2 Physical Methods Part (iii) Theoretical Organic Chemistry and ESCA By D. T. CLARK Department of Chemistry University of Durham 1 Introduction Over the past few years there has been a spectacular increase in the level of sophistication of theoretical treatments of molecules of interest to organic chemists. Unfortunately the single-quantum jump with small but finite proba- bility which was required to excite organic chemists over the inertial barrier for understanding the theoretical background to say extended Hiickel calculations has now been supplanted by a double-quantum process with an apparently vanishingly small probability when it comes to a consideration of ‘ab initio’ quantum-chemical calculations. This is clearly evidenced by considering the contents of the previous section in Annual Reports that was devoted solely to Theoretical Organic Chemistry in 1964.At that stage of development organic chemists were encouraged to study texts by Roberts’ and Streitweiser.2 Things have reached such a stage now where this Reporter would recommend every organic chemist to study the text by Richards and Hor~ley.~ The 1960’s may fairly be classified as a qualitative era in that the application of semi-empirical (EHT CNDO INDO MINDO etc.) quantum-mechanical treatments has led to a qualitative understanding of the structures bonding and reactivities of a wide variety of organic molecules. The most outstandingly successful example of this is the development of the ideas embodied in Woodward and Hoffman’s ‘principles of conservation of orbital ~ymrnetry’.~ To paraphrase (and misquote) Salem,5 ‘The start of the new decade may well mark the beginning of a new era in which the very concept of organic reactions will undergo a pro- found change.There are indications that the beautiful mechanistic schemes used by organic chemists to interpret organic reactions will shortly be supple- ’ J. D. Roberts ‘Notes on Molecular Orbital Calculations,’ W. A. Benjamin New York 1961. A. Streitweiser ‘Molecular Orbital Theory for Organic Chemistry,’ J. Wiley New York and London 196 1. W. G. Richards and J. A. Horsley ‘Ab Initio Molecular Orbital Calculations for Chemists,’ Clarendon Press Oxford 1970. R. B. Woodward and R. Hoffman ‘The Conservation of Orbital Symmetry,’ Academic Press New York 1970.L. Salem Accounts Chem. Res. 1971 4 322. 43 D.T. Clark mented and may eventually be replaced by a detailed picture of the dynamic behaviour of the reacting species on a complex potential-energy surface. Ex- tremely small but often highly instructive fragments of potential-energy surfaces for some elementary organic reactions have already been calculated by ‘ab initio’ methods. In the coming years one can confidently predict the total resolu- tion of several organic transition states and of the potential-energy surfaces surrounding them as well as preliminary calculations of the dynamical pathways on these surfaces’. The major portion of this Report details some of the important advances made in the past year or so in the application of non-empirical quantum-chemical methods to organic systems.Valuable review articles of a more qualitative nature are listed in reference 6. The remaining part of the Report considers application of the important new technique of ESCA (Electron Spectroscopy for Chemical Analysis) to structure and bonding in organic systems. (Rather more space will be devoted to ESCA in next year’s Report). 2 Theoretical Organic Chemistry Introduction.-Before discussing the developments which have taken place in 1970-71 it is perhaps worthwhile sounding a note of caution. With the ready availability of standard computer packages the application of semi-empirical MO treatments to organic systems has proliferated at an alarming rate over the past five years.It is inevitable that a certain percentage of the published work has little scientific value and this raises serious questions if this situation is maintained with respect to non-empirical program packages and large amounts of valuable computer time are thereby wasted. There is perhaps an inbuilt safety barrier in the indiscriminate application of non-empirical treatments to organic molecules in that compared with say a corresponding calculation at the CND0/2 level the computing power required is 2-3 orders of magnitude greater and therefore more difficult to come by. However it will be a pity if indiscriminate and unscientific applications sow the seeds of doubt as to the usefulness of applying the more rigorous theoretical treatments to organic systems.Since there is a real danger of lack of communication between theoreticians on the one hand and practising organic chemists on the other (which if allowed to develop would be unfortunate) it is felt to be worthwhile spending a little time outlining the background and some of the terminology involved in non-empirical quantum-chemical treatments. With very few exceptions electronic wavefunctions of molecules have been approached by the Hartree-Fock method in which the wavefunction is taken as an anti-symmetrized product (determinant) of spatial and spin functions i.e. for a closed shell the total wavefunction V is defined as in equation (1). The = A [$,(I )a(1)$,(2)8(2)‘ ’ ’ $,(2n)P(2n)l (1) molecular orbitals $i are expanded as linear combinations of a set of basis func- (a) R.Hoffmann Accounts Chem. Rrs. 1971 4 1; (b)K. Fukui ibid.,p. 57; (c) R. G. Pearson ibid. p. 152; (d)H. E. Zimmerman ibid.p. 272; (E) M. J. S. Dewar Angew. Chem. Internat. Edn. 1971 10 761. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA tions 'p as shown in equation (2). The q,,are normally centred on the atoms so the expansion of equation (2) is often described as the linear combination of atomic orbitals (LCAO) approximation. The LCAO coefficients CPi are deter- mined by the variational principle so as to minimize the total energy [equation (3)] where 2 is the many-electron Hamiltonian. Within the LCAO approxima-tions the MO's (@J can be more accurately represented the larger the basis set (q,) since this allows greater flexibility in representation.However the amount of computation that is necessary increases rapidly (by a factor of -n4) with the number of basis functions (n) so that a compromise must generally be struck between accuracy and the sheer physical possibility (in terms of computer power time and money available) of carrying out the calculation with a very large basis set. Molecular orbital theory is simplest to apply and interpret if the basis set is minimal that is it consists of the least number of atomic orbitals (of appropriate symmetry) for the atomic ground-state. Thus for typical organic molecules a minimal basis set consists of a 1s orbital for hydrogen Is 2s 2px 2p, 2p for carbon nitrogen etc.and Is 2s 2px 2py 2p, 3s 3px 3py 3p for phosphorus sulphur etc. If a larger number of basis functions than the minimal is used the basis set is usually described as extended. Once the LCAO MO's are determined the charge density can be analysed in terms of the basis functions 'p,. If there are two electrons per molecular orbital the total charge density is p as defined in equation (4),where P,, is the occ density matrix defined by P," = 2 1CPiCvi.This matrix contains detailed 1 information about the electronic charge distribution. The diagonal element P, is the coefficient of the distribution q,' and measures the electron population for this orbital. The off-diagonal elements PPyare overlap populations related to the charge density associated with the overlap q,q,.Since organic chemists like to be able to talk in terms of a charge distribution in a molecule (i.e. to assign a specific charge to each atom in a molecule) use is often made of a Mulliken population analysis. The gross population for an orbital q is then defined as qr(,as shown in equation (5),where S, is an overlap integral and the net charge A charge = ZA-cqp P assigned to atom A is given by equation (5a) where Z is the atomic number and the sum is over atomic orbitals on atom A. It should be emphasized however D.T. Clark that ascribing the electron population to a given atom just because an orbital is centred on that atom is a simplification especially if the orbital concerned is diffuse and there is also the rather arbitrary way in which the overlap populations are divided between atoms.A Mulliken population analysis should therefore only be regarded as giving a crude idea of the electron distribution in a molecule and the absolute values of 'charges' at atoms that may be calculated in this way depend quite markedly on the basis set used. However despite its limitations a population analysis is conceptually close to qualitative organic ideas about charge distribution in molecules. A much clearer picture of the overall electron distribution in a molecule is obtained from plotting density contour maps. The total electron density p(F),at a point r" is given by equation (6) where Cijis the molecular orbital coefficient (normalized to the proper electron occupancy) ij for the i'th molecular orbital and the j'th normalized orbital qj.Contour maps linking points of equal densities may then be plotted and are not so critically dependent on minor changes in the basis set. Of particular value in illuminating features of chemical bonding is the 6 function 6(F) = p&) -pA(F) which represents the difference between the total molecular electron density p&) and the sum of the juxtaposed atomic densities at r" pA(7). The general problem of finding LCAO coefficients Cpi by the variational method was solved by Roothaan who derived equation (7) where the E~ are one-electron energies and Fp is the Fock matrix defined in equation (8). Here H, is the matrix of the one-electron Hamiltonian for motion in the field of bare nuclei and (pvIAo)is the two-electron integral [see equation (9)J Since the density matrix P, depends on the MO coefficients Cpi,the family of equations (7) are not linear and have to be solved by an iterative procedure ; they are therefore described as self-consistent-field (LCAO MO SCF)equations.The most difficult part of LCAO MO SCF theory is the evaluation of the large number of two-electron integrals. To take a simple example in a minimal- basis-set calculation on benzene there are 222 l l l two-electron integrals to be computed. The simplest type of atomic orbital to use in a minimal basis set involves Slater-type orbitals (STO) of the form shown in the expression (lo) %l(& CPY -exp ( -ir) (10) where Y,,JB q) is a spherical harmonic describing the angular dependence and in the radial portion n is the principal quantum number and ( is a scale factor Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA which determines the size of the orbital.(An extended basis set in which each atomic orbital is represented by two STO’s is called a double-zeta basis-set). However for polyatomic molecules the evaluation of the three- and four-centre two-electron repulsion integrals (pvJh)is exceptionally difficult and time-consuming and hence comparatively few systems of interest to organic chemists have been investigated using a basis set of STO’s. The spectacular growth of non-empirical treatments of organic molecules stems from the use7 of gaussian- type functions [exp ( -crr2)]to represent the radial part of a given basis function rather than a simple exponential as for a STO.The attractive aspect of employing gaussian-type orbitals (GTO) is that the product of two GTO’s is another GTO and hence the three- and four-centre integrals can be readily computed. The computational simplicity accruing from using a gaussian basis set is offset to a certain degree by the fact that for a Is orbital for example a single GTO has an incorrect radial dependence in the vicinity of the nucleus as compared with a single STO. A linear combination of several GTO’s having different values of the exponent (a) is therefore required to compensate for this and hence for calculations of comparable quality many more integrals need to be computed for a GTO basis set than for a STO basis set.Nonetheless at the present time the much faster evaluation of integrals more than offsets this so that nearly all calculations on molecules of interest to organic chemists have been carried out with GTO basis sets. The assessment of the proper angular dependence for these gaussians has proceeded along two lines. The first involves multiplication of the radial term by the appropriate spherical harmonic XJO cp) in direct analogy to the construction of STO’s and these are called Cartesian gaussian basis sets. Secondly Preusss has proposed that the desired angular characteristics can also be obtained by taking a linear combination of simple gaussians rather than multiplying by the spherical harmonics. These sums of gaussians are referred to as lobe functions.For example a p-type gaussian lobe function can be ex-pressed as in equation (I l) where 7 is a unit vector and R is a constant defining gLp(jj) = Nt,{exp [-a(r -R0J)’] -exp [ -a(r + R07)’]) (1 1) the distance from the origin (usually but not necessarily a nuclear co-ordinate) of the centre for the two simple gaussians. The apparent disadvantage of using gaussian lobe functions is the extra constants (R,); however it can be shown that if R is set equal to Ca-* where a is the gaussian exponent and C is a constant (C -0.03) then for a given set of gaussian functions using the same exponents the results are closely similar whether Cartesian or lobe basis sets are employed.’ Mention should also be made of a further type of gaussian basis set which is giving very promising results for quite large molecules using Floating Spherical Gaussian Orbitals (FSGO).With few exceptions calculations involving car- tesian- and lobe-type GTO’s as basis sets have centred these functions on the ’ S. F. Boys Proc. Roy. Sac. 1950 A200 542. H. Preuss 2.Naturforsch. 