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15Journal of Siberian Federal University. Chemistry 2 (2009 2) 110-132
УДК 541.27, 544.163, 544.169
Quantum Chemical Study of Atomic Structure and Spin States of the Cox(C 60)и (x=1-8, «=1-3) Complex Nanoclusters
Pavel V. Avramova,b*, Felix N. Tomilina,b, Alexander A. Kuzubova,
Polina Artushenkoa and Sergey V. Kachina
a Center of Joint Use of Siberian Federal University, 79 Svobodny, Krasnoyarsk, 660041 Russia b L.V. Kirensky Institute of Physics SB RAS, 50 Academgorodok, Krasnoyarsk, 660036 Russia 1
Received 20.05.2009, received in revised form 27.05.2009, accepted 04.06.2009
The main features of the local atomic structure of novel Con(C60)x (n=1-8, x=1-3) complexes and Con clusters as well were studied using the ab initio GGA calculations for a set of low and high energy isomers in different spin states. It is shown that high-spin low-symmetry structure of free-standing Con clusters is determined by Jahn-Teller distortions. For the Co(C60)x (x=1-3) isomers the spin state S=1/2 is energetically preferable whereas the low energy isomers of Co2(C60)x (x=1-3) have an intermediate spin state of S=1. The rf (6-6 edge of C60) type of cobalt ion coordination is preferable for both n=1 and n=2 cases. The ц2' (coordination with 6-5 edge) and even the ц5 (C5 fragment) types serve as low and high energy intermediates for the cobalt ion's migration around the C60 cage. Formation of cobalt dimers can be the final stage of evolution of Con(C60)x atomic structure approaching the equilibrium atomic geometry. For higher n (3-8) the formation of ц2, ц2' or ц1 coordination bonds between Con fragment and C60 molecules through carbon hexagons results in stable complex nanoclusters with nonmonotonic change of average spin momentum upon the number of cobalt atoms in the Con cores. The theoretical results are compared with corresponding experimental data.
Keywords: Co/C60 mixtures, local atomic structure, DFT, complex compounds.
Introduction
The magnetism of transition metal clusters (TMC) constitutes a fundamental challenge (see, for example, Ref. 1) since atomic and bulk properties are intrinsically different. The TMC physical properties clearly differ from both the atomic and bulk materials [2]: atomic magnetism is due to electrons that occupy localized J-orbitals, while in the transition metal solids like cobalt, the ferromagnetism properties are caused due to indirect coupling of predominantly
* Corresponding author E-mail address: paul@iph.krasn.ru
1 © Siberian Federal University. All rights reserved
localized J-like electrons through a small number of itinerant J-like electrons [3].
The TMCs have been of the significant interest as possible building blocks for magnetic storage and spin-dependent transport devices. For magnetic nanoparticles, this research is stimulated by effort to overcome the supermagnetic limit in magnetic storage devices. Recently, Co-C60 films composed of the Co-C60 compound matrix and Co clusters dispersed therein were found to exhibit an anomalously
large tunnel magnetoresistance (MR) effect as large as 1000% [4-12].
Transition metals, like cobalt, favorably form strong coordination bonds with environments based on carbon. Complex mixtures of C60 fullerenes and transition metals (TM) have attracted attentionbecause ofpossible applications as promising functional materials (see, for example, [4, 13-14]). The TMx/C60 composites can be considered condensed complex compounds with incredibly controllable compositions and are the products of various types of vapor codeposition of transition metals and C60 [4, 15-16]. Actually, the TMx/C60 composites synthesized using the atomic and molecular beams can be considered as complex mixtures of TM„(C60)m compounds. To date, the atomic structure of the TMx/C60 composites has not been well studied by either experimental or theoretical approaches. The further development of such compounds to obtain novel materials is impossible without detailed theoretical study of the species using sophisticated quantum chemical approaches. In contrary with the TMx/C60 composites, the TM„(C60)m complexes with constant composition are well known objects of coordination chemistry (see, for example, detailed reviews [17-18]) and can be synthesized and characterized using various chemical and spectroscopic methods.
The C60 cages can coordinate metallic ions in different fashions [4, 15]. We denote here the coordination of a metal ion by a 6-6 edge of C60 as an n2 type of coordination. Another possibility is coordination of an ion by a 6-5 edge. We denote this type of coordination as n2' as well. The n5 and n6 types of coordination mean a complex bond between the metal and the C5 or C6 fragments of the C60, respectively. The n3 type means coordination of a metallic ion bonded to a C3 fragment of the carbon hexagon. And finally the n1 type denotes coordination by one carbon atom of the C60 cage.
For the transition metals, the C60 fullerenes can serve as ligands of different hapticity and exhibit all possible types of coordination (n1, [17] (Pt-fullerenil radical), n2, [17-19] n3, [16, 20] n5, 21-22 and n6 [18, 23-24]. Some exotic structures like C60[Ir2Cl2(1,5-COD)2]2 may contain up to six metal ions as complex centers [25-28].
In contrast with the cobaltocene Co(C5H5)2, the Cox/C60 species exhibit either n2 or n3 type of coordination [16, 18-19]. In the work of Ref. 16 the Con(C60)m clusters were produced by a combination of laser independent vaporization - of the cobalt and C60 rods - and molecular beam method. The vaporized cobalt and C60 molecules were cooled to room temperature by He carrier gas at 5-7 atm. pressure and then grown into the Co„(C60) m clusters. For a qualitative study of the atomic structure of the species, mass spectroscopy (MS) method was used in combination with chemical probe analysis. Detailed analysis of the data [16] shows the presence of large or sufficient amounts of the C60, CoC60, Co(C60)2, Co(C60)3, Co2(C60)2, Co2(C60)4, Co3(C60)4 and Co,,^^ species. The reaction of the species with probe gases (CO, O2, NH3) in combination with the mass spectroscopy method allowed authors [16] to make conclusions about the coordination type of the cobalt ions in the Co„(C60)m complexes.
