6194
J. Phys. Chem. 1996, 100, 6194-6198
Toward a Planar σ3-Phosphorus La´ szlo´ Nyula´ szi Department of Inorganic Chemistry, Technical UniVersity of Budapest, H-1521 Budapest, Hungary ReceiVed: September 20, 1995; In Final Form: NoVember 29, 1995X
Correlated ab initio calculations show that the near 20 kcal/mol inversion barrier about phosphorus in phosphole can be reduced to 4.0 kcal/mol (CCSD(T)/6-311G(2D)//MP2/6-311G(2D)) by incorporating two σ2,λ3phosphorus atoms into the five-membered ring, which decrease the ring strain. If the σ2,λ3-phosphorus atom is situated in R-position from the σ3-phosphorus atom, the planar structure is more stable with respect to the minimum energy structure than with a β-positioned σ2,λ3-phosphorus atom. The planar structures obtained show significant bond length equalization, characteristic for aromatic compounds. For systems having low inversion barrier, the bond length equalization is still significant for the nonplanar structures, which are minima on the potential energy surface. The nonbonding orbital of phosphorus in these cases is mixed considerably with the π-system. The bond lengths tend toward equalization. These facts indicate that aromatic stabilization has a considerable impact on these nonplanar molecules and is presumably influencing their chemical reactivity as well.
Introduction Phosphole, the heavy-atom-containing analogue of pyrrole is known to be a nonplanar, nonaromatic molecule.1 This behavior is due to the nonplanarity of phosphorus, a fact that is often described as a “consequence” of the inert pair effect.2 It has recently been shown that planarized phosphole would be aromatic.3,4 Furthermore, several substituent groups have been shown to reduce the inversion barrier about phosphorus in phospholes.3 Only the planar structure is considered to benefit from cyclic conjugation. Thus, the reduction of the inversion barrier about phosphorus in phospholes (with respect to phospholenes) is thought to be the consequence of aromaticity.1-6 To planarize phosphole, not only the inversion barrier about phosphorus should be circumvented but also the increase of the ring strain by opening the CPC angle should be taken into account. In a five-membered ring the carbon atoms already suffer from ring strain even with nonplanar phosphorus.7 If phosphorus is planarized (to the sp2 hybrid state) its bonding angles tend to increase from the usual near 90° 8 toward 120°, resulting in further strain. Therefore, replacement of the carbon atoms in the ring with atoms having a smaller bonding angle can release this increased strain resulting in a decrease of the inversion barrier about phosphorus. We showed that the replacement of carbon by phosphorus in aromatic systems results in little change in the conjugative properties.9 In a recent work it has indeed been shown that incorporation of phosphorus to the thiophene or selenophene rings forming thia- and selenaphospholes results in some increase of the aromatic stabilization.10 The aim of the present work was the investigation of the inversion barrier and the aromatization of phospholes containing (apart from the σ3-phosphorus) one and two σ2,λ3-phosphorus atoms. Among these compounds only 1,3-diphosphole had previously been investigated by theoretical means using the semiempirical MNDO method.11 Although complexes as well as anionic salts of triphospholes were investigated experimentally in detail,12 the first example of substituted 1,2,4-triphospholes has been reported only recently.13 The synthesis of a substituted pentaphosphole, however, was reported to be unsucX
Abstract published in AdVance ACS Abstracts, March 1, 1996.
