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Mechanistic Investigation of the Carbon−Iodine Bond Activation on the Niobium−Carbon Cluster Turbasu Sengupta,*,† Muntazir S. Khan,† and Sourav Pal*,‡ †

Physical Chemistry Division, CSIR National Chemical Laboratory, Pune 411008, India Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

‡

S Supporting Information *

ABSTRACT: The activation process of carbon−iodine (C−I) bond on neutral and cationic niobium metcars (Nb8C12) is investigated using density functional theory and related computational techniques. Metallocarbohedrenes or metcars are a class of stable metal−carbide clusters of specific stoichiometry and of great interest to cluster chemists since their first discovery. The detailed reaction mechanism along with the overall energy profile of the C−I dissociation reaction on niobium metcar and its cations is presented in this paper. The tunneling-corrected rate constants and their related reaction parameters such as the pre-exponential factor are also included alongside. The major differences between the reaction mechanism of the neutral and cationic metcars are also highlighted as well. Despite the available experimental results, the C−I bond dissociation on metcars has remained an unexplored problem in the theoretical and computational domains. Thus, the present investigation can fill in the gap and may also provide new insights provoking further developments in cluster and materials chemistry in future.

1. INTRODUCTION In the realm of inorganic and materials chemistry, atomic clusters are small-sized multiatomic particles with variable composition and unique properties. Being the only link between the atoms and the bulk materials known to mankind till date, atomic clusters have been the prime motif of material investigation since past four or five decades. Throughout all these years, both theoretical and experimental investigations have not only enriched the respective research fields with interesting outcomes but also introduced the scientific community to a vast new domain of material chemistry which was never explored before. Starting from the concept of the third dimension of the periodic table as alternate building blocks1−3 to novel motifs with fascinating magnetic, optical, and catalytic properties,4−19 the studies in the field of clusters are no short of captivating outcomes for practical manifestation in near future. In spite of these promises, there lies a major complication to incorporate these marvelous ideas into reality. Most atomic clusters are usually metastable and highly reactive in nature and therefore can only be synthesized in vacuum or inert atmosphere. Hence, past few years have seen a substantial increment in the number of experimental or theoretical research focused on the stabilization of nanoclusters.8,20−22 Beginning with the concept of jellium shell closure23,24 in either pristine or impure clusters, rigid matrix-based stabilization to the implementation of superatomic complex theory,8,20−22,25,26 it is fortuitous that cluster chemists now have an entire set of © 2017 American Chemical Society

arsenal for stabilizing the metastable clusters to some extent just enough to make them suitable for small-scale experimental manifestation. In addition to that, the added insights by the latest theoretical developments have further enhanced the indepth understanding of the stabilization process of nanoclusters, resulting in new types of artificial stable motifs. However, beside the new developments, at this point, it is also important to recollect the fact that although somewhat rare, there are a few classes of clusters which are naturally stable. One of the most well-known examples of these types is the family of fullerenes, the first prototype (i.e., C60) of which was invented in 1985 at Rice University.27,28 The legacy of fullerenes which followed soon after the innovation and their impact on modern materials science is certainly a familiar topic to every material chemists. However, fullerenes are not the only species that can be classified as stable clusters. The second example of similar carbon-containing stable clusters is the metallocarbohedrenes, discovered by Castleman and co-workers29−31 nearly 7 years after the innovation of C60. Metallocarbohedrenes, commonly abbreviated as “metcar” is a class of stable metal carbide clusters with chemical stoichiometry M8C12, where “M” is usually an early “d” block element. The presence of first metcar (Ti8C12+) was detected as a dominant Received: June 29, 2017 Accepted: August 18, 2017 Published: September 1, 2017 5335

DOI: 10.1021/acsomega.7b00894 ACS Omega 2017, 2, 5335−5347

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“supermagic” peak much similar to that of C60 in the mass spectrum during an attempt to dehydrogenate hydrocarbons by titanium metal.29 Related experiments soon established the fact that the term “metcar” indicates an entire class of clusters including binary ones, rather than a single entity.30,32−35 This captivating innovation paved the ground for new studies including physical and chemical properties, reactivities, and structural characterizations including bonding and stability of individual metcars.36−54 The most remarkable among these is definitely the structural characterization of titanium metcar (Ti8C12). On the basis of the stoichiometry of the cluster as obtained from the mass spectrometry, the initial structural prediction of Ti8C12 was a regular dodecahedron with Th symmetry, similar to that of C20 fullerene.29−31 This speculated structure was definitely a logical choice, primarily because of two separate reasons. First, as the total atom count of both Ti8C12 and C20 is the same, the Ti8C12 cluster can be considered a derivative of C20 simply by replacing two carbon atoms from each pentagonal ring by titanium keeping the skeleton intact. Second , the reaction of polar molecules with Ti8C12 and V8C12 results in the adsorption of upto eight molecules, which signifies that all the eight metal sites are equivalent by coordination and also that the regular dodecahedron structure is among the five platonic solids, all of which are very well-known abundant stable structures, often preferred by nature. However, theoretical calculations showed the possibility of two different structures which are of D2d and Td symmetry, and they were found to be lower in energy than the Th symmetric structure proposed earlier.55−61 Detailed investigations in this regard soon established the fact that the theoretical calculations are indeed correct, and the distorted Td structure is confirmed to be the ground state geometry, later verified by experiments.62 Aside from the structural characterization of metcars, the chemical response of the clusters also attracts considerable attention of chemists since their first discovery. Reaction with polar (e.g., H2O, CH3OH, NH3, and (CH3)2CO) as well as non-polar molecules (e.g., benzene, methane, and ethylene) is studied in-depth and also supported by theoretical calculations.36,41−43,45,63−65 The studies with non-polar molecules are of special importance because it is observed that only a maximum of four non-polar molecules can be attached with a single metcar. This observation indirectly proves the existence of two separate set of metal sites in the cluster, thus confirming the tetrahedral-shaped ground state consisting of a smaller inner tetrahedron surrounded by a larger outer tetrahedron each composed with four metal atoms around each vertices. These investigations further elucidate the reactivity trend of different metcars, and it is observed that the titanium metcar cation is more chemically stable compared to the vanadium or niobium metcar cations which are found to be more reactive in comparison. The difference in reactivity in-between different metcars is also observed in the dissociation reaction of carbon− halogen bond using metcar as a catalyst.62,66 Upon using methyl iodide as the reactant, experimental observation reveals that while Ti8C12+ is only able to abstract single halogen atom from CH3I, the vanadium and niobium metcar cations are able to form bonds with multiple number of iodine atoms. Even both these metcar cations are able to dissociate much stronger halocarbon bonds such as C−Br and C−Cl and also form bonds with multiple number of chlorine and bromine atoms. Throughout all these years, studies on metcars have still remained popular and investigations regarding hydrogen

