J. Am. Chem. zyxwvuts SOC. zyxwvu 1987, 109, zyxwvu 4189-4192 4189 Metaphosphate and Tris(methy1ene)metaphosphate (P( CH&) Anions. Do They Have Three Double Bonds to Phosphorus? Andrzej Rajca,' Julia E. Rice, Andrew Streitwieser, Jr.,* and Henry F. Schaefer, III* Contribution from the Department zyxwvu of Chemistry, University of California, Berkeley, California 94720. Receiued August 25, zyxwvu 1986 Abstract: Ab initio studies are presented for metaphosphate ion, PO3- (l), and tris(methy1ene)metaphosphate ion, P(CH2)< (2). Using good basis sets at the SCF level, the minimum energy structure of 2 is a zyxwvu D3 structure with the CH2 groups twisted by 19' from the molecular plane, but this structure lies only 1 kcal mol-' below the constrained D,,, planar structure. Inclusion of electron correlation increases this energy difference by only 1 kcal mol-'. The charge distributions correspond to highly polar structures with large negative charges on the oxygens and methylene groups of PO3- and P(CH2)3-, respectively. The best simple representation of these compounds is as dipolar structures; double bonding to phosphorus is relatively weak. Metaphosphate ion, PO3- (l), and its methylene counterpart, P(CH& (2), present interesting problems in bonding and elec- tronic structure. The least dipolar Lewis-type structure of 1, for example, is the hypervalent structure la which formally requires -0 o>p-o- -O\ zyxwvutsrqpo /P +- -0 \p2+-0- O/ -0 -0/ la lb IC expansion of the phosphorus octet, presumably with 3d orbitals. Three equivalent such structures could contribute to a resonance hybrid. An important alternative Lewis structure is the phos- phonium dioxide structure lb in which all atoms have normal octets. Again, three equivalent such structures could contribute to a resonance hybrid. Structure lb emphasizes the potential availability on the central phosphorus of a 3p orbital that could be involved in a-bonding to the oxygens. zyxwvutsrq In this respect this system differs from the phosphinate-type structures we studied previously2 in which four atoms are bonded to phosphorus. Finally, if multiple bonding is weak, structure IC is a highly polar Lewis structure with a phosphorus sextet similar in character to the carbonium oxide structure of a carbonyl compound, R,C+-O-. Metaphosphate ion plays an important role in biochemical mechanisms3 and is a stable gas-phase species," but has received only two previous a b initio s t ~ d i e s . ~ . ~ The present paper also presents a detailed theoretical study of the trismethylene analogue 2. Structure 2a shows its formal relationship to la. An important HZC\ //P--CH2- 2a distinction is that in 2 the energy effect of the relative mutual orientation of the methylene groups can provide an important gauge of the role of a-bonding. That is, as in the accompanying paper on hypophosphite ion,* the structural effects of relative orientations of the methylene groups provide a measure of the electronic effects of conjugation in these systems. The study of different methylene group orientations in 2 also provides a probe for the roles of Hiickel and Mobius conjugation in 1. Note that (1) Miller Institute Fellow, 1985-87. (2) Streitwieser, A,, Jr.; Rajca, A,; McDowell, R. S.; Glaser, R. J. Am. Chem. SOC. preceding paper in this issue. (3) Some recent references: Herschlag, D.; Jencks, W. P. J. Am. Chem. Sor. 1986, 108, 7938-46. Cussis, P. M.; Rous, A. J. Ibid. 1986, 108, 1298-1300. Ramirez, F.; Marecek, J.; Minore, J.; Srivastava, S.; Le Noble, W. Ibid. 1986, 108, 348-9. Recent reviews: Westheimer, F. H.; Calvo, Kim C. Stud. Org. Chem. (Amsterdam) 1983, 13, 261-75; Westheimer, F. H. ACS Symp. Ser. 1981, 171, 65-8 Chem. Rec;. 1981, 81, 313-326. (4) Henchman, M.; Viggiano, A. A.; Paulson, J. F.; Freedman, A,; Wormhoudt, J. J. Am. Chem. Sor. 1985, 107, 1453-5. (5) Loew, L. M.; MacArthur, W. R. J. Am. Chem. SOC. 1977, 99, (6) O'Keeffe, M.; Domenges, B.; Gibbs, G. V. J. Phys. Chem. 1985, 89, 101 9-25. 2304-9. Table I. Relative Energies and PC Bond Lengths for 2 (RHF/3-2 1 +G*) re1 energy. kcal mol-' PC bond length. 8, 0 3 0.0 1.672 D3h 1 .o 1.672 C2a 1 13.4 1.667, 1.667, 1.703 C2" 1 2 42.1 1.651, 1.715, 1.715 O3613 1 12.0 1.725 c3 c 62.4 1.756 &(30°) 1.16 1.672 D3(40°) 5.98 1.674 Table 11. Geometriesu and Energies' for the Two Lowest Energy Structures 2-D3,, and 2-0, basis 3-21+G* DZ+P DZ+Pd 2-D3h CH 1.078 1.076 1.077 CP 1.672 1.672 1.667 PCH 120.7 120.4 120.4 energy SCF -455.535 923 -457.71 8 986' -457.736 483 CISD -458.216 197 MP2 -458.376 123 2-D3 CH 1.078 1.077 1.077 CP 1.672 1.672 1.667 PCH 120.6 120.4 120.3 HCPC 20.4 18.4 19.0 energy SCF -455.537584 -457.720 150d -457.737 736 CISD -458.218 639 MP2 -458.379 827 "All bond lengths in 8, and angles in degrees. 'In hartrees, with Davidson correction for unlinked clusters for CISD. 'ZPVE = 16 804 cm-'. dZPVE = 17 125 cm-'. 1 and 2 are also valence isoelectronic with trimethylenemethane dianion, the prototypical candidate for the putative Y aromatic- it^.'-^ The synthesis and structure of a wbstituted derivative of 2 has recently been reported.1° Theoretical Approach 1 was studied theoretically with the first of the following basis sets; 2 was examined with all three. 1. 3-21+G* with sp-diffuse functions at carbon (oxygen) and d functions at all heavy atoms; the exponents were aSp(C) = 0.0438, ad(P) = 0.55, ad(c) = ad(0) = 0.8, asp(0) = 0.0845.'1~'2 (7) Agranat, I.; Skancke, A. J. Am. Chem. SOC. 1985, 107, 867. (8) Gund, P. J. Chem. Educ. 1972, 49, 100-103. Finnegan, R. A. Ann. N. Y. Arad. Sci. 1969, 169, 242-266. Klein, J.; Medlik, A. J. Chem. SOC., Chem. Commun. 1973, 275-6. (9) Rajca, A.; Tolbert, L. M. J. Am. Chem. Sor. 1985, 107, 698. (10) Appel, R.; Gaitzsch, E.; Knoch, F. Angew. Chem., Inr. Ed. Engl. 1985, 24, 589-590. 0002-786318711509-4189$01.50/0 , 0 1987 American Chemical Society