Article pubs.acs.org/JPCC
Thermo Neutral SN2 Reaction within Pristine and Stone−Wales Defective BNNTs and CNTs P. Ravinder and V. Subramanian* Chemical Laboratory, Council of Scientific and Industrial Research−Central Leather Research Institute, Adyar, Chennai 600 020, India ABSTRACT: The density functional theory (DFT) calculations have been performed to understand the effect of confinement on the Cl− exchange bimolecular nucleophilic substitution (SN2) reaction inside pristine and Stone−Wales (SW) defective boron nitride nanotubes (BNNTs). Results have also been compared with that of the same reaction inside the carbon nanotubes (CNTs). The kinetics of thermo neutral SN2 reaction is significantly influenced by the inner phase (concave-face) of the tubes. This evidence clearly reinforces that inner phase can act as a nanoreactor in accordance with the previous reports. It is also possible to note that the polarizabilities of BNNTs (CNTs) and being associated inside dielectric medium (solid solvation) influence the energetics of the reaction. Furthermore, the enhancement in the central energy barrier of the (SN2) reaction arises due to the nuclophile stabilization in the nanotube confinement through the noncovalent interactions. Comparison of results obtained from tubes of various sizes highlight that structural confinement significantly affects the energetics of reaction in addition to the effect of solid solvation.
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INTRODUCTION Numerous experimental and theoretical studies have been made to understand the kinetics of bimolecular nucleophilic substitution (SN2) reaction in the different mediums.1−18 In this context, the symmetric and thermo neutral gas phase reaction between chloride anion (Cl−) and chloromethane (CH3Cl) has been considered as the archetypical model for SN2 reaction. In SN2 reactions, the nucleophile approaches the carbon center from the backside, which leads the concerted nucleophilic attack and expulsion of the leaving group.1−18 The double-welled potential energy surface (PES) of this reaction clearly exemplifies the nature of this reaction.1,2 Further, it is well-known that the surrounding environment plays a crucial role on the energetics of reaction and the stereochemistry of the product.1−3 However, the gas phase computational calculations on the reactions provide a crucial blueprint for the experiments. Hence, several theoretical studies have been made to understand the effect of a variety of solvent environments on the barrier of SN2 reaction.3,8−15 Numerous investigations have been made to understand the reactivities of the inside and outside surfaces of carbon nanotubes (CNTs).19−24 It is found that the outside (convex) surface is more reactive than the inside (concave) surface of CNTs. Previous studies have shown that the inside region of CNTs provides a new kind of structural confinement and surrounding environment to host atoms and molecules as well as to carry out chemical reactions.23,24 The experimental observation of peapod-based CNTs confirms the aforementioned findings.22 © 2013 American Chemical Society
Schlegel and co-workers have studied the effect of confinement introduced by the pristine (8,0) and (9,0) CNTs on Menshutkin SN2 reaction (NH3 + H3CCl → H3NCH3+ + Cl−) using hybrid density functional theory (DFT)-based B3PW91 method.23 Evidence from the results shows the effect of confinement on the reaction and trend in the energetics of the reaction closely resembles the same reaction in a low-dielectric solvent medium.23 Raghavachari and co-workers have investigated the role of confinement offered by the (6,6)CNT on the Cl− exchange SN2 reaction (Cl− + CH3Cl → ClCH3 + Cl−) employing the computational model chemistry method.24 They have reported that the nanotube confinement enhances the barrier height of the reaction by 6.6 kcal/mol.24 The enhancement in the reaction barrier arises due to the large polarizability of carbon nanotube.24 Further, the inner phase of CNT presents an interesting environment for chemical reactions, offering the potential for differential chemical stabilization.24 Recently, a number of studies have been focused on boron nitride nanotubes (BNNTs) due to their structural similarity to CNTs.25−27 However, they exhibit distinctly different electronic and other properties.25 The BNNTs are also found to be nontoxic due to their chemical inertness and structural stability.26,27 In addition, the reactivities of the inside and outside surfaces of the BNNT are different from that of CNT due to the electronegativity difference between the B−N Received: November 13, 2012 Revised: February 22, 2013 Published: February 23, 2013 5095
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bonds.28,29 Thus, the inside region of the BNNTs offers a different kind of chemical environment when compared to that of CNTs.29 Although, studies have been carried out on the chemical reaction inside the CNTs, investigations on the effect of structural and electronic confinement on the SN2 reaction inside pristine BNNTs are scarce. In addition, it is of immense interest to evaluate the part played by the Stone−Wales (SW) defect on the energetics of the reaction. Therefore, systematic attempt has been made in this study to probe the Cl− exchange reaction within various confinements, viz. pristine BNNTs and the same tubes with SW defects. Results have also been compared with those values obtained from calculations on pristine and defective CNTs with the same chiralities.
