J. Phys. Chem. 1995, 99, 4923-4928
4923
Isomers of Neutral Ti Met-Car: A Theoretical Study Arshad Khan Chemistry Department, The Pennsylvania State Universiry, DuBois, Pennsylvania 15801 Received: October 16, 1994@
Different isomer structures of neutral Ti met-car (Ti8C12)have been studied in order to compare their stabilities and structural features. These isomers include distorted dodecahedral (DD) and metal decorated C12 cage (MDC) structures. As in the cationic cluster (already reported), the MDC gives two similar isomers. In one isomer eight Ti atoms are arranged at the comers of a distorted cube (cubic isomer), and in the other isomer (noncubic) the metal atoms show a remarkable variation from the cubic arrangements and give the most stable Ti met-car structure. The DD structure is found to be less stable than the MDC structure and fails to explain the photodissociation results. The MDC structure can explain both the photodissociation as well as the other reported experimental results and is the most likely formed cluster type in the experiment.
Introduction The metal-carbon clusters (met-cars) like TigC12 and Ti&12+ are highly stable compounds discovered recently by Castleman and co-workers.' It was postulated that each of these met-cars has a regular dodecahedral cage structure with 12 pentagonal rings of titanium and carbon atoms.' Each pentagonal ring structure was considered to be formed by two titanium and three carbon atoms. Recently we reported2 that the cationic met-car has a C12 cage structure (distorted icosahedron) surrounded by eight Ti atoms. We have also shown how our calculated structure explains all the features of photodissociation experiments on cationic met-car3 in which metal atoms (M) dissociate successively without the elimination of carbon atoms. A regular dodecahedral structure or a distorted one (which may accommodate M-M and M-C bond length variation) cannot explain the elimination of six to seven metal atoms in certain met-cars without the elimintion of carbon atoms.2 We also reported the existence of two distinct isomer structures for the cationic Ti met-car.2 In one isomer the metal atoms are arranged at the comers of a distorted cube (cubic isomer), and in the other, the noncubic isomer, the metal atoms exhibit a significant variation from the cubic arrangement around the C12 cage. Since our first report on the structure of cationic met-car, we discovered similar highly stable isomer structures for the neutral in addition to a less stable distorted dodecahedral structure. Our structures were obtained for singlet and triplet states of neutral met-car by applying the intermediate neglect of differential overlap self-consistent field unrestricted HartreeFock method (INDO SCF UHF) by using the ZINDO series of programs developed by Zemer and c o - ~ o r k e r s . ~We - ~ should point out that systems like met-cars, having a large number of electrons, cannot be studied by an accurate ab initio method. A suitable quantum mechanical method that can be applied must be based on approximations in which certain time-consuming integrals are not calculated. In ZINDO the error introduced due to approximations is compensated by the use of parameters determined through comparison of calculation with experiment. Even though ZINDO is based on INDO approximations, the appropriate choice of parameters based on experimental results can give quite reliable molecular structures with the advantage of a much smaller amount of computation time compared to accurate ab initio calculations.* We already parametrized Ti (beta d value -33.0 eV) and tested with a number of Fi'Abstract published in Advance ACS Abstracts, March 15, 1995.
organometallic compounds having Ti-C, C-C, and Ti-Ti bonds.2 In each test case a good agreement was obtained between the calculated and the experimental results which, hence, suggests a suitable choice of parameters for the structural studies of Ti met-cars involving Ti and C atoms. We should point out that quite a number of other structures have so far been proposed for neutral Ti met-car? Almost all of these structures (in ref 9) were obtained either by constraining the molecular geometry to certain symmetry g r ~ ~ p ~ , ~ ~ , ~ - ~ - g , ~ like Th, D2h, D3d, D2d, CzV,etc., during geometry optimization or by allowing small distortions from a regular dodecahedral The calculations involved the application of a wide range of theories and models, the Huckel model,gbvalence bond theory,9c ab initio theory with effective core potential^,^^ and (rest in ref 9) density functional (DF) approximations. When neither the experimental structure nor its symmetry group is known, the calculated molecular structure with an assumed symmetry may lead to an incorrect cluster structure, especially when the most stable structure may not have such a symmetry. In addition, by allowing small distortions from the regular dodecahedral structure, one can only examine a limited number of structures close to that of the dodecahedron and may miss more stable structures which are significantly different from the starting geometry. This may be the case in the present situation in which all the structures proposed in ref 9 are certain forms of distorted dodecahedral structures. The basic structural features are almost the same (C-C distance around 1.4 A, Ti-C around 2.0 A) except for certain variations in Ti-Ti bond lengths and angles. It should be pointed out that the calculations of cationic2 or neutral (presented here) met-car structure did not assume any such molecular symmetry during geometry optimization, and hence, we could study a wide range of structural variations from the proposed dodecahedral structure.
