- Email: [email protected]
Structure and degree of aromatic character in furan, pyrrole, and thiophene
Journal of Molecular Structure, 85 (1981) 163-178 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam
-Printed
STRUCTURE AND DEGREE OF AROMATIC FURAN, PYRROLE, AND THIOPHENE
FLOYD
R. CORDELL
Department (Received
and JAMES
of Chemistry, 27 October
in The Netherlands
CHARACTER
IN
E. BOGGS
The University
of Texas, Austin,
Texas
78712
(U.S.A.)
1980)
ABSTRACT The ab initio gradient method has been used to optimize the geometries of furan, pyrrole, and thiophene by SCF ab initio computation. The effect of augmenting a 4-21 split valence shell basis set by addition of d functions to oxygen, nitrogen, and sulfur has been investigated, and for furan a basis set including d functions on all heavy atoms has been used. The use of polarization functions is necessary to obtain realistic C-O and C-S bond distances, but otherwise any differences are minimal. Electron density difference plots give a graphic illustration of the basis set effects. The question of relative aromatic character of these compounds is investigated by means of Mulliken population analysis of the B electron distributions, determination of the spatial extent of the localized orbitals involved in the electron delocalization, determination of the deviations of bond lengths from typical single and double bond values, and plots of total electron density in planes parallel to, but far enough removed from, the molecular plane that the density is dominated by the contribution from the molecular TI system. Extensive conjugation within the C=C-C=C portion of the ring is found for all three compounds, but the ability to obtain true “aromatic” character by extension of this conjugation over the heteroatom is found to depend markedly on the size of the heteroatom. In pyrrole, the nitrogen atom is of ideal size to permit extension of the conjugation around the entire ring, and aromatic character is maximized. The oxygen atom in furan is too small and the sulfur atom in thiophene is too large to facilitate complete cyclic conjugation. It is suggested that electron delocalization within a portion of the ring does not constitute “aromaticity”, but rather a system is required such that the conjugation can extend completely around the ring. INTRODUCTION
Furan, pyrrole, and thiophene, like benzene, have 4n + 2 n-electrons and are therefore considered to be aromatic. Much discussion has centered around the relative degree of aromaticity of these compounds and efforts have been made to produce at least semi-quantitative estimates of their aromatic character. For example, a study involving several different experimental methods [l] concludes that thiophene is more aromatic than furan. Another study of relative reactivities in Diels-Alder reactions [ 21 has suggested the order of aromaticity to be thiophene > pyrrole > furan. The difficulty in establishing a rank ordering of the aromaticity of these ring systems, and especially in attempting to place a numerical value on their 0186-1280/81/0000-0000/$02.75
0 1981
Elsevier
Scientific
Publishing
Company
164
aromatic character, arises from the fact that the definition of aromaticity is essentially an operational one. Aromaticity is identified by the structural or kinetic consequences of a delocalization of electron density in a ring system. Experimental studies utilize different diagnostic features to probe for such delocalization and consequently can differ markedly in the degree of aromatic character ascribed to a particular molecule, even though the identification of the existence of some extent of delocalization may be straightforward. It might seem that quantum chemical computation could lead to a simple numerical characterization of the degree of aromatic character of a molecule, and this may be true, but again the result depends on the criterion used in partitioning the electron density within the molecule, once more introducing a degree of arbitrariness into the result. As is seen below, it may be more profitable to examine directly the electron density distribution when making comparisons between molecules rather than to attempt somewhat artificial subdivisions of that density. Numerous quantum chemical computations have been made for pyrrole [3--8, 10, 12, 141 and for furan [6, 7, 9, 11, 13,141. Thiophene has been the subject of fewer theoretical studies [ 14--161. The geometries were not optimized in any of these calculations except for a minimal basis set STO-3G calculation for furan [ll].Two of the calculations [14, 151 have suggested the order of aromaticity to be thiophene = pyrrole > furan. We have now completed structure optimizations for furan, pyrrole, and thiophene using a sufficiently large basis set to provide reliability in the results. The results of these studies are compared with experimental evidence concerning the structures of these molecules, and the electronic wavefunctions are used to interpret the varying degrees of aromaticity of these substances on the basis of the delocalization of electron density in their ring systems. Further conclusions about the concept of aromaticity arise from the results. METHOD
All of the calculations reported here were performed with the ab initio gradient program TEXAS [ 171. The basis set used for sulfur is Skancke’s 3-3-21 [ 181 augmented with d polarization functions. For carbon, oxygen, nitrogen, and hydrogen, Pang’s 4--21 basis set [ 191 was used. The furan and pyrrole geometries were also optimized with the 4421 basis set augmented by d functions on the heteroatom. These basis sets will be referred to as 4---21&O* and 4--21-N* sets. The furan geometry was additionally determined with the 4-21 basis set augmented with d functions on both carbon and oxygen. This basis set will be called the 4-21** set. All d functions are defined as suggested by Pulay [ 171 with an orbital exponent of 0.8. The final geometries were optimized until the changes in bond lengths were less than 0.002 a and bond angles less than 0.2”.
165
Mulliken population analyses [ 201 and orbit& localized according to the Boys criterion [ 211 were calculated at the optimized geometries. Molecular orbital plots were produced with programs developed by one of us (F.R.C.) based on the NCAR contouring routine CONRECSMTH [ 221. RESULTS
The calculated structures for furan, pyrrole, and thiophene are shown in Table 1. The numbering scheme is shown in Fig. 1. Table 1 also shows the results of very thorough microwave spectroscopic investigations of the structures of these three substances. All of the spectroscopic data shown are r, structures and therefore contain some residual effects of unknown magnitude from vibrational averaging of the distances and angles. These ring molecules are rather stiff, however, and it might be anticipated that the rs structures are not greatly different from the equilibrium re structures which they are supposed to approximate. The computed structures are subject to error because of neglect of electron correlation and use of finite basis sets for expansion of the molecular wavefunction. It has been argued that for a sufficiently large basis set such errors are of constant magnitude for a given type of bond parameter [ 19, 261. With the 4-m-21 basis set, for example, angles around carbon atoms are expected to have an error smaller than 1”. Angles around oxygen or nitrogen may have larger errors with this basis set, but are expected to give correct values if polarization functions are added, as in the 4--21--O* or 4-21-N* bases used here 1261. Comparison of the results in Table 1 show that these expectations are realized, and there is in fact a very satisfying reproduction of the differences in the ring angles found experimentally for the three molecules. Computed bond lengths, unlike angles, show distinct but consistent deviations from the true values, even at the Hartree-Fock limit. In ethylene, for example, the C=C bond length computed with the 4-21 basis set is 0.022 a shorter than the best experimental value [ 191 . The corresponding errors for the double bonds in furan, pyrrole, and thiophene shown in Table 1 are 0.023, 0.025, and 0.026 8. Since the experimental values in Table 1 may be slightly longer than true re values, we regard this as remarkably good consistency. For ethane, the C-C single bond is calculated with the 4-21 basis to be 0.015 a longer than the best experimental value [ 191. For furan, pyrrole, and thiophene, the corresponding errors are 0.021, 0.015, and 0.018 8, again an extremely consistent set of offset values. It should be pointed out that this consistency is noted on the assumption that C-C single bonds should have a constant offset value and C=C double bonds should have another constant, but different, value. This is reasonable, but the results do not follow the linear variation with bond length suggested on the basis of the limited data in ref. 19. Comparison of the three calculated furan structures offers some very interesting insights into basis set effects. The structural effect of adding d functions to the oxygen atom only is very strongly localized around that atom;
166
NNNNN uo
cO
o~
~-"Nq
b'-¢O'~O0
OOLO000~
LO
Z
I
0
0
I
0
0
0
~
0 0
0
n
0
I 0
0
~ o
0
0
0
0
~
167
HI\
/x\ /HI
1
Cl
I!