storage67−71 or related to the synthesis of novel materials72,73 are still widely available in the modern literature. The oxidative dissociation of carbon−halogen bond is one of the pivotal reaction steps in common chemistry, especially, because carbon−iodine (C−I) bond dissociation is one of the major intermediate steps of the coupling reactions which are among the very few techniques available to organic chemists which results in the direct formation of the important C−C bond.74 Because of this reason, a significant portion of recent investigations has solely been focused on the understanding of detailed mechanisms including thermodynamic and kinetic data of carbon−halogen bond dissociation. Aside from the most commonly used catalysts75,76 such as palladium, platinum, and nickel, in-depth theoretical and experimental studies on more unconventional materials such as gold77,78 and even aluminum clusters5 are also available. However, to the best of our knowledge, no such theoretical investigation encompassing the reaction mechanism and other related aspects of C−I activation on metcars has been carried out earlier. The present paper includes such a theoretical investigation of C−I dissociation on niobium metcars using density functional theory (DFT) as a computational tool of choice. The calculated results are analyzed and compared with the earlier experimental results available in the literature. The next section (section 2) contains the computational details of the calculations presented in the paper. Section 3 includes the results and discussion regarding the thermodynamic and kinetic data of C−I dissociation on both neutral and cationic niobium metcars in addition to other associated calculations. Section 4 concludes the article.

2. COMPUTATIONAL DETAILS The initial guess geometry of tetrahedral Nb8C12 is taken from the Td symmetric metcar structure reported in the earlier literature.55−61 The neutral and the cationic structures of Nb− metcar are optimized by assigning different spin multiplicities using both M06-2X and B3LYP functional using Triple Zeta Valence Plus Polarization (TZVP) basis for “C” atoms and LANL2DZ-ECP basis for niobium. It is observed that with both the functionals, the neutral and cationic Nb8C12 clusters with minimum spin multiplicity are lowest in energy (see Supporting Information). As organic molecules containing C−I bond, we have chosen three common molecules similar to our earlier works.79,80 The pre-reaction complexes (P.R.Cs) are derived by attaching the R−I molecule in all possible sites within the cluster, and only the lowest energy conformer is considered in each case. Similar to the neutral and cationic metcars, all the P.R.Cs are further optimized incorporating different spin multiplicities to identify the lowest energy conformer, which is found to be of minimum spin as earlier. The binding energies of R−I molecule with Nb8C12 and Nb8C12+ metcars are calculated by the following formula ΔE b = Emetcar···I − R − E R − I − Emetcar

(1)

All the optimizations included in the present paper are performed using the Berny optimization method in Gaussian 09.81 The normal modes of vibration in all the optimized structures are scrutinized, and it is made sure that all normal modes of vibration are real for global minima, whereas only one significant imaginary frequency that corresponds to the C−I bond is present in the case of the first-order saddle points (transition states). Intrinsic reaction coordinate (IRC) calculations are further performed for the transition states, and it is verified that the IRC path properly connects to the 5336


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Figure 1. Schematic reaction coordinate (M06-2X) diagram of the reaction of neutral Nb8C12 with (a) H3C−I, (b) H2CCH−I, and (c) Ph−I. The ΔH (blue) and ΔG (red) values of each step are also included. ref BPIA − B = (EIA − EIref A ) − (EIB − EIB )

complexes on both sides of the saddle point. The condensed Fukui indices (fA+) at each stationary point of the overall reaction coordinate are calculated using Hirshfeld population analysis using M06-2X functional. The condensed Fukui indices for the nucleophilic attack of an atom “A” within a molecule containing a subtotal of “N” electron are expressed as fA + ≃ qA, N + 1 − qA, N

The EIA and EIB terms denote the energy index (EI) of respective atoms within the molecule, and EIref terms are the EI obtained from homonuclear reference molecules of atoms A and B. The definition of EI of an atom “A” within a molecule is presented as

(2) val

where qA,N+1 and qA,N are the Hirshfeld population of atom A in the (N + 1) and N electronic molecular systems, respectively, both having the same equilibrium geometry. All the thermodynamic parameters and related data presented in the paper are calculated in 298.15 K temperature and 1 atm pressure. The classical as well as Wigner tunneling-corrected rate constants (denoted as TST and TSTW, respectively) and other associated kinetic data are calculated using an open source Kinetic and Statistical Thermodynamical Package (KiSThelP).82 The classical rate constant, that is, kTST is defined as k TST = σ ×

⧧ ,0 kBT ⎛ RT ⎞Δn ⎟ ·⎜ × e−ΔG / kBT h ⎝ P0 ⎠

EIA =

(4)

where all the included terms have their usual significance. χ(T) is the transmission coefficient which is calculated by the imaginary frequency of the unbound mode at the respective saddle point 2 1 ⎛ h Im(ν ⧧) ⎞ ⎜ ⎟ χ (T ) = 1 + 24 ⎝ kBT ⎠