Results and Discussions Metal Decorated CIZCage (MDC) Structures. Cubic and Noncubic Structures. Each of the two highly stable structures of neutral Ti met-cars has the same basic structure, a 12-carbon cage structure surrounded by eight Ti atoms (Figures 1-41, As in cationic met-car2 two distinctly different isomers were obtained; in one the Ti atoms are arranged at comers of a distorted cube (cubic isomer, Figures 3 and 4), and the other, the more stable isomer, shows a remarkable variation from the cubic arrangement of Ti atoms and forms a bicapped trigonal
0022-3654/95/2099-4923$09.oo/o 0 1995 American Chemical Society
Khan
4924 J. Phys. Chem., Vol. 99, No. 14, 1995
h
8
TABLE 1: Calculated Distances (A) in TisClt Antiprism Structure (Figure 1) a. Ti-Ti Distance Ti-Ti distance from Ti atoms in colum 1 (A)
Ti atom
(3) 4.55 (4) 3.57 (6) 4.72 (7) 4.59
(4) 2.87 (5)
4.46 (7) 4.67
(5)
4.52 (7) 4.54
(6) 4.66
(8)
3.59
(8)
2.87
Figure 1. Ti~C12bicapped antiprism structure is presented with eight titanium atoms lying outside of the distorted D 3 h carbon cage structure.
b. Ti-C Distance Ti-C distance from C in column 1
C atom (1)
(9) (10) (11)
(12) (13) (14) (15) (16) (17) (18)
Figure 2. Ti~C12antiprism structure is presented in space-fill model with metal atoms shown by outer filled circles surrounding a carbon cage structure.
(19) (20)
C atom
2.36 2.40 3.59 2.38 2.45 3.65 4.52 4.49 3.51 3.62 4.50 4.49
(2) (3) (4) (5) (6) (7) (8) 2.45 3.58 2.48 3.54 4.50 4.50 4.93 3.72 2.40 2.29 4.48 3.59 4.50 4.78 2.45 2.36 2.48 4.50 4.54 3.63 4.82 3.65 4.51 3.84 2.37 3.58 4.49 3.91 4.59 3.64 3.71 3.66 2.38 4.51 3.82 4.60 2.43 3.71 4.61 2.43 3.65 3.70 3.65 2.38 3.84 4.60 3.65 2.43 3.71 2.38 3.57 3.98 3.65 4.51 2.39 3.84 2.36 4.49 3.97 2.36 4.50 3.59 3.98 4.50 4.54 4.83 2.46 2.37 3.58 2.41 4.48 3.59 4.78 3.74 2.40 2.39 2.28 3.55 4.51 4.93 2.45 3.59 2.38 2.48 c. C-C Distance C-C distance from C in column 1
Figure 3. TigC12 cubic structure is presented with eight titanium atoms at comers of a distortedcube surrounding a distorted icosahedral carbon cage structure. (20) 1.60
Figure 4. TixC12 cubic structure is presented in space-fill model with metal atoms shown by outer filled circles surrounding a carbon cage structure. antiprism structure (noncubic isomer, Figures 1 and 2). Among all the Ti met-cars (both cationic and neutral) that we characterized, the singlet state of this noncubic antiprism structure represents the most stable isomer (Figures 1 and 2 ) and is more stable than the neutral cubic structure (singlet,
Figures 3 and 4) by about 147 kcaVmol and the neutral noncubic triplet and cationic noncubic doublet2 structures by about 56 and 147 kcaYmol, respectively. The singlet and triplet cubic structures of neutral met-cars have about the same energy. Even though these relative energy values may be overestimated to some extent, the relative stabilities are correctly predicted in most situations.'0-12 Figure 1 shows the structure of the most stable isomer of Ti met-car with carbon atoms forming a cage structure surrounded by eight Ti atoms forming a bicapped trigonal antiprism. Tables la-c give different interatom distances in this isomer. Figure 2 represents a space-fill model (based on van der Waals radii of Ti and C atoms) for the same isomer in which Ti atoms are the outer filled circles with the Clz cage structure lying inside. Figures 3 and 4 represent the
Isomers of Neutral Ti Met-Car
J. Phys. Chem., Vol. 99, No. 14, 1995 4925
TABLE 2: Calculated Distances (A) in Ti& Structure (Distorted, Figure 3)
Cubic
a. Ti-Ti Distance Ti-Ti distance from Ti atoms in column 1 (A)
Ti atom
(3) 5.32 (6) 3.86 (7) 4.70
(5) 4.70
(4) 4.23
b. Ti-C Distance
Ti-C distance from C in column 1
C atom (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)
(1) 2.34 2.29 2.35 3.57 3.70 3.97 4.43 4.40 4.65 3.68 3.53 3.84
(2) (3) (4) 3.13 3.71 2.38 2.32 4.34 3.96 3.75 5.20 3.49 4.56 4.59 2.37 3.40 2.41 2.35 2.44 2.14 3.88 3.92 4.42 4.36 4.39 3.74 2.92 3.63 2.88 3.82 2.36 3.67 4.50 3.83 5.35 4.49 4.96 5.85 3.88
(5) 4.42 3.75 2.88 3.67 5.35 5.86 3.72 4.34 5.21 4.60 2.41 2.14
(6) 4.35 2.90 3.81 4.50 4.49 3.88 2.39 3.96 3.49 2.36 2.35 3.88
(7) 4.43 4.41 4.66 3.68 3.53 3.85 2.34 2.28 2.35 3.57 3.71 3.98
(8) 3.91 4.39 3.63 2.36 3.83 4.96 3.12 2.32 3.74 4.56 3.40 2.44
c. C-C Distance
C atom
C-C distance from C in column 1 (1 1) 1.61 (18) 1.56 (19) 1.65 (20) 1.55 (17) 1.65 (18) 1.55 (17) 1.61
(12) 1.64 (19) 1.66
(13) 1.54
(18) 1.64
(19) 1.54