namic parameters were calculated in the gas phase at 298.15 K temperature and 1 atm pressure. Interaction Energy. Furthermore, to gain insight into the stability of R/P, RC/PC, and TS encapsulated nanotube, the interaction energy (ΔE) of the complexes was calculated. The ΔE value was taken as the indicator of stability. To calculate the ΔE, the optimized geometries obtained from the ONIOM(B3LYP/6-31+G*:B-3LYP/3-21G*) level of theory were utilized. The single-point calculations were performed on the same geometries at the M05-2X/6-31G* level of theory.32,33 The interaction energy (ΔE) was calculated using a supermolecule approach, applying the following equation:
MODELS In the present investigation, both pristine and SW defective BNNTs and CNTs of chiralities (8,0) and (9,0) were considered as model systems. The molecular formulas of corresponding BNNTs are N48B48H16 and B54NC54H18, respectively. The molecular formulas of pristine (8,0)CNT and (9,0)CNTs are C96H16 and C108H18, respectively. The isolated geometrical parameters of these tubes were optimized using B3LYP/3-21G* level. The lengths of (8,0)BNNT and (9,0)BNNT are 13.84 Å and corresponding radii are 3.27 and 3.68 Å, respectively. Thus available volumes of these tubes are 465.11 and 589.06 Å3, respectively. The calculated lengths of both (8,0) and (9,0)CNTs are equal to 13.56, Å and average radii are 3.18 and 3.57 Å, respectively. Therefore, corresponding volumes are 430.96 and 543.15 Å3, respectively. The pristine tubes were represented as (n,0)BNNTs and (n,0)CNTs. The defective tubes were designated as (n,0)*BNNTs and (n,0)*CNTs. The gas-phase reactants (CH3Clb + Cl−a), reactant/product complex (Cla···CH3Clb or ClaCH3···Clb), and transition structure (Cla···CH3···Clb) are presented as R, RC/PC, and TS, respectively, in the remaining part of the text. The reacting system within pristine and defective tubes were designated as G@(n,0)BNNT and G@(n,0)*CNT (G = R, RC, or TS), respectively. For example, R(CH3Clb + Cl−a) in pristine and defective BNNTs are represented as R@(8,0)BNNT and R@(8,0)*BNNT, respectively.
