Small Dianionic Carbon Clusters: General Aspects on Their Stability

8914

J. Phys. Chem. 1994,98, 8914-8920

Small Dianionic Carbon Clusters: General Aspects on Their Stability and Results for CiT. Sommerfeld,' M. K. Scheller, and L.

s. Cederbaum

Theroretische Chemie. Physikalisch- Chemisches Institut, Universitat Heidelberg, Im Neuenheimer Feld 253, 0-691 20 Heidelberg, Germany Received: March 18, 1994; In Final Form: May 10, 1994'

Studies on several geometrical configurations of the free doubly negative carbon cluster Ci- are performed at the Hartree-Fock level as well as at the configuration interaction and outer-valence Green's function levels of theory. Most of the Ci- isomers inspected are found to be stable with respect to fragmentation, but only two structures, a branched cluster and a Dgh symmetrical isomer, emerge also as stable with respect to electron autoejection. The characteristic properties which allow small free dianionic carbon clusters to bind two excess electrons are discussed. Qualitative structural criteria for the existence of these cluster dianions are extracted by comparing and generalizing the results for C;-, Ct-, Ci-, and C$. Predictions of possible structures of stable higher carbon cluster dianions are made.

1. Introduction

pasi-linear isomer (I) (CZ,symmetry)

The observation of free long-lived doubly negative charged carbon clusters Ci- (7 In I28)' in 1990 has stimulated a number of theoretical studies concerning the mechanisms which allow free molecules as small as C:- to bind two excess electrons. As animportant result, it has been established that thegeometrical structure of these cluster dianions has a major impact, in particular, on their stability with respect to electron autoejection. First the experimentalists proposed a linear chainlike configuration for the cluster dianions up to C&. But in a comprehensive theoretical study at highly correlated levels, the linear clusters C:- and Ci-, which have open-shell electronic configurations, were found to be unstable with respect to vertical electron removal.2 Proceeding from these contradictory experimental and theoretical findings, in a recent article,' we have investigated possible nonlinear structures of C:-, which allow a closed-shell electronic configuration for this dianion. Indeed, we found a triangular D3h symmetrical nuclear arrangement, referred to as C(C2)i-, which is predicted to be stable with respect to vertical and adiabatic electron loss as well as to all low-energy fragmentation channel^.^ (In this context adiabatic ionization potential refers to the total energy difference between C(C,)f and C(C,); in their separately optimized D3h geometrical configurations. The linear monoanion CY is in fact lower in energy than the triangular one, but the D3h equilibrium geometry of the C(C,); cluster is a local minimum on the PES of CY.) From these findings it emerges that the geometrical configuration of the small dianionic carbon clusters is crucial to their electronic stability. In particular, nuclear arrangements which allow for a closed-shell electronic ground state are especially promising candidates. Proceeding from our results on the C:cluster, we report in the present article possible nonlinear isomers of the (electronically unstable) linear Ci- cluster. In the first part of this work we present from the calculations on many isomers our ab initio data for the four isomers of the Ci- cluster depicted in Figure 1. Two of these isomers-the D3h symmetrical arrangement (IV)and the branched isomer ( m a r e predicted to be stable not only with respect to dissociation but also with respect to vertical electron loss. In the second part of this communication our results for the 2 ' ;- cluster will be compared to the findings for C:-,3 Ci-, and C:i2*4 with the objective to pin down and systematize basic concepts. This will *Abstract published in Advance ACS Abstracts, June 15, 1994.

hhain

+ ring isomer (11) (Czv symmetry)

)ranched isomer (111) :CzVsymmetry)

Cl

c7

I c2 I

~~6

C8

'C,5

I

c4

I

c7, C9

Figure 1. Structures of the four Cj-isomers discussed in the text. The total energiesof thedianions I-IV are collectedin Table 2, and geometrical parameters are found in Table 4. Many other structures have been investigated, too, but have been found to k'less stable (see text).

guide us to a qualitative understanding of the properties which determine the electronicstabilityof small dianionic carbon clusters and, furthermore, will lead us to the prediction of possible structures for higher carbon cluster dianions. 2. Computational Details

The data at the independent particle level were obtained using the standard self-consistentfield (SCF) restricted HartreeFock (RHF) and restricted open-shell HartreeFock (ROHF) techniques. The calculations employed Guassian-type d o u b l e r plus