structure of the singlet state of the neutral cubic met-car. Tables 2a-c give the interatom distances in this isomer. The Mulliken charges on the carbon cage structure is about -2.0, and the rest of the charge lies on Ti atoms in each met-car isomer and suggests certain ionic character in metal-carbon bonds. A greater stability of the antiprism structure (Figures 1 and 2) compared to the cubic one (Figures 3 and 4) can be understood from the number of Ti-Ti (Tables l a and 2a) and Ti-C (Tables l b and 2b) bonds. While in antiprism structure there are four Ti-Ti bonds (Table la) involving Ti atoms 1, 3, 4, 6, 7, and 8, in cubic structure there are two such bonds (involving Ti atoms 1, 2, 7, and 8; Table 2a) at a distance of around 2.87 A, shown with Ti-Ti solid lines in Figures 1 and
3, respectively. Besides, each Ti atom in antiprism structure gives four Ti-C bonds (except the Ti atoms 4 and 8 in Figure 1, each of which has three such bonds) at a distance of around 2.40 8,. In cubic structure there are three such Ti-C bonds involving each Ti atom, except the Ti atoms 4 and 6 (Figure 3), each of which has four bonds. The above-mentioned bond distances (hence strengths) are fairly close to those existing in stable organometallic^'^ in which the Ti-Ti shortest distance is around 2.90 and that of Ti-C is around 2.1-2.3 8,. The C12 in the antiprism structure (Figure 1) respresents a distorted D3h cage, and in cubic structure a distorted icosahedral cage (Figure 3). We have shown in our previous paper2 that in a symmetrical icosahedral cage structures each carbon atom is bonded to five other carbon atoms at a distance of around 1.60 8,. Each carbon (in regular icosahedron), in addition to its involvement with the triangular face (giving 60" angle) of the icosahedron, is also involved with pentagonal ring formation (giving around 108" angle). In the antiprism structure (Figure 1) each C is bonded to four other C atoms, and in cubic structure (Figure 3) each C has three to five such bonds (shown with solid lines). In antiprism structure, there are three distinct Ti-Ti distances of around 2.87,3.58, and 4.59 8, with standard deviations (SDs) of around 0.00, 0.01, and 0.07 respectively (Table la). There are also the three Ti-C distances (Table Ib) of around 2.40, 3.69, and 4.58 8, with SD values of around 0.05, 0.13, and 0.14, respectively. The average C-C distance in this cluster is around 1.60 8, with the SD value of around 0.03 (Table IC). There are three distinct C-C-C angles of around 60,90, and 120" in this cluster. Each carbon is involved with tirangular or rectangular faces or both in addition to its involvement with hexagonal ring structures giving the above angles. For example, in Figure 1, carbon atom 10 is involved with two triangular faces (giving 60" angles) with carbon atoms, 9, 11 and 13, 14 and two rectangular faces (giving 90" angles) with carbon atoms 11, 15, 14 and 9, 12, 13. In addition, carbon 10 is also part of two hexagonal rings (giving 120" angles) defined by carbon atoms 10, 14, 19, 20, 17, 9, and 10, 13, 18, 20, 16, 11, respectively. The carbon cage in the cubic isomer is much less symmetrical (Figure 3) with C-C-C angles varying from 60 to 133". The average C-C distance is ca. 1.59 8, with the SD value of around 0.04 (Table 2c), and the Ti-C distances range from ca. 2.3-5.9 8, (Table 2b). As in antiprism structure, there are three distinct Ti-Ti distances of ca. 2.83, 3.84, and 4.58 8, with the SD values of ca. 0.00, 0.03, and 0.53, respectively. Tables of Ti-Ti, Ti-C, and C-C interatom distances for singlet isomers are given in which specific atoms are represented by numbers in parentheses and each interatom distance is given (under an atom number) relative to an atom in column 1. Distorted Dodecahedral (DD) Structure. As we mentioned earlier, our calculations also predict a stable DD structure (Figures 5 and 6) which is quite comparable to most of the structures proposed in ref 9. In this structure both Ti and C atoms lie close to the surface of a sphere (Figure 6), distinctly different from the cubic or noncubic MDC (metal decorated carbon cage) structure. From another view we can say that in the DD isomer (Figure 5 ) there are 12 C atoms lying in pairs over the six faces of a distorted cubic. Tables 3a-c represent relevant Ti-Ti, Ti-C, and C-C distances in the DD isomer. Each C atom is bonded to a Ti atom at a distance of around 2.10 8, (shown with solid lines in Figure 5) and two others (on the cubic face) at around 2.30 8, each (shown with dashed lines). For clarity all the Ti-C bonds are not shown in Figure 5 . The nearest neighbor C-C distances range from 1.33 to 1.44 8, and suggest a double bond character. The second nearest neighbor C atom is at a significantly large distance (around 3.25 8,) and
