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DFT study on the reaction of neutral Ti and Ni atoms with CS2
Journal of Molecular Structure: THEOCHEM 724 (2005) 125–133 www.elsevier.com/locate/theochem
DFT study on the reaction of neutral Ti and Ni atoms with CS2 Taohong Lia, Xiaoguang Xiea, Shulin Gaoa, Chuanming Wangb, Weixian Chengc, Xulin Panc, Huai Caoa,c,* a
Department of Chemistry, Yunnan University, Kunming 650091, China b Department of Biology, Honghe University, Mengzi 661100, China c Modern Biological Research Center, Yunnan University, Kunming 650091, China Received 14 January 2005; revised 6 March 2005; accepted 7 March 2005 Available online 29 April 2005
Abstract The reaction mechanisms of the ground state (3F) of neutral Ti atom, the lowest triplet (3F) and singlet state (1D) of Ni atom with CS2: MCCS2/MSCCS (MZTi, Ni) have been investigated by using DFT method B3LYP with DZVP basis set. Two reaction channels have been identified for the reactions of both Ti (3F) and Ni (3F) atoms with CS2, and one channel has been identified for the reaction of Ni (1D) with CS2. These reactions are initiated by different mechanisms, but all the reaction channels involve the insertion of metal atoms into the C– S bond of CS2 yielding insertion intermediates SMCS from C–S bridged intermediates M–(h2-CS)S or cyclic complexes M–(h2-S2)C. The reaction of triplet ground state Ti with CS2 requires no activation energy, whereas the reactions of Ni atom with CS2 proceed with 7, 20 and 17 kcal/mol activation energies for the two triplet and one singlet pathways, respectively. The reaction of Ni with CS2 was shown to occur preferentially on triplet surface and the experimentally observed species, Ni–(h2-CS)S and SNiCS, have been explained according to the mechanisms revealed in this work. q 2005 Elsevier B.V. All rights reserved. Keywords: B3LYP; Neutral titanium and nickel atoms; Carbon disulfide; Reaction mechanism; Insertion
1. Introduction The chemistry of transition metals and their compounds has been an active area of both theoretical and experimental researches due to their important role in catalytic and material science. Carbon dioxide (CO2), carbon disulfide (CS2) and carbonyl sulfide (OCS) are the ligands of great interest which can coordinate with metal atoms and ions to produce metal oxides, metal sulfides and some new species of organometallic compounds. Reactions of the first row neutral transition metal atoms with CO2 have been extensively studied by both experiment and theory [1–14]. Both experimental and theoretical studies show that the early first row neutral transition metal atoms, such as Sc, Ti, V, can react with CO2 with no or low activation energy
* Corresponding author. Address: Modern Biological Research Center, Yunnan University, Kunming 650091, China. Tel.: C86 871 5033496; fax: C86 871 5036373. E-mail address: [email protected] (H. Cao).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.03.024
and yield MO, OMCO, and some species of M–(CO2) complex, whereas the late ones, such as Ni [1,5,10], have much lower reactivity with CO2, and in low temperature Ni only forms a 1:1 complex with CO2. Compared with CO2, the reaction of transition metal atoms with CS2 is relatively unexplored. Zhou et al. [15] reported a matrix isolation IR study on the reactions of ablated Co, Ni and Cu atoms and cations with CS2, they also carried out a DFT calculation on the observed products (SMCS, M–(h2-CS)S, M–CS2, and MCSC 2 ), but the reaction mechanisms were not reported. Pa´pai et al. [11] have reported a theoretical study on the reactions of V(s2d3)CXCY/XVCY/VXCCY with XCYZCO2, CS2 and OCS, and it was found that from C–S or C–O side-bonded complexes V can insert into C–S or C–O bond with no or low energy barrier yielding insertion species XVCY. Can a similar reaction mechanism be applicable to the reactions of other neutral transition metal atoms with CS2? Are there new reaction channels? What are the different behaviors between the early transition metal atoms and the late ones in the reactions with CS2? Promoted by these questions, we investigated the reactions CS2CM/MSCCS (MZTi, Ni) in detail. Although there is no experimental study reported on the reaction of Ti atom with CS2, a comparative theoretical
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study on the reactions of Ti and Ni atoms with CS2 is interesting and important since Ti is a representative of the first row early transition metal atoms while Ni belongs to the late and both of them have the same ground electronic state 3F. According to Zhou et al. [15], the observed Ni–(h2-CS)S complexes appear to be in singlet state but the insertion products SNiCS appear to be in triplet state. Considering that the singlet and triplet PESs may across, the reactions of the lowest triplet (3d84s2, 3F) and singlet (3d94s1, 1D) electronic states of Ni with CS2 were investigated, and for Ti, only the ground state (3F) is considered. The main aim of the present study is to give qualitative models that explain how Ti and Ni atoms react with CS2, and to compare the reactivity of these two atoms with CS2.
molecules calculated at the B3LYP/DZVP level of theory are compared in Table 1 with both the experimental data and the results obtained with B3LYP/6-311CG(2d) [11] and CCSD(T) levels [20]. As expected, the geometries, the spectroscopic and the thermochemical data provided by B3LYP/DZVP reflected the experimental trends well and the accuracy of B3LYP/DZVP is comparable to B3LYP/ 6-311CG(2d) and CCSD(T) levels of theory. 3.1. The reaction of Ti (3d84s2, 3F) with CS2 (1SC) Two possible reaction pathways (pathways A and B) have been found for the reaction: TiCCS2/TiSCCS. The optimized geometries of all stationary points involved in the two pathways are shown in Fig. 1, and the sketch of the PESs is shown in Fig. 2. The ZPEs, the ZPE corrected relative energies and the harmonic vibration frequencies of all the species involved in the reaction are listed in Table 2.
2. Methods All molecular geometries (reactants, intermediates, transition states and products) were fully optimized by using density functional theory method B3LYP [16] with DZVP [17] basis set. The choice of B3LYP method is motivated by its reliability and efficiency as a practical tool in transition metal chemistry [18]. Harmonic vibration frequencies were obtained 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 transition states to the corresponding minimums. To analyze the bond characteristics of the molecules, the NBO calculations were carried out. To ensure that the obtained wave functions are stable, the stabilities of the wave functions were tested. All calculations were carried out with GAUSSIAN 98 program [19].
3.1.1. Pathway A In this pathway the reaction proceeds via two steps. When Ti collides with CS2 a stabilized T-shape C-coordinated complex Ti–CS2 (3B1) (C2v) is initially formed with binding energy of 39 kcal/mol. Then Ti–CS2 (3B1) evolves to the C–S bridged complex Ti–(h2-CS)S (3A 00 ) via TS1 (3A 00 ) with a small barrier of 4 kcal/mol. The complex Ti–(h2-CS)S (3A 00 ) also lies below the reactants by 39 kcal/mol. From Ti–(h2-CS)S (3A 00 ) the reaction proceeds to produce the insertion product STiCS (3A 00 ) via TS2 (3A 00 ) with a small insertion barrier of 1 kcal/mol. This small insertion barrier suggests that once the C–S bridged complex Ti–(h2-CS)S (3A 00 ) forms the insertion reaction will take place immediately. The insertion product STiCS (3A 00 ) is the global minimum on this surface, and its relative energy is 45 kcal/mol lower than the reactants. NBO calculation shows that in STiCS (3A 00 ) two triple bonds have formed between Ti and S2, C and S1 atoms. The STi–CS binding energy is 41 kcal/mol which can basically be attributed to the Ti–C bond arising from a CS/Ti s-donation and a simultaneous Ti/CS p-backdonation as Pa´pai et al. [7] suggested for the OTiCO species. The strong interaction of 3d lone pair orbital of Ti with
3. Results and discussions Before the discussion on the mechanisms of the reactions MCCS2/MSCCS, we first present the results obtained for the ground state reactants and products involved in these reactions. Some selected molecular properties of these
Table 1 Calculated (B3LYP/DZVP) and experimental equilibrium properties of the ground states of CS2, CS, TiS and NiS CS2 (1SC)a
Re ue D0
CS (1SC)a
TiS (3D)b
NiS (3SK)b
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
1.566 [1.558] 1546, 675, 399 [1532, 668, 398] 104.9 [105.4]
1.556
1.547 [1.535] 1296 [1296] 160.4 [162.6]
1.534
2.093 (2.083) 562 (575) 109.5
–
1.981 (1.980) 513 (636) 71.4
–
1535, 658, 397 104.0
1285 169.4
– 109.5
˚ , vibration frequencies (ue) in cmK1, ZPE corrected bond dissociation energies (D0) in kcal/mol. Units: bond lengths (Re) in A a The values in square brackets calculated at B3LYP/6-311CG(2d) level and the experimental data are taken from Ref. [11]. b The values in brackets calculated at CCSD(T) level and the experimental data are taken from Ref. [20].