1956 lla 823; Internat. J. Quantum Chem. 1968 2 651. S. Shih R. J. Buenker S. D. Peyerimhoff and B. Wirsam Theor. Chirn. Acta 1970 18 277. D.T. Clark atoms in a molecule and the results are therefore readily interpreted in terms with which organic chemists are already familiar. This does not apply with FSGO's defined in equation (12) where pi is the radius of orbital i and Riis its position.cp = N exp [-(I. -R,)Z/p,Zl (12) For a given basis set the energy of a molecule is then minimized with respect to the positions of the gaussian orbitals and their radii. The great virtue of the FSGO approach is its computational simplicity but the results are not directly related to an organic chemist's qualitative ideas concerning bonding. The number of integrals which have to be stored particularly when using a basis set of GTO's (in which all coefficients are settled variationally) ensures that for large molecules the storage problems rapidly become insuperable The number of stored integrals can be considerably reduced by taking appropriate linear combinations of GTO's (with coefficients fixed) and such a basis set is then referred to as a contracted gaussian basis set (CGTO)." A particular variant of this treatment is to expand a basis set of STO's in terms of linear combinations of nGTO's the coefficients and exponents being determined by some least-squares fit criterion.Such a basis is known as an STOnG set.' The objectives of non-empirical quantum-chemical investigation of organic systems can be classified roughly as follows (i) For known species to give fundamental insights into their electronic struc- ture and to allow fuller interpretation of relevant experimental data. (ii) Prediction of electronic properties and hence of the chemistry of species which are at present unknown or have not been isolated. (iii) Elucidation of the details of the processes occurring during chemical reac- tions by computing potential-energy surfaces.In this ambition theoretical chemists have a distinct advantage over their experimental brethren in that they can choose the nuclear configuration and reaction paths and can examine in detail the changes in bonding for each likely course of a reaction. For the experimentalist a direct observation of a transition state in a reaction is in principle impossible since by definition this represents the point of highest energy on the lowest free-energy path from reactants to product. A theoretical limitation is that as previously pointed out nearly all non- empirical calculations on organic systems have been made within the Hartree- Fock (HF) one-electron model which neglects correlation and relativistic effects (for most molecules of interest to organic chemists relativistic effects are unimportant).Although the Hartree-Fock method takes adequate account of the average interaction between an electron and all the other electrons in a molecule it does not take account of the instantaneous correlation of electronic motions. For a two-electron atom for example (both electrons described by the same spatial wavefunction with different spin parts) the HF method would I" E. Clementi Spec. IBM Tech. Report IBM Research Lab. San Jose California 1965. W. J. Hehre K. F. Stewart and J. A. Pople J. Chern. Ph?js. 1969 51 2657. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA not accommodate the fact that at any instant ifone electron had a high probability of being on one side of the nucleus then the other electron would have a high probability of being on the opposite side; and if one was close in to the nucleus the other would be further away.As a result the main deficiency of the HF method is its inability to properly describe the processes of stretching and break- ing a bond. It is important to grasp this point since this is the single most important error that is likely to arise from the indiscriminate use of program packages without understanding the underlying theory. This failure of HF theory is best illustrated by a simple example the H2 molecule. Expansion of the h v, w w -.go a -1.20 t 1 1 I 1 I I 1 0.0 1.0 2.0 3.0 4.0 5.0 R (a.u.) Figure 1 The energy of H as obtained from Hartree-Fock calculations compared with the exact non-relativistic energies single-determinantal wavefunction corresponding to the ground state for H2 shows that at large internuclear distances instead of arriving at a dissociation limit 2H' the HF wavefunction behaves incorrectly.This arises from spurious ionic terms. By definition the correlation energy is given as the difference between the Hartree-Fock energy and the exact non-relativistic energy. From Figure 1 it is clear that since the HF energy curve and the exact energy curve are parallel to one another up to -2.5 a.u. a distance corresponding to ca. twice the H-H bond length the correlation energy remains fairly constant in this region. At large internuclear distances the correlation energy increases rather rapidly and it is in this region that the HF method goes seriously astray.The lesson to be learnt from this is that bond stretching up to a certain point will be adequately treated by HF theory i.e. we will be some way from the exact solution but parallel to it.* In the extreme case of atomization of a molecule the correlation errors * It should be emphasized however that in general one of the most readily calculable properties of a molecule even with a poor basis set is its geometry (cf ref. 12). l2 L. Radom W. A. Lathan W. J. Hehre and J. A. Pople J. Arner. Chem. SOC. 1971,93 5339. D. T. Clark will mount up and hence heats of atomization are poorly described by HF calculations ;however this is not quite so serious a deficiency as it sounds.To sum up calculations within the Hartree-Fock one-electron model are likely to be adequate for attaining objectives (i) and (ii) at least for closed-shell species and in certain cases also objective (iii). However in a large number of situations arising in studying potential-energy surfaces the HF model will be inadequate and the more complicated (and computationally more expensive) multi-configuration SCF (MC SCF) theory will be required. One outstanding application has already been published and is discussed below. The published work discussed in this Report can be classified roughly into the three categories set out as the objective of non-empirical quantum-chemical treatments although inevitably there is a certain amount of overlap between these broad classifications.Barriers to Rotation.-Neutral Molecules. An important application in which theory can provide insight not readily available experimentally is in studying barriers to rotation. Internal rotation in ethane has been extensively studiedI3 and the following points of interest emerge. A minimum-basis-set STO calcula- tion in which electron correlation has been partly taken into account by a second-order perturbation treatment has shown that the barrier to rotation is decreased by only 0.13 kcal mol- by correlation effects.14 This important result confirms that barriers to rotation in simple molecules can be understood within the Hartree-Fock method and that correlation effects are unimportant. (It is worth noting that an extended STO basis-set calculation on the barrier to inversion in NH3 has also shown that correlation effects are negligible for this type of process).’ It is interesting to note that the experimental barrier to rotation in ethane (2.93kcal mol- ’) is satisfactorily reproduced even by calculations using a limited basis set (cf.Table l) the exception being the FSGO basis-set calculations which might more properly be described as ‘sub’-minimal. It is salutary to recognize the fact that the calculated barriers to rotation are minute fractions of the total energies (-1/20 000th) and their measurement can be compared to the feat of weighing a captain by noting the displacement of his ship when he is or is not on board. A slight increase in C-C bond length is predicted in going from the staggered to the eclipsed conformation.Interesting insights into the factors determining the barrier height may be obtained from detailed analysis of the wavefunction in terms of attractive and repulsive energy components. To provide a physical and mathematical basis for understanding the barrier origin Allen” has proposed that the total energy and Vrepulsive, be divided into two components Vattractive where V, = V, (potential energy due to nuclear electron attraction) and Vrep= V, + V, + T (V, is the potential energy due to electron-electron repulsion V, is the potential energy due to nuclear-nuclear repulsion and T is the electronic kinetic energy). Table 2 l3 E. Clementi and W. von Niessen J. Chem.Phys. 1971 54 521 and references therein l4 B. Levy and M. C. Morreau J. Chem. Phys. 1971 54 3316. ’‘ R. M. Stevens J. Chem. Phys. 1971 55 1725. L. C. Allen Chem. Phys. Letters 1968 2 597. Table 1 Non-empirical barriers to rotation Neutral Species Calculated barrier Total energy1a.u. Comments Basis set Ref kcal mol- ' for staggered conformer Ethane 3.32 rigid rotation assumed 16 STo 4G 3.33 -78.862315 potential constants evaluated STO 3G* } 2.90 -78.30618 staggered D,,;rc-c I ,538A STO3G ' n rC-H 1.086 A HCH 108.2" [Experimental values rc-c 1.531 A rC-H 1.096 A n HCH 107.8"] > 17 Eclipsed D, ;rc-c I .548 A n rC-H 1.086A HCH 107.8" 2.80 -79.1 1582 Staggered D,,% 1.529 A STO 431G rCVH1.083A HCH 107.7' 1 0 Eclipsed ;as for STO 3G G 2.58 -78.9781 10 Rigid rotation.Analyses C 10s 6p H 4s GTO 3 barrier in terms of attractive C GTO**(2s 2p 2s) 18 R' and repulsive terms. Comparison with ethyl fluoride i 5.17 -67.347295 Rigid rotation. Expt. geometry Minimal FSGO } 19 also calc. rc-c 1.397 A 3.14 -79.203142 Rigid rotation. Experimental C 9s 5p H 4s GTO } 13 geom. 3.65 -79.23770 Staggered D3d; rc-c 1.551A C 11s 7p H 6s GTO EH 107.3' S 3p 3s C GTO 20 Eclipsed D, ;rc-c I .570 A augmented by 3d, ,3d,, and eH 107.0" 2p polarization function CH3CHO ul c Exptl. 1.16 kcal; most 1.09kcal -152.85495 using exptl. geom. rigid 50s 45p GTO 24 stable conformer H rotation C GTO (4s 6p,2s) eclipsing oxygen Neutral Species Calculated barrier Total energy1a.u.Comments kcal mol- for staggered conformer Me H \/ H'/c=c\ H Exptl. 1.98 kcal; most 1.25 kcal -116.92656 using exptl. geom. rigid stable conformer H rotation eclipsing C=C 1.418 -115.656681standard model geom. rigid rotation 1.547 -115.657787 partially flexible 1.491 -116.488399) CCC optimized Me F \I c=c H / \ H cis-fluoropropene Exptl. 1.07 kcal mol-' ; 1.07 -215.71120 Exptl. geometry most stable conformer H eclipsing C=C Me H \/ H /c=c\ F trans-fluoropropene Exptl. 2.20 kcal mol- ; 1.34 -21 5.70738 Exptl. geometry most stable conformer H eclipsing C=C Basis set Ref g C 10s 5p H 5s GTO C }26 C GTO (3,1,l) STO 3G STO 3G 16 STO 3G C F 10s 5p H 5s GTO C F C GTO (3,1,1) ? Y C F 10s 5p H 5s GTO C F } 26 2 C GTO (3,1,1) s.Me-CEC-Me -153.036672 Exptl. geometry STO 3G Exptl. 30 cal mol- ' -154.140064 rigid rotation STO 4c) Exptl. geometry CH rCH2 -rigid rotation Exptl. cis-trans energy cis-trans energy diff. STO 3G diff. 2.3 kcal mol-'; 2.92 kcal mol -'; trans-cis barrier trans-cis barrier 5.0 kcal mol -' 6.61 kcal mol- '; partially flexible rotation cis-trans energy diff. -. h -. 2.05 &a1 mol -'; C. W trans-cis barrier 6.73 kcal mol- ' Ethylene 138.6 -77.07121 Exptl. geometry rigid rotation STO 3G Exptl. 65 kcal mol-' Allene 91.9 -114.41941 Exptl. geometry rigid rotation STO 3G 16 0 Butatriene 73.9 -151.77131 Exptl. geometry rigid rotation STO 3G 16 42 -.l6 L. Radom and J. A. Pople J. Amer. Chem. Soc. 1970,92 4786. W. A. Latham W. J. Hehre and J. A. Pople J. Amer. Chem. Soc. 1971 93 808. L. C. Allen and H. Basch J. Amer. Chem. Soc. 1971 93 6373. l9 R. E. Christoffersen D. W. Genson and G. M. Maggiova J. Chem. Phys. 1971,54 239. '' A. Veillard Theor-. C'him. Acta 1970 18 21. * STO nG least-squares expansion of STO basis set in terms of nGTO per STO. CJ ref. 11. ** C GTO (2s 2p 2s) contracted gaussian basis set consisting of 2s,2p functions for C 2s for H. ul P Table 2 Energy c0mponentsla.u. .for ethane and ethylfluoride ET Vne = Vat Ke V"n T GJ-staggered -177.94095 -579.27127 144.1 5666 78.86430 178.30936 40 1.33037 C2H5F {eclipsed -177.93682 -579.36739 144.20185 78.89841 178.33030 40 1.43057 staggered -79.14755 -267.25143 67.19480 41.93098 78.97811 188.10388 C2H6 {eclipsed -79.14344 -267.28342 67.20999 41.93845 78.99155 188.13999 Energy component difSerences AET A Vrep A Vatt C,H,F 0.0041275 0.1002455 0.0961151 DifSerenceJkcalmol 2.59 C2H6 0.0041 113 0.036 1037 0.0319939 DifSerencelkcal mol -' 2.58 Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA shows the energy components obtained for ethane and for comparison those for ethyl fluoride obtained with a comparable basis set.' The energy component dif-ferences (eclipsed-staggered) are also shown in Table 2.Figure 2 shows the opposing phase relationships between the attractive and repulsive components and this is a characteristic feature of every barrier (rotation inversion etc.) in every molecule.For both molecules AV,, >AVatt,and the barriers are therefore denoted as repulsive-dominated. From Table 2 and Figure 2 it is clear that the absolute magnitudes of the energy component differences are larger for ethyl fluoride than for ethane although the calculated barriers are almost identical. It is almost as if an extra potential-energy term is being added (approximately equally) to Val and Vrep in going from ethane to ethyl fluoride. This can be attributed to the difference in effective potential between the fluorine and hydrogen atoms. Since the radius of the fluorine atom is close to that of hydrogen we are simply seeing the effect of lowering the potential well around one of the rotating atoms due to the high charge density of fluorine....... C,H,F --C,H .lo.\ .oa !?' .06-.. ;: ?#i " !i ..... 0" 60" (eclipsed) (staggered) Figure 2 V,, and Vrep energy components for ethyf JIuoride ( ...) and ethane (-) (Reproducedby permission from J. Amer. Chem. Soc. 1971 93 6373) In an attempt to shed insight of a kind closer to the traditional viewpoint of organic chemists Clementi and Von Niessen13 have decomposed the ethane total energy as a function of rotational angle into one- two- three- and four-centre contributions. The three-centre term undergoes the greatest change of magnitude but the direction of its change is opposite to that of the barrier 56 D. T. Clark itself and it therefore appears that the bond-energy analysis scheme22 provides no simple physical or chemical concept for understanding the barrier.As an example of a different type of barrier Allen and co-w~rkers~~ have shown that in acetaldehyde the barrier is attractive-dominated (Figure 3) and therefore provides a useful counterpart to the repulsive-dominated ethane barrier. 