/2-c2, H2 Fig. 1. Labelling
H2 of the atoms
in furan
(X = 0),
pyrrole
(X = NH), and thiophene
(X = S).
i.e., only the C-O bond length is markedly affected with a small effect on the O-C,--C, angle. The large decrease in the bond length is consistent with earlier studies [ 261 showing the importance of an augmented basis set for the proper description of bonding around atoms, such as oxygen, having lone pairs of electrons. In the present case, however, the angle at the oxygen atom appears to have been nearly adequately described without the added polarization functions, in agreement with unpublished results obtained for dimethyl ether. Addition of d functions to the carbon atoms, using the 4-21”” basis, makes very little change in any part of the computed structure, except to shorten the C-0 bonds still a little more, bringing them down below the experimental value, as would be expected near the Hartree-Fock limit. The effect of the addition of d functions may be shown in more detail through electron density difference plots. Figure 2(a) shows the electron density in the molecular plane calculated from the 4-21-O* wavefunction minus the electron density in the molecular plane calculated at the 4-21-O* optimized geometry with the 4--21 wavefunction. The localization of the shifts in electron density is clear, with the major effect being an increase of electron density in the C-O bonding region. This, of course, correlates with the shorter C-O bond length calculated when d functions were added to the oxygen basis set. It can be seen from Fig. 2 that much of this electron density comes from a region just inside the ring near the C, atoms, the electron density decrease perhaps accounting for the 1.1” increase in the O-C--C, angle when d functions were used. One effect of the improved description of the electron density with the 4--21--O* basis is to decrease the polarity of the C-O bond, as shown in Fig. 2. Figure 2(b) shows a plot of the 4--21 ** electron density minus the 4-21 electron density in the molecular plane of furan. Additional shifting of electron density into the bonding regions can be seen, although the change produced by addition of d functions to the ring carbon atoms is not as profound as that given by the addition of d functions to the oxygen atom. The carbon atom is already better described by the 4-21 basis than is the oxygen atom. Comparison of the calculated and experimental geometries shown in Table 1 shows that the geometry obtained with the 4-21-O* basis set gives the best agreement with experiment. The good agreement is, of course,
Fig. 2. Effect of augmenting the basis set for furan with d functions. (a) Electron density in the molecular plane calculated with the 4-21-O* basis minus that with the 4-21 basis. Calculated at the 4--21-O* geometry. Contour interval = 0.003 electrons bohr3. (b) Electron density in the molecular plane calculated with the 4-21** basis minus that with the 4-- 21 basis. Calculated at the 4-21** geometry. Contour interval = 0.004 electrons bohr-“,
169
attributable to the cancellation of error between neglect of electron correlation and basis set effects. The largest discrepancy is in the shorter C=C double bond length obtained from the calculation. Recent work on ethylene shows that the short C=C double bond length is caused entirely by neglect of electron correlation. The experimental C=C bond length in ethylene is 1.334 A [27]. The bond length of 1.312 A calculated with the 4-21 basis is already nearly at the Hartree--Fock limit, since a geometry optimization with a 6- -3lG** basis changes the length only to 1.318 A [19] . Approximation of the electron correlation effect by second-order perturbation theory gives a result of 1.335 A [ 281, in essentially perfect agreement with experiment. Comparison of the calculated geometries for pyrrole shows that the addition of d functions to nitrogen has a very similar effect to that of addition of d functions to oxygen, although the magnitude of the differences is much smaller. The electron density difference plot shown in Fig. 3 illustrates this in a graphical manner. It can be noted here that the deficiency of the 4-21 basis set for nitrogen does not have an off-bond component; the addition of d functions does not draw electron density from the region inside the ring in the neighborhood of the C, atoms. Consequently, the change in the 0-C,-C, angle noted for furan does not have a counterpart in the case of pyrrole. The ability of the computations to reproduce differences in bond lengths in spite of essentially constant offset errors in absolute magnitude is well illustrated by the differences between furan and pyrrole. The calculation (with the 4--21-X* basis sets) shows the C=C double bond to be 0.021 X
Fig. 3. Effect of augmenting the basis set for pyrrole with d functions. Electron density in the molecular plane calculated with 4-21-N* basis minus that with the 4-21 basis. Calculated at the 4-21-N* geometry. Contour interval = 0.002 electrons bohr-3.
