Mechanism of the Ring− Chain Rearrangement in Phosphiranes

Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium, and ... Budapest University of Technology and Economics...
0 downloads 0 Views 189KB Size
Download PDF
J. Org. Chem. 2001, 66, 5671-5678

5671

Mechanism of the Ring-Chain Rearrangement in Phosphiranes: Hydrogen versus Halogen Migration Janka Ma´trai,†,‡ Alk Dransfeld,† Tama´s Veszpre´mi,‡ and Minh Tho Nguyen*,† Department of Chemistry, University of Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium, and Department of Inorganic Chemistry, Budapest University of Technology and Economics, Gelle´ rt te´ r 4, H-1521 Budapest, Hungary [email protected] Received March 31, 2000 (Revised Manuscript Received June 15, 2001)

Ab initio quantum chemical calculations including HF, MP2, CCSD(T), CASSCF(10,10)/CASPT2, and B3LYP methods with the 6-31G(d,p) basis set were used to probe the mechanism of the ringchain rearrangement of halogeno-phosphiranes. It is confirmed that the lowest energy interconversion between C-halogenated-(X)-phosphiranes and vinylphosphines, with X ) H, F, Cl, and Br, is a one-step process in which the C-P bond cleavage and X-sigmatropic migration from C to P occur in a concerted manner in a single transition structure. The migration of a hydrogen from CH(H) is slightly favored over that of CX(H), and thus, the cleavage of the C(X)-P bond is preferred. The energy barrier for the whole process involving hydrogen migration in the parent phosphirane is calculated to be about 45 ( 5 kcal/mol. The migratory aptitude of the atoms X in the uncomplexed species is found as follows: H > Br > Cl > F, either in the gaseous phase or in aqueous and DMSO solutions. The solvation enthalpies that were estimated using a polarizable continuum model (PCM) are rather small and do not modify the relative ordering of the energy barriers. Such a trend is at variance with recent experimental findings on metal-phosphinidene complexes in which only halogen migration was observed. This might arise from a peculiar effect of the metal fragments W(CO)5 used in the experimental studies to stabilize the phosphorus species that induce a quite different mechanism. Calculations of the 31P chemical shifts using the GIAO/B3LYP/6-311+G(d,p) method show a remarkable correlation between the δ31P(X) chemical shifts of X-phosphiranes and those of X-phosphines (XCH2PH2), suggesting that the large β substituent effect is not inherent to the small rings. 1. Introduction Phosphiranes (I), phosphorus analogues of cyclopropanes, are attracting considerable interest as synthons for larger phosphorus heterocycles through a variety of ring expansions and as complexing agents in coordination chemistry.1 Haber et al.2 observed in 1992 the existence of a chain-ring equilibrium between a vinylphosphine (II) and a phosphirane (I) at 500 °C (eq 1). The II-I interconversion formally involves a ring closure of vinylphosphine and in addition a sigmatropic shift of a hydrogen atom. In a subsequent theoretical study,3 we have demonstrated that the chain-ring rearrangement II-I is an energetically concerted process in which the C-P bond formation in I and the H-shift from

P to C occur simultaneously in a single transition structure. Although the energy barrier of about 56 kcal/ mol, computed at the QCISD(T)/6-311G(d,p)+ZPE level for the unsubstituted system, is rather large, it is not inconsistent with the experimental thermal conditions at 500 °C. Starting from phosphirane, the conversion to vinylphosphine I-II has been found to be the most favored process among its many possible transformations. More recently, Tran Huy and Mathey4,5 reported their experimental observations that a phosphirane (I-M), complexed to metal fragments such as W(CO)5, formed in a previous step by a [2 + 1] cycloaddition of vinyl halogenide with a terminal phosphinidene complex, cleanly rearranges at a moderate temperature to give a complexed vinylhalogeno-phosphine (II-M) (cf., eq 2).

†

University of Leuven. Budapest University of Technology and Economics. (1) Mathey, F. Chem. Rev. 1990, 90, 997. (2) Haber, S.; Le Floch, P.; Mathey, F. J. Chem. Soc., Chem. Commun. 1992, 1799. (3) Nguyen, M. T.; Landuyt, L.; Vanquickenborne, L. G. J. Chem. Soc., Faraday Trans. 1994, 90, 1771. ‡

The halogen atoms considered in the experimental studies4,5 include chlorine and bromine. The most salient (4) Tran Huy, N. H.; Mathey, F. Synlett 1995, 353. (5) Tran Huy, N. H.; Mathey, F. J. Org. Chem. 2000, 65, 652.

