J . Phys. Chem. 1989, 93, 7780-7784
7780
LUMO's do not show any specific variations. The most available LUMO is that of CF,C=CH.
calculation are given in Table VII. Isodesmic reaction energies, A E , at these levels for reactions 1-21 are given in Table VIII.
Appendix The total energies of the fluoroallenes and fluoroacetylenes at the DZ+D,/SCF, DZ+D,/MP-2, and DZ+P/SCF levels of
Registry No. CH,==C==€H, 463-49-0; CH,=C=CHF, 5 1584-22-6; CHF=C=CHF, 5 1584-23-7; CHZ=C=CFz, 430-64-8; CHF=C=CF, 51 584-24-8; CF,=C=CF~, 461-68-7; CH,C=CH, 74-99-7; CH,C=CF. 32039-23-9; CF3C=CH, 661-54-1; CF,C=CF, 20174-1 1-2.
Theoretical Studies of Phosphfrane and Phosphetane Steven M. Bachrach Department of Chemistry, Northern Illinois University, DeKalb, Illinois 601 IS (Received: February 6 , 1989; In Final Form: May 9, 1989)
The optimized structures of phosphirane and phosphetane, obtained by using the 3-21G, 3-21G(*), and 6-31G* basis sets, are reported at the HF-SCF level. The lowest energy isomer of phosphetane is puckered and has the P-H bond axial. The ring strain energies are estimated as 20.1 kcal mol-' in phosphirane and 17.9 kcal mol-' in phosphetane. The relatively small strain energies are explained in terms of geometrical parameters and surface delocalization of electron density. Topological electron density analysis of these compounds are also reported and compared with previous results. Inversion barriers are estimated for both molecules. The barrier heights (calculated at MP2/6-3lG*//HF/6-3lG* with ZPE(3-21G*)) are 68.28 kcal mol-' in phosphirane and 42.65 kcal mol-] in phosphetane. The ring flip barrier in phosphetane is calculated to be 2.45 kcal mol-'.
Small rings have fascinated chemists for a variety of reasons. Small rings possess strained bonds and angles that test the limits of structural stability and bonding theories.' While a great deal is known about the prototypical small rings cyclopropane (1) and cyclobutane (2), the effects of phosphorus substitution into these rings have only recently been investigated.2 The ability to synthesize small rings containing phosphorus is still limited, though growing2 We have recently begun a systematic investigation of organophosphorus compounds using theoretical technique^.^ In this study, we examine phosphirane (3) and phosphetane (4), the mono-phosphorus-substituted analogues of 1 and 2. Using ab initio methods and topological analysis, we will explore the effects of the phosphorus substitution on geometry, density distribution, ring strain, and inversion energy. Computational Methods All structures were fully optimized at the Hartree-Fock S C F level by using GAUSSIAN-86.4 Calculations were performed using the 3-21G, 3-21G(*) (d-functions added to P only), and 6-31G* . ~ topological analysis5 basis sets as supplied in G ~ u s s I ~ N - 8 6The was performed using a suite of programs developed by Bader. Critical points were located by using EXTREME.^ Vibrational frequency analysis was performed for all structures at the HF/3-21 C//H F/3-21 G and HF/3-21G( *)//HF/3-21G(*) levels. Frequency analyses using the 6-3 1G* basis set are too large for our computational resources. Our main interest in the frequency analysis is to identify a structure as either a local minimum (no imaginary frequencies) or a transition structure (one imaginary frequency). The nature of each structure examined here was (!) (a) Greenberg, A.; Liebman, J. F. Strained Organic Molecules: Academic Press: New York, 1978 and references therein. (b) Wiberg, K. Angew. Chem. Int. Ed. Engl. 1986 25, 312. (2) (a) Marinetti, A.; Mathey, F. Organometallics 1984, 3, 456. (b) Mathey, F.; Marinetti, A . Bull. SOC.Chim. Belg. 1984, 93, 533. (3) Bachrach, S. M. J . Comput. Chem. 1989, 10, 392. (4) Frisch, M.: Binkley, J . S.; Schlegel, H. B.; Raghavachari, K.; Martin, R.; Stewart, J. J . P.: Bobrowicz, F.; Defrees, D.; Seeger, R.: Whiteside, R.; Fox. D.; Fluder, E.: Pople, J. A. GAUSSIAN-86, Release C, Carnegie-Mellon University. ( 5 ) (a) Bader, R. F. W. Arc. Chem. Res. 1985, 18, 9. (b) Bader, R. F. W.: Nguyen-Dang, T. T.Adu. Quant. Chem. 1981, 1 4 , 63. (6) (a) Biegler-Konig, F. W.; Nguyen-Dang, T. T.; Tal, Y.; Bader, R. F. W.; Duke, A. J . J . Phys. E. 1981, 14, 2739. (b) Biegler-Konig, F. W.; Bader, R. F. W.; Tang, T. H . J . Compur. Chem. 1982,3,317. We thank Prof. Bader and P. MacDougall for the Vax copy of these programs.
