Article pubs.acs.org/JPCA
Theoretical Investigations of the Reactions of Phosphino Disilenes and Their Derivatives with an EE (E = C, Si, Ge, Sn, and Pb) Double Bond Bo-Ying Li and Ming-Der Su* Department of Applied Chemistry, National Chiayi University, Chiayi 60004, Taiwan S Supporting Information *
ABSTRACT: The potential energy surfaces for the reactions of phosphino dimetalalkenes featuring an EE double bond, Rea-EE, where E = group 14 elements, were investigated using density functional theory (B3LYP/LANL2DZ). Three types of chemical reactions (i.e., the rearrangement reaction, the transition metal complexation reaction, and the [2 + 2] cycloaddition with a diazene) were used to study the reactivity of the Rea-EE molecules. The theoretical findings reveal that the smaller the singlet−triplet splitting (ΔEst) of the Rea-EE, the lower are its activation barriers and, in turn, the more rapid are its chemical reactions. Theoretical observations suggest that the relative reactivity increases in the order Rea-CC < Rea-SiSi < Rea-GeGe < Rea-SnSn < Rea-PbPb. In other words, the smaller the atomic weight of the group 14 atom (E), the smaller is the atomic radius of E and the more stable is its phosphino Rea-EE to chemical reaction. It is thus predicted that the phosphino Rea-CC and Rea-SiSi molecules should be stable and readily synthesized and isolated at room temperature, since they are quite inert to chemical reaction. The computational results are in good agreement with the available experimental observations. The theoretical results obtained in this work allow a number of predictions to be made.
I. INTRODUCTION Since the isolation of the first, thermally stable molecule possessing a silicon−silicon double bond by West et al., in 1981,1 the chemistry of disilenes has experienced significant and exciting progress, as reflected in the many review articles published during the last few decades.2 Thanks to the use of bulky groups, it is now possible to synthesize and structurally characterize these species bearing a SiSi double bond if they are kinetically and thermodynamically stabilized by appropriate substitution. Because of their unique geometrical and electronic structures, such molecules are particularly interesting and important from both an academic and a practical viewpoint.2 Nevertheless, to the best of the authors’ knowledge, only a few disilenes with heteroatomic substitution have so far been reported.3 More recently, the elegant studies performed by Scheschkewitz and co-workers have isolated phosphino disilenes (Tip2SiSi(Tip)PR2; Tip = 2,4,6-triisopropylphenyl, R = Ph, i-Pr, cyclohexyl, and t-Bu) and iododisilene (Tip2SiSi(Tip)I), which is the first example of an iodo functionalized disilene. The main conformations available so far concern their synthesis and X-ray structures.4 They also found that the thermal rearrangement of a phosphino disilene (Tip2SiSi(Tip)PPh2; 1) via a CH insertion reaction yields the diastereomic mixture of a 1-phospha-2,3-disilaindane, whose structure was determined by X-ray diffraction.4 Most importantly, the synthesis of the first transition metal complexes of Tip2Si Si(Tip)PPh2 and Tip2SiSi(Tip)P(i-Pr)2 by their coordination to the [Pd(PCy3)] (Cy = cyclohexane) fragment was reported.4 See Scheme 1. However, as far as the authors are © 2012 American Chemical Society
aware, no detailed mechanisms for the reactions have been reported, either experimentally or theoretically. Scheme 1
It is this fascinating experimental improvement that has inspired this study. If a phosphino disilene featuring a SiSi double bond is so chemically versatile, it should be possible to extrapolate this feature to other molecular systems containing the EE (E = C, Ge, Sn, and Pb) double bonds. As mentioned earlier, no quantum chemical calculations for such reactions of phosphino disilenes have yet been performed, let alone a systematic theoretical study of elemental effects on the Received: July 19, 2012 Revised: August 30, 2012 Published: August 31, 2012 9412
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Table 1. Bond Distances (Å) and Bond Angles (deg) of Tip2SiSi(Tip)I, 2 (Tip = 2,4,6-Triisopropylphenyl), at Several Levels of Theorya
a
1
2
3
LANL2DZ Def2-SV(P) CRENBL ECP LANL2DZ+dp
2.208 2.213 2.288 2.181
1.905 1.907 1.934 1.891
2.589 2.511 2.620 2.491
LANL2DZ Def2-SV(P) CRENBL ECP LANL2DZ+dp Expl.b
2.203 2.205 2.256 2.180 2.191
1.901 1.900 1.924 1.889 1.874
2.567 2.487 2.586 2.476 2.452
4 B3LYP 1.931 1.930 1.957 1.912 B3PW91 1.927 1.923 1.946 1.909 1.902
5
6
7
basis functions
1.919 1.918 1.944 1.903
110.1° 109.8° 107.7° 110.7°
113.7° 113.9° 112.5° 114.2°
567 830 1060 1227
1.916 1.914 1.934 1.901 1.898
110.3° 110.1° 109.3° 110.9° 110.0°
114.2° 114.4° 113.7° 114.6° 109.0°
567 830 1060 1227
Hydrogens are omitted for clarity. bTaken from ref 4.