Khan
4926 J. Phys. Chem., Vol. 99, No. 14, 1995 11
TABLE 3: Calculated Distances (A) in Ti&,* Distorted Dodecahedral Structure (Figure 5)
I2
C / c
a. Ti-Ti Distance Ti-Ti distance from Ti atoms in column 1 (A)
3 TI I.
Ti atom
14
T
(1) (2) (3) (4) (5) (6) (7)
(2) 2.90
15
Figure 5. Ti&,Z distorted dodecahedral structure is presented in which all the Ti-C bonds are not shown for clarity. The solid and dashed lines joining the Ti and C atoms represent bond distances of around 2.10 and 2.30 A, respectively. The Ti-Ti and C-C distances (shown with solid lines) are around 2.98 and 1.40 A, respectively. This structure is less stable than the cubic or the antiprism structure.
(11) (13)
Figure 6. Ti8C12 distorted dodecahedral structureis presented in spacefill model with metal atoms shown by filled circles and carbon atoms by shaded circles. suggests no bonding between one C=C group to another. The nearest neighbor Ti-Ti distances range from 2.90 to 3.01 A with an average of around 2.98 A (close to a single bond length) and suggest Ti-Ti bonding in this structure. The DD isomer (Figure 5 , singlet) is less stable than the neutral cubic isomer (Figures 3 and 4, singlet or triplet) by about 202 kcaymol. As already pointed out, the noncubic antiprism (singlet) is the most stable isomer among all the Ti met-car isomers that we characterized so far (neutral and cationic) and is more stable than its cubic isomer by about 147 kcal/mol and the DD singlet isomer by about 349 kcalhol. The DD triplet structure is slightly less stable than that of the singlet state. As has been pointed out, the relative energy values, even though may be overestimated, the relative order of stabilities are expected to be correct. The following binding energy calculation for the antiprism structure and a comparison of its value with that reported for the DD (distorted dodecahedral) isomer further support the stability of the antiprism MDC (metal decorated carbon cage) structure. Binding Energy of Antiprism Structure. Because of the size of this problem, involving transition metal atoms and a large number of electrons, an accurate binding energy calculation is not possible. Even though the density functional (DF) theory has been applied in energy calculations of many large systems, like the DD structure of the Ti met-car, one needs to be careful in applying this method for energy calculations of the carbon cage structures. In this regard the recent DF calculations by
(15) (17) (19)
(5) 3.00 3.23 4.98 3.60
(1) (2) (3) (4) 3.38 2.31 4.93 4.59 2.11 2.31 5.07 4.09 2.08 2.30 3.37 2.32 3.37 2.32 2.08 2.30 5.06 4.07 2.11 2.31 4.92 4.57 3.38 2.30 4.92 4.57 5.07 4.08 5.07 4.07 4.93 4.59 5.08 2.23 2.57 4.44 5.23 2.73 2.36 4.05 2.57 4.42 5.08 2.22 2.36 4.04 5.24 2.74
(6) 4.92 2.96 4.43 4.92 2.96
(7) 4.97 3.58 3.01 3.24 3.31 3.04
(8) 4.43 4.92 4.93 2.98 3.05 4.98 3.05
(5) (6) (7) 2.29 2.11 4.16 2.31 3.30 4.69 4.17 5.10 4.69 4.70 4.97 4.17 4.69 4.70 2.31 4.16 5.10 2.29 2.31 3.40 2.30 2.30 2.14 2.31 4.54 2.65 3.34 4.13 2.40 2.14 3.34 5.80 4.52 2.15 4.89 4.12
(8) 5.11 4.97 4.97 5.10 3.40 2.11 2.14 3.41 5.81 4.90 2.65 2.40
c. C-Ca Distance C-C distance from C in column 1
C atom (9) (10)
(4) 2.94 3.16 2.90
b. Ti-C Distance Ti-C distance from C atom in column 1
C atom (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20)
(3) 4.86 2.93
(10) 1.43 (11) 3.25 (12) 1.44 (14) 1.43 (16) 1.41 (18) 1.33 (20) 1.33
(11) 4.09 (12) 4.12
(12) 4.54 (16) 4.09
(16) 3.25 (17) 4.21
(17) 3.47 (19) 4.12
(20) 4.01 (20) 3.28