⎡ ΔE ⎤ k = AT n exp⎢ − a ⎥ ⎣ RT ⎦

val

∑i ηi Θi ,A

(8)

3. RESULTS AND DISCUSSION To acquire a brief understanding of the C−I bond dissociation process on neutral and cationic Nb8C12 clusters, both the structures were first optimized using an appropriate guess structure as a starting point. The global minima for both neutral and cationic Nb8C12 are found to be slightly distorted from the ideal tetrahedral structure. This observation is indeed consistent and can be confirmed from the earlier studies on other metcars as well.88 By comparing the optimized (M06-2X) structures of both Nb8C12 and Nb8C12+ metcars with the standard Td symmetric reference structure reveals that the root-meansquare deviations (RMSD) are 0.139 and 0.146 Å, respectively. The RMSD value within the neutral and cationic Nb8C12 clusters is found to be much smaller 0.0246 Å, signifying a small structural deviation in-between the neutral and the cationic Nb metcars. As already mentioned, three very common organic compounds with variable C−I bond strength, namely, methyl (−CH3), vinyl (−C2H3), and phenyl (−C6H5) iodide, are chosen for the study. Except CH3I, which is the only one with experimental validation,5 the choice of other two iodides is completely arbitrary and included only to ensure enough variation in the calculated results because of their uneven bond strength. The bond dissociation enthalpy (ΔH0298K in kcal/mol) order of these three iodides is observed to be89

(3)

k TSTW = χ (Τ) × k TST

∑i εiηi Θi ,A

where Θi,A signifies the composition of atom A in the ith molecular orbital (MO). ηi and εi are the occupation number and energy of the ith MO, respectively. The summation of eq 8 only runs over all the valence MOs. The Wiberg bond indices (WBIs) are calculated for individual geometries as well as geometries along the IRC path as required using the NBO 3.1 package87 as implemented in Gaussian 09.

and the expression for the Wigner tunneling-corrected rate constant (kTSTW) is

The three parametric Arrhenius equation is defined as

(7)

(5) 83

(6)

where A is the pre-exponential factor, and “n” is a constant. The other used terms have their usual significance. The deformation density plot is constructed by subtracting the respective threedimensional density data of the complex from its individual components. The bond polarity index (BPI) and the atoms in molecules (AIM) analysis are performed by an open source Multiwfn package84 utilizing the output file obtained from the Gaussian 09 package. The common definition of BPI of a bond between atom “A” and “B” within a molecule is given as85,86

C6H5−I (65.0 ± 1.0) > H 2CCH−I (61.9 ± 1.0) > H3C−I (57.1 ± 0.5) 5337


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Figure 2. Schematic reaction coordinate diagram of the reaction of cationic Nb8C12 with (a) H3C−I, (b) H2CCH−I, and (c) Ph−I. The ΔH (blue) and ΔG (red) values of each step are also included.

characteristic of the newly formed Nb−I bond in both the clusters. The top panels of Figure 3a,b depict the snapshots of deformation density plots of the initial approach of the CH3I molecule toward the neutral and cationic clusters, respectively. From the plots, it is pretty evident that there exist slight differences in the bond formation process of CH3I with Nb metcar and its cation. In the case of neutral Nb8C12 (Figure 3a), it is observed that a significant amount of charge density is accommodated around the R−I molecule. As a result, the formation of Nb−I bond results from the major contribution of iodine atom and the Nbo atom of the metcar provides minor contribution as a donor. However, when the system is cationic (Figure 3b), it can be seen that the electron density around the incoming iodine atom is widely depleted and in this case, the Nbo atom acts as the major donor to form the bond with the iodine atom. These variations in the bond formation process of R−I with neutral and cationic metcars create a difference in the ionic nature of both bonds, and the resulting bond in the cationic metcar shows higher binding energy because of its high ionic character. This conclusion is further confirmed via the calculation of BPI in M06-2X functional. The BPI is a direct representation of the polarity of a chemical bond in terms of numerics rather than simple visualization, allowing quantitative characterization of the type of that particular bond in the process. Calculation of BPI of Nb−I bond for both metcars reveals that the BPINb−I of [Nb8C12···ICH3] is higher (−0.118 a.u.) than the BPINb−I obtained for [Nb8C12···ICH3]+ complex (−0.154 a.u.). The lower (more negative) value of BPINb−I bond in [Nb8C12···ICH3]+ complex indicates that the Nb−I bond in the cationic complex is more ionic in nature than its neutral counterpart. The bond order of Nb−I in the cationic P.R.C is also observed to be slightly higher than that in the neutral P.R.C. Thus, while the WBI of the Nb−I bond in [Nb8C12···ICH3] complex is found to be 0.59, the WBINb−I for the same in the cationic complex is observed to be slightly higher (0.70). As expected, the calculated WBIs of the newly formed Nb−I bond indicate that they are indeed partial in nature in both neutral and cationic P.R.Cs, signifying that the bond formation process is not yet complete. It is also important to mention that although the binding energies of the R−I molecule differ because of the nature of the newly formed Nbo−I bond on the Nb8C12 and Nb8C12+ metcars, the binding energy values seem nearly invariant on the type of the “R” group attached with iodine. Thus, for both the neutral and cationic Nb metcars, the binding energies for all three R−I molecules are observed to be very close, as evident from the rightmost column of Tables 1 and 2.