because they represent various doubly bonded EE molecular reactions that have already been investigated in a previous paper.4 As experimental values and trends are not readily available for such phosphino dimetalalkene systems, especially for heavy phosphino analogues, computational study plays an important role in the study of both their chemical and physical properties. It is thus hoped that the predicted molecular parameters presented in this work can serve as a guide for any future experimental studies of unknown phosphino dimetalalkene compounds.
reactivity of compounds bearing EE double bonds. The correct evaluation of transition state (TS) geometries and energies is a useful approach in the study of reaction mechanisms, so in order to understand the reaction mechanisms of the EE doubly bonded species possessing the phosphino substituent groups, this study undertakes a systematic investigation of the potential energy surfaces of the following model reactions, using density functional theory (DFT):
II. THEORETICAL METHODS Geometries were fully optimized with hybrid density functional theory, at the B3LYP5 and B3PW916 levels, using the GAUSSIAN 03 package of programs.7 Several basis sets were tested for B3LYP and B3PW91 calculations. The reasonable basis sets, LANL2DZ,8 LANL2DZ+dp,9 Def2-SV(P),10 and CRENBL ECP,11 were employed for the atoms studied in this work. All of these basis sets are incorporated in the GAUSSIAN package.7 It is noteworthy that the model reactant (Tip2Si Si(Tip)I; 2) has a total of 568, 830, 1060, and 1228 (254 electrons) basis functions for the LANL2DZ, Def2-SV(P), CRENBL ECP, and LANL2DZ+dp basis sets, respectively. As can be seen in section III (Table 1), given available CPU time and disk space, the computational results demonstrate that the B3LYP/LANL2DZ level of theory is the best method for this study. Details can be found in section III. That is, the LANL2DZ basis sets are using pseudopotentials for heavier group 14 elements, except for the C atom. Further, spinunrestricted (UB3LYP) formalism was used for the open-shell (triplet) species. The computed expectation values for the spin-
This study uses five types of phosphino dimetalalkene molecules, Tip2EE(Tip)PPh2 (E = C, Si, Ge, Sn, and Pb). These species are similar in that they are valence-isoelectronic compounds. The above reactions (eqs a, b, and c) are chosen 9413
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squared operator ⟨S2⟩ were in the range 2.003−2.012, for all triplet species considered here. These values are very close to the correct value of 2.0, for pure triplets, so their geometries and energetics are reliable, for the purposes of this study. Frequency calculations were performed on all structures, to confirm that the reactants and products had no imaginary frequencies and that the transition states (TSs) possessed only one imaginary frequency. The relative energies, at 0 K, were thus corrected for vibrational zero-point energies (ZPE, not scaled). The thermodynamic corrections to 298 K, ZPE corrections, heat capacity corrections, and entropy corrections (ΔS) obtained were applied at the B3LYP/LANL2DZ level. The relative free energy (ΔG) at 298 K was also calculated at the same level of theory. Cartesian coordinates, calculated for the stationary points at the B3LYP level, are available as Supporting Information.