Although the structural data of work of Ref. 16 is indirect, qualitative and measured for the positively charged clusters (this fact could lead to additional changes in structure and reactivity ofthe species), it is really important for understanding the structure and properties of the Cox/C60 composites. Combining the mass-spectroscopic data and chemical probe analysis the authors of the work of Ref. 16 show that the cobalt ions in Co„(C60)m clusters probably exhibit the n3-type of coordination in some cases, but definitely not n5 or n6 ones. The Co(C60)2 cluster is considered [5] to be a bent structure bridged with a Co ion between the fullerene cages, whereas the Co(C60)3 cluster
is a triangular planar structure. The Co4(C60)4 has an unusual "composite di-tetrahedral" structure with a Co4 pyramid inserted into a (C60)4 pyramid. Each side of the resulting structure is a Co(C60)3 triangle with a cobalt ion between the fullerenes - each vertex of the (C60)4 tetrahedron belongs simultaneously to 3 different Co(C60)3 planes [16]. Actually, the Co4(C60)4 cluster is a tetramer of the Co(C60)3 one [16]. In the same sense, the Co2(C60)4 is a dimer and the Co3(C60)4 is a dimer and trimer of the Co(C60)3 unit [16]. In the last cases, only two or three (C60)3 planes of the (C60)4 tetrahedron contain cobalt ions [16]. Finally, the structure of Co2(C60)2 cluster is considered [16] to be two bridged cobalt ions between two fullerene cages. No evidence of the existence of linear Co-C60-Co-C60 clusters has been recorded [16].
Several attempts were made to describe -theoretically - the structure and properties of the TMC60 complexes using empirical tight binding (TB) models and TB based molecular dynamics (MD) simulation technique (see, for examples, Ref. 29-30). Even on the TB level, the structural features of the TM^X and TM2^)2 (TM=Ni, V) were correctly described in comparison with the existing experimental data [23].
The atomic and electronic structure of the allyl, metallocen, and bis-n6 benzene (TM(C2H4) n, n2 type of coordination, TMCp2, n5 type of coordination, Cp=C5H5 and TMBz2, n6 type of coordination, Bz=C6H6, respectively) sandwich complexes with d- and /-elements and was studied using a more advanced ab initio DFT approach [3138]. It was shown that the DFT theory correctly describes the type of coordination, symmetry and TM-C interatomic distances with high accuracy for all species.
Based on the Becke, Lee, Yang and Parr (BLYP) version of the General Gradient approximation (GGA), a Car-Parrinello MD simulation of the structure and the dynamics of the atomic base of the C60Ta3 system was performed
[38]. It was shown that one Ta ion coordinates with C60 in a n2 fashion, whereas the Ta2 dimer reveals high mobility along the C60 cage. The ease of migration of the Ta2 fragment around the C60 cage is the main structural peculiarity of the C60Ta3 complex.
The conditions of synthesis [15] for Cox/C60 composites, using atomic and molecular beams with consequent condensation of the mixtures imply, that all possible types (both low and high energy species) of local atomic structures could be formed during the experiment. Because of this, the atomic structure of the species can evolve during - or shortly after - the synthesis to achieve relatively stable positions of the cobalt ions and the C60 cages. Migration of the Co ions around and between the fullerene cages is the most probable mechanism to achieve this. The first step to study the atomic structure evolution process is to find all possible local Con(C60) m isomers and intermediates. From a general point of view, hundreds of Con(C60)m structures in low and high energy and spin states can be realized. Unfortunately, due to the big number and complexity of the structures (hundreds of atoms including several TMs) it is hardly possible to find appropriate transition states on the isomerization reaction pathways. Because of this, we can only judge the atomic structure evolution of the Cox/C60 composites based on the information about the atomic structure of all possible isomers and intermediates.
Presented here is a systematic theoretical ab initio DFT investigation of the atomic structure evolution of the Co/C60 composites in terms of the structure and energetic characteristics of a number of Con(C60)m clusters. This study is organized as follows: Section II describes the computational methods and objects under investigation, followed by results and discussion in Section III. Conclusions are presented in Section IV.
Computational details
The Gaussian 03 [39] code was used to calculate the electronic structure of Con(C60)m clusters as well as free standing Con clusters. Geometry optimization was performed by using the analytic energy gradients at a B3LYP/6-31G* level of theory [40] and GGA PBE approximation. [41, 42] as well. It has been shown that the PBE potential gives good results for metallic systems, [43] which is important for the Cox clusters.
All relative energies were calculated taking into account the basis set superposition error (BSSE). Based on the electronic structure calculations of the Con(C60)m clusters at the GGA/6-31G* level for the Con(C6o)m systems the BSSE was estimated in the range 35 - 55 kcal/mol. Taking the BSSE corrections into account is really important to predict the correct energy values and relative stability of the species.
To study the atomic and electronic structure of the metallocene systems, [31] HF approach as well as a wide variety of DFT potentials (BHLYP, B3LYP, BLYP, BP86, LSDA) were used. It was shown [31] that the B3LYP method [40] gives the best results among the approximations listed above. At present, the B3LYP method is probably the best tested approach among all ab initio DFT ones. It was designed [40] especially for correct description of the dissociation limit of a wide variety of molecules. The accuracy of the B3LYP method in describing the dissociation energies estimated for the G2 set is equal to 3.5 kcal/mol [40, 44-45].
The free-standing Cox clusters were allowed to change freely during atomic structure optimization without symmetry restrictions. Some initial structural types for geometry optimization were taken from Refs. 48-51. All possible spin states were tested to discover the
ground states of the Cox clusters at GGA PBE/6-31G* level of theory.