where Ecomplex is the total energy of the complex, ENT is the total energy of the corresponding nanotube, and EG is the total energy of the encapsulated guest (G = R/P, RC/PC, and TS) species. The monomer energies were calculated from the respective monomer geometries in the complexes. The calculated ΔEs were corrected for the BSSE using the counterpoise method suggested by Boys and Bernardi.34 All the calculations were performed using the Gaussian 09 suite of programs.35
ΔE = Ecomplex − (E NT + EG)
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RESULTS AND DISCUSSION
Geometry. All the important geometrical parameters of R, RC, and TS in gas-phase and the same within the different nanotube confinements are given in Table 1. The optimized geometries of TSs within various nanotubes are given in Figure 1. It can be noticed that the geometrical parameters of reactant undergo only marginal changes inside nanotubes. Typically, the calculated gas-phase C−H and C−Clb bond lengths of CH3Clb are 1.09 and 1.81 Å, respectively. These values vary from 1.07 to 1.09 and 1.79 to 1.82 Å, respectively, in different nanotube confinements. The reported C−H and C−Clb bond lengths in the case of R@(6,6)CNT are 1.09 and 1.77 Å, respectively. The marginal variations observed in the geometrical parameters may be due to different chiralities of nanotubes employed in this investigation. The calculated geometrical parameters of gas-phase intermediate (Cla···CH3Clb) are significantly different (except C−H bond length) when compared with same parameters within nanotubes. The gas-phase C−Clb and C···Cla bond lengths are 1.86 and 3.20 Å, respectively. The same distances within nanotube vary from 1.80 to 1.83 and 3.15 to 4.69 Å, respectively. The C···Cla distance is significantly longer for the complex within defective tube than that of pristine tube. Thus, it is worthwhile to mention that the changes in π-electron cloud appreciably influence the geometrical parameters of the complex. The geometrical parameters of TS in different nanotube confinements marginally deviate from the conventional trigonal bipyramidal geometry of TS corresponding to those of conventional SN2 thermo neutral reaction in gas phase. Both the diameter and shape of tube (with and without SW defect) play an important role in affecting the geometrical parameters of TS. The position of the C atom of CH3 is marginally displaced form the center of the tubes. Close analysis of geometrical parameters of TS in gas-phase and the same within nanotube reveals that the geometry of TS in gas-phase undergoes noticeable changes due to confinement.
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COMPUTATIONAL DETAILS Geometry Optimization. The geometries of reactants (products), RC/PC, and TS were fully optimized using DFTbased Becke’s three parameter hybrid exchange functional and Lee−Yang−Parr correlation functional (B3LYP) employing the 6-31+G* basis set.30,31 The same geometries were again optimized without any geometrical constraints (except reactant/product case) within different nanotubes using our own N-layered integrated molecular orbital and molecular mechanics (ONIOM) approach. The reactants/products, RC/ PC, and TS were treated at the B3LYP/6-31+G* level of theory. The nanotube was treated at the B3LYP/3-21G* level. During the optimization of reactant molecules within nanotubes, the geometries of reactants (Cl− + CH3Cl) were constrained, and the distance between the C atom of (CH3Cl) and Cl was fixed to be 7.5 Å. The nature of the critical point structures was verified by frequency calculations at the same level of theory. The existence of characteristic single imaginary frequency confirmed the transition structure. The thermody5096
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Table 1. Geometrical Parameters of Cl− Exchange SN2 Reaction in Gas-Phase and within Various Nanotubes (BNNTs and CNTs) (Calculated Using ONIOM(B3LYP/631+G*:B3LYP/3-21G*) R@
C−H1
gas-phase (8,0)BNNT (9,0)BNNT (8,0)CNT (9,0)CNT (8,0)*BNNT (9,0)*BNNT (8,0)*CNT (9,0)*CNT RC@ C−H1
C−H2
C−H3
C−Clb
1.09 1.08 1.09 1.07 1.08 1.08 1.09 1.08 1.08 C−H2
1.09 1.08 1.09 1.08 1.09 1.08 1.09 1.08 1.09 C−H3 C−Clb
1.09 1.08 1.09 1.07 1.09 1.08 1.09 1.08 1.09 C−Cla
1.81 1.79 1.81 1.80 1.81 1.79 1.82 1.80 1.81 ∠Cla···C−Clb
gas-phase (8,0)BNNT (9,0)BNNT (8,0)CNT (9,0)CNT (8,0)*BNNT (9,0)*BNNT (8,0)*CNT (9,0)*CNT TS@
1.09 1.08 1.08 1.08 1.08 1.08 1.09 1.08 1.09 C−H1
1.09 1.08 1.08 1.08 1.09 1.08 1.09 1.08 1.09 C−H2
1.09 1.08 1.08 1.08 1.09 1.08 1.09 1.08 1.09 C−H3
1.86 1.81 1.83 1.81 1.81 1.80 1.82 1.80 1.82 C−Clb
3.20 3.21 3.38 3.15 3.54 4.23 3.88 4.69 3.51 C−Cla
179.98 179.98 179.74 179.70 178.65 175.18 170.87 176.65 177.13 ∠Cla···C···Clb
gas-phase (8,0)BNNT (9,0)BNNT (8,0)CNT (9,0)CNT (8,0)*BNNT (9,0)*BNNT (8,0)*CNT (9,0)*CNT
1.07 1.07 1.08 1.07 1.07 1.07 1.08 1.07 1.07
1.07 1.07 1.08 1.07 1.07 1.07 1.07 1.07 1.07
1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07 1.07
2.37 2.34 2.30 2.29 2.35 2.34 2.39 2.30 2.34
2.37 2.29 2.40 2.29 2.34 2.29 2.33 2.30 2.34
180.00 179.73 179.61 179.83 179.38 176.58 177.49 176.96 179.36
Figure 1. Optimized geometries of TSs in various nanotubes (calculated using ONIOM(B3LYP/6-31+G*:B3LYP/3-21G*)).