– 81.4
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Fig. 1. Optimized geometries of the reactants, intermediate complexes, products and transition states for the lowest triplet pathways of the TiCCS2/TiSCCS ˚ and angles in degrees). reaction at B3LYP/DZVP level of theory (bond lengths in A
the p-antibonding (C–S1)* orbital results in the relatively ˚ ). long C–S1 bond length (1.57 A The potential energy profile of this pathway is shown in Fig. 2. Obviously, the reaction requires no activation energy, since TS1 (3A 00 ) and TS2 (3A 00 ) lie below the reactants by 36 and 38 kcal/mol, respectively, which suggests that the reaction could take place spontaneously. The high feasibility of Ti insertion into C–S bond of CS2 yielding STiCS species is very similar to the case of Ti insertion into C–O bond which has been confirmed by both experimental and theoretical studies [1,7,8,13]. Thus ablated Ti atoms reacting with CS2 molecules to give primarily products STiCS is foreseeable, although there is no experiment reported so far. The reaction of TiCCS2/TiSCCS is predicted to be exothermic by 5 kcal/mol at B3LYP/DZVP level plus ZPE, and this result is very close to the experimental value 6 kcal/mol calculated as D0(Ti–S)–D0(S–CS) by using the bond dissociation energies in Table 1.
It is worth mentioning that in the theoretical studies on the reactions of VCCS2/VSCCS [11] and VCCCS2/ VSCCCS [21], only one transition state like TS2 (3A 00 ) which connects the V–(h2-CS)S and the insertion product SVCS was located, and the analogues to Ti–CS2 (3B1) and TS1 (3A 00 ) were not given. In the study on the reaction of FeC with CS2 [22], an analogue to Ti–CS2 (3B1), FeC–CS2 (C2v), was located, and from this complex FeC inserted into C–S bond via a transition state like TS2 (3A 00 ) yielding a linear insertion species SFeCSC. Obviously, this mechanism is also different from the case of Ti in which Ti atom inserts into the C–S bond from the C–S bridged complex Ti–(h2-CS)S (3A 00 ) as discussed above. 3.1.2. Pathway B In pathway B, from an initially formed cyclic complex Ti–(h2-S2)C (3B1) (C2v) stabilized by 39 kcal/mol the Ti inserts directly into C–S2 bond via a non-planar and highly
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Fig. 2. Potential energy diagram for the TiCCS2/TiSCCS reaction in the lowest triplet electronic states calculated at B3LYP/DZVP level. All relative energies (including ZPE) are given in kcal/mol with respect to CS2CTi.
distorted transition state TS3 (3A) yielding a new species of insertion intermediate which is an isomer of STiCS (3A 00 ) and denoted as iso-STiCS (3A). The insertion barrier is 23 kcal/mol which is much higher than that of pathway A. The iso-STiCS (3A) can convert to STiCS (3A 00 ) via an isomerization transition state TS4 (3A), and the barrier is only 3 kcal/mol which indicates that the isomerization is very easy. NBO analysis shows that the bonding characteristics of iso-STiCS (3A)(C1) are similar to those of STiCS (3A), and there is no bond between the S1 and Ti atoms, which agrees ˚ . So it is determined as a new with the S1–Ti distance 2.58 A type of insertion product which is an isomer of STiCS (3A 00 ). Because of the non-planar and distorted structure, isoSTiCS (3A) is less stable than the planar STiCS (3A 00 ) by 9 kcal/mol. It can be seen from Fig. 1 that TS3 (3A) and TS4 (3A) lie above TS1 (3A 00 ) and TS2 (3A 00 ) by 20 and 5 kcal/mol, respectively, which implies that pathway B is energetically less favorable than pathway A. However, the activation energies of TS3 (3A) and TS4 (3A) relative to the reactants are K16 and K33 kcal/mol, so this reaction could also take place spontaneously and this mechanism should be also important for the reaction CS2CTi/CSCTiS. In the theoretical studies on the reactions of V, VC and C Fe with CS2 [11,21,22] the mechanism similar to pathway B was not proposed. Interestingly, in the study on the reaction of Ti with CO2 [13], besides the insertion mechanism like the second step of pathway A, a complex analogue to Ti–(h2-S2)C, Ti–(h2-O2)C was also identified, but from Ti–(h2-O2)C the Ti atom abstracted one O atom directly via a cyclic planar transition state to form the complex COTiO in which CO and TiO were weakly bonded.
3.2. Reactions of Ni with CS2 (1SC) Two pathways for the reaction of triplet Ni atom with CS2 have been found (pathways A and B), and only one pathway for the reaction of singlet Ni atom with CS2 has been found. The fully optimized geometries of all species involved in these reactions are shown in Fig. 3, the energy profile of these surfaces is shown in Fig. 4. The ZPEs, the imaginary frequencies of the transition states (IMG), the total energies and ZPE corrected relative energies of all the species involved in these reactions are listed in Table 3. 3.2.1. Pathway A Three minima (NiSCS (3A 00 ), Ni–(h2-CS)S (3A 00 ) and SNiCS (3A 00 )) and two first-saddle points (TS1 (3A 00 ) and TS2 (3A 00 )) on this triplet surface have been located. Table 2 Total energies (E, in hartree) and relative energies (DE, in kcal/mol) including zero-point energies (ZPE in kcal/mol) correction at B3LYP/DZVP level for the stationary points (reactants, intermediate complexes, transition states, and products) shown in Fig. 1, and the imaginary vibrational frequencies (cmK1) (IMG) for the transition states Species
ZPE
CS2CTi Ti–CS2 (3B1) TS1 (3A 00 ) Ti–(h2-CS)S (3A 00 ) TS2 (3A 00 ) STiCS (3A 00 ) Ti–(h2KS2)C (3B1) TS3 (3A) iso-STiCS (3A) TS4 (3A) CSCTiS
4.3 4.2 4.1 4.1 3.7 3.9 4.0 3.0 3.4 3.5 2.7
IMG
K143 K223
K322 K158
DE
E
0.0 K39.4 K35.7 K39.4 K38.3 K45.2 K39.0 K16.0 K36.0 K33.2 K4.6
K1683.673455 K1683.735998 K1683.729924 K1683.735923 K1683.733416 K1683.744784 K1683.735029 K1683.696824 K1683.729239 K1683.7249706 K1683.678121
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Unlike the pathway A in the reaction of Ti with CS2, at the initial reaction step the Ni atom attaches to one S atom of CS2 with the formation of a planar end-bonded complex NiSCS (3A 00 ), and this complex is only stabilized by 6 kcal/mol relative to the reactants. Via TS1 (3A 00 ) the NiSCS (3A 00 ) intermediate converts to a C–S bridged
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complex Ni–(h2-CS)S (3A 00 ) which lies below the reactants by 10 kcal/mol and it is an analogue to Ti–(h2-CS)S (3A 00 ). This step proceeds with a negative activation energy of K2 kcal/mol. Similarly, from Ni–(h2-CS)S (3A 00 ) the reaction proceeds to the insertion product SNiCS (3A 00 ) via TS2 (3A 00 ) whose geometry is similar to that of Ti TS2
Fig. 3. Optimized geometries of the reactants, intermediate complexes, products and transition states for the lowest triplet and singlet pathways of the NiC ˚ and angles in degrees). CS2/NiSCCS reaction at B3LYP/DZVP level of theory (bond lengths in A
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Fig. 4. Potential energy diagram for the NiCCS2/NiSCCS reaction in the lowest singlet and triplet electronic states calculated at B3LYP/DZVP level. All relative energies (including ZPE) are given in kcal/mol with respect to CS2C3Ni.