0022-3654/96/20100-6194$12.00/0
cessful.14 Thus, in the present work, ring systems with a maximum of three phosphorus atoms will be considered. Calculations Ab initio calculations were carried out by the GAUSSIAN 92 suite of program,15 at the HF/6-31G* and MP2/6-31G* levels of theory. In a previous work on phosphole3 it was shown that the MP2/6-31G* level gives a rather accurate description (compared to higher correlated levels and experimental results) of the inversion barrier and the aromaticity effects in the case of phosphole. The barrier of inversion about phosphorus was slightly underestimated3 (by about 2-3 kcal/mol) (overestimating the stability of the planar, aromatic structure). At the HF/ 6-31G* level, however, the inversion barrier was overestimated by as much as 5-6 kcal/mol. Therefore, the present discussion will be based on the MP2/6-31G* results, and the differences with the noncorrelated results will be pointed out. The structures were optimized both fully, and with planarity constraint about phosphorus and the ring, and second derivatives were calculated on the resulting structures. The fully optimized structures were real minima, while the planar structures were first-order saddle points with respect to the out-of-plane bending about phosphorus, as concluded from the single imaginary harmonic frequency calculated. For the structures with the lowest inversion barriers, further calculations were made with increased basis set (6-311G(2d)) to estimate the effect of the increse of the basis set on the inversion barrier. Second derivatives, however, were not calculated at these structures, since the changes in the optimized geometries were only minor. For these optimized structures CCSD(T)/6-311G(2d)//MP2/6-311G(2d) calculations were carried out as well, to obtain improved barrier heights. Results and Discussion The calculated total energies, inversion barriers (∆E) and optimized MP2/6-31G* structural parameters for the investigated phospholes are shown in Table 1. Comparing the total energies for the rings with the σ2,λ3-phosphorus in the R- and the β-positions (with respect to the σ3-phosphorus atom), the R-substituted ring is more stable. From the comparison of the total energies of 1,2,4- and 1,3,4-triphospholes, the former © 1996 American Chemical Society
Toward a Planar σ3-Phosphorus
J. Phys. Chem., Vol. 100, No. 15, 1996 6195
TABLE 1: Some Structural and Energetic Parameters for the Investigated Compounds at the MP2/6-31G* Level of Theory P c d e
P
P P P
P
P
P
P P
P
P P
P
P
b
α
P
a
-Etot ab bb cb db eb Rc ∆Ed
plan. a
∑3e ∑5e
P
P
nonpl.
495.69940 1.715 1.800 1.397 1.362 1.412 1.456 1.397 1.362 1.715 1.800 99.3 90.82 17.19 (26.46) 190 203 346 264
plan.
nonpl.
797.96826 2.081 2.161 1.754 1.720 1.401 1.429 1.397 1.371 1.715 1.776 103.1 94.2 8.17 (3.82) 188 206 337 267
plan.
nonpl.
797.95546 1.700 1.783 1.746 1.706 1.760 1.801 1.391 1.362 1.710 1.786 104.5 95.4 10.56 (18.62) 184 199 351 280
plan.
nonpl.
1100.23797f 2.079 1.754 1.394 1.754 2.079 111.0 2.69 (4.81) 196 340
2.122 1.736 1.408 1.736 2.122 106.0 193 277
plan.
nonpl.
1100.21724 1.695 1.755 1.744 1.714 2.130 2.171 1.744 1.714 1.695 1.755 109.2 100.9 4.35 (9.54) 161 164 339 278
plan.
nonpl.
1100.23413 1.715 1.766 1.389 1.369 1.754 1.783 2.129 2.090 2.065 2.135 110.5 102.5 4.43 (10.55) 166 188 326 271
plan.
nonpl.
1100.22331g 2.073 2.133 1.748 1.722 1.746 1.772 1.741 1.715 1.706 1.753 110.1 102.9 3.79 (8.09) 185 199 344 291
a Total energy for the nonplanar structure in au. b Bond length as indicated at the top of the table. c Bonding angle in degrees as indicated at the top of the table. d MP2/6-31G*+ZPE inversion barrier in kcal/mol, HF/6-31G*+ZPE barriers in parentheses. e The sum of the double bond characters for b, c and d (∑3) and for all the five bonds (∑5). f MP2/-311G(2D) and CCSD(T)/6-311G(2D)//MP2/6-311G(2D) total energies are 1100.351 52 and 1100.424 06 au, respectively. g MP2/6-311G(2D) and CCSD(T)/6-311G(2D)//MP2/6-311G(2D) total energies are 1100.337 26 and 1100.409 93 au, respectively.