498.27000 1 345.43000 498.27500 345.42500 498.28000 345.4200 -J 3 a W 498.28500 a H ECLIPSItIG 0 H ECLIPSING H Figure 3 Energy and energy components vs. torsional angle for acetaldehyde (Reproduced by permission from J. Chem. Phys. 1971,54 2828) With this in mind Allen and J~rgensen~~ have carried out a charge-density analysis of the rotational barriers for both molecules.This analysis provides an enlightening physical understanding of the origin of the two types of barrier. Considering ethane it is clear even from the results of a Mulliken population analysis that the origin of the repulsive-dominated barrier is likely to be under- standable in terms of the change in electron distribution as a function of rotation. It is convenient to define a 6 function 6(F) that is applicable to rotational barriers. Such a function [equation (13)]yields the difference between the electron density for the less-stable conformer pLs(F) and that for the equilibrium conformer pE(F)at r in terms of the rotational barrier. By convention in plotting such a function a solid contour indicates an increase in electron density and a dashed contour indicates a decrease in electron density.Solid letters correspond to the location of atomic nuclei and dashed letters represent projections of nuclei onto the plane of the plot. (1 a.u. of density = le u0-3= 6.74873 A-3). Analyses of charge-density difference maps for barriers to rotation are com- plicated by the fact that there are two sources contributing to the difference. First there are substantial changes due to the different location of atomic orbitals in the two conformers. This is not of particular relevance and it is the second source due to the difference in actual molecular orbital coefficients which is 22 CJ B. Nelander J. Chem. Phys. 1971 54 2949. 23 R. B. Davidson and L. C. Allen J. Chem. Phys. 1971 54 2828.24 W. L. Jorgensen and L. C. Allen J. Amer. Chem. SOC.,1971 93 567. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA responsible for the more subtle distortions associated with the nature of the barrier. This is a point which had not been fully appreciated by previous workers. It is possible to circumvent this by selecting planes perpendicular to the C-C axis that are far enough from the rotated atoms that the change in the location of their atomic orbitals does not obscure the charge distortions caused by the difference in the MO coefficients. For example Figure 4 shows the difference Figure 4 Difference plot of the eclipsed ethane electron density minus the staggered ethane electron density 0.5 a.u. behind the plane of the stationary methyl hydrogens.Contour 1 is at +0.00002 a.u. and the contour interval is +0.00002 a.u. (Reproduced by permission from J. Amer. Chem. Soc. 1971 93 567.) plot for eclipsed minus staggered ethane in the plane positioned 0.5 a.u. behind the hydrogen in the stationary methyl group (the xy plane at z = -1.2). This clearly shows that there is more charge behind the stationary hydrogen atoms in eclipsed ethane than in staggered. This results from the increase in repulsion between the eclipsing hydrogen atoms an increase which forces charge behind them. The increased repulsion is confirmed by the H(l)-H(4) overlap population (Table 3). A decrease in electron density behind the carbon atom in the stationary methyl group is also observed. This decrease is consistent with the fact that the C-C bond in the eclipsed ethane is slightly weaker than that in staggered ethane [C-C bond length slightly greater C(1)-C(2) bond overlap population slightly smaller].The interaction between the methyl groups in rotating from their position in staggered to that in eclipsed ethane follows the same pattern of charge decrease between the centres of repulsion and charge increase behind them as is observed in the interaction between two helium atoms (Figure 5). D. T. CIark Table 3 Mulliken overlap populations for ethane Staggered ethane Eclipsed ethane Atom 1 Atom 2 P12 (staggered) p1 (eclipsed) C1 c2 0.49281 0.48096 c Hl 0.76877 0.76998 Cl H -0.04931 -0.04940 Hl H4 -0.00174 -0.00587 HI H6 0.00105 0.00085 Hl H2 -0.01364 -0.01355 Atomic charges from population analysis for ethane Atom Staggered Eclipsed C 6.81657 6.817 19 H 0.72784 0.72761 For acetaldehyde since the barrier is attractive-dominated the electron-density distributions should reflect a loss of attraction in rotating from the H-eclipsing0 to the less stable configuration.This is nicely illustrated by a consideration of the difference of the H-eclipsing-H minus the H-eclipsing-0 electron density in the plane of the C-C-0 fragment (Figure 6). It is clear that virtually no change in the electron density near the aldehyde hydrogen is caused by the rotation (i.e. interactions between methyl group and aldehyde hydrogen do not significantly contribute to the barrier).The plot reveals a large charge build-up in the region around the oxygen atom and between the C=O double bond and its eclipsing methyl C-H bond in the more stable H-eclipsing-0 conformer. In the ethane case the opposite effect was observed i.e. there was a charge loss between the C-H bonds when they became eclipsed. The charge increases between the eclipsing bonds and around the oxygen are therefore the charge distortions responsible for the attractive- dominant nature of the rotational barrier. It is the loss of this highly favourable interaction between the methyl group and the oxygen in the H-eclipsing-0 conformer that causes the increase in V, which occurs when the methyl group is rotated to the higher-energy configuration. The large charge build-up around oxygen results from its high electronegativity which draws electron density from the methyl hydrogens.This is supported by the population analysis in Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 5 Figure 5 Diflerence plot of the helium dimer electron density minus the sum of the electron I densities of two helium atoms at an internuclear separation of 2.0 a.u. Contour 1 is at f0.002 a.u. and the contour interval is 0.004 a.u. (Reproduced by permission from J. Amer. Chem. SOC.,1971 93 567) H Figure 6 Diflerence plot of the H-eclipsing-H acetaldehyde minus the H-eclipsing-0 acetaldehyde electron density in the plane of the CCC fragment the yz plane being at x = 0. Contours are 1 = kO.001 2 = k0.004,3 = k0.007 4 = kO.01 5 = k0.05 6 = f0.15 7 = f0.25 a.u.(Reproduced by permission from J. Amer. Chem. SOC. 1971 93 567) 60 D. T. Clark which there are positive overlap populations between the oxygen and all of the methyl hydrogens for the more stable conformer whereas in the H-eclipsing-H conformer the oxygen has a positive bond overlap population only with the most distant methyl hydrogen (Table 4). A part of the charge increase between the C-0 bond and its eclipsing C-H bond is due to the change in location of the methyl hydrogen orbitals but even allowing for this the conclusions remain the same. It is evident in studying the calculated barriers to rotation in ethane that with the exception of the FSGO basis set the results are not particularly sensitive Table 4 Mulliken overlap populations for acetaldehyde H-eclipsing-0 xk H-eclipsing-H p,,(H-eclipsing-0) 0.46322 -0.15938 0.75861 0.74345 0.74345 -0.15743 1.12466 -0.07350 -0.05209 -0.05209 0.78107 0.00783 0.00155 0.00155 -0.13351 -0.03576 0.03576 0.00382 -0.04067 0.00228 0.00228 Atomic charges from population analysis for acetaldehyde Atom H-eclipsing-0 Cl 6.58751 c2 5.78991 0 8.35078 HI 0.78728 H2 0.80796 H3 0.80796 H4 0.86860 p12 (H-eclipsing-H) 0.41908 -0.13911 0.76302 0.73026 0.76302 -0.16309 1.09329 -0.060 19 -0.04986 -0.06019 0.81203 -0.00164 -0.00164 0.00408 -0.12952 -0.04148 -0.026 17 0.00298 -0.04 148 0.0041 8 0.00298 H -eclipsing-H 6.58941 5.80340 8.35049 0.78758 0.81937 0.78758 0.86217 Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 61 to the basis set employed.Thus the computed barrier with Pople's limited STO 3G basis set is comparable with that from Veillards' extended-basis-set calcula- tion which approaches the Hartree-Fock limit. This is an important result because the STO 3G basis set is sufficiently small to allow much larger organic systems to be studied. In an extensive series of papers Pople and co-~orkers~~ have studied a wide variety of molecules and ions of interest to organic chemists and this work overall represents the single most important contribution to theoretical organic chemistry.The great wealth of information derived from non-empirical calculations may be illustrated by selection of a few examples. For propene the calculated barriers to rotation are in good agreement with experiment. Allen and Scarzafava26 have also investigated the effect of replacing H by F in the double bond and they have successfully reproduced the anoma- lously low barrier to rotation in cis-fluoropropene. This represents one example of a phenomenon which is becoming clearer with the advent of more rigorous theoretical treatments of the quite drastic effects on barriers to rotation of relatively remote substituents ((5section on carbonium ions p. 62). Component energy analysis reveals that the barrier for cis-fluoropropene is attractive- dominated whereas those for propene and trans-fluoropropene are repulsive- dominated.In but-2-yne the two methyl groups are separated by an acetylenic linkage and the interaction between them is extremely small (calculated barrier 5-4 cal mol-I); even so the staggered conformation is predicted to be the most stable." A detailed study of rotation about the central C-C bond in buta-1,3- diene shows the importance of geometry optimization where steric interactions are large. Both the cis-trans energy difference and the barrier to rotation are well accounted for on the basis of a flexible- as opposed to a rigid-rotor model.I6 Barriers to rotation about double bonds have been investigated for ethylene allene and butatriene.I6 The accurate representation of barriers to rotation in these cases is not possible within the Hartree-Fock method since correlation effects are important.(This can be thought of nai'vely as a special case of breaking a bond and the single-determinantal wavefunction again contains spurious ionic terms). The calculated barriers are therefore too large; however the trends should be correctly predicted i.e. the barriers decrease along the cumulene series. For small angles of twist the single-determinantal wavefunction provides an adequate description and this can be seen from the calculated force-constants and hence twisting wavenumbers. The values of 1237cm-' and 1022cm-' obtained for ethylene and allene can be compared with the experimental values of 1027 cm-' and 812 cm- respectively so that both are rather too high but in the correct order.The discussion so far has centred on barriers to rotation which can be com- pared directly with those determined by experiment. In the case of reactive intermediates such as free radicals or carbonium ions experimental data are 25 W. A. Latham W. J. Hehre R. F. Curtiss and J. A. Pople J. Amer. Chem. SOC.,1971 93 6377 and references therein. 26 E. Scarzafava and L. C. Allen J. Amer. Chem. SOC.,1971 93 3 11. 62 D.T. Clark more often than not lacking so that theoretical studies can provide especially valuable insight in these situations. Free Radicals. It is interesting to compare the calculated barriers to rotation for ethyl and acetyl radicals with those for ethane and acetaldehyde respectively.Ethyl radical is predi~ted'~ to have a staggered configuration with a barrier to rotation of 0.46 kcal mol-' (STO 3G) or 0.62 kcal mol-' (STO 4.31G) which as expected is much smaller than that for ethane. Correspondingly since the attractive barrier in acetaldehyde is dominated by the favourable interaction between oxygen and the eclipsing hydrogen atom removal of the aldehydic hydrogen only lowers the barriers slightly (calculated 0.38 kcal mol- ') and the most stable conformer is the eclipsed.27 (Unrestricted Hartree-Fock calculations on acetyl radicals also give a good account of the hyperfine splitting constant^).^' Carboniurn Ions. Barriers to rotation in a number of carbonium ions have been investigated with interesting results (Table 5).Clearly the traditional viewpoint of organic chemists that in simple alkyl carbonium ions there is essentially free rotation is not entirely correct. Without discussing all of these results in detail a few features are worth commenting on. The fluoroethyl cation is isoelectronic with acetaldehyde and in fact the barriers to rotation are very similar. Both t-and 2-fluoroethyl cations have been shown to possess attractive-dominated barriers whereas 2-chloroethyl cation has a repulsive-dominated barrier. A re-markable feature is the long-range effects of substituents in the substituted propyl cations. These results can be rationalized in terms of preferential stabiliza- tion of the perpendicular staggered conformations through interaction of the CH2X group with the 2p(C+)orbital leading to its increased p~pulation.~' Barriers to Inversion.-Barriers to inversion have been calculated for several species of interest to organic chemist^,^ 1-33 and provide data which are difficult to obtain experimentally (Table 6).Comparison of the corresponding iso- electronic nitrogen and carbanionic species shows that in general barriers to inversion increase in going from the former to the latter when the inversion centre is part of a ring.