10.1021/jo000493q CCC: $20.00 © 2001 American Chemical Society Published on Web 08/02/2001

5672

J. Org. Chem., Vol. 66, No. 17, 2001

Scheme 1. Three Possible Pathways for Ring Opening of a Substituted 2-X-Phosphirane

Ma´trai et al. minima or transition structures on the potential energy surface. To check further the influence of higher excitations and/or multireference wave functions on the relative energies related to the ring-opening mechanism of phosphirane, coupledcluster theory CCSD(T) calculations, as well as complete active-space second-order perturbation theory CASSCF/CASPT2 calculations, were performed for the unsubstituted system. For the latter, atomic natural orbitals (ANOs) have also been employed. In the construction of the CASSCF wave functions, the active spaces of 10 electrons in 10 orbitals have been selected. Because the system does not have any symmetry and the orbitals are strongly mixed, it is rather difficult to clearly identify their nature. Therefore, the orbitals employed in the active space simply include the five highest occupied molecular orbitals (HOMOs) and five lowest unoccupied molecular orbitals (LUMOs) generated from corresponding SCF wave functions. To probe the effect of the bulk solvent on the relative energies, the polarizable continuum model (PCM)9 approach was applied at the B3LYP/6-31G(d,p) level of theory. The chemical shifts were evaluated from GIAO/B3LYP/6-311+G(d,p) computations.7 The optimized geometrical parameters and calculated energies are given in the Supporting Information (Cartesian coordinates, Z-matrices, and comparison of MP2 and B3LYP values in Tables I-V).

3. Results and Discussion features of reaction 2 are as follows: (i) in both cases, a migration of a halogen atom from carbon to phosphorus is involved rather than a hydrogen migration, and (ii) the C-P bond situated at the opposite site of the C-X group is actually broken. Thus, the observed ring-chain rearrangement presents a high selectivity, because there are, as seen in Scheme 1, at least three distinct migration channels accompanying the ring opening that could in principle be opened: a halogen migration giving X4 or a migration of a hydrogen of X1 which is attached to one of the two carbon atoms C1 and C2, giving rise to X2 and X3, respectively. The experimental observations4,5 raise a number of interesting questions regarding the reaction mechanism, namely (1) what the actual mechanism of the rearrangement of the halogenated phosphiranes is, that is, whether or not the reaction remains concerted; (2) how the competition between the different pathways as depicted in Scheme 1 occurs; (3) if there is any significant effect of the halogen on the hydrogen migration; and (4) how large could the solvent effect be. In an attempt to further address these questions, we have carried out ab initio quantum chemical calculations on a series of halogenated X-phosphiranes, including X ) H, F, Cl, and Br. The reaction energetics were also considered in a solvent continuum. Another aim of the study is to find out whether there is any relationship between the 31P NMR chemical shifts and the geometric or electronic properties of phosphiranes that might explain the strong magnetic shielding in the three-member rings.6

2. Methods of Calculation Quantum chemical calculations were carried out using the Gaussian 987 and Molcas-48 program packages. The geometries of the studied structures were fully optimized at both the HF and MP2 levels of molecular orbital theory, as well as with the hybrid B3LYP method of density functional theory, in conjunction with the 6-31G(d,p) basis set. Second derivatives of energies and harmonic frequencies were calculated for all considered structures to establish whether they are either real (6) Nguyen, M. T.; Dransfeld, A.; Landuyt, L.; Vanquickenborne, L. G.; Scchleyer, P. v. R. Eur. J. Inorg. Chem. 2000, 103.

As a convention, each of the structures discussed hereafter is defined by a combination of letters and numbers as described in Scheme 1: (a) X1 stands for a starting phosphirane with X ) H, F, Cl, and Br, and the halogen substitution occurs at the carbon C2; (b) X2, X3, or X4 stands for a vinylphosphine product formed by one of the three possible ring opening modes given in Scheme 1; and (c) the transition structure (TS) linking a phosphirane X1 to a vinylphosphine Xn is designated by X1/ Xn, with n ) 2, 3, or 4. (A) Phosphiranes. The four phosphiranes considered in this work are shown in Figure 1, and their parameters optimized at both MP2 and B3LYP levels are recorded in the Supporting Information (Table I). The molecular structure of the parent phosphirane H1 has been analyzed in much detail in previous papers.3,10 The only additional information reported here concerns the B3LYP method, which seems in general to provide slightly larger distances of the ring (up to 0.15 Å), as compared with the MP2 ones. However, these variations induce only small changes on the computed rotational constants (A, B, and C) that differ by about 1% from the available experimental values.3 We refer to previous papers for detailed information on the rotational constants (refs 3 (7) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (8) Fuelscher, M. P.; Olsen, J.; Malmqvist, P. A.; Roos, B. O. Molcas, version 4.0; Department of Theoretical Chemistry, Chemical Centre: Lund, Sweden, 1999. (9) (a) Miertus, S.; Scrocco, E.; Tomasi, J. Chem. Phys. 1981, 55, 117. (b) Tomasi, J.; Persico, M. Chem. Rev. 1994, 94, 2027. (c) Cossi, M.; Barone, V.; Cammi, R.; Tomasi, J. Chem. Phys. Lett. 1996, 255, 327. (10) Barach, S. J. Comput. Chem. 1989, 10, 392; J. Phys. Chem. 1989, 93, 7780 and references therein.