Thus, the C−I bond in phenyl iodide is the strongest where methyl iodide can be considered as the weakest among the three. These variations in the bond dissociation energies among the iodides are expected to influence the computed reaction parameters which in turn may provide more insights into the C−I dissociation process on both the metcars. All the necessary thermodynamic and kinetic data presented in this paper are evaluated for all three iodides by using three different DFT functionals. However, for specific mechanistic related discussions, we have solely restricted ourselves with the results obtained for CH3I in M06-2X functional. The major reason of this choice is twofold. First, as already mentioned, methyl iodide is the only organoiodide with available experimental results. Second, Minnesota functionals such as M06-2X are very well-known for their superior performance in determining accurate molecular structures and activation barrier and even can take care of small-to-medium range dispersion effects.90−92 Hence, the structure and thermochemical parameters included in the figures also consist solely of results obtained from the M06-2X functional if not stated otherwise. 3.A. Account of Reaction Mechanism. The overall energy landscape of C−I bond dissociation of all three iodides on Nb8C12 and Nb8C12+ metcars is depicted in Figures 1 and 2, respectively. The thermodynamic parameters calculated using three different functionals are enlisted in Tables 1 and 2 as well. As predicted, the first step of the reaction is the formation of P.R.C via the adsorption of an R−I molecule on the surface of the metcar. Because of the dual tetrahedral structure of the metcar, the incoming R−I molecule can either attach itself with Nb atoms located in either inner (Nbi) or outer (Nbo) tetrahedra. DFT investigations indicate that the P.R.C in which the R−I molecule is attached with Nbo is more thermodynamically stable than the other structure. The electronic energy difference between the two structures in M06-2X functional is calculated to be about 6 kcal/mol for the attachment of CH3I on neutral Nb8C12. The binding energies (Tables 1 and 2) of the R−I molecules on both neutral and cationic metcars are also found to be quite significant, possibly because of energetically favorable orbital matching between iodine and niobium resulting in higher stability. Comparing with other results available in the current literature, the calculated binding energies are found to be much higher than that of the smallsized neutral aluminum cluster79 and also than most of the neutral and cationic gold clusters78 of similar size range (3 ≤ n ≤ 20). It is interesting to observe that the binding energies of R−I molecules with Nb8C12+ are relatively higher (about ∼6 kcal/mol) than the neutral metcar. To understand these discrepancies, we have studied the formation process and the 5338


ΔG

23.67 23.75 10.14

⧧

⧧

ΔG

⧧

15.28 9.38 12.69

ΔEa2

13.39 7.59 11.16

ΔH

M06-2X ΔH 13.97 9.81 8.16

⧧

ΔG

⧧

⧧

ΔG

⧧

20.64 13.72 19.06

ΔEa2 19.34 11.51 17.00

ΔH

B3LYP

13.11 9.18 12.55

ΔEa1 ΔH 22.63 24.10 13.73

⧧

ΔG

⧧

5339

ΔH

12.39 16.67 8.39

R−I

CH3I H2CCHI PhI

⧧

ΔG

⧧

⧧

ΔG

⧧

19.97 17.10 16.60

ΔEa2

19.13 15.63 15.09

ΔH

M06-2X

11.53 14.68 8.25

ΔEa1 ΔH 6.37 8.97 6.29

⧧

⧧

ΔG

⧧

23.91 15.35 20.90

ΔEa2 22.28 14.91 19.00

ΔH

B3LYP ⧧

4.66 8.45 8.82

ΔG

ΔEa1

activation barrier

6.57 8.81 1.92

ΔH

⧧

4.96 7.86 4.65

⧧

ΔH

24.49 19.61 21.87

⧧

ΔG

⧧

ΔG

⧧

20.22 10.02 9.31

24.63 21.11 23.51

ΔEa2

BHandHLYP ΔG

ΔEa1

ΔH

ΔEa2 19.02 7.95 6.52

⧧

BHandHLYP

22.42 25.46 17.75

ΔEa1

Table 2. Thermodynamic Data (kcal/mol) of C−I Bond Activation on Nb8C12+ Metcar

ΔH

23.50 24.14 11.03

R−I

CH3I H2CCHI PhI

⧧

ΔEa1

activation barrier

Table 1. Thermodynamic (kcal/mol) Data of C−I Bond Activation on Neutral Nb8C12 Metcar

ΔG −59.84 −65.05 −63.58

ΔH −60.49 −66.12 −62.20

M06-2X

ΔG −71.47 −74.77 −74.11

ΔH −71.14 −72.94 −71.37

M06-2X ΔH

ΔG −72.16 −74.48 −71.25

ΔH −59.70 −63.00 −62.37

ΔG −60.27 −62.22 −63.59

B3LYP

exothermicity

−71.64 −72.93 −73.85

B3LYP

exothermicity

ΔG −79.44 −81.08 −81.39

−68.11 −74.77 −72.10

ΔH

−68.12 −73.00 −71.89

ΔG

BHandHLYP

−78.63 −81.22 −80.88

ΔH

BHandHLYP

−24.83 −24.30 −25.96

ΔEb

M06-2X

binding energy

−18.57 −18.04 −18.58

ΔEb

M06-2X

binding energy

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Figure 3. Deformation density plots of the initial approach of H3C−I toward (a) neutral Nb8C12 and (b) cationic Nb8C12 clusters. The lower panels of (a,b) show the deformation density plots of the P.R.C and structure [A] and structure [B], respectively.

the structure of the cluster itself. As mentioned earlier, because of the tetrahedral structure of metcars, the metal atoms present on the surface can be classified into two separate categories (inner (Nbi) and outer (Nbo) for our present case) based on the coordination of the metal atoms. Attaching the dissociated “−R” functional group with each types of Nb atoms yields two separate postreaction complexes with different thermodynamic stabilities. Hence, for each iodide, the TS-1 leads to the cleavage of C−I bond from the P.R.C, resulting in simultaneous attachment of the dissociated R group to the nearest Nbi atom (structure [A] in Figures 1 and 2). The second reaction step starts from the resulting complex [A] and directs toward the most thermodynamically stable postreaction complex. This proceeds via TS-2 which involves a direct intracluster migration of the R group from the Nbi atom to the Nbo atom via a threemembered transition state. The final structure (structure [B] in Figures 1 and 2) where the “R” functional group is attached to the Nbo atom is observed to be the most thermodynamically