0022-3654/89/2093-7780$01.50/0
determined by using the 3-21G and 3-21G* frequencies, and these gave identical results. For this reason, and the fact that the 3-21G(*) and 6-31G* optimized geometries are very similar (vide infra), we believe the frequency analysis at 3-31G(*) will differ only minimally from the 6-31G* analysis. Frequencies were scaled by 0.89 to obtain corrected zero point energies (ZPE). Two conformations of phosphirane were optimized. The first, 3a is the minimum energy structure having C, symmetry. The other conformer, 3b, has a planar P atom and is CZc.This conformer is the transition structure for P inversion. Drawings of 3a and 3b are presented in Figure 1. Four conformations of phosphetane were optimized. The lowest energy structure, 4a, has the P-H bond in the axial position while structure 4b has the P-H bond in the equatorial position. Two distinct processes interconvert 4a and 4b, namely ring flip and P inversion. To locate the transition structure for the ring flip process, we first located the local minimum energy structure of phosphetane, restricting the four-membered ring to planarity. Starting with this structure, we then optimized the geometry (OPT=TS) allowing for a puckered ring. The final geometry, 4c, was confirmed to be a transition structure since one and only one imaginary frequency was found at both the 3-21G and 321G(*) levels. Optimization of phosphetane with the restriction of a planar P atom led to a geometry having a nearly planar ring as well. We then reoptimized the geometry under C,, symmetry, leading to structure 4d, the transition structure for P inversion. 4d has one imaginary frequency at the 3-21G and 3-21G(*) levels. Drawings of 4a-d are given in Figure 1. The topological method, developed by Bader and co-w~rkers,~ examines the total electron density distribution p(r), its gradient Vp(r), and Laplacian V2p(r) fields. Points where the gradient vanishes, Le., Vp(r) = 0, are called critical points and designated r,.' The ratio of positive to negative eigenvalues of the Hessian matrix evaluated at the critical points distinguishes types of critical points. Of interest for this work are bond and ring critical points. A bond critical point is a local density maximum in two orthogonal directions and a local minimum in the third. Bond points are found in the common surface that separates two neighboring atoms. A ring critical point is a local minimum in two directions and a maximum in the third. The presence of a ring critical point _
_
_
~
(7) Bader, R F W ,Anderson, S G ; Duke, A J J Am Chem Soc 1979, 101, 1389
0 1989 American Chemical Society
Theoretical Studies of Phosphirane and Phosphetane
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 7781 TABLE I: Geometrical Parameters of Phosphirane 3' 3-21Gb
C-P-C
526"
r(P-C) r(C-C) r(P-H) r(C-H,) r(C-H,) fC-P-C fP-C-C fH-P-C fC-C-H, fC-C-H,
3b
3a n
6=
1.9281 1.4932 1.4283 1.0716 1.0721 45.56 67.22 96.22 117.99 117.70
3-21G(*)b 4-31G(*)' 1.8419 1.5166 1.4029 1.0731 1.0740 48.62 65.69 97.01 117.24 117.00
1.844 1.504 1.407 48.1 66.0 96.47 117.5 117.86
6-31G*"
exW
1.8526 1.4920 1.4043 1.0754 1.0765 47.49 66.25 97.15 117.88 117.61
1.867 1.502 1.428 1.092 1.093 47.4 66.3 95.2 118.0 117.5
151 8
'All distances are in angstroms and all angles are in degrees. bThis work. cSee ref 8a. "See ref 8b and this work. CSeeref 7. 1,406
TABLE 11: Geometrical Parameters of Phosphetane 4a and 4b' 4a 4b r(P-C) r(C-C) r(P-H) fC-P-c f P-c-c f
c-c-c
f H-P-Xb
f6= c-P-c 100.8
58
Figure 1. Optimized structures of 3-5 at generally indicates the presence of a chemical ring. Gradient paths trace out paths of steepest ascent through the density by following Vp(r). Two gradient paths originate at bond critical points and trace out the maximum density path to each neighboring atom. The union of these two paths is called the bond path.* The network of all bond paths generally is in a 1:l correspondence with chemical bond networks commonly drawn. There is some evidence that suggests very large basis sets (particularly including two sets of polarization functions) are required for accurate electron density a n a l y ~ i s . We ~ report here topological results using the 6-31G* basis set for a number of reasons. First, optimizations of these molecules, particularly phosphetane, with very large basis sets are extremely time consuming and beyond our computational capacity. More importantly, we have found that the 6-31G* basis set gives similar topological results to those evaluated using significantly larger basis sets and wish to compare the results of 3 and 4 with our earlier data.