(3A 00 ). The activation barrier for this step is 7 kcal/mol and it is the rate-determining step of this reaction. The triplet insertion product SNiCS (3A 00 ) lies below the initial reactants by 11 kcal/mol and it is more stable than its singlet counterpart which will be discussed later by 13 kcal/mol. Thus 3A 00 is predicted to be the ground electronic state of the insertion product with B3LYP/DZVP, and this is in agreement with Zhou et al.’s [15] B3LYP and BP86/6-311G* calculations, but the triplet–singlet energy gap was not given in their report. The calculated SNi–CS binding energy is 45 kcal/ mol at B3LYP/DZVP level which may give a rationale for the detection of SNiCS species and explain that there is no NiS observed in experiment [15]. The geometry of SNiCS (3A 00 ) is similar to that of STiCS 3 00 ( A ). One may notice that the C–S1 bond length of SNiCS (3A 00 ) is even shorter than that of free CS molecule, which seems unusual and the similar situation was also found in singlet insertion product SNiCS (1A 0 ). Experiment [15] assigned a band of 1335 cmK1 to the C–S2 stretching vibration of SNiCS (3A 00 ), and this frequency was calculated at 1352 cmK1 with B3LYP/DZVP which is equal to the value obtained by B3LYP/6-311G* [15]. Whereas the calculated and experimentally observed vibrations for C–S stretching in CS molecule are 1297 and 1285 cmK1, respectively, which indicates that C–S triple bond in SNiCS (3A 00 ) is stronger than the isolated C–S bond of CS molecule indeed. NBO analysis shows that the interaction of the lone pair orbitals of Ni atom with the p-antibonding (C–S)* orbital is slight. Moreover, in the C–S1 bond, the s orbitals of both C and S1 atoms contribute to the s bond, while in free CS molecule the triple bond is formed by the overlap of p orbitals of S and C atoms. The combination of the above effects may explain the contraction of C–S1 bond in SNiCS (3A 00 ).
Despite the similarity of this reaction channel to pathway A in the reaction of Ti (3F) with CS2, the reaction of Ni (3F) with CS2 exhibit distinct differences in energetics. First, the Ni–(CS2) complexes formed in the reaction are less stable than Ti–(CS2) complexes relative to their corresponding reactants. Second, the reaction of Ni (3F) with CS2 requires a positive activation energy of 7 kcal/mol, whereas the reaction of Ti (3F) with CS2 proceeds with a negative activation energy of K36 kcal/mol. Moreover, the NiC CS2/NiSCCS reaction is predicted to be endothermic by 34 kcal/mol at the B3LYP/DZVP level of theory which overestimated the experimental value 24 kcal/mol Table 3 Total energies (E, in hartree) and relative energies (DE, in kcal/mol) including zero-point energies (ZPE in kcal/mol) correction at B3LYP/DZVP level for the stationary points (reactants, intermediate complexes, transition states, and products) shown in Fig. 3, and the imaginary vibrational frequencies (cmK1) (IMG) for the transition states Species
ZPE
CS2C3Ni NiSCS (3A 00 ) TS1 (3A 00 ) Ni–(h2-CS)S (3A 00 ) TS2 (3A 00 ) SNiCS (3A 00 ) Ni–(h2-S2)C (3B2) TS3 (3A) iso-SNiCS (3A 00 ) CSC3NiS CS2C1Ni Ni–(h2-S2)C (1A1) TS4 (1A 0 ) Ni–(h2-CS)S (1A 0 ) TS5 (1A 0 ) SNiCS (1A 0 ) CSC1NiS
4.3 4.4 4.5 4.3 3.6 3.9 4.0 3.1 3.2 2.2 4.3 3.8 3.5 4.7 3.9 4.2 2.4
IMG
K286 K301
K219
K663 K227
E
DE
K2342.454995 0.0 K2342.4652758 K6.4 K2342.4569353 K1.6 K2342.4707272 K9.9 K2342.4428909 6.9 K2342.4721202 K11.1 K2342.4655618 K6.9 K2342.4208151 20.3 K2342.4368449 10.2 K2342.3989483 33.5 K2342.4492146 3.6 K2342.4308918 14.6 K2342.4207837 20.6 K2342.4972463 K26.1 K2342.4488919 3.5 K2342.4522123 1.6 K2342.3576535 60.0
T. Li et al. / Journal of Molecular Structure: THEOCHEM 724 (2005) 125–133
(calculated as D0(Ni–S)–D0(S–CS) by using the bond dissociation energies in Table 1) by 10 kcal/mol, while the TiCCS2/TiSCCS is calculated to be exothermic by 5 kcal/mol at the same level of theory. 3.2.2. Pathway B Similar to the pathway B in the case of Ti, from a cyclic complex with C2v symmetry, Ni–(h2-S2)C (3B2), the reaction proceeds to produce an isomer of SNiCS (3A 00 ), iso-SNiCS (3A 00 ), via a non-planar and distorted transition state TS3 (3A). The geometry of the cyclic complex Ni–(h2-S2)C (3B2) is similar to that of Ti–(h2-S2)C (3B1), but they have the different lowest triplet electronic states, and the binding energy of Ni–(h2-S2)C (3B2) is lower than that of Ti–(h2-S2)C (3B1) by 32 kcal/mol. Different from iso-STiCS (3A 00 ), iso-SNiCS (3A 00 ) is planar and it is less stable than SNiCS (3A 00 ) by 21 kcal/mol. TS3 (3A) is the transition state connecting Ni–(h2-S2)C 3 ( B2) and iso-SNiCS (3A 00 ), and the insertion barrier is 27 kcal/mol. We have tried to locate the transition state that connects iso-SNiCS (3A 00 ) and SNiCS (3A 00 ) but all our attempts failed. From the viewpoint of overall energetics, the reaction for pathway B requires a positive activation energy of 20 kcal/mol which is higher than that of pathway A by 13 kcal/mol, so this pathway is energetically less favorable than pathway A, and should not play an important role in the reaction of Ni with CS2, especially in low temperature condition. 3.3. Singlet surface of the reaction of Ni (3d94s1, 1D) with CS2 (1SC) The energy difference between the lowest triplet (3d84s2, F) and singlet (3d94s1, 1D) electronic states of Ni was calculated as 4 kcal/mol at B3LYP/DZVP level (Fig. 4), significantly underestimating the experimental value of 10 kcal/mol. As mentioned by Mebel et al. [10] in the study on the reaction of Ni with CO2, the singlet–triplet energy gap is difficult to reproduce by the single-reference-based ab initio method. In their study, B3LYP/6-311CG(3df) gave this energy gap as 3 kcal/mol and even with the CCSD(T)/ 6-311CG(3df) this energy was computed as 1.5 kcal/mol, while B3LYP and CCSD(T) with the smaller 6-311G* basis set greatly overestimated the experimental value, giving this energy as 18 and 26 kcal/mol, respectively. In fact, compared with molecular systems, it is more difficult to achieve the accuracy for atom calculations. In the study of the reaction of Ti with CO2 [13], the same problem was encountered, and all the single-reference-based ab initio methods failed to reproduce the experimental energy gaps between Ti (3F) and (1D) and (5F). To get better agreement with experiment, a multi-reference-based ab initio method must be employed, but this is beyond the scope of the present study. 3