TABLE 2: MP2/6-31G* Bond Lengths (Å) between Heavy Atoms (Obtained for the Simplest Hydrogenated Derivatives Containing the Respective Bond) CH3-CH3 CH2dCH2 PH2-CH3 PHdCH2 H2CdPHdCH2 HPdPH H2P-PH2 HPdPHdPH
1.524 1.334 1.857 1.675 1.653 2.039 2.183 2.053
compound is more stable. This is in agreement with the fact that in the synthesis of an alkylated triphosphole from the corresponding triphospholide anion only the 1,2,4- but not the 1,3,4-triphosphole derivative has been reported.13 The inversion barriers show gradual decrease as the number of the σ2,λ3-phosphorus atoms increases in the ring in accordance with the expected release of the ring strain. Likewise the total energies, the ∆E values are smaller in case of the rings with the σ2,λ3- and σ3-phosphorus in the R-positions. Similarly to the case of phosphole itself,3 the barrier is larger at the HF than at the MP2 level (see Table 1; HF data are in parentheses). This finding can be substantiated by the fact that the equalization of the bond length was found to be significantly smaller at the HF than at the MP2 level, indicating that the aromatic character is considerably larger at the correlated level. Similarly, by calculating isodesmic reaction energies for five-membered heterocycles, the stabilization was always larger at the correlated level.16 At the MP2/6-311G(2D)//MP2/6-311G(2D)+ZPE level, the inversion barrier of 1,2,5- and 1,2,4-triphospholes decreases to 2.01 and 1.67 kcal/mol, respectively. At the CCSD(T)/6311G(2D)//MP2/6-311G(2D) level the corresponding inversion barriers were 3.70 and 4.35 kcal/mol, respectively. Similar behavior was observed in case of phosphole itself too, when using larger basis set and higher level of electron correlation.3 The equalization of the bond lengths indicate significant aromatic character in the planar forms for all diphospholes and triphospholes. For these structures the CC bond lengths are between 1.389 and 1.412 Å (cf. with the 1.396 Å value for benzene obtained at the same level of theory). The CP bonds exhibit values between 1.710 and 1.754 Å (cf. with the 1.739 Å in phosphinine,17 all calculated at the MP2/6-31G* level of theory). If the b and e bonds are considered in the planar 1,2diphosphole, for example, the difference in the bond length is only 0.039 Å, although b and e are double and single bonds,
respectively, according to the classical (1a) structure (with σ3,λ3phosphorus), used for the description for the five membered heterocycles. Therefore, similarly to the parent phosphole,3 in di- and triphospholes for the description of the planar forms significant weight should be devoted to the resonance structure with σ3,λ5-phosphorus atom (1b).
P
P
1a
1b
It has been shown before3 that the sum of the double bond characters18 of the b, c, and d bonds (∑3 in Table 1) is a measure of the a vs b structures. ∑3 values about 160 and below correspond to a structure with larger b than a character. From the data (shown in Table 1) it seems that with the σ2,λ3phosphorus in β-position (with respect to σ3-phosphorus) the b type structure has somewhat larger weight than with the σ2,λ3phosphorus in R-position. The changes, however, are small with the exception of 1,3,4- and 1,2,3-triphospholes. Summation of the double bond characters for all the five bonds (∑5) results in small changes. This behavior is in agreement with the known similarities of the CdC and the σ2,λ3-PdC bonds. Since this index is between 326 and 351 for the compounds investigated, the average double bond character (I), which was shown as a measure of aromaticity, is between 0.65 and 0.70 for the planar phospholes (cf. with the I ) 0.67 value for benzene,16 calculated a the same level of theory). From these facts it can be concluded that incorporation of a σ2,λ3-phosphorus decreases the inversion barrier but has, as expected, only a small effect on the aromatic character of the planar phosphole. From Table 1 it is clearly seen that with the increasing number of σ2,λ3-phosphorus atoms in the ring, the R angle is getting larger, in accordance with the preliminary expectations. (The corresponding values for planar and nonplanar phosphole were 99.3 and 90.8°, respectively.) Angle R is larger in case of the planar systems than in the nonplanar ones (cf. ref 3). The difference of this angle between the planar and nonplanar forms of triphospholes is only 4-5°. This value is much smaller than the near 9° change in the case of phosphole itself.3 With the decrease of the inversion barrier, the structural characteristics of the planar and nonplanar forms are approaching each other. For the nonplanar form of 1,2,5-triphosphole,
6196 J. Phys. Chem., Vol. 100, No. 15, 1996
Nyula´szi TABLE 3: Isodesmic Reaction Energies (kcal/mol) for the Planar and Nonplanar Forms of Phosphole and 1,2,5- and 1,2,4-Triphospholes 1 2 3
nonplanar
planar
0.43 17.60 17.41
16.98 32.23 29.46
reaction, called “semihomodesmic”.16 The corresponding reactions for phosphole and 1,2,4- and 1,2,5-triphospholes are (1)(3). The reactions can be written with both planar and nonplanar + PH3 + 2C
C
C
C
C
C + 2C
C
PH2
(1)
P + PH3 + 2C
P
P
C
C
P + 2C
P
PH2
(2)
+ PH3 + 2C
P
P
P
Figure 1. Shape of the highest occupied MO of 1,2,5-triphosphole at its MP2/6-31G* optimum geomerty as plotted by the MOLDEN program.19 Density contour is given at 0.1.