Table 2. Interaction Energies (ΔE) of Various Nanotube Endohedral Complexes (Calculated Using M05-2X/631G*)a
Energetics of Formation of Endohedral Complexes. The qualitative analysis of the void space (volume) available in the nanotube and the geometrical parameters of CH3Cl and Cl− (and their complexes) elicit the feasibility of formation of nanotube based endohedral complexes. To gain insight in to the stability in the present investigation, the ΔEs of R@, RC@, and TS@ various nanotubes were calculated using M05-2X/631G* method. The calculated ΔEs of various complexes are given in Table 2. Scrutiny of interaction energies of various species reveals that (i) the encapsulation of various species is energetically (thermodynamically) stable, (ii) encapsulation of various components (R/P, RC/PC, and TS) in the BNNT is energetically more stable when compared with the same chirality CNT, and the same is true for both pristine and defective, and (iii) the interaction energies of both R(P)@ nanotube and RC(PC)@nanotube are significantly higher than that of TS@nanotube. The interaction of various encapsulated species arises due to the confinement effect of nanochemical reactors. The lower ΔE value of TS@nanotube may be expected due to the formation of bipyramidal structure of TSs inside the tube, and the charge is delocalized in six atoms [Cl···CH3···Cl]− in the TSs formation. Interaction energy is larger for the species having more localized charge. Previous theoretical study on the structure and stability of anion encapsulated nanotubes revealed that the diameter of the NT plays a vital role in the energetics of the formation of nanopeapods with anionic seed.29 The effect of the size of the
component
BNNT
ΔE
component
CNT
ΔE
RC@
(8,0) (8,0)* (9,0) (9,0)* (8,0) (8,0)* (9,0) (9,0)* (8,0) (8,0)* (9,0) (9,0)*
−32.42 −37.65 −44.14 −43.46 −30.45 −32.29 −35.80 −34.43 −33.62 −37.73 −39.22 −44.77
RC@
(8,0) (8,0)* (9,0) (9,0)* (8,0) (8,0)* (9,0) (9,0)* (8,0) (8,0)* (9,0) (9,0)*
−8.55 −15.84 −22.84 −22.58 −4.33 −3.61 −19.80 −18.94 −7.35 −5.53 −23.32 −22.21
TS@
R@
a
TS@
R@
All interaction energies (ΔE) are in kcal/mol.
