INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY SYMP. NO. 7, 261-267 (1973)

A Semi-Empirical Investigation of the Electronic Structure and Stability of the Oxycumulenes

PETER LINDNER, YNGVE OHRN, AND JOHN R. SABIN Departments of Physics and Chemistry. University of Florida, Cainesville, Florida 32601

Abstract A semiempirical investigation using the INDO and EWMO methods is carried out on the oxycumulenes

in an attempt to explain the relative stabilities of the odd and even carbon compounds.

Introduction

In recent years there has been an increasing interest in the stable oxycumulenes, which may be represented as O=C,=O. Much is known about the lowest member of this series, namely, carbon dioxide, but until recently the higher members have not been studied. The lack of experimental work has been due to the low stability and difficulty of preparation of pure samples, while the theoretical stumbling block has been sheer size of the molecules.

With the advent of large computational facilities, a number of recent computa- tions on carbon suboxide C , 0 2 have appeared [l-51. These have been prompted by new techniques which have allowed preparation, purification, and study of this compound.* In general, the properties predicted by calculation have been in good agreement with the experimental results, and problems such as the very low bending frequency about the central carbon (63.0 cm- ') [6] have been adequately explained [3,5]. The question of the linearity of the molecule is still undecided, however, with the most recent ab initio calculation [S] predicting a bent (C2J structure, while electron diffraction [7] seems to produce inconclusive results.

The only other member of the oxycumulene series which has been studied is pentacarbon dioxide (C,O,), which was experimentally reported [S] and disputed [9] in the 1930's. Recently this compound has been the subject of a calculational study [5], and its geometry and some calculated properties have been reported.

In any case, it seems that the O=C,=O molecules are extant for odd n, but with decreasing stability as n increases. Initial consideration might thus lead one to believe that the even carbon oxycumulenes should also be more or less stable, at least for small n, and they should be observable. This in fact does not seem to be the case, and the even carbon compounds have yet to be observed.

*See References [3] and [S] for a bibliography of experimental papers.

26 1 0 1973 by John Wiley & Sons, Inc.

262 LINDNER, OHRN, AND SABIN

Traditionally, the greater stability of the odd than even n oxycumulenes has been explained in terms of resonance stabilization of the odd carbon compounds [lo, 111. In particular, in addition to the normal doubly bonded structures for CO, (I) and C 3 0 2 (IV), there are a number of ionic structures (11-111, V-VI) which contribute significantly. It is readily seen, however, that structures of this sort are not possible for the even carbon compounds, and the observation “That materials with even n are unknown is probably related to this fact” ([ll], p. 695). Alternatively, such compounds may be so highly reactive that they are not seen.

0-+o I IV

-o-eo+ I1 + 0 & 4 e C - o - V

+o-c-o- 111 - o - ~ c - c ~ o + VI

In order to explore the subject of the stability of the carbon oxycumulenes further, a semiempirical study of the series for n = 1 -+ 6 has been carried out using two quite different schemes, and the results of these investigations are reported below.

Computational Methods

Two semiempirical schemes have been used in this work. One method, the well- known INDO scheme [12], was used to study these molecules as a function of geome- try. As the method has been well described elsewhere [12], we will not elaborate further, except to say that it is a semiempirical LCAO-MO-SCF scheme.

A second method, the energy weighted maximum overlap (EWMO) scheme [13], was also used, primarily for calculation of one electron energy levels. This method derives from a molecular model Hamiltonian obtained from the decoupling of the chain of equations for the molecular electron propagator. In the simplest case, the Hamiltonian obtained in this way derives from the idea that a molecfle is essentially a collection of undisturbed atoms, with the bonding arising from overlapping atomic charge distributions, and the electrons distributing themselves in the molecule according to the atomic one-electron energies. This idea leads to the determination of molecular electron binding energies from the eigenvalues of

- K ( l + S ) K where S is the overlap matrix of the atomic basis and K = (- E)’”. Here E is a diagonal matrix of atomic one-electron energies. The values for the elements of E have been taken from atomic Hartree-Fock calculations [14], and S has been calculated from analytical Hartree-Fock wave functions for the participating atoms [14].

Results and Discussion As CO, and C,O, are the best known and studied molecules in this series,

calculations were first carried out on these molecules, using a linear configuration and 0-C and C-C distances of 1.20 and 1.30 A, respectively. The orbital energies obtained and the experimental ESCA energies are given in Table I. As is the general

ELECTRONIC STRUCTURE AND STABILITY OF OXYCUMULENES 263

TABLE I . Calculated and experimental ionization energies for CO, and C,O,, in eV.