From the reaction coordinates as depicted in Figures 1 and 2, it is observed that the overall reaction pathway toward the most thermodynamically stable product is not as simple as that expected from the first glance. Although the dissociation of the C−I bond is found to be a one-step process goes via the first transition state (TS-1), DFT investigations indicate that the resulting C−I dissociated complex ([A]) is certainly not the most thermodynamically stable postreaction complex. There exists a possibility of another postreaction complex [B] along the reaction coordinate which is thermodynamically more stable than complex [A] and connected with [A] via a second transition state (TS-2). Thus, the overall reaction pathway for each individual R−I molecule must be characterized by two separate activation barriers ΔEa1 and ΔEa2, as presented in Tables 1 and 2, respectively. The existence of two separate postreaction complexes along the reaction coordinate may seem baffling at first look, but the explanation of this observation is rather simple and can be provided by recollecting 5340


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Figure 4. Sample IRC plots of the two reaction steps (a,b) of the reaction between Nb8C12 and H3C−I. (b,d) the changes in the length of selected bonds along the IRC.

3.B. Account of Thermodynamics and Kinetics. As mentioned earlier, the thermodynamic parameters regarding TS-1 and TS-2 and also the exothermicity values in M06-2X, B3LYP, and BHandHLYP functionals are enlisted in Tables 1 and 2. The overall range of both the activation barriers (ΔG⧧) in all three DFT functionals is found to be varied from low to medium range (∼4.6−26 kcal/mol), ensuring decent catalytic activity of the metcar on the C−I bond. A close look of the first activation barrier (ΔEa1) reveals that for all three iodides and in all three functionals, the cationic Nb8C12 shows lower activation barrier than the neutral one, which signifies the higher catalytic activity of Nb 8 C 12 + compared to Nb 8 C 12 toward the dissociation of C−I bond. The ΔEa1 values calculated for Nb8C12+ are observed to be often comparable with the activation barrier obtained for the case of small-sized aluminum clusters.79 The lowest first activation barrier is calculated to be ΔG⧧ = 4.65 kcal/mol, which is obtained in BHandHLYP functional for the oxidative addition of C6H5I on Nb8C12+. As a matter of fact, the Ea1 obtained for C6H5I in all three functionals is observed to be the lowest among all three iodides, whereas the activation barriers calculated for CH3I and H2C CHI are usually either in close proximity with each other or one is higher than the other without any predictable patterns. The result is interesting because the C−I bond in C6H5I has the maximum dissociation energy among the three iodides. The observed low activation barrier of Nb8C12+ compared to the neutral metcar can be justified by the calculated highest occupied molecular orbital (HOMO)/singly occupied molecular orbital (SOMO)−lowest unoccupied molecular orbital (LUMO) gaps of the respective metcar. The SOMO−LUMO gap of Nb8C12+ is found to be 2.47 eV (1.03 eV in B3LYP), which is lower by 0.3 eV compared to the HOMO−LUMO gap obtained for the neutral metcar (2.77 eV in M06-2X and 1.25 in B3LYP functional). The lower energy gap signifies slightly high

stable postreaction complex within the whole reaction coordinate. Thus, structure [A] serves as an intermediate between the TS-1 and TS-2, which connects with the stable postreaction complex [B]. The enthalpy difference (ΔH) between [A] and [B] is observed to be 24.6 and 18.3 kcal/mol for the reaction of MeI on neutral and cationic Nb8C12, respectively. Structure [C] shown in both Figures 1 and 2 is the dissociated postreaction complex as included in the corresponding experimental paper.62 The dissociated complex [C] is observed to be energetically closure with [A] than [B] for each iodide. Also from Figures 1 and 2, it is observed that the gaps (both ΔH and ΔG) with either [A] or [B] complex with [C] are found to be higher in the cationic systems than that in the neutral ones. The increments are usually found to be ∼10 kcal/ mol for the ΔH and ΔG separation between [A] and [C] and ∼4−7 kcal/mol for the ΔH and ΔG separation between [B] and [C]. This whole reaction coordinate is further confirmed by IRC calculations. Figure 4 collects two sample IRC plots for both steps of the reaction between CH3I and Nb8C12 clusters in M06-2X functional. The resulting changes of the bond lengths of specific preselected bonds along the IRC are also presented in Figure 4b,d. As can be seen from Figure 4a,c, both the transition states properly connect with the predicted chemical species on both positive and negative sides of their respective IRCs. Thus, the TS-1 connects to the P.R.C on the negative direction of the IRC and smoothly converges to complex [A] on the positive direction of the IRC (Figure 4a). The next reaction step is confirmed by a second IRC calculation included in Figure 4c. The TS-2 also connects with complex [A] on the left-hand side and converges to the thermodynamically stable complex [B] on the positive direction of the IRC. Similar conclusion can be drawn from the other calculated IRCs on both neutral and cationic Nb−metcars, thus validating the reliability of the results. 5341


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Table 3. Kinetic Data of the First Reaction Barrier (ΔEa1) of C−I Bond Activation on Neutral and Cationic Nb8C12 Metcars in M06-2X Functional TST k