* A notable exception included for comparison arises for cyclo- propenyl anion and the elusive 2H-azirine both of which are formally classified as being anti-aromatic. The calculated barrier to inversion for vinyl radical is quite small compared with that for vinyl anion which can therefore be regarded as being stereochemically rigid.The high barrier to inversion in vinyl anion raises the possibility that rotation about the double bond might be a competitive process as shown in Scheme 1. In an elegant study Lehn and co-workers have investigated these possibilities for the isoelectronic sequence X = Ot N and C-(R' = R2 = R3 = H). The '' A. Veillard and B. Rees Chem. Phys. Letters 1971. 8. 267. 31 D. T. Clark 2nd International Jerusalem Symposium on Quantum Chemistry and Biochemistry Israel Academy of Sciences and Humanities 1970 p. 238. 32 J. M. Lehn B. Munsch and Ph. Millie Theor. Chim. Acta 1970 16 351. " A. Veillard and B. Reed Theor. Chim. Acta 1971 8 267. * In this respect a double bond behaves as a two-membered ring.Table 5 Barriers to rotation in substituted ethyl cations s s X Calculated Most stable Comments Basis set Ref. $-barrierslkcal mol-conformer I 'a XCH,CH,+ H 0.0 -Rigid rotation C 7s 3p H 3s GTO 28 P h 0.0 -Rigid rotation STO 3G 17 e 0.22 -Flexible rotation STO 3G -. W F 10.53 Eclipsed Rigid rotation C 7s 3p H 3s GTO 29 C GTO (3 1 1) } 3 c1 1.40 Staggered Rigid rotation STO 3G 28 8 CH3 2.52 Staggered Rigid rotation STO 3G s. CH2CH3 3.73 Staggered Rigid rotation STO 3G 5 CH,F 2.1 1 Staggered Rigid rotation STO 3G 0 CH20H 0.91 Staggered Rigid rotation STO 3G 30 6;; CH2CN 0.87 Staggered Rigid rotation STO 3G 3 17.54 Staggered Rigid rotation STO 3G 5' (bisected) CH3-CHF+ 0.62 Eclipsed C 7s 3p H 3s GTO C GTO (3 1 1) 28 D.T. Clark XXIIIrd International Congress of Pure and Applied Chemistry Butterworths London 1971 vol. 1 p. 31. 29 D. T. Clark and D. M. J. Lilley Ch5m. Comm. 1970 603. 30 L. Radom J. A. Pople V. Buss and P. von R. Schleyer J. Amer. Chem. SOC.,1970 92 6987. 64 D. T.Clark Table 6 Calculated barriers to inversion Calculated Barriers to Basis set Ref Molecule barrier/ rotation1 kcal mol-' kcal mol -' 'r 20.85 -C 5s 2p H 2s GTO C 5s 2p H 2s GTO > 31 52.0 __ C 5s 2p H 2s GTO 35.14 -C 5s 2p H 2s GTO 2 H 17.2 31.4 C 0 10s 6p H 5s GTO \ /H CGTO (5 3,3) /=O+ H H 27.9 57.5 C 0 10s 6p H 5s GTO 32 \ /H CGTO(5,3,3) /c=N3 H C 0 10s6p H 5s GTO CGTO(5,3,3) C 0 10s 6p H 5s GTO 33 CGTO(5,5,3) CH3\ 29.0 C 0 10s 6p H 5s GTO 33 CGTO(4s,2p,2) oC=O Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA R’ R3 \/ c-x 4 R2 R3 =H Rotation Scheme 1 barriers to both the inversion and rotation increase in the same order and the sequence of inversion barriers may be rationalized in terms of a balance of attractive and repulsive terms.The calculations clearly demonstrate that in- version in these species is energetically much more favourable than rotation. Electronic Structures of Molecules Radicals and Ions.-A considerable amount of literature already exists concerning non-empirical wavefunctions for molecules of interest to organic chemists and it has been comprehensively covered by Richards et al.in 1970.34 In an extensive series of investigations Pople and co-workers have studied a large number of molecules and acquired some interest- ing data.25 A few of the more important papers are discussed in detail below. Substituent EfSects. The physical organic chemist’s views concerning the elec- tronic effects of substituents attached to both saturated and unsaturated centres derive largely from measurements of acidities basicities and substitution rates (electrophilic nucleophilic and free-radical). The feature common to all of these measurements is that they invariably refer to the liquid phase and yet in deriving magnitudes and signs of substituent effects scant attention has been paid to the role of the solvent. With an ‘ab initio’ treatment one might reasonably expect to predict what would happen in the gas phase to isolated molecules and knowing this it should then be possible to say what can and cannot be ascribed to solvent effects in such systems.Detailed non-empirical calculations are therefore likely to provide by default important information on the role of the solvent. It is becoming increasingly evident that the traditional (simplistic) view of substituent effects currently held by a majority of organic chemists will have to be drastically 34 W. G. Richards T. E. H. Walker and R. K. Hinkley ‘Bibliography of Ab lnitio Molec-ular Wave Functions,’ Clarendon Press Oxford 1970. 66 D.T. Clark modified in the next few years. We mention here one particularly striking example concerning the electronic properties of the methyl group.The tradi- tional views concerning (a)the acidities of simple alcohols MeOH > EtOH > Pr'OH > Bu'OH and (b)the basicities of simple amines Me,N > MeNH > NH ,has led to the postulate that methyl is electron-releasing (relative to hydro- gen). Fortunately the development of ion cyclotron resonance spectroscopy now allows the evaluation of gas-phase acidities3' and ba~icities,,~ and the interesting result emerges that the order (a)for the solution phase is completely reversed for the gaseous phase. In an important theoretical study Pople and Hehre have shown37 that in alcohols and amines a methyl group is overall electron-attracting with respect to hydrogen. However if the total energies of the neutral and protonated or deprotonated systems are calculated then the experimental ordering of gas-phase proton affinities is reproduced.The relevant results are shown in Table 7. This emphasizes the fact that energies of proton- transfer reactions do not necessarily correlate with charge densities on the atom Table 7 Energies and atomic p~pulations~~ Molecule E1a.u. E (Proton E (Proton 4xa ha addition)/ removal)/ kcal mol-' kcal mol-' NH3 -55.45254 -258.3 555.3 -0.481 0.160 MeNH -94.03005 -266.0 539.0 -0.405 0.157 Me,NH -132.60922 -271.2 523.8 -0.332 0.156 Me3N -171.18930 -274.7 -0.263 -H*O -74.96072 -228.6 568.0 -0.372 0.186 MeOH -113.54550 -235.8 535.4 -0.308 0.189 Me,O -152.13214 -239.7 -0.244 -qX,qH are Mulliken populations on the neutral molecules.qx is the charge on the atom from which the proton is to be removed and 4 is the charge on the hydrogen to be removed. to which the proton is attached and a more reasonable qualitative explanation of the results is that a methyl group provides an extended structure which can be polarized more effectively (than hydrogen) by both cationic and anionic centres. Pople and co-workers3' have made an extensive study of charge distributions in alkanes alkenes and alkynes and fluorinated analogues and have demon- strated the widespread alternation in charge in both the fluorine-substituted unsaturated and saturated hydrocarbons. This confirms an earlier result from the computationally simpler semi-empirical CND0/2 SCF MO treatment.Typical results for ethane ethylene and acetylene and their monofluoro- derivatives are given in Table 8. The energy of each molecule has been minimized 35 J. I. Braumann L. K. Blair E. L. Rufford and L. B. Young J. Amer. Chem. SOC. 1971,93. 4609. 36 J. I. Braumann and L. K. Blair J. Amer. Chem. Soc. 1971 93 391 1. 37 W. J. Hehre and J. A. Pople Tetrahedron Letters 1970 1959. 38 W. H. Hehre and J. A. Pople J. Amer. Chem. SOC.,1970 92 2191. Physical Methods-Part (iii)Theoretical Organic Chemistry and ESCA Table 8 Charge distributions and orbital exponentsfor some simple organic moIecules3 Molecule Charge distribution Basis set Optimum exponentsfor valence electron) orbitals (2s 2p for C and F 1sfor H) H H Hf9 \I -26/ 1.76 CH3CH3 c-c STO 3G / I \ 1.18 H HH CH3CH2F +llH H H-'; \I -58C-C I/ +zag STO 3G 1.79 1.76 2.56 /\ +13H F-165 1.19 1.18 H ~+78 CH,=CH2 \ -156 H / H STO 3G 1.70 1.23 1.76 1.68 CH2=CHF STO 3G 2.57 1.21 1.23 1.68 HCECH STO 3G 1.31 HCrCF STO 3G 1.74 1.64 2.59 1.33 with respect to the exponents (5)of the basis functions (minimal basis set STO expressed as least-squares fit to 3GTO) and the exponents provide interesting extra insight into the changes in electron distribution brought about by fluorine substitution.For example for fluoroethylene the higher exponents for valence 2s and 2p orbitals on C(l) attached to fluorine show that these orbitals are more compact than those on C(2). The hydrogen 1s orbital in fluoroacetylene is also more compact (5 =1.33)than in ethane say (<=1.18) and this arises from the much larger positive charge on the atom.Charge distributions in the series CH, CHF CF have been discussed and used to interpret the degree of electro-philicity of these carbene~.~~ The concept of CT-nseparation in MO calculations was originally based on an assumption of the independence of the n-electrons above and below the plane J9 J. F. Harrison J. Amer. Chem. SOC.,1971 93 4112. D.T.Clark of the molecule and the a-electrons localized near the molecule plane. The fact that there is strong interpenetration of the a-and n-electron densities is nicely demonstrated by a minimal-basis-set STO treatment,40 in which density contours have been plotted for individual CT and 7r MO’s.Figure 7 for example shows a superposition of the 3e, (a)and lei,(71) molecular orbitals for benzene and indicates significant interaction between the a-and n-electrons. Figure 7 Superposition of the 3e, (0)and le, (n)molecular orbitals in benzene. Plane perpendicular to the molecular plane of benzene and bisecting opposite C-C bonds. Contours start at 0.004 contour interval 0.004 a.u. (Reproduced by permission from J. Amer. Chem. Soc. 1971,93 2603) Geometries. One of the most readily calculable properties of a molecule is its equilibrium geometry and even with a relatively poor basis set bond angles and bond lengths can normally be computed to within a few percent. (a) Neutral molecules. Reference has already been made to geometry optimiza- tions in discussing barriers to rotation in simple molecules in the previous section.Calculations have mainly been oriented towards studying systems for which accurate experimental data are available as functions of the basis set. This is a necessary preliminary step if one hopes to use non-empirical calculations to predict geometries for species which have either not been isolated or for which structural data are not yet available (see the following section on carbonium ions). The agreement between theory and experiment is impressive (Table 9). (b) Carbenes. Table 10 displays the result^'^,^^ for some carbenes which have been studied experimentally. For methylene itself there are two points of major ‘O R.M. Stevens E. Switkes E. A. Laws and W. N. Lipscomb J. Amer. Chem. Soc. 1971,93,2603. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 69 Table 9 Calculated geometries for neutral species' Molecule Experimental CH4 rc-n 1.0858 C2H2 rc-H 1.061 A rc-c 1.203A 1.541A' 1.086A 1.086 A 1.089 A n H,C,C 111.2" 10.7" STO 3G A > H,C,C2 111.2" 10.7" n H,ClH3 107.7" 08.2" -C,C,C 112.4" 12.4" n-I H,C,H 106.1' 107.2" interest. First there is the geometry of the ground (triplet) state for which earlier spectroscopic evidence indicated a linear structure and secondly the triplet-singlet energy gap. All non-empirical studies so far reported have indicated a bent structure for 3B methylene in apparent conflict with the existing experimental data.However Herzberg has re-interpreted the data to give a bond angle of 136",a value that is in good agreement with the theoretical estimates. The calculated triplet-singlet separations range from 22-40 kcal mol- '. (c) Radicals. Pople and co-workers have studiedI4 several radicals of funda- mental importance to organic chemists and the results are summarized in Table 11. Methyl radical is predicted to be planar however as a prototype for studying the effect of angle deformation. Allen Von Schleyer and Buss4' have considered distorted methyl radical in which for equal C-H bond lengths the carbon and two hydrogen atoms are in a plane with an HCH angle of 90". The distorted radical is then predicted to be non-planar with a barrier to inversion of 1.2 kcal mo1-'.The e.s.r. data on cyclopropyl and 7-norbornyl radicals support the conclusion that angle-strained radicals are non-planar. For free ethyl radical a bridged structure is found to be very unfavourable and the ground-state structure is well represented by the classical formulation. (d) Carbonium ions. A representative series of carbonium ions which have been studied is given in Table 12. C2H3' and C2H5+ are prototypes for addition of a proton to an alkyne and alkene respectively whereas CHSf and C2H,+ are prototypes for protonated alkanes. Whereas methyl and vinyl cations are predicted to be planar about the electron-deficient centre in ethyl cation the carbonium centre C( 1) is slightly non-planar the distortion being toward a staggered configuration about the C-C bond.14 For the methyl 0x0-carbonium ion of interest from the standpoint of the Friedel-Crafts reaction the calculated 41 V.Buss P. von R. Schleyer and L. C. Allen A.C.S. Meeting University of Delaware 1970. Table 10 Calculated geometries of some carbenes Carbene Electronic state Calculated Exptl. Comments Basis set Ref. structure structure CH2 3B rCUH1.082A rC-H 1.029 A originally assigned linear A STO 3G HCH 125O.5 HCH 136" structure from exptl. data rC-H 1.069A STO4.31G n HCH 132.0' n HCH 132.5" Using exptl. rCpH C 10s lop gaussian lobe contracted 4s 2p. H 5s lA1 contracted 2s 14 -rC-H 1.123 A rC-H 1.1 I A Calculated energy difference ---.-/----HCH 100.5' HCH 102.4" (3B -'A,) -40 kcal mol -STO 3G rC-H 1.100 A -37 kcal mol- n STO4.31G HCH 105.4' n HCH 105.0' Using exptl.C 10s lop gaussian lobe rC-H = -22 kcal mol-' contracted 4s 2p. H 5s ---.