CHAPTER 1
Theoretical Aspects of Organosulphur, Organoselenium, and Organotellurium Compounds
1 Introduction
This report covers the period April 1969 — March 1970. However, for the sake of completeness some earlier and later work is also discussed.
The title is to some extent misleading, since there has been little of theoretical significance published concerning organo-selenium or -tellurium compounds, and indeed it seems unlikely that the situation will improve dramatically in the near future, at least for the latter. For the most part, therefore, we shall be concerned with organosulphur compounds. Fortunately there have been a few important developments in this area.
Although good SCF wave-functions have been available for various electronic states of the sulphur, selenium, and tellurium atoms for some considerable time, even as late as 1966 the only non-empirical calculations on molecules were restricted to H2S and C0S. Even semi-empirical PPP π-electron calculations on sulphur-containing heterocycles were few and far between at that stage, and discussions of bonding in organosulphur compounds were mostly restricted to Huckel treatments (for a review see ref. 2).
In the past two years in particular, however, the situation has improved dramatically as far as our understanding of bonding in organosulphur compounds is concerned, although the situation with regard to selenium and tellurium compounds has remained roughly static. Before discussing in some detail the results, it is worth digressing on the reason for this relatively sudden improvement.
The past decade has seen a tremendous change in the level of sophistication of theoretical treatments of molecules of interest to organic chemists. Thus, even as late as 1960, ab initio treatments of organic molecules were restricted to those containing just one carbon atom. With the lack of any semi-empirical treatments to include σ-electrons as well, organic chemists had to be satisfied with the vast body of π-electron calculations within the Huckel or Pariser–Parr–Pople (PPP) SCF formalism. However, in the past four years in particular, the situation has changed dramatically.
The extension of Huckel theory to include all valence electrons and the development of semi-empirical SCF all-valence-electron treatments has transformed the situation, and semi-empirical all-valence-electron calculations on a wide variety of medium-sized organic molecules have appeared in the literature. The spectacular advance in computer capability, coupled with the use of Gaussian Type (GTF) instead of Slater Type (STF) basis functions in the expansion method, has seen the development of non-empirical all-electron treatments on large numbers of polyatomic molecules.
Not unnaturally, the increased problems of dealing with second-row atoms has meant that there has been much less attention paid to organosulphur compounds than to, say, organo-nitrogen or -oxygen compounds. With regard to non-empirical calculations, whilst optimized orbital exponents for Slater type orbitals for sulphur have been available for some time, calculations on polyatomic sulphur-containing molecules have been limited by the lack of efficient programs for the evaluation of three- and four-centre two-electron integrals. The situation is already improving, however, and good calculations have appeared on hydrogen sulphide and thiiran. In contrast, whilst efficient programs for evaluation of multicentre integrals over Gaussian functions have been available for some time, it is only within the past year or so that optimised exponents have become available, and good calculations on a wide variety of sulphur compounds have appeared. Whilst the situation looks very hopeful for improving our knowledge of bonding in organosulphur compounds over the next few years, it seems unlikely that good non-empirical wave-functions for organo-selenium and -tellurium compounds will become available. The main hope in these cases must be in the development of adequate approximate SCF MO treatments. In this connection, the experimental results obtained by photoelectron spectroscopy, both X-ray and u.v., are likely to be of considerable importance.
2 d-Orbital Participation in the Ground States of Organosulphur Compounds
Reviews relevant to this section are given in refs. 24 — 27.
The role of d-orbital participation in the ground state of organosulphur compounds has interested chemists for many years. Despite numerous theoretica and experimental investigations, it is only now that a clear picture of the situation is emerging. Most theoretical investigations until 1968 had concentrated on π-bonding between divalent sulphur and carbon ; the interesting feature being that there was little measure of agreement between various workers as to the importance of d-orbital participation. This is not too surprising, since both the Hückel and PPP π SCF MO procedures are unsuitable for attempting to establish the extent to which the d-orbitals are involved in bonding, because of the large number of parameters whose values must be estimated but which are decisive in deriving orbital occupation numbers.
The question of d-orbital participation can really only adequately be dealt with by non-empirical quantum mechanical treatments, and perhaps the most significant theoretical advance has been in this area. We start off with a detailed discussion of recent work on H2S, which for the purist, no doubt, is classified as an inorganic molecule. Nonetheless, a number of very important points are illustrated in this work.