170
longer in pyrrole than in fur-an; the experimental difference is 0.021 * 0.005 A. The C-C single bond is 0.016 .& shorter in fur-an than in pyrrole by computation; by experiment, the difference is 0.013 ? 0.003 8. These differences are, of course, the relevant quantities in discussing aromaticity. Very similar results are seen in the results for thiophene. The 3--3--21” basis set used for sulfur should be most closely analogous to the 4-21-O* and 4-21-N* bases for oxygen and nitrogen, so comparison will be made with those results. By calculation, the C=C bond length is 0.005 a longer and the C-C bond is 0.004 a shorter than in furan. The corresponding experimental values are 0.009 f 0.002 a longer and 0.003 f 0.002 ,& shorter. Although there is no evidence for comparison, the 0.017 K difference between the computed and experimental C-S bond lengths does not seem to be unreasonable for a basis set of the size used here. AROMATICITY
Aromaticity may be defined as delocalization of electron density within a cyclic system. This definition does not provide any direct method for obtaining quantitative measures of the relative degree of aromaticity in a series of related molecules, so a number of alternative empirical tests have been adopted. Unfortunately, they do not always lead to the same results. Experimentally, the amount of aromatic character in a molecule has been determined from the rates of Diels-Alder reactions, NMR shifts, studies of ring currents, determination of “resonance” energies, and by other methods. Theoretically, the degree of aromaticity may be examined by computation of resonance energies, use of other techniques for partition of the energy among various components, or by any of several approaches to identify delocalization of the 7~system. Palmer and co-workers [ 15, 161 found the order of aromaticity to be pyrrole > thiophene > furan using calculated resonance energies. Unfortunately, they did not optimize the molecular geometries. Given the closeness of the computed resonance energies of thiophene (29.6 kcal mol-’ ) and pyrrole (35.6 kcal mall’), one cannot be certain that pyrrole is more aromatic than thiophene from this result alone. Use of computed resonance energies also suffers from the neglect of electron correlation which may be different enough between the two compounds to interchange the order of thiophene and pyrrole, and there may also be difficulties with the proper choice of reference bond energies. In this study, we use a number of techniques for examining the electron density directly rather than using computed energies. One approach is to use Mulliken population analyses to determine the 71 electron population associated with each atom. If the electron density were completely delocalized, each ring atom would have 1.20 71electrons associated with it; complete localization would have 2.00 electrons on the heteroatom and 1.00 on each carbon. The 77populations shown in Table 2 clearly show that some degree of delocalization exists in all three molecules. The de-
171 TABLE
2
Atomic
populations
0, N, or S C, C,
from Mulliken
analysis
using 4-21-X*
basis sets
Furan
Pyrrole
Thiophene
1.76 1.04 1.08
1.65 1.07 1.10
1.76 1.09 1.03
localization is greater in pyrrole than in furan, but the result for thiophene exhibits quite a different pattern than for the other two molecules. A much greater 71density appears on C, than on C2, reversing the behavior seen for furan and pyrrole. This may be taken as an indication that the situation is somewhat more complicated than can be represented by the Mulliken population analysis using its standard method for partitioning the electron densities into components. A somewhat better indication of the relative extent of aromaticity in these compounds may be obtained through use of orbitals localized according to the Boys criterion, although here again there is an arbitrary partitioning of the electron density. Within that limitation, the orbitals corresponding to the 71 system (the out-of-plane lone pairs and C=C double bonds) of each molecule may be identified. One may then calculate (I?‘) - x2 - yz - .z2, where (R2)is the expectation value of the square of the position of the electron and X, y, and z are the coordinates of the center of charge of the orbital. The resulting quantity is a measure of the size of an orbital and therefore a measure of the extent of its delocalization. The results are shown in Table 3. The sulfur lone pair is much larger than either the nitrogen or oxygen lone pairs, as would be expected because of the construction of the sulfur lone pair from the more diffuse 3p, atomic orbitals. Comparing the size of the nitrogen and oxygen lone pairs clearly shows that the nitrogen lone pair is much more delocalized than the oxygen lone pair, indicating that pyrrole is more aromatic than furan. Comparison of the size of the localized double bond orbitals conforms this result and suggests that thiophene may be intermediate, but nearly as aromatic as pyrrole. The latter conclusion should be tempered by the realization that the distortions due to the larger size of the sulfur atom may be influencing the size of the C=C double bond orbitals. TABLE “Size”
Lone c=c
3 of localized
pair
orbitals
(see text)
Furan
Pyrrole
Thiophene
2.67 3.29
3.69 3.49
8.72 3.42
172
All of the tests for aromatic&y applied heretofore have involved some sort of partitioning of either energy or electron density and have consequently contained a degree of arbitrariness. However, the total electron density and the electron density of a given symmetry type are invariant with respect to any unitary transformation and any direct use which is made of them does not have the arbitrariness of the other procedures. The accuracy of the information obtained is limited only by the reliability of the wavefunction that is used. In order to avoid all localization procedures, we may therefore investigate plots of the total electron density for evidence of aromaticity. The total electron density 0.2 A above the molecular plane is shown in Fig. 4 for each of the molecules. The C-H bond densities may still be seen in the plots, indicating that the total electron density still contains a considerable amount of CJcharacter at this height above the molecular plane. It is interesting to note that the maximum amount of electron density in the double bonds and in the C-C single bonds is almost identical at the position of this cut through the bonding system for all three molecules. The total electron density plotted 0.8 a above the molecular plane is shown in Fig. 5. The sampling plane is now far enough above the molecular plane to ensure that the total electron density is dominated by the 71 electrons, but not so far as to make the electron density devoid of all features. The plot of the electron density of furan in Fig. 6(a) clearly shows the reason for furan’s low degree of aromaticity. Compared with nitrogen, the oxygen 2p, orbital, which is the main component of the out-of-plane lone pairs, has contracted, limiting the amount of overlap which may occur between the 71 system of the double bonds and the oxygen lone pairs. The
173
Fig. 4. Total electron density 0.2 A above the molecular plane calculated with the 4--21-O*, 4--21--N*, or 4-21-S* basis set. (a) Furan. Contour interval = 0.06 electrons bohr-‘. (b) Pyrrole. Contour interval = 0.05 electrons bohr-‘. (c) Thiophene. Contour interval = 0.08 electrons bohrm3.
174
delocalization between the two C=C groups in furan is much what would be cspected in cis-butadiene, while pyrrole shows much more interaction of this portion of the molecule with the heteroatom. Comparison of the electron density plots of thiophene and pyrrole to the furan plot (Fig. 5) shows that both have a higher degree of delocalization and, hence, may be said to be more aromatic. The thiophene plot at 0.8 A is dominated by the sulfur lone pair. Comparison of the thiophene plot with that for furan shows that the electron density has decreased in the C-C single bond region and the density at the heteroatom end has greatly increased. This is in accord with the n electron density found at C, in the Mulliken analysis (Table 2). There appears to be a very good delocalization over the C-S--C system, but the degree of delocalization in the carbon system has decreased slight,ly. Comparing the pyrrole electron density plot to the other two, it can be seen that pyrrole has the most uniform electron delocalization of the three molecules. The electron density highs in pyrrole differ by only 0.08 electron bohrm3, while the density peaks in thiophene and furan vary by 5 and 3 times that amount. The carbon framework and the C-N-C region both show extensive delocalization. The examples reported here also show the great importance of the relative sizes of the atoms in a cyclic system in determining the degree to which aromaticity is possible. Figure 6 shows a projection of the electron densities of the three molecules in a plane perpendicular to the molecular plane, passing through the heteroatom (shown at the top of the figures) and bisecting the CC bond. The N-H group in pyrrole is of an optimum size to
175 L
LL
[ t L
~
f i l l
rr
LL
i
LI
L ~ t L I L L I I I I L ~ t
IT
rr
z ~ r
r i ~ r l l r
b
~
[
[
~
L
~
L
L
~
t
-. I
I
~ i
I
f
f
;
r
L
L
L
L
L
L
I
[
~
I
// f
[
f
f
f
f
f
I
[
f
I
f
I
C
Fig. 5. Total e l e c t r o n d e n s i t y 0.8 A above the molecular plane calculated with the 4 - - 2 1 - O*, 4 - - 2 1 - - N * , or 4 - - 2 1 - - S * basis set. (a) Furan. C o n t o u r interval = 0.003 e l e c t r o n s b o h r -3. (b) Pyrrole. C o n t o u r interval = 0.003 e l e c t r o n s b o h V 3. (c) T h i o p h e n e . C o n t o u r interval = 0.006 e l e c t r o n s b o h r 3.