Structures The structure of phosphirane (3) has been determined experimentally by microwave spectroscopy.I0 The reported parameters are listed in Table I. A number of theoretical calculations on 3a have also been reported." Gonbeau and Pfister-Guillouzo"a (8) Runtz, G. R.; Bader, R. F. W.; Messer, R. R. Can. J . Chem. 1977,55, 304Q. (9) (a) Boatz, J. A.; Gordon, M. S.J . Phys. Chem. 1988, 92, 3037. (b) Cremer, D.; Gauss, J.; Cremer, E. J . Mol. Sfruct. (THEOCHEM)1988, 169, 531. (10) Bowers, M.; Beaudet, R. A.; Goldwhite, H.; Tang, R. J . Am. Chem. Soc. 1969, 91, 17. ( 1 1 ) (a) Gonbeau. D.; Pfister-Guillouzo, G. Inorg. Chem. 1987, 26, 1799. (b) Dobbs. K. D.: Bongs. J. E.: Barron. A. R.; Cowlev. A. H. J . Phvs. Chem. 1988, 92, 4886. (c) &iter, R.; Schafer, W.; Baudlei, M. J . Am. Chem. Soc. 19%5,107.8043. (d) Absar, I.; Schaad, L. J.; Van Wazer, J. R. Theor. Chim. Acta 1973, 29, 173.
3-21G
3-21G(*)
6-31G*
3-21G
3-21G(*)
6-31G*
1.9380 1.5618 1.4312 14.53 91.46 91.42 97.55 156.96
1.8776 1.5665 1.4058 76.66 9 1.07 96.05 91.46 156.62
1.8801 1.5444 1.4079 75.72 90.88 96.68 98.01 155.63
1.9375 1.565 1 1.4285 75.31 91.15 98.27 101.06 155.47
1.8775 1.571 1 1.4039 77.52 90.47 96.86 102.29 154.68
1.8789 1.5474 1.4057 76.21 89.50 97.07 105.60 151.83
'All distances are in angstroms and all angles are in degrees. b X is the midpoint of the C2-C4 axis. 'Pucker angle; see Figure 1.
report the structure of 3a at the HF/4-31G(*) level. Dobbs, Boggs, Barron, and Cowleyllb optimized the structure of phosphirane at HF/6-31G*. Their results are reported in Table I along with our results using the three basis sets. As reported earlier, in order to obtain reasonable structures of organophosphorus compounds, polarization functions are required on both C and P.j A structural trend was found for the different basis set levels in the phosphines, phosphaalkenes, and phosphaalkynes. 3-21G predicts bond lengths that are too long; the addition of polarization functions to P results in overly contracted bond lengths. The 6-31G* basis set predicts structures in quite reasonable agreement with experiment. This same trend exists for the geometry of phosphirane predicted by using the three basis sets, though the differences in the geometries at 3-21G(*) and 6-31G* are very small. Polarization functions on P are critical in order to obtain accurate bond distances. The bond angles in 3a are rather insensitive to basis set, primarily due to the rigid nature of the three-membered ring. Nevertheless, bond angles are improved with larger basis sets. The structures obtained with the 3-21G(*) and 6-31G* basis sets are in excellent agreement with experiment. The P-C and C-C distances are within 0.018 A and the internal ring angles are equivalent within experimental error. No previous studies of phosphetane have been reported in the literature, though theoretical studies of other heterosubstituted cyclobutanes have been p u b l i ~ h e d . ' ~Phosphetane .~~ can exist in two conformers having C, symmetry. These conformers have puckered rings and differ in whether the H bonded to P is endo (axial), 4a, or exo (equatorial), 4b, to the ring (see Figure 1). Both structures were confirmed to be local minima at 3-21G and 321G( *) via analytical frequency analysis (no imaginary frequencies). We list in Table I1 the geometrical parameters of 4a and 4b for the optimized structure using the three basis sets. Again, there are only minor geometrical difference between the 3-21G(*) and 6-31G* optimized structures. Since the 6-31G* basis set has accurately described the geometries of a broad variety of organophosphorus c o m p o ~ n d s ,we ~ feel that the 6-3 1G* structure should agree with experiment within a few hundredths (12) Boatz, J. A,; Gordon, M. S.; Hilderbrandt, R. L. J . Am. Chem. SOC. 1988, 110,
352.