CO, c30, INDO EWMO ESCA' INDO EWMO ESCA"

n4 14.9 16.7 13.8 nu 11.8 14.2 10.8 n" 23.3 21.8 17.6 % 19.5 19.6 15.0 fJ" 18.6 17.1 18.1 R" 23.6 22.0 16.0 fJfl 22.4 21.7 19.4 fJ" 18.6 15.8 17.3 0" 43.9 40.0 37.1 fJ9 19.9 18.7 17.5 fJe 45.4 45.5 37.1 fJ" 28.5 24.1 21.9 fJ,(C,J - 308.7 297.5 fJP 38.9 34.5 25.6 f J g . . ( 0 1 J - 562.5 540.8 fJ" 44.8 44.0 35.5

fJ!3 44.9 44.1 35.5 fJg(C IS)

vfl, Y (C 1 s)

fJ4. Y (0 IS)

~ 308.4 291.5 308.7 294.9

~ 562.5 537.7 -

"Reference [4].

case, the INDO results are seen to overstabilize the orbitals, and particularly the low lying n orbital with respect to the highest u orbital. The EWMO results are a little better, but the highest a-n orbital inversion is still obtained. Variation of bond distances in these two compounds gave minima in the energy at Rco z 1.20 A and R,, NU 1.30 A. These distances are quite close to the most recently measured C=O and C=C distances in C302 [7b], and consequently they were used for subsequent calculations on other members of the series. It is not expected that these assumed distances will introduce any large errors. The bending potential for C302 about the central carbon atom was developed, and no evidence of an energy minimum for a bent configuration was found up to a central angle of 120". Beyond 120" conver- gence problems were encountered. The curve was very flat near the minimum corresponding to a bending force constant of 0.073 mdyn/& in good agreement with previously calculated values ([ll], p. 695).

As CZO2 is the first compound in the even carbon oxycumulene series, most of the effort in this area was spent on it. It has been traditionally easy to explain the instability of C,O, by saying that it has an easy mode of decomposition to two carbon monoxide molecules. Even though such decomposition modes to very stable products are not available to the higher even carbon compound% it has been felt that such decomposition would account for the lack of observation of the most stable of the even carbon series, and the higher members would certainly be less stable than C,O,,in analogy with the odd carbon series. Thus the energy of C,O, as a function of C-C distance was calculated, and the compound was found to be stable with respect to 2CO at all distances, the minimum energy being found at Rcc = 1.30A.

Consideration of the molecular orbitals of C,Oz shows that the highest occupied orbital is of the nu type and is half filled, giving a ground state triplet. The calculations reported above were also run for the triplet, and no qualitative difference in results was found.

264 LINDNER, OHRN, AND SABIN

The C,O, potential for both singlet and triplet as a function of C-C distance was very sharp, corresponding to a stretching force constant of 24 mdyn/& compared to an average value of 9.6 mdyn/A for a normal C==C bond [15]. In addition, the well is much too deep. Results of this sort are not unexpected, however, as INDO is well known to produce stretching potentials which are too steep and overbound [12]. As the INDO potential is obviously qualitative at best, it will be of great interest to see the results of a detailed Hartree-Fock calculation of this potential.

It has been suggested [5] that compounds of this sort might exist in bent forms (VII and VIII), and consequently calculations were carried out for the cis and trans bent configurations. Both structures were found to be energetically unfavorable with respect to the linear form, and the triplet was in all cases more stable than the singlet up to an 0-C-C angle of about 40". It thus appears that C,O, has a minimum energy for the linear triplet.

t rans li 0 \ \ / I " c=c cis

VII 0 VIII Calculations were then carried out on the rest of the series. Orbital energies

obtained from INDO and EWMO results for n = 1-5 are presented in Figure 1. From the figure it can be seen that in all the cases even carbon oxycumulenes have a highest occupied molecular orbital which is of n type, and which is half filled, giving a triplet ground state. In all cases this orbital lies considerably higher in energy than do the corresponding highest n orbitals of the adjacent odd carbon compounds, thus indicating considerably less stability in the even series.

The net atomic populations, as calculated from the INDO scheme, of the various compounds are presented in Table 11.

The INDO method is known to overpolarize electron distributions, and the magnitude of the net charges is therefore undoubtedly too large. The results are probably qualitatively meaningful, however. Two features of the charge distribution are evident. First it is seen that the charge polarization is much larger in the stable odd carbon compounds, with alternation of net charge as one goes down the chain. The difference is most pronounced near the center of the molecule and tends to be less striking as n increases. Second, the even carbon compounds all have net charges of the same sign on the two central carbons, while in the odd carbon series the central carbon is adjacent to two atoms with the opposite net charge. Such proximity of two like net charges is another indication of the lesser stability of the even versus odd carbon series.