Ring-Chain Rearrangement in Phosphiranes

J. Org. Chem., Vol. 66, No. 17, 2001 5673 Table 1. Computeda 31P NMR Chemical Shiftsb of 2-X-phosphiranes, (CH2)(PH)(CHX), and Phosphines, PH2CH2X, with X ) H, CH3, F, Cl, and Br X H1 ) H1′ Me1 Me1′ F1 F1′ Cl1 Cl1′ Br1 Br1′

Figure 1. Selected geometrical parameters of the four phosphiranes X1 considered, with X ) H, F, Cl, and Br.

and 11). Substitution of a hydrogen at a carbon atom of the three-membered skeleton (C2, Figure 1) by a halogen atom, in either F1, Cl1, or Br1, gives rise to two trans and cis isomers with respect to the disposition of both CX and PH groups. Only the trans conformers are displayed here. Halogen substitution brings about rather marginal modifications on the C-P bond lengths; while the vicinal C2-P distance b tends to be compressed, the opposite C1-P c seems to be stretched, which is in line with an electron-withdrawing effect of the halogens. Of the three substituted ring structures, F1 is the least equalized molecule in which there is the largest difference between both b and c bonds and so forth. Overall, the bond angle C-P-C around the P atom remains almost unchanged. In particular, the molecule F1 also presents the longest C-H bond distances. The geometries of the vinylphosphine isomers (II) were also optimized. However, because of the large amount of data, they are omitted here for the sake of simplicity. Only their relative energies with respect to the corresponding phosphiranes will be given hereafter in the different potential energy profiles. It is also of interest to examine the NMR chemical shifts of the 31P atoms in 2-X-phosphiranes, to assist with the differentiated identification of the syn and anti conformers. The anti conformer in which the X substituent is oriented trans to the PH bond is consistently lower in energy than the syn (or cis) isomer in all of the 2-Xphosphiranes considered. Magnetic shieldings at phosphorus (computed using the GIAO/B3LYP/6-311+G(d,p) method and B3LYP/6-31G(d,p) optimized geometries) of the parent phosphirane H1, both trans and cis conformers of F1, Cl1, and Br1, as well as those of 2-methylphosphirane Me1, are recorded in Table 1. The computed 31P magnetic shielding of 2-X-phosphiranes displays a remarkable dependency on the conformation of the CX group (Table 1). Although the absolute values of 31P NMR chemical shifts, δ31P, actually deviate significantly from the experimental values, trends are expected to be relatively well reproduced. For the parent phosphirane H1, the calculated value of -307 ppm is upfield compared with the experimental one of -341 ppm reported earlier by Wagner et al.12 With (11) Bowers, M. T.; Beaudet, R. A.; Coldwhite, H.; Tang, R. J. Am. Chem. Soc. 1969, 91, 17.

H CH3 CH3 F F Cl Cl Br Br

orientationc

phosphirane

phosphine

a,g s,a a,g s,a a,g s,a a,g s,a

-307 -279 -259 -268 -259 -260 -233 -263 -226

-142 -121 -98 -129 -108 -119 -73 -116 -58

a Calculated at GIAO/B3LYP/6-311+GDP for geometries optimized at the B3LYP/6-31GDP level. b Magnetic shieldings of phosphorus were transformed to NMR chemical shifts by the equation shift(M) - shift(ref) ) - shield(M) + shield(ref), with shield(ref ) PH3) ) 567.1 ppm (using a MP2(fc)/6-31G(d,p) geometry) and shift(ref ) PH3) ) -240 ppm. c The notation a,g indicates that the relative orientation of the substituent X in the anti conformer of the phosphirane is similar to that in the gauche rotamer of XCH2PH2 molecules. The notation s,a indicates that the relative orientation of the substituent X in the syn conformer of the phosphirane is similar to that in the anti rotamer of XCH2PH2 molecules.