nanotube can be clearly seen from the variation of ΔE values of various complexes with the chirality of nanotubes. The effect of SW defect can also be noticed from the interaction energy calculation. Therefore, the calculated energies using DFT(M052X) method clearly reveals that the encapsulation of reactant molecules is energetically favorable. Energetics of Reaction. The calculated energies of Cl− exchange SN2 reaction in both gas-phase and confined environments are given in Table 3. The formation energy of RC, enthalpy of RC, and free energy of RC represented as ΔERC, ΔHRC, and ΔGRC. The activation energy, activation enthalpy, and activation free energy are designated as ΔE‡, ΔH‡, and ΔG‡, respectively. It can be seen that the relative ΔERC and ΔE‡ in gas-phase are −9.53 and −0.87 kcal/mol, respectively, which are in agreement with previously reported 5097
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Table 3. Energetics of Cl− Exchange Reaction in Gas-Phase and within Various Nanotubes (BNNTs and CNTs) (Calculated Using ONIOM(B3LYP/6-31+G*:B3LYP/3-21G*)a RC@
RC@
system
ΔERC
ΔHRC
ΔGRC
system
ΔERC
ΔHRC
ΔGRC
(8,0)BNNT (9,0)BNNT (8,0)*BNNT (9,0)*BNNT
−5.00 −6.52 −8.77 −2.60
−5.04 −4.73 −8.23 −1.51 TS@
−4.96 −9.12 −10.43 −3.83
(8,0)CNT (9,0)CNT (8,0)*CNT (9,0)*CNT
−6.35 0.40 −9.84 −0.94
−3.82 0.20 −9.56 0.90 TS@
−5.45 0.08 −12.52 −1.99
system
ΔE‡
ΔH‡
ΔG‡
system
ΔE‡
ΔH‡
ΔG‡
(8,0)BNNT (9,0)BNNT (8,0)*BNNT (9,0)*BNNT
7.27 4.85 11.00 14.04
6.63 5.57 10.61 14.07
6.19 2.85 9.71 13.69
(8,0)CNT (9,0)CNT (8,0)*CNT (9,0)*CNT
7.37 14.85 10.98 14.16
8.29 15.62 10.54 15.78
8.83 13.23 8.12 12.99
All the energies are in kcal/mol; calculated ΔEInt, ΔHInt, and ΔGInt for the gas phase reaction are −9.53, −9.39, and −4.02 and ΔE‡, ΔH‡, and ΔG‡ are −0.87, −1.69, and 6.53, respectively. a
values by Raghavachari and co-workers.24 Since the present reaction is thermo neutral in gas-phase, the overall change in the energy and enthalpy during complete reaction is zero. The relative energy profiles of Cl− exchange SN2 reaction in gas-phase and within various nanotube confinements are presented in Figure 2. The stability of RC in gas-phase is significantly different when compared to that inside the nanotube. The calculated ΔERC values in (8,0)BNNT and (9,0)BNNT are −5.00 and −6.52 kcal/mol, respectively. The same values for (8,0)*BNNT and (9,0)*BNNT are −8.77 and −2.60 kcal/mol, respectively. It can also be noticed that the values of ΔERC in pristine CNTs are lower than that obtained inside defective CNTs. Typically, calculated ΔERC values in (8,0)CNT and (9,0)CNT are −6.35 and 0.40 kcal/mol, respectively. Corresponding values in SW defective tubes ((8,0)*CNT and (9,0)*CNT) are −9.84 and −0.94 kcal/ mol. A previous study on the same reaction within (6,6)CNT has shown the ΔERC value to be −4.7 kcal/mol.24 A significant difference in ΔEInt value can be ascribed to the differences in diameters of tubes and chiral angles. It can be noticed that the trend observed in ΔERC values of pristine and defective BNNTs are different from those values obtained for CNTs. Therefore, it is worthwhile to mention that the stability of RC also depends on the nature of the electronic and structural confinement. Further, both ΔHRC and ΔGRC follow a trend similar to that of ΔERC. The relative energy profile reveals that the energy barrier in gas-phase is significantly lower when compared to that of reaction within nanotube confinement. The enhancement in central energy barrier (ΔΔE‡) was calculated using activation energies of both gas-phase and within nanotube employing the equation ΔΔE‡ = (ΔE‡ in nanotube − ΔE‡ in gas-phase). The calculated ΔΔE ‡ values for (8,0)BNNT, (9,0)BNNT, (8,0)*BNNT, and (9,0)*BNNT are 8.16, 5.74, 11.89, and 14.93 kcal/mol, respectively. Corresponding values in the case of CNTs are 8.26, 15.74, 11.87, and 15.05 kcal/mol, respectively. The higher central barrier of the reaction in the nanotube confinement has been traced. In previous work, it has been shown that anion stabilizes within (endohedraly) various nanotubes and fullerenes. Therefore, the additional stabilization of nucleophile (anion) in nanotube confinement prevents the same to undergo SN2 reaction. In another theoretical study, the enhancement in the central barrier was claimed due to the marginal changes in the geometrical parameters of TS within
Figure 2. Relative energy profile of Cl− exchange in gas-phase and within various nanotubes (CNTs and BNNTs) (calculated using ONIOM(B3LYP/6-31+G*:B3LYP/3-21G*)).