“The distances of the second nearest neighbor C atoms are also presented for carbon atoms 9 and 10. Raghavachari et al.14 on the C ~cluster O can be mentioned. The DF calculations at the LDA (local density approximation) level predict the cage to be much more stable than the ring structure. Inclusion of gradient correction, however, reverses the energy ordering making the ring structure much more stable than the cage (by more than 7 eV). The ab initio energy calculation with the 6-31G* basis and correlation correction at the MP2 level, on the other hand, predicts the cage to be significantly more stable than the monocyclic ring and contradicts the results of the D F r calculation with gradient correction. Because of a reliable track record of energy prediction by the ab initio method at the MP2/6-31G* level, one can consider the ab initio result to be accurate and, thus, may suspect the accuracy of the DFT results for the carbon cage structures. Since the MDC (metal decorated carbon cage) structure has a strained C12 cage, the DFT method cannot be applied for a reliable binding energy calculation. The present approach, therefore, involves an ab initio energy calculation of the C12 cage that appears in the antiprism met-car structure, by using the 6-31G* basis set with correlation correction at the MP2 level, followed by the consideration of the number of Ti-C and Ti-Ti bonds and their energies (experimental). Before these calculations, we tested whether the C-C bond energy is correctly predicted
Isomers of Neutral Ti Met-Car by the above basis sets and level of correlation correction. These involved geometry optimizations of the ethane and methyl radical by applying the ZINDO method followed by the single point energy calculations with 6-3 lG* basis and correlation correction at the MP2 level. The calculated value is 98 kcal/ mol and compares quite well with that of the experiment (97 kcaUmo1) .I The single point energy calculation (MP2/6-3 1G*) for the Cl2 cage, which appears in the antiprism MDC structure (Figure l), gives a binding energy of 51.71 eV (or 4.31 eV/atom) relative to separated triplet C atoms. This energy value per atom is comparable to that of a N2 (4.9 eV/atom) molecule and, hence, the C12 cage structure represents a thermally stable cluster. Even though similar calculations also predict a monocyclic ring (5.9 eV/atom) or a linear chain (5.7 eV/atom) structure to be more stable than the cage structure,” one cannot rule out the existence or formation of a cage structure solely on the basis of these energy values. The high energy cage structure may still form (may even form faster than a larger ring structure, as larger than six-membered rings are known to be very difficult to formIs) and survive owing to a rapid cooling during the beam expansion. In general, it is believed that the small carbon clusters are highly reactiveIg for which no cage molecules fewer than 60 C atoms have so far been isolated. For the same reason an accurate experimental determination of these cluster structures has not yet been possible. Our postulated mechanism of met-car formation is in line with the high reactivity of these clusters; that is, the C12 cage structure formed during the beam expansion and cooling, undergoes a rapid attachment of eight metal atoms2 The stabilization energy is also increased significantly as a result of the Ti-C bond formation. As presented in Table lb, there are six C atoms in the C12 cage, each of which is bonded to three Ti atoms, and the other six C atoms are each bonded to two Ti atoms at a distance of around 2.3 8,. This distance of Ti-C is about the same as that we calculated for the Ti(CHzPh)4 molecule2having the bond energy of 264 kJ/mol (2.74 eV).20 Hence, in the present calculation, each Ti-C bond formation at around 2.3 8, is considered to involve an energy of 2.74 eV. Since in the antiprism structure there are six C atoms, each of which forms three Ti-C bonds, the other six C atoms, each giving two Ti-C bonds (Table Ib), the net Ti-C bond formation energy is around 82.1 eV. As we mentioned before, the bond formation energy for the C12 cage structure is 51.7 eV. The Ti-Ti bond at a distance of around 2.90 8, represents a single bond character with an average bond energy of 126 kJ/mol (1.30 eV).21 There are four such Ti-Ti bonds (Table la) in the antiprism structure with the net bond formation energy of 5.2 eV. Thus, the overall bond formation energy is calculated to be around 139 eV or 6.95 eV/atom. It should be pointed out that the angular strain in the antiprism MDC structure is primarily due to the C12 cage structure, the energy of which (carbon cage) has been calculated quite accurately. Except for the four Ti-Ti bonds, most of the Ti-Ti distances are quite large and, thus, the angular strain due to eight Ti atoms arranged around the carbon cage can be neglected. In addition, the Ti-C bond formation energy at a distance larger than 2.5 8, is neglected. T h e binding energy of 6.95 eV/atom for the antiprism MDC (metal decorated cage) structure is larger than most of the reported results on the distorted dodecahedral (DD) structure which range from 6.1 to 6.6 eV/atom (ref 9d,h,l,m). It is interesting to point out that the DFT calculation with a nonlocal correction provides a binding energy value of 6.54 eV/atom (ref 9m) for the DD structure, which is, however, increased by about 1 eV (7.47 eV/atom), when such a correction is not applied. Since the nonlocal correction generally provides a more accurate result, one can assume 6.54 eV to be a better estimate of the