III. THE GEOMETRY OF IODODISILENE (Tip2Si Si(Tip)I) Because the structure of Tip2SiSi(Tip)I (2) has already been identified by X-ray diffraction study, 4,12 its geometry optimization was first carried out at both the B3LYP and B3PW91 levels of theory, using different basis sets, in order to test their reliability. The key geometrical parameters of Tip2SiSi(Tip)I are given in Table 1, together with some known experimental values.4 At any level of calculation, it is readily seen that there is reasonable agreement between calculated and experimental values for the SiSi, SiC, and SiI bond distances and some bond angles, with a variation of only 0.14 Å in bond length and of 5.6° in bond angle. As a result, the geometrical parameters of the real molecule, 2, at various levels, listed in Table 1, should give valuable information about the reactivity of dimetalalkenes. Nevertheless, in the case of mechanistic studies, especially when examining barrier heights and TS structures, larger basis sets prove to be prohibitively expensive in terms of available computation time and disk space. Because of these shortcomings and the good agreement between the B3LYP method with the shorter basis set (LANL2DZ) and the available experimental values,4 this study uses the B3LYP/LANL2DZ method. Before going further, the other disilene structures containing the phosphino ligands in Figure 1, i.e., 3, 4, and 5, are also examined. Again, on the whole, the calculated bond lengths and bond angles are in good agreement with the values determined by X-ray crystallography,4 even using the B3LYP/LANL2DZ method. As a result, from the above comparisons between experimental and computational data, it is expected that the same relative accuracy should also apply to the geometries and energetics predicted for the other dimetalalkenes with heavy group 14 elements. This, in turn, should provide reliable information for the discussion of the reaction mechanisms, for which experimental data are still not available. The B3LYP/ LANL2DZ level of theory is thus hitherto used in this work.
Figure 1. B3LYP/LANL2DZ optimized geometries (in Å and deg) of the molecules 3, 4, and 5. The experimental values (see ref 4) are in parentheses. Hydrogens are omitted for clarity.
The computational studies based on the B3LYP calculations indicate that these Rea-EE molecules all possess a singlet ground state. As expected, regardless of whether there is a singlet or triplet of the group 14 Rea-EE species, both EE double bond lengths show a monotonic increase, from carbon to lead. The same phenomena are also noted for the other E C and EP bond distances. Additionally, the B3LYP calculations predict that the EE double bond lengths for the singlet state of the Rea-EE molecules are estimated to be 1.391 (CC), 2.206 (SiSi), 2.436 (GeGe), 2.892 (Sn Sn), and 3.027 (PbPb) Å, which is in consistent agreement with the experimental values (1.356,13 2.139−2.360,14 2.212− 2.509,15 2.601−2.961,16 and 2.990−3.53717 Å). Moreover, the theoretical investigations also reveal that the EE distance is longer for the triplet than for its corresponding singlet group 14 Rea-EE compound. The reason for this phenomenon can be readily explained by considering their electronic structures (vide infra). In order to gain a fuller insight into the nature of the chemical bonding in the series of phosphino Rea-EE reactants, the valence molecular orbitals, based on the B3LYP/LANL2DZ calculations, are presented in Figure 3. As
IV. RESULTS AND DISCUSSION (1). The Geometries and Electronic Structures of Phosphino Dimetalalkene Species. In this work, model reactants Tip2EE(Tip)PPh2 (Rea-EE; E = C, Si, Ge, Sn, and Pb) are calculated both as singlet and as triplet species. Their geometric parameters are listed in Figure 2. 9414
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Figure 2. B3LYP/LANL2DZ optimized geometries (in Å and deg) of the reactants (singlet and triplet) Rea-EE (E = C, Si, Ge, Sn, and Pb). Hydrogens are omitted for clarity.