respect to the parent H1, all substituted derivatives have chemical shifts at lower fields (cf., Table 1). The relative orientation of the substituent X (the torsion angle H-P-C-X being close to 180°) is similar to that in the gauche rotamer of the phosphine X-CH2PH2 molecules. The alternative syn (or cis) conformations of the 2-X-phosphiranes that are referred to as F1′, Cl1′, Br1′, and Me1′ in Table 1 (H1 and H1′ being identical), have a similar orientation of CX toward the phosphorus lone pair (Lp) as the anti rotamer of XCH2PH2 (the torsion angle Lp-P-C-X being around 120° or larger). The β substituent effect on δ31P turns out to be smaller in the anti than in the syn conformers of phosphiranes. For Br1′, the largest difference of the δ31P with respect to that of the parent H1 is found (a change of ∆δ31P ) 81 ppm). The difference between the δ31P values in both trans and cis phosphiranes is also largest in bromo derivatives (X ) Br) and smallest in fluoro derivatives (X ) F). Compared with all the halogens considered, the methyl substituent has induced the smallest effect on the δ31P values. Figure 2 shows a remarkable correlation between the δ31P(X) of syn 2-X-phosphiranes and the δ31P(X) of anti XCH2PH2 phosphines; the correlation coefficient square is 0.946. This correlation points out that the large extent of the β substituent effect is not inherent to the small ring. The relationship between the chemical shifts of anti 2-X-phosphiranes and gauche XCH2PH2 phosphines is less pronounced (correlation coefficient being 0.80). Further extensive statistical evaluation of a variety of relations of δ31P in these molecules with their electronic and geometric parameters shows however no significant correlation. We note that the values δ31P of -167 and -110 ppm were reported for complexed bromo and chloro phosphiranes, respectively.4,5 It is likely that the larger differences between the computed and observed values for the latter molecules arise from a strong influence of the metal fragments present in the experiments. 31P

(12) Wagner, R. I.; Freeman, L. D.; Goldwhite, H.; Roswell, D. G. J. Am. Chem. Soc. 1967, 89, 1102.

5674

J. Org. Chem., Vol. 66, No. 17, 2001

Ma´trai et al. Table 2. Calculated Energy Barrier in the Nonsubstituted System (H1, H1/H2) Using Different Levels of Theory with the 6-31G(d,p) Basis Set method//geometry

total energy of H1 (hartree)

energy barriera (kcal/mol)

HF//HF MP2//MP2 B3LYP//B3LYP CCSD//MP2 CCSD(T)//MP2 CASSCF(10,10)//MP2 CASPT2(10,10)//MP2b

-419.328 263 -419.736 798 -420.549 971 -419.774 996 -419.790 062 -419.459 868 -419.778 431

62.65 66.09 55.55 65.28 61.84 54.00 51.4

a Including zero point energy corrections; the ZPEs of H1 and H1/H2 are 39.8 and 37.1 kcal/mol, respectively. b The relative CPU times for single point electronic energies are roughly the following: HF, 1; MP2, 4; B3LYP, 3; CASSCF/CAPT2, 10; and CCSD(T), 100, using the same basis set. The lack of symmetry is a disadvantage for coupled-cluster calculations. For geometry optimizations, both MP2 and B3LYP require comparable CPU times.

Figure 2. Correlation between 31P NMR chemical shifts, δ31P, of 2-X-phosphiranes and XCH2PH2 phosphines, with X ) H, Me, F, Cl, and Br. Squares indicate syn phosphiranes and anti phosphines, and triangles indicate anti phosphiranes and gauche phosphines.

Figure 3. Selected geometric parameters of the transition structures X1/X2. The F atom in F1/F2 needs to be replaced by Cl and Br to form Cl1/Cl2 and Br1/Br2, respectively.

(B) Rearrangement of the Unsubstituted Phosphirane. The ring opening of the unsubstituted phosphirane has been investigated in detail in an earlier study3 in which the geometry of the TS H1/H2 was optimized at the MP2/6-31G(d,p) level and the energy barrier estimated using single-point energy QCISD(T)/ 6-311G(d,p)+ZPE computations. A comparison with the B3LYP parameters is given in Table II of the Supporting Information (cf., Figure 3 for the atom numbering). As expected, the parameters obtained from these two distinct methods differ somewhat from each other, especially for those around the ring skeleton and migrating hydrogen. The B3LYP method seems to suggest a less opened γ angle around C2; as a consequence, the B3LYP value for the broken C1-P distance c is smaller than the corresponding MP2 value. With regard to the migrating atom (noted as Hm), the bonds d1 between Hm and C2 and d2 between Hm and P both have shorter distances