P
P P
P
P
Figure 2. Shape of the highest occupied MO of phosphole at its MP2/ 6-31G* optimum geomerty as plotted by the MOLDEN program.19 Density contour is given at 0.1.
which is a real minimum on the potential energy surface, the CC bond length (bond c in Table 1) is 1.408 Å. This value is closer to the 1.396 Å CC bond length of benzene than the 1.418 Å obtained for the corresponding bond in thiophene!16 The ∑5 value is smaller than for the planar system, resulting in an average double bond character of 0.55 for the nonplanar system. This value is the same as the one obtained in the case of furan.16 From this bond length equalization which is characteristic, although in a lesser extent, even in the nonplanar form, a considerable interaction can be concluded in this molecule between the phosphabutadienic π-system and the phosphorus lone pair. In the case of the nonplanar structure the substituting hydrogen is tilted away by 51.7° from the PPP plane, and thus the pz atomic orbitals are not coplanar. Similar out-of-plane angles (OOP) were obtained for the other triphospholes. The same bond angle, however, was much larger, 72.3°, for phosphole itself. In spite of the nonplanar arrangement, the interaction between the phosphorus lone pair and the dienic unit can be seen on the uppermost a′ MO of 1,2,5-triphosphole. This orbital is basically a phosphorus lone pair with significant MO coefficients at the pz orbitals of the carbon atoms as is shown in Figure 1. The corresponding orbital of phosphole is a nearly pure phosphorus lone pair orbital, almost in the plane of the molecule (Figure 2). The conjugative interaction should result in aromatic stabilization. A proper measure for this stabilization in the case of five-membered heteroaromatic systems was the isodesmic
C
P
C +C
P
PH2 + P
C
PH2
(3)
σ3,λ3-phosphorus atoms (see ref 3). The stabilization energies from these reactions are shown in Table 3. In the case of phosphole no stabilization was obtained for the nonplanar structure, in agreement with Gordon’s conclusions, obtained from a superhomodesmic reaction.20 Schleyer1e obtained a small stabilization (7 kcal/mol) from a different homodesmic reaction, which considered the effect of steric strain, but did not account for the stabilization of the butadienic unit. The stabilization obtained for 1,2,5- and 1,2,4-triphospholes amounts 17.60 and 17.41 kcal/mol, respectively, even for their nonplanar structure. This value is comparable to that obtained for furan (12.32 kcal/ mol). The stabilization in the case of the planar forms is larger than for the nonplanar structures. The effect of the σ2,λ3phosphorus atoms is to increase the isodesmic reaction energies.16 Since it has been shown before3 that by selecting proper substituents the inversion barrier about phosphorus can be significantly reduced, the effect of the BH2 group (shown to be the most efficient in this respect3), has been investigated in positions 1, 2, and 5, for 1,2,5- and 1,3,4-triphospholes. The methyl group in position 1 was considered as well in order to simulate the electronic effect of a bulky substituent (tert-butyl, adamantyl, trimethylsilylmethyl, or alkyl-aryl group) which can be beneficial in the planarization. The calculated structures and the inversion barriers are collected in Table 4. The inversion barriers of the 1-boro-substituted derivatives (Table 4) were decreased, in certain cases well below 1 kcal/mol, but complete planarization could not be achieved. In the case of 2,5-diboro-1,3,4-triphosphole, both the planar and the nonplanar structures were real minima at the HF/631G* leVel of theory. The nonplanar structure was the more stable one, with an energy difference of 2.14 kcal/mol. The planar structure can be characterized as b type, similar to the case of the parent 2,5-diborophosphole,3 while the nonplanar structure is of a type. At the MP2/6-31G* level of theory both planar and nonplanar forms have similar bond lengths, close to the b formula. The nonplanar structure was more stable by 0.77 kcal/mol (without ZPE correction). Second derivatives could not been calculated at the correlated level for this compound. However, since the structural characteristics for the planar and the nonplanar forms are close to each other and the nonplanar form is at lower energy, it seems that at the correlated level the only minimum is the nonplanar form. Calculating both
Toward a Planar σ3-Phosphorus
J. Phys. Chem., Vol. 100, No. 15, 1996 6197
TABLE 4: Some Structural and Energetic Parameters for Substituted Triphospholes at the MP2/6-31G* Level of Theory P P P c d e
b
α
P
P
P
P BH2
P
P P
P BH2
P Me
P P H2B
P Me
P H
P P P Me
BH2
a
plan.