A

TSTW n

k

R−I

A

n

CH3I

neutral cation R−I

2.76 × 10−5 2.18 × 104

3.92 × 107 4.63 × 109

1.89 1.44


2.43 × 10−5 1.07 × 102

2.88 × 107 6.30 × 107

2.08 2.36

neutral cation

2.30 × 105 5.59 × 106

1.93 × 1010 1.57 × 1010

1.23 1.08

3.23 × 10−5 2.52 × 104

8.49 × 106 1.08 × 109

2.10 1.64

3.11 × 10−5 1.19 × 102

4.62 × 106 1.86 × 107

2.33 2.53

2.59 × 105 8.05 × 106

5.22 × 109 2.66 × 109

1.41 1.31

H2CCHI

PhI

Table 4. Kinetic Data of the Second Reaction Barrier (ΔEa2) of C−I Bond Activation on Neutral and Cationic Nb8C12 Metcars in M06-2X Functional TST k

A

TSTW n

R−I

k

A

n

4.03 × 101 1.50 × 10−2

4.60 × 1011 4.34 × 1010

0.05 0.67

CH3I


3.83 × 101 1.40 × 10−2

8.98 × 1011 1.07 × 1011

−0.04 0.54


8.21 × 105 1.79 × 100

3.96 × 1011 1.67 × 1011

0.11 0.32

neutral cation

3.06 × 103 4.16 × 100

2.93 × 1011 1.13 × 1011

0.22 0.37

H2CCHI 8.29 × 105 1.90 × 100

3.44 × 1011 7.63 × 1010

0.13 0.43

3.08 × 103 4.19 × 100

2.72 × 1011 1.01 × 1011

0.23 0.38

PhI

reactivity of the cationic metcar over the neutral one and thus explains the trend obtained in the calculated activation barrier. The variation of the activation barriers can be viewed in a more prominent way by looking at the respective rate constants for Nb8C12 and Nb8C12+ presented in Tables 3 and 4, respectively. As already mentioned in the computational details, the rate constants included in the present paper are calculated using two different methods, the classical transition state theory (TST) and the Wigner tunneling corrected version of classical transition state theory (TSTW). The calculated rate constants are also associated with pre-exponential factor (A) and the constant (n) in accordance with the three-parameter Arrhenius equation. From Tables 3 and 4, it is observed that the value of temperature-dependent constant (n) of the three-parametric Arrhenius equation is found to be usually higher (>1) for the first reaction barrier, whereas for the second reaction barrier, the values of “n” lie below 1 and in one specific case a small negative value close to zero is also observed. From theoretical perspective, the higher value of “n” for the first reaction barrier signifies that the first reaction barrier of C−I dissociation on both Nb8C12 and Nb8C12+ is more sensitive on the temperature than the second barrier. The exothermicity values (which is the enthalpy difference between the complex [B] and the P.R.C) listed in Tables 1 and 2 are observed to be really high, ranging within ∼−70 to −81 kcal/mol for neutral Nb8C12 and within ∼−60 to −75 kcal/mol for Nb8C12 cation as calculated for all three iodides and using the three different DFT functionals. To gain further insights into the overall reaction mechanism, we have presented additional calculations in this research article. One of such calculations included in Figure 5a,b represents the change of the WBI of selected bonds in the natural atomic orbital (NAO) basis along the IRC of the TS-1

Figure 5. Variation of WBIs of Nbo−I and C−I bonds along the IRC points of TS-1 for (a) Nb8C12 + H3C−I and (b) Nb8C12+ + H3C−I reaction.

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Figure 6. The variation of Fukui function ( f+) of selected atoms (upper panel) and the HOMO/SUMO−LUMO gap (bottom panel) along the reaction coordinate of the dissociation of H3C−I on neutral and cationic Nb8C12.

the respective f+ value of the Nbo atom is significantly lowered compared to the value obtained in the P.R.C. However, in Nb8C12+, an opposite trend is noticed, in which the f+ value of the attached iodine in TS-1 is found to be lower than that in the P.R.C, and the f+ value of the Nbo atom seems to have a higher value in TS-1 than in the P.R.C. The explanation of this unusual trend can be provided by reciting the charge-transfer trend in between Nbo and iodine atoms as observed in the P.R.C. As explained earlier, in the neutral Nb−metcar, as iodine is electron-rich, a major portion of the electron density needed to form the Nbo−I bond is contributed by the iodine atom. Because the Nbo−I bond is still partial in the P.R.Cs, it is therefore expected that the flow of electron density will continue until the WBI of the Nbo−I bond reaches a value of ∼1 and therefore provides a stronger coordination. Thus, in the neutral metcar, the f+ value of iodine shows a gradual increase because of the loss of electron density. On the other hand, the f+ value of the Nbo atom shows a slight decrement as the incoming electron density from iodine is much greater than the contribution provided by the Nbo atom for the bond formation. An opposite situation occurs for the cationic system, where the Nbo atom provides the major contribution toward the bond formation and iodine atom plays a minor part. The WBI calculation indeed confirms this explanation, and the Nbo−I bond formation process is observed to be nearly complete in the TS-1 itself. For neutral system, the WBI of the Nbo−I bond is found to be 0.98 and is observed to be about 1.21 for the cationic system, that is, higher than the neutral one. The C−I bond is also found to be mostly cleaved at the TS-1 as expected, having a WBI of 0.38 and 0.34 in neutral and cationic systems, respectively. After the intermediate ([A]), f+ values of both the