nanotube. Therefore, the height of central energy barrier in confinement state is significantly higher than that of gas-phase reaction. It can be seen that the variations in ΔΔE‡ values of pristine (8,0)BNNT and (8,0)CNT are only marginal. However, the same variations are found to be large in the case of pristine 5098
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Table 4. Calculated Polarizability (α) Components of Various Nanotubes (Using B3LYP/3-21G* Level of Calculation)a
a
pristine
αxx
αyy
αzz
defective
αxx
αyy
αzz
(8,0)BNNT (9,0)BNNT (8,0)CNT (9,0)CNT
574.79 671.65 922.51 978.10
574.78 671.65 922.50 978.10
950.24 1056.62 2475.53 2579.42
(8,0)*BNNT (9,0)*BNNT (8,0)*CNT (9,0)*CNT
595.09 693.51 970.07 1301.75
571.22 663.97 892.48 1154.00
951.79 1057.96 2092.10 2474.57
All polarizability components are in a.u.
Table 5. Calculated Symmetric C−H Stretching Frequency Shift in Gas-Phase and within Various Nanotubes (Calculated Using ONIOM(B3LYP/6-31+G*:B3LYP/3-21G*) symmetric C−H stretching frequencies shift (ΔνC−H in cm−1)a
a
tube
R@BNNTs
RC@BNNTs
TS@BNNTs
R@CNTs
RC@CNTs
TS@CNTs
(8,0) (9,0) (8,0)* (9,0)*
136.56 48.76 142.88 53.22
114.45 23.98 45.65 −4.74
91.16 20.94 69.42 9.31
191.84 60.12 100.17 47.77
108.73 10.76 44.99 −2.71
103.41 26.81 73.77 6.57
The ΔνC−H calculated with respect to the free gas-phase optimized geometries.
IR Spectra. The calculated shifts in symmetric C−H stretching frequencies of R, RC, and TSs are given in Table 5. The calculated symmetric C−H stretching (νC−H) values of reactant, intermediate, and TS in gas-phase are 3092.75, 3143.78, and 3227.79 cm−1, respectively. It can be noticed from Table 5 that the C−H stretching frequency shows maximum blue shift in (8,0)NTs. Evidence from the ΔνC−H values reveals that the reactant molecules show the maximum blue shift when compared with corresponding RC and TSs. Furthermore, ΔνC−H value decreases as the tube diameter increases. It can also be noticed that both RC@(9,0)*BNNT and RC@(9,0)*CNT exhibit red shift. The calculated ΔνC−H values are −4.74 and −2.71 cm−1, respectively. Variation in the ΔνC−H value in (9,0)NTs clearly indicates the marginal effect of confinement on the reacting system.
(9,0)BNNT and (9,0)CNT. Furthermore, the changes in ΔΔE‡ values of (8,0)*BNNT and (8,0)*CNT are negligible. Similar findings can be observed for (9,0)*BNNT and (9,0)*CNT. Although only marginal variations in ΔΔE‡ can be seen in BNNT and CNT with the same chirality, considerable changes can be noted in the diameter of the tube. Therefore, it is worthwhile to mention that the tube diameter is one of the determining factors, which plays a decisive role in the reaction kinetics. It can also be noticed from Table 3 that, except (9,0)CNT and (9,0)*CNT, the barrier height of Cl− exchange reaction in pristine tube is significantly higher in contrast to that in defective tubes of same chiralities. The computed ΔE‡ values of (9,0)CNT and (9,0)*CNT are 14.85 and 14.16 kcal/mol, respectively. Thus, it is also noteworthy to mention that the interruption in the π-electron cloud, which arises due to the defect, influences the kinetics of the endohedral reaction. Polarizability. The calculated components of polarizability (α) of pristine and defective tubes are given in Table 4. It can be seen that the component of α along the tube axis (αzz) is significantly (