The atomic structure of Cox/C60 systems is characterized by its complexity [4, 15-16]. Only general information such as Co-C interatomic distances and possible coordination numbers, can be extracted from the structural spectroscopic experiments [15-16]. The unique atomic structure of C60 cage and the synthesis conditions are the reasons for the complex and irregular nature of the Cox/C60 composites [15]. At the local atomic structure level, this should reveal [16] a large variety of possible coordination types of cobalt ions with close or equal coordination numbers. A large variety of interatomic distances and different spin states should also be found. The presence of the transition metal ions and partially negative charges of the fullerene cages (because of the oxidation of the cobalt ions by C60 [52]) should be followed by the electronic correlations [53]. As the result of all factors described above, no symmetry restrictions can be applied a priori to the Con(C60)m clusters. The complexity of the objects and a great number of possible isomers in different spin states make it hardly possible - without taking into account of available experimental data and some basic features of atomic structure of C60 cages - a theoretical design of the preliminary structural models of the Con(C60)m clusters.
To study the atomic structure of the Co/C60 species, we theoretically designed a number of Con(C60)m clusters with n=1-8 and m=1-3 with all possible coordinations of the cobalt ions and C60 sites. Such restrictions of the n and m numbers are based on the previous experimental study of the species presented in the work of Ref. 16. For the Co1 systems (Co(C60)2 and Co(C60)3 clusters) all possible types of coordination (n6, n5, n3, n2, n2' and n1) in low (S=1/2) and middle (S=3/2) spin states were chosen as initial types of structures. Later, we will show that - for the neutral Co1
systems - the low S=1/2 state is energetically preferable.
To study the atomic structure of the Co/C60 systems with higher indexes (x=3-8 and «=1-3) we designed a number of Cox(C60)n clusters with all possible spin states and n2, n2' and n1 coordination types for the cobalt ions. . In general, the Cox cores can be coordinated with C60 cages through 1, 2, 3 or even 4 cobalt ions, so, the notations for the complex interfaces between the Cox and C 60 parts can be designed using up to four nk characters.
To compare the theoretical results with the experimental mass-spectroscopic and chemical probe method data, [16] we performed calculations on positively charged Col clusters in low (S=0) and middle (S=1) spin states. It was shown that the low (S=0) spin state is preferable for such types of objects. Finally, the structure of 89 Con(C60)m (n=1, 2, m=2, 3) neutral and positively charged clusters in low and intermediate spin states were determined at the B3LYP/6-31G* level.
No high energy n6 isomers or intermediates have been determined in our B3LYP/6-31G* calculations. We have determined the atomic structure of only a couple of isomers of the n3-type of coordination.
Each C60 site has its own coordination type with a cobalt ion. For the n=1, we introduced special notations for the mixed structures like n2/n2 (coordination of a cobalt ion by two 6-6 edges of different C60 cages), n2/n2' (one 6-6 and one 6-5 edge), n2/n5 (the 6-6 edge and C5 fragment) and n5/n5 (two C5 fragments). For the n=1 no n5/n2', n2/n3, n2'/n2', n3/n2', n3/n3 or n3/n5 structures were detected.
The case of n=2 is more complex: it is necessary to consider the coordination types of both cobalt ions. For the n=2, the n5 fashion can be realized only in the case of one bridged cobalt ion between the C60 cages. Later we will show that such type of structure have really high relative energies. For the m and n=2 all possible
combinations of n2 and n2' types of coordination
(n2:n2/n2:n2, n2n2/n2:n2, n2:n2/n2:n2, n2':n2/n2:n2',
n2:n2/n2:n2' and n2':n2'/n2':n2', the colon separates coordination types of both cobalt ions within the same C60 cage whereas the slash symbol separates different C60 sites) were determined as well as two high energy mixed isomers with n3:n2/n2:n2 and n3:n2/n3n2 types (the last structure has two additional sp3 C-C bond between the C60 cages). By keeping the initial nature of the cobalt ion's coordination fashion, the number of possible isomers of Co2(C60)2 in different spin states becomes really large (several dozens) because the relative positions of the C60 cages can be different.
The linear or bent Co2(C60)3 structures mostly manifest the n=1 types of coordination because of the absence of direct Co-Co interactions like in Co2(C60)2 systems. In general, there are only a few unequivalent Co - Co positions which differ from each other by the Co - Co distance and coordination fashion. Like in the case of n=1, the n2 type of coordination (n2/n2:n2/n2, the n2/n2 type of coordination for both cobalt ions) has the lowest energy. The n2/n2n2/n2' fashion is the second in energy and the n5/n5n5/n5 one has the highest energy. Energetically, the mixed structures (such as n5/n5n5/n2 or n2/n5n5/n2 etc.) are between them.
Results and discussion
a) Cox free-standing cores
The information of the atomic structure and spin state of free Cox clusters is summarized in Table 1. The PBE/6-31G* results qualitatively correspond to the previously published DFT (mostly different types of GGA approximation) [49-50] and TB [48, 51] data for free-standing cobalt clusters giving the same symmetries but sometimes different orders of the Cox isomers. Unfortunately the authors of [48, 51] did not publish the key interatomic distances and angles, 114 -
Table 1. Symmetry, interatomic distances (A) and the number of unpaired spins of the ground states of the Co, clusters
Composition General view Symmetry Interatomic distances, A Numeber of unpaired spins (spin/atom)
Co3 A C2v 2.189 1.998 9 (3)
Co4 C2h 2.288 2.119 10 (2.5)
Co5 Cs 2.248 2.153 2.129 2.103 13 (2.6)
Co6 Ci 2.215 2.214 2.213 14 (2.33)
Co7 Cs 2.275-2.186 15 (2.14)
Co8 Cs 2.306-2.182 16 (2)
so we can not make direct comparison of the atomic structures in this work. For example, the TB results [48, 51] give the same symmetries of global minima for Co6, and Co7 clusters, whereas for the rest of them the TB treats the second in energy isomers at PBE level of theory as ground states. The BLYP [49-50] gives the same symmetries of ground states for Co4, Co5 and Co6 clusters predicting different energy order for Co3, Co7 and Co8 clusters. Atomic coordinates of all free-standing cobalt cores can be downloaded
from Supporting Information section of the JPCC website.