176
permit overlap of electrons with the rest of the ring while the oxygen atom in furan is too small and the sulfur atom in thiophene is too large. The fact that there is extensive delocalization within the C=C-C=C system for all three of the molecules studied here is amply illustrated by the electron density plots. It can also be seen by the C=C and C-C bond lengths. The C=C bond length, calculated at the 4-21 level, is 1.312 a in H,C=CHI and 1.384 a for complete conjugation in benzene [ 191. The corresponding length is seen to be 1.360 A in pyrrole, 1.344 a in thiophene and 1.339 a in furan. The C-C bond lengths are also intermediate between the 1.541 ,& of H3C-CHj [ 191 and the 1.384 a of benzene, being 1.429 a in pyrrole, 1.441 a in thiophene, and 1.445 a in furan. All of these values are consistent with a degree of delocalization in the order pyrrole > thiophene > furan, but they are misleading in that they provide information only about the C=CC=C portion of the molecule rather than about the entire ring. In our opinion, the definition of aromaticity as electron delocalization in a cyclic system is not adequate to convey the intuitive meaning that is given to this concept, arising as it does from cases such as benzene where all atoms in the ring are identical. In the specific cases studied here, furan shows strong delocalization of electron density over the CX-C=C portion of the ring, but the delocalization does not continue around the C-t< region. Thiophene, on the other hand, shows less delocalization in the C=C-C=C region but greater withdrawal of electron density from this part of the ring into the region of the heteroatom. From these examples, it seems clear that varying experimental and theoretical tests for delocalization can arrive at different conclusions if they are more sensitive to electron density in different parts
177
I
\
1
++
F i l l f r t l P r r r ~ r [ l [ r t
b
Jr
ru
+ r r r l r l I I f r f l f l f l f f t J f i f
G
Fig. 6. T o t a l e l e c t r o n d e n s i t y in t h e p l a n e p e r p e n d i c u l a r to t h e m o l e c u l a r plane, passing t h r o u g h t h e h e t e r o a t o m a n d bisecting t h e C--C b o n d . Calculated w i t h the 4 - - 2 1 - - O * , 4 - - 2 1 - - N * , or 4 - - 2 1 - - S * basis set. C o n t o u r interval = 0 . 0 0 8 A. (a) F u r a n . (b) Pyrrole. (c) T h i o p h e n e .
178
of the cyclic system. If the concept of “aromaticity” should include an element of uniformity of delocalization through the cyclic system, pyrrole meets the test far better than either of the other rings studied, and furan is clearly the worst. ACKNOWLEDGEMENT
This research Foundation.
has been supported
by a grant from The Robert
A. Welch
REFERENCES 1 F. Fringuelli, G. Marino, A. Taticchi and G. Grandolini, J. Chem. Sot. Perkin Trans. 2, (1974) 332. 2 M. H. Palmer, Structure and Reactions of Heterocyclic Compounds, Arnold, London, 1967. 3 E. Clementi, H. Clementi and D. R. Davis, J. Chem. Phys., 46 (1967) 4725. 4 R. W. Kramling and E. L. Wagner, Theor. Chim. Acta, 15 (1969) 43. 5 G. Berthier, L. Prauch and J. Serre, Jerusalem Symp. Quantum Chem. Biochem., 2 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
(1970) 40. M. H. Palmer and A. J. Gaskell, Theor. Chim. Acta, 23 (1971) 52. M. H. Palmer, A. J. Gaskell and M. S. Barker, Theor. Chim. Acta, 26 (1972) 357. S. Cradock, R. H. Findlay and M. H. Palmer, Tetrahedron, 29 (1973) 2173. I. G. John, G. L. D. Ritchie and L. Radom, J. Chem. Sot. Perkin Trans. 2, (1977) 1601. K. Tanaka, T. Nomura, T. Noro, H. Tatewaki, T. Takada, H. Kashiwagi, F. Sasaki and K. Ohno, J. Chem.Phys., 67 (1977) 5738. I..G. John and L. Radom, J. Am. Chem. Sot., 100 (1978) 3981. W. Butscher and K-H. Thunemann, Chem. Phys. Lett., 57 (1978) 224. T. K. Ha, J. Mol. Struct., 51 (1979) 87. M. H. Palmer, R. H. Findlay and A. J. Gaskell, J. Chem. Sot. Perkin Trans. 2, (1974) 420. M. H. Palmer and R. H. Findlay, J. Chem. Sot. Perkin Trans. 2, (1975) 974. M. H. Palmer and R. H. Findlay, Tetrahedron Lett., (1972) 4165. P. Pulay, Theor. Chim. Acta, 50 (1979) 299. P. N. Skancke, G. Fogarasi and J. E. Boggs, J. Mol. Struct., 62 (1980) 259. P. Pulay, G. Fogarasi, F. Pang and J. E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. R. S. Mulliken, J. Chem. Phys., 23 (1955) 1833. S. F. Boys, in P. 0. Liiwdin (Ed.), Quantum Theory of Atoms, Molecules and the Solid State, Academic Press, 1968, pp. 253~-262. T. Wright, NCAR Technical Note, NCAR Graphics Software, 1978. F. Mata, M. C. Martin and G. 0. Stirensen, J. Mol. Struct., 48 (1978) 157. L. Nygaard, J. F. Nielson, J. Kirchheiner, G. Maltesen, J. Rastrup-Andersen and G. 0. S&ensen, J. Mol. Struct., 3 (1969) 491. B. Bak, D. Christensen, L. Hansen-Nygaard and J. Rastrup-Andersen, J. Mol. Spectrosc., 7 (1961) 58. F. R. CordelI and J. E. Boggs, J. Mol. Struct., Theochem, 76 (1981) 329. J. L. Duncan, Mol. Phys., 28 (1974) 1177. J. A. Pople, R. Krishnan, H. B. Schlegel and J. S. Binkley, Int. J. Quant. Chem. Symp., 13 (1979) 225. B. Bak, L. Hansen and J. Rastrup-Andersen, Discuss. Faraday Sot., 19 (1955) 30.