with the frontier molecular orbitals of ethylene, both the π and π* orbitals of the Rea-EE molecules are situated on the HOMO and LUMO, respectively. Consequently, it is apparent that in the triplet state one electron is situated in the LUMO (π*), in which antibonding interactions exist between the group 14 E atoms. However, a bonding interaction exists between the two E atoms in the HOMO. The double bond distance, EE, is therefore expected to be longer for the triplet than for the singlet. This prediction is already confirmed by the B3LYP/LANL2DZ results for all cases, as shown earlier. It is also noteworthy that the HOMO(π)−LUMO(π*) energy gaps for the phosphino Rea-EE reactants are calculated to be 115 (Rea-CC), 75 (Rea-SiSi), 63 (Rea-GeGe), 55 (ReaSnSn), and 55 (Rea-PbPb) kcal/mol, respectively. Indeed, for Rea-EE species with group 14 elements, the singlet−triplet energy splitting (ΔEst = Etriplet − Esinglet) follows a similar trend. For example, the computational results reveal an intriguing trend for ΔEst of 51 (Rea-CC) > 26 (Rea-SiSi) > 22 (Rea-GeGe) > 21 (Rea-SnSn) > 19 (Rea-PbPb) kcal/mol at the B3LYP level of theory. That is to say, the ΔEst for the phosphino Rea-EE molecule decreases as the atomic number of the central E atoms increases.18 This result is used to explain the origin of barrier heights for their chemical reactions in a later section. (2). The Isomerization Reactions of Phosphino Dimetalalkenes. Scheschkewitz and co-workers reported that melting of 1 produces the 1-phospha-2,3-disilaindane in an analogous fashion, involving 1,2-phosphino shift to produce a mixture of diastereomers of the CH insertion product (eq a).4 In order to understand the formation of such thermal rearrangement compounds, B3LYP calculations were performed. The isomerization mechanisms are thought to proceed as follows: reactant (Rea-EE) → a-TS1 → a-Int-E-E → aTS2 → a-Pro-E-E (see Figure 4). The optimized geometries
Figure 3. Calculated frontier molecular orbital for the Rea-EE (E = C, Si, Ge, Sn, and Pb) species at the B3LYP/LANL2DZ level of theory. For more information, see the text.
for these TSs and Pros were calculated using the B3LYP/ LANL2DZ method, and their selected geometrical parameters are listed in Figures A−D (Supporting Information), respectively. The corresponding relative energies at the B3LYP level of theory are given in Table 2, and the potential energy profiles based on the DFT data are summarized in Figure 5. There are several noteworthy features of Figures 4 and 5 and Table 2. The TS (a-TS1) was calculated for the 1,2-phosphino shift in the Rea-EE → a-Int-EE process. All the transition states at the B3LYP level of theory are confirmed by calculation of the energy Hessian, which shows only one imaginary vibrational frequency: 173i cm−1 (a-TS1-C), 152i cm−1 (a-TS1-Si), 136i cm−1 (a-TS1-Ge), 146i cm−1 (a-TS1-Sn), and 112i cm−1 (aTS1-Pb). It is noted that the primary similarity between these transition states is a three-center pattern involving phosphorus and the two main group 14 atoms (E), as shown in Figure 4. In addition, as seen in Table 2, the results suggest that the activation energy for such a 1,2-phosphino shift decreases in the order (in kcal/mol) 125 (C) > 47 (Si) > 29 (Ge) > 25 (Sn) > 21 (Pb). That is, the greater the atomic weight of the central atom E, the smaller is the barrier height and the easier the 1,2phosphino migration occurs. It should be mentioned that a relatively small distance (1.391 Å) between the central carbon atoms in the Rea-CC reactant might lead to steric crowding of the large phenyl groups during the 1,2-shift reaction. This 9415
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Figure 5. Potential energy surfaces for the isomerization reactions of the Rea-EE (E = C, Si, Ge, Sn, and Pb) species. The relative energies (kcal/mol) are taken from the B3LYP/LANL2DZ level, as given in Table 2.