A more telling argument probably lies in a consideration of the ground state electronic configuration of these compounds, however. In each case the highest occupied molecular orbital of the odd carbon series is a filled n type orbital, im- plying a relatively unreactive singlet ground state. In the even carbon series, however, the highest occupied molecular orbital is not only high in energy, but is a half filled n orbital, i.e., a triplet ground state. Compounds of this sort are well known to act as diradicals and to have the very high reactivity characteristic of such species. It

ELECTRONIC STRUCTURE AND STABILITY OF OXYCUMULENES 265

Ev

-10

-a

-33

-40

-308.5

-562.5

n U -

0

n 8

0

cpz "

Figure 1. Orbital energies for O=C,=O, n = 1-5, obtained by the EWMO method.

TABLE 11. Net atomic populations of O=C,=O.

0 C C C

COZ - 0.30 + 0.61 C*OZ" - 0.15 + 0.15 G O , - 0.29 + 0.50 - 0.42 GOZ* - 0.20 + 0.27 - 0.08 C5OZ - 0.24 + 0.46 - 0.38 + 0 32 C602" - 0.21 + 0.32 - 0.16 + 0.05

"Open-shell calculation for triplet.

266 LINDNER, OHRN, AND SABIN

thus seems apparent that the even carbon oxycumulenes are not only electronically less stable than their odd carbon analogues, but that they are to be expected to be extremely reactive, thus accounting for their lack of experimental observability. The inference might then be drawn that it should be possible to observe at least the lower one or two members of the even series, provided that it were to be prepared under very stringent, gas phase, inert atmosphere conditions.

It is also interesting to speculate on the possibility of a low-frequency bending mode at the central carbon in the oxycumulenes, similar to the 63 cm-’ bend in C302 [6]. The origin of this low-frequency mode has been postulated by Smith and Leroi [ 161 as being3ualitatively due to the nu highest occupied molecular orbital in C302. In this case, electron density is predominantly concentrated on the central carbon atom. As the molecule bends, the nu state splits into a, and b, states, but the magnitude of the splitting is small, and the center of the split levels remains essentially unchanged from the linear form. Therefore the bending mode is not energetically costly. In cases where the highest occupied molecular orbital is of ng symmetry, however, there is little electron density at the central carbon, and the split levels resulting from the ng state rise in energy due to electron repulsion. Con- sequently the molecule becomes more rigid.

Such an explanation has been successful [3,16] when comparing the low- frequency mode of C302 to the much higher frequency bend in C02 , and might be extended to the other molecules in this series.

The nodes of the highest occupied molecular orbitals in the C,Oz series are shown schematically in structures IX to XIV.

Ix

X

XI

XI1

XI11

XIV

It is seen that in the odd carbon series, only C 3 0 2 has the required nu highest occupied molecular orbital and high density at the central carbon (Table 11) necessary for the low-frequency bend. Thus neither C 0 2 nor C,O, would be expected to have such low-frequency modes, as both have ng highest occupied orbitals and low densities at the central carbon. This is born out by recent calculations by Weimann and Christoffersen [ S ] . It is to be expected, however, that C,02 would have a highest occupied orbital of the nu type (XV) and would therefore probably have such a low frequency mode.

T I xv

ELECTRONIC STRUCTURE AND STABILITY OF OXYCUMULENES 267

As can be seen in structures XI1 to XIV, none of the even carbon compounds has the local ‘?cU symmetry” in the highest occupied molecular orbital necessary to produce a low-frequency bending mode, that is, there is no atom in any of these compounds with an antinode on both atoms adjacent to the one where bending would occur. Thus we speculate that the even carbon compounds will not exhibit such a low-frequency bending mode. This expectation is born out when the force constant for the trans bend (VIII) in C,O, is calculated and found to be 0.40 mdynlbi, or considerably larger than is the force constant for the low-frequency mode in C30, . It should be noted that the above arguments are based only on the electronic structure of the linear systems, and there is evidence [S] that at least some of these compounds might not be linear in their ground states.

Finally, there has been a good deal of interest recently in other cumulenes, such as the hydrocumulene series H,C===€,=CH, [ 5 ] . This series of compounds is isoelectronic with the oxycumulenes, and to the extent that the 7c electron systems behave in a similar way. One might expect the above arguments to apply qualitatively to the hydrocumulenes as well.

Acknowledgments

Thanks are due to Proffesor Ralph Christoffersen for helpful comments on the manuscript. Acknowledgment is made to the donors of the Petroleum Research Fund administered by the American Chemical Society (JRS) and to the National Science Foundation (Grant GP-16666 to Y. Ohrn) for support of this work. Thanks are also due to the University of Florida Computing Center for a grant of computer time.

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