-Etot ab bb cb Rc OOPd ∆Ee ∑3f ∑5f
a
nonpl.
1125.58985 2.111 2.119 1.737 1.734 1.409 1.410 107.6 106.8 31.9 0.40/0.15 193 196 293 284
plan.
nonpl.
1139.41633 2.080 2.107 1.755 1.744 1.393 1.402 110.2 107.1 40.6 1.61/1.63 181 188 325 294
plan.
nonpl.
1125.56875 1.729 1.735 1.729 1.718 2.165 2.165 104.5 103.9 27.6 0.22/0.51 165 164 305 298
plan.
nonpl.
1139.41099 1.695 1.714 1.746 1.722 2.129 2.160 108.6 102.1 51.9 3.59/4.85 158 164 336 292
plan.
nonpl.
1150.90238 1.696 1.716 1.755 1.762 2.114 2.126 112.0 108.8 36.3 -0.77g/2.14 160 144 336 298
plan.
nonpl.
1139.35530 2.078h 2.121h 1.751h 1.734h 1.746h 1.767h 109.3 104.1 180 336
2.77/4.89 189 296
a Total energy for the nonplanar structure in au. b Bond length as indicated at the top of the table. c Bonding angle in degrees as indicated at the top of the table. d OOP, the out-of-plane angle (in degrees) is defined as the angle of the phosphorus-substituent bond and the plane formed from σ3-phosphorus and the two neighboring ring atoms. e MP2/6-31G*+ZPE inversion barrier in kcal/mol, HF/6-31G*+ZPE barriers separated by slash. f The sum of the double bond characters for the b, c and d (∑3) and for all the five bonds (∑5). g The MP2/6-31G* value is calculated without ZPE correction. At the HF/6-31G* level (given in italics) both planar and nonplanar structures are real minima; see text. Thus the barrier to inversion should be higher than the data given in the table. h Bond lengths d/e (for the notation see the scheme in the table) are 1.746/1.706 and 1.726/1.741 Å for the planar and nonplanar forms, respectively.
structures by the density functional method, using Becke's correlated functional,21 the nonplanar structure was obtained as minimum only, being by 0.41 kcal/mol more stable than the planar one. The structural parameters of the planar and nonplanar forms show significant variance at the different levels of the theory, while the energy difference of the two structures is hardly effected. Probably the most reliable structrue is the one obtained at the MP2 level as was recently shown on several five-membered rings by Chesnut.22 When substituting 1,2,5- and 1,3,4-triphospholes at the σ3phosphorus by a methyl group, the inversion barrier was again reduced by about 0.8 kcal/mol with respect to the parent compound. The length of bond c in case of the nonplanar form of 1-methyl-1,2,5-triphosphole was getting even shorter than in 1,2,5-triphosphole, which approaches the 1.396 Å value of benzene. This behavior suggests that the attachment of an alkylbased bulky substituent group at phosphorus will indeed exert a stabilizing effect on the planar structure not only by its size but by its electronic effect as well. The calculated structural paramaters of 1-methyl-1,2,4-triphosphole match favorably with the data obtained from the X-ray structure of an alkylated 1,2,4triphosphole derivative.13 Conclusions From the present calculations carried out for di- and triphospholes it can be concluded that replacement of a carbon atom in the phosphole ring by a σ2,λ3-phosphorus atom reduces the inversion barrier about the σ3-phosphorus atom. This behavior is due to the alleviation of the ring strain of the planar form of these phospholes. The smallest inversion barrier (3.70 kcal/mol) was obtained for 1,2,5-triphosphole at the CCSD(T)/ 6-311G(2D)/MP2//6-311G(2D) level. Similarly to phosphole itself, the planar forms show large aromatic character according to their geometrical features. Even the pyramidal form exhibits significant bond length equalization. The delocalization of the phosphorus lone pair into the π-system, as is shown on the MO’s, is significant, even in the nonplanar forms of triphospholes. Isodesmic reaction energies indicate similar stabilization energies for the nonplanar structures of triphospholes with the lowest inversion barriers, as reported16 in the case of furan. The effect of alkyl and boro substituents is a further reduction of the inversion barrier. Complete planarization, however, was not achieved for the compounds investigated. Presumably, the