Figure 4. B3LYP/LANL2DZ optimized structures of the stationary points obtained during the thermal rearrangement reactions. The heavy arrows indicate the main atomic motions in the transition state eigenvector. For detailed geometrical parameters, see the Supporting Information. Hydrogens are removed for the sake of clarity.
results in a larger than expected activation barrier for the ReaCC system. However, a large distance between the E atoms (in particular, 2.892 or 3.027 Å for Rea-SnSn or Rea-Pb Pb) reduces the crowding and, in turn, results in a lower barrier height, as shown in Table 2 and Figure 5. As seen in Figure 4, after the 1,2-phosphino shift, the reaction produces an intermediate (a-Int-E-E) that has a P-E-E three-membered ring. The DFT computations indicate that the relative energies (kcal/mol) of these intermediates decrease in the order 69 (a-Int-C-C) > 34 (a-Int-Si-Si) > 26 (a-Int-GeGe) > 19 (a-Int-Sn-Sn) > 14 (a-Int-Pb-Pb), all of which are more than the energy of the corresponding reactant. Again, the large difference in energy between the formation of a-Int-E-E (E = Si, Ge, Sn, and Pb) and a-Int-C-C strongly implies that the central carbon is more reluctant to form a three-membered structure, because of its smaller atomic radius, which induces severe steric congestion in the bulky substituents. According to the configuration mixing (CM) model developed by Pross and Shaik,19,20 the stabilization of the transition state of a thermal rearrangement depends on the ΔEst of the reactant Rea-EE. That is to say, a smaller ΔEst results in a more stable transition state, a lower activation energy, and a lower reaction enthalpy for the product. This study’s model calculations confirm this prediction and suggest a decreasing trend in ΔEst for the ReaEE species as the atomic weight of the group 14 element E increases from C to Pb. Table 2 shows that this result is in good agreement with the trend in activation energies (ΔETS1⧧), as well as reaction enthalpies (ΔEInt), for the 1,2-phosphino migration of the Rea-EE systems. Subsequently, the a-Int-E-E intermediate undergoes a CH bond insertion (a-TS2) when a phenyl group on the phosphorus attacks one central E atom to yield the final
Table 2. Relative Energies (in kcal/mol) for Singlet and Triplet Phosphino Dimetalalkene Rea-EE (E = C, Si, Ge, Sn, and Pb) and for the Process Rea-EE → a-TS1 → a-IntE-E → a-TS2 → a-Pro-E-Ea,b relative energies
ReaCC
Rea-Si Si
Rea-Ge Ge
Rea-Sn Sn
Rea-Pb Pb
ΔEstc ΔETS1⧧ d
51.1 125 (127) 69.4 (72.7) 90.2 (91.1) 9.44 (12.6)
26.0 47.1 (48.5) 33.8 (36.3) 35.1 (36.4) −20.8 (−26.9)
22.3 29.0 (30.0) 26.3 (31.7) 34.9 (37.1) −25.5 (−18.2)
20.6 24.6 (31.9) 19.0 (22.3) 42.3 (45.9) −9.00 (−5.21)
19.1 20.5 (28.5) 14.3 (22.6) 66.9 (73.6) 19.9 (21.5)
ΔEInte ΔETS2⧧ f ΔHProg a
All at the B3LYP/LANL2DZ level of theory. For the B3LYP optimized structures of the stationary points, see Figures A−D (Supporting Information). bEnergy differences have been zero-pointcorrected and used the Gibbs free energy (ΔG, in parentheses). See the text. cEnergy relative to the corresponding singlet state. A positive value means the singlet is the ground state. dThe activation energy of the transition state (a-TS1-E-E), relative to the corresponding reactant. eThe energy of the intermediate (a-Int-E-E) relative to the corresponding reactant. fThe activation energy of the transition state (a-TS2-E-E), relative to the corresponding reactant. gThe reaction enthalpy of the product (a-Pro-E-E) relative to the corresponding reactant.