at the B3LYP level. Nevertheless, both methods suggest that, in the TS H1/H2, the C2-Hm bond remains almost intact, whereas the new P-Hm bond is not formed yet. To obtain an estimate for the effect of higher order electron correlation on the energy barrier, we have carried out both coupled-cluster theory CCSD(T) and multiconfigurational treatment, followed by a secondorder perturbation theory, CASSCF/CASPT2 computations making use of MP2 optimized geometries. The TS geometry was not reoptimized using the CASSCF level. In the CASSCF/CASPT2 computations, we used an atomic natural orbital (ANO) basis set having a comparable quality with the 6-31G(d,p) and selected finally the active space of 10 electrons in 10 orbitals. As mentioned above, the orbitals employed for variable occupancy that include the five HOMOs and five LUMOs generated from the corresponding SCF wave functions largely cover the important orbitals involved in the electronic reorganization accompanying the process under consideration. As seen in Table 2, incorporation of dynamic electron correlation tends to decrease the barrier. The B3LYP method gives a value closest to the CASSCF one. The CCSD(T) barrier turns out to be about 10 kcal/mol higher than the latter. Figure 4 shows the most important orbitals of the active space, namely the HOMO-2, HOMO-1, HOMO, and LUMO of the TS H1/H2 and the corresponding occupation numbers as derived following the CASSCF optimization procedure. The occupation numbers of the HOMO and LUMO amount to 1.95 and 0.33, respectively. The weights of the Hartree-Fock reference and the doubly excited configuration from HOMO to LUMO amount to 0.82 and 0.15, respectively, in the CAS wave function. Such an electronic distribution suggests that the actual transition state structure for ring opening of phosphirane accompanied by hydrogen migration may have a significant biradical character. To quantify the contribution of such a biradical configuration to the total energy of the TS H1/H2, and thereby to the energy barrier, we have attempted to reoptimize both minimum and TS structures at the CASSCF level. Despite many attempts, we were unfortunately not successful in locating the TS because of the lack of analytical Hessians of the CASSCF energy in the Molcas-4 program. We then have tested the internal stability of RHF wave functions by mixing the orbitals and allowing the restricted scheme to become unrestricted. As expected, while the RHF wave function of the phosphirane ring is stable under orbital

Ring-Chain Rearrangement in Phosphiranes

Figure 4. Shapes and occupation numbers of the HOMOs and LUMO of TS H1/H2 derived from CASSCF(10,10) computations.

mixture, that of the TS H1/H2 is not stable. Nevertheless, the UHF wave function of the closed-shell singlet state becomes severely contaminated (〈S2〉 larger than 1.0), indicating a strong mixture of the triplet state. The TS geometry has been optimized using the unrestricted density functional formalism, UB3LYP/6-31G(d,p), which also shows a large spin contamination, 〈S2〉 being 0.45. Although the latter is smaller than that in the UHF counterpart mentioned above, it is unusual for the DFT methods. On the other hand, a single-point UB3LYP calculation on the RB3LYP optimized geometry shows that the total energy is lowered by 1.5 kcal/mol. A full UB3LYP geometry optimization for the singlet TS H1/ H2 leads to an energy lowering of about 3 kcal/mol. We have also considered the triplet state of the TS H1/ H2. At the B3LYP/6-31G(d,p) level, we could not locate a triplet TS for ring opening with hydrogen migration. Actually, a triplet TS for ring opening without hydrogen migration does exist which actually lies 6 kcal/mol below the singlet TS H1/H2. It is obvious that the triplet state follows another reaction mechanism, and an intersystem crossing could be involved and needs to be considered in future studies. It appears that an energy lowering of, at most, 3 kcal/ mol is rather small in comparison with the expected error bars of (5 kcal/mol on energetic quantities obtained from the theoretical methods employed. Moreover, the cost for such an “improvement” is quite high in terms of the quality of the wave functions (severe spin contamination). It seems reasonable to admit that the wave function of the TS H1/H2 has some biradical character, but the contribution of the latter to the system’s total energy is rather small. From a technical point of view, the time ratio given in Table 2 indicates once more that the DFT/B3LYP is a quite efficient treatment. Overall, the energy barriers listed in Table 2 are in the same order of magnitude as the QCISD(T)/6-311G(d,p)+ZPE value of 56 kcal/mol obtained in the earlier study.3 It is expected that extension of the atomic basis functions tends to decrease