---.. contracted 2s CHF A' HCF 104" HCF 101.8' Using exptl. rC-H and rC-F C F 10s lop gaussian lobe rC-H 1.12 A contracted 4s 2p. H 5s rCAF1.31 contracted 2s -3Aff HCF 122' -Using rC-H and TC-F as for A' Calculated singlet-triplet ' 39 ---. n separation 0.0 kcal mol-' lA1 FCF 105.0" FCF 104" Using exptl. rC-F C,F 10s lop gaussian lobe rC-H 1.30 a contracted 4s 2p. H 5s contracted 2s 3B1 FCF 120" Using exptl. rC+ singlet-C,F 10s lop gaussian lobe triplet separation contracted 4s 2p. H 5s 39 kcal mol-' contracted 2s Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA II 009 4 L m c e- 21 wL c 2 L V Table 12 Calculated geometries for some carbonium ions h) Ion Calculated structure Experimental Comments Basis set Re& CH 3+ planar STO 3G YC-" 1.120 A rC-" 1.076 A STO 4.31H 2 C2H3' H rl 1.281 r\ r2 = r3 = 1.106 A STO 3G rKy)<", C7-C-Hl rd = 1.106A I H-14 With same basis set bridged structure 5 6.76 kcal mol-' higher in energy STO 3G H4C2H = HlClH2= a r; 1.091 A ri 1.115 A r 1.403 A r2 1.348 A a = 102.2' p = 177.1" r3 1.099& 8 = 2.5' e = 46.60 5 = 113.6",vl = 116.7'.CI = 118.8" tY CH3CO+ rc-c 1.457 A 1.452 A in rc-o 1.11 A C,O 7s 3p H 3s GTO Y [CH3CO+SbC16-] rC-H (4,2,2) 1.09 A)assumed lCG.0 rc-c 1.452 A 1.452 A in rc-o 1.11 A C,O 9s 5p H 4s GTO 42 g [CH3CO+SbC16-] rC-H 1.09 A}assumed CGTO (5,3,3) % Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA m* d b m 0 2 2 0 2 0 5; L4 5; cn h I .-v) h ....4-33 -mmnc LLLL ern LL 74 D.T.Clark bond length is in good agreement with experiment and a population analysis reveals that the positive charge is essentially localized on the carbonyl carbon.42 The electronic structures of protonated methane and ethane have been extensively investigated. It is of interest to compare the results of Pople’s minimal-basis-set (STO 3G)14 calculations with those of Ray,43 using a very small basis set of FSGO’s.Both calculations indicate a structure of C symmetry looking roughly like a methyl cation plus a hydrogen molecule. From the location of the FSGO’s it is clear that CH5+ might be regarded as having three two-centre two-electron bonds and one two-electron three-centre bond. Interestingly enough the two approaches predict different results for C2H +. Pople’s STO 3G calculations predict a symmetrical bridged structure a noteworthy feature being the very long C-C bond length suggesting ready bond cleavage on protonation of alkanes. The FSGO basis-set calculation predicts a structure analogous to that for CH5+ i.e. a loose C2H5+-H2 complex. However Pople specifically con- sidered this type of structure and obtained an energy 11 kcal higher than for bridge-protonated ethane.It would therefore appear that limited-basis-set FSGO calculations are not entirely adequate for discussing the geometries of molecules. Thermochemical Data.-Relative Energies of Isomeric Species. It has already been noted in the Introduction to Section 2 that calculations within the Hartree- Fock formalism are incapable of reproducing heats of atomization of molecules as a result of the neglect of correlation energies. This deficiency is not necessarily as serious as it sounds because a large part of chemistry deals with the transforma- tions of one molecule into another or into smaller molecules. Where such trans- formations involve no change in the number of electron pairs correlation energy changes are quite small and hence calculations within the Hartree-Fock limit can often provide valuable thermochemical data.Some workers have expended considerable effort in parametrizing semi-empirical SCF MO treatments to accurately produce heats of atomization the most successful being Dewar’s MIND0 schemes.44 By incorporating experimental data into the theoretical schemes correlation energy changes on atomization can be accommodated. Unfortunately it would appear that the parametrization is highly specific with regard to the classes of compounds for which reliable results are produced and for charged species in particular the stabilities of species with a high degree of connectivity (e.g.bridged ions) are seriously ~verestimated.~~ This is an important point to appreciate for the average organic chemist who is not too much interested in the theory but more in the numbers that come out of the end of a program package.42 B. Rees A. Veillard and R. Weiss Theor. Chim. Acra 1971 23 266. 43 N. K. Ray Theor. Chim. Acta 1971 23 11 1. 44 C’ N. Bodor M. J. S. Dewar A. Hargret and E. Haselbach J. Arner. Chem. SOC. 1970 92 3854 and references therein. 45 C’ R. Sustmann J. E. Williams M. J. S. Dewar L. C. Allen and P. von R. Schleyer J. Amer. Chem. SOC.,1969,91,5350; N. Bodor and M. J. S. Dewar J. Amer. Chem. SOC. 1971,93 6685. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 75 In an elegant series of investigations Pople and co-worker~~~-~~ have shown how the limitations of the Hartree-Fock method for calculating heats of forma- tion may be circumvented by studying bond-separation reactions.The aim of this procedure is to estimate the energy of an organic molecule containing at least three heavy (non-hydrogen) atoms relative to the energies of simpler mole- cules containing only two heavy atoms but with the same types of bond. As an example consider a formal reaction in which a large molcule is one of the reactants and the products are the simplest molecules containing similar bonds between heavy atoms. Propene for example has one C-C bond and one C=C bond so that the products would be ethane and ethylene and hence to maintain the stoicheiometry a methane molecule must be added to the reactants uiz. CH,-CH=CH + CH -+ CH3-CH3 + CH2=CH2 A unique reaction of this type can be set down for any large molecule which can be represented by a classical valence structure without unpaired electrons or formal charges.Changes in correlation energy in such a reaction are very small and therefore with an adequate basis set the bond-separation energies may be accur- ately calculated. A few examples are given in Table 13. Having demonstrated the validity of this calculation the next step forward is to take the experimentally determined heats of formation for the small molecules together with the bond- separation energy in order to calculate the heat of formation of the original molecule (Table 13). In an extensive series of investigation^,^^.^' Pople and co-workers have provided valuable information on (a) isomerization in saturated systems (b) prototropic rearrangements and (c) isomerization of single- plus triple-bond systems to cumulated double bonds.The information thus provided (see Table 13) is invaluable since in many cases the relative energies of species can only be inferred from experimental data. It is evident from the few values given in Table 13 that even the minimal-basis- set STO 3G can give surprisingly good values for heats of formation in this way. It is interesting to compare the isomerization energies that have been obtained directly as calculated energy differences and those that have been derived from bond-energy analysis ; these are shown together for a representative series of systems in Table 13.Of particular note are the calculated energetic preferences of acetaldehyde over vinyl alcohol formaldoxime over nitrosomethane and keten over hydroxyacetylene. Heats of hydrogenation may also be successfully discussed. The application of even the minimal STO 3G basis set to larger organic molecules is computationally expensive and an interesting approach to looking -26 R. Ditchfield W. J. Hehre J. A. Pople and L. Radom Chem. Phys. Letters 1970 5 13. 47 W. J. Hehre R. Ditchfield L. Radom and J. A. Pople J. Amer. Chem. Soc. 1970 92 4796. 4H L. Radom W. J. Hehre and J. A. Pople J. Amer. Chem. Soc. 1971 93 289. L. Radom W. J. Hehre and J. A. Pople J. Chem. SOC.(A) 1971 2299. Table 13 Thermochemical information derived from non-empirical LCAO MO SCF calculations (1) Bond separation energieslkcal mol -Reaction Theory Exptl.Basis set CH3CHzCH2 + CH + C2H6 + C2H4 4.1 5.0 STO 4.31G CH2=C=CH2 +CH4 -+ 2C2H -4.6 -4.0 STO 4.31G NH2CH0 +CH4 -+ CH3NH2 +CH20 32.4 29.8 STO 4.31G (2) Heats offormationlkcal mol- ' CH3CH2CH3 -23.1 -24.82 STO 3G -23.8 STO 4.31G CH3CH2NH2 -10.0 -11.27 STO 3G -11.4 STO 4.31G CH3CH20H -53.6 -56.19 STO 3G -55.7 STO 4.31G CH3CH2F -61.8 -62.5 STO 3G -64.5 STO 4.31G (3) Isomerization energieslkcal mol- in saturated systems Process F-3 CH3CH2NH2 + CH3NHCH3 8.5 9.0 6.8 STO 4.31G -CH3CH2OH -+ CHjOCH 11.6 15.2 12.2 -OHCH20H + OHOCH 63.4 64.5 62.6 (4) Isomerization energieslkcal mol for prototropic rearrangements Process CH3CH=0 -+ CH2=CH-OH 12.9 14.6 CH3-N=NH -+ CH2=N-NH2 2.0 5.3 -STO 4.31G CH3-N=0 -+ CH2=N-OH -12.6 -3.1 NH2-CH=0 -+ NH=CH-OH 23.0 25.6 PhysicaI Methods-Part (iii) Theoretical Organic Chemistry and ESCA \D2 u? -1 I I l l ! l I l l I hs u?3- SO In I -cn m 4 -z 0-c h v s .- 0 ,p.0 c 2 9 - QJ M .- u,6 78 D. T.Clark at larger molecules has been developed by Christ~ffersen.’~ Basically the ap- proach is to use the computationally inexpensive FSGO basis set the non- linear parameters for each basis function (orbital radii location of FSGO’s) being determined by investigating suitable small fragments. (For hydrocarbons for example CH and CH,. have been used). Using the molecular fragment data ‘ab initio’ SCF calculations can be carried out relatively inexpensively on quite large molecules.The basis sets are very limited and typically produce values that are ca. 86 % of the Hartree-Fock energy whereas a minimal-basis-set STO-type calculation would typically give >96 % of the total energy. Nonethe- less for relative energies the method can give useful results. Calculations have been carried out on benzene and isomeric species fulvene 2,3-dimethylenecyclo- butene trimethylenecyclopropane and Dewarbenzene. Naphthalene azulene and fulvalene have also been investigated. The results are given in Table 13. It is clear that absolute energy differences are considerably overestimated (e.g. Dewarbenzene is probably -60 kcal less stable than benzene).It is interesting to note that the MIND0 procedure predicts51 the ordering benzene > fulvene > 2,3-dimethylenecyclobutene > Dewarbenzene > trimethylenecyclopropane. The electronic structures and relative energies of ortho- rneta- and para- benzynes have been evaluated ’ in an SCF treatment followed by configuration interaction (CI) to accommodate correlation-energy differences particularly between different electronic states. The results are given in Table 13. The salient features are as follows. At the geometry considered (corresponding to benzene with two hydrogens removed) ortho-benzyne is predicted to have a singlet ground-state. A single-determinantal SCF calculation predicts a triplet ground- state but the many-determinant CI wavefunction corrects for the large correlation- energy difference between singlet and triplet states.The Pauli exclusion principle ensures that correlation effects are built into the triplet wavefunction so that the effect of CI is to lower the energy of the singlet more than the triplet. A single-determinantal wavefunction does not adequately describe the weak interaction between the lone-pair-like a-orbitals owing to the undue weighting given to ionic terms (cf earlier sections). Both rneta-and para-benzyne are predicted to have triplet ground-states but with energetically relatively accessible singlet states. In absolute energies the predicted orders of stability are singlet states ortho > meta > para; triplet states para > meta > ortho and this order applies even for the single-determinantal treatments.Hydrogen-bonds. Deserving of special mention because of several notable aspects is a study ofthe interaction between molecules in the particularly import- ant case of the hydrogen-bonded guanine<ytosine base pair.53 For the Guinness Book of Records this enormous computational problem required 8 days of cpu time on the largest commerical computer available and involved the computa- tion sorting retrieving and processing of some 70 000 000 000 integrals over 50 R. E. Christoffersen J. Amer. Chein. Soc. 1971 93 4104. 51 N. C. Baird and M. J. S. Dewar J. Amer. Chem. Soc. 1969 91 352. 52 D. L. Wilhite and J. L. Whitten J. Amer. Chem. Soc. 1971 93 2859. 53 E. Clementi J. Mehl and W. von Niessen J.Chem. Phys. 1971 54 508. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 4 h-b-3 n22 GUANINE CYTOSINE h '2 ? * 1 I I I v 9 It 13 '1 15 ' 2 -I h-b-3 -2 --3 I I 1 I I I 1 Figure 8 Positions of the H atom along the three hydrogen-bonds in the guanine-cytosine base pair (Reproduced by permission from J. Chem. Phys. 1971,54 508) 80 D.T.Clark gaussian functions. It is a tribute to both computer manufacturers and more importantly to the large number of man years devoted to writing efficient pro- grams that calculations on this scale would not have been envisaged even 10 years ago. Nevertheless it would seem unlikely that computations of this order of magnitude will be undertaken in university environments in the foreseeable future.The calculations clearly illustrate the importance of the contraction technique since for the uncontracted basis set of 334GTO's -2.41 x lo9 integrals would have to be processed in the SCF calculation for each point on the potential-energy surface. The storage space required would occupy a few hundred magnetic tapes and would be physically impracticable. With a contracted basis set of 105 functions however the integrals can be stored on two magnetic tapes. For the base pair as shown in Figure 8 calculations were performed corres- ponding to independent movement of the hydrogens in each of the three hydrogen- bonds the geometries of and separation between the bases being fixed. The potential-energy curves are shown in Figure 9 and it is clear that only a single minimum is calculated for each hydrogen-bond.This contrasts with earlier semi- empirical work which predicted double minima. It should be pointed out however that despite the huge computational effort involved in producing Figure 9 the treatment cannot be regarded as providing an adequate overall picture for hydrogen-bonding in this system. Each hydrogen-bond was studied independently of the other two (the other two have the hydrogens fixed at the equilibrium position). Co-operative effects may well be important and this would require a much larger computational program to be carried out with the geo- metry searches over a three-dimensional grid. It is also undoubtedly true that there will be small changes in geometry (particularly about the carbonyl and amino-groups involved in hydrogen-bonding) as a function of the positions of the hydrogens although in a co-operative motion this effect would tend to cancel.Potential-energy Surfaces for Organic Reactions.