The Jahn-Teller effect plays an important role in the symmetry lowering of the free-standing Cox cores due to correlation effects in rich Co-d shells of the clusters. The species display only low-symmetry groups (C2v (Co3) and Cs (Co4, Co5 and Co8)) or total absence of symmetry (Co6 and Co7 clusters) with significant variations of interatomic Co-Co distances (Table 1). It is necessary to note that a Co3 cluster configuration with 7 unpaired
Fig. 1. Number of unpaired spins per cobalt atom in Cox cores of Cox(C60)n nanoclusters. Pink squares denote the free-standing Co3, Co4, Co5, Co6, Co7 and Co8 clusters. Blue diamonds denote Co3C60, Co4C60, Co5C60, Co6C60, Co7C60 and Co8C60. Red triangles denote Co3(C60)2,
Co4(C60)2, Co5(C60)2, Co6(C 60)2, Co7(C60)2 and Co8(C60)2.
Three dashed lines are the guides to eyes
spins is only 0.6 kcal/mol higher in energy than the lowest energy isomer with multiplicity equal to 10 (9 unpaired spins).
The increase in size (or, what is the same, the number of cobalt atoms) of the species leads to a visible decrease in number of unpaired spins per cobalt atom. A non-monotonic dependence of the average number of unpaired spins per cobalt atom (Fig. 1) displays a local maximum for Co5 cluster, which is close to the results of the previous works [48-51]. For example, the GGA approach [49-50] gives the same dependence with one maximum for Co6 cluster (instead Co5 in our case). The TB results [48, 51] also display maximum for Co6.
a) Co(C60)2 and Co(C60)3 clusters
Tables 2 and 3 present the relative energies, types of coordinations and structural images (general and closest cobalt neighborhood) of all
Co(C60)2 and Co(C60)3 (Table 2) as well as Co(C60)2+ and Co(C60)3+ (Table 3) clusters in low spin states (S=1/2 and 0 respectively). On the B3LYP/6-31G* level the doublet - quartet splitting for the neutral systems is from 2.5 kcal/mol (n5/n5 complex) to 36.4 (n2/rf complex) kcal/mol. Because of this, we present the data of the low spin states only. All relative energies were calculated taking into account the basis set superposition error. The left/lower carbon atoms are in black, the right/ upper carbon fragments are shown in green/blue and the cobalt atom is in red.
Even though the positively charged clusters cannot play any role in the formation of the local atomic structures of Cox/C60 composites, they can be used as test systems to check the accuracy of the quantum chemical calculations. The theoretical B3LYP/6-31G* atomic structure of positively charged systems confirms the indirect experimental results [16] shown in Table 3: the Co(C60)2+ has a bent structure and the formation of additional Co-C bonds (Co(C60)3+ complex, with absolute minimum or zero relative energy) which sufficiently lowers the energy of the cluster (19.0 kcal/mol). Creation of an additional C-C sp3 bond between the C60 cages (Co(C60)2+ with C-C bond) lowers the relative energy up to 7.6 kcal/ mol above 0 and makes the bent angle bigger. Creation of additional C-C sp3 bonds between the C60 cages (Co(C60)3+ with additional 6 C-C bonds) does not change the energy of the system (0.3 kcal/mol on 6-31G* level). The lowest in energy -Co(C60)3+ cluster - has triangular planar structure like in the work of Ref. 16 with rf/rf/rf type of coordination (which is common for the cobalt-fullerene complexes) [18]. We have determined some additional types of coordination such as rf/ n2' (see above the Computation Details Section) as well as n5/n5 and rf/rf ones. These isomers have high relative energies (up to 41 - 29 kcal/ mol for the neutral systems). In spite of the rf5/ rf isomer having the highest energy, this type of 116 -
Table 2. Coordination Types, structures and relative energies (kcal/mol) of Co(C60)2 and Co(C60)3 clusters (S=1/2). All relative energies were calculated taking into account basis set superposition error. The left/lower carbon atoms are in black, the right/upper carbon fragments are shown in green/blue and cobalt is in red
Type of coordination
General view
Closest cobalt neighborhood
Relative Energy (kcal/mol)
41.4
rf/rf
32.8
rf/rf with one C-C bond
30.5
28.9
rf/q2
15.2
rf/rf/q2 with 3 C-C bonds
13.3
0.0
n5/n5
Table 3. Types of coordinations, structures and relative energies (kcal/mol) of Co(C60)2+ and Co(C60)3+ clusters (S=0). All relative energies were calculated taking into account basis set superposition error. The left/lower carbon atoms are in black, the right/upper carbon fragments are shown in green/blue and cobalt is in red
Type of coordination
General view
Closest cobalt neighborhood
Relative Energy (kcal/mol)
rf/rf
M
19.0
rf/rf'
17.4
8.9
rf/rf with one C-C bond
7.6
rf/rf
5.2
rf/rf/rf with 3 C-C bonds
0.3
rf/rf/rf
0.0
coordination was detected in the works of Refs. 21 and 22 and explained [36-37] by stabilization of the n5 position by some saturation groups on the outer surface of fullerenes.
A comparison of the positively charged systems (Table 3) and the neutral systems (Table 2) shows that ionization can cause some energetic and structural changes. For example, the staggered rf/rf and n2/n2/n2 (three 6-6 edges) types of coordination are preferable for the neutral Co(C60)n (n=2, 3) clusters. Formation of additional C-C bonds between the fullerenes sufficiently increases the energy of the clusters (as low as 13.3 kcal/mol for Co(C60)3 and as high as 30.5 kcal/mol for and Co(C60)2 clusters). The eclipsed n2/n2 configuration of the Co(C60)2+ cluster has the highest energy (Table 3). Ionization results not only in the changing of relative stability of the system, but in the symmetry state as well.