J. Phys. Chem., Vol. 99, No. 14, 1995 4921
binding energy. Besides, the binding energy value of 6.54 eV is more in line with the other reported results for the DD isomer. From these calculated results, one can suggest that the antiprism structure is more stable than the DD structure by at least 0.30.4 eV/atom or about 140-180 kcaUmo1. Because of the inaccuracies involved in various calculations, and the fact that the higher energy product may form faster than the lower energy isomer and dominate, if rapidly cooled (which may happen in beam expansion), one must rely on experimental results for the identification of the structure predominantly formed in the experiment. Comparison with Experimenal Results. Since each of the DD or MDC structure has eight Ti atoms in the exposed position, each can explain the product formation of the type LsTisClz, where L represents a relatively smaller sized ligand bonded to the metal atom of met-car. As we already mentioned, the experimental results on the photodissociation3 of different met-cars (expected to have similar basic structures) cannot be explained on the basis of a DD structure2 and, thus, may suggest either the nonexistence of a DD isomer or the presence of only a negligibly small amount of it. These experiments suggest that in certain met-cars six to seven metal atoms dissociate successively without the elimination of carbon atoms. By referring to the DD structure (Figure 5 ) , one can say that, after the photodissociation of metal atoms 1, 2, and 5, if the atom 6 dissociates, it must carry away the carbon atoms 9 and 10. The distances of the second nearest neighbor carbon atoms from carbon atoms 9 and 10 are presented in Table 3c. From these values, one can readily conclude that there is no bonding between one C=C unit to another because of a large distance (> 3 8,) from each other. Thus, it is highly unlikely that during photodissociation of metal atoms a drastic rearrangement will take place so that all C atoms will cluster together from such a long distance to prevent its elimination. On the other hand, the MDC (metal decorated cage) structure, in which metal atoms are arranged around the carbon cage, can explain the photodissociation experiments2 and, hence, is most likely formed in the experiment. Among the two isomers of MDC (metal decorated cage), the antiprism structure is expected to dominate because of its greater stability. Are All Metal Sites Equivalent? It is necessary at this point to address the issue of whether all the metal sites are equivalent or not in the met-car structure. The photodissociation experiment by Pilgrim and Duncan3 suggests that in TisC12+ up to three Ti atoms and in CrsC12+up to seven Cr atoms dissociate, and the fragmentation pattern does not change when the laser power is increased (532 nm to 308 nm). This observation may suggest that three Ti atoms are more weakly held than the five other Ti atoms in Ti met-car, and seven Cr atoms are more weakly held than the remaining one in Cr met-car. If the metal sites were all equivalent, the fragmentation pattern would have changed with an increased laser power or internal energy.22In this regard, it is appropriate to mention the experimental results of Farrar and Lee,23 which dealt with the question of energy randomization and decomposition of a number of activated molecules (like C2H4F and C4HsF). In these experiments it was observed that the energy randomization favors cleavage of weaker bonds in excited molecules, and a significant part of the internal energy, even when increased, is used up in providing kinetic energy to the dissociating fragments. It appears that, in met-car photodissociation, a similar mechanism is valid. That is, an increased laser power or internal energy does not change the fragmentation pattern as most of the energy goes to the dissociation of the weaker Ti-C or Cr-C bonds and their dissociated fragments, This mechanism of dissociation will certainly indicate the presence of nonequivalent metal sites.