of both neutral and cationic Nb8C12. The WBIs of both the dissociated C−I bond as well as newly forming Nbo−I bond are included in the figure. The crossover point, that is, where the bond indices of both the breaking and newly forming bonds are become equal to each other, is also clearly shown in Figure 5a,b. Figure 5a shows that for neutral Nb8C12 the WBI promptly converges from ∼1 in the P.R.C to nearly zero at the end of the corresponding plot. At the same time, the Nbo−I bond index starts to increase from 0.6 in the P.R.C and finally proceed toward a WBI value of 1.23 in complex [A]. In a similar fashion, according to Figure 5b, in cationic Nb8C12, the WBI of the C−I bond decreases from ∼1 and converges toward zero, whereas in the case of the newly formed Nbo−I bond, the WBI starts to increase from a value of 0.7 in the P.R.C and finally converges toward the value of 1.46 as calculated in [A]. The observed higher bond order of Nbo−I as obtained in complex [A] of cationic Nb8C12 can again be attributed to the ionic character of the respective bond as described earlier. In Figure 6, we have included the change of the Fukui function (f+) (Figure 6a,b) and the HOMO−LUMO or SOMO− LUMO gap (Figure 6c,d) along the reaction pathway for the reaction of CH3I with Nb8C12 and Nb8C12+. The major differences of the C−I dissociation process on both neutral and cationic Nb−metcars are evident from all the four plots (Figure 6a−d). The dissimilarities are especially prominent at the position of TS-1 in comparison to other portions of the plots. Focusing first on the change of f+ along the reaction pathway, it can be seen that at the position of TS-1, the trend of f+ values of Nbo and the attached I atom follows an opposite pattern in the neutral Nb−metcar compared to the cation. Thus, in neutral Nb8C12, the f+ value of the I atom shows a large increment and 5343


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Figure 7. Molecular graphs of P.R.Cs, structure [A] and structure [B] of the dissociation of CH3I molecule on Nb8C12 (top panel) and Nb8C12+ (bottom panel).

atoms follow a near parallel path upto complex [B] in both neutral and cationic Nb−metcars. The value of the nucleophilic Fukui index for the Nbi atom in both neutral and cationic Nb− metcars is observed to be nearly constant till TS-1; then after a sudden drop at the intermediate [A], it again steadily increases and converges to the value obtained in complex [B]. The f+ value of the “C” atom is observed to be the least perturbed throughout the reaction coordinate, and only a single minor increment is noticed at the TS-1 on neutral Nb8C12. The unperturbed nature of f+ of the carbon atom throughout the reaction coordinate may be due to the simultaneous bond breaking and formation process as observed in both the transition states. In both Figure 6a,b, the Nbo atom, in which the CH3 group finally gets migrated to form complex [B] (denoted as NbCo in Figure 6a,b), shows a continuous decrement in the respective Fukui function value from TS-1 up to complex [B]. Similar to the Fukui index, the trend in the HOMO/SOMO−LUMO gaps (Figure 6c,d) along the reaction coordinate is also found to be unique for the neutral and the cationic clusters. The overall range of the HOMO−LUMO gap calculated by using both M06-2X and BHandHLYP functional is found to be within 2−3 eV. The prime differences in between Figure 6c,d are again found to be located at the position of the TS-1. In Figure 6a, the HOMO−LUMO gap shows a sudden drop at TS-1, signifying a low HOMO−LUMO gap of the TS-1 compared to the P.R.C. On the contrary, the SOMO−LUMO gap in the case of cationic metcars shows a steady increase till reaching maximum at complex [A] followed by a steady decrease and finally reaching a value of 2.66 (2.7 in BHandHLYP) at complex [B]. Except for the BHandHLYP calculated results shown in Figure 6c, the intermediate complex [A] is shown to have a high HOMO/SOMO−LUMO gap,

ensuring its high stability as an intermediate. To have further information, we have performed an AIM analysis on the optimized structures of key complexes as obtained along the reaction pathway for the dissociation of CH3I on both neutral and cationic Nb−metcars. The molecular graphs of such a kind are assembled into two groups in Figure 7. The position of four different types of critical points along with the bond paths is clearly visible. The values of four important parameters, for example, electron density (ρ), Laplacian of electron density (∇2ρ), local energy density (H(r)), and the electron localization function at two of the most important bond critical points are also included in Figure 7.

4. CONCLUSIONS The present article presents a concise theoretical account of the reaction mechanism along with the kinetic and thermodynamic details of the C−I bond dissociation reaction on niobium metcar and its cation. The C−I dissociation reaction is the only experimentally validated abstraction reaction observed on metcars till date. The C−I activation process is also of enormous significance to synthetic chemists. In-depth DFT investigation has shown that although the dissociation process is a single step, the “R” group migration is completed within an overall of two reaction steps consisting of two transition states separated by an intermediate complex. This investigation also signifies that there exists few fundamental differences of the C− I dissociation process on neutral and cationic metcars which are responsible for significantly altering the calculated reaction parameters. Considering the overall range of calculated activation barriers, Nb8C12+ is found to be more reactive toward C−I dissociation. The first activation barrier is observed to be of low-to-medium range, signifying a decent catalytic 5344