Comparison of the atomic structure of the zero energy Co(C60)3 cluster with the structural XAFS data [15] shows that B3LYP/6-31G* calculations (Table 2) can correctly describe both the coordination number for the Cox/C60 composites (equal to 6 for the Co(C60)3 cluster) and the Co-C interatomic distance with good accuracy (2.01 A is the experimental value and 2.06 A the theoretical one). Formation of the additional Co-C complex bonds (transition from a Co(C60)2 system to a Co(C60)3 system) decreases the energy up to 15.2 kcal/mol. The Co(C60)2 clusters with different types of coordination (n2/n2', n2/n5 and n5/n5) have sufficiently higher relative energies (from 28.9 up to 41.4 kcal/mol).
b) Co2(C60)2 clusters
Only three structural types of Co2(C60)2 clusters can be realized due to the specific atomic structure of C60 cage. The first one can be characterized by existance of cobalt dimers bonding the C60 cages. The C60 cages of the second type can be bounded by both cobalt ions
without formation of a metallic dimer, due to the possible formation of additional C-C bonds between fullerene cages. The C60 cages of the third type can be bonded by one cobalt ion only, whereas the second ion coordinates with only one C60 cage. Later we will show that the second and the third types of clusters have high relative energies (~50 - 100 kcal/mol).
The B3LYP/6-31G* calculations show that low energy Co2(C60)2 isomers have the triplet spin state (Table 4). We determined 27 Co2(C60)2 isomers in the triplet state and 28 Co2(C60)2 ones in the singlet state within all three types. All isomers in the triplet state keep the main peculiarities of the atomic structure of the singlet analogs such as type of coordination, relative positions of C60 cages and Co-C distance (~1.9 ^ 2.1 A). The typical singlet-triplet splitting for all isomers is equal to 40 - 70 kcal/mol. The transition from singlet to triplet state leads only in enlarging the Co-Co distance of cobalt dimers by approximately 0.2 ^ 0.5 A.
Some of the Co2(C60)2 isomers are presented in Table 4. The cobalt ions in metallic dimers present the n2 and n2' or, in less extent cases, the n3 types of coordination (see Table 4). The atomic structure of the 3 lowest energy isomers (isomers 1, 2 and 3, S=1) clearly confirm the indirect structural data [5] - two cobalt ions between the C60 cages. Formation of the cobalt dimers is energetically preferable, even in the case of formation of additional C-C sp3 bonds between the C60 cages (isomers 5 and 6). This fact is really important to understand the structures and properties of the Cox/C60 composites. In some extent, during synthesis [4] such Co2(C60)2 complexes can be realized because of radical character of C60 cages with attached metal ions. [34] Once formed, they can prevent the system from changing the positions of the cobalt ions because of the high energy required to destroy the additional sp3 C-C bonds between the C60 cages.
Table 4. Types of coordinations, structures and relative energies (kcal/mol) of some Co2(C60)2. All relative energies were calculated taking into account basis set superposition error. The lower carbon atoms are in black, the right/ upper carbon fragments are shown in green and cobalt is in red
Number
General view
Detailed view
Coordination type
Energy (kcal/mol
Rco-cc« Â
4
5
6
1
(S=1)
n2:n2/n2:n2
2.73
2
(S=1)
n2:n2/n2n2
9.4
2.98
3
(S=1)
n2:n2/n2:n2'
19.1
2.973
4
(S=1)
(65:66:65/66:66)
30.4
2.41
5
(S=1)
n2:n2/n2:n2'
49.0
3.21
6
(S=1)
n3:n2/n3:n2 (66:66:65/66:66:65)
80.3
5.61
1
2
3
0
The three lowest energy isomers are characterized by n2 and n2' coordination type. The C60 cages of the first isomer (relative energy 0 kcal/mol) are connected by a cobalt dimer through two C6 fragments of both fullerenes (Table 4). The first C60 cage bonds with the Co2 fragment through the middle of the C6 fragments using 6-6 and 6-5 edges, whereas the second fullerene bonds with the Co2 through two 6-6 edges (n2:n2/n2:n2 coordination type). The second isomer has the relative energy equal to 9 kcal/ mol and has an n2:n2/n2n2 type of coordination of the Co2 fragment through four 6-6 edges of the C6 fragment. The third isomer has the relative energy equal to 19.1 kcal/mol and an n2:n2/n2'n2' type of coordination through two C6 fragments. In this case the Co2 dimer connects with two 6-6 edges of one C6 fragment and with two 6-5 edges of the second one. All other n2-type isomers have higher relative energies (from 23 up to 120 kcal/mol) and can be obtained by combining all possible coordinations of the two C60 cages and Co2 fragment.
Two isomers of Co2(C60)2 clusters (numbers 4 and 6, Table 4) reveal the n3-type of coordination through a specific point on the C6 fragment surface. Both isomers can only play some role during the atomic structure evolution because of the high relative energies (30 and 80 kcal/mol correspondingly).
The initial presence of a wide set of Co2(C60)2 clusters in the Cox/C60 mixtures 4 with simular energies can be followed by the process of isomerization (the Co ions hopping through the n2, n2' and n3-points on the surface of the C60 cages). The n2:n2/n2:n2 and n2:n2/n2n2 types of coordination are preferable, but other high energy isomers can play some role as intermediate complexes in the process. Formation of additional C-C bonds between the C60 cages is not energetically preferable but may occur. If this happens, the new bonds should prevent the
migration of the cobalt ions around the fullerene cages.
c) Co2(C60)3 clusters
As it was mentioned in the Introduction and Computational Details sections, the linear or bent Con(C60)m clusters were not detected in the MS experiment [16]. Because of presence of other types of high clusters like Co2(C60)2, Co2(C60)4, Co3(C60)4 and Co4(C60)4, one would imagine the probability of the random formation of the liner/ bent Co2(C60)3 structures should be sufficiently higher than zero. The absence of the Co2(C60)3 clusters and high amount of the Co2(C60)2 ones can be partly explained by the fast transformation of Co2(C60)3 to Co2(C60)2. This occurs when the cobalt ions migrate around the central C60 cage, followed by the removal of one C60 when a double bridged Co2(C60)2 cluster is formed.