-Printed
STRUCTURE AND DEGREE OF AROMATIC FURAN, PYRROLE, AND THIOPHENE
FLOYD
R. CORDELL
Department (Received
and JAMES
of Chemistry, 27 October
in The Netherlands
CHARACTER
IN
E. BOGGS
The University
of Texas, Austin,
Texas
78712
(U.S.A.)
1980)
ABSTRACT The ab initio gradient method has been used to optimize the geometries of furan, pyrrole, and thiophene by SCF ab initio computation. The effect of augmenting a 4-21 split valence shell basis set by addition of d functions to oxygen, nitrogen, and sulfur has been investigated, and for furan a basis set including d functions on all heavy atoms has been used. The use of polarization functions is necessary to obtain realistic C-O and C-S bond distances, but otherwise any differences are minimal. Electron density difference plots give a graphic illustration of the basis set effects. The question of relative aromatic character of these compounds is investigated by means of Mulliken population analysis of the B electron distributions, determination of the spatial extent of the localized orbitals involved in the electron delocalization, determination of the deviations of bond lengths from typical single and double bond values, and plots of total electron density in planes parallel to, but far enough removed from, the molecular plane that the density is dominated by the contribution from the molecular TI system. Extensive conjugation within the C=C-C=C portion of the ring is found for all three compounds, but the ability to obtain true “aromatic” character by extension of this conjugation over the heteroatom is found to depend markedly on the size of the heteroatom. In pyrrole, the nitrogen atom is of ideal size to permit extension of the conjugation around the entire ring, and aromatic character is maximized. The oxygen atom in furan is too small and the sulfur atom in thiophene is too large to facilitate complete cyclic conjugation. It is suggested that electron delocalization within a portion of the ring does not constitute “aromaticity”, but rather a system is required such that the conjugation can extend completely around the ring. INTRODUCTION
Furan, pyrrole, and thiophene, like benzene, have 4n + 2 n-electrons and are therefore considered to be aromatic. Much discussion has centered around the relative degree of aromaticity of these compounds and efforts have been made to produce at least semi-quantitative estimates of their aromatic character. For example, a study involving several different experimental methods [l] concludes that thiophene is more aromatic than furan. Another study of relative reactivities in Diels-Alder reactions [ 21 has suggested the order of aromaticity to be thiophene > pyrrole > furan. The difficulty in establishing a rank ordering of the aromaticity of these ring systems, and especially in attempting to place a numerical value on their 0186-1280/81/0000-0000/$02.75
0 1981
Elsevier
Scientific
Publishing
Company
164
aromatic character, arises from the fact that the definition of aromaticity is essentially an operational one. Aromaticity is identified by the structural or kinetic consequences of a delocalization of electron density in a ring system. Experimental studies utilize different diagnostic features to probe for such delocalization and consequently can differ markedly in the degree of aromatic character ascribed to a particular molecule, even though the identification of the existence of some extent of delocalization may be straightforward. It might seem that quantum chemical computation could lead to a simple numerical characterization of the degree of aromatic character of a molecule, and this may be true, but again the result depends on the criterion used in partitioning the electron density within the molecule, once more introducing a degree of arbitrariness into the result. As is seen below, it may be more profitable to examine directly the electron density distribution when making comparisons between molecules rather than to attempt somewhat artificial subdivisions of that density. Numerous quantum chemical computations have been made for pyrrole [3--8, 10, 12, 141 and for furan [6, 7, 9, 11, 13,141. Thiophene has been the subject of fewer theoretical studies [ 14--161. The geometries were not optimized in any of these calculations except for a minimal basis set STO-3G calculation for furan [ll].Two of the calculations [14, 151 have suggested the order of aromaticity to be thiophene = pyrrole > furan. We have now completed structure optimizations for furan, pyrrole, and thiophene using a sufficiently large basis set to provide reliability in the results. The results of these studies are compared with experimental evidence concerning the structures of these molecules, and the electronic wavefunctions are used to interpret the varying degrees of aromaticity of these substances on the basis of the delocalization of electron density in their ring systems. Further conclusions about the concept of aromaticity arise from the results. METHOD
All of the calculations reported here were performed with the ab initio gradient program TEXAS [ 171. The basis set used for sulfur is Skancke’s 3-3-21 [ 181 augmented with d polarization functions. For carbon, oxygen, nitrogen, and hydrogen, Pang’s 4--21 basis set [ 191 was used. The furan and pyrrole geometries were also optimized with the 4421 basis set augmented by d functions on the heteroatom. These basis sets will be referred to as 4---21&O* and 4--21-N* sets. The furan geometry was additionally determined with the 4-21 basis set augmented with d functions on both carbon and oxygen. This basis set will be called the 4-21** set. All d functions are defined as suggested by Pulay [ 171 with an orbital exponent of 0.8. The final geometries were optimized until the changes in bond lengths were less than 0.002 a and bond angles less than 0.2”.
165
Mulliken population analyses [ 201 and orbit& localized according to the Boys criterion [ 211 were calculated at the optimized geometries. Molecular orbital plots were produced with programs developed by one of us (F.R.C.) based on the NCAR contouring routine CONRECSMTH [ 221. RESULTS
The calculated structures for furan, pyrrole, and thiophene are shown in Table 1. The numbering scheme is shown in Fig. 1. Table 1 also shows the results of very thorough microwave spectroscopic investigations of the structures of these three substances. All of the spectroscopic data shown are r, structures and therefore contain some residual effects of unknown magnitude from vibrational averaging of the distances and angles. These ring molecules are rather stiff, however, and it might be anticipated that the rs structures are not greatly different from the equilibrium re structures which they are supposed to approximate. The computed structures are subject to error because of neglect of electron correlation and use of finite basis sets for expansion of the molecular wavefunction. It has been argued that for a sufficiently large basis set such errors are of constant magnitude for a given type of bond parameter [ 19, 261. With the 4-m-21 basis set, for example, angles around carbon atoms are expected to have an error smaller than 1”. Angles around oxygen or nitrogen may have larger errors with this basis set, but are expected to give correct values if polarization functions are added, as in the 4--21--O* or 4-21-N* bases used here 1261. Comparison of the results in Table 1 show that these expectations are realized, and there is in fact a very satisfying reproduction of the differences in the ring angles found experimentally for the three molecules. Computed bond lengths, unlike angles, show distinct but consistent deviations from the true values, even at the Hartree-Fock limit. In ethylene, for example, the C=C bond length computed with the 4-21 basis set is 0.022 a shorter than the best experimental value [ 191 . The corresponding errors for the double bonds in furan, pyrrole, and thiophene shown in Table 1 are 0.023, 0.025, and 0.026 8. Since the experimental values in Table 1 may be slightly longer than true re values, we regard this as remarkably good consistency. For ethane, the C-C single bond is calculated with the 4-21 basis to be 0.015 a longer than the best experimental value [ 191. For furan, pyrrole, and thiophene, the corresponding errors are 0.021, 0.015, and 0.018 8, again an extremely consistent set of offset values. It should be pointed out that this consistency is noted on the assumption that C-C single bonds should have a constant offset value and C=C double bonds should have another constant, but different, value. This is reasonable, but the results do not follow the linear variation with bond length suggested on the basis of the limited data in ref. 19. Comparison of the three calculated furan structures offers some very interesting insights into basis set effects. The structural effect of adding d functions to the oxygen atom only is very strongly localized around that atom;
166
NNNNN uo
cO
o~
~-"Nq
b'-¢O'~O0
OOLO000~
LO
Z
I
0
0
I
0
0
0
~
0 0
0
n
0
I 0
0
~ o
0
0
0
0
~
167
HI\
/x\ /HI
1
Cl
I!