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isomerization product (a-Pro-E-E). As shown in Table 2, the B3LYP results show that the overall barrier heights are determined to be in the order Rea-CC > Rea-PbPb > Rea-SiSi ≈ Rea-GeGe ≈ Rea-SnSn. Moreover, the DFT computations predict that the free energies of a-Pro-C-C and a-Pro-Pb-Pb exceed those of the corresponding reactants by 13 and 22 kcal/mol, respectively. Consequently, the theoretical results suggest that the thermal rearrangement of Rea-CC and Rea-PbPb is unlikely to proceed, whereas the isomerization process for the Rea-SiSi, Rea-GeGe, and Rea-SnSn species is easier. This prediction is in accordance with available experimental observations.4 (3). The Transition Metal Complexation Reactions of Phosphino Dimetalalkenes. The synthesis of a transition metal complex of 1 and isomers by their coordination to the [Pd(PCy3)2] fragment has been reported.4 Despite much attention being recently focused on the reactions of transition metal complexes with silicon−silicon doubly bonded species,21 their formation mechanisms and the controlling key factors that affect their reactivity remain uncertain, so this study uses the B3LYP/LANL2DZ method to investigate the mechanisms for the cycloaddition of a 12-electron palladium fragment to these phosphino doubly bonded molecules (Rea-EE), which proceeds via eq b. Selected geometrical parameters and relative energies at the DFT are summarized in Figure 6 and Table 3. There are several important conclusions from these results, to which attention should be drawn. In the present work, it is found that these cycloaddition reactions adopt the Rea-EE + Pd(PCy3) → b-TS → b-ProE-E pathway. The five optimized transition states (b-TS-C-C, b-TS-Si-Si, b-TS-Ge-Ge, b-TS-Sn-Sn, and b-TS-Pb-Pb) and the calculated transition vectors are shown in Figure 6. The arrows in the figure indicate the directions in which the atoms move in the normal coordinate corresponding to the imaginary frequency. It is readily seen that these transition states connect the corresponding reactants to the cycloaddition product, providing excellent confirmation of the concept of the cycloaddition process. That is, the reactants approach each other with their molecular planes parallel and two new bonds (PdE) are formed at the same time. These reactions appear to be concerted, since it was possible to locate only one TS for each reaction and to confirm that it is a true TS, by frequency analysis. A comparison of the five TSs shows several interesting trends. As can be seen in Figure 6, the primary similarity between these optimized TSs is a three-membered-ring-like structure with C1 symmetry. There is also a dramatic effect on the intramolecular distances at the saddle points. An increase in the atomic number of the group 14 atoms in the Rea-EE species causes a large increase in the EE distance. Moreover, the present calculations indicate that, in these five TS cases, one of the approaching PdE bonds is longer than the other. In particular, the greater the atomic weight of the group 14 atom, E, the greater is the asynchronicity of the [1 + 2] cycloaddition reaction. The corresponding product geometries (b-Pro-C-C, b-ProSi-Si, b-Pro-Ge-Ge, b-Pro-Sn-Sn, and b-Pro-Pb-Pb) were further optimized, as given in Figure 6. The B3LYP calculations suggest that the EE bond is stretched by 5.6, 2.9, 0.66, 6.5, and 11% for b-TS-C-C, b-TS-Si-Si, b-TS-Ge-Ge, b-TS-Sn-Sn, and b-TS-Pb-Pb, respectively, relative to its corresponding value for b-Pro-E-E. According to the Hammond postulate,22 an earlier transition state with a smaller barrier and more
Figure 6. Optimized structures of the transition states (b-TS) and addition products (b-Pro-E-E). The heavy arrows indicate the main atomic motions in the transition state eigenvector. For the B3LYP/ LANL2DZ relative energies for each species, see Table 3. Hydrogens are omitted for clarity.
Table 3. Relative Zero-Point Energies and Relative Gibbs Free Energies (in Parentheses) at 298 K at the B3LYP/ LANL2DZ Level of Theory for the Process Rea-EE + Pd(PCy3) → b-TS → b-Pro-E-Ea system
ΔE⧧ b (kcal mol−1)
Rea-CC Rea-SiSi Rea-GeGe Rea-SnSn Rea-PbPb
35.6 (50.6) 11.1 (15.8) 8.77 (14.6) 6.51 (13.8) 3.37 (9.60)
ΔHc (kcal mol−1) 29.1 −22.7 −31.0 −32.4 −33.1
(46.8) (−14.4) (−16.5) (−20.7) (−34.4)
a
The selected B3LYP optimized structures of the stationary points; see Figure 6. bThe activation energy of the transition state, relative to the corresponding reactants. cThe reaction enthalpy of the product, relative to the corresponding reactants.