Calculations with §later-type Basis Functions. — Non-empirical LCAO MO SCF calculations using a minimal Slater basis set have been reported by two groups of workers, and the results are shown in Table 1. (The discrepancy between the atomic populations and dipole moments for the two calculations including 3d orbitals is somewhat puzzling.) However, the striking feature is the minute effect of including d-orbitals on the total energy. This can be contrasted with the change in the population analyses and computed dipole moments. Here we have an apparent dilemma : the total energies show quite clearly that d-orbital participation is negligible, but some computed properties would tend to give weight to an opposite view. This situation is a direct consequence of using a minimal basis set and the variational principle for determining the best energy and corresponding coefficients. If we added 4f functions on sulphur and, say, 3d functions on the hydrogens, the change in energy would be very small but there would still be small electron populations in these orbitals, and, what is more, the population of the 3d orbitals on sulphur would almost certainly have changed. This emphasizes the fact that no sound chemical conclusion can properly be drawn from such small orbital populations, but if they turn out to be large, then the situation is quite different. If the calculations had shown a large change in energy and orbital populations, then the situation is still not necessarily clear-cut because it could mean that the basis set describing the s and p basis set (i.e. H1s, S1s,2s,3s,2p,3p) was so inadequate that the functions we were adding were making up for the deficiencies. In carrying out calculations, therefore, it is important to ensure that the basis set of functions (either Slater or Gaussian) is adequate and gives a physically balanced, and as far as possible a formally balanced, wave-function.
A physically unbalanced basis set gives erroneous results for well-defined physical quantities (dipole moments etc.), while formal unbalance gives unreasonable results for charges on atoms. Clearly, the main effect of the 3d orbitals on sulphur in H2S is not to build hybrids in the normal chemical sense, but to polarize s and p valence-orbitals.
This discussion illustrates an important point. Inclusion of d-orbitals on sulphur (for formally dicovalent sulphur compounds see later) niakes very little difference to the total energy, and when organic chemists havc invoked d-orbital participation it is usually this aspect which has been under consideration, e.g. in discussing the relative energics of two molecules. This shows that 3d orbitals on sulphur are acting like polarization functions, much as, say, a 2p function on hydrogen. Inclusion of polarization function will have a significant effect, however, on such properties as gross atomic population and hence charge on an atom. The difficulty of defining the latter, and its detailed dependence on basis set, point out the difficulty of using 'charge densities' in discussing the chemistry of organic molecules in general, as organic chemists have been wont to do. Whatever other theoretical arguments may be levelled at using this concept, for discussing reactivities for example, this factor alone should caution organic chemists against the indiscriminate use of charge densities.
Calculations with Gaussian-type Basis Functions. — A number of workers have published exponents for Gaussian basis sets for sulphur in the past year. Following the pioneering work of Csizinadia and Rauk with a very limited number of functions (5s, 2p, 2d), Huzinaga and Veillard have published optimized 17s, 12p and 12s,9p Gaussian basis sets respectively for sulphur. An extended Gaussian lobe basis set for sulphur has also appeared; however, as yet no calculations have been carried out on organosulphur compounds using such a basis set. Probably the most significant work, however, has been that of Roos and Siegbahn, who have published, optimized exponents for a 9s, 5p and l0s, 6p basis set for sulphur and investigated in considerable detail the inclusion of d-orbitals on sulphur. It is instructive to compare the inclusion of d-orbitals in calculations on water and hydrogen sulphide, since this illustrates a number of important points. Comparative calculations on the extent of d-orbital participation in H2O and H2S have been carried out by two groups of workers. The results are shown in Tables 2 and 3. On the basis of comparison between calculated and experimentally determined first ionization potentials and dipole moments, Hillier and Saunders concluded that 3d orbitals on sulphur are important in discussing bonding in H2S. On the basis of total energy this is clearly not the case, and it is evident that the 3d orbitals on sulphur are acting in much the same manner as 3d orbitals on oxygen, i.e. as polarization functions (cf. Tables 2 and 3). This is shown up very nicely in the detailed investigation of Roos and Siegbahn, and emphasizes the fact that it is extremely difficult to say anything about the extent of d-orbital participation in bonding by comparing such properties as dipole moments and ionization potentials; for the former property, because of the problems in ensuring that a physically balanced basis set does not become unbalanced by addition of polarization functions to just one atom, and for the latter, because of the approximations inherent in Koopmans' theorem.
The s and p basis sets of contracted Gaussian functions of Roos and Siegbahnl*" are considerably better than those of Hillier and Saunders, the total energies being lower by some 0.924 a.u. and 3.723 a.u. for H2O and H2S respectively. This has the effect of giving a better estimate of the extent of d-orbital participation as such, since there is always the problem of making up for deficiencies in the s and p basis set. For example, in calculations on sulphate anion, where d-orbitals are of some importance in bonding, the energy lowerings on inclusion of d-orbitals in two calculations are 0.838 a.u. and 0-232 a.u. respectively. The much larger value for the former almost certainly arises for this reason.
The effect of adding 3d orbitals on oxygen parallels that for sulphur, and for both H2O and H2S the inclusion of polarization functions on hydrogen is of comparable importance. Roos and Siegbahn have optimized the d-orbital exponents, and it is of interest to compare the radial maxima for their functions with those for the valence p-orbitals. Their results are shown in Table 4. Since the main effect of the 3d orbitals is to polarize the valence orbitals, the former should have charge densities which overlap strongly with the 2p and 3p orbitals for O and S respectively. The charge density maxima for the 3d orbitals lie on the outer side of the maxima for the 2p and 3p orbitals, (1.06 a.u., 0.84 ax.) and (1.67 a.u., 1-59 a.u.) respectively.