/2-c2, H2 Fig. 1. Labelling
H2 of the atoms
in furan
(X = 0),
pyrrole
(X = NH), and thiophene
(X = S).
i.e., only the C-O bond length is markedly affected with a small effect on the O-C,--C, angle. The large decrease in the bond length is consistent with earlier studies [ 261 showing the importance of an augmented basis set for the proper description of bonding around atoms, such as oxygen, having lone pairs of electrons. In the present case, however, the angle at the oxygen atom appears to have been nearly adequately described without the added polarization functions, in agreement with unpublished results obtained for dimethyl ether. Addition of d functions to the carbon atoms, using the 4-21”” basis, makes very little change in any part of the computed structure, except to shorten the C-0 bonds still a little more, bringing them down below the experimental value, as would be expected near the Hartree-Fock limit. The effect of the addition of d functions may be shown in more detail through electron density difference plots. Figure 2(a) shows the electron density in the molecular plane calculated from the 4-21-O* wavefunction minus the electron density in the molecular plane calculated at the 4-21-O* optimized geometry with the 4--21 wavefunction. The localization of the shifts in electron density is clear, with the major effect being an increase of electron density in the C-O bonding region. This, of course, correlates with the shorter C-O bond length calculated when d functions were added to the oxygen basis set. It can be seen from Fig. 2 that much of this electron density comes from a region just inside the ring near the C, atoms, the electron density decrease perhaps accounting for the 1.1” increase in the O-C--C, angle when d functions were used. One effect of the improved description of the electron density with the 4--21--O* basis is to decrease the polarity of the C-O bond, as shown in Fig. 2. Figure 2(b) shows a plot of the 4--21 ** electron density minus the 4-21 electron density in the molecular plane of furan. Additional shifting of electron density into the bonding regions can be seen, although the change produced by addition of d functions to the ring carbon atoms is not as profound as that given by the addition of d functions to the oxygen atom. The carbon atom is already better described by the 4-21 basis than is the oxygen atom. Comparison of the calculated and experimental geometries shown in Table 1 shows that the geometry obtained with the 4-21-O* basis set gives the best agreement with experiment. The good agreement is, of course,
Fig. 2. Effect of augmenting the basis set for furan with d functions. (a) Electron density in the molecular plane calculated with the 4-21-O* basis minus that with the 4-21 basis. Calculated at the 4--21-O* geometry. Contour interval = 0.003 electrons bohr3. (b) Electron density in the molecular plane calculated with the 4-21** basis minus that with the 4-- 21 basis. Calculated at the 4-21** geometry. Contour interval = 0.004 electrons bohr-“,
169
attributable to the cancellation of error between neglect of electron correlation and basis set effects. The largest discrepancy is in the shorter C=C double bond length obtained from the calculation. Recent work on ethylene shows that the short C=C double bond length is caused entirely by neglect of electron correlation. The experimental C=C bond length in ethylene is 1.334 A [27]. The bond length of 1.312 A calculated with the 4-21 basis is already nearly at the Hartree--Fock limit, since a geometry optimization with a 6- -3lG** basis changes the length only to 1.318 A [19] . Approximation of the electron correlation effect by second-order perturbation theory gives a result of 1.335 A [ 281, in essentially perfect agreement with experiment. Comparison of the calculated geometries for pyrrole shows that the addition of d functions to nitrogen has a very similar effect to that of addition of d functions to oxygen, although the magnitude of the differences is much smaller. The electron density difference plot shown in Fig. 3 illustrates this in a graphical manner. It can be noted here that the deficiency of the 4-21 basis set for nitrogen does not have an off-bond component; the addition of d functions does not draw electron density from the region inside the ring in the neighborhood of the C, atoms. Consequently, the change in the 0-C,-C, angle noted for furan does not have a counterpart in the case of pyrrole. The ability of the computations to reproduce differences in bond lengths in spite of essentially constant offset errors in absolute magnitude is well illustrated by the differences between furan and pyrrole. The calculation (with the 4--21-X* basis sets) shows the C=C double bond to be 0.021 X
Fig. 3. Effect of augmenting the basis set for pyrrole with d functions. Electron density in the molecular plane calculated with 4-21-N* basis minus that with the 4-21 basis. Calculated at the 4-21-N* geometry. Contour interval = 0.002 electrons bohr-3.