Khan
4928 J. Phys. Chem., Vol. 99, No. 14, 1995
It is interesting to point out that the experiments of Cartier et al.24 with T i c and Zr in the molar ratio of 4:l show a consistent drop in the concentration of products from pure Ti met-car to mixed clusters of increased number of Zr atoms, that is, from TisC12+to Ti,ZrClz+, TiZr2C12+,Ti&Cn+, and T@&12+ clusters. This observation has been explained24by assuming equivalent metal sites in the met-car structure (regular dodecahedron). The reasoning was, that, if the metal sites were not equivalent, then certain combinations of metals (Ti and Zr) would give more stable clusters than the others and dominate among the mixed clusters rather than showing a decreasing concentration as the number of Zr atoms is increased. These results appear to contradict the photofragmentation results of Pilgrim and D ~ n c a nas , ~discussed above. A careful examination will, however, suggest that the Cartier et al.’s results do not unambiguously establish the existence of equivalent metal sites. Since the the number of Ti atoms was 4 times larger than that of the Zr atoms in the experiment, a large excess of Ti atoms was available to combine with the C12 cage, and thus the random attachment of metal atoms to carbon cage led to a larger concentration of pure Ti met-car and a decreasing concentration of clusters with an increased number of Zr atoms. The reported results merely suggest that the rate of cluster formation determines the product concentration. Since the beam expansion (during cluster formation) causes a rapid cooling of the newly formed clusters, both the high and the low energy products may survive, and thus the mixed cluster population is determined by the rate of their formation. The calculated structures, both DD and MDC type, suggest the existence of nonequivalent metal sites. For example, in the antiprism structure, each of the metal atoms 4 and 8 has only three Ti-C bonds, while the other metal atoms have four such bonds (Table lb) at a distance of around 2.3-2.4 8,. Each of the metal atoms 4 and 8, however, forms two Ti-Ti bonds (Figure 1 and Table la), and metal atoms 1, 3, 6, and 7 form a single Ti-Ti bond. Considering the above-mentioned bond formation energies, one can say that the Ti atoms 4 and 8 will be more weakly held than the atoms 2 and 5 by about 0.14 eV. Even between the Ti atoms 2 and 5 , one may expect a difference in the binding energy value as the nearest neighbor Ti-C distance (average) for the Ti atom 5 is around 2.41 A and for 2 is around 2.40 8, making the former bonding weaker than the latter. In the DD structure, similar but more pronounced nonequivalent metal sites can be discovered. For example, each of the metal atoms (Table 3b, Figure 5) 1, 3,6, and 8 has three Ti-C bonds at a distance ranging from 2.1 to 2.3 8, and a fourth bond (a weaker one) at a distance of around 2.6 A. Each of the metal atoms 2,4,5, and 7 has five Ti-C bonds at a distance of around 2.3 A. In addition, each of the metal atoms 2 and 4 has a sixth bond (weaker one) at a distance of around 2.7 A. Thus, the metal atoms 1, 3,6, and 8 are more weakly held than the others in the DD cluster by at least a Ti-C bond energy (2.74 eV). This analysis suggests that there is a more noticeable nonequivalency of metal sites in the DD structure than in the antiprism MDC structure.
Concluding Comments Based on this study one can conclude that the met-car has a MDC (metal decorated cage) rather than a DD (distorted dodecahedral) type structure. The photodissociation result can only be explained by the MDC and not by the distorted or a regular dodecahedral structure. Since the MDC is the most likely formed met-car structure, one needs to address a key question, that is, if the 12 carbon cage formation takes place in met-car, why have no experiments so far reported the existence of a C12 cage structure? One possible answer may be the high
reactivity of the smaller cage structure, which soon after the formation may attach to other elements present nearby and, hence, escapes detection as a pure 12-mer carbon cage structure. In our postulated mechanism of the met-car formation, a C12 cage is initially formed followed by a rapid attachment of eight metal atoms. All the reported experimental results can be explained by this MDC structure.