(13) (a) Skancke, P. N.; Fogarasi, G.; Boggs, J. E. J . Mol. Struct. 1980, 62, 259. (b) Catalan, J.; Mo, 0.;Yanez, M. J . Mol. Struct. 1978, 43, 251.
1782
The Journal of Physical Chemistry, Vol. 93, No. 23, I989
TABLE Ill: Energies (in hartrees) of 3 and 4 compd HF/3-21G
-417.163 247 -41 7.054 098 -455.993 490 -455.991 478 -455.991 441 -455.922 889
3a 3b 4a 4b 4c 4d
H F/3-2 1G ( *)
(0.0)
-41 7.268 6 18 (0.0) -41 7.149 128(74.98) -456.096 770 (0.0) -456.094 640 (1.34) -456.094 579 (1.37) -456.017 806 (49.55)
(68.49) (0.0) (1.26) (1.28) (44.30)
Bachrach H F/6-3 1G * 263 (0.0)
-419.328 -419.211 -458.367 -458.365 -458.364 -458.283
651 210 488 699 183
MP2/6-31G* -419.694484 -419.583 974 -458.860 841 -458.858 950 -458.856660 -458.791 754
(73.18) (0.0) (1.08) (1.58) (46.45)
(0.0) (69.35) (0.0) ( I . 19) (2.62) (43.35)
TABLE IV: Topological Parameters of 1-4 Calculated at HF/6-31G*//HF/6-31C* point 1
2 3a 4a
C-C ring C-C ring P-C C-C ring P-C C-C ring
p(r,)'
0.2490 0.2044 0.2483 0.0855 0.1415 0.2618 0,1274 0.1515 0.2468 0.0646
Values in au.
V*p(r,)' -0.5331 0.0661 -0.6352 0.3876 -0.0216 -0.6443 0.0878 -0.0518 -0.6350 0.2746
Distances in
c'
P
0.4897
1.4974
1.5069 0.63
0.0001
1.5452
1.5474 0.14
0.5743 0.2387
1.8526 1.4923
1.8755 1.24 1.4966 0.29
0.1067 0.0069
1.8801 1.5444
1.8860 0.31 1.5452 0.05
A. Defined as R
r,,,hb
RC
3a
e
= ((rpath/r)- 1 .O) X
100.
of an angstrom for any distance and within 1 ' for any angle. The lowest energy conformer has the H axial, which enables the P lone pair to spread out away from the ring. The equatorial isomer lies 1.08 kcal mol-' higher in energy at MP2/6-3lG*//HF/6-3lG* ZPE(3-21G*) (see Table 111) and is destabilized relative to the axial isomer due to P lone pair C(3)-H repulsion. These calculations are in marked contrast to previous studies of azetidine. Geometry optimization of the structure of azetidine identified only one minimum, the equatorial isomer.I3 Previous attempts by both Skancke et al.13aand Catalan et to locate the axial isomer of azetidine failed, though analytical gradient techniques were not employed. A gas-phase 'H N M R study indicates the presence of both azetidine isomers but conclusive demonstration of energy ordering of the isomers was not provided.I4 Microwave and electron diffraction experiments indicate the equatorial form of azetidine is about 2.5 kcal mol-' more stable than the axial i ~ o m e r . ' ~I n contrast, our calculations of phosphetane indicate that the axial and equatorial isomers are local minimum and close in energy, with the axial form slightly lower. As expected, the structure 4a is similar to cyclobutane,I6 azetidine,15 and ~ilacyclobutane.'~These molecules are puckered to nearly the same extent, 155.63' in 4a and 154' in 2, 146' in azetidine, and 146.4' in silacyclobutane. The internal angle at P is smaller than the angles at C, since bonds to P contain greater p-character. The angles at C are larger in 4a than in 2 (where they are 88.54'), due to the small angle at P, suggesting less strain in the former. The internal angle in silacyclobutane is 80.8' about Si, slightly larger than the angle about P in 4a.