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(7) Reber, A. C.; Khanna, S. N.; Roach, P. J.; Woodward, W. H.; Castleman, A. W., Jr. Reactivity of Aluminum Cluster Anions with Water: Origins of Reactivity and Mechanisms for H2 Release. J. Phys. Chem. A 2010, 114, 6071−6081. (8) Luo, Z.; Reber, A. C.; Jia, M.; Blades, W. H.; Khanna, S. N.; Castleman, A. W., Jr. What Determines if a Ligand Activates or Passivates a Superatom Cluster? Chem. Sci. 2016, 7, 3067−3074. (9) Burgert, R.; Schnöckel, H.; Grubisic, A.; Li, X.; Stokes, S. T.; Bowen, K. H.; Ganteför, G.; Kiran, B.; Jena, P. Spin Conservation Accounts for Aluminum Cluster Anion Reactivity Pattern with O2. Science 2008, 319, 438−442. (10) Neumaier, M.; Olzmann, M.; Kiran, B.; Bowen, K. H.; Eichhorn, B.; Stokes, S. T.; Buonaugurio, A.; Burgert, R.; Schnöckel, H. The Reaction Rates of O2 with Closed-Shell and Open-Shell Alx- and GaxClusters under Single−Collision Conditions: Experimental and Theoretical Investigations toward a Generally Valid Model for the Hindered Reactions of O2 with Metal Atom Clusters. J. Am. Chem. Soc. 2014, 136, 3607−3616. (11) Burgert, R.; Stokes, S. T.; Bowen, K. H.; Schnöckel, H. Primary Reaction Steps of Al13− Clusters in an HCl Atmosphere: Snapshots of the Dissolution of a Base Metal. J. Am. Chem. Soc. 2006, 128, 7904− 7908. (12) Reveles, J. U.; Clayborne, P. A.; Reber, A. C.; Khanna, S. N.; Pradhan, K.; Sen, P.; Pederson, M. R. Designer Magnetic Superatoms. Nat. Chem. 2009, 1, 310−315. (13) Robles, R.; Khanna, S. N.; Castleman, A. W., Jr. Stability and Magnetic Properties of T2Sin(T= Cr, Mn, 1 ≤ n ≤ 8) clusters. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 77, 235441. (14) Grubisic, A.; Ko, Y. J.; Wang, H.; Bowen, K. H. Photoelectron Spectroscopy of Lanthanide−Silicon Cluster Anions LnSin−(3 ≤ n ≤ 13; Ln= Ho, Gd, Pr, Sm, Eu, Yb): Prospect for Magnetic Silicon-Based Clusters. J. Am. Chem. Soc. 2009, 131, 10783−10790. (15) Wang, M.; Huang, X.; Du, Z.; Li, Y. Structural, Electronic, and Magnetic Properties of a Series of Aluminum Clusters Doped with Various Transition Metals. Chem. Phys. Lett. 2009, 480, 258−264. (16) Alikhani, M. E.; Shaik, S. A Topological Study of the Ferromagnetic “No-Pair Bonding” in Maximum-Spin Lithium clusters: n+1 Lin (n = 2−6). Theor. Chem. Acc. 2006, 116, 390−397. (17) Aguilera-Granja, F.; Longo, R. C.; Gallego, L. J.; Vega, A. Structural and Magnetic Properties of x12y (x, y= Fe, Co, Ni, Ru, Rh, Pd, and Pt) Nanoalloys. J. Chem. Phys. 2010, 132, 184507. (18) Montejano-Carrizales, J. M.; Aguilera-Granja, F.; Morán-López, J. L. Structural and Magnetic Properties of FemYn (m+n=7, Y= Ru, Rh, Pd, and Pt) Nanoalloys. Eur. Phys. J. D 2011, 64, 53−62. (19) Varas, A.; Aguilera-Granja, F.; Rogan, J.; Kiwi, M. Structural, Electronic, and Magnetic Properties of FexCoyNiz (x+y+z= 13) Clusters: A Density Functional Theory Study. J. Magn. Magn. Mater. 2015, 394, 325−334. (20) Clayborne, P. A.; Lopez-Acevedo, O.; Whetten, R. L.; Grönbeck, H.; Häkkinen, H. Evidence of Superatom Electronic Shells in LigandStabilized Aluminum Clusters. J. Chem. Phys. 2011, 135, 094701. (21) Walter, M.; Akola, J.; Lopez-Acevedo, O.; Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Whetten, R. L.; Grönbeck, H.; Häkkinen, H. A Unified View of Ligand-Protected Gold Clusters as Superatom Complexes. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 9157−9162. (22) Jung, J.; Kang, S.; Han, Y.-K. Ligand Effects on the Stability of Thiol-stabilized Gold Nanoclusters: Au25(SR)18−, Au38(SR)24, and Au102(SR)44. Nanoscale 2012, 4, 4206−4210. (23) Knight, W. D.; Clemenger, K.; de Heer, W. A.; Saunders, W. A.; Chou, M. Y.; Cohen, M. L. Electronic Shell Structure and Abundances of Sodium Clusters. Phys. Rev. Lett. 1984, 52, 2141−2143. (24) Knight, W. D.; de Heer, W. A.; Clemenger, K.; Saunders, W. A. Electronic Shell Structure in Potassium Clusters. Solid State Commun. 1985, 53, 445−446. (25) Kacprzak, K. A.; Lehtovaara, L.; Akola, J.; Lopez-Acevedo, O.; Häkkinen, H. A Density Functional Investigation of ThiolateProtected Bimetal PdAu24(SR)z18 Clusters: Doping the Superatom Complex. Phys. Chem. Chem. Phys. 2009, 11, 7123−7129.

activity of Nb−metcar toward monohalogen abstraction compared to the commonly used catalysts. Aside from the mechanistic details, few other useful reaction parameters such as the rate constants, pre-exponential factor, and the temperature-dependent constant in accordance to the three parametric Arrhenius equation are also included. Further insights are gathered from the Fukui indices, HOMO/SOMO−LUMO gap, and via the AIM analysis. The detailed mechanism of C−I dissociation on metcars is still mostly unexplored, and hence the current study may be able to provide a decent contribution to enlighten some of the riddles encompassing metcars till this day.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.7b00894. Cartesian coordinates and harmonic frequencies of the optimized structures, thermodynamic data, and additional information (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (T.S.). *E-mail: [email protected] (S.P.). ORCID

Sourav Pal: 0000-0002-4836-639X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the University Grant Commission (UGC) and the Council of Scientific & Industrial Research (CSIR) for providing Senior Research Fellowship (SRF) for T.S. and CSIR−Nehru Science Postdoctoral Research Fellowship for M.S.K. The authors also acknowledge the Center of Excellence in Scientific Computing at CSIR−NCL and the CSIR 12th five year plan MSM project (csc 0129) grant. S.P. acknowledges the J. C. Bose Fellowship grant of DST toward partial fulfillment of this work.

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REFERENCES

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