Computational Study on C80 Enclosing Mixed Trimetallic Nitride

5770

J. Phys. Chem. C 2008, 112, 5770-5777

Computational Study on C80 Enclosing Mixed Trimetallic Nitride Clusters of the Form GdxM3-xN (M ) Sc, Sm, Lu) Jianhua Wu Computational Center for Molecular Structure and Interactions, Department of Physics, Atmospheric Sciences, and Geoscience, Jackson State UniVersity, Jackson, Mississippi 39217

Frank Hagelberg* Department of Physics, Astronomy, and Geology, East Tennessee State UniVersity, Johnson City, Tennessee 37614 ReceiVed: December 18, 2007; In Final Form: February 8, 2008

Metallofullerenes of composition GdxM3-xN@C80 with 0 e x e 3 and M ) Sc, Sm, Lu, were investigated with respect to their geometric, electronic, energetic, and magnetic properties by Density Functional Theory, using the generalized gradient approximation in combination with an on-site correlation approach. Equilibrium structures were identified for both the free GdxM3-xN (0 e x e 3, M ) Sc, Sm, Lu) units and the composite of the trimetallic nitride core and the fullerene cage. Although the core clusters generally tend toward planarity upon encapsulation into C80, some species containing Sm atoms show a reversal of this trend. The electronic interaction between the cage and the core is characterized by the formation of a covalent region between both components. This effect proves to be strongest in those cases where no core rotation has been detected by experiment. Ferromagnetic ordering is favored by the free trimetallic nitride clusters involving Gd and Sm constituents. For GdxM3-xN@C80 (0 e x e 3 and M ) Sc, Sm, Lu), the ferromagnetically and antiferromagnetically ordered isomers are seen to be near-degenerate. A slight preference for the former alternative is found for Sm3N@C80 while complexes containing Gd tend toward the latter.

I. Introduction A rich diversity of fullerene types with endohedral metallic clusters consisting of three or four atoms have been discovered in the recent past.1,2 In particular, various trimetallic clusters stabilized by a central nitrogen atom have been fabricated, for example (M1)x(M2)3-xN or ScxM3-xN where 0 e x e 3, and in all cases M, M1, and M2 are lanthanide atoms.3-5 Small clusters of magnetic metal atoms possess magnetic moments often substantially exceeding those of isolated atoms.6,7 This opens the prospect of designing novel MRI contrast agents by enclosing small rare earth atom ensembles in fullerene cages. In view of the confirmed high stability of many fullerene structures, enclosing toxic metal atoms in fullerenes is expected to be safer than the prevailing chelate technology. Furthermore, recent experiments have demonstrated that water-soluble polyhydroxyl forms of Gd@Cn,8 clusters of composition Gd@Cn(OH)m, n ) 60, 82,9-11 as well as Gd@C60[C(COOH)10]12 achieve substantially higher relaxation rates than conventional MRI contrast agents such as [Gd(DPTA)(H2O)]2- (Magnevist). This feature allows one to reduce MRI contrast agent doses administered to the patient proportionally. Some of the recently detected metallofullerenes enclosing trimetallic cores could display unprecedented proton relaxivities, making them essential elements of new and truly novel MRI contrast agents. Furthermore, Stevenson et al. identified a cluster of the form Lu3N@C80,4,13 involving three atoms of the heaviest element in the lanthanide series, lutetium. This species has been discussed as a candidate for a novel X-ray contrast agent. In * Corresponding author. E-mail [email protected].

