J. Phys. Chem. 1993,97, 4031-4035
4031
Strain Energies in Sulfur Rings, S,, n = 3-8 D. Scott Warren and Benjamin M. Gimarc' Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208 Received: October 22, 1992; In Final Form: January 25, 1993
We report strain energies of sulfur monocycles containing three to eight atoms. Strain energies are related to energy changes for reactions that convert rings into chains. Those energy changes can be obtained from experimentally determined heats of formation of products and reactants, from MNDO calculated heats of formation, and from a b initio calculated total energies. We chose model reactions of types that favor the cancellation of errors involved in the a b initio calculation of molecular total energies. Such reactions preserve numbers of electron pairs between reactants and products (isogyric), conserve numbers of bonds of different types (isodesmic), maintain atomic valence environments (homodesmotic), and more. The sources of experimental heats of formation are reviewed. MNDO heats of formation are taken from the published work of Dewar and McKee (J.Comput. Chem. 1983,484) and Baird (J. Comput. Chem. 1984,5,35). We performed additional a b initio calculations to supplement the collection of total energies of S, and H2S, previously reported by Dixon and Wasserman (J. Phys. Chem. 1990,94,5772). The availability of experimental data allows the comparison of calculated and experimental strain energies at several different levels. Comparisons, however, require the reservation that S3 and Sq rings are experimentally unknown. At the most reliable level of theory, the ab initio based strain energies are within a few kilocalories per mole of the experimentally based results. Among cycloalkanes, strain energies are known to decline from a maximum at n = 3 to zero at n = 6 with subsequent increases for n = 7 and 8. Among sulfur rings, we find the strain energy of S4 to be greater than that of either S3 or SSwith a decline to near zero for s g .
Introduction Recently we have shown that estimates of strain energies in Pq and some Pg and P8 clusters are only fractions of the values for the analogousisoelectronicand isostructural hydrocarbons. Those clusters consisted mainly of rings fused to form threedimensional polycyclic structures. The results made us realize how little we knew about strain energies in individual rings composed of main-group elements other than carbon. Theelement sulfur comes immediately to mind because it is known to form rings and a large volume of thermochemical data exists against which theoretical estimates can be compared. In this paper we report the strain energiesof sulfur rings, S,,n = 3-8, and compare them with strain energies of the corresponding cycloalkanes (CHdn. X-ray diffraction studies of Sg, S7,and s8 show them to be nonplanar rings connected by S S single Less direct experimental evidence suggests that SSmay also be a nonplanar ring.'2 Although S3 and S4 have been detected by infrared and Raman spectroscopy and in mass spectra, their structures are still contr~versial.'~-'~ S3 and S4 are generally believed to be chains rather than rings, but recent ab initio calculations with extensive basis sets and including corrections for the effects of electroncorrelation suggest that chain and cyclic structures differ by only a few kilocalories per mole and therefore both structures are likely to be observed.I6-I9 These calculations reveal that the cyclic form of s3 is planar with D3h symmetry and three s a bonds of equal length and the S4 ring is nonplanar, D z ~with , four equal SS bonds.
Ring Strain and Strain Energy Ring strain in cyclic alkanes is usually said to result from deviations of bond angles at carbon atoms from the preferred value of 109.5' appropriate for sp3 hybridized atomic orbitals on carbon.20.2' Strain in S, rings may have a different origin. For sulfur the story is that ring strain arises from dihedral or torsional angles that are forced to deviate from a preferred value of 90'. The prototypicalexampleis Pauling's description22of the bonding 0022-3654/93/2097-403 1$04.00/0
in H S S H as involving unhybridized 3s and 3p AOs. For each sulfur one 3p A 0 forms the bond to hydrogen, another forms the bond to the other sulfur, and the third 3p A 0 holds a lone or unshared pair of electrons. A second unshared pair occupies the 3s orbital. Repulsions between lone pairs occupying 3p AOs on adjacent sulfurs are minimized if they are 90' apart, thus establishing the gauche conformation as the preferred structure of H S S H with a dihedral angle of approximately 90'. Indeed, the dihedral angle found experimentally in H S S H is 85', very close to the preferred value.23 Steudel and co-workers have pointed out that the greater the deviation of dihedral angles in SSS S - chains from 90°, the longer, and presumably the weaker, the central S-S bond in this c o m b i n a t i ~ n . ~ . ~For - ~ example,