0022-3654/94/2098-8914$04.50/0 0 1994 American Chemical Society

The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 8915

Small Dianionic Carbon Clusters

TABLE 1: Total Energies of Linear Singly Negative Charged Fragmentation Products of Ci-.The Energy Values Presented Should Be Compared to the Energies of the CGIsomers I-IV in Table 2. The Data Were Computed at the SCF/DZP Level of Theory fragments energy (au) fragments energy (au)

c- + c, c; + c,

-340.3433 -340.3749

c; + c; c; + c;

-340.3406 -340.3840

polarization (DZP) and triple-!: plus polarization (TZP) basis sets. The DZP andTZP sets comprised, respectively, Huzinaga’s 9s5p and 10s6p5primitive set in the 4s2p6 and 5s3p7contraction scheme of Dunning augmented with a Cartesian d-type polarization function with an exponent of 0.75.* The basis sets were not augmented with diffuse functions, since it is known that the effect of diffuse basis functions on the properties of carbon cluster monoand dianions is small2-3and their omission will certainly not affect our qualitative conclusions. The single plus double excitation configuration interaction (SDCI) results were obtained using theDZPbasisset. In thesecalculationsthecarbon lscoreorbitals were frozen and their corresponding virtual counterparts were discarded. The geometry optimizations at the SCFlevels of theory were performed straightforwardly. Due to the large number of geometrical parameters, structureoptimizations a t the SDCI level of theory have not yet been performed. The harmonicvibrational frequencies for the different Ci- and C, isomers have been computed at the SCF level but are not reported here in detail. At the S C F level (ASCF) and the SDCI level (ASDCI) of theory the electron detachment energies (EDE) have been obtained by computing the difference between the total energies of the monoanion and its corresponding dianion. In addition, the outervalence Green’s function (OVGF) approach has been used to compute the binding energies of the excess electrons. This technique has been discussed in detail el~ewhere,~ and we only briefly note here that it includes electron correlation and relaxation effects. The applied basis sets and theoretical techniques are known to yield reliable results with a reasonable accuracy. The ab initio packages used stem from the GAMESS system of programs.10

3. Results and Discussion on Ck In this section we report our results obtained for the dianionic carbon cluster Ci-. From previous investigations11J2 it is established that the principal energetic questions pertaining to free dianionic systems are whether they (1) can bind the two excess electrons and (2) are stable with respect to fragmentation. From Watts’and Bartlett’s findings,2as wellas fromour previously published results,3 it is known that due to the strong covalent bonding in these compounds requirement 2 is usually fulfilled for the carbon cluster dianions C k . But in the range of up to 10 carbon atoms, the electronic stability of the dianionic clusters is limited to distinct geometrical configurationsand thus 1 represents the dominating factor determining the existence of carbon cluster dianions. Let us begin with an inspection of requirement 2. In order to establish that a particular molecular system is stable with respect to dissociation, one has to investigate possible fragmentation pathways. Corresponding studies require a tremendous computational effort for a nine-atomic species like the Ci-cluster due to the large number of geometrical parameters and possible structures. But, as mentioned above, the dianionic carbon clusters are usually thermodynamically stable with respect to dissociation due to their strong covalent bonding. We base this statement on the energetic data presented in Tables 1 and 2 for isomers of Ci- and their low-energy dissociation products. Furthermore, we refer to more sophisticated discussed e l ~ e w h e r e . ~ . ~ Beyond the thermodynamic stability, the questions to answer are whether a considered geometrical arrangement represents a

TABLE 2 Total Energies (in au) of the Four Ci- Isomers Displayed in Figure 1. Capital Roman Numbers in the First Column Refer to the Labeling of Figure 1 isomer method basis set dianion“ monoanionO monoaniod I I1 I11

IV

SCF SCF SDCI SCF SCF SDCI SCF SCF SDCI SCF SCF SDCI

DZP TZP DZP DZP TZP DZP DZP TZP DZP DZP TZP DZP

-340.4353 -340.4919 -341.2654 -340.44 19 -340.5031 -341.2750 -340.4301 -340.4900 -341.2626 -340.4372 -340.4992 -341.2699

-340.4586 -340.5224 -341.2850 -340.4560 -340.5154 -341.2880 -340.4200 -340.4760 -341.2356 -340.4183 -340.4157 -341.2422

