sulfur transition-metal complexes in catalysis poisoning [1]. In many biological systems, it has been found that sulfur coordination is necessary for the functioning of numerous biological transition-metal centers [2,3]. CS2 and COS are important sulfur-transfer reagents, which have been considered as possible sulfur sources for preparing thin layers of semiconductor materials [4]. Schwarz’s and Armentrout’s research groups have reported a serial of studies on the reactions of the whole 3d metals with CS2 using Guided Ion Beam Mass Spectrometer (GIB), where the sulfur-metal bond energies were determined [5–9]. They found the dominant products are MS+ (M = Sc Zn) and [M, C, S]+ (which was safely assigned as the metal-thiocarbonyl cation, M–CS+, at the lowest energy). According to the experimental observations, they predicted that the S–M+– C–S species could be an intermediate in these reactions, and they proposed that these reactions could proceed in an insertion–elimination mechanism. The general reaction pathway could be described as M+ + CS2 ? S–M+–C–S ? MS+ + CS or [M, C, S]+ + S. The previous DFT theoretical studies on the reactions of V+ and Fe+ with CS2 have confirmed this mechanism, and the experimentally observed products have been rationalized [6,10]. However, due to the different electronic structures, the reactions of V+ and Fe+ are different in details including mechanism and potential energy surfaces (PES). It can be expected that the reactions of all 3d metal ions could be different from each other. For example, by comparing the thermochemical data of the reactions of different ions with CS2, * Corresponding author. E-mail address: [email protected] (T.H. Li). 0009-2614/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2008.04.057
it was found that for Sc+ Co+ the formation of MS+ is always energetically favorable than that the formation of [M, C, S]+ [5–8], whereas for Ni+ the formation of the [Ni, C, S]+ species has a lower threshold energy than NiS+ [9]. What is the most stable structure for [Ni, C, S]+? Further, Ni+ has a doublet ground state of 2D (3d9), but the ground state of the product NiS+ is a quartet state 4R. Thus, the formation of ground state products from ground state reactants is formally spin-forbidden: Ni+(2D) + CS2(1R) ? NiS+(4R) + CS(1R). As a result, the intersystem crossing between the doublet and quartet potential energy surfaces occurs when the total energy of the system is close to the energy of the crossing point and this has been pointed out by Armentrout et al. as well. Is this true? And where is the crossing point located? Providing answers for these questions needs the theoretical studies to provide correct mechanism and accurate potential energy surfaces. As a supplement of experimental study, we present here a theoretical study of the reaction of the late 3d ion Ni+ with CS2 aiming to give a reasonable model that how Ni+ activates the C–S bond in CS2 and explaining the products observed in experiment. Further, in this study the reaction of Ni+ will be compared with those of V+ and Fe+. 2. Computational method All geometries (reactant, products, intermediates and transition states) were fully optimized by using density functional theory method B3LYP [11,12] with TZVP [13] basis set. Harmonic vibration frequencies were calculated at the same level to characterize the stationary points and to estimate the contributions of zero-point vibration to relative energies. The intrinsic reaction coordinate (IRC) method was used to track the reaction pathways from the transition states to the corresponding minimums. The choice of B3LYP method is motivated by its reliability and efficiency as a practical tool in transition-metal chemistry [14–20]. The quality of B3LYP/TZVP level has been tested in previous studies of transition-metal-containing sys-
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tems, and it has been shown to be computational efficiency to provide reasonable accurate geometries and energies [16–18]. To obtain more reliable potential energetic picture for the reaction, all energies of B3LYP/TZVP optimized geometries were recalculated by the conjunction of B3LYP with the larger standard basis set 6-311+G* [21,22]. To confirm that the lowest energy solution to SCF equations was found for each stationary point, the wave function stability was always tested. All calculations were carried out with GAUSSIAN 03 program package [23]. 3. Results and discussion
tion energy and bond dissociation energies of the reactant and products are compared in Table 1. The relevant energies are collected in Table 2. To evaluate the reliability of chosen method, we first calculated the excitation energy of Ni+ and the bond dissociation energies (BDE) of the ground state of CS2(1R), NiS+(4R) and NiCS+(2R) at different levels. By comparing the calculated values with experimental results, we found that the B3LYP/6-311+G* gave the smallest absolute errors and the results at this level are in good agreement with experimental findings. Unless otherwise specified, all energies discussed in the text refer to the results obtained at B3LYP/ 6-311+G* level.