170
longer in pyrrole than in fur-an; the experimental difference is 0.021 * 0.005 A. The C-C single bond is 0.016 .& shorter in fur-an than in pyrrole by computation; by experiment, the difference is 0.013 ? 0.003 8. These differences are, of course, the relevant quantities in discussing aromaticity. Very similar results are seen in the results for thiophene. The 3--3--21” basis set used for sulfur should be most closely analogous to the 4-21-O* and 4-21-N* bases for oxygen and nitrogen, so comparison will be made with those results. By calculation, the C=C bond length is 0.005 a longer and the C-C bond is 0.004 a shorter than in furan. The corresponding experimental values are 0.009 f 0.002 a longer and 0.003 f 0.002 ,& shorter. Although there is no evidence for comparison, the 0.017 K difference between the computed and experimental C-S bond lengths does not seem to be unreasonable for a basis set of the size used here. AROMATICITY
Aromaticity may be defined as delocalization of electron density within a cyclic system. This definition does not provide any direct method for obtaining quantitative measures of the relative degree of aromaticity in a series of related molecules, so a number of alternative empirical tests have been adopted. Unfortunately, they do not always lead to the same results. Experimentally, the amount of aromatic character in a molecule has been determined from the rates of Diels-Alder reactions, NMR shifts, studies of ring currents, determination of “resonance” energies, and by other methods. Theoretically, the degree of aromaticity may be examined by computation of resonance energies, use of other techniques for partition of the energy among various components, or by any of several approaches to identify delocalization of the 7~system. Palmer and co-workers [ 15, 161 found the order of aromaticity to be pyrrole > thiophene > furan using calculated resonance energies. Unfortunately, they did not optimize the molecular geometries. Given the closeness of the computed resonance energies of thiophene (29.6 kcal mol-’ ) and pyrrole (35.6 kcal mall’), one cannot be certain that pyrrole is more aromatic than thiophene from this result alone. Use of computed resonance energies also suffers from the neglect of electron correlation which may be different enough between the two compounds to interchange the order of thiophene and pyrrole, and there may also be difficulties with the proper choice of reference bond energies. In this study, we use a number of techniques for examining the electron density directly rather than using computed energies. One approach is to use Mulliken population analyses to determine the 71 electron population associated with each atom. If the electron density were completely delocalized, each ring atom would have 1.20 71electrons associated with it; complete localization would have 2.00 electrons on the heteroatom and 1.00 on each carbon. The 77populations shown in Table 2 clearly show that some degree of delocalization exists in all three molecules. The de-
171 TABLE
2
Atomic
populations
0, N, or S C, C,
from Mulliken
analysis
using 4-21-X*
basis sets
Furan
Pyrrole
Thiophene
1.76 1.04 1.08
1.65 1.07 1.10
1.76 1.09 1.03
localization is greater in pyrrole than in furan, but the result for thiophene exhibits quite a different pattern than for the other two molecules. A much greater 71density appears on C, than on C2, reversing the behavior seen for furan and pyrrole. This may be taken as an indication that the situation is somewhat more complicated than can be represented by the Mulliken population analysis using its standard method for partitioning the electron densities into components. A somewhat better indication of the relative extent of aromaticity in these compounds may be obtained through use of orbitals localized according to the Boys criterion, although here again there is an arbitrary partitioning of the electron density. Within that limitation, the orbitals corresponding to the 71 system (the out-of-plane lone pairs and C=C double bonds) of each molecule may be identified. One may then calculate (I?‘) - x2 - yz - .z2, where (R2)is the expectation value of the square of the position of the electron and X, y, and z are the coordinates of the center of charge of the orbital. The resulting quantity is a measure of the size of an orbital and therefore a measure of the extent of its delocalization. The results are shown in Table 3. The sulfur lone pair is much larger than either the nitrogen or oxygen lone pairs, as would be expected because of the construction of the sulfur lone pair from the more diffuse 3p, atomic orbitals. Comparing the size of the nitrogen and oxygen lone pairs clearly shows that the nitrogen lone pair is much more delocalized than the oxygen lone pair, indicating that pyrrole is more aromatic than furan. Comparison of the size of the localized double bond orbitals conforms this result and suggests that thiophene may be intermediate, but nearly as aromatic as pyrrole. The latter conclusion should be tempered by the realization that the distortions due to the larger size of the sulfur atom may be influencing the size of the C=C double bond orbitals. TABLE “Size”
Lone c=c
3 of localized
pair
orbitals
(see text)
Furan
Pyrrole
Thiophene
2.67 3.29
3.69 3.49
8.72 3.42
172
All of the tests for aromatic&y applied heretofore have involved some sort of partitioning of either energy or electron density and have consequently contained a degree of arbitrariness. However, the total electron density and the electron density of a given symmetry type are invariant with respect to any unitary transformation and any direct use which is made of them does not have the arbitrariness of the other procedures. The accuracy of the information obtained is limited only by the reliability of the wavefunction that is used. In order to avoid all localization procedures, we may therefore investigate plots of the total electron density for evidence of aromaticity. The total electron density 0.2 A above the molecular plane is shown in Fig. 4 for each of the molecules. The C-H bond densities may still be seen in the plots, indicating that the total electron density still contains a considerable amount of CJcharacter at this height above the molecular plane. It is interesting to note that the maximum amount of electron density in the double bonds and in the C-C single bonds is almost identical at the position of this cut through the bonding system for all three molecules. The total electron density plotted 0.8 a above the molecular plane is shown in Fig. 5. The sampling plane is now far enough above the molecular plane to ensure that the total electron density is dominated by the 71 electrons, but not so far as to make the electron density devoid of all features. The plot of the electron density of furan in Fig. 6(a) clearly shows the reason for furan’s low degree of aromaticity. Compared with nitrogen, the oxygen 2p, orbital, which is the main component of the out-of-plane lone pairs, has contracted, limiting the amount of overlap which may occur between the 71 system of the double bonds and the oxygen lone pairs. The
173
Fig. 4. Total electron density 0.2 A above the molecular plane calculated with the 4--21-O*, 4--21--N*, or 4-21-S* basis set. (a) Furan. Contour interval = 0.06 electrons bohr-‘. (b) Pyrrole. Contour interval = 0.05 electrons bohr-‘. (c) Thiophene. Contour interval = 0.08 electrons bohrm3.
174
delocalization between the two C=C groups in furan is much what would be cspected in cis-butadiene, while pyrrole shows much more interaction of this portion of the molecule with the heteroatom. Comparison of the electron density plots of thiophene and pyrrole to the furan plot (Fig. 5) shows that both have a higher degree of delocalization and, hence, may be said to be more aromatic. The thiophene plot at 0.8 A is dominated by the sulfur lone pair. Comparison of the thiophene plot with that for furan shows that the electron density has decreased in the C-C single bond region and the density at the heteroatom end has greatly increased. This is in accord with the n electron density found at C, in the Mulliken analysis (Table 2). There appears to be a very good delocalization over the C-S--C system, but the degree of delocalization in the carbon system has decreased slight,ly. Comparing the pyrrole electron density plot to the other two, it can be seen that pyrrole has the most uniform electron delocalization of the three molecules. The electron density highs in pyrrole differ by only 0.08 electron bohrm3, while the density peaks in thiophene and furan vary by 5 and 3 times that amount. The carbon framework and the C-N-C region both show extensive delocalization. The examples reported here also show the great importance of the relative sizes of the atoms in a cyclic system in determining the degree to which aromaticity is possible. Figure 6 shows a projection of the electron densities of the three molecules in a plane perpendicular to the molecular plane, passing through the heteroatom (shown at the top of the figures) and bisecting the CC bond. The N-H group in pyrrole is of an optimum size to
175 L
LL
[ t L
~
f i l l
rr
LL
i
LI
L ~ t L I L L I I I I L ~ t
IT
rr
z ~ r
r i ~ r l l r
b
~
[
[
~
L
~
L
L
~
t
-. I
I
~ i
I
f
f
;
r
L
L
L
L
L
L
I
[
~
I
// f
[
f
f
f
f
f
I
[
f
I
f
I
C
Fig. 5. Total e l e c t r o n d e n s i t y 0.8 A above the molecular plane calculated with the 4 - - 2 1 - O*, 4 - - 2 1 - - N * , or 4 - - 2 1 - - S * basis set. (a) Furan. C o n t o u r interval = 0.003 e l e c t r o n s b o h r -3. (b) Pyrrole. C o n t o u r interval = 0.003 e l e c t r o n s b o h V 3. (c) T h i o p h e n e . C o n t o u r interval = 0.006 e l e c t r o n s b o h r 3.