-340.4832‘

-340.425 1 -340.4813 -341.2413 -340.4265 -340.4839 -341.2524

0 Data obtained at the equilibrium geometry of the dianion. b Data obtained at the equilibriumgeometry of the monoanion. The equilibrium structure of the h e a r monoanion is of D,h symmetry.

minimum on the potential energy surface (PES) of the C:cluster and whether the energy barriers to rearrangement of this isomer are large enough to guarantee its nuclear stability. Now, energy barriers associated with rearrangement of carbon-carbon bonds do usually show heights of several electronvolts,~3since the covalent carbon-rbon bonds are strong and strongly directional. Thus, the energy wells belonging to minima on the PES of a carbon cluster dianion are usually deep enough to represent nuclear stable isomers. Therefore, one can expect nuclear stability for a geometrical configuration if all vibrational frequencies have real values. Before we turn to the electronic stability (1) of the different isomers of the Ci- cluster dianion, let us recall that there are a great many structural types which nine carbon atoms can adopt. We investigated many different isomers, among these the four geometrical structuresdisplayed in Figure 1 as well as monocylic, bicyclic, and three-dimensional arrangements. A first criterion for the electronic stability of the investigated Ci- isomers is Koopmans’ theorem.14 From previous investigations it is known that the EDEs of the double negative carbon clusters are overestimated by Koopmans’ theorem.24 Consequently,dianionic carbon clusters can be said to be unstable with respect to electon loss if their EDE is negative already at the theoretical level of Koopmans’ theorem, indicating that one or more electrons are not bound. On the other hand, a positive EDE predicted on the basis of Koopmans’ theorem providesa hint that the carbon cluster dianion may be stable to electron autodetachment, but this prediction has to be verified at correlated levels of theory. On these grounds we restrict our discussion to the four isomers of the Ci- cluster depicted in Figure 1, which are the only structures we found to be stable with respect to electron loss on the level of Koopmans’ theorem. Let us now consider these four Ci- isomers in more detail. When we first started our studies, we assumed a linear structure in agreement with the observations for the neutral and the singly charged carbon cluster^^^-^^ and the experimentalists’ proposal. We thought about a linear chain of carbon atoms to represent a promising starting point sinceit provides a potentially maximum separation between the charges of the two extra electrons which should efficiently minimize their mutual Coulomb repulsion. However, similar to our experience with the linear cluster C:-,3 a D,J, symmetrical Ci- cluster is not a minimum on the corresponding PES at the independent particle level geometry optimization; i.e. there are vibrational frequencies which have imaginary values. Consequently, we repeated the geometry optimization, relaxing the symmetry to Ch and by this means allowing the chain to fold. At the C, equilibrium structure (Figure 1, I), we found all harmonic frequencies to have real values, and thus, this structure may be looked at as a true minimum