exothermicity should occur for the Pd(PCy3) cycloaddition reaction of the phosphino Rea-EE containing the heavy group 14 E elements. Indeed, as already shown in Table 3, the DFT calculations demonstrate that the order of activation energy (ΔE⧧) follows the same trend as the reaction enthalpy (ΔH). Thus, considering both the kinetics and the thermodynamics of eq b, it is concluded that [1 + 2] cycloaddition of phosphino dimetalalkenes with Pd(PCy3) should produce a three-membered-ring cycloadduct compound in a single step (i.e., in a concerted manner), so it should be stereospecific. In 9417
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other words, such cycloaddition reactions should be favored for the production of stereoretention products. In order to ascertain the key factors that determine the general features of these [1 + 2] cycloaddition reactions (eq b), the CM model shown earlier was also used to gain a better understanding of the reactivity of the various reactants.19,20 According to the conclusions provided by this model, the energy barriers governing processes and the reaction enthalpies should be proportional to the ΔEst of a phosphino Rea-EE. Namely, the smaller the value of ΔEst for Rea-EE, the lower is the barrier height and the more exothermic and, in turn, the faster is the [1 + 2] cycloaddition reaction. As already detailed in Table 3, this result is consistent with the trends in activation energy and enthalpy (ΔE⧧ and ΔH) for the [1 + 2] cycloaddition of a phosphino dimetalalkene with a 12-electron palladium fragment. (4). The Cycloaddition Reactions of Phosphino Dimetalalkenes. The [2 + 2] cycloaddition reactions of phosphino dimetalalkenes with HNNH (diazene), i.e., eq c, were also calculated at the B3LYP/LANL2DZ level. Although this reaction has not been experimentally investigated,23 it is believed that the computational results presented in this work provide information for future experimentation. The key geometrical parameters for these reactions are listed in Figure 7, and the calculated reaction energetics are given in Table 4. The major conclusions to be drawn from the current study can be summarized as follows. As shown in Figure 7, at the start of the reaction, the diazene molecule undergoes cycloaddition with dimetalalkene to yield the TS. These optimized TSs, along with the calculated transition vectors, are referred to as c-TS-C-C, c-TS-Si-Si, cTS-Ge-Ge, c-TS-Sn-Sn, and c-TS-Pb-Pb, respectively. As expected, an increase in the atomic weight of the central E atoms in the Rea-EE species causes a large increase in the EE distance of the TS. Moreover, there is a significant effect on the intermolecular distances at the saddle points. That is, the greater the atomic radius of the central atoms, E, the more asynchronous is the [2 + 2] cycloaddition reaction. For instance, for the cases of c-TS-C-C, c-TS-Si-Si, c-TS-Ge-Ge, cTS-Sn-Sn, and c-TS-Pb-Pb, one of the stretching EN bonds is longer than the other. In addition, as seen in Table 4, the Gibbs free barrier height for the cycloaddition reaction decreases from c-TS-C-C to c-TS-Pb-Pb. In other words, the larger the atomic number of the E elements involved in the Rea-EE species, the smaller is the reaction barrier for [2 + 2] cycloaddition. The optimized product structures (c-Pro-C-C, c-Pro-Si-Si, c-Pro-Ge-Ge, c-Pro-Sn-Sn, and c-Pro-Pb-Pb) are also obtained using the DFT method. Again, as Figure 7 shows, the order of the EE bond length for c-Pro-E-E increases as the atomic weight of the central atoms, E, increases. The same phenomenon can also be found in both of the EN bond distances of the final product. Interestingly, the order of the Gibbs free enthalpy follows the same trend as that of the activation energy. It should be noted that only the energy of cPro-C-C exceeds that of its corresponding starting materials. This strongly implies that diazene cycloaddition by Rea-CC is energetically unfavorable and would be endothermic at room temperature. These DFT results can be explained using a CM model, as stated earlier.19,20 According to this model, the stabilization of a cycloaddition transition state is dependent on the ΔEst of the reactant group 14 Rea-EE; i.e., a smaller ΔEst results in
Figure 7. Optimized structures of the transition states (c-TS) and cycloaddition products (c-Pro-E-E). The heavy arrows indicate the main atomic motions in the transition state eigenvector. For the B3LYP/LANL2DZ relative energies for each species, see Table 4. Hydrogens are omitted for clarity.
