J . Phys. Chem. 1993, 97, 12229-12231
Theoretical Studies of Nucleophilic Substitution at Phosphorus. 1. PH3 + H-
-
12229
H-
+ PH3
Steven M. Bachrach' and Debbie C. Mulhearn Department of Chemistry, Northern Illinois University, DeKalb, Illinois 601 I5 Received: August 13, 1993'
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The reaction of hydride with phosphine was examined a t the HF/6-311+G* and MP2/6-3 1 l+G** levels. The CZ, structure is a stable intermediate along the reaction path. Pseudorotation of this structure occurs through a C4" transition state with a barrier of 2.10 kcal mol-'. This study suggests that nucleophilic substitution reactions a t phosphorus follow an addition-elimination pathway.
Nucleophilic substitution at heteroatoms is an attractive synthetic option. Mechanistic studies of these reactions are few and much of our general understanding of nucleophilic substitution at heteroatoms is based on analogy to carbon chemistry. Beak has recently begun a series of examinations of heteroatom nucleophilic substitution reactions using the endocyclic restriction test to determine the geometric relationship between nucleophile, heteroatom, and leaving group.' In a recent communication, Li and Beak2 examined substitution at phosphorus. Contrary to many previous studiesS7 that claimed a classic sN2 mechanism, based principally on exclusive inversion product (see Scheme I), Li and Beak found that the substitution reaction in Scheme I1 occurs intramolecularly. For a classic sN2 mechanism to be occurring, which requires a near linear nucleophile-P-leaving group arrangement, an intermolecular process is required. Li and Beaksuggested an addition-elimination mechanism (Scheme 111) whereby a tetracoordinate intermediate is formed followed by pseudorotation to allow for an apical leaving group. In this paper, we report ab initio calculations of the simplest nucleophilic substitution at phosphorus: hydride addition to phosphine, reaction 1. Examination of the geometries, energies,
H-
+ PH,
-.
PH,
+ H-
(1)
and electron distributions fully support the conclusions of Li and Beak2-an intermediate four-coordinate anion does occur along the reaction pathway.
Computational Method The key test of this study is the structure and nature of PH4-. Toward this end, we completely optimized a number of conformations of this anion under the restriction of the appropriate point group symmetry. Since the structure and energy of anions are sensitive to basis set, we optimized all structures a t the H F / 6-311+G** level. This basis set is quite flexible, having polarization functions on all atoms and diffuse functions on phosphorus. The nature of all of the HF/6-31 l+G** structures were characterized using analytical frequencies. Ground states have only real frequencies while transition states have one imaginary frequency. Since electron correlation may also play a role in determining the relative energies of these structures, we also optimized these structures at MP2/6-31 l+G**. The geometries of these MP2 structures are drawn in Figure 1. The calculated energiesat both computational levels are listed in Table I. The zero-point vibrational energies a t HF/6-31 l+G**, reported in Table I, are scaled by 0.89. All calculations were performed using GAUSSIAN-90.8 We were unable to find the ion-dipole structure at the MP2 level. Repeated attempts to locate this structure resulted in the *Abstract published in Aduance ACS Abstracts. November 1, 1993.
0022-3654/93/2097- 12229$04.00/0
SCHEME I
.. P
BuLI -
P
..