To study the atomic structure evolution of Cox/C60 composites, we calculated four sets of Co2(C60)3 clusters to model the process of cobalt ion migration around the C60 cages. Based on the calculations for the Co1 systems (Table 2), we propos the n2/n2:n2/n2 and n2/n2:n2/n2' types of coordination of Co2(C60)3 clusters as energetically preferable and the pure n5/n5n5/n5 and mixed n5/n5:n5/n2n5 as the ones highest in energy. It is necessary to note that regardless of the high energy of the species, during the chemical synthesis, [4] even the n5/n5n5/n5 and n5/n5n2/n5 intermediates can play some role in the Cox/C60 composite characterization.
The conformable n5/n5:n5/n5 and n5/n5:n5/n2n5 complexes, with close Co-Co distances, are 10-15 kcal/mol higher in energy than the n2/n2:n2/n2 and n2/n2:n2/n2' ones (Tables 5 and 6). The smaller the Co-Co distance the lower the energy of the n5-type complexes. However, the n5 structures are not suitable for the formation of the cobalt dimer structures because of features of the atomic structure of the species. The formation of the
Table 5. Structures and relative energies (kcal/mol) of rf-.rf-lrf-.rf-type Co2(C60)3 clusters. All relative energies were calculated taking into account basis set superposition error
Table 6. Structures and relative energies (kcal/mol) of n2:nr/n2;n2-type Co2(C60)3 clusters. All relative energies were calculated taking into account basis set superposition error
Fig. 2. Schlegel diagram of cobalt ions migrating around the central C60 cage of the Co2(C60)3 type of clusters. The first cobalt ion (red dot Co1) has a fixed position and is placed in the center of the 6-6 edge. The initial position of the second cobalt ion (pink dot Co2) is in the center of the opposite 6-6 edge. Migration of the second cobalt ion around C60 cage, through 6-5 and 6-6 edges, is presented by red broken arrows and color dots reflecting the relative energies of isomers (n2:n2/ n2:n2 type of coordination) and intermediates (n2:n2/ n2:n2 type of coordination). The carbon atoms are presented in black. The two lowest and highest carbon atoms are equivalent and presented as half circles because of the specific Schlegel diagram projection. The Co2 has a mirror image in the bottom of the figure (light pink dot) as well as the 6-6 edge bonded with it. Two violet empty circles denote the beginning of an alternative reaction pathway of the cobalt migration. The traffic sign "do not stop" denote absence of the intermediate state on the particular 6-5 edge
dimer structures, such as isomer 1 of Co2(C60)2 (Table 4), requires sufficient rearrangement of the cobalt ion's coordination type - from n5 to n2 ones and from n5 to n2' ones. Because of this the n5 complexes cannot play any role as direct precursors in the formation of cobalt dimers.
The n2/n2:n2/n2 and mixed n2/n2n2/n2' types of Co2(C60)3 structures have the lowest energy among the Co2(C60)3 clusters. The energy dependence of the n2/n2;n2/n2 clusters upon the Co-Co distance (Table 5, Fig. 2) has a non-pattered character, whereas the energy dependence of the n2/n2n2/n2' ones has maximum exactly at the middle of Co
pathway (Table 6 and Fig. 2). The energies of the n2/n2n2/n2 structures are 8 - 13 kcal/mol lower than the n2/n2n2/n2' ones.
The linear and bent Co2(C60)3 structures can be transformed to the Co2(C60)2 clusters through hopping of cobalt ions among the n2 and n2' sites with, ultimately, the formation of cobalt dimers and subsequent removal of C60 fullerene. The possible reaction pathway of the cobalt ion migrating around the central C60 cage through n2/n2:n2/n2 and n2/n2:n2/n2' sites is presented on Fig. 2 by the color dots and red broken arrows. The colors of the dots reflect relative energies of the isomers and intermediates. The initial positions of both cobalt ions on the opposite sites of the central C60 cage are marked by a Co1 and a Co2 symbols (the first and second ions respectively).
Without taking into account the relative orientation ofthe C60 cages in the Co2(C60)2 clusters, there are only 3 possible types of cobalt dimer coordinations around the C6 fragments of the C60 cage. The first one is the global minimum Isomer 1 of n2:n2' type (Table 4, the only one structure). This structure is schematically presented on the Fig. 2 by a broken red line connecting the Co1 position (red dot) and the brown dot reflecting the final position of the second cobalt ion (Co2).
The second coordination of n2:n2 type (the most representative example is Isomer 2 (relative energy 9.4 kcal/mol) in Table 4) is presented by two red circles connected by a broken red line. This structure can be obtained through the same intermediate state (the dark blue circle) as the Isomer 1. Finally, the last high energy isomer of n2:n2' type (the light blue circle connected to the red Co1 position by solid red line) can be obtained through alternative reaction pathways starting from the empty blue circles (in reality these positions were not calculated, but the relative energies of the n2' intermediates should be close to the neighboring highest intermediate structure, violet circle, 49.2 kcal/mol). 124 -
The formation mechanism of the highest energy n2n2' structure is really special and proceeds without formation of an intermediate structure neighboring the C6 fragment (like in the case of two previous clusters). The absence of the corresponding intermediate structure is represented on Fig. 2 by a "Do not stop" traffic sign. The resulting Co2(C60)3 cluster, number 5 from Table 6 (the analog of Isomer 7 from Table 4), can be characterized by the existence of direct Co-Co chemical bond with a length of 2.530 A.