+
Density Analysis Topological electron density analysis provides density distribution information without resorting to any particular set of molecular orbitals5 The method has been applied to a variety of chemical systemsi8and we have recently reported a topological (14) Friedman, B. R.; Chauvel, J. P., Jr.; True, N. S. J . Am. Chem. Soe. 1984, 106, 7638.
( I 5) Gunther, H.;Schrem, G.; Oberhammer, H. J . Mol. Speetrose. 1984, 104, 152. ( I 6 ) Takabayashi, F.; Kambara, H.; Kuchitsu, K. Presented at the Seventh
Austin Symposium, Austin, TX, 1978. (17) Mastryukov, V. S.; Dorofeeva, 0. V.; Vilkov, L. V.; Cyvin, B. N.; Cyvin, S. J. J . Sfruet. Chem. 1975, 116, 438. ( I 8) a) Bader, R. F. W.; Tang, T.-H.; Tal, Y.; Biegler-Konig, F. W. J. Am. Chem. SOC.1982, 104. 940,946. (b) Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. H. J . Am. Chem. SOC.1987, 109, 985, 1001. (c) Ritchie, J. P.; Bachrach, S. M .J . A m . Chem. SOC.1987, 109, 5909. (d) Knop, 0.;Boyd, R. J . ; Choi, S. C. J . A m . Chem. Soe. 1988, 110, 7299. (e) Bachrach, S. M.; Streitwieser. A.. Jr., J . Comput. Chem. 1989, IO. 514.
'f 4a
Figure 2. Bond path networks of 3a and 4a. Bond critical points are indicated by (*) and ring critical points are indicated with small untilled circles.
survey of 15 organophosphorus compound^.^ We can compare the topological density results for phosphirane and phosphetane with these standards along with the density analyses of 1 and 2. The topological electron density values for 1, 2, 3a, and 4a at HF/6-31G* are listed in Table IV. Plots of the bond path networks of 3a and 4a are shown in Figure 2. The value of p(r,) is an excellent indicator of bond order and bond length.3J8a*'8dTypical values of p(r,) (evaluated by using 6-3 1G* wave functions) in P-C single bonds range from 0.1504 to 0.1 569 e au13.3 The value of p(r,) in 4a is normal, while p(r,) in 3a is slightly smaller than this range. This is not reflected in the P-C distance in 3a, which is similar to typical P-C distances, but rather in the very long bond path (1.8755 A). The P-C bond path in 3a is 1.2% longer than the bond distance, the largest differences in any organophosphorus molecule reported, indicating the highly bent nature of the P-C bond. The bent bond path is seen in the bond path network of 3a in Figure 2. The C-C bond path is relatively unbent, being only 0.29% longer than the internuclear distance. For comparison, the C-C bond path in cyclopropane, which is clearly bent, is 0.63% longer than the C-C distance. The bond path lengths in the four-membered rings are very close to the internuclear separation. Ellipticity (e) measures the degree of noncylindrical density distribution at the bond critical point by taking the ratio of the eigenvalues of the Laplacian corresponding to the two directions perpendicular to the bond path.I9 The larger the ellipticity, the greater the concentration of density in one direction over the other. This has been identified with 7r-type bonding.I9 Cremer and Kraka*O have used ellipticity to argue for surface delocalization of electrons in three-membered rings. They argue (19) Bader, R. F. W.; Slee T. S.; Cremer, D.; Kraka, E. J . Am. Chem. SOC. 1983, 105, 5061. ( 2 0 ) Cremer, D.; Kraka, E. J . Am. Chem. Soe. 1985, 107. 3800.
Theoretical Studies of Phosphirane and Phosphetane that the large ellipticity at the C-C bond critical point in 1 indicates a concentration of density in the plane of the ring (surface delocalization). Density does not decrease dramatically near the center of the ring; the value of p at the ring critical point (p(r,) = 0.2044 e a ~ - is~ about ) 80% of the value at the C-C bond point (p(rb) = 0.2490 e a ~ - ~ Surface ). delocalization2’ was suggested as corroboration of o-aromaticity,22a proposal that claims aromatic-like properties for three-membered rings. Similar density features are found in 3a. The ellipticity at the P-C critical point is 0.574, comparable to ellipticities found in phosphaalkenes. The ellipticity at the C-C critical point is 0.239, somewhat diminished from its corresponding value in 1. The value of p at the ring critical point (0.1274 e a ~ - is~ 90% ) of the value at the P-C bond point (0.1415 e a ~ - and ~ ) 49% of the value at the C-C critical point (0.2618 e a ~ - ~ Density ). is spread over the ring in 3a, but not to the extent it is in 1, primarily due to the long P-C bond length. This long distance positions the C-C bond critical point far from the ring point, causing the larger decrease in density between the bond and ring points. The surface delocalization of density is not seen in the fourmembered rings. The ellipticities at the P-C and C-C bond points are 0.107 and 0.007, respectively. The value of the density at the ring point is 43% of the P-C value and only 26% of the C-C value. These results are similar to the values for 2 , where the ellipticity at the C-C bond point is 0.0 and p(r,) is only 34% that of p(rb).