J. Org. Chem., Vol. 66, No. 17, 2001 5675

further the barrier, but not to a large extent, in such a way that it amounts in reality to around 45 kcal/mol, with an expected error of (5 kcal/mol. Although this is rather a rough estimate, it is in line with the view that the ringchain rearrangement of phosphirane is a rather difficult thermal process to achieve.2 It is of interest to compare the present mechanism with that of the ring-chain rearrangement of the analogous silirane (silacyclopropane). According to Skancke et al. and Sengupta and Nguyen,13 the latter ring prefers a downgrade migration mode giving rise to the ethyl silylene isomer, HSiCH2CH3, rather than to vinyl silane, H3SiHCdCH2, such as in the phosphirane case considered here. The energy barrier associated with the silirane-ethylsilylene rearrangement was computed to be about 24 kcal/mol using CASSCF(12,12)/CASPT2/6-31G(d,p) wave functions. This is also in line with experimental observations in the gaseous phase.14 Such a contrasting behavior in the opening of both three-membered cycles can be understood by the fact that the silylene is a stable singlet species, whereas the singlet phosphinidene counterpart, PCH2CH3, does not exist at all as a stationary point.3 It is known that alkyl phosphinidenes have a triplet electronic ground state.15,16 (C) Rearrangement with Hydrogen Migration in Halogeno-Phosphiranes. In this section, the results concerning the trans conformers of C-halogenated phosphiranes are presented. The reactivity of the cis counterparts is not considered. Figure 3 shows the shape of the TSs F1/F2, Cl1/Cl2, and Br1/Br2 corresponding to the ring opening of substituted X1 in which the hydrogen atom on C2, rather than the halogen X, actually migrates from C2 to P. In this context, the X atom plays the role of a substituent influencing the hydrogen migration. In the Supporting Information, the optimized MP2 and B3LYP parameters are compared in Table II, whereas the related total and zero point energies are recorded in Table III. During the course of the reaction, in all transition structures X1/X2, the c bonds and γ angles are increased, whereas the d2 bonds are decreased. The d1 and b bonds are not changed significantly or even slightly decreased, as in the case of F1/F2, as compared with the corresponding ones in the ring molecules. There exists a certain correlation between the broken c bond distances in TSs and the type of the halogen: the smaller the substituting atom, the shorter the c bond, in such a way that the c bond distance is smoothly increased in going from H1/H2 to Br1/Br2 (cf., values given in Table II, Supporting Information). Figure 5 displays the schematic potential energy profiles concerning the ring opening with H-migration in four phosphiranes, computed using B3LYP/6-31G(d,p) geometries and total and zero point energies. It is clear that the halogen atom consistently induces a stabilization of the vinylphosphine product X2, H2PCXdCH2, relative to phosphirane X1, and thereby the energy barrier decreases, even though the reduction is not large, amounting to, at most, 3 kcal/mol in the fluorine case. The fact (13) (a) Skancke, P. N.; Hrovat, D. A.; Borden, W. T. J. Am. Chem. Soc. 1997, 119, 8012. (b) Sengupta, D.; Nguyen, M. T. Mol. Phys. 1996, 89, 1567. (14) Dickinson, A. P.; O’Neal, H. E.; Ring, M. A. Organometallics 1991, 10, 3513. (15) Nguyen, M. T.; Van Keer, A.; Vanquickenborne, L. G. J. Org. Chem. 1996, 61, 7077. (16) Nguyen, M. T.; Van Keer, A.; Erkisson, L. A.; Vanquickenborne, L. G. Chem. Phys. Lett. 1996, 254, 307.

5676

J. Org. Chem., Vol. 66, No. 17, 2001

Figure 5. Schematic potential energy profiles showing the ring-chain rearrangement of X-phosphiranes with H-migration through TS X1/X2. Relative energies were obtained from B3LYP/6-31G(d,p)+ZPE computations.

Figure 6. Selected geometric parameters of the TS X1/X3. The F atom in F1/F3 needs to be replaced by Cl and Br to form Cl1/Cl3 and Br1/Br3, respectively.

that halogeno-vinylphosphines X2 become slightly more stable than X1 could be accounted for by the differences in energies of the CsX bonds that are bonded to a double CdC and single CsC bond, respectively. As shown in Scheme 1, a ring opening accompanied by a hydrogen migration from the carbon C1 atom is equally possible. The corresponding TSs X1/X3 with X ) F, Cl, and Br are shown in Figure 6 and their geometries listed in Table IV of the Supporting Information, whereas the schematic potential energy profiles are compared in Figure 7. It appears that each of the TSs X1/X3 lies lower in energy than the corresponding X1/ X2, even though the differences in their energies are rather small. Comparison of Figures 5 and 7 indicates that an interchange occurs in the ordering between the TSs of Cl and Br, but again, the energy difference involved is quite small to be really significant. In both cases, fluorine brings about the largest reduction of the barrier. The largest difference between H1/H2 and F1/ F2 amounts to 3.1 kcal/mol, and that between H1/H2 and F1/F3 to 7.2 kcal/mol. These data indicate that a halogen substitution induces a reduction of at most 3 kcal/mol on the energy barrier of the H(C2) migration and a somewhat larger reduction, up to 7 kcal/mol, on that of the H(C1) migration. An analysis of the electronic reorganization during the ringopening process3 suggested that the H atom migrates with an electron pair and could be regarded as a partial hydride H- anion, creating thus a positive carbon center.