increase in aromatic stabilization near the planar structure is smaller than the energy needed to the further opening of the CPC angle. Although no planar phosphole was found according to the present investigations, triphospholes even in their nonplanar form benefit from aromatic stabilization, which should influence their chemical reactivity too. It is conceivable that using a sterically demanding substituent, like the 2,4-di-tert-butyl-6methylphenyl-group, used by Quin et al. on phosphole23 triphospholes would have planar equlibrium structure. Acknowledgment. Financial support from OTKA T 014955 is gratefully acknowledged. The author is highly indebted to Prof. J. F. Nixon and Prof. L. D. Quin for providing a preprint of their papers (refs 13 and 23). References and Notes (1) (a) Mathey, F. Chem. ReV. 1988, 88, 437. (b) Hughes, A. N. Phospholes and Related Compounds in Handbook Organophosphorus Chemistry; Robert, E., Ed.; Marcel Dekker: New York, 1992. (c) Mathey, F. J. Organomet. Chem. 1990, 400, 149. (e) In a recent theoretical treatment: Schleyer, P. v. R; Freeman, P. K.; Jiao, H.; Goldfuss, B. Angew. Chem., Int. Ed. Engl. 1995, 34, 337, some small stabilization was found in a certain homodesmic reaction. (2) Kutzelnigg, W. Angew. Chem., Int Ed. Engl. 1984, 213, 272. (3) Nyula´szi, L. J. Phys. Chem. 1995, 99, 586. (4) Chesnut, D. B.; Quin, L. D. J. Am. Chem. Soc. 1994, 116, 5779. (5) Coggon, P.; Engel, J. F.; McPhail, A. T.; Quin, L. D. J. Am. Chem. Soc. 1970, 92, 5779. (6) Hughes, A. N.; Edscombe, K. E. Heterocycles 1992, 33, 563. (7) The PCC and the CCC bond angles for the MP2/6-31G* optimized structure of phosphole were 110.6 and 114.2°, respectively. (8) Schoeller, W. W. In Bonding Properties of Low-Coordinated Phosphorus Compounds, in Multiple Bonds and Low Coordination in Phosphorus Chemistry; Regitz, M., Scherer, O., Eds.; G. Thieme: Stuttgart, Germany, 1990. (9) Nyula´szi, L.; Veszpre´mi, T.; Re´ffy, J. J. Phys. Chem. 1993, 97, 4011. (10) Nyula´szi, L.; Va´rnai, P.; Regitz, M.; Krill, S. J. Chem. Soc., Perkin II 1995, 315. (11) Scha¨dler, H-D.; Schmidt, H.; Frenzel, M. Phosphor, Sulfur, Silicon 1991, 56, 189. (12) Mathey, F. Coord. Chem. ReV. 1994, 137, 52. (13) Caliman, V.; Hitchcock, P. B.; Nixon, J. F. J. Chem. Soc., Chem. Commun. 1995, 1661. (14) Baudler, M.; Akpapoglou, S.; Ouzounis, D.; Wasgestian, F.; Meinigke, B.; Budzikiewitz, H.; Mu¨nster, H. Angew. Chem., Int. Ed. Engl. 1988, 27, 280. (15) GAUSSIAN 92/DFT, Revision F. 3. Frish, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, W.; Foresman, J.
6198 J. Phys. Chem., Vol. 100, No. 15, 1996 B.; Robb, M. A.; Head-Gordon, M.; Repolgle, E. S.; Gomperts, M.; Andrews, J. A.; Ragchavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, J.; Baker, J.; Stewart, J. P.; Pople, J. A. Gaussian, Inc.: Pittsburgh PA, 1993. (16) Nyula´szi, L.; Va´rnai, P.; Veszpre´mi, T. THEOCHEM 1995, 358, 55. (17) Nyula´szi, L.; Keglevich, Gy. Heteroatom. Chem. 1994, 5, 131. (18) The double bond character is defined as in ref 3 by the following formula: (rX-Y - r)/(rX-Y - rXdY), where rX-Y and rXdY are the single and double bond lengths in Table 2 for atoms X and Y. (19) Schaftenaar, G. MOLDEN 2.5; Caos/Camm Center: Nijmengen, The Netherlands, 1994.
Nyula´szi (20) Baldridge, K. K.; Gordon, M. S. J. Am. Chem. Soc. 1988, 110, 4204. (21) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (22) It has recently been shown (Chesnut, D. B. J. Comput. Chem. 1995, 16, 1227) that in fivemembered heteroaromatic systems the geometry is better reproduced at the MP2 level than by using the BLYP functional.22 (23) Quin, L. D.; Ionkin, A. S.; Kalgkutkar, R.; Keglevich, Gy. Phosphorus, Sulfur, Silicon, in press.
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