addition, the composition scheme (M1)x(M2)3-xN@Cn of the newly fabricated group of metallofullerenes makes it possible to design multifunctional contrast agents, for instance by choosing Gd for M1 and Lu for M2. These units combine MRI and X-ray contrast agents in one unit, where emphasis can be shifted between these two functions by variation of the index x. An alternative mixed-metal species might contain both Lu and Ho atoms and thus act simultaneously as X-ray contrast agent and therapeutic or diagnostic radiopharmaceutical. Other elements besides Gd, Ho, and Lu have been substituted for M1 and M2 in the laboratory14 justifying the expectation that metallofullerenes with trimetallic nitride cores may be developed into a new class of tunable medical agents that can be adjusted to suit a wide range of possible diagnostic or therapeutic purposes. According to very recent observation,15 fullerenes encapsulating trimetal nitride units are potentially of high relevance to the design of fullerene-based nanomaterials. Thus, it has been shown for the case of D3h (78:5) Sc3N@C78 that the endohedral impurity exerts regional control over adduct docking locations. Specifically, the favored attachment sites for N-tritylpyrrolidino monoadducts have been shown to be 6:6 junctions that are offset from the horizontal plane defined by the Sc3N core, which has been attributed to the presence of the latter species. Because this study focuses on C80 enclosures, it might be objected that regional selectivity plays a lesser role here, since Sc3N has been demonstrated by both experiment and theory (ref 16 and references therein) to undergo free rotation in the C80 cage. This finding, however, does not carry over to lanthanide containing core clusters. Thus, the Gd3N core was found by Raman

10.1021/jp711862w CCC: $40.75 © 2008 American Chemical Society Published on Web 03/26/2008

Computational Study on C80 spectroscopy to form a bond with the C80 cage of sufficient strength to prevent intramolecular cluster rotation.17 The present work aims at understanding the geometric, energetic, electronic, and magnetic properties of experimentally detected GdxM3-xN@C80 (0 e x e 3, M ) Sc, Sm, Lu) complexes4,5,13-17 from first principles. The choice of C80 is motivated by the fact that metallofullerenes enclosing trimetallic nitride clusters were generally found to be most abundant with C80 as the host.5,6,12,16,18,19 Because the relation between the magnetic properties of the metallofullerenes as a whole and the 4f magnetism of their trimetallic subsystems is a matter of particular interest, the metal constituents have been chosen to represent elements with empty (Sc), completely filled (Lu), precisely half-filled (Gd), and less than half-filled (Sm) 4f shells. This contribution focuses specifically on the interaction between the GdxM3-xN (0 e x e 3, M ) Sc, Sm, Lu) core and the fullerene cage. Density Functional Theory (DFT) has been applied to obtain the equilibrium structures of the GdxM3-xN@C80 species, as well as those of the free core clusters. In particular, the extent to which the geometry and the magnetism of the free trimetallic nitride clusters are modified by encapsulation into the fullerene cage is evaluated in the present work. II. Computational Details The systems considered here have been treated by Density Functional Theory (DFT)20 within periodic boundary conditions. The finite temperature version of Local Density Functional (LDF) Theory21 was utilized in conjunction with the exchangecorrelation functional given by Ceperley and Alder and parametrized by Perdew and Zunger,22 as implemented in the Vienna ab initio Simulation Package (VASP).23 The geometry optimizations performed were based on the Hellmann-Feynman scheme, which yields a valid description of the forces within the DFT formalism also at finite temperature. Instead of Fermi-Dirac broadening of the one-electron energies, it may be computationally convenient to choose Gaussian broadening, which was employed in this work. The width of the Gaussian distribution was selected as 0.01 eV. The total energy of the system refers to the limit of vanishing width. The generalized Kohn-Sham equations were solved employing a residual minimization scheme, namely the direct inversion in the iterative subspace (RMM-DIIS) method24 for all of the molecules except those including Lu metal atoms. For the latter, the Kohn-Sham equations were solved employing a Davidson block iteration scheme. The interaction of valence electrons and core ions is described by the projector-augmented wave (PAW) method.25 All DFT calculations involved the gradient correction (GGA) for the exchange-correlation functional as prescribed by Perdew, Burke, and Ernzerhof.26 In order to represent systems with localized f electrons, spin-polarized DFT with on-site Coulomb interaction (GGA + U) has been applied. This procedure makes it possible to include the Sm, Gd, and Lu 4f electrons in the valence electron subsystem. The corresponding valence electron configuration for Sm, Gd, and Lu are 4f65s25p66s2, 4f75s25p65d16s2, and 4f145s25p65d16s2, respectively. The GGA + U scheme was realized by adopting the simplified rotationally invariant approach by Dudarev and co-workers.27 The parameters for the on-site interaction (U) and exchange interaction (J) are: U ) 5.4 and 6.7 eV, J ) 0.6 and 0.7 eV for Sm and Gd, respectively. No convergence was attained upon applying the GGA + U formalism to the Lu metal atom. Lu was therefore treated by the GGA method, without inclusion of the on-site Coulomb interaction. Periodic boundary conditions were imposed on a cubic cell of dimension 20 × 20 × 20 Å3. From inspection of the