Ma´trai et al.

Figure 7. Schematic potential energy profiles showing the ring-chain rearrangement of X-phosphiranes with H-migration through TS X1/X3. Relative energies were obtained from B3LYP/6-31G(d,p)+ZPE computations.

Figure 8. Selected geometric parameters of the TS X1/X4. The F atom in F1/F4 needs to be replaced by Cl and Br to form Cl1/Cl4 and Br1/Br4, respectively.

As a consequence, any effect which reinforces the positive C center is expected to favor the whole process. It is, however, interesting to note that the halogen creates a larger effect when it is a remote spectator exercising apparently a through-bond effect. Again, the halogensubstituted vinylphosphine products X3 have lower energy than the corresponding rings X1. Figures 5 and 7 also reveal an irregular trend with respect to the Hammond postulate. (D) Rearrangement with Halogen Migration in Halogeno-Phosphiranes. We now consider the last possibility of the reaction shown in Scheme 1, in that the ring opening is in concert with a migration of the halogen atom from C2 to P. The shape of the TS X1/X4 is illustrated in Figure 8, and the energy profiles are compared in Figure 9. The corresponding optimized MP2 and B3LYP geometries are listed in Table V of the Supporting Information. Except for the parameters related to the X atom, the TS X1/X4 is in general comparable to X1/X2. In each TS, the moving atom lies almost perpendicular to the C1-C2-P framework. One can in addition notice that, for the b, c, and d2 bonds as well as for the γ, δ, , and so forth angles, there are fewer differences between the X1/X4 than the X1/X2. As in the case of F1/F2, F1/F4 is also the most structurally similar to H1/H2. In a TS X1/X4, the distance d1 is more stretched and the distance d2 more compressed, as compared with those in X1/X2 and X1/X3. It follows that while, in X1/X2 and X1/X3, the migrating Hm is still

Ring-Chain Rearrangement in Phosphiranes

J. Org. Chem., Vol. 66, No. 17, 2001 5677 Table 3. Solvation Energies of the Phosphiranes and TSs using a PCM Method at the B3LYP/6-31G(d,p) Level and Gas Phase Geometries ∆G(solv) (kcal/mol)

Figure 9. Schematic potential energy profiles showing the ring-chain rearrangement of halogeno-phosphiranes with halogen-migration through TS X1/X4. Relative energies were obtained from B3LYP/6-31G(d,p)+ZPE computations.

bound to C2 and the Hm-P bond is not formed, in X1/ X4, the C-Xm bond still exists but the Xm-P bond is already significantly formed. In the latter, the migrating halogen seems to interact fully with the 2p orbitals of the C-P bond.17 We can note here much larger variations among the energetic values than in the two previous cases. It is clear from Figure 9 that the character of the migrating halogen has a determining effect on the energy barrier rather than the energy of the products. Fluorine induces thus the largest stabilization of the product X4, owing to the peculiar strength of the P-F bond,18-19 but it is also associated with the highest energy barrier for ring opening. It is not surprising that ring opening with a F-migration exhibits the highest energy barrier (72.7 kcal/mol, Figure 9), as it is well-known that F is a quite poor migrating atom. In contrast, the pure 1,3-chlorine migration is a rather facile process associated with a low free energy of activation of about 10-15 kcal/mol.20,21 Although the basis set employed here is of moderate quality, we do not think that its further extension could reverse the relative ordering of the related barriers. As mentioned previously, the experimental results by Tran Huy and Mathey4,5 show that, in the case of complexed chloro- or bromo-substituted phosphiranes, the product, in major part, is a vinyl-halogeno-phosphine X4. This means that the favored reaction is a ring opening with a halogen migration corresponding to the TS X1/X4 instead of a hydrogen migration. Obviously, our calculated energy barriers recorded in Figures 7 and 9 for uncomplexed molecules are at variance with these findings observed for the complexed systems. (E) Solvent Effect. In view of the inconsistency between the discussed calculated results that are mainly (17) Pachioni, G.; Bagus, P. S. Inorg. Chem. 1992, 31, 4391. (18) Nguyen, M. T.; Vansweevelt, H.; Vanquickenborne, L. G. Chem. Ber. 1992, 125, 923. (19) Fitzpatrick, N. J.; Brougham, D. F.; Groarke, P. J.; Nguyen, M. T. Chem. Ber. 1994, 127, 969. (20) Koch, R.; Wong, M. W.; Wentrup, C. J. Org. Chem. 1996, 61, 6809. (21) Nguyen, M. T.; Landuyt, L.; Nguyen, H. M. T. Eur. J. Org. Chem. 1999, 401.