Ring Strain Ring strain energy (RSE) results from the distortion of bond angles from typical values to the small angles required to close a ring. RSE is evaluated relative to some arbitrary reference which has no strain. This is accomplished usually by creating a balanced chemical equation in which products and reactants differ by the presence of a ring. Isodesmicz3and h o m ~ d e s m i creactions ~~ have been used to obtain RSE. We have chosen to use a variant of the homodesmic method that also conserves chemical groups as defined by B e n ~ o n . The ~ ~ reaction for defining strain energies in phosphorus substituted rings is given in eq I . Using this equation, our best estimate (HF/6-31G*//HF/6-31G* + ZPE(3-21G(*))) of RSE is 20.1 kcal mol-’ in phosphirane and 17.9 kcal mol-’ in phosphetane. (CH2),,-PH + 2CH3PH2 ( n - 2)CH3CH3 CH,PHCH, + 2CH3CH2PH2+ ( n - 3)CH3CH2CH3(1)
-
+
-
The RSE in 3 and 4 are considerably smaller than 1 (27.8 kcal mol-’) or 2 (26.8 kcal mol-’).26 E s t i m a t e ~ I ~of - ~RSE ’ in silacylopropane and silacylcobutane (43.4 kcal mol-l and 26.6 kcal mol-I, respectively) are also much higher than in the phosphorus analogues. The relatively small RSE in 3 is likely due to a combination of effects. The small angle about P allows for a wider angle about C in 3 than the 60’ in 1. This also reduces the degree of bending in the C-C bond path, creating a stronger C-C bond. While the degree of surface delocalization in 3 is less than in 1, density is spread over the face of the ring affording some energetic stabilization. The small RSE of 4 is due to the long bonds which allow for the angles about C to be only slightly diminished from their normal values. (21) Cremer, D.; Gauss, J. J . A m . Chem. SOC.1986, 108, 7467. (22) (a) Dewar, M . S. J. Bull. SOC.Chim. Belg. 1979.88.957. (b) Dewar, M . S. J J . Am. Chem. SOC.1984,106,669. (c) Cremer, D. Tetrahedron 1988, 44, 7427. (23) (a) Hehre, W. J.; Ditchfield, R.; Radom, L.; Pople, J. A. J . A m . Chem. SOC.1970,92,4796. (b) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A . Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (24) (a) George, P.; Trachtman, M.; Bock, C. W.; Brett, A. M . Tetrahedron 1976, 32, 317. (b) George, P.; Trachtman, M.; Brett, A. M.; Bock, C. W. J . Chem. Soc., Perkin Trans. 2 1977, 1036. (c) Dill, J . D.; Greenberg, A.; Liebman, J. F. J . A m . Chem. SOC1979, 101, 6814. (25) Benson, S.W. Thermochemical Kinetics; 2nd ed.;Wiley: New York, 1976. (26) Calculated by using eq 1 and experimental heats of formation from:
Pedly, J . B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds, 2nd ed.; Chapman and Hall: London, 1986. (27) Gordon, M . S. J . Am. Chem. SOC.1980, 102, 7419.