The optimized geometries are shown in Fig. 1, and the sketch of the PES is shown in Fig. 2. The calculated and experimental excita-
Fig. 1. Optimized geometries for the stationary points and the structure of the crossing point on the PESs of Ni+(2D, 4F) + CS2 reaction at B3LYP/TZVP level of theory (distances in Å and angles in degrees).
T.H. Li et al. / Chemical Physics Letters 458 (2008) 19–23
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Fig. 2. Potential energy diagram for the Ni+(2D, 4F) + CS2 reaction at B3LYP/6-311+G* level of theory (relative energies in kJ/mol).
Table 1 The singlet–triplet splitting energy for Ni+ and the bond dissociation energies for NiS+ and NiCS+ (energies in kJ/mol)
4
DE (2D ? F) D0 (CS–S) D0 (Ni+–S) D0 (Ni+–CS) a
B3LYP/TZVP
B3LYP/6-311+G*
Experimentala
92.8 432.6 211.5 274.6
120.8 436.4 224.0 228.2
104.5 433.9 237.0 234.1
Excitation energies and BDEs taken from Ref. [9].
Table 2 Total energies (E, in hartree), zero-point energies (ZPE in kJ/mol), imaginary frequencies (IMG, cm1) and ZPE-corrected relative energies (Erel, in kJ/mol) B3LYP/6-311+G*
Species
B3LYP/TZVP E
ZPE
Ni+ + 1CS2 2 IM1 2 TS1 2 IM2 4 Ni+ + 1CS2 4 IM3 4 TS2 4 IM4 4 TS3 4 IM5 4 TS4 4 NiS+ + 1CS 2 NiS+ + 1CS 2 NiCS + 3S 4 NiCS + 3S
2342.570669 2342.628824 2342.566181 2342.574073 2342.535322 2342.573117 2342.558558 2342.565891 2342.549959 2342.577296 2342.517036 2342.492074 2342.476486 2342.509306 2342.434025
18.0 18.8 15.9 15.9 18.0 18.0 14.6 15.9 13.8 15.9 11.7 10.5 10.0 13.8 10.9
2
IMG
290
614 392 120
Erel
E
Erel
0.0 151.7 9.7 11.3 92.8 6.3 28.4 10.5 50.2 19.6 134.6 198.6 239.1 156.8 369.9
2342.512493 2342.56660 2342.502636 2342.510749 2342.466523 2342.507596 2342.489444 2342.501002 2342.485417 2342.513283 2342.444013 2342.428535 2342.417556 2342.431693 2342.364584
0.0 141.3 23.8 2.5 120.8 13.0 57.3 28.4 66.9 4.2 173.5 211.9 241.2 207.7 388.3
3.1. The doublet surface of the reaction of Ni+(2D) with CS2 The reaction of ground state of Ni+(2D, 3d9) with CS2 was found to be a typical insertion–elimination mechanism. As shown in Fig. 1, all the intermediates and transition state have the Cs symmetry and 2A00 electronic state, which means there must be a 2A0 surface as well. Considering this 2A0 surface may provide additional information for the C–S bond activation process, we have also located this surface. But it was found that this surface lies much higher above the 2A00 surface. Thus the reaction on this surface unlikely contributes to the formation of the products. Therefore this 2 0 A surface will not be discussed.