structure

H2O

DMSO

H1 F1 Cl1 Br1 H1/H2 F1/F2 Cl1/Cl2 Br1/Br2 F1/F3 Cl1/Cl3 Br1/Br3 F1/F4 Cl1/Cl4 Br1/Br4

-1.42 -3.63 -2.28 -2.49 -5.67 -4.58 -3.07 -4.14 -5.54 -6.40 -1.10 -2.56 -1.52 -1.90

-1.50 -2.48 -1.77 -2.00 -3.25 -2.23 -0.89 -1.90 -2.73 -3.23 -0.74 -1.22 -0.58 -0.97

valid for reactions occurring in the gas phase and the experimental ones derived for processes in solution, we have attempted to evaluate the effect of the bulk solvent on the energy barriers by putting the whole supermolecule in a solvent continuum which is mainly characterized by its dielectric constant. We have first utilized the gas phase optimized geometries of the stationary points and then carried out their solvation energies using a polarized continuum model (PCM).9 The calculated solvation energies of different equilibrium and transition structures in both aqueous and DMSO solutions are summarized in Table 3. It turns out that the solvation energies are small and similar to each other in such a way that the overall changes in the energy barriers are small, amounting to at most 3 kcal/mol. More importantly perhaps, the relative position of the barriers through the TSs X1/X2, X1/X3, and X1/X4 remains almost unchanged, suggesting that, even in solution, the ring opening with hydrogen migration is still favored over that with halogen migration. Although a reoptimization of the geometries including the continuum effect might allow a more definitive conclusion to be drawn, we do not think that this could reverse the observations made above from simple PCM computations, because of the similarities of the electrostatic contributions to the solvation energies in both equilibrium and transition structures. It is known that the Coulomb interactions are the dominant terms in the PCM model. The fact that the solvent continuum is not a crucial effect changing the gas phase results suggests that the important role of the coordination sphere of metal fragments is likely to be responsible for a reserved migration ordering. It could be postulated that formation of a phosphirane-metal complex by addition of a phosphinidene-metal complex to a vinyl halide should be readily reversible (cf., eq 3). Such an equilibrium between two

metal complexes might be siphoned off by a slower but irreversible insertion of the phosphinidene complex into a carbon-halogen bond, giving rise to an apparent rearrangement as seen in eq 3. In other words, the reaction mechanism in uncomplexed systems studied in

5678

J. Org. Chem., Vol. 66, No. 17, 2001

this work differs fundamentally from the experimentally observed one in systems containing metal complexes. 4. Concluding Remarks The present theoretical paper presents a comparison of transition structures and energy barriers related to the three distinct modes of ring-chain rearrangement of halogenated phosphiranes. The most interesting chemical results emerging from this theoretical study are perhaps the findings that (i) the phosphirane-vinylphosphine rearrangement in substituted systems remains a one-step process in which the ring opening of phosphirane is in concert with a X-migration from C to P, (ii) in the unsubstituted parent system, the energy barrier amounts to about 45 ( 5 kcal/mol, (iii) the reaction mode involving a hydrogen migration is consistently favored over that implying a halogen migration, and (iv) the effect of the bulk solvent is small and does not modify the relative sequence of the computed energy barriers, namely H < Cl ) Br < F. These findings in free systems differ from those reported in recent experimental studies that show ring opening with halogen migration in metal-complexed phosphiranes. This difference indicates that the metal fragments, namely the W(CO)5, employed in the experi-

Ma´trai et al.

mental studies to stabilize the starting phosphinidenes, are likely to play a crucial role in inducing a different reaction mechanism and thereby favoring the migration of the halogen. A remarkable correlation between the calculated 31P NMR chemical shifts, using the GIAO/B3LYP/6-311+G(d,p), of X-phosphiranes and X-phosphines (X-CH2-PH2) suggests that the large β substituent effect is not inherent to the small rings.

Acknowledgment. This work was carried out in the framework of a Bilateral Cooperation Agreement between the governments of the Flemish Community of Belgium and Hungary (Project BIL-98/21). The Leuven group is indebted to the FWO-Vlaanderen and KULeuven Research Council. The Budapest group thanks the OTKA for financial support (Project TO34768). Supporting Information Available: Cartesian coordinates, Z-matrixes, and total energies for all structures considered at both MP2 and B3LYP levels (12 pages), together with detailed comparisons of the geometrical parameters and zero point energies (Tables I-V). This information is available free of charge via the Internet at http://pubs.acs.org. JO000493Q