Acknowledgment. We thank Professor Castleman for sending us reprints of relevant papers on the neutral Ti met-car structure. All of our quantum mechanical calculations were performed by using an IBM ES/3090-600S computer at the facilities of the Pennsylvania State University Center for Academic Computing. We also acknowledge the assistance of M. M. Greene with graphics. References and Notes (1) Guo, B. C.; Kems, K. P.; Castleman, A. W. Science 1992,255, 141 1. (2) Khan, A. J . Phys. Chem. 1993,97, 10937. (3) Pilgrim, J. S.; Duncan, M. A. J . Am. Chem. SOC. 1993,115,4395. (4)Zemer, M. C. Quantum Theory Project, University of Florida, Gainsville, FL 3261 1. (5) Zemer, M. C.; Loew, G. H.; Kirchner, R. F.; Muller-Westerhoff, U. T. J . Am. Chem. SOC. 1980,102,589. (6) Culberson, J.; Knappe, P.; Rosch, N.; Zemer, M. C. Theor. Chim. Acta 1987, 71,21. (7) Bacon, A. D.; Zemer, M. C. Theor. Chim. Acta 1979,53,21. (8) (a) Zemer, M. C. In Reviews in Computational Chemistry: 11; Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers: Deerfield, FL,1991; p 313. (b) Stewart, J. J. P. In Reviews in Computational Chemistry, Lipkowitz, K. B., Boyd, D. B., Eds.; VCH Publishers: Deerfield, FL, 1990: p 45. (9) (a) Grimes, R. W.; Gale, J. D. J . Chem. SOC.,Chem. Commun. 1992, 1222. (b) Ceulemans, A.; Fowler, P. W. J. Chem. Soc., Faraday Trans. 1992,88, 2797. (c) Pauling, L. Proc. Natl. Acad. Sci. 1992,89, 8175. (d) Reddy, B. V.; Khanna, S. N.; Jena, P. Science 1992,258,1640. (e) Rohmer, M.; Vaal, P.; Benard, M. J . Am. Chem. SOC. 1992,114,9696. (0 Lin, Z.; Hall, M. B. J . Am. Chem. SOC.1992,114,10054. (g) Rantala, T.; Jelski, D. A.; Xia, X.; George, T. F. 2.Phys. D 1993,26, S255. (h) Methfessel, M.; Schilfgaarde, M. V.; Scheffler, M. Phys. Rev. Lett. 1993, 70,29; 71,209. (i) Hay, P. J. J. Phys. Chem. 1993,97,3081. (i) Dance, I. J . Chem. Soc., Chem. Commun. 1992,1779. (k) Reddy, B. V.; Khanna, S. N. Chem. Phys. Lett. 1993,209, 104. (1) Li, Z.-Q.; Gu, B.-L.; Han, R.-S.; Zheng, Q.-Q. Z. Phys. D 1993,27,275.(m) Chen, H.; Feyereisen, M.; Long, X. P.; Fitzgerald, G. Phys. Rev. Lett. 1993,71, 1732. (10) Fonslick, J.; Khan, A.; Weiner, B. J . Phys. Chem. 1989,93,3836. (1 1) Khan, A. J . Chem. Phys. 1992,96, 1194. (12) Martin, J. M. L.; Francois, J. P.; Gijbels, R. J . Comput. Chem. 1991, 12,52. (13) F’ruchnik, F. P.; Duraj, S. A. Organometallic Chemistry of the Transition Elements; Plenum Press: New York, 1990: (a) p 518, (b) p 160, 170. (14) Raghavachari, K.; Strout, D. L.; Odom, G . K.; Scuserio, G. E.; Pople, J. A.; Johnson, B. G.; Gill, P. M. W. Chem. Phys. Lett. 1993,214, 357. (15) Parasuk, V.; Almlof, J. Chem. Phys. Lett. 1991,184, 187. (16) Hehre, W. J.; Radom, L.; Schleyer, P.; Pople, J. A. In Ab Initio Molecular Orbital Theory: John Wiley: New York, 1986: p 278. (17) Khan, A. Unpublished results. (18) Morrison, R. T.; Boyd, R. N. Organic Chemistry 4th ed.; Allyn and Bacon: Boston, 1983; p 173. (19) Yang, S. H.; Pettiette, C. L.; Conceicao, J.; Cheshnovsky, 0.; Smalley, R. E. Chem. Phys. Lett. 1987,139,233 and references therein. (20) F’ruchnik, F. P.; Duraj, S. A. Organometallic Chemistry of the Transition Elements; Plenum Press: New York, 1990: p 202. (21) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand Reinhold Co.: New York, 1979; p 642. (22) Forst, W. Theory of UnimolecularReactions; Academic Press: New York, 1973; pp 260, 261. (23) Farrar, J. M.; Lee, Y. T. J . Chem. Phys. 1976,65, 1414. (24) Cartier, S. F.; May, B. D.; Castleman, A. W., Jr. J . Chem. Phys. 1994,100, 5384. JP9427950
