Journal of Molecular Structure (Theochem), 137 (1986) 171-181 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

A QUANTUM CHEMICAL STUDY OF THE CYCLIC OXOCARBON DIANIONS C,,O; (n = 3,4,5 AND 6)

I. Ground state properties

CLAUDIO PUEBLA

Institute of Physical Chemistry, University of Ziirich, Winterthurerstr. 190, 8067 Ziirich (Switzerland)

TAE-KYU HA*

Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Zentrum, 8092 Ziirich (Switzerland)

(Received 11 September 1985)

ABSTRACT

The ground state of the title compounds has been studied by the semiempirical MNDO and ab initio methods. The LMO- and PMO-analysis of the ground state reveal a weak- ening of the C-C bond and a reinforcement of the C-O bond with increasing ring size. Some ground state properties have also been calculated such as infrared frequencies and diamagnetic anisotropies.

INTRODUCTION

In the early 1960’s the family of the cyclic oxocarbon dianions C,O;* was postulated to be aromatic [ 11. At that time only two members of the family were known, the rhodizonate (n = 6) and the croconate (n = 5) ions, both of which had already been synthesized nearly 150 years before. Soon a new member, the squarate ion (n = 4) was added [2] and recently the syn- thesis of the deltate ion (n = 3) has been reported [3], this being the smallest cycle member. Attempts to synthesize the higher members of the family (n = 7 and above) have been, until now, unsuccesful. These compounds can be regarded as cyclic polymers of carbon monoxide where the smallest term with the formula CZOi2 has been postulated for the dialkali salts of dihy- droxyacetylene ~M+(OC!ECO)-~ [4], and this is thus formally the smallest member of the series C,0i2.

The ground state properties of the cyclic oxocarbon dianions have been studied with the MINDO/B [5] method and recently with ab initio procedures [ 61. They give some regularities in the calculated geometries for the members with II = 4 to 7. They predicted, however, for the deltate

*Author to whom correspondence should be addressed.

0166-1280/86/$03.50 0 1986 Elsevier Science Publishers B.V.

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dianion unusually short lengths for the C-C bonds and unusually long lengths for the C-O bonds. This result can be rationalized on the basis of the high strain of the C-C bonds in that ion. This point has not been con- firmed because a crystal structure study for the deltate ion is still lacking.

The existence of different geometries in the family leads directly to the controversial question about the aromaticity of the compounds. In fact West et al. [7] postulated the series to be aromatic on the basis of the (4iV + 2) electron rule and the HMO picture. This assumption has recently been questioned with results for the resonance energy obtained from graph theory [ 81. Definitive experimental data confirming the existence of aromaticity do not, however, exist. In this context the study of the dia- magnetic anisotropy might provide conclusive arguments for clearing up this crucial point. In fact the diamagnetic anisotropy of a croconic ammonium salt has been determined [9] ; however, the prediction of the ring current anisotropy derived from these results seems to be a difficult task and the final calculated value is not considered to be very reliable [8].

In the present theoretical study, a systematic comparison of the C-C and C-O bonds in the oxocarbons dianions C,0i2 was performed by means of semiempirical and ab initio calculations. The vibrational frequencies and force constants were calculated employing the optimized geometries, and the molecular electronic structure of the ground state was studied in terms of LMO- and PMO-analysis, and by some calculated one-electron properties.

DETAILS OF THE CALCULATIONS

Ab initio SCF calculations were carried out employing the split-valence 4-31G basis [lo], and the minimal STO-3G basis [ll] for the rhodizonate dianion. Calculations were also performed for the deltate dianion by using the double-zeta DZ(4s 2~) basis [ 121 from Huzinaga’s (9s 5~) set [ 131 plus a set of diffuse p functions with exponents of 0.034 for carbon and 0.059 for oxygen [ 141.

The molecular geometries were optimized by the force method as imple- mented in the MONSTERGAUSS program [ 151.