The Journal of Physical Chemistry, Vol. 93, No. 23, 1989 1783 Inversion Barrier The geometry about phosphorus is pyramidal and thus an inversion process interrelates the two possible isomers. This inversion barrier is well-known for nitrogen; the inversion barriers in dimethylamine,28 a ~ i r i n eand , ~ ~azetidine14 are 4.4, 17.23, and 17.9 kcal mol-’, respectively. We have performed calculations to estimate the inversion barriers in 3 and 4. In order to understand the barriers in the ring compounds, we first examined the inversion barrier of dimethylphosphine (5). This molecule contains two P-C bonds and a P-H bond about the inverting P atom, making it the appropriate acyclic analogue of 3 and 4. The inversion barrier was determined by optimizing the structure of dimethylphosphine in the planar arrangement 5b. This structure has one imaginary frequency at 3-21C(*). The energy difference between pyramidal 5 and 5b is 41.51 kcal mol-’ (HF/6-3lG*//HF/6-31G* + ZPE(3-21G(*)). This barrier is reduced to 38.25 kcal mol-’ at MP2/6-3 lG*//HF/6-31G* with ZPE corrections. For comparison, Yabushita and Gordon30 estimated the inversion barrier (MP3/6-31G*//3-21G*) of phosphine and methylphosphine as 35.6 and 36.5 kcal mol-’, respectively. The inversion barrier of phosphorus is much larger than for nitrogen. This large P inversion barrier has been argued in terms of the large p-character of the P-H bonds30 and the small HOMO-LUMO gap.,’ To obtain the inversion barrier in 3, the planar geometry 3b was optimized. Cowley and co-workers’lb reported that their attempts to optimize the geometry of 3b led to dissociation of the molecule into ethylene and PH. We had no such problems and report the structural parameters at 3-31G* in Figure I . Vibrational frequency analysis at 3-21G(*) revealed one imaginary frequency, indicating that the calculated structure is a transition state for the inversion process. The inversion barrier was calculated to be 72.1 1 kcal mol-’ at HF/6-31G*//HF/6-31G* + ZPE(321G(*)) and 68.28 kcal mo1-I at MP2/6-3lG*//HF/6-3lG* + ZPE(3-21 G( *)). This extremely large inversion barrier results for a number of reasons. The inversion barrier in three-membered rings is greater than acyclic compounds due to the geometric restrictions imposed by the ring. The H-P-C angle in the planar conformer is 153.64’, dramatically larger than the corresponding angle in 3a (97.15 ’ ) . The increased s-character in the bonding orbitals of P makes for shorter P-H and P-C bonds in 3b but the C-C distance is much shorter in 3a (1.4920 8, in 3a compared with 1.5800 8, in 3b). The unfavorable H-P-C angle and stretched C-C bond in 3b impose a severe energetic barrier toward planarity at P. In addition to the strains involved in planarization, the topological analysis suggests that there is a loss of stabilization energy associated with surface delocalization of electron density. Cremer20,2’has suggested that three-membered rings are stabilized by the delocalization of electrons in the ring, which requires that density does not decrease markedly between the bond critical point and the ring interior. In 3a, the value of the electron density at the ring critical point is 90% the value at the P-C bond critical point, while in 3b, the density at the ring critical point is 83% of the value at the P-C critical point. Evidently less density delocalization occurs in 3b than in 3a, leading to destabilization of the former. This is also seen by the direction of the “soft” eigenvalue of the Hessian matrix (the direction of less rapid density decrease). For 3a, where surface delocalization is present, the soft eigenvalue corresponds to the ring plane. In contrast, the soft eigenvalue at the P-C critical points of 3b points perpendicular to the ring plane. Finally, the P lone pair must reside in a pure p-orbital in 3b instead of an orbital containing significant s-character in 3a.32 This is reflected in the orbital energies of the HOMO, -0.3658 au in 3a and -0.2637 au in 3b, indicating a much higher HOMO (28) Wollrab, J. E.; Laurie, V. W. J . Chem. Phys. 1968, 48, 5058. (29) Carter, R. E.; Drakenberg, T.; Bergman, N.-A. J . A m . Chem. Soc. 1975, 97, 6990. (30) Yabushita, S.; Gordon, M . S . Chem. Phys. Lett. 1985, 117, 321. ( 3 1 ) Cherry, W.; Epiotis, N . J . A m . Chem. SOC.1976, 98, 1 1 3 5 .
7184
The Journal of Physical Chemistry, Vol. 93, No. 23, I989
TABLE V: Geometrical Parameters of 4c and 4d at HF/6-31G*//HF/6-31G*"
r(P-C) r(C-C) r(P-H) LC-P-C
4c
4d
1.8806 1.5518 1.4057 77.56
1.8365 1.5669 1.3800 84.23
LP-C-C LC-C-C LH-P-Xb L6C
4c
4d
91.57 98.76 102.25 172.22
86.07 103.63 180.0 180.0
'All distances are in angstroms and all angles are in degrees. b X denotes the midpoint of the C2-C4 axis. 'Pucker angle; see Figure I .