It is worth noting that the optimized S 3d exponent for a Slater type orbital of 1•707 (corresponding GTO exponents 0•49) found by Lipscomb and Boer corresponds very closely with the optimized GTO exponent of Roos and Siegbahn of 0.54.
Organosulphur Compounds. — The question of d-orbital participation in organosulphur compounds has received considerable attention either directly or indirectly, and non-empirical calculations have appeared on CS, COS, CS2, thiiran, hydrogen methyl sulphoxide and its anion, dimethyl sulphoxide and its anion, the carbanions derived from hydrogen methyl sulphone and sulphide, dimethyl sulphide dianion, and thiophen. The results of these investigations will be discussed in some detail in the next section, and at this stage evidence will be considered relevant to the contribution of 3d orbitals on sulphur to bonding in these molecules.
Carbon Monosulphide: CS. Calculations have been carried out in a limited Gaussian basis set, and it is of interest to compare the results with that for carbon monoxide. Inclusion of 3d orbitals on the sulphur and oxygen atoms in the two molecules results in energy lowering of 0.062 a.u. and 0-081 a.u. respectively, indicating that the 3d orbitals are acting as polarization functions for both oxygen and sulphur.
Carbonyl Sulphide and Carbon Disulphide: COS and CS2. Calculations carried out with an extended contracted Gaussian-type basis set have been reported by Gelius, Roos, and Siegbahn. For COS, calculations were performed in which 3d orbitals were included on sulphur, and π-type d-orbitals on carbon, oxygen, and sulphur. The results are shown in Table 5. Again it is clear that the S 3d orbitals are acting as polarization functions. This is also true for CS2, the energy lowering on inclusion of 3d orbitals on sulphur being 0-075 a.u. in this case.
Thiiran : C2H4S. Calculations employing a minimal Slater basis set have been carried out by Scrocco et al. on the formally dicovalent sulphur compound thiiran. The energy lowering on inclusion of d-orbitals amounts to 0.040 a.u., again indicating the role of 3d orbitals as polarization functions.
Thiophen : C4H4S. Thiophen, above all organosulphur compounds, has been the most studied. The pioneering Pariser–Parr–Pople π-electron and CNDO all-valence-electron semi-empirical LCAO MO SCF treatments, in which 3d orbitals on sulphur were first explicitly considered, indicated that inclusion of the latter did not significantly affect the total energy. However, the large number of approximations inherent in these treatments inevitably means that the results obtained are not as clear-cut as one would like. One of the most significant advances in theoretical aspects of organosulphur compounds in the past year has been the extension of non-empirical treatments to molecules the size of thiophen. Although still a small molecule in the chemical sense, the 44-electron system presents considerable computational problems. Two groups of workers have now published preliminary communications on 'ab initio' calculations on thiophen and the extent of d-orbital participation therein. The different approaches both have their merits and give the same answer; namely that d-orbitals are involved to only a minor extent in bonding on thiophen, thus settling a question which has intrigued chemists for some 30 years. The approaches differ in choice of basis set of GTF and contracted GTF, and the method of dealing with the d-orbitals. With the usual definition of GTF there are six d-type functions ([MATHEMATICAL EXPRESSION OMITTED]) instead of the usual five. It is possible to effect a linear transformation of this set to a 3s-type ([MATHEMATICAL EXPRESSION OMITTED]) five 3d-type ([MATHEMATICAL EXPRESSION OMITTED]) functions before carrying out the SCF procedure. At the same time, the 3s-type function can be deleted, and this simplifies the interpretation of the results. However, in doing this a valuable degree of variational freedom is lost. By allowing the coefficients of the six d-type functions to be determined in the SCF procedure, a better wave-function should be obtained since distorted s- and d-type orbitals can be accommodated. The results, however, are correspondingly more difficult to interpret.
The basis sets used and the results of the calculations are given in Tables 6 and 7. The S basis set used by Clark and Armstrong is considerably larger than that used by Gelius et al., but is more heavily contracted. The energy lowering on introducing 3d orbitals on S amounts to 0.0527 a.u., and it is interesting to compare this with the effect of introducing polarization functions on hydrogen. The energy lowering then amounts to 0.0224 a.u., and this emphasizes that the 3d orbitals on S are indeed polarization functions. This is also shown by the other calculation, but in this case the small but significant energy lowering of 0•1179 a.u. on introduction of d-orbitals on sulphur arises almost solely from the increased variational freedom in the S basis set due to the added 3s-type function (the contribution is actually from a distorted orbital). This is most readily appreciated by inspection of the eigenfunctions and by calculations on the spherically symmetric sulphide ion (S2-). The total energies for the latter with and without inclusion of d functions are – 396•8185 a.u. and – 396•7094 a.u. In this case, the energy lowering of 0•1091 a.u. arises solely from the added 3s-type function. The small degree of participation in bonding of the five d-type orbitals in thiophen is also illustrated by the gross atomic populations given in Table 6. It is clear that the major difference in atomic population occurs from the 3s function of sulphur. The lower contribution in the case of the calculation including d-orbitals is offset to a considerable extent by the population of the 3s-type orbital formed from the 3d functions (actually a distorted 3s-type function).