The localized molecular orbitals (LMO) were obtained by the method of Foster-Boys [ 161 using the Boyloc program [ 171.

The geometry of the benzene molecule was also optimized using the split- valence 4-31G basis resulting in bond lengths (C-C. 1.385 A; C-H: 1.072 A) and the vibrational force constants were calculated for comparison.

The geometries of the cyclic oxocarbon dianions were also optimized using the MNDO program [ 181, along with vibrational frequency calculations as implemented in that system.

RESULTS AND DISCUSSION

The geometries of the cyclic oxocarbons dianions (n = 3 to 6) were opti- mized using the ab-initio procedure; the results are given in Table 1. For the

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TABLE 1

C&O;: : optimized geometries (in A )

n MNDO

C-G C-C

Ab initio

C-C C-C

3 1.2623 1.4413 1.2910

3a - - 1.3038 4 1.2531 1.4866 1.2572 5 1.2515 1.4938 1.2471

Sb 1.2519 1.4971 1.2613

aBasis augmented with diffuse orbitals. bSTO-3G basis calculations.

1.4160

1.4176 1.4784 1.4612

1.5027

oxocarbons with II = 3 to 5 the 4-31G basis was used, for the rhodizonate dianion the minimal STO-3G basis was used. The results do not differ very much from the previously published data [6]. The deltate dianion has shorter C-C and longer C-O bond lengths compared with the other members of the family. The MNDO results (included in Table 1) show similar geo- metries. Although the MNDO method reproduces the trend well, in that the deltate dianion has a different geometry from the other members of the family, the difference is not so pronounced as that calculated by the ab- initio method. In this context the earlier data calculated by the MINDO/B method [5] agrees better with the ab-initio geometry for this dianion. The MNDO bond lengths are predicted to be rather similar for the whole series, and thus the highly strained C-C bonds of the deltate dianion seem not to be taken fully into account. This is however an error already noted in previous applications of the MNDO method [ 191.

Table 2 shows the bond orders and valencies as calculated by the MNDO method, indicating an increase in the bond order for the C-O and a dec- rease for the C-C bond with increasing ring size, which is in agreement

TABLE 2

Ground-state results: MNDO bond orders and valencies, and ab initio net charges

n Bond order Valency Net charges

PC0 pee 0 C q(C) q(G)

3 1.365 1.144 1.678 3.918 0.273 -0.940

3s - - - - 0.047 -0.713 4 1.502 1.008 1.815 3.905 0.351 -0.851 5 1.589 0.972 1.897 3.902 0.369 -0.769

6b 1.648 0.951 1.950 3.898 0.053 -0.387

aBasis augmented with diffuse orbitals. bSTO-3G calculations.

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with the predicted geometry. The same agreement can be observed in the net charges obtained by ab initio calculations, also included in Table 2.

The optimized geometries were used for the calculation of infrared frequencies at both ab-initio and MNDO levels. The results are shown in Tables 3-5. The calculated frequencies compare well with the observed ones, especially those calculated from ab-initio results. Table 6 gives the calculated force constants (fee and fco) for deltate, squarate and croconate dianions which agree well with the trend shown by the experimental values [l] . However, because the normal coordinate analysis of the infrared spectra was based on a Urey-Bradley potential a strict numerical comparison with the ab-initio values reported here is not possible. Instead, the force constant

TABLE 3

C,O;*: infrared frequencies (cm-‘)

Ab initio MNDO ExperimentaP

1 1838.5 2367 .O Raman 1835.0 -4; 2 1627.2 1869.7 IR 1470.0 E' 3 1283.4 988.2 Raman -

4 1012.2 967.2 IR 995.0 E'

5 866.7 649.0 Raman 803.0 AI 6 784.0 474.7 Raman 689.0 E" 7 296.6 325.4 Raman 341.0 E' 8 159.3 298.8 IR 236.0 A;

aFrom ref. 26.