in the planar form and consequent destabilization. The inversion barrier of 3 is much larger than for the acyclic dimethyl phosphine, due to the dramatic strains placed on the planar conformer 3b as outlined above. The inversion barrier in 3 is also much larger than in azirane. This is expected since P is more pyramidal than N and significantly larger hybridization changes must occur during inversion at P than at N.32 Conversion of 4a to 4b can proceed by two possible pathways. The first involves ring flip. The second pathway is inversion at phosphorus. We have investigated the energetics of both paths. In order to locate the transition structure for the ring flip, we first located the minimum-energy structure of phosphetane restricted to a planar ring. Then, beginning with this structure, we optimized to the transition state, 4c. Geometrical parameters of 4c are listed in Table V. This structure was confirmed to be a transition state by frequency analysis at 3-21G and 3-21G(*). As anticipated via the Hammond postulate,33 the transition structure 4c is very productlike. The P-H bond in 4c is in the equatorial position and the ring is only 10.4' less puckered than in 4b. The barrier for the ring flip is 1.41 kcal mol-' at HF/631G*//HF/6-31G* ZPE, and is increased to 2.45 kcal mol-' at MP2/6-31G*//HF/6-31G* + ZPE. This barrier in not much larger than the ring flip barrier in cyclobutane (found experimentally34to be approximately 1.4 kcal mol-'). For a comparison of the adequacy of the computational model, creme^--'^ reported the ring flip barrier of 0.90 kcal mol-' for cyclobutane at HF/ 6-3lG'. The transition state for phosphorus inversion was obtained by first locating the minimum-energy structure with the restriction
+
(32) Kutzelnigg, W . Angew. Chem. Int. Ed. Engl. 1984, 23, 272. ( 3 3 ) Hammond. S. Sor. 77. 334. ~ ~ G . - .~ - J ... A m.. Chem. . . . ~1955. . (34) (a) Ueda, T.; Shimanouchi, T. J . Chem-Phys.' 1968, 49, 470. (b) Stone, J . M. R.; Mills, 1. M. Mol. Phys. 1970, 18, 631. (c) Miller, F. A,; Capwell, R. J . Spectrochim. Acta A 1971, 27a, 947. (35) Cremer, D. J . Am. Chem. SOC.1977, 99, 1307. \..,
~
_
l
~
~
Bachrach of a planar P atom. We then optimized the geometry under C,, symmetry to give 4d, which was confirmed to be a transition structure via frequency analysis. Geometrical parameters of 4d are listed in Table V. All bonds to P in 4d are shorter than the corresponding bonds in 4a or 4b, consistent with the planar P atom having more s-character in its bonds than in the pyramidal
structure^.^^ The phosphorus inversion barrier in 4 is 45.75 kcal mol-' at HF/6-31G*//HF/6-31G* ZPE. At MP2/6-31G*//HF/631G* ZPE, the barrier is 42.65 kcal mol-'. This inversion is significantly smaller than the inversion process in 3, since the larger ring can more readily accept the wider angles at P. The inversion barrier of 4 is similar to the inversion barrier in dimethylphosphine (5). Apparently, the geometric restrictions of a four-membered ring impose little additional strains to those associated with inversion at P. This is different from the nitrogen analogue where the inversion barrier in azetidine is 13.5 kcal mol-' larger then the barrier in dimethylamine.
+
+
Conclusion Optimization of phosphirane and phosphetane require basis sets containing polarization functions on P only. The differences between the optimized geometries at 3-21G(*) and 6-31G' are quite minor. Small rings containing phosphorus are less strained than their hydrocarbon analogues. The ring strain in phosphirane and phosphetane is estimated as 20.1 and 17.9 kcal mol-', respectively. Topological analysis of phosphirane indicates that a nearly unbent C-C bond and significant surface delocalization of electron density contribute to the low ring strain. The inversion barrier at phosphorus is much larger than for nitrogen, consistent with the greater degree of p-character in bonds to P than to N. While the inversion barrier in phosphirane (68.28 kcal mol-') is much larger than the barrier in dimethylphosphine (38.25 kcal mol-'), the inversion barriers for phosphetane (42.65 kcal mol-') and dimethylphosphine are similar. The ring flip barrier in phosphetane is calculated to be 2.45 kcal mol-'. All barrier heights calculated here are relatively unchanged by inclusion of correlation through MP2.
Acknowledpment. Acknowledgment for their sumort of this research is maude to the donors of :he Petroleum Research Fund, administered by the American Chemical Society, and to the Northern Illinois University Graduate School for a Research and Artistry Grant. Registry No. 3, 6569-82-0; 4, 287-26-3.