8916 The Journal of Physical Chemistry, Vol. 98, No. 36, 1994

TABLE 3: Electron Detachment Energies (in eV) of the Four Ci- Isomers I-IV. Capital Roman Numbers in the Top Row Refer to the Labeling of Firmre 1 vertical EDE (ev) method basis set I I1 I11 IV Koopmans' DZP +0.33 +0.58 +1.53 +1.13 theorem TZP +0.34 +0.69 +1.68 +1.31 ASCF DZP -0.63 -0.38 +0.27 +0.51 TZP -0.61 -0.33 +0.38 +0.64 ASDCI DZP -0.53 -0.35 +0.73 +0.75 OVGF DZP -0.65 -0.36 +0.93 +0.85 on the PES of the Ci- dianion. We refer to this CZ, geometry of Ci- as the quasilinear isomer. The optimized geometrical parameters of the quasilinear Ci- cluster are collected in Table 4 while the energetic data can be found in Table 2. The quasilinear dianion has a closed-shell 'Al groundstateanda positiveKoopmans'EDEof0.33 eV (Table 3). According to our Mulliken and L6wdin population analysis data (Figure 2, I), the charges of the excess electrons are for the most part distributed on the two terminal Cz-groupsof the chain, whereas the central carbon atoms carry only small amounts of negative charge. Thus, the two excess charges are separated by approximately six carbon-carbon bond lengths. But, with theoretical techniques beyond Koopmans' theorem the quasilinear Ci- isomer is predicted to be electronically unstable: At the ASCF level of theory the vertical EDE of the quasilinear dianion I is -0.63 eV, and at the correlated ASDCI and OVGF levels of theory the vertical EDEs are about -0.53 and 4 6 5 eV, respectively. Therefore, we predict the linear (see also ref 2) and quasilinear isomers of Ci- to be unstable with respect to vertical electron loss. Another way to construct an isomer which provides a potentially large separation between the two excess charges is with the Cz, symmetrical carbon cluster I1 in Figure 1. It consists of a threemembered ring which is anellated to one end of a linear chain encompassingsix carbon atoms. Its CZ,geometricalconfiguration (Table 4) represents a true local minimum on the PES of the Ci- cluster (all vibrational frequencies show real values). The bond lengths in the six-membered chain show a strong alternation and resemble the acetylenic bond structure of the even-numbered linear cluster dianions.2~4 The Ci- isomer I1 has a closed-shell 'A1 ground state, and its energetic data are compiled in Table 2. According to our population analysis data the excess charge of isomer I1 is largely localized on the terminal Cz-group of the chain and on the three-membered ring (Figure 2, II), i.e. at the "ends" of the molecular system. This charge distribution is comparable to that of the quasilinear isomer I. We not that the amount of negative charge distributed over the three-membered ring is almost equal to that carried by the terminal Cz-group as well as to the excess charge located on the terminal Cz-units of the quasilinear isomer (Figure 2, I). These results indicate that a terminal C2-group has about the same capability of accommodating excess charges as the substructure "terminal" threemembered ring has, which implies that a terminal C2-unit has a larger electron affinity per carbon atom. Thus, in particular in small carbon clusters, Cz-groups increase the overall electron affinity more efficiently than three-membered rings. Returning to the stability of dianion I1 with respect to electron loss, we found its vertical EDE to be positive at the level of Koopmans' theorem (0.58 eV). By inclusionof electron relaxation and correlation effects, the EDE value is decreased below zero and pertains to 4 . 3 8 , -0.35 and -0.36 eV using ASCF, ASDCI, and OVGF, respectively. From these findings we predict that the nonlinear isomers of (2;- I and I1 decompose by emission of an excess electron. It is worth noting that these results for the two C;- isomers I and I1 are closely related to our findings for the C:- cluster.3

Sommerfeld et al. Obviously a structure providing a potentially large separation between the charges of the extra electrons does by no means guarantee the stability of a small dianion with respect to electron autoejection. For C:- we have shown that there are more efficient ways to overbalance the mutual Coulomb repulsion between the two excess electron^.^ In the following we will examine structures for Ci- which can be derived from extensions of the electronically stable cluster dianion C(C,);: An eye-catchingsystematicextension scheme for the triangular C(C& cluster is the increase of the length of one, two, or all of the terminal chains by any number of C2-units. This leads to a series of odd-numbered carbon clusters C(Ch)(Ck)(CJZ- where h, k, and 1 are even integers. As we will show in section 4, it is energeticallynot favorable to extend the terminal chains by single carbon atoms. The Ci-cluster originating via this scheme is the branched isomer C(C4)(Cz)i- displayed in Figure 1 (III). Another extension of the triangular C(C2):- cluster concept is the DJh symmetrical Ci- isomer IV sketched in Figure 1. The latter is constituted of a central three-membered ring and three terminal C2-units, one at each ring atom. The three-membered ring replaces the central trigonal carbon atom of the C(C,):system. The corresponding structure scheme can as well be extended to higher (odd) numbers of carbon atoms by increasing the lengths of the three terminal chains by any number of Czunits. Investigating the branched Ci- isomer III and the triangular Ci- structure IV, we found both to have a closed-shell ground state of 'Al and 'A' symmetry, respectively. Both geometries represent true minima on the PES of the Ci- cluster; i.e. all vibrational modes show real frequencies. The optimized geometrical parameters are collected in Table4, and the total energies can be found in Table 2. At Koopmans' level of theory the Ci- isomers III and IV have positive EDEs of 1.53 and 1.13 eV, respectively. The inclusion of relaxation and electron correlation again decreases the vertical EDEs of the two isomers, but the EDE values remain positive; i.e. structures III and IV of Ci- are predicted to be stable with respect to electron autoejection. For isomers III and IV the EDEs are 0.27 and 0.51 eV at the ASCF, 0.73 and 0.75 eV at the ASDCI, and 0.93 and 0.85 eV at the OVGF levels of theory, respectively (Table 3). Since ASCF describes relaxation effects, we note that the inclusion of correlation stabilizes the Ci- dianion with respect to selfemission of an excess electron. From these findings we predict the branched (111) and the triangular (IV) Ci- structures to be stable with respect to fragmentation as well as with respect to vertical electron loss. Having established that the Ci- isomers I11 and IV are stable with respect to vertical electron removal, we now have to examine their stability with respect to adiabatic electron autoejection. At this point we mention that the existence of a positive vertical EDE is a necessary but not sufficient condition to guarantee stability with respect to the loss of an electron. In principle an electron can autodetach if the PES of C; drops anywhere in the nuclear coordinate space below the energy of C;- in its vibrational ground state. If the geometries are far from each other, the autodetachment will, however, be suppressed by unfavorable Franck-Condon factors. The predicted fairly largevertical EDEs of isomers 111and IV indicate that the crossover may only occur at nuclear coordinates far away from the equilibrium structure of Ci-. Since rearrangements of the molecular structure of carbon clusters are in general associated with high-energy barriers as discussed above, it follows that the electronic stability of a carbon cluster dianion is ensured if in the surrounding region of its equilibrium structure the PES of the correspondingmonoanion is higher in energy than the dianionic PES. In the following discussions we will use the term adiabatic stability to electron loss in the latter sense.