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Interestingly, in this singlet reaction pathway the C–S bridged complex Ni–(h2-CS)S (1A 0 ) is produced from a planar cyclic initially formed complex Ni–(h2-S2)C (1A1) (C2v) via a cyclic transition state TS4 (1A 0 ) (Cs), and the barrier of this step is 6 kcal/mol. The mechanism of this step is different from the initial steps of all the reactions discussed above. From Ni–(h2-CS)S (1A 0 ) the reaction proceeds to produce the singlet insertion intermediate SNiCS (1A 0 ) via transition state TS5 (1A 0 ) with an insertion barrier of 30 kcal/mol. The geometry of Ni–(h2-S2)C (1A1) is the analogue to the triplet complex Ni–(h2-S2)C (3B2), but the former is less stable by 22 kcal/mol. Moreover, Ni–(h2-S2)C (1A1) lies above the singlet reactants by 11 kcal/mol, which seems abnormal. One of the possible reasons to explain this is that there may be a so-called entrance transition state [14] lying between the singlet reactants and the complex Ni–(h2-S2)C (1A1), but all our attempts to locate such transition state were unsuccessful at B3LYP/DZVP level. Ni–(h2-CS)S (1A 0 ) is the most stable complex among all the triplet and singlet complexes, and it is more stable than its triplet counterpart Ni–(h2-CS)S (3A 00 ) by 16 kcal/mol at the B3LYP/DZVP level, so 1A 0 should be the ground electronic state of Ni–(h2-CS)S, and this is also suggested by Zhou et al.’s [15] B3LYP and BP86/6-311CG* calculations. The fact that Ni–(h2-CS)S (1A 0 ) is more stable than Ni–(h 2-CS)S ( 3A 00 ) indicates that the singlet surface has crossed into the triplet surface in the course of Ni–(h2-CS)S formation, but the geometries of TS4 (1A 0 ) and TS1 (3A 00 ) are different and there is an energy gap of 22 kcal/mol between them, so this intersystem crossing may not be important for the reaction mechanism. In Zhou et al.’s [15] experiment, the Ni–(h2-CS)S (1A 0 ) species was verified and two bands of 1208 and 626 cmK1 were assigned to the terminal C–S1 and the ring C–S2 stretching vibrations, respectively. The two frequencies above were calculated at 1265 and 631 cmK1 with B3LYP and 1244 and 613 cmK1 with BPB6 by using 6-311CG* basis set [15]. Our B3LYP/DZVP calculation gave these two frequencies at 1259 and 650 cmK1, respectively. Similarly, along the reaction coordinate, Ni–(h2-CS)S 1 0 ( A ) can convert to an insertion species of Ni into the C–S2 bond, SNiCS (1A 0 ), which is less stable than its triplet counterpart SNiCS (3A 00 ) by 13 kcal/mol. Obviously, the intersystem crossing between the singlet and triplet PESs has occurred again in the course of Ni insertion into the C–S bond to lead the system to the energetically more favorable triplet PES. Considering that the energies of TS5 (1A 0 ) and TS2 (3A 00 ) are close (4 and 7 kcal/mol, respectively) and their geometries are similar, this intersystem crossing should be important for the reaction mechanism. To evaluate the binding energy of SNi–CS (1A 0 ), a calculation has been carried out on singlet NiS molecule. As shown in Fig. 4, the energy splitting between the lowest singlet state 1SC and the ground state 3SK of NiS is 27 kcal/ mol at B3LYP/DZVP level. To our knowledge, there is no
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experimental data available for comparison with our theoretical value on this energy difference in NiS. The SNi–CS binding energy of SNiCS (1A 0 ) is calculated as 58 kcal/mol. The activation barriers of TS4 (1A 0 ) and TS5 (1A 0 ) are 17 and K0.1 kcal/mol relative to the singlet reactants, respectively, which indicates that the first reaction step is the rate-determining step. The reaction Ni (1D)CCS2/ NiS (1SC)CCS is predicted to be endothermic by 56 kcal/mol. It was found in the matrix isolation IR study [15] that the C–S bridged species Ni–(h2-CS)S were observed on annealing, while the insertion products SNiCS only appeared after photolysis, which indicates that the reaction may terminate at the step of Ni–(h2-CS)S formation before photolysis. Compare the triplet (pathway A) and singlet surfaces, it can be seen that the first reaction step producing Ni–(h2-CS)S (3A 00 ) proceeds with no activation barrier, while for the singlet reaction channel, the first step producing Ni–(h2-CS)S (1A 0 ) proceeds with an activation energy of 17 kcal/mol. This result suggests that the reaction occurred preferentially on the triplet surface (pathway A), and the Ni–(h2-CS)S (1A 0 ) should be mainly produced by Ni–(h2-CS)S (3A 00 ) returning to singlet ground state on annealing. Moreover, the fact that the insertion products were not observed before photolysis may be attributed to an existing activation barrier required in insertion reaction on triplet surface, and a low barrier (7 kcal/mol at B3LYP/DZVP level) can be considerable under the low-temperature (10–30 K) reaction condition and with low concentration of reactants as gas phase reaction. It may be inferred that the Ni–(h2-CS)S (1A 0 ) converted from Ni–(h2-CS)S (3A 00 ) on annealing could not evolve to SNiCS (1A 0 ) because of the insertion barrier of 30 kcal/mol on the singlet surface. Of course, if Ni–(h2-CS)S (1A 0 ) was directly produced by the collisions between Ni atoms and CS2 molecules, the insertion reaction could occur with no activation barrier on the singlet surface as shown in Fig. 4, and we cannot rule out this possibility, but combine the experimental findings and the mechanisms revealed in our present study, this kind of direct pathway is highly unlikely. Due to the complexity of the photochemical reaction, especially for systems containing transition metals, it is difficult to tell the exact mechanism of the reaction on photolysis that produces the insertion products. Besides Ni–(h2-CS)S (1A 0 ) and SNiCS (3A 00 ), another species of complex Ni–(h1-C)S2 (C2v)was also observed in experiment [15]. We have carried out calculations on this species, and no new mechanisms were found for them. So they are probably directly formed in collisions. Considering that the properties of this species have been calculated by Zhou et al., the discussions on them are not included in the present study. It is worth mentioning that in the theoretical study [10] on the reaction of Ni atom with CO2, the insertion
mechanism was not proposed. In this study from a cyclic complex Ni–(h2-O2)C the reaction proceeds to produce a weakly bonded CONiO complex, and on both singlet and triplet surfaces the activation energies with respect to corresponding reactants are high, 64 and 53 kcal/mol, respectively. But this is not surprising since C–S bonds are weaker than C–O bonds and the S atom is more polarizable than O atom.
4. Conclusions A DFT study on the title reactions has been carried out by using the B3LYP method. Two reaction channels have been identified for the reactions of both Ti (3F, 3d24s2) and Ni (3F, 3d8s2) atoms with CS2, and one channel has been identified for the reaction of Ni (1D, 3d94s1) with CS2. All the reactions channels involve the breaking of C–S bond and the formations of Ti–C and Ti–S bonds and yield insertion products from C–S bridged complexes M–(h2-CS)S or cyclic complexes M–(h2-S2)C, but these reactions are initiated by different mechanisms. Except for Ni–(h2-S2)C (1A1), all the initial complexes form without activation energies. For the reactions of Ni atom with CS2, the reaction is shown to occur preferentially on the triplet surface (pathway A). The mechanisms of the reactions of Ti (3F) and Ni (3F) atoms with CS2 are different in details but the insertion processes are similar. All the Ti–(CS2) complexes in the different coordinations are more stable than the Ni–(CS2) complexes relative to their corresponding reactants. Moreover, the reactions of Ti with CS2 require no activation energy, whereas in the case of Ni, positive activation energies of 7 and 20 kcal/mol for pathways A and B are required, respectively. It can be concluded that Ti (3F) is more reactive than Ni with CS2, which is in agreement with the trend revealed in the reported studies on the reactions of the first row neutral transition atoms with CO2.