TABLE 4

C,O;z : infrared frequencies (cm-’ )

Ab initio MNDO ExperimentaP

1 1781.1 2239.0 Ramall 1794.0 Al, 2 1654.8 1971.1 Raman 1593.0 B 3 1413.3 1974.2 IR 1530.0 E:g 4 1159.5 1203.2 Raman 1123.0 B 5 1063.9 1098.5 IR 1090.0 E:g 6 879.8 774.3 Raman -

7 723.5 890.3 Raman 723.0 -41, 8 733.9 587.7 Raman 662.0 Es 9 709.5 666.2 Raman -

10 643.1 580.7 Raman 647.0 B 28 11 342.4 322.5 Raman 294.0 B,s 12 322.2 366.2 IR 350.0 % 13 286.3 295.2 IR 259.0 A zu 14 109.8 77.0 Raman -

aFrom ref. 27.

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TABLE 5

C,O;* : infrared frequencies (cm-‘)

Ab initio MNDO Experimentala

1 1848.2 2135.6 Raman 1718.0 -4; 2 1721.7 1951.1 Raman 1591.0 E; 3 1526.4 1859.5 IR 1570.0 E; 4 1338.5 1366.3 Raman 1243.0 E; 5 1131.4 1114.9 IR 1100.0 E; 6 883.1 827.5 Raman - 7 727.4 777.2 Raman -

8 652.8 739.9 Raman 637.0 A; 9 558.8 520.2 Raman 555.0 E;

10 643.1 515.8 Raman -

11 373.5 394.5 IR 374.0 E; 12 322.2 386.6 Raman -

13 272.1 291.7 IR 248.0 A ”

aFrom ref. 27.

TABLE 6

Force constants calculated with the 4-31G basis set (in millidyne/A )

C30$ 6.639 8.183 C,O;’ 5.812 9.163 c,o;* - 10.593

WI, 8.428 -

for the C-C bond of benzene, as calculated with the ab initio method is given for comparison.

The coordinates of the centroids of charge of localized molecular orbitals (LMO, see Fig. 1) can provide a method for describing the nature of the chemical bonding in these molecules. In fact, the concept of localization means the separation of electron pairs and, therefore, the correspondence between orbitals and bonds. The present case is, however, particularly difficult to describe, because the compounds are negatively double charged (i.e., the two electrons are thus treated on the basis of a pair) and also the high symmetry of the molecules provides with many equivalent sites for the localization of this pair leading to many equivalent structures. For these reasons the calculated pictures can only be understood on the basis of average structures that do not correspond to a particular “resonance struc- ture” (for example with those given in [ 203 ). Instead, the pair of electrons corresponds to an orbital of their own, in the present case situated in the middle of the molecule, as shown in Fig. 1, and thus giving an indication for the existence of a ring current in the present compounds. Further the

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(a) (b)

A Cd)

Fig. 1. The contribution of the centroids of LMO charges in the cyclic oxocarbon dianions (valence shells only): (a) C30;‘; (b) C,O;‘; (c) C,O,‘; (d) C,0i2.

method gives some insight in the nature of the C-O bonds in the family. For example, for dianions with n = 4 to 6, the C-0 bonds are described by two equivalent orbit&, indicating double-bond character in these molecules. In the case of the deltate dianion, however, one of these orbitals is shifted towards the oxygen, allowing the second orbital to acquire a stronger u-, i.e., single-bond character.