-The most exciting deveiop- ment in the past three years in theoretical organic chemistry has been the applica- tion of rigorous quantum-chemical techniques to the study of organic reaction mechanisms. Since the p~blication~~ in 1969 of the first non-empirical cross- sections through a potential-energy surface for an organic reaction (the cyclo- propyl-ally1 cation transformation) progress has been made with regard to several reactions of fundamental importance. The single most detailed study due to Salem and co-worker~,~~ has defined a transition state for the geometrical isomerization of cyclopropane.The electrocyclic transformation of cyclobutene to butadiene has been st~died,~~,~~ and also cross-sections through the potential- energy surfaces for prototype bimolecular nucleophilic displa~ernents~~-~~ and 54 D. T. Clark and D. R. Armstrong Theor. Chim. Acra 1969 13 365. L. Salem XXIIIrd International Congress of Pure and Applied Chemistry Butterworths London 1971 vol. I p. 197. 56 K. Hsu R. J. Buenker and S. D. Peyerimhoff J. Amer. Chem. SOC.,1971,93,2117. 57 R. J. Buenker S. D. Peyerimhoff and K. Hsu J. Amer. Chem. SOC.,1971 93 5005. 5h A. Dedieu and A. Veillard Chem. Phys. Letters 1970 5 328. sy A. Dedieu and A.Veillard 21'"' Reunion Annuelle de la Societe de Chimie physique Paris Sept. 1970. '' A. J. Duke and R. F. W. Bader Chem. Phys. Letters 1971 10 631. t -92802 C -92804 --92806-3 0 -$ -92808 -z -92810 -i I -92812 1 1 -928 14 L 1--92815 DISTANCES (0 u 1 Figure 9 Potential energy curves for h-b-1 h-b-2 and h-b-3 for guanine-cystosine base pairs (Reproduced by permission from J. Chem. Phys. 1971,54 508) 82 D.T. Clark electrophilic additions to olefins.28 In probably the most significant paper theoretically Basch61 has calculated a reaction path for the dimerization of methylene including a large part of the correlation change in a multi-configura- tion SCF treatment. The Geometrical Zsomerization of Cycl~propane.~~ In a Report of this size it is not possible to do justice to this major contribution to the chemical literature.Any chemist who wants to get a feel for the difficulties inherent in constructing a multi-dimensional potential-energy surface for even a simple organic reaction can do no better than read Salem's paper.55 This meticulous and painstaking attempt at the total resolution ofa transition state for an organic reaction extended over 2 years required 350 hours of IBM 360/75cpu time and involved the computation of -700 points on the 21-dimensional surface. The calculations employed a minimal STO basis set and in the region of trimethylene diradical (see later) a 3 by 3 configuration interaction calculation was performed between the ground (tj') doubly excited [(tj')2],and singly excited (4~') configurations.This accounts for a considerable portion of the correlation energy of one electron pair. The steps in the construction of the potential-energy surface then proceeded along the following lines. The geometry of cyclopropane itself was first optimized together with thsO exponents. The calculated geometry Rc-c = 1.479 A RC+ = 1.082A HCH = 112.8" is in good agreement with experiment (Rc-.c = 1.510 +_ 0.002& RC+ = 1.089 +_ 0.003 A and-= 115.1" & lo). Possible reaction mid-points having reflection symmetry were then investigated followed by a study of 'Type I' reaction pathways constrained to proceed uia such mid-points. This initial search relies on the fact that reactant and product (cyclopropane) are mirror images with respect to the plane of the carbon atoms so that the reaction can proceed via a mid-point which has the mirror plane as a symmetry element and this corresponds to a synchronous narcissistic process (see ref.5). Having studied such a reaction path the constraint of passing through a symmetrical mid-point was lifted and 'Type 11' pathways which avoid a symmetrical mid-point were investigated. The final structure of the transition state is shown in Figure 10. Although the minimum-energy pathway to the transition state has not yet been finally elaborated Figure 11 shows a typical calculated pathway which could be followed by the molecule during geometrical isomerization. The C-C bond first lengthens until at a CCC angle of 113" the face to face [FF] configuration of trimethylene diradical is reached.(The CI treatment ensures that the extensive bond-lengthening is relatively well described). At this point 48.4kcal mol- have been expended. The isomerization process now occurs in an enlarged ring with very little energy change the calculated activation energy being 52.6 kcal mol- '. From face-centred trimethylene diradical the terminal CH groups undergo an initial conrotatory motion; however between 60 and 90" in angle of rotation of the principal group the other terminal group reverses into a disrotatory motion. At 90" the edge-to-face 61 H. Basch J. Chem. Phys. 1971 55 1700. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 00 -.-.1 z 0 t- -L 0 60" 80' 90" 95" (.(I 112.5 *& aH~ (EFI' TS HB'P q%HB 180" ' HA ~e-3 100' 120" 140' 160" "HA (FF)' 'HA Figure I1 "on-minimum' energy pathway via the transition state in the geometrical isomerization of cyclopropane.The methylene rotation angle 4 is shown in the lower centre (Reproduced by permission from XXIIIrd International Congress of Pure and Applied Chemistry Butterworths London 1971 vol. 1 p. 197) 7 0 ij-% Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA configuration of trimethylene diradical is reached in which both methylene groups are pyramidalized on the same side of the plane. Proceeding via the transition state the forward rotation of the principal group is assisted by a forward-backward-forward rotation of the other group until at 180" the face-to- face configuration of trimethylene with pyramidalization at the principal group is reached.Depyramidalization is then followed by ring closure to complete the geometrical isomerization. The pathway is chiral without any symmetric mid- point (Type 11). The non-synchroneity of such a pathway is apparent from the delayed crossing of the carbon-carbon plane by the external hydrogen atom A relative to the internal hydrogen B. The transformation can thus be seen as a stretching motion involving a steep energy surface followed by rotational motions on a fairly flat surface. S,2 Reactions. Cross-sections through the potential-energy surfaces for the following SN2reactions have been c~mputed.~~-~' (a) H-+ CH4 + (CH5)--+ CH4 + H- (b) H-+ CH3F + (CFH4)-+ CH,F + H- (c) F-+CH3F + (FCH,F)-* CH3F +F- (d) CN-+CH3F -* (CNCH,F)-+ CH,CN +F-' It is important to realize that a sufficiently large and flexible basis set must be used in studying such systems to accommodate the considerable changes in electron distribution in proceeding from reactants to products.To describe adequately the diffuse charge distribution in the non-bonding regions in CN- for example a large basis set including polarization functions is required.60 (From this point of view it is probably true that results for anionic species are more critically dependent on basis set than those for cationic species).These represent important prototype systems for assessing the importance of solvation terms in S,2 reactions since the calculations refer to isolated mole- cules in the gas phase. The salient features are given in Table 14. For the hypo- thetical reaction involving CH and H-the transition state is calculated to have D3h symmetry and the calculated activation energy is 60.2 kcal mol-'. The calculations show that there is a decrease in the C-H bond length compared with CH for the hydrogens in the plane. This is also apparent in the reaction CH,F + H-+CH,F + H-. There are two interesting features evident in comparing the calculations. First replacement of H by F at the reaction centre lowers the activation energy to 55.3 kcal mol-' and secondly all the C-H bonds are significantly shortened.The reaction F-+ CH,F -+CH,F + F-has been studied by Veillard and Dedie~~~,~~ and also by Bader and Duke,60 and the two sets of results are in good agreement. It is interesting to note that although Veillard and Dedie~~*?~~ used a larger basis set of primitive functions by choosing a better grouping in the contracted functions Bader and Duke6' obtained lower total energies. The calculated activation energies are in good agreement and again the C-H bonds are somewhat shorter than in the reactant. The extensive delocalization of the negative charge is evident from the density contour map,60 00 Table 14 Non-empirical calculations on S,2 reactions m Reaction Heat of reaction Activution Geometry of T.S.Basis set /kcal mol -burrier /kcal mol- \ H-+CH + CH,+ H-0 60.2 H,/' C 1 Is 7p,Id GTO contracted 1.063 A 5s 3p Id H 6s lp GTO i 4\11709A contracted 3s lp H-C-H Hq-H 2 > 59 H-+CH3F -+ CH3F +H- 0 55.3 9 5 4 GTO 5 3 3 C GTO C-F distance kept at 1.42 A since optimization leads to departure of F-J F-+CH3F + CH3F +F- 0 7.9 Geometry optimized with basis set as for H-+ CH3F. Activation barrier calculated with basis set for H-+ CH F-+CH3F -+ CH3F +F- 0 7.14 9 5 4GT0 5 3 3 C GTO for geometry searches F-+ CH3CN -+ CH3F + CN-5.24 17.33 Energy differences from final geometries C F N 10,6 60 7 6 GTO 5 3 3 CGTO augmented by polarization functions for CN s and p c polarization x. functions add.Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 87 and by spatial partitioning of the molecular charge distribution the approximate charges are -0.86e on each fluorine and +0.73e on the CH fragment. This is in line with the experimental observation that electron-releasing substituents are activating. This also suggests that the solvation of the transition state will be considerably smaller than that for the reactants and thus solvation energy terms are expected to contribute a substantial portion to the observed activation energies for S,2 reactions. For the F- + CH3CN reaction a heat of reaction of -5.24 kcal mol- is computed. An approximate geometry optimization for the (FCH,CH)- species shows it to be 17.33kcal mol- ’ higher in energy than the reactants.It is note- worthy that the C-F bond is calculated to be rather long so that the transition state looks rather more like the reactants. This provides a striking theoretical verification of the oft-used Hammond-Polanyi6’ postulate. Dinzerization of Methylenes. The dimerization of methylenes to produce ethylene might be considered as the simplest concerted cycloaddition (a double bond being considered as a two-membered ring) and hence provides a simple case where the results of a rigorous theoretical treatment can be compared with qualitative ideas based on conservation of orbital symmetry. The least-motion coplanar approach of two singlet methylenes to form ground-state ethylene is readily shown to be symmetry-forbidden due to a level crossing.This crossing in the orbital correlation diagram should lead to an avoided crossing in the state-level diagram. This could arise from the situation that the lowest-energy electronic configuration of ethylene is not the lowest-energy configuration of two singlet coplanar methylenes at large distances from each other. The single-determinantal Hartree-Fock theory is unable to describe such a situation correctly. A multi-configuration approach (see ref. 63) improves on the Hartree-Fock result by including the important parts of the correlation energy error implicit in going to the wrong dissociation limits and in the over-estimation of ionic term contribu- tions to the single-configuration-wavefunction formalism. The implementation of MC SCF theory has proved computationally difficult for other than diatomic molecules but an important step forward has now been taken by Basch6’ in studying the reaction path for the dimerization of methylenes.The ground state of ethylene is given by 11) = (core)”(02)(n2) whereas the electronic configuration of two appropriately oriented singlet methylenes is 111) = (core)”(o)’(o*)’ differing from that for ethylene by the pair excitation (x’ -+ a*’). Other configurations which might be considered which involve the o,n,o*,and n*-orbitals are 1111) = (core)’2(o)2(n*)2 (IV) = (core)’2(n)2(n*)2 IV) = (core)’2(n)2(o*)2 IVI) = (core)’2(n*)2(o*)2 62 G. S. Hammond J. Atnrr. Chem. SOC.,1955 77,334. 63 E. Clementi Chem. Rev. 1968 68 341.88 D.T. Clark and these form a complete set of functions with regard to distributing two (spin- paired) electrons over four orbitals. The multi-configuration wavefunction may then be written as $ = C,II) + CI,lII) + CIlIIIII)+ C,,IIV) + CvIV) + CvllVI). The total energy is then minimized by applying the variational principle to both the orbitals and the configuration expansion coefficients and by constraining the orbitals to be normalized. Calculations were carried out at nine carbon-carbon internuclear distances and the results are shown in Figure 12 for the two lowest- energy solutions. -77.10 -.60-5-.80--78.00 -I I 0 2 4 6 8 AR Figure 12 The lowest-energy MC SCF solutionsfor the dimerization of methylene (Reproduced by permission from J.Chem. Phys. 1971,55 1700) Before considering these results it is interesting to recall the results obtained by Hoffmann et a/. using extended Huckel theory.64 They found that the lowest- energy singlet configuration of the methylene dimer changes at a C-C distance of -3 I$ with 11) being the lowest-energy configuration at the normal ethylene geometry and 111) the lowest-energy configuration at large internuclear separa- tions. This analysis then purports to show that there will be an avoided crossing and therefore a barrier to be overcome during the reaction. The MC non- empirical study shows this not to be the case. Analysis of the two wavefunctions as R + ashows that the dissociation limit for the lower energy pathway corres- ponds to two triplet-state methylenes (two triplets can be coupled to give the proper spin and space symmetry to interact with the closed-shell ethylenic electronic configuration).The coplanar interaction of two triplet methylenes (the triplet state is in fact the ground state of methylene cf Section on molecular geometries p. 68) is therefore predicted to occur without activation barrier 64 R.Hoffmann R. Gleiter and F. B. Mallory J. Amer. Chem. Soc. 1970 92 1460. Physical Methods-Part (iii)Theoretical Organic Chemistry and ESCA to produce ground-state ethylene. Analysis of the higher-energy repulsive path- way shows that the dissociation limit does in fact correspond to two singlet methylenes which are therefore predicted not to dimerize since the reaction path is completely repulsive.This detailed MC treatment shows the deficiencies of not only simple MO treatments of bond making and breaking but also at the non-empirical level of the Hartree-Fock method. The Electrocyclic Transformation of Cyclobutene to cis-Butadiene. One of the early successes of conservation of orbital symmetry arguments was the rational- ization of the stereospecific thermal conrotatory ring-opening of cyclobutene derivative^.