References [1] J. Mascetti, M. Tranquille, J. Phys. Chem. 92 (1988) 2177. [2] R. Caballol, E. Sa´nchez, J.-C. Barthelat, J. Phys. Chem. 91 (1987) 1328. [3] M. Sodupe, V. Branchadell, A. Oliva, J. Phys. Chem. 99 (1995) 8567. [4] M. Sodupe, V. Branchadell, A. Oliva, J. Mol. Struct. (THEOCHEM) 371 (1996) 79. [5] F. Galan, M. Fouassier, M. Tranquille, J. Mascetti, I. Pa´pai, J. Phys. Chem. A 101 (1997) 2626. [6] M. Zhou, L. Andrews, J. Am. Chem. Soc. 120 (1998) 13230. [7] I. Pa´pai, J. Mascetti, R. Fournier, J. Phys. Chem. A 101 (1997) 4465. [8] M. Zhou, L. Andrews, J. Phys. Chem. A 103 (1999) 2066. [9] M. Zhou, B. Liang, L. Andrews, J. Phys. Chem. A 103 (1999) 2013.
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DFT study on the reaction of neutral Ti and Ni atoms with CS2 Taohong Lia, Xiaoguang Xiea, Shulin Gaoa, Chuanming Wangb, Weixian Chengc, Xulin Panc, Huai Caoa,c,* a
Department of Chemistry, Yunnan University, Kunming 650091, China b Department of Biology, Honghe University, Mengzi 661100, China c Modern Biological Research Center, Yunnan University, Kunming 650091, China Received 14 January 2005; revised 6 March 2005; accepted 7 March 2005 Available online 29 April 2005
Abstract The reaction mechanisms of the ground state (3F) of neutral Ti atom, the lowest triplet (3F) and singlet state (1D) of Ni atom with CS2: MCCS2/MSCCS (MZTi, Ni) have been investigated by using DFT method B3LYP with DZVP basis set. Two reaction channels have been identified for the reactions of both Ti (3F) and Ni (3F) atoms with CS2, and one channel has been identified for the reaction of Ni (1D) with CS2. These reactions are initiated by different mechanisms, but all the reaction channels involve the insertion of metal atoms into the C– S bond of CS2 yielding insertion intermediates SMCS from C–S bridged intermediates M–(h2-CS)S or cyclic complexes M–(h2-S2)C. The reaction of triplet ground state Ti with CS2 requires no activation energy, whereas the reactions of Ni atom with CS2 proceed with 7, 20 and 17 kcal/mol activation energies for the two triplet and one singlet pathways, respectively. The reaction of Ni with CS2 was shown to occur preferentially on triplet surface and the experimentally observed species, Ni–(h2-CS)S and SNiCS, have been explained according to the mechanisms revealed in this work. q 2005 Elsevier B.V. All rights reserved. Keywords: B3LYP; Neutral titanium and nickel atoms; Carbon disulfide; Reaction mechanism; Insertion
1. Introduction The chemistry of transition metals and their compounds has been an active area of both theoretical and experimental researches due to their important role in catalytic and material science. Carbon dioxide (CO2), carbon disulfide (CS2) and carbonyl sulfide (OCS) are the ligands of great interest which can coordinate with metal atoms and ions to produce metal oxides, metal sulfides and some new species of organometallic compounds. Reactions of the first row neutral transition metal atoms with CO2 have been extensively studied by both experiment and theory [1–14]. Both experimental and theoretical studies show that the early first row neutral transition metal atoms, such as Sc, Ti, V, can react with CO2 with no or low activation energy
* Corresponding author. Address: Modern Biological Research Center, Yunnan University, Kunming 650091, China. Tel.: C86 871 5033496; fax: C86 871 5036373. E-mail address: [email protected] (H. Cao).
0166-1280/$ - see front matter q 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2005.03.024
and yield MO, OMCO, and some species of M–(CO2) complex, whereas the late ones, such as Ni [1,5,10], have much lower reactivity with CO2, and in low temperature Ni only forms a 1:1 complex with CO2. Compared with CO2, the reaction of transition metal atoms with CS2 is relatively unexplored. Zhou et al. [15] reported a matrix isolation IR study on the reactions of ablated Co, Ni and Cu atoms and cations with CS2, they also carried out a DFT calculation on the observed products (SMCS, M–(h2-CS)S, M–CS2, and MCSC 2 ), but the reaction mechanisms were not reported. Pa´pai et al. [11] have reported a theoretical study on the reactions of V(s2d3)CXCY/XVCY/VXCCY with XCYZCO2, CS2 and OCS, and it was found that from C–S or C–O side-bonded complexes V can insert into C–S or C–O bond with no or low energy barrier yielding insertion species XVCY. Can a similar reaction mechanism be applicable to the reactions of other neutral transition metal atoms with CS2? Are there new reaction channels? What are the different behaviors between the early transition metal atoms and the late ones in the reactions with CS2? Promoted by these questions, we investigated the reactions CS2CM/MSCCS (MZTi, Ni) in detail. Although there is no experimental study reported on the reaction of Ti atom with CS2, a comparative theoretical
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study on the reactions of Ti and Ni atoms with CS2 is interesting and important since Ti is a representative of the first row early transition metal atoms while Ni belongs to the late and both of them have the same ground electronic state 3F. According to Zhou et al. [15], the observed Ni–(h2-CS)S complexes appear to be in singlet state but the insertion products SNiCS appear to be in triplet state. Considering that the singlet and triplet PESs may across, the reactions of the lowest triplet (3d84s2, 3F) and singlet (3d94s1, 1D) electronic states of Ni with CS2 were investigated, and for Ti, only the ground state (3F) is considered. The main aim of the present study is to give qualitative models that explain how Ti and Ni atoms react with CS2, and to compare the reactivity of these two atoms with CS2.
molecules calculated at the B3LYP/DZVP level of theory are compared in Table 1 with both the experimental data and the results obtained with B3LYP/6-311CG(2d) [11] and CCSD(T) levels [20]. As expected, the geometries, the spectroscopic and the thermochemical data provided by B3LYP/DZVP reflected the experimental trends well and the accuracy of B3LYP/DZVP is comparable to B3LYP/ 6-311CG(2d) and CCSD(T) levels of theory. 3.1. The reaction of Ti (3d84s2, 3F) with CS2 (1SC) Two possible reaction pathways (pathways A and B) have been found for the reaction: TiCCS2/TiSCCS. The optimized geometries of all stationary points involved in the two pathways are shown in Fig. 1, and the sketch of the PESs is shown in Fig. 2. The ZPEs, the ZPE corrected relative energies and the harmonic vibration frequencies of all the species involved in the reaction are listed in Table 2.
2. Methods All molecular geometries (reactants, intermediates, transition states and products) were fully optimized by using density functional theory method B3LYP [16] with DZVP [17] basis set. The choice of B3LYP method is motivated by its reliability and efficiency as a practical tool in transition metal chemistry [18]. Harmonic vibration frequencies were obtained 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 transition states to the corresponding minimums. To analyze the bond characteristics of the molecules, the NBO calculations were carried out. To ensure that the obtained wave functions are stable, the stabilities of the wave functions were tested. All calculations were carried out with GAUSSIAN 98 program [19].
3.1.1. Pathway A In this pathway the reaction proceeds via two steps. When Ti collides with CS2 a stabilized T-shape C-coordinated complex Ti–CS2 (3B1) (C2v) is initially formed with binding energy of 39 kcal/mol. Then Ti–CS2 (3B1) evolves to the C–S bridged complex Ti–(h2-CS)S (3A 00 ) via TS1 (3A 00 ) with a small barrier of 4 kcal/mol. The complex Ti–(h2-CS)S (3A 00 ) also lies below the reactants by 39 kcal/mol. From Ti–(h2-CS)S (3A 00 ) the reaction proceeds to produce the insertion product STiCS (3A 00 ) via TS2 (3A 00 ) with a small insertion barrier of 1 kcal/mol. This small insertion barrier suggests that once the C–S bridged complex Ti–(h2-CS)S (3A 00 ) forms the insertion reaction will take place immediately. The insertion product STiCS (3A 00 ) is the global minimum on this surface, and its relative energy is 45 kcal/mol lower than the reactants. NBO calculation shows that in STiCS (3A 00 ) two triple bonds have formed between Ti and S2, C and S1 atoms. The STi–CS binding energy is 41 kcal/mol which can basically be attributed to the Ti–C bond arising from a CS/Ti s-donation and a simultaneous Ti/CS p-backdonation as Pa´pai et al. [7] suggested for the OTiCO species. The strong interaction of 3d lone pair orbital of Ti with
3. Results and discussions Before the discussion on the mechanisms of the reactions MCCS2/MSCCS, we first present the results obtained for the ground state reactants and products involved in these reactions. Some selected molecular properties of these
Table 1 Calculated (B3LYP/DZVP) and experimental equilibrium properties of the ground states of CS2, CS, TiS and NiS CS2 (1SC)a
Re ue D0
CS (1SC)a
TiS (3D)b
NiS (3SK)b
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
Calculated
Experimental
1.566 [1.558] 1546, 675, 399 [1532, 668, 398] 104.9 [105.4]
1.556
1.547 [1.535] 1296 [1296] 160.4 [162.6]
1.534
2.093 (2.083) 562 (575) 109.5
–
1.981 (1.980) 513 (636) 71.4
–
1535, 658, 397 104.0
1285 169.4
– 109.5
˚ , vibration frequencies (ue) in cmK1, ZPE corrected bond dissociation energies (D0) in kcal/mol. Units: bond lengths (Re) in A a The values in square brackets calculated at B3LYP/6-311CG(2d) level and the experimental data are taken from Ref. [11]. b The values in brackets calculated at CCSD(T) level and the experimental data are taken from Ref. [20].