176
permit overlap of electrons with the rest of the ring while the oxygen atom in furan is too small and the sulfur atom in thiophene is too large. The fact that there is extensive delocalization within the C=C-C=C system for all three of the molecules studied here is amply illustrated by the electron density plots. It can also be seen by the C=C and C-C bond lengths. The C=C bond length, calculated at the 4-21 level, is 1.312 a in H,C=CHI and 1.384 a for complete conjugation in benzene [ 191. The corresponding length is seen to be 1.360 A in pyrrole, 1.344 a in thiophene and 1.339 a in furan. The C-C bond lengths are also intermediate between the 1.541 ,& of H3C-CHj [ 191 and the 1.384 a of benzene, being 1.429 a in pyrrole, 1.441 a in thiophene, and 1.445 a in furan. All of these values are consistent with a degree of delocalization in the order pyrrole > thiophene > furan, but they are misleading in that they provide information only about the C=CC=C portion of the molecule rather than about the entire ring. In our opinion, the definition of aromaticity as electron delocalization in a cyclic system is not adequate to convey the intuitive meaning that is given to this concept, arising as it does from cases such as benzene where all atoms in the ring are identical. In the specific cases studied here, furan shows strong delocalization of electron density over the CX-C=C portion of the ring, but the delocalization does not continue around the C-t< region. Thiophene, on the other hand, shows less delocalization in the C=C-C=C region but greater withdrawal of electron density from this part of the ring into the region of the heteroatom. From these examples, it seems clear that varying experimental and theoretical tests for delocalization can arrive at different conclusions if they are more sensitive to electron density in different parts
177
I
\
1
++
F i l l f r t l P r r r ~ r [ l [ r t
b
Jr
ru
+ r r r l r l I I f r f l f l f l f f t J f i f
G
Fig. 6. T o t a l e l e c t r o n d e n s i t y in t h e p l a n e p e r p e n d i c u l a r to t h e m o l e c u l a r plane, passing t h r o u g h t h e h e t e r o a t o m a n d bisecting t h e C--C b o n d . Calculated w i t h the 4 - - 2 1 - - O * , 4 - - 2 1 - - N * , or 4 - - 2 1 - - S * basis set. C o n t o u r interval = 0 . 0 0 8 A. (a) F u r a n . (b) Pyrrole. (c) T h i o p h e n e .
178
of the cyclic system. If the concept of “aromaticity” should include an element of uniformity of delocalization through the cyclic system, pyrrole meets the test far better than either of the other rings studied, and furan is clearly the worst. ACKNOWLEDGEMENT
This research Foundation.
has been supported
by a grant from The Robert
A. Welch
REFERENCES 1 F. Fringuelli, G. Marino, A. Taticchi and G. Grandolini, J. Chem. Sot. Perkin Trans. 2, (1974) 332. 2 M. H. Palmer, Structure and Reactions of Heterocyclic Compounds, Arnold, London, 1967. 3 E. Clementi, H. Clementi and D. R. Davis, J. Chem. Phys., 46 (1967) 4725. 4 R. W. Kramling and E. L. Wagner, Theor. Chim. Acta, 15 (1969) 43. 5 G. Berthier, L. Prauch and J. Serre, Jerusalem Symp. Quantum Chem. Biochem., 2 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
(1970) 40. M. H. Palmer and A. J. Gaskell, Theor. Chim. Acta, 23 (1971) 52. M. H. Palmer, A. J. Gaskell and M. S. Barker, Theor. Chim. Acta, 26 (1972) 357. S. Cradock, R. H. Findlay and M. H. Palmer, Tetrahedron, 29 (1973) 2173. I. G. John, G. L. D. Ritchie and L. Radom, J. Chem. Sot. Perkin Trans. 2, (1977) 1601. K. Tanaka, T. Nomura, T. Noro, H. Tatewaki, T. Takada, H. Kashiwagi, F. Sasaki and K. Ohno, J. Chem.Phys., 67 (1977) 5738. I..G. John and L. Radom, J. Am. Chem. Sot., 100 (1978) 3981. W. Butscher and K-H. Thunemann, Chem. Phys. Lett., 57 (1978) 224. T. K. Ha, J. Mol. Struct., 51 (1979) 87. M. H. Palmer, R. H. Findlay and A. J. Gaskell, J. Chem. Sot. Perkin Trans. 2, (1974) 420. M. H. Palmer and R. H. Findlay, J. Chem. Sot. Perkin Trans. 2, (1975) 974. M. H. Palmer and R. H. Findlay, Tetrahedron Lett., (1972) 4165. P. Pulay, Theor. Chim. Acta, 50 (1979) 299. P. N. Skancke, G. Fogarasi and J. E. Boggs, J. Mol. Struct., 62 (1980) 259. P. Pulay, G. Fogarasi, F. Pang and J. E. Boggs, J. Am. Chem. Sot., 101 (1979) 2550. R. S. Mulliken, J. Chem. Phys., 23 (1955) 1833. S. F. Boys, in P. 0. Liiwdin (Ed.), Quantum Theory of Atoms, Molecules and the Solid State, Academic Press, 1968, pp. 253~-262. T. Wright, NCAR Technical Note, NCAR Graphics Software, 1978. F. Mata, M. C. Martin and G. 0. Stirensen, J. Mol. Struct., 48 (1978) 157. L. Nygaard, J. F. Nielson, J. Kirchheiner, G. Maltesen, J. Rastrup-Andersen and G. 0. S&ensen, J. Mol. Struct., 3 (1969) 491. B. Bak, D. Christensen, L. Hansen-Nygaard and J. Rastrup-Andersen, J. Mol. Spectrosc., 7 (1961) 58. F. R. CordelI and J. E. Boggs, J. Mol. Struct., Theochem, 76 (1981) 329. J. L. Duncan, Mol. Phys., 28 (1974) 1177. J. A. Pople, R. Krishnan, H. B. Schlegel and J. S. Binkley, Int. J. Quant. Chem. Symp., 13 (1979) 225. B. Bak, L. Hansen and J. Rastrup-Andersen, Discuss. Faraday Sot., 19 (1955) 30.