Small Dianionic Carbon Clusters

The Journal of Physical Chemistry, Vol. 98, No. 36, 1994 8917

TABLE 4 Optimized Bond Lengths (in A) and Bond Angles (in deg) of the Four Ct- Isomers I-IV (the Numbering Scheme for the Atoms Is Consistent with Figure 1). The Geometrical Parameters of the Monoaluonic Isomers Corresponding to Structures 111 and IV Are Also Given. The Data Were Obtained at the SCF/DZP and the SCF/TZP Levels of Theory, Respectively isomer I isomer I1 isomer III isomer IV dianion monoanion dianion dianion dianion monoanion DZP TZP DZP TZP DZP TZP DZP TZP DZP TZP DZP TZP 1-2 2-3 3-4 4-5 1-2-3 2-3-4 3 4 5 4-5-6

1.243 1.371 1.229 1.367 179.5 179.5 172.6 125.1

1.244 1.373 1.230 1.370 179.4 180.0 173.0 126.9

1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9

1.237 1.388 1.206 1.390 1.203 1.422 1.374 1.465

1.228 1.379 1.200 1.382 1.197 1.414 1.366 1.451

1-2 2-3 3-4 4-5 5-6 6-8 6-5-7

1.238 1.381 1.208 1.425 1.396 1.244 122.3

1.230 1.373 1.203 1.420 1.390 1.235 122.1

1.271 1.369 1.199 1.460 1.373 1.252 128.2

1.263 1.360 1.193 1.455 1.367 1.243 128.1

1.377 1.399 1.237

1.370 1.389 1.228

1.404 1.355 1.259

1.396 1.344 1.249

some1 111

homer I 0,4 '3

03

Q

T

3\

7'

li

B

1-2 1-4 4-7

-

-0.6 '

l

1

2

3

4

S

6

5

6

7

U

9

~

Isomer I1 0,4

03

i

4-'9

Isomer 111

I

1

2

3

4

homer N

I

n

0,4

03

7

L

'

c

1

2

3

4

5

6,7

@P

8,9

Figure 3. Schematicdepiction of the highest occupied molecular orbital (HOMO) of the branched Ci- cluster III and the triangular dianion IV

(Figure 1). Shown are the p-components perpendicularto the molecular plane, which for both clusters constitute the HOMO. The relative phase of the p-components is indicated, and in this way a schematicpicture of the bonding character of the HOMO is provided. Figure 2. Mulliken (white bars) and LBwdin (black bars) population

analysis data for the four Ci- isomers graphically depicted in Figure 1. The numbering scheme is consistent with Figure 1 and Table 4. In order to determine the adiabatic stability with respect to electron autodetachment of the presently examined Ci- isomers 111and IV, we have optimized the geometries of the structurally related monoanionic C, isomers by starting from the equilibrium structures of the dianionic clusters. In this way we found two local minima on the PES of the C, monoanion (all vibrational frequencies of the monoanions have real values) closely related to the equilibrium structures of the Ci- isomers 111and IV. Our results are compiled in Tables 2 and 4 and show that the branched Ci- isomer 111as well as the triangular cluster IV are both stable with respect to vertical and to adiabatic electron loss. With the overall stability of the branched and triangular Ci- isomers having been established, let us now discuss which properties of these dianoinic clusters actually determine whether they can bind the two extra electrons. In comparison to the