– 81.4
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Fig. 1. Optimized geometries of the reactants, intermediate complexes, products and transition states for the lowest triplet pathways of the TiCCS2/TiSCCS ˚ and angles in degrees). reaction at B3LYP/DZVP level of theory (bond lengths in A
the p-antibonding (C–S1)* orbital results in the relatively ˚ ). long C–S1 bond length (1.57 A The potential energy profile of this pathway is shown in Fig. 2. Obviously, the reaction requires no activation energy, since TS1 (3A 00 ) and TS2 (3A 00 ) lie below the reactants by 36 and 38 kcal/mol, respectively, which suggests that the reaction could take place spontaneously. The high feasibility of Ti insertion into C–S bond of CS2 yielding STiCS species is very similar to the case of Ti insertion into C–O bond which has been confirmed by both experimental and theoretical studies [1,7,8,13]. Thus ablated Ti atoms reacting with CS2 molecules to give primarily products STiCS is foreseeable, although there is no experiment reported so far. The reaction of TiCCS2/TiSCCS is predicted to be exothermic by 5 kcal/mol at B3LYP/DZVP level plus ZPE, and this result is very close to the experimental value 6 kcal/mol calculated as D0(Ti–S)–D0(S–CS) by using the bond dissociation energies in Table 1.
It is worth mentioning that in the theoretical studies on the reactions of VCCS2/VSCCS [11] and VCCCS2/ VSCCCS [21], only one transition state like TS2 (3A 00 ) which connects the V–(h2-CS)S and the insertion product SVCS was located, and the analogues to Ti–CS2 (3B1) and TS1 (3A 00 ) were not given. In the study on the reaction of FeC with CS2 [22], an analogue to Ti–CS2 (3B1), FeC–CS2 (C2v), was located, and from this complex FeC inserted into C–S bond via a transition state like TS2 (3A 00 ) yielding a linear insertion species SFeCSC. Obviously, this mechanism is also different from the case of Ti in which Ti atom inserts into the C–S bond from the C–S bridged complex Ti–(h2-CS)S (3A 00 ) as discussed above. 3.1.2. Pathway B In pathway B, from an initially formed cyclic complex Ti–(h2-S2)C (3B1) (C2v) stabilized by 39 kcal/mol the Ti inserts directly into C–S2 bond via a non-planar and highly
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Fig. 2. Potential energy diagram for the TiCCS2/TiSCCS reaction in the lowest triplet electronic states calculated at B3LYP/DZVP level. All relative energies (including ZPE) are given in kcal/mol with respect to CS2CTi.
distorted transition state TS3 (3A) yielding a new species of insertion intermediate which is an isomer of STiCS (3A 00 ) and denoted as iso-STiCS (3A). The insertion barrier is 23 kcal/mol which is much higher than that of pathway A. The iso-STiCS (3A) can convert to STiCS (3A 00 ) via an isomerization transition state TS4 (3A), and the barrier is only 3 kcal/mol which indicates that the isomerization is very easy. NBO analysis shows that the bonding characteristics of iso-STiCS (3A)(C1) are similar to those of STiCS (3A), and there is no bond between the S1 and Ti atoms, which agrees ˚ . So it is determined as a new with the S1–Ti distance 2.58 A type of insertion product which is an isomer of STiCS (3A 00 ). Because of the non-planar and distorted structure, isoSTiCS (3A) is less stable than the planar STiCS (3A 00 ) by 9 kcal/mol. It can be seen from Fig. 1 that TS3 (3A) and TS4 (3A) lie above TS1 (3A 00 ) and TS2 (3A 00 ) by 20 and 5 kcal/mol, respectively, which implies that pathway B is energetically less favorable than pathway A. However, the activation energies of TS3 (3A) and TS4 (3A) relative to the reactants are K16 and K33 kcal/mol, so this reaction could also take place spontaneously and this mechanism should be also important for the reaction CS2CTi/CSCTiS. In the theoretical studies on the reactions of V, VC and C Fe with CS2 [11,21,22] the mechanism similar to pathway B was not proposed. Interestingly, in the study on the reaction of Ti with CO2 [13], besides the insertion mechanism like the second step of pathway A, a complex analogue to Ti–(h2-S2)C, Ti–(h2-O2)C was also identified, but from Ti–(h2-O2)C the Ti atom abstracted one O atom directly via a cyclic planar transition state to form the complex COTiO in which CO and TiO were weakly bonded.
3.2. Reactions of Ni with CS2 (1SC) Two pathways for the reaction of triplet Ni atom with CS2 have been found (pathways A and B), and only one pathway for the reaction of singlet Ni atom with CS2 has been found. The fully optimized geometries of all species involved in these reactions are shown in Fig. 3, the energy profile of these surfaces is shown in Fig. 4. The ZPEs, the imaginary frequencies of the transition states (IMG), the total energies and ZPE corrected relative energies of all the species involved in these reactions are listed in Table 3. 3.2.1. Pathway A Three minima (NiSCS (3A 00 ), Ni–(h2-CS)S (3A 00 ) and SNiCS (3A 00 )) and two first-saddle points (TS1 (3A 00 ) and TS2 (3A 00 )) on this triplet surface have been located. Table 2 Total energies (E, in hartree) and relative energies (DE, in kcal/mol) including zero-point energies (ZPE in kcal/mol) correction at B3LYP/DZVP level for the stationary points (reactants, intermediate complexes, transition states, and products) shown in Fig. 1, and the imaginary vibrational frequencies (cmK1) (IMG) for the transition states Species
ZPE
CS2CTi Ti–CS2 (3B1) TS1 (3A 00 ) Ti–(h2-CS)S (3A 00 ) TS2 (3A 00 ) STiCS (3A 00 ) Ti–(h2KS2)C (3B1) TS3 (3A) iso-STiCS (3A) TS4 (3A) CSCTiS
4.3 4.2 4.1 4.1 3.7 3.9 4.0 3.0 3.4 3.5 2.7
IMG
K143 K223
K322 K158
DE
E
0.0 K39.4 K35.7 K39.4 K38.3 K45.2 K39.0 K16.0 K36.0 K33.2 K4.6
K1683.673455 K1683.735998 K1683.729924 K1683.735923 K1683.733416 K1683.744784 K1683.735029 K1683.696824 K1683.729239 K1683.7249706 K1683.678121
T. Li et al. / Journal of Molecular Structure: THEOCHEM 724 (2005) 125–133
Unlike the pathway A in the reaction of Ti with CS2, at the initial reaction step the Ni atom attaches to one S atom of CS2 with the formation of a planar end-bonded complex NiSCS (3A 00 ), and this complex is only stabilized by 6 kcal/mol relative to the reactants. Via TS1 (3A 00 ) the NiSCS (3A 00 ) intermediate converts to a C–S bridged
129
complex Ni–(h2-CS)S (3A 00 ) which lies below the reactants by 10 kcal/mol and it is an analogue to Ti–(h2-CS)S (3A 00 ). This step proceeds with a negative activation energy of K2 kcal/mol. Similarly, from Ni–(h2-CS)S (3A 00 ) the reaction proceeds to the insertion product SNiCS (3A 00 ) via TS2 (3A 00 ) whose geometry is similar to that of Ti TS2
Fig. 3. Optimized geometries of the reactants, intermediate complexes, products and transition states for the lowest triplet and singlet pathways of the NiC ˚ and angles in degrees). CS2/NiSCCS reaction at B3LYP/DZVP level of theory (bond lengths in A
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Fig. 4. Potential energy diagram for the NiCCS2/NiSCCS reaction in the lowest singlet and triplet electronic states calculated at B3LYP/DZVP level. All relative energies (including ZPE) are given in kcal/mol with respect to CS2C3Ni.