Table 4. Relative Zero-Point Energies and Relative Gibbs Free Energies (in Parentheses) at 298 K at the B3LYP/ LANL2DZ Level of Theory for the Process Rea-EE + H NNH → c-TS → c-Pro-E-Ea system Rea-CC Rea-SiSi Rea-GeGe Rea-SnSn Rea-PbPb
ΔE⧧ b (kcal mol−1) 80.9 49.2 37.2 27.8 21.4
(95.3) (70.3) (58.5) (41.8) (32.6)
ΔHc (kcal mol−1) 43.3 −30.6 −34.9 −43.4 −44.7
(56.5) (−19.2) (−21.2) (−30.8) (−36.7)
a
The selected B3LYP optimized structures of the stationary points; see Figure 7. bThe activation energy of the transition state, relative to the corresponding reactants. cThe reaction enthalpy of the product, relative to the corresponding reactants.
greater transition state stabilization, a lower activation energy, a faster cycloaddition reaction, and a more exothermic reaction. As discussed previously, the B3LYP results suggest a decreasing trend in ΔEst for the Rea-EE reactant. This result is consistent with the trends in activation energy and reaction enthalpy (ΔE⧧, ΔH) for the [2 + 2] cycloaddition of group 14 Rea-EE species with diazene, as illustrated above.
V. CONCLUSION In this work, the B3LYP level of theory is used to study the mechanisms for three types of chemical reactions of phosphino dimetalalkenes Rea-EE (E = C, Si, Ge, Sn, and Pb) that 9418
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possess an EE double bond featuring the phosphino substituent. It should be mentioned that this study provides the first theoretical demonstration of the reaction trajectory and the first theoretical estimation of the activation energy and reaction enthalpy for these chemical processes. Considering the aforementioned five phosphino dimetalalkene systems and their related chemical reactions studied in this paper together, the following conclusions can be drawn: (1) This theoretical work reveals that both the palladium complexation reactions and [2 + 2] diazene cycloadditions of phosphino Rea-EE molecules produce the final cycloadduct in a concerted manner but via an asynchronous transition state. That is, these cycloadditions proceed stereospecifically, resulting in cycloproducts with retained stereochemistry. (2) The theoretical findings suggest that the chemical reactivity of phosphino Rea-EE molecules increases in the order Rea-CC < Rea-SiSi < Rea-GeGe < Rea-SnSn < Rea-PbPb. (3) In other words, the theoretical results indicate that the centric EE double bond has an important influence on the isolability of a phosphino Rea-EE molecule.2 In consequence, a phosphino dimetalalkene containing a substituted EE double bond with lighter group 14 elements (such as E = C and Si) should be stable, so these compounds can be readily synthesized and isolated at room temperature. (4) This study shows that knowledge of the singlet−triplet splitting (ΔEst) of the phosphino dimetalalkenes is of great importance in achieving a deeper understanding of their reactivity, since it is the driving force for the related reactions. (5) This study shows that the heavier the atomic weight of group 14 elements, E, involved in the phosphino dimetalalkenes Rea-EE, the smaller is the ΔEst, the lower is the activation barrier and the larger is the enthalpy of the final product. It is ultimately hoped that this study will aid further developments in phosphino dimetalalkene chemistry.
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ASSOCIATED CONTENT
S Supporting Information *
B3LYP/LANL2DZ optimized geometries and B3LYP energies. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors are grateful to the National Center for HighPerformance Computing of Taiwan for generous amounts of computing time. They also thank the National Science Council of Taiwan for the financial support. Special thanks are also due to referee 1 and referee 2 for very helpful suggestions and comments.
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REFERENCES
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