The migration of the second cobalt ion (Co2) approaching the first one (Co1) proceeds through a set of isomers and intermediates (see Fig. 2). The energy difference between the initial Co2(C60)3 Co2 position (pink circle, 35.3 kcal/mol) and the highest energy intermediate (violet circle, 49.2 kcal/mol), located exactly in the middle of the reaction pathway, is equal to 13.9 kcal/mol. From this point, an approaching of the second cobalt ion to the first one leads to the consequent decrease of the energy of the system. After formation of the cobalt dimer, one C60 can be removed from the Co2(C60)3 system with formation of some kind of Co2(C60)2 isomer. The formation of the two lowest energy Co2(C60)2 isomers of n2:n2' and n2:n2 types of coordination (0 kcal/mol and 9.4 kcal/mol) can proceed through the same intermediate state (43.5 kcal/mol, dark blue circle). The absence of Co2(C60)3 clusters in the mass-spectra of the Co/ C60 composites 5 confirms the instability of the species.
b) CoxC60 (x=3-8) clusters with one C60 site
Coordination of one C60 cage by a Cox core dramatically changes the structure and spin states of TM cores (Table 7). Most Cox fragments demonstrate rf or n2' types of coordination, but an rf one can be found as well for the Co8C60 cluster. The coordination of the C60 cage by a Cox part is followed by complete reconstruction of
the interface with even a formation of irregular rhombic cobalt facets at the CoxC60 interface (Co5, Co7 and Co8 cores), or transformation of the distorted rhombic Co4 free-standing cluster to a tetrahedral structure. The atomic coordinates of all CoxC60 clusters can be downloaded from Supporting Information section of JPCC website.
The Co-C interatomic distances (Table 7) of the CoxC60 clusters demonstrate strong interactions of the metallic cores with the C60 cage. The experimental Co-C distance in Cox/C60 species [15] at the lower limit of cobalt concentration is 2.01 A, whereas the theoretical GGA B3LYP/6-31G* distance is 2.06 A [23]. The theoretical GGA PBE/6-31G* Co-C distances in CoxC60 clusters demonstrate wide variations of the lengths: from 1.815 to 2.230 A for the Co8C60 cluster. The Co-C distances for other CoxC60 clusters are inside this interval (Table 7). It does directly indicate the wide variation of chemical bonds between the Cox cores and the C60 cages with variations of the Co-Co interatomic distances as well.
The electronic correlation effects in rich Co-J shells play an important role in determination of the atomic structure features of the CoxC60 species. Even in the simplest Co3C60 case (the Co3 fragment coordinates to the carbon hexagon of the C60 site through three n2 positions) the Jahn-Teller effect leads to complete cancellation of the high initial symmetry of the constituting parts (icosahedral of the C60 cage and C2v (Table 1) of the Co3 core) and formation of the C1 symmetry structure of the Co3C60 cluster with three nonequivalent Co-C distances (2.439, 2.455 and 2.482 A, Table 7). It is necessary to note that in the absence of electronic correlations the resulting structure should display C3v symmetry. Actually, the symmetry of the Co3C60 cluster is just a strongly distorted C3v group. The GGA PBE/6-31G* results correlate well with the Co-Co distances
Table 7. Type of coordination, Co-C and Co-Co interatomic distances (A) and the number of unpaired spins of the ground states of the CoxC60 clusters
General view
Type of coordination
Interatomic Co-C distances, Â
Interatomic Co-Co distances, Â
Co3
rf/rf/rf
1.951-1.!
2.482-2.439
7
(2.33)
Co4
rf/rf/rf
1.920-1.882
2.695-2.364
10 (2.5)
Co5
n2/n2/n2/n2'
2.093-1.833
2.704-2.268
11 (2.2)
Co«
n2/n2/n2
1.903-1.870
2.621-2.291
12
(2)
Co7
n2/n2/n2/n2'
2.161-1.818
2.889-2.96
Co8
n2/n2/n'/n2'
2.230-1.815
2.810-2.171
12
(1.5)
in Co2(C60)2 isomers at the GGA B3LYP/6-31G* level of theory (2.41-2.98 A) [54].
The Co4C60 cluster with tetrahedral coordination of the cobalt core displays relatively less geometric distortions with resulting Cs symmetry (Table 7). As in the case of the Co3C60 cluster, the Co3 fragment of Co4 core is coordinated to the carbon hexagon through three n2 sites. These correlations
distort the ideal C3v group to a Cs symmetry structure with three nonequvivalent Co-C distances (1.920, 1.900 and 1.883 Â). One more CoxC60 cluster with an even number of cobalt ions and tetrahedral cobalt coordination (Co6C60) also displays Cs symmetry (Table 7). As in the cases of Co3 and Co4 cores, the Co6 fragments coordinates to the carbon hexagon of the C60 ligand through three n2 sites with
Cox core
three nonequivalent Co-C distances (1.871 1.892 and 1.903 A).
All other Cox clusters (Co5, Co, and Co8) form distorted rhombic interfaces (Table 7) with complex types of coordinations of TM core fragments with the C60 site: rf/rf/rf/rf' (Co5 and Co7) and rf/rf/rf/rf' (Co8). The Jahn-Teller effect completely destroys the symmetry of the clusters with formation of strongly distorted Q structures with wide variations of the Co-C distances (Table 7).
The number of unpaired spins per cobalt ion displays a non-monotonic dependence with two maxima (Co4 and Co7 cores, Fig. 1). For all CoxC60 clusters spin density is mainly localized at Cox fragments. Different behavior of the spin states in comparison with free-standing Con clusters (Table 1, Fig. 1) clearly demonstrates the main role of complex bond formation in determination of the non-monotonic behavior of average number of unpaired spins per cobalt atom in the complexes. The C60 cage significantly changes the chemical state of the cobalt ions with total reconstruction of the atomic and electronic structures of the Cox cores due to oxidation of all or some cobalt atoms. Only for the Co4C60 and Co7C60 species the average number of unpaired spins per cobalt atom is equal to the corresponding Co4 and Co7 clusters. In other cases the formation of the complex Co-C bonds leads to noticeable decrease in the average number of unpaired spins.
c) Cox(C60)2 (x=3-8) nanoclusters
The structural data and spin states for Cox(C60)2 clusters are summarized in Table 8. Coordination of the second C60 cage by the TM cores consequently changes the structure and spin states of cobalt nanoparticles. As in the case of the CoxC60 clusters, the TM cores demonstrate n1, n2 and n2' types of coordination. The coordination of the second C60 cage by the TM part is followed by similar reconstruction of the interface region
with formation of the additional tetragonal (Co3, Co4, Co5, Co6 and Co7 cores) or irregular rhombic (Co7) cobalt facets. It is necessary to note, that for the Co5(C60)2 cluster a state with 9 unpaired spins is only 0.2 kcal/mol higher in energy than the lowest energy isomer with multiplicity equal to 8 (7 unpaired spins). The atomic coordinates of all nanoclusters can be downloaded from Supporting Information section of JPCC website.