2 IM1 is the initial complex formed as Ni+ and CS2 approach with each other. In this C–S bridged complex the Ni+ ion coordinates to C–S side forming a triangular structure with the Ni+–C and Ni+–S distances of 2.088 and 2.234 Å, respectively. The bridged C–S bond was not broken although this bond is stretched to 1.630 Å. This complex is mainly resulted from the p-s interaction between the p (C–S) orbital and the empty 4s orbital of Ni+. As shown in Fig. 2 2 IM1 is more stable than the ground state reactants by 151.7 kJ/ mol and it is the global minimum on both doublet and quartet PESs. The structure of 2IM1 is basically similar to the species found in the V+ + CS2 [6] and Fe+ + CS2 [10] systems, but closer to the corresponding complex of V+ with CS2. The main difference is that the S–C–S angle in 2IM1 is only slightly bent (170.2°) whereas this angle is more bend (<140°) in the complexes of Fe+ with CS2. It should be pointed out that in the reaction of Fe+ with CS2, a sulfur-bound encounter complex was found to locate before the C–S bridged complex, and the two complexes are connected by a transition state with a structure similar to 2IM1. Although numerous trials were taken to search for an earlier possible sulfur-encounter complex and a transition state lying before 2IM1, no such stationary points were located. Thus we conclude that the 2IM1 is the initial complex in the reaction, and its formation is a barrierless process. Starting from 2IM1, Ni+ inserts into the activated C–S bond via a transition state 2TS1 which is 165.1 kJ/mol above 2IM1. The distance between C and S in 2TS1 is greatly elongated to 2.505 Å and the Ni–S and Ni–C distances are significantly shortened, which indicates the C–S bond is nearly broken and Ni–S and Ni–C bonds are forming. With the complete rupture of C–S bond, the insertion intermediate 2IM2 is finally formed and it is more stable than 2TS1 by only 21.3 kJ/mol and slightly above the ground state reactants. Amentrout and co-workers have proposed the existence of the insertion intermediate of S–Ni+–C–S [9]. This proposition has been confirmed by our calculations. The experimentally observed products can be explained by the cleavages of different bonds in this insertion species. The dissociation products of NiS+ and CS can be formed through the cleavage of Ni–C bond. As shown in Fig. 2, this reaction is endothermic by 241.2 kJ/mol. According to the rule of spin conservation, the product NiS+ should be in its doublet state since CS is in its singlet ground state. However, our calculation and previous studies indicate that the doublet state (2P) is the excited state of NiS+ whereas the high spin quartet state (4R) is the
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ground state [24,25]. Therefore, the formation of ground state product NiS+ from the ground state reactants should be resulted from the spin-forbidden reaction Ni + (2D) + CS2(1R) ? + 4 1 NiS ( R) + CS( R) through the doublet–quartet surface crossing. To confirm the above propositions, we also investigated the quartet surface of the reaction which will be discussed later. Another main product observed in experiment is the structurally un-determined [Ni, C, S]+ species [9]. This product can be explained by the cleavage of S–Ni bond in 2IM2 leading to the product NiCS+ and S. Then two product channels are possible: 2 NiCS+ + 3S and 4NiCS+ + 3S. Our calculation indicates that NiCS+ has a doublet ground state of 2R with linear structure, whereas the quartet NiCS+ with an electronic state of 4A00 and Cs symmetry was found to be 180.6 kJ/mol (Table 2) higher in energy. Thus the formation of 2NiCS+ is energetically more favorable. As shown in Fig. 2, this reaction is endothermic by 207.7 kJ/mol, close to the experimental result 199.4 ± 8.8 kJ/mol. Another possible structure for [Ni, C, S]+ is CNiS+ which corresponds to the cleavage of C–S bond in 2IM2. As shown in Fig. 1, the C–S bond in 2IM2 is even shorter than that of separate CS, which indicates that the cleavage of this bond must be very unfavorable in energy. As suggested by Zhang et al. in the reaction of Fe+ with CS2, the formations of ground state and excited state of CFeS+ are endothermic by 646.2 and 909.2 kJ/mol at B3LYP/6-311+G* level [10], respectively. Such processes are impossible at low energy condition. Despite this, we also investigated this process for the reaction of Ni+ with CS2, but we found that the CNiS+ spices does not exist on both doublet and quartet surfaces. Therefore, we conclude that the observed product [Ni, C, S]+ should be NiCS+ (2R), and this is in agreement with Armentrout et al.’s assignment of this species. 