^ Clearly however more information besides the symmetry rule is needed before one can state that the reaction mechanism is understood. For example does the rotation in a conrotatory (or disrotatory) fashion occur before after or during the bond-breaking process? More generally it is desirable to determine the true reaction path since only then is it possible to calculate the activation energy.Buenker Peyerimhoff and Hsu~~ have now analysed in detail several cross-sections through the potential-energy surface for this trans- formation. In the process of deducing the minimum energy path in the trans- formation it is necessary to take account of 24 degrees of freedom so that some simplifying assumptions need to be made. It seems reasonable to assume that in a \ Figure 13 Dejinition of geometrical parameters for the C,H system (Reproduced by permission from J. Amer. Chem. SOC. 1971 93 2 1 17) concerted process a certain degree of symmetry is maintained throughout the course of reaction and this reduces the number of independent geometrical parameters.Figure 13 shows the C,H system in such a symmetrical con- figuration. Knowing the experimental geometries of both cyclobutene and buta- diene an intelligent guess can then be made as to which parameters remain essentially unchanged throughout the transformations (the C-H bond lengths D.T. Clark for example). Clearly the parameters which exhibit the largest changes as the reaction proceeds are the out-of-plane angle of rotation of the methylene groups and the C(lFC(4) bond distance R. Parameters which exhibit significant but not exceptionally large changes during the isomerization are the other C-C bond distances RB(central bond) and RD(lateral bond) and the angles CI and B. The distances R and RDcan conveniently be defined in terms of an auxiliary para- meter varying continuously from 0-1.The general procedure utilized therefore is to treat the C( 1)-C(4) distance R and the methylene rotation angle as principal independent variables and the other less critical parameters may then also be varied but not optimized as thoroughly. The interesting features which emerge from the study are as follows. The energetically favoured mode of rotation of the methylene groups in the ring opening of cyclobutene is critically dependent on the distance R. For R = 2.9 a.u. (approx. the distance in cyclobutene itself) rotation of the methylenes into the plane is energetically very expensive (-400 kcal mol- ') and in fact the favoured mode is then the disrotatory. The energy required to effect this transformation is calculated to drop quite rapidly as R increases and the favoured mode then becomes the conrotatory.For every distance R the lowest-energy conformation is calculated to have 8 either equal to 0 or 90" and this raises the question as to how the rotation takes place for either the forward or the reverse reaction. The only reasonable answer seems to be that the methylene rotation takes place entirely at the distance R (or at least a very narrow range of R) for which the 0 and 90" conformations have approximately equal energy. This implies that as in the geometrical isomerization of cy~lopropane,~~ rather then being a smooth continuous transformation there is first of all a bond-stretching process which is then followed by rotation of the methylenes with very little change in ring geo- metry before there is a final relaxation into the cis-butadiene structure.The crossing point at which the energies of 8 = 0 and 8 = 90 conformations are equal is calculated to occur at R = 4.32a.u. SCF calculations corresponding to 15" intervals in rotation at this distance were investigated and the result- ing potential curves are shown in Figure 14. The conrotatory mode is clearly favoured the potential-energy curve being fairly symmetrical with a maximum barrier height (0 = 51") of 20 kcal mol-'. Since there is a change in ground-state electronic configuration for the disrotatory mode a configuration interaction cal- culation is required in order to adequately describe this mode of transformation.The results of CI calculations are also shown in Figure 14,and the conrotatory mode is calculated to be approximately 13.6 kcal mo1-l lower in energy than the disrotatory one. The distance R at which the 8 = 0 and 90" conformations have the same energy is computed to be slightly longer (4.49a.u.) when CI is taken into account. The energy required to stretch the C-C bond to this distance starting from cyclobutene is calculated to be -27 kcal mol- ',and for the pure conrotatory motion at this bond length a further -20 kcal mole-' is required. The overall activation energy is therefore calculated to be -47 kcal mol -' in reasonable agreement with experiment (dimethylcyclobutene 35 kcal mol -I). Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 91 1 -90-\ \ -110 \ \ '3Ot THETA POTENTIAL CURVES AT R ?I7Pk -19 67, I Figure 14 Total energy for the con- and dis-rotatory C,H structures as a .function of the rotation angle 0.The lower curves refer to the CI calculctions and the energies for cyclobutene and cis-butadiene are also given (Reproduced by permission from J. Amer. Chem. SOC. 1971,93 21 17) The striking feature evident in this study and in the geometrical isomerization of cyclopropane is the demonstration that these simple concerted organic reactions proceed in distinct stages of bond stretching followed by rotation rather than proceeding in a continuous manner. The fact that rotation takes place over a very narrow range of R indicates that it is at this distance that one should calculate orbital and state correlation diagrams for comparison with the qualitative Woodward and Hoffman diagrams.In a further paper Buenker Peyerimhoff and Hsu' have in fact analysed qualitative theories of electrocyclic transformation in terms of the results of 'ah initio' SCF and CI calculations. 3 Electron Spectroscopy for Chemical Analysis (ESCA) Introduction.-In the previous section of the Report the results of non-empirical calculations on a wide variety of organic systems were discussed in some detail. Such calculations explicitly consider all the electrons both core and valence 92 D. T. Clark and hence give (via Koopmans’ theorem) the energy levels in a molec~le.~~~~~ Electron Spectroscopy for Chemical Analysis* (ESCA) developed by Professor Kai Siegbahn at Uppsala University gives an experimental technique for the direct observation and measurement of both core and valence energy levels of molecule^.^^*^^ Although the technique has been developed over the past 20 years or so it is only in the past few years that applications in organic chemistry have revealed the great potential of the technique for studies of structure and bonding.The range of application is already very great ranging from systematic studies of substituted effects in simple organic molecules69 to quantitative evaluation of cereal grain nutritional value.” Clearly the next few years will witness a dramatic growth in applications of ESCA to organic chemistry across a broad front.The principal advantages of the technique are as follows (1) The sample may be a solid liquid or gas (it is as easy to study a high- molecular-weight polymer as it is to study a gaseous sample). (ii) The sample requirement is modest. In favourable cases 1 mg of solid 0.1 ,d of liquid or 0.5 cm3 of gas (at STP) will suffice. (iii) The technique has high sensitivity is independent of the spin properties of any nucleus and is applicable in principle to any element of the Periodic Table. (iv) The information it gives is directly related to the electronic structure of a molecule and the theoretical interpretation is relatively straightforward. (v) Information can be obtained on both the core and valence energy levels of a molecule. In terms of the sheer amount of useful data produced per sample ESCA is probably the most powerful spectroscopic tool available to chemists.The actual experiment performed is extremely simple and involves the measurement of binding energies of electrons in molecules by determining the energies of electrons ejected by the interaction of a molecule with a mono-energetic beam of X-rays. In principle all electrons from the core to the valence levels can be studied and in this respect the technique differs from U.V. photoelectron spectros- copy in which only the lower-energy valence levels can be studied. For a variety of reasons the most commonly useful X-ray sources are AlKcr,, and MgKcc,,, 65 W. G. Richards internat. J. Mass Spectrometry ion Phys. 1969 2 419.66 D. T. Clark and M. Barber Chem. Comm. 1970 22. 67 K. Siegbahn C. Nordling A. Fahlman R. Nordberg K. Hamrin J. Hedman G. Johansson T. Bergmark S.-E. Karlsson I. Lindgren and B. J. Lindberg ESCA- Atomic Molecular and Solid State Structure Studied by Means of Electron Spec- troscopy’ Nova Acta Regiae Soc. Sci. Upsaliensis Ser. IV Vol. 20 1967. Revised edition in preparation by North-Holland Publishing Co. Amsterdam. 68 K. Siegbahn C. Nordling G. Johansson J. Hedman P. F. Heden K. Hamrin U. Gelius T. Bergmark L. 0. Werme R. Manne and Y. Baer ‘ESCA Applied to Free Molecules North-Holland Publishing Co. Amsterdam 1969. 69 D. T. Clark and D. Kilcast J. Chem. Soc. (A) 1971 3286. 70 M. P. Klein and L. N. Kramer Improving Plant Protein Nucl. Tech. Proc. Symposium Lawrence Radiation Lab.Tech. Report 243-52 1970; (Chern. Ah. 1971,75 105 912a). * Also variously called X-ray Photoelectron Spectroscopy (XPS) Induced Electron Emission Spectroscopy (IEES) and High-Energy Photoelectron Spectroscopy (HEPS). Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 93 with photon energies of 1486.6and 1253.7 eV respectively. Relevant background material is given in references 67 and 68. Major fields of application of ESCA in organic chemistry in the past year are detailed below and rather more space will be devoted to the topic in subsequent Reports. Analysis.-Since the binding energies of core levels are characteristic of an element one obvious area of application is in chemical analysis.The constituent elements of a molecule are readily identifiable (Figure 15 shows a trivial example)69 and with calibration of relative cross-sections the empirical formula may also be determined. A novel application due to Klein and Krame~-,~' employed ESCA to analyse the quantity and quality of grain protein. The sample requirement of a few milligrams and the non-destructive nature of the technique are of particular relevance in this connection since it is feasible to excise a small section of a seed for analysis whilst retaining the remainder for planting. With modern instrumentation an analysis can be performed in -10 minutes. The quantity of protein may be determined by integration of the total photoelectron peak associated with the N, levels. Two measurements of the quality of protein were employed.The basic amino-acids lysine arginine and histidine can be estimated from a deconvolution of the N, levels into amino and amide types. The sulphur-containing amino-acids cystine cysteine and methionine can be estimated from the Szpcore levels. Typical data for Rapida Oats and Light Red Kidney Bean are included in Table 15. Table 15 Comparison of results for analysis of grain protein using ESCA and conventional analysis Seeti Elemental analysis "/,N (ESCA) "N (wet %S (ESCA) %S (wet analysis) analysis) Rapida Oats 2.2 f0.2 1.9 0.2 0.1 f0.3 0.02 0.02 Light Red Kidney Bean 3.2 f0.3 4.1 & 0.3 0.08 f0.04 0.13 f0.06 Light'x basic Red Kidney Bean A.A. 17.5 f5 17.4 It should perhaps be emphasized that in studying solids ESCA is essentially a surface technique and depending on the core level studies and using the usual photon sources the escape depth of photoelectrons is in the range CrlOOA.Thus ESCA provides a powerful tool for surface analysis and applications in biological chemistry (e.g. cell walls) will undoubtedly be of considerable import- ance in the future. Preliminary studies on nucleic acid bases" and t-RNA72 have already appeared. 7' M. Barber and D. T. Clark Chrtn. Cnmm. 1970 22 23 24. 72 L. D. Hulett and T. A. Carlson Clinical Chem. 1970 16 677. f1s A x10 U 'lt1' --t.f't ' 25.fi.l. 695 I 690 610 630 650 292 288 284 278 270 206 198 28 50 32. 16 8 Binding energylev Kinetic cnergyleV Binding energy / eV Figure 15 High-resolution photoelectron spectrum of CF,CHCI excited by MgKa,, Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA Theoretical Chemistry.-Having measured a spectrum one is posed with the problem of interpreting it qualitatively and quantitatively in terms of the elec- tronic structure of the molecule.In general however it is not the absolute binding energy of a given core level which is of interest but the ‘shifts’ with respect to some reference. It has been shown73 from extended-basis-set calculations on small molecules that ‘shifts’ in core binding energies may be quantitatively described by considering the orbital energies of the neutral molecules. It is of considerable interest therefore to see if minimal-basis-set ‘ab initio’ calculations on larger molecules can also adequately describe shifts in core binding energies.In an extensive series of studies Clark and co-w~rkers~~~~ have now investigated this point for a considerable number of important organic molecules for which non-empirical calculations are available. Of particular interest are the results for the five-membered ring heterocycles pyrrole furan and thiophen 74 the and six-membered ring heterocycles pyridine and pyra~ine,~~ the bicyclic hydrocarbon naphthalene.’ The five-membered ring heterocycles have also been investigated by Siegbahn and co-~orkers~~ and the results are compared in Table 16. The results are in good overall agreement notable features being Table 16 Calculated and observed C, shifts Molecule ShiftIeV Experimental Re$ calculatedfrom shiftlev orbital energies Py rr ole ~(2~3) 1.25 0.90 74 0.98 77 1.10 74 1.20 77 Thiophen C(2)-C(3) 0.0 0.0 74 0.3 0.3 77 Pyridine C(2tC(3) C(2)-C(4) -0.8 -0.6 -0.4 76 Pyrazine Naphthalene C-C(2) (pyridine) C( 2)-C( 9) 0.5 1.o 0.6 0.8 76 75 the observed and calculated trends of shifts in the order thiophen < pyrrole < furan for the five-membered rings and the alternation in binding energies in the pyridine ring.For naphthalene the higher binding energies of the bridgehead carbons are confirmed. Non-empirical calculations are not feasible on the vast majority of compounds of interest to the organic chemist and a considerable effort has therefore been 73 Cf.D. W. Davis J. M. Hollander D. A. Shirley and T. D. Thomas J. Chrm. Phys. 1970,52 3295. 74 D. T. Clark and D. M. J. Lilley Chem. Phys. Letters 1971 9 234. 75 D. T. Clark and D. Kilcast J. Chem. SOC.(B) 1971 2243. ’‘ D. T. Clark R. D. Chambers D. Kilcast and W. K. R. Musgrave J. C. S. Faruduy II 1972 68 309. ’’ U. Gelius C. J. Allan G. Johansson H. Siegbahn D. A. Allison and K. Siegbahn UUIP 746 Institute of Physics Uppsala 1971. D.T.Clark expended to develop reliable theoretical models which can be used to quantify results for larger molecules. By expanding the expression for the Fock orbital energies it is possible to show that the binding energy of a core level is related to the charge distribution in a molecule.68 The relationship [equation (14)]has been extensively discussed in the literature and shifts in C, levels for substituted aliphatic,6y aroma ti^,'^ and heterocyclic molecule^^^"^ can be quantitatively described by the charge potential model in terms of CND0/2 SCF MO charge distributions.(Figure 16 shows one such correlation for aromatic hydrocarbons and their perfluoro- analogue^).^^ The model can also be used to assign core levels when there is ambiguity. For thiazole for example the CISspectrum appears as three distinct peaks and the assignment Figure 16 Plot of binding energieslev corrected ,for the Madelung potential against the charge as calculated by the CNDOI2 method for the C, levels for aromatic hydro- carbons and perjluoro-analogues may be made74 on the basis of CND0/2 calculations.The results are shown in Table 17. From equation (14) it is evident that molecular core binding energies reflect the overall potential at each atom provided by the valence electron distribution and therefore they tend to parallel what might be termed the organic chemists’ Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 97 Table 17 Calculated and experimental electron binding energies of thiazole Atom Calculated rel. E~perimental’~ binding energylev binding energylev urom equation ( 1411 C(4) +0.7 +0.4 (32) (0.0) (0.0) (25) -1.2 -0.7 ‘intuitive’ charge distributions derived from considering the chemistry of the This most valuable feature of ESCA that the shifts in binding energies can be quantitatively described by calculations on the ground-state molecule will be discussed in more detail below.Relationship to Other Data.-Thermodynamic Data. In a brilliantly original approach Jolly and Hendrick~on~**~~ have shown that it is possible to estimate thermodynamic data from measured core binding energies and vice versa. Particularly valuable information which may be obtained in this way includes the gas-phase proton affinities for organic molecules. Table 18shows some represen- tative data.77 Table 18 Proton afinitie~,~* estimated using ESCA Compound Proton afinitylkcal mole-Pyrrole 247 CH,NH 247 CH,CONH 239 n-C,H,OH 202 C,H50H 192 Clark and Adamsso have utilized the equivalent-core thermodynamic approach in a study of shifts of core binding energy in halogenated methanes.Theoretically calculated heats of reaction give a good overall account of shifts in C, levels within the limited series of fluorinated and chlorinated methanes. This provides an alternative to the use of the charge-potential model for assigning and quantita- tively discussing shifts in core binding energies. N.M.R. Chemical Shifts. The shift in core binding energies on a given nucleus can be related theoretically to the diamagnetic contribution to the (n.m.r.) chemical shift for that nucleus.*’ It seems likely therefore that ESCA studies will provide valuable information complementary to that obtained in many cases by n.m.r. For a closely related series of compounds it can be shown that the 78 W.L. Jolly and D. N. Hendrickson J. Amer. Chetn. Soc. 1970 92 1865. 79 Cj J. M. Hollander and W. L. Jolly Accounts Chem. Res. 1970 3 193. 8o D. T. Clark and D. B. Adams Nature Physical Science 1971 234 95. ’’ H. Basch Chem. Phys. Letters 1970 5 337. 98 D.T.Clark factors dominating the screening constant for a given nucleus are similar to the factors contributing to the shift in molecule core binding energy.69 This has been nicely dem~nstrated~~ for the series CH, CH,Cl, CHCI, CCl, and a linear relationship between 13C chemical shift and C1 binding energy exists. These data69 also illustrate the limitations of ESCA in terms of resolution compared with high-resolution n.m.r. spectroscopy. In going from CH to CCl for example the C, shifts span a range of 7.1 eV with typical line- widths of 1.2 eV using MgKa,.photon source. The corresponding figures for 13C n.m.r. are 100 p.p.m. and -0.1 p.p.m. By far the largest contribution to the C,,linewidths comes from the photon source (-0.8 eV) and the advent of X-ray monochromators with the concomitant decrease in photon linewidth will considerably improve the attainable resolution in ESCA. It should be empha- sized however that the natural linewidths of core levels of interest to organic chemists are not inconsiderable e.g. for C, 5 0.2eV so that even with mono- chromatization the ratio of total shift to natural linewidth will still be considerably larger fdr 13C n.m.r. ESCA does of course have many areas of application in organic chemistry where n.m.r.spectroscopy cannot compete (e.g. the study of certain polymers study of surfaces etc.); however in many fields of application the two techniques give complementary data and hence too much stress should not be Fut on competition between the two as structural tools. One point which may not yet be appreciated is the fact that ESCA gives the chemist one of the fastest timescale measurements typically -10-l5 s and can therefore provide information for some systems not available to the relatively long timescale encountered in n.m.r. spectroscopy. Application to Organic Systems.-Systematic Investigations of Substituent Eflects. The results of systematic investigations have been published for a wide variety of organic molecules ranging from organosulphur compounds8 to halogenated aliphati~,~~?~ aroma ti^,^^^^^ and heterocyclic corn pound^.^^.^^ The factors determining substituent effects are now well understood and the results may be quantified in terms of either non-empirically calculated orbital energies or the charge-potential model.A few representative examples illustrate the immediacy of results. The shifts in C1 binding energies as a function of substituent X in the series CC1,X and CC1,HX have been investigated and the results are shown in Figure 17. Overall electron-attracting groups (with respect to H) increase the binding energy e.g C1 CF, Br CCl, whereas electron- releasing substituents such as Ph decrease the binding energy. The shifts in core binding energy therefore reflect fairly directly the organic chemists’ qualita- tive ideas concerning the charge distribution about the carbon atom.This is also shown by the results for monosubstituted benzenes.84 In fluorobenzene for example the order of decreasing C, binding energy is C(l) > C(3)C(5) 82 U. Gelius P. E. Heden J. Hedman B. J. Lindberg R. Manne R. Nordberg C. Nord-ling and K. Siegbahn Phys. Scriptu 1970 2 70. 83 B. J. Lindberg J. Bernt K. Hamrin G. Johansson U. Gelius A. Fahlman C. Nordling and K. Siegbahn Phys. Scriptu 1970 1 286. 84 D. T. Clark D. Kilcast and W. K. R. Musgrave Chem. Comm. 1971 516. Physical Methods-Part (iii)Theoretical Organic Chemistry and ESCA Figure 17 Correlation between C, levels for the series CC1,X and CHC1,X (meta) > C(2)C(6)(ortho)> C(4)(para) and this again parallels the organic chemists’ ‘intuitive’ charge distributions.The effect of halogen substitution on molecular core binding energies has been extensively investigated for polycyclic aromatic hydrocarbons’ and six-membered-ring heterocycle^.^ With the information derived from fundamental series such as these the way is now open to development of the technique as a major structural tool. Structural Applications. (a)Carbonium ions. Preliminary accounts of two exciting applications of ESCA to carbonium ion chemistry have been reported. Olah and co-~orkers~~ have measured the C, levels of t-butyl trityl and tropylium cations. The measured C, levels for t-butyl cation reveal the high positive charge at C(1) and the shift between C( 1) and the methyl carbons of 3.4 eV may be compared with the results obtained from an ‘ab initio’ calculation of orbital energy differences of 4.45eV.(There are sound theoretical reasons why the two should not be identical since the calculation neglects lattice contributions to the shift which are of some importance for charged species.) By contrast both trityl and tropylium cations studied as their hexafluoroantimonates show only a single C, line behaviour that is consistent with extensive charge de- localization. A preliminary account has also been presented of studies on 1- adamantyl and norbornyl cations.86 By comparing the two it would appear that the formal charge in norbornyl cation is extensively delocalized which strongly suggests a non-classical structure for the ion.(b) Structure ofthiathiophthens. The electronic structure of 6a-thiathiophthens has intrigued chemists for some considerable time and the question of a sym- *’ G. A. Olah G. D. Mateescu L. A. Wilson and M. H. Gross J. Atner. Chem. Soc. 1970 92 7232. 86 G. D. Mateescu and J. L. Reimen-Schneider Asilomar International Conference on Electron Spectroscopy 1971 to be published by North-Holland Publishing Co. Amsterdam. 100 D.T. Clark metrical (1) or unsymmetrical (2) structure has now been investigated by ESCA.S~-S~ m s-s s By measuring the sulphur molecular core binding energies in principle a fundamental distinction may be made between the two possible structures. CNDO SCF MO calculations for example on symmetrical and unsymmetrical structures used in conjunction with the charge potential model predict that in the symmetrical structure the core levels of the central sulphur atom should be much more tightly bound than those for the two outer sulph~rs.~~*~~ For an unsymmetrical structure however the three sulphurs are predicted to have different core binding energies in the order S(6) < S(l) 4S(6a).For the un- symmetrically substituted 2-methylthiathiophthen and for the sterically crowded 3,4-diphenylthiathiophthen the results are clear-cut and the observation of three distinct sulphur core binding energies for each molecule demonstrates that these molecules have unsymmetrical ring geometriess8 (i.e. one short and one long S-S bond).For the 3,4-diphenyl derivative this result confirms the X-ray crystallographic data. For the symmetrically substituted 2J-dimethyl derivative an interesting situation has developed since Clark et a/.* have interpreted these results in terms of a symmetrical ring structure whereas Lindberg et al. prefer an unsymmetrical ring str~cture.'~ The difference in interpretation may arise from different linewidths for the central and terminal sulphurs. If Lindberg's datas9 are re-interpreted in terms of a symmetrical structure the two sets of data in regard to absolute binding energies and shifts between terminal and central sulphurs are in complete agreement. Clearly further work is indicated to be necessary in this system. (c) Polymers. An interesting feature of ESCA as a spectroscopic tool is the relatively small increase in linewidth (in the absence of specific interactions such as hydrogen-bonding) in going from the gaseous to the solid phase.Since the factors which determine the shifts of core levels are of relatively short range [see equation (14)] it seems likely that linewidths for polymers might be little different from those for monomers. This has now been confirmed. Clark and Kilcast" have made a detailed study of both the core and valence energy levels of polytetrafluoroethylene. The spectrum (Figure 18) shows that line-widths for the core levels of the homopolymer are only some 20 % larger than those for the monomer. This points to the likely utility of ESCA for structural studies in 87 D.T. Clark D. Kilcast and D. H. Reid Chem. Cornm. 1971 638. " D. T. Clark and D. Kilcast Terrahedron 1971 27 4367. 89 R. Gleiter V. Hamrig B. Lindberg S. Hogberg and N. Lozach Chem. Phys. Letters 1971 11 401. 90 D. T. Clark and D. Kilcast Nature Phys. Sci.,1971 233 77. Physical Methods-Part (iii) Theoretical Organic Chemistry and ESCA 101 organic polymers since the resolution will be little different from that obtainable on monomeric systems. The sharp well-defined valence energy levels have been assigned on the basis of SCF MO calculations on model systems and in order of decreasing binding energy the peaks may be assigned to core-like F2sorbitals C-C bonding orbitals C-F bonding orbitals and Fzplone-pair orbitals. Carbon 1s Valence band 5xld c.ps.B CD x3 Fluorine Is A \ 694 692 690 688 20 Figure 18 Fluorine 1s and carbon 1s core levels and the valence levels of a pressedjilm of PTFE on a gold backing obtained with MgKa,,2 radiation (Reproduction by permission from Nature Phys. Sci. 1971 233 77)