J. Phys. Chem. C, Vol. 112, No. 15, 2008 5771

Figure 1. Equilibrium geometry of Gd3N@C80.

converged equilibrium geometries, the nearest-neighbor distance between atoms in adjacent supercells is larger than 12 Å, making the interaction between supercells negligible. Finally, the geometry was optimized enforcing a difference of less than 1 meV between the total energies obtained in two subsequent steps as convergence criterion. In some selected cases, comparison was made with the results of a finite basis approach.28 Here, the B3PW91 potential29 was used in conjunction with the cep-121 basis set.30 For each cluster considered, the energy gap was evaluated. The energy gap, Egap, of the system is defined as the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). For the magnetic systems, the gap is defined as the difference between the highest HOMO and the lowest LUMO energy within the majority and minority spin subsystems. III. Results and Discussion In what follows, we highlight the geometric and energetic properties of GdxM3-xN@C80 (0 e x e 3, M ) Sc, Sm, Lu) complexes as obtained from our DFT computations (III.A), followed by a discussion of the intramolecular electron transfer in III.B and the magnetic features of the considered systems in III.C. III.A. Structure and Stability of Free and Encapsulated Core Clusters. As the trimetallic nitride cluster is encapsulated into the fullerene cage, the two subsystems undergo mutual stabilization, resulting in the equilibrium geometry of the respective metallofullerene. The stabilization mechanism involves, apart from purely geometric adjustment due to the relative size of the cage and the cluster enclosed, transfer of electrons, proceeding from the trimetallic cluster to the fullerene. This process strongly impacts the geometry of both the cage and the core. On account of electron addition to the cage, the most stable C80 isomer satisfying the isolated pentagon rule, namely a D2 symmetry structure, usually does not provide the most favorable enclosure for metal core clusters.31 For endohedral trimetallic nitride clusters, cage structures based on the Ih isomer of C80 have been identified as maximally stable.16,32 Figure 1 shows a structural model of M3N@C80 by the example of M ) Gd. The HOMO of the pure C80 unit is fourfold degenerate but occupied by two electrons only. Donation of six electrons by the encapsulated metal atoms to the fullerene therefore yields a C806- (Ih) closed-shell configuration. The electron-transfer also exerts influence on the core cluster geometry. This effect may be illustrated by a molecular orbital