SCHEME I1
SCHEME 111
(2%structure only. Therefore, the ion-dipole structure shown in Figure 1 is determined a t HF/6-311+G**. Integrated electron populations were obtained using the topological electron density method. Critical points were located using EXTREME and integrations evaluated using PROAIM.9
Results
-
Buhl and SchaeferIo recently examined nucleophilicsubstitution at nitrogen. For the reaction F- + NHzF FNH2 + F-, they found a Cb transition structure with the F-N-F angle nearly linear (162.6O a t TZ+P/CISD). This result suggests that nucleophilic substitution occurs in a classic sN2 fashion, i.e., backside attack of the nucleophile. Based on this work and the experimental studies of K ~ b a 3 -and ~ Mikolajczyk,6,7 we first optimized the Chstructure of PHd-, expecting to find the transition structure for reaction 1. Instead, the C , structure we found (see Figure 1) is a ground state, having only real vibrational frequencies. The MP2/6-311+G** Cb geometry is very similar to those reported11J2 earlier: the axial P-H bonds are much longer than the equatorial bonds. We next optimized the Ch structure and found it to have one imaginary frequency. This Chstructure is the transition structure for pseudorotation. The P-H bond length in the transition structure is intermediate that of the two different P-H bonds in the Cb ground state. The calculated barrier for pseudorotation in PH4- is 2.10 kcal mol-' a t MP2/6-311+G**, much less than the value of 9 kcal mol-' calculated by Trinquier et al." using an a b initio effective potential method. These authors note that another pseudorotation mode is possible where the lone pair leaves the equatorial position; however, we could not find a C I transition structure. Our PH4- pseudorotation barrier is quite similar to that calculated'' for PHs (2.0 kcal mol-' at CIPSI). The optimized D4h structure has relatively short P-H bonds of 1.4492 A. The D4hstructure lies 7.86 kcal mol-' above the cb 0 1993 American Chemical Society
12230 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
H , H ,
- P - H, - P - H,
Bachrach and Mulhearn
TABLE II: Integrated Charges symmetry atom Cb Hdr 164.4' 104.6'
Hqutori.~
C4,
1.6751
D4h
1.4798
Td C, ion-dipole
H H
H Ho~mplexd
H-1
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Hqutori.~
I
n
Hi- P - H1155.8'
3.0094
Td
C, ion dipole
Figure 1. Optimized MP2/6-31 l+G** geometries of PHd-. All angles are in angstromsand all angles are in degrees. The C, ion-dipolestructure
was optimized at HF/6-31 l+G**.
TABLE I: Energies of PHI- Isomers HF/6-311+GSS
sym
E' -342.954 C4, -342.946 041 -342.933 C3" -342.898 Td -342.876 C, (ion-dipole) -342.960 CJ ('W -342.954 PH3 H-342.994
Cb
+
386 492 949 330 019 199 384 663
Emib 0.00 4.95 12.82 35.18 49.18 -3.65 0.002 6.31
ZPEC 15.21 (0) 16.31 (1) 17.32 (1) 12.73 (2) 16.80 (0) 15.34 (0) 15.10 (1)
MP2/6-31 l+G**
E' -343.246 -343.242 -343.233 -343.197 -343.173
Erelb
137 791 606 797 584
0.00 2.10 7.86 30.33 45.53
-343.220 340 16.19
Total energy in au. Relative energy in kcal mol-'. Zero-point vibrational energy in kcal mol-] scaled by0.89. The number of imaginary frequencies is listed in paranthesis. structure. In the D4h structure, the lone pair is placed into a p orbital, which accounts for its higher energy. This structure is a transition state for inversion a t phosphorus, connecting mirror images of the ground-state CZ, structure. The C3,form of PH4-places the lone pair into the axial position. As expected, this is quite unfavorable: it lies 30.33 kcal mol-' above the CZ, structure and it has two imaginary vibrational frequencies. We also optimized a Td form of PH4- to confirm the results of Ortiz.I2 Our Td structure has slightly longer P-H bonds that Ortiz found. We also find that this structure is a local minimum, having only real vibrational frequencies. The Td structure lies 45.5 kcal mol-' above the ground-state CZ, structure. Gas-phase studies of substitution reactions indicate that an intermediate ion-dipole complex between the substrate and the nucleophile is formed prior to reaction.13-Is Theoretical studies of substitution reactions have confirmed the ion-dipole intermediate.I0JsJ6 We were able to locate an ion-dipole intermediate at the HF level. The complex has C, symmetry with a very long P-H distance of 3.0094 A. The ion-dipole intermediate is 3.65 kcal mol-' more stable than the CZ, PH4- structure and is 6.31 kcal mol-' lower in energy than isolated reactants. The reaction path connecting the ion-dipole to the CZ, structure requires shrinking the long P-H distance, forming this bond, and
net charge -0.66 -0.68 4.70 -0.69 -0.90 -0.92 -0.67 -0.64
lengthening the P-H distance, forming the second axial P-H bond. The transition structure for this reaction lies 0.002 kcal mol-' above the CZ,structure and is geometrically nearly identical to the Ca structure, having however only C, symmetry. Using the MP2/6-3 11+G** method, we could not locate an ion-dipolecomplex. Repeated attempts to optimize this structure (with C,, C3,, CZ,, and CIsymmetry) yielded the CZ,structure only. While we cannot rule out the existence of the ion-dipole complex, the CZ,structure is certainly stabilized by the inclusion of electron correlation energy. This is also seen in the enhanced stability of the CZ,structure relative to reactants at MP2(-16.19 kcal mol-') compared to at HF (-6.31 kcal mol-'). Using the topological method of Bader,17 we have determined the integrated net charge on hydrogen in the PH4 anions. The net charge on hydrogen in PH3 is -0.62. In the ion-dipole complex, the complexed hydrogen has transferred only 0.08 electrons to phosphine. The Ca,C, and 0 4 1 structures have nearly identical electron distributions: the hydrogens bear a charge of about -0.65. Therefore, charge is transferred from the incoming hydride to phosphorus in forming PH4-. Interestingly, the charge on the hydrogens in the T4d structure is very large. Each hydrogen has an integrated net charge of -0.90.