The C-C bonds are not predicted to be pure single bonds, but do possess to some extent some double bond character, as can be seen from the values of atom participation in Table 7. This table gives the contribution of a given atomic center to a particular LMO along with that of two consecutive neighbouring atoms in a line. For the dianions with n = 3 to 5 for example, the lone pairs of the oxygen atoms are fully localized on the central atom with nearly no participation of the adjacent carbon. This picture remains unchanged for the whole series (the different values for rhodizonate dianion can be explained by the different basis used in the calculations) Rather dif- ferent is the picture for the CO bonds as can also be seen in Figs. la-d. Both LMOs are localized on the CO group except in the case of deltate dianion, where the shifting towards the oxygen is clearly seen for the higher lying orbital. More striking is the behavior of the C-C ring bonds. Although they are localized between the atoms the participation of the carbon adjacent to the group increases dramatically for the case of deltate dianion resulting in an increase of the double bond character for this compound. Also, the localization of the central orbital in the C ring can be observed from the values of participation normalized by the number of CO groups present

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TABLE 7

C,O-,I: LMO bond identification (atoms per LMO)

n 0, Cl C3 Per CO group

0 C

3 cc - 0.288 0.288 0.193 co 0.340 0.200 0.009 co 0.545 0.044 0.007 G(n) 0.624 0.035 Ring 0.023 0.147

3a cc -- 0.305 0.305 0.119 co 0.306 0.256 0.006 co 0.580 0.040 0.009 G(n) 0.636 0.037 Ring 0.026 0.181

4 cc - 0.260 0.260 0.030 co 0.420 0.138 0.011 G(n) 0.629 0.040 Ring 0.031 0.104

5 cc - 0.264 0.264 0.050 co 0.397 0.149 0.007 G(n) 0.637 0.047 Ring 0.037 0.080

Sb cc - 0.340 0.340 0.010 :;, 0.452 1.050 0.293 0.038 0.001

Ring 0.060 0.100

eBasis augmented with diffuse orbitals. bSTO-3G calculations.

0.0077 0.0490

0.0087 0.0603

0.0078 0.0260

0.0074 0.0160

0.0100 0.0170

(ring participation divided by n) on the last column of the Table 7. The par- ticipation of the carbon atoms is highest for the deltate dianion and dec- reases with increasing ring size. For the oxygen atoms inverse behavior is observed.

This picture is supported by the results obtained from the ‘quantitative” PM0 analysis [ 21-231, where the molecule is split into fragments and the interaction energies between them are calculated as they contribute to the HOMO orbital. The ab-initio results show that the HOMO is composed exclusively of n orbitals of the constituent atoms for all the members of the family, according to the LCAO coefficients. This means that the main part of the stabilization energy is given by the interaction between the R orbitals of the fragments.

Three types of fragmentation have been performed for the oxocarbon dianions as shown in schemes 1-3:

These fragmentation schemes have been chosen in such a way as to study the behavior of the C-C and C-O bonds with varying ring size. The

178

P -y-_ _T_ . c ’ \ I 1’ ‘I (CO)” G, ‘L3 ” ”

Scheme 1 Scheme 2 Scheme 3

TABLE 8

C&O:: interaction energies in the PM0 analysis (in a.u.)

n Fragment- Scheme 1 Scheme 2 Scheme 3 interaction AEij AEij

(R--CO) W--O) AEij Eii

P--R) P-0)

3 "AnB -0.508 0.496 -3.027 -1.172 nAG - -1.744 - 0.177 "PB 0.203 0.133 0.173 0.076 slprg - 0.019 - -0.007

nA"B -3.003 0.415 -2.915 -2.767 TA6 - -2.363 - 0.256 TPB 0.312 0.194 0.148 0.149 VrpTg - 0.035 - -0.011

=A"B -2.793 0.128 -2.676 -2.971 "A"& - -2.620 - 0.329 +B 0.294 0.250 0.113 0.205 nT\nT, - 0.038 - -0.015

interaction energies are given on Table 8 from which it can be seen that the stabilization energy of the C-O bonds increases and that of the C-C bonds decreases with increasing ring size. An interesting point is the high gain in the stabilization for the squarate and croconate dianions (Scheme 1) as compared with the value for the deltate dianion.