quasilinear isomer I and the cluster dianion 11, the most obvious ingredient to the electronic stability of the Ci- dianions 111and IV is the increased number of electron affine, i.e. electron accommodating, substructures. Whereas the former isomers I and I1 have only two electron affine substructures (two terminal C2-groups or a terminal C2-group and the three-membered ring, respectively), the latter clusters 111and IV provide three terminal C2-units to accommodate their extra electrons. In this way the overall electron affinity of the clusters 111and IV is enhanced in comparison to that of structures I and 11, and thus the excess electrons of 111 and IV can be bound more efficiently. We note that the HOMO of the dianionic systems 111 and IV is composed of the p-components perpendicular to the plane of the molecules as shown schematically in Figure 3. For both clusters 111 and IV the HOMO clearly has an overall bonding character. It is true that the HOMOSare partly antibonding in character especially between the central three-membered ring of isomer 111and its three terminal C2-groups, but these effects are overbalanced by the bonding character within the central and

8918

The Journal of Physical Chemistry, Vol. 98, No. 36, 1994

terminal units. However, the bonding character of the HOMO does not imply that the two extra electrons accommodated in these orbitals have themselves to be bound. But it emerges that the occupation of the HOMO does not result in a destabilization of the molecular systems but rather tends to stabilize the bonding in the dianions. From the population analysis data shown in Figure 2 we find that in the dianionicisomers III and IV the negative excess charge is distributed over the three terminal C2-units representing the electron affine substructures. In analogy to the C(C,)i- cluster, the central units-the trigonal carbon atom of isomer III and the three-membered ring of isomer IV-are positively charged. Let us remark at this point that the central unit of the triangular Ci- cluster, i.e. the three-membered ring, may be thought of as a two-electron aromatic system comparable to, e.g., the cyclopropylium ion.” By this means the second key ingredient to the electronic stability of the dianionic carbon clusters is provided, i.e. favorable electrostatic effects. In detail this means that the mutual Coulomb repulsion of the two excess charges is contrasted with a Coulombicattraction between the negative terminal groups and the positive central unit. Thus, the strong covalent bonding of the terminal groups is augmented by ionic bonding. In the following, we will see that the latter is of particular importance for a stable binding of the excess electrons.

Sommerfeld et al. compact than, e.g., the clusters III and IV. Thus, the mutual Coulomb repulsion of the two extra electrons increases in going from isomer III or IV to the cluster C(C,)i-. On the other hand, the central quadruply coordinated carbon atom of the tetrahedral Ci- dianion has to make use of all its valence orbitals to form the four u-bonds to the four C2-groups. Consequently, the central carbon atom cannot be charged positively (in contrast to, e.g., the Be2+ ion in BeFi-) without moving u-electron density to the terminal groups, but this would weaken thecorrespondingu-bonds. Therefore, no additional ionic bonding can be achieved without weakening the covalent bonding, and an electrostatic stabilization comparableto the alkalineearth halide dianions cannot be realized for the C(C2)p system. 4. Small Dianionic Carbon Clusters: General Aspects