Discussion Unlike substitution a t nitrogen, where Biihl and Schaefer'o found classic S N backside ~ attack, the attack of hydride to phosphine does not occur via a linear attack. Optimization of the structure starting with the backside attack geometry leads to the C, structure which isa local minimum. Pseudorotation can occur through a C, structure with a barrier of only 2.10 kcal mol-'. The CZ,structure can invert through a D4h transition structure with a barrier of 7.86 kcal mol-'. The calculations are in agreement with the endocyclic restriction studies of Li and Beak.* Since the reaction given in Scheme I1 proceeds intramolecularly, the angle formed by the nucleophile, the phosphorus atom, and the leaving group cannot be 180O. Our calculations suggest that a four-coordinate intermediate is f o r m 4 by addition of the nucleophile. The orientation of the nucleophile, central P atom, and leaving group can then be around 90°, which can readily be accommodated in a cyclic transition state, as required by theendocyclic test. The intermediatecan thenquickly pseudorotate, since the calculated barrier is low, positioning the leaving group into the axial position for the final elimination. Our studies, therefore, completely corroborate Scheme 111, as proposed byLi and Beak. Unfortunately, we cannot adequately determine the status of an ion-dipole intermediate. This ion-dipole is located on the HF/6-311+G** surface and it lies 3.65 kcal mol-' below the tetracoordinate intermediate. However, all attempts to locate the ion-dipole structure a t MP2 resulted in the CZ, structure. This is probably an artifact of the computational method. Nevertheless, whether the ion-dipole is present or not on the surface in no way affects the conclusions concerning the substitution mechanism. Examination of the electron distribution during the reaction is consistent with the addition-elimination mechanism. Charge is transferred from the nucleophile (hydride) to the phosphorus
Nucleophilic Substitution at Phosphorus atom. Pseudorotation is accomplished with very little electronic reorganization. The Td isomer has an unusual charge distribution. The hydrogens carry nearly a full negative charge each. Electrons are distributed towards the periphery of the molecule. Oritz12 has suggested that PH4- may be a double Rydberg species, and the electron distribution at the periphery is consistent with this explanation.
References and Notes
Conclusion
Foresman, J. B.; Schlegel, H. B.; Raghavachari, K.; Robb, M.; Binkley, J. S.; Gonzalez, C.; DeFrees, D. J.; Fox, D.; Whiteside, R. A,; Seeger, R.; Melius, C.F.;Baker, J.;Martin,R.L.;Kahn,L.R.;Stewart,J. J.P.;Topiol,S.;Pople, J. A. Gaussian, Inc.: Pittsburgh, PA, 1990. (9) Biegler-Konig, F. W.; Bader, R. F. W.; Tang, T. H. J. Comput. Chem. 1982,3, 317-328. (10) Biihl, M.; Schaefer, H. F., I11 J. Am. Chem. Soc. 1993, 115, 364-
Substitution reactions at phosphorus do not proceed through a classic Sp~2mechanism of backside attack. Rather, the mechanism appears to be addition+limination, with a stable tetracoordinate intermediate. For the prototype reaction explored in this paper, PHI H-, the intermediate has Cb symmetry and undergoes pseudorotation through a Ch transition structure that lies only 2.10 kcal mol-' above the ground structure. These results are in complete agreement with the recent experimental work of Li and Beak.2 Further theoretical studies of substitution reactions at phosphorus are underway.
+
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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12231
Acknowledgment is made to the National Science Foundation and the donors of the Petroleum Research Fund, administered by the American Chemical Society, for support of this research. D.C.M. is a recipient of a Graduate Assistance in Area of National Need fellowship from a US. Department of Education grant.
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