(3A 00 ). The activation barrier for this step is 7 kcal/mol and it is the rate-determining step of this reaction. The triplet insertion product SNiCS (3A 00 ) lies below the initial reactants by 11 kcal/mol and it is more stable than its singlet counterpart which will be discussed later by 13 kcal/mol. Thus 3A 00 is predicted to be the ground electronic state of the insertion product with B3LYP/DZVP, and this is in agreement with Zhou et al.’s [15] B3LYP and BP86/6-311G* calculations, but the triplet–singlet energy gap was not given in their report. The calculated SNi–CS binding energy is 45 kcal/ mol at B3LYP/DZVP level which may give a rationale for the detection of SNiCS species and explain that there is no NiS observed in experiment [15]. The geometry of SNiCS (3A 00 ) is similar to that of STiCS 3 00 ( A ). One may notice that the C–S1 bond length of SNiCS (3A 00 ) is even shorter than that of free CS molecule, which seems unusual and the similar situation was also found in singlet insertion product SNiCS (1A 0 ). Experiment [15] assigned a band of 1335 cmK1 to the C–S2 stretching vibration of SNiCS (3A 00 ), and this frequency was calculated at 1352 cmK1 with B3LYP/DZVP which is equal to the value obtained by B3LYP/6-311G* [15]. Whereas the calculated and experimentally observed vibrations for C–S stretching in CS molecule are 1297 and 1285 cmK1, respectively, which indicates that C–S triple bond in SNiCS (3A 00 ) is stronger than the isolated C–S bond of CS molecule indeed. NBO analysis shows that the interaction of the lone pair orbitals of Ni atom with the p-antibonding (C–S)* orbital is slight. Moreover, in the C–S1 bond, the s orbitals of both C and S1 atoms contribute to the s bond, while in free CS molecule the triple bond is formed by the overlap of p orbitals of S and C atoms. The combination of the above effects may explain the contraction of C–S1 bond in SNiCS (3A 00 ).
Despite the similarity of this reaction channel to pathway A in the reaction of Ti (3F) with CS2, the reaction of Ni (3F) with CS2 exhibit distinct differences in energetics. First, the Ni–(CS2) complexes formed in the reaction are less stable than Ti–(CS2) complexes relative to their corresponding reactants. Second, the reaction of Ni (3F) with CS2 requires a positive activation energy of 7 kcal/mol, whereas the reaction of Ti (3F) with CS2 proceeds with a negative activation energy of K36 kcal/mol. Moreover, the NiC CS2/NiSCCS reaction is predicted to be endothermic by 34 kcal/mol at the B3LYP/DZVP level of theory which overestimated the experimental value 24 kcal/mol Table 3 Total energies (E, in hartree) and relative energies (DE, in kcal/mol) including zero-point energies (ZPE in kcal/mol) correction at B3LYP/DZVP level for the stationary points (reactants, intermediate complexes, transition states, and products) shown in Fig. 3, and the imaginary vibrational frequencies (cmK1) (IMG) for the transition states Species
ZPE
CS2C3Ni NiSCS (3A 00 ) TS1 (3A 00 ) Ni–(h2-CS)S (3A 00 ) TS2 (3A 00 ) SNiCS (3A 00 ) Ni–(h2-S2)C (3B2) TS3 (3A) iso-SNiCS (3A 00 ) CSC3NiS CS2C1Ni Ni–(h2-S2)C (1A1) TS4 (1A 0 ) Ni–(h2-CS)S (1A 0 ) TS5 (1A 0 ) SNiCS (1A 0 ) CSC1NiS
4.3 4.4 4.5 4.3 3.6 3.9 4.0 3.1 3.2 2.2 4.3 3.8 3.5 4.7 3.9 4.2 2.4
IMG
K286 K301
K219
K663 K227
E
DE
K2342.454995 0.0 K2342.4652758 K6.4 K2342.4569353 K1.6 K2342.4707272 K9.9 K2342.4428909 6.9 K2342.4721202 K11.1 K2342.4655618 K6.9 K2342.4208151 20.3 K2342.4368449 10.2 K2342.3989483 33.5 K2342.4492146 3.6 K2342.4308918 14.6 K2342.4207837 20.6 K2342.4972463 K26.1 K2342.4488919 3.5 K2342.4522123 1.6 K2342.3576535 60.0
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(calculated as D0(Ni–S)–D0(S–CS) by using the bond dissociation energies in Table 1) by 10 kcal/mol, while the TiCCS2/TiSCCS is calculated to be exothermic by 5 kcal/mol at the same level of theory. 3.2.2. Pathway B Similar to the pathway B in the case of Ti, from a cyclic complex with C2v symmetry, Ni–(h2-S2)C (3B2), the reaction proceeds to produce an isomer of SNiCS (3A 00 ), iso-SNiCS (3A 00 ), via a non-planar and distorted transition state TS3 (3A). The geometry of the cyclic complex Ni–(h2-S2)C (3B2) is similar to that of Ti–(h2-S2)C (3B1), but they have the different lowest triplet electronic states, and the binding energy of Ni–(h2-S2)C (3B2) is lower than that of Ti–(h2-S2)C (3B1) by 32 kcal/mol. Different from iso-STiCS (3A 00 ), iso-SNiCS (3A 00 ) is planar and it is less stable than SNiCS (3A 00 ) by 21 kcal/mol. TS3 (3A) is the transition state connecting Ni–(h2-S2)C 3 ( B2) and iso-SNiCS (3A 00 ), and the insertion barrier is 27 kcal/mol. We have tried to locate the transition state that connects iso-SNiCS (3A 00 ) and SNiCS (3A 00 ) but all our attempts failed. From the viewpoint of overall energetics, the reaction for pathway B requires a positive activation energy of 20 kcal/mol which is higher than that of pathway A by 13 kcal/mol, so this pathway is energetically less favorable than pathway A, and should not play an important role in the reaction of Ni with CS2, especially in low temperature condition. 3.3. Singlet surface of the reaction of Ni (3d94s1, 1D) with CS2 (1SC) The energy difference between the lowest triplet (3d84s2, F) and singlet (3d94s1, 1D) electronic states of Ni was calculated as 4 kcal/mol at B3LYP/DZVP level (Fig. 4), significantly underestimating the experimental value of 10 kcal/mol. As mentioned by Mebel et al. [10] in the study on the reaction of Ni with CO2, the singlet–triplet energy gap is difficult to reproduce by the single-reference-based ab initio method. In their study, B3LYP/6-311CG(3df) gave this energy gap as 3 kcal/mol and even with the CCSD(T)/ 6-311CG(3df) this energy was computed as 1.5 kcal/mol, while B3LYP and CCSD(T) with the smaller 6-311G* basis set greatly overestimated the experimental value, giving this energy as 18 and 26 kcal/mol, respectively. In fact, compared with molecular systems, it is more difficult to achieve the accuracy for atom calculations. In the study of the reaction of Ti with CO2 [13], the same problem was encountered, and all the single-reference-based ab initio methods failed to reproduce the experimental energy gaps between Ti (3F) and (1D) and (5F). To get better agreement with experiment, a multi-reference-based ab initio method must be employed, but this is beyond the scope of the present study. 3