3.2. The quartet surface of the reaction of Ni+(4F) with CS2 The reaction of the excited state of Ni+(4F, 3d84s1) with CS2 is more complex than that of ground state of Ni+ with CS2. Two possible pathways were identified for Ni+(4F) + CS2 reaction. The reaction pathways and the geometrical parameters of the stationary points on the surfaces have been demonstrated in Fig. 1. At the initial step of the first reaction pathway, an encounter complex 4IM3 was located. In this complex, Ni+ coordinates to the two S atoms in CS2 to form a quadrangular structure with C2v symmetry and 4B1 electronic state. This complex is more stable than the excited reactants by 107.8 kJ/mol. It should be noted that the intermediate like 4IM3 was not found in the reactions of V+ and Fe+ with CS2 [6,10]. 4IM3 can interconvert to 4IM4 via 4TS2 that is 44.3 kJ/mol above 4IM3. As shown in Fig. 1 4IM4 is also a C–S bridged complex which is analogous to 2IM1. Compared with 2 IM1, 4IM4 has a shorter C–Ni bond but a longer S–Ni bond. Further, the S–C–S angle is more bended in 4IM4. Calculations at both theoretical levels indicate that 4IM4 lies above its doublet counterpart 2IM1 by around 160 kJ/mol. Similar to the insertion process on the doublet surface, from 4 IM4, Ni inserts into the activated C–S bond via 4TS3 leading to the insertion intermediate 4IM5. The barrier of this step is 38.5 kJ/mol, much lower than that on doublet surface (165.1 kJ/ mol). 4 IM5 is structurally similar to its doublet counterpart 2IM2. Note that the calculations at both theoretical levels indicate that 4 IM5 is slightly more stable than 2IM2. This result can be understandable if the insertion intermediate is viewed as the complex of NiS+ and CS. Two results are possible when CS interacts with NiS+: (1) the SNi–C–S+ keeps its ground state as quartet, that is to say, the relatively weaker interaction between CS and NiS+ does not change the ground state configuration of NiS+ (1r22r21p41d43r12p2). (2) The stronger interaction between CS and NiS+ drives the 3r1 orbital up in energy such that the NiS+ con-
figuration within the SNi–CS+ changes to doublet state (1r22r21p41d43r02p3). But this moves the doublet state above the quartet state. The longer Ni+–C bond in 4IM5 than that in 2 IM1 may confirm the above analysis. The cleavages of C–Ni and S–Ni bonds in 4IM5 will lead to the ground state products of NiS+(4R) + CS(1R) and NiCS+(2R) + S(3P), respectively. As shown in Fig. 2, both of the two processes are endothermic by 91.1 and 86.9 kJ/mol, respectively. Although the reaction above is described as a two-step mechanism, we can not rule out the possibility that the C–S bridged complex 4IM4 can be initially formed as Ni+ and CS2 approach with each other. Starting from the quadrangular complex 4IM3, another reaction pathway was identified. As shown in Fig. 1, via 4TS4, one of the S atoms is abstracted by Ni+. IRC calculation confirmed that as the C–S bond was broken the Ni moved close to the C atom to form C–Ni bond. Finally, the insertion intermediate 4IM5 was formed. 4 TS4 is higher in energy than the excited reactants and lies above 4 TS2 and 4TS3 by 116.2 and 106.6 kJ/mol, respectively. But once the reaction energy reach the threshold energy of the products both the one-step and two-step mechanisms can make contributions, because the threshold energies of the products are higher than all the transition states. Interestingly, such an abstraction– insertion mechanism was not found in the reactions of Fe+ and V+ with CS2 [6,10]. 3.3. Doublet–quartet crossing As we mentioned above, the NiS+ has a quartet ground state 4R. Thus, the energetically favorable channel of the NiS+ formation from ground state reactants is: Ni+(2D) + CS2(1R) ? NiS+(4R) + CS(1R), but this channel is spin-forbidden and has to go through intersystem doublet–quartet crossing. From the calculations at B3LYP/TZVP and B3LYP/6-311+G*, we can acquire the following information: (1) the quartet insertion transition state 4TS3 lies above the doublet counterpart 2TS1 by around 40 kJ/mol and they are similar in structure. (2) The insertion intermediate 4IM5 is slightly more stable than its counterpart 2IM1 and they are strikingly similar in structure. (3) NiS+(4R) is more stable than NiS+(2P) by around 