Finally, some one-electron properties have been calculated, which include the diamagnetic susceptibility and anisotropy, the quadrupole moment and the electric field gradient for the oxygen in the present series. Unfortunately in almost all cases there are, as yet, no experimental values available for comparison.

The diamagnetic susceptibility and anisotropy are the most important properties in the present case, because the anisotropy has been proposed as a measure of the ring current, i.e., the degree of aromaticity for the series; however, only data for the croconate dianion is available.

Table 9 shows the calculated susceptibilities and anisotropies for the whole series. Although the calculated electronic contribution to the suscep- tibility is known to be reliable [ 241, the total diamagnetic susceptibility and anisotropy are more difficult to reproduce, the contribution of the nuclei are normally underestimated thus giving incorrect results for the total

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TABLE 9

C,Gz: diamagnetic susceptibilities and anisotropies (c.g.s.)

n X xx =XYY XZZ Ax Axbulk %Jcala ~'x,nL

3 -359.53 -653.24 -293.71 -26.08 -17.7 -8.4

3b -366.57 -664.35 -297.78 -26.88 -17.7 -9.2 4 -558.07 -1031.82 -473.75 -35.36 -26.6 -8.8 5 -811.31 -1520.03 -- 708.72 - 45.06 -37.5 -7.6

6c -1159.45 -2215.85 -1056.40 -46.44 -48.4 0.0

aCalculated with the data from ref. 25. bBasis augmented with diffuse orbitals. %TO-3G calculations.

anisotropy. In this study the nuclear contribution to the bulk anisotropy has been calculated along the same lines as for the electronic contribution, a procedure that seems adequate for the present series and gives satisfactory results for the croconate dianion. In fact, the calculated value for this com- pound is -45.06 c.g.s. and compares well with the experimental value of --52.5 c.g.s. Further, taking the values for the local and group anisotropies published in the literature [25], the local contributions to the diamagnetic anisotropy can be substracted leaving only the ring current anisotropy as shown in the last column of Table 9. These values indicate in fact a decreas- ing ring current, i.e., aromaticity degree with increasing ring size.

The calculated electric field gradient (q) and asymmetry parameter (77) for oxygen, quadrupole moment (Q), and the (r2> values are listed in Table 10. The (r2) value serves as a measure of the extent of electronic charge distribution. It shows that this value becomes sucessively larger in going from II = 3 to 6. The calculated q and Q values may serve as a guide for future experimental studies for this series.

TABLE 10

C,O;*: electric field gradient for oxygen and quadrupole moments (in a.u.)”

n 9 xx QYY 9 z* fib Qxx =Q,, Qzz tr2)

3 1.357 0.354 --1.711 0.586 -10.33 20.65 -119.52

3c 1.449 0.439 -1.888 0.535 -10.64 21.28 -124.30 4 -1.346 - 0.251 1.597 0.685 -14.00 28.00 -156.21 5 -1.157 -0.695 1.852 0.249 -17.85 35.69 -193.25

6d -1.540 -0.607 2.146 0.434 -18.39 36.78 -195.97

aPrincipal axis system. d STO-3G calculations.

bAsymmetry parameter. =Basis augmented with diffuse orbitals.

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CONCLUSIONS

A systematic study on the nature of the C-C and C-O bonds has been carried out using the ab-initio method. As has been anticipated in the recent literature, the cyclic oxocarbon dianions show a delocalization of the two “extra” electrons of the double charge, thus probably contributing to the overall stability. This is fully in accord with recent studies based on avalence- bond picture that revealed the lack of this stability contribution in the uncharged species [28] . The question about the origin of the different geo- metry of deltate dianion is also a closely related matter. It has been shown in this study that the interaction between the oxygen and carbon atoms increases strongly in going from the deltate to squarate, but more smoothly as the ring size continues to increase. On the other hand the interactions between neighbouring carbon atoms decreases with increasing ring size, but not in the dramatic way as for the C-0 interaction. The LMO-analysis also indicates double bond character for the C-C bonds in all members of the series. Both facts agree fully with the suggestion of the existence of reso- nance structures, which are probably crucial in the stabilization of the compounds.