The Co-C interatomic distances (Table 8) of the Cox(C60)2 species demonstrate strong interactions between the metallic cores and the C60 cage with wide variations the distances from 1.846 to 2.125 A for the ^^0)2 cluster. The CoCo distances are also influenced by formation of complex bonds with the second C60 cage, with a noticeable decrease in the difference between the maximal (2.696 A) and minimal (2.201 A) values compared with the CoxC60 species (2.889 and 2.171 A, respectively, Table 7).
The electronic correlation effects in rich Co-d shells plays the leading role in determination of the main features of the atomic structure of the Cox(C60)2 species. Only the Co3(C60)2 cluster displays low C2 symmetry (the Co3 fragment coordinates to the carbon hexagons of the C60 sites through three n2 positions). The Q symmetry group of Co8(C60)2 cluster is in fact a strongly distorted C2 group. All other clusters have no symmetry due to Jahn-Teller distortions of their atomic structure. The GGA PBE/6-31G* results for Cox(C60)2 species also correlate well with the Co-Co distances in Co2(C60)2 isomers at the GGA B3LYP/6-31G* level of theory (2.98-2.41 A) [54].
The formation of the complex bonds with the second C60 site undergoes through the same coordination types (Table 8) between the TM cores and C60 cages. As in the case of CoxC60, the most favorable is n2/n2/n2 coordination of a cobalt triangle by a C6 fragment of C60 cage. Also, n2' and n1 types of coordination in different combinations can be found (Table
Table 8. Type of coordination, Co-C and Co-Co interatomic distances (A) and the number of unpaired spins of the ground states of the Cox(C60)2 clusters
Cox core General view Type of coordination Interatomic Co-C distances, A Interatomic Co-Co distances, A Numeber of unpaired spins (spin/atom)
Co3 #N§i rf/rf/rf rf/rf/rf 1.976-1.965 2.646-2.629 3 (1)
Co4 rf/rf/rf rf/rf' 2.120-1.881 2.629-2.345 8 (2)
Co5 9/tir rf/rf/rf/rf' rf/rf/rf 2.125-1.846 2.860-2.201 7 (1.4)
Co6 V » V rf/rf/rf/rf' rf/rf/rf/rf 2.094-1.885 2.549-2.321 12 (2)
Coy rf/rf/rf rf/rf/rf/rf 1.944-1.865 2.653-2.208 13 (1.86)
Co8 rf/rf'/rf/rf' r 2/r '/r 2/r ' 2.096-1.845 2.696-2.239 18 (2.25)
8). The most complex case is coordination of the cobalt core of the Co8(C60)2 cluster to the C60 sites. The interface regions are in fact non-equivalent strongly distorted rhombuses with unique geometry and different types of coordination (rf/rf'/rf/rf' and rf/rf/rf/rf). The unique atomic structure of the Co8(C60)2 cluster is the direct consequence of the Jahn-Teller distortions caused by electronic correlations in rich Co ^-shells.
For all Cox(C60)2 clusters the main part of spin density is also localized at Cox fragments. The number of unpaired spins per cobalt ion displays non-monotonic dependence with three maxima (Co4, Co6 and Co8 cores, Fig. 1). Different behavior of the spin states of free-standing Cox, CoxC60 and Cox(C60)2 clusters (Tables 1, 7, 8, Fig. 1) clearly demonstrates the main role of complex bond formation in determination of the magnetic properties of the Cox/C60 composites. Formation
of complex bonds between the second C60 cage with Cox clusters is favorable to enhance the average number of unpaired spins per cobalt atom due to electron charge transfer from cobalt ions to the C60 cages.
Conclusions
The atomic structure and relative energetic stability of a wide set of neutral and positively charged Con(C60)m (n=1-8, m=1-3) clusters with all possible coordinations of cobalt ions and C60 cages in different spin states (S=0, 1/2, 1 and 3/2) were determined based on the GGA/6-31G* calculations. Theoretical results directly confirm the existing experimental structural data for the Cox/C60 species. Results indicate that the n2 type of coordination is energetically preferable for all combinations of m and n numbers. For the neutral systems with n=1 the low spin state S=1/2 is energetically preferable. For the n=2 cases, the intermediate S=1 spin state is preferable. It was shown that, for the n=2 case, the formation of the cobalt dimers is energetically preferable and can be realized through cobalt ion hopping between the n2 (6-6 edge) and n2' (6-5 edge) sites of C60 cages. The n2' types of structures as well
as the n5 type of structures - and mixed ones - can be realized in the complex Cox/C60 mixtures during chemical synthesis as intermediate states and high energy isomers.
In most cases the formation of the Cox/ C60 (x=3-8) interfaces is followed by complete structural reconstruction of the TM cores. The Cox fragments are bonded with a C6 fragment of the C60 cages through distorted triangular or rhombic interface structures. The individual cobalt ions at the interface regions display n2, n2, or rf/types of coordination. The electron correlations lead to significant structural distortions with complete destroying of initial high-symmetry structures of constituting parts. The formation of complex bonds with one C60 cage leads to non-monotonic dependence of average number of unpaired spins per cobalt atom. The attaching of the second C60 site to a Cox core leads to consequent changes of the electronic structure, increasing the average number of unpaired spins. The obtained theoretical data can be used to synthesize novel nc-Co/Cox(C60)y compounds with optimized magnetic properties varying the Co/C60 content and synthesis conditions.
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