40 kJ/mol. All these results suggest that the formation of NiS+(4R) + CS(1R) from Ni+(2D) + CS2(1R) involves a change of spin and must therefore proceed through a crossing of doublet surface to quartet surface with relative efficiency, while at higher energies the spin-allowed reaction Ni+(2D) + CS2(1R) ? NiS+(2P) + CS(1R) can occur. It should be mentioned here that the intersystem crossing in the reaction of Fe+ and V+ with CS2 was also suggested [6,10]. The aim of our following calculations is to determine the region where the spin inversion occurs, and to acquire the structure and energy of the crossing point. By analyzing the structural similarities of the insertion transition states and insertion intermediates on both surfaces (Fig. 1), we speculate that the crossing point should be located after both of the doublet and quartet insertion transition states. To locate this crossing point, we chose a simple approach suggested by Yoshzawa et al. [26], for approximately locating the crossing points of the two PESs of different multiplicities. The main idea of this approach is to perform a series of single point calculations of one spin state along the IRC of the other spin state and vice versa. Starting from the doublet insertion transition state, along the IRC of 4 TS3 ? 4IM5, a series of single point calculations were carried out with quartet multiplicities at B3LYP/TZVP level, we obtain the quartet potential energy surface (Fig. 3a). It was found that these two surfaces cross at IRC = 0.80 with relative energy of 22.6 kJ/mol. The structure of this crossing point (CP1) is collected in Fig. 1. Similarly, another crossing point along the IRC of 2 TS1 ? 2IM2 was located at IRC = 0.80 with relative energy of 0.8 kJ/mol. According to Yoshiza et al. [26], CP2 would be the
T.H. Li et al. / Chemical Physics Letters 458 (2008) 19–23
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Fig. 3. Doublet potential energy along the quartet IRC from 4TS3 ? 4IM5 (a) and quartet potential energy along the doublet IRC from 2TS1 ? 2IM2 (b) at the level of B3LYP/ TZVP. (Energies relative to the ground state reactants, kJ/mol).
energy-minimum crossing point, and CP1 would be the energymaximum crossing point between the doublet and quartet surfaces in the reaction pathway from the C–S bridged complex to the insertion intermediate. As the reaction goes on, the reaction system should change its spin multiplicity from doublet state to quartet state in this region and move to the quartet PES which provides a lower energy pathway to the insertion intermediate 4IM5. Thus, the favorable reaction pathway for the formation of ground state NiS+ could be described as Ni+(2D) + CS2(1R) ? 2IM1 ? 2TS1 ? CP ? 4IM5 ? NiS+(4R) + CS(1R). Our calculation indicates that this reaction is endothermic by 211.9 kJ/mol, which is in agreement with the experimental threshold energy for the formation of NiS+ + CS (211.9 ± 7.5 kJ/mol). And our calculations support the experimental result that the product NiS+ has a slightly higher threshold than NiCS+ [9] (207.7 kJ/mol calculated and 199.4±8.8 kJ/mol experimentally measured). 4. Conclusions The reaction of Ni+ with CS2 was investigated in details by using DFT method B3LYP with TZVP and 6-311+G* basis sets. The products observed in experiment have been rationalized. The main conclusions of this work can be drawn as following: 1. The spin-allowed reaction of ground state of Ni+(2D) with CS2 was found to proceed according to a typical insertion–elimination mechanism leading to the excited state product NiS+(2P) and the ground state product NiCS+(2R). Our calculation indicates that the CNiS+ species does not exist and NiCS+(2R) is the most stable structure for the [Ni, C, S]+ species in experiment. 2. Two possible reaction pathways have been identified for the reaction of excited state of Ni+(4F) with CS2. Both of them start from a quadrangular S-bound encounter complex, but one undergoes through a two-step insertion mechanism, whereas another undergoes through a one-step abstraction–insertion mechanism. 3. The spin-forbidden reaction Ni+(2D) + CS2 ? NiS+(4R) + CS(1R) was found to proceed through a doublet–quartet surface crossing. The crossing seam was approximately calculated.
4. The results of our calculations indicate that the product NiCS+ has slightly lower threshold energy than NiS+, which is in agreement with experimental measurement.
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