In this section we aim at rationalizing the structure of small carbon cluster dianions from a more qualitative point of view. In this context we briefly recall the qualitative principles which are known to govern the structures of small neutral (and monoanionic) carbon clusters and what is known about the geometrical configurations of the individual dianionic clusters C:- to Cii. Let us begin with the neutral carbon clusters C,, for which a wealth of e ~ p e r i m e n t a l l Jand ~ ~ theoreticaF20-21 ~ data exist in the literature. For up to nine carbon atoms the neutral clusters Our hitherto findings for the stable Ci- isomers 111and IV are C, are experimentally observed to exhibit linear cumulenic illuminated by comparison to the structurally related structures. We note that theoretically for even n the monocyclic MX:--type alkali halides.1lJ8 The alkali halide dianions are geometrical configurations are predicted to be slightly lower in based on the followingconstruction principle: a positive-charged energy, but as Pitzer and Clementi pointed out22in the highunit (the metal atom) constitutes the center of a trigonal-planar temperature condition of carbon vapors or similar environments, arrangement of negative-chargedgroups (the halide atoms). These entropy may favor the linear chains. Since in many resent species are almost purely ionic in character (one can think of, experimentsthe carbon clusters are produced by laservaporization, e.g., LiFi- as [Li+(F-)3I2-), and thus these systems are bound the mechanism of graphite fragmentation and the nature of the purely by electrostatic effects:in the region O f the D3h equilibrium surface could also be crucial to the isomeric population. Carbon structure the Coulomb attraction M+/X- is strong and overclusters larger than CSshow first monocyclic structures, and for compensates the mutual Coulomb repulsion of the two extra n 1 20 polycyclic and fullerene structures gradually become charges which dominates the PES at large distances. The stable.23-2s equilibrium structure is a local minimum on the PES of the alkali The transition from linear to cyclic structures at n N 10 has halide dianions, and the barrier along the minimal energy a simple interpretation: Small carbon clusters have linear fragmentation pathway leading to LiF; and F- is high and broad geometrical configurations if the energy stabilization gained by enough to guarantee stabilitywith respect to dissociation. Clearly, ring closure (Le. the formation of an additional carbon-carbon the bonding in the MXf alkali halide dianions strongly rebond) is less than the destabilizationcreated by ring strain. (These sembles the stabilizing electrostatic effects which originate from carbon chains have a cumulenic character, and therefore the the charge distribution in the dianionic carbon clusters III and “natural” bond angle is 1 8 0 O . ) Thus, the structure of small neutral IV as described above. But whereas the alkali halide dianions carbon clusters can be understood in terms of a balance between are almost purely ionic bound, the ionic bonding in the carbon these two factors. Furthermore, the results of Yang et a1.16 and cluster dianions 111 and IV is an addition to the already strong Arnold et al.” confirm that the same scheme applies to the covalent bonding. monoanionic clusters C;. Finally, let us briefly discuss a third conceivable extension of For the corresponding dianionic systems C k the situation is the C(C2):- structure represented by the tetrahedral dianion remarkably different. The mutual Coulomb repulsion of their C(C )iwhich in its geometrical configuration resembles the two extra electrons represents an additional destabilizing factor, in particular, for thesmallest clusters. Indeed the smallestcluster MX!--type alkaline earth halide dianions. The latter are Conpredicted to be stable with respect to electron a ~ t o e j e c t i o n . ~ ~ J ~dianion which has been detected experimentally is Since the tetrahedral structural possesses four electron affine cerning the geometrical configuration of the dianions Ci-, Watts terminal C2-groups, on first sight one would expect its ability to and Bartlett predicted, in a theoretical study,2 Cg- and C$ to accommodate excess electrons to increase compared, e.g., to the exhibit linear acetylenic structures, whereas the doubly negative case for the branched isomer 111. Indeed our data on the ASCF carbon chains with n II and n = 9 were found to be unstable (and ASDCI) level(s) of theory indicate that the tetrahedral with respect tovertical electron loss. Our theoretical results have cluster is stable with respect to vertical electron loss, but our confirmed these statements, and we found a stable isomer of investigationshave not been completed so far. However, we find C:- which has a branched triangular structure (&h ~ymmetry).~ the C(C2):- dianion to have an open-shell 3T (t4) ground state In addition, our present study has shown that two nonlinear isomers and to lie about 7 eV higher in energy than the branched (2:of Ci- (111and IV) are electronically stable as well as stable with dianion 111. Thus, we predict the C(C2):- cluster to be therrespect to fragmentation. modynamically unstable with respect to fragmentation (see Table The molecular structures of the dianions Ci- are very different 1). We plan some future work in this direction. from those observed for the neutral and monoanionic species, because for the dianions the possibilityof electronautodetachment The thermodynamic instability of the C(C,):- isomer with exists. This additional decay channel of the dianions entails that, respect to dissociation can be rationalized by some qualitative in contrast to the neutral and monoanionic systems, the global considerations. On the one hand, the tetrahedral isomer is more

Small Dianionic Carbon Clusters minimum of the dianionic PES may be an electronically unstable structure. Thus, one has to investigate structures which are both minima on the PES and stable with respect to loss of an electron. In our opinion the structure of small dianionic carbon clusters can nevertheless be rationalized in terms of only a few attributes similar to the neutral (and monoanionic) molecules. But, these attributes are not so clear cut as ring strain versus an additional carbon