The question about the degree of aromaticity of the series cannot, however, be answered in a definitive form. In principle the concept of aro- maticity has been tied to the existence of a ring current; taking this as a criteria and taking into account that the calculated values of the diamagnetic anisotropies suggest strongly the existence of a ring current, one should conclude the series to be aromatic; the degree of aromaticity decreasing with increasing ring size.

ACKNOWLEDGEMENT

We express our appreciation to the computer centers of ETH Zurich and University of Zurich for providing computer time for this study and to Prof. G. Wagniere for encouragement and advice.

REFERENCES

1 For a recent review on the subject see: R. West (Ed.), Oxocarbons, Academic Press, New York, 1980.

2 S. Cohen, J. R. Lather and J. D. Park, J. Am. Chem. Sot., 81(1969) 3480. 3 D. Eggerding and R. West, J. Am. Chem. Sot., 98 (1976) 3641. 4 E. Weiss and W. Buchner, Helv. Chim. Acta, 46 (1963) 1121; Z. Allg. Chem., 330

(1964) 251;Chem. Ber., 98 (1965) 126. 5 C. Leibovici, J. Mol. Struct., 13 (1972) 185. 6 L. Farnell, L. Radon1 and M. A. Vincent, J. Mol. Struct. (Theochem), 76 (1981) 1. 7 R. West, N. Y. Niu, D. L. Powell and M. V. Evans, J. Am. Chem. Sot., 82 (1960)

6204. 8 J. Aihara, J. Am. Chem. Sot., 103 (1981) 1633. 9 R. West, in R. West (Ed.), Oxocarbons, Academic Press, New York, 1980, Chap. 1

and references therein.

181

10 W. J. Hehre, R. Ditchfield and J. A. Pople, J. Chem. Phys., 56 (1972) 2257. 11 W. J. Hehre, R. Ditchfield and J. A. Pople, J. Chem. Phys., 51(1969) 2667. 12 T. H. Dunning, Jr., J. Chem. Phys., 53 (1970) 2823. 13 S. Huzinaga, J. Chem. Phys., 42 (1966) 1293. 14 T. H. Dunning, Jr. and P. J. Hay, in H. F. Schaeffer, III (Ed.), Modern Theoretical

Chemistry, Vol. 3, Plenum Press, New York, 1976, p. 24. 15 M. R. Peterson, R. A. Poirier and I. G. Csizmadia, MONSTERGAUSS program,

University of Toronto, Canada, 1981. 16 S. J. Boys, Rev. Mod. Phys., 32 (1960) 296. 17 D. Peteers, Boyloc Program, Q.C.P.E., No. 330. 18 J. J. P. Stewart, MOPAC Program Package, Q.C.P.E., No. 464. 19 M. J. S. Dewar and W. Thiel, J. Am. Chem. Sot., 99 (1977) 4907. 20 A. Moyano and F. Serratosa, J. Mol. Struct. (Theochem), 90 (1982) 181. 21 M.-H. Whangbo, H. B. Schiegel and S. Wolfe, J. Am. Chem. Sot., 99 (1977) 1296. 22 D. Kost, H. B. SchIegel, D. J. Mitchell and S. Wolfe, Can. J. Chem., 57 (1979) 729. 23 For a recent review see M.-H. Whangbo, in I. G. Csizmadia and R. Daudel (Eds.)

Computational Theoretical Organic Chemistry, NATO Adv. Series Inst., Vol. C-67, Reidel Pub. Co., Dordrecht, 1981 pp. 233.

24 B. Day and M. G. Papadopoulos, Chim. Chron., 8 (1979) 131. 25 C. L. Norris, R. C. Benson, P. Beak and W. H. Flygare, J. Am. Chem. Sot., 95 (1973)

2766.