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Interestingly, in this singlet reaction pathway the C–S bridged complex Ni–(h2-CS)S (1A 0 ) is produced from a planar cyclic initially formed complex Ni–(h2-S2)C (1A1) (C2v) via a cyclic transition state TS4 (1A 0 ) (Cs), and the barrier of this step is 6 kcal/mol. The mechanism of this step is different from the initial steps of all the reactions discussed above. From Ni–(h2-CS)S (1A 0 ) the reaction proceeds to produce the singlet insertion intermediate SNiCS (1A 0 ) via transition state TS5 (1A 0 ) with an insertion barrier of 30 kcal/mol. The geometry of Ni–(h2-S2)C (1A1) is the analogue to the triplet complex Ni–(h2-S2)C (3B2), but the former is less stable by 22 kcal/mol. Moreover, Ni–(h2-S2)C (1A1) lies above the singlet reactants by 11 kcal/mol, which seems abnormal. One of the possible reasons to explain this is that there may be a so-called entrance transition state [14] lying between the singlet reactants and the complex Ni–(h2-S2)C (1A1), but all our attempts to locate such transition state were unsuccessful at B3LYP/DZVP level. Ni–(h2-CS)S (1A 0 ) is the most stable complex among all the triplet and singlet complexes, and it is more stable than its triplet counterpart Ni–(h2-CS)S (3A 00 ) by 16 kcal/mol at the B3LYP/DZVP level, so 1A 0 should be the ground electronic state of Ni–(h2-CS)S, and this is also suggested by Zhou et al.’s [15] B3LYP and BP86/6-311CG* calculations. The fact that Ni–(h2-CS)S (1A 0 ) is more stable than Ni–(h 2-CS)S ( 3A 00 ) indicates that the singlet surface has crossed into the triplet surface in the course of Ni–(h2-CS)S formation, but the geometries of TS4 (1A 0 ) and TS1 (3A 00 ) are different and there is an energy gap of 22 kcal/mol between them, so this intersystem crossing may not be important for the reaction mechanism. In Zhou et al.’s [15] experiment, the Ni–(h2-CS)S (1A 0 ) species was verified and two bands of 1208 and 626 cmK1 were assigned to the terminal C–S1 and the ring C–S2 stretching vibrations, respectively. The two frequencies above were calculated at 1265 and 631 cmK1 with B3LYP and 1244 and 613 cmK1 with BPB6 by using 6-311CG* basis set [15]. Our B3LYP/DZVP calculation gave these two frequencies at 1259 and 650 cmK1, respectively. Similarly, along the reaction coordinate, Ni–(h2-CS)S 1 0 ( A ) can convert to an insertion species of Ni into the C–S2 bond, SNiCS (1A 0 ), which is less stable than its triplet counterpart SNiCS (3A 00 ) by 13 kcal/mol. Obviously, the intersystem crossing between the singlet and triplet PESs has occurred again in the course of Ni insertion into the C–S bond to lead the system to the energetically more favorable triplet PES. Considering that the energies of TS5 (1A 0 ) and TS2 (3A 00 ) are close (4 and 7 kcal/mol, respectively) and their geometries are similar, this intersystem crossing should be important for the reaction mechanism. To evaluate the binding energy of SNi–CS (1A 0 ), a calculation has been carried out on singlet NiS molecule. As shown in Fig. 4, the energy splitting between the lowest singlet state 1SC and the ground state 3SK of NiS is 27 kcal/ mol at B3LYP/DZVP level. To our knowledge, there is no
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experimental data available for comparison with our theoretical value on this energy difference in NiS. The SNi–CS binding energy of SNiCS (1A 0 ) is calculated as 58 kcal/mol. The activation barriers of TS4 (1A 0 ) and TS5 (1A 0 ) are 17 and K0.1 kcal/mol relative to the singlet reactants, respectively, which indicates that the first reaction step is the rate-determining step. The reaction Ni (1D)CCS2/ NiS (1SC)CCS is predicted to be endothermic by 56 kcal/mol. It was found in the matrix isolation IR study [15] that the C–S bridged species Ni–(h2-CS)S were observed on annealing, while the insertion products SNiCS only appeared after photolysis, which indicates that the reaction may terminate at the step of Ni–(h2-CS)S formation before photolysis. Compare the triplet (pathway A) and singlet surfaces, it can be seen that the first reaction step producing Ni–(h2-CS)S (3A 00 ) proceeds with no activation barrier, while for the singlet reaction channel, the first step producing Ni–(h2-CS)S (1A 0 ) proceeds with an activation energy of 17 kcal/mol. This result suggests that the reaction occurred preferentially on the triplet surface (pathway A), and the Ni–(h2-CS)S (1A 0 ) should be mainly produced by Ni–(h2-CS)S (3A 00 ) returning to singlet ground state on annealing. Moreover, the fact that the insertion products were not observed before photolysis may be attributed to an existing activation barrier required in insertion reaction on triplet surface, and a low barrier (7 kcal/mol at B3LYP/DZVP level) can be considerable under the low-temperature (10–30 K) reaction condition and with low concentration of reactants as gas phase reaction. It may be inferred that the Ni–(h2-CS)S (1A 0 ) converted from Ni–(h2-CS)S (3A 00 ) on annealing could not evolve to SNiCS (1A 0 ) because of the insertion barrier of 30 kcal/mol on the singlet surface. Of course, if Ni–(h2-CS)S (1A 0 ) was directly produced by the collisions between Ni atoms and CS2 molecules, the insertion reaction could occur with no activation barrier on the singlet surface as shown in Fig. 4, and we cannot rule out this possibility, but combine the experimental findings and the mechanisms revealed in our present study, this kind of direct pathway is highly unlikely. Due to the complexity of the photochemical reaction, especially for systems containing transition metals, it is difficult to tell the exact mechanism of the reaction on photolysis that produces the insertion products. Besides Ni–(h2-CS)S (1A 0 ) and SNiCS (3A 00 ), another species of complex Ni–(h1-C)S2 (C2v)was also observed in experiment [15]. We have carried out calculations on this species, and no new mechanisms were found for them. So they are probably directly formed in collisions. Considering that the properties of this species have been calculated by Zhou et al., the discussions on them are not included in the present study. It is worth mentioning that in the theoretical study [10] on the reaction of Ni atom with CO2, the insertion
mechanism was not proposed. In this study from a cyclic complex Ni–(h2-O2)C the reaction proceeds to produce a weakly bonded CONiO complex, and on both singlet and triplet surfaces the activation energies with respect to corresponding reactants are high, 64 and 53 kcal/mol, respectively. But this is not surprising since C–S bonds are weaker than C–O bonds and the S atom is more polarizable than O atom.
4. Conclusions A DFT study on the title reactions has been carried out by using the B3LYP method. Two reaction channels have been identified for the reactions of both Ti (3F, 3d24s2) and Ni (3F, 3d8s2) atoms with CS2, and one channel has been identified for the reaction of Ni (1D, 3d94s1) with CS2. All the reactions channels involve the breaking of C–S bond and the formations of Ti–C and Ti–S bonds and yield insertion products from C–S bridged complexes M–(h2-CS)S or cyclic complexes M–(h2-S2)C, but these reactions are initiated by different mechanisms. Except for Ni–(h2-S2)C (1A1), all the initial complexes form without activation energies. For the reactions of Ni atom with CS2, the reaction is shown to occur preferentially on the triplet surface (pathway A). The mechanisms of the reactions of Ti (3F) and Ni (3F) atoms with CS2 are different in details but the insertion processes are similar. All the Ti–(CS2) complexes in the different coordinations are more stable than the Ni–(CS2) complexes relative to their corresponding reactants. Moreover, the reactions of Ti with CS2 require no activation energy, whereas in the case of Ni, positive activation energies of 7 and 20 kcal/mol for pathways A and B are required, respectively. It can be concluded that Ti (3F) is more reactive than Ni with CS2, which is in agreement with the trend revealed in the reported studies on the reactions of the first row neutral transition atoms with CO2.
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