5772 J. Phys. Chem. C, Vol. 112, No. 15, 2008 (MO) analysis of the reference unit Sc3N. The bonding pattern described by the three highest occupied MOs may be understood in analogy to the corresponding orbitals of the ammonia molecule. In this paradigmatic case, a totally symmetric HOMO preceded by a HOMO-1 of C3V doublet character represents the interaction between the Sc3 subsystem and the N atom that gives rise to pyramidal ground-state geometry. As one depopulates the Sc3N counterparts of these orbitals and thus prepares the Sc3N6+ ion in the equilibrium geometry of neutral Sc3N, the initial three-dimensional structure of this ion is found to collapse into planarity, followed by Coulomb explosion of the molecule. The latter effect is prevented by enclosing Sc3N into the fullerene void where it adopts planar geometry, as shown by both experiment4,33,34 and computation16,18,19 for three fullerene types, namely Cn with n ) 68, 78, and 80. The Gd3N molecule, however, stabilizes as a pyramid when encapsulated into the C80 enclosure, as established by X-ray spectroscopy on crystals of composition Gd3N@C80 (NiC36H44N4) 1.5(C6H6)5 as well as DFT analysis of [email protected] Our plane wave GGA + U approach confirms this effect. On comparison with the gas-phase species, Gd3N as endohedral impurity in C80 is markedly compressed along its symmetry axis. From Table 1, the GdN-Gd angle deforms from 99.8° to about 114° upon insertion into the fullerene. Although the latter result agrees with the average of the Gd-N-Gd angles as observed by spectroscopy, individual deviations of the measured angles among each other and from the computational results recorded in Table 1 can be related to the use of a functionalized system in the experimental study,5 reducing the C3 symmetry of the pure Gd3N@C80 cluster. The systems with cores that combine Sc and Gd components, Gd2ScN and GdSc2N, exhibit a similar structural change upon inclusion into the C80 cage. All M1-N-M2 angles (M1, M2 ) Sc, Gd) are substantially increased in the metallofullerene as compared to the pure core cluster. The N-M1 (M2) distances of Gd2ScN contract slightly as this species is encapsulated, while no such tendency is found for GdSc2N. Analogous statements can be made for the clusters containing Lu atoms. For core clusters involving Sc and Lu as metal species besides Gd, a trend toward planarity is the defining geometric change as the trimetallic nitrides are enclosed into C80. This phenomenon is least pronounced, although still present, in the case of Lu3N, which undergoes the change from an almost flat free unit to a perfectly planar metallofullerene core. The geometric data related to core clusters containing Sm, however, demonstrate that the flattening of trimetallic nitride upon inclusion in C80 is not a universal trend. This result is interpreted as a cluster size related effect, as will be outlined in the following. As shown in Figure 2a and b, the Sc3N@C80 and Gd3N@C80 species realize two different geometric prototypes. Although the Sc ligands point at a C-C bond shared by a hexagon and a pentagon, they are directed toward the center of a hexagon in case of Gd. The complex Lu3N@C80 belongs to the former, Sm3N@C80 to the latter type. The orientation within the cage can be correlated with the spatial extension of the free as well as the encapsulated M3N core cluster: In both situations, the N-M bond distances for M ) Gd, Sm distinctly exceed those for M ) Sc, Lu (see Table 1). Thus, the respective averages for the endohedral clusters are (2.09 and 2.11 Å) for (Gd, Sm) and (2.03 and 2.06 Å) for (Sc, Lu). These values, in turn, reflect the order of both the atomic and ionic radii of the included metal elements, which increase according to Sc < Lu < Gd < Sm.34 It is expected that the larger core clusters induce a higher amount of strain in the fullerene than the smaller ones. To account for

Wu and Hagelberg TABLE 1: Geometric and Energetic Properties of GdxM3-xN and GdxM3-xN@C80 (0 e x e 3, M ) Sc, Sm, Lu) molecule Gd3N Sc3N Lu3N Sm3N Gd2ScN GdSc2N Gd2LuN GdLu2N Gd2SmN GdSm2N Gd3N@C80 Sc3N@C80 Lu3N@C80 Sm3N@C80 Gd2ScN@C80 GdSc2N@C80 Gd2LuN@C80 GdLu2N@C80 Gd2SmN@C80 GdSm2N@C80

dMMa

dMNb

θMNMc

3.324 3.324 3.322 2.851 2.851 3.030 3.558 3.558 3.557 3.580 3.650 3.973 3.130 3.159 3.159 3.166 3.016 2.836 3.144 3.293 3.293 3.583 3.582 3.462 3.275 3.431 3.401 3.556 3.556 3.703 3.504 3.516 3.522 3.510 3.520 3.538 3.572 3.565 3.549 3.463 3.465 3.466 3.594 3.460 3.583 3.679 3.615 3.283 3.578 3.505 3.606 3.545 3.571 3.571 3.513 3.490 3.475 3.503 3.481 3.451

2.172 2.172 2.172 1.960 1.960 1.995 2.062 2.062 2.063 2.187 2.191 2.193 2.152 2.152 1.933 2.134 1.981 1.951 2.133 2.133 2.087 2.060 2.082 2.080 2.074 2.084 2.342 2.026 2.251 2.251 2.091 2.093 2.094 2.033 2.034 2.034 2.057 2.057 2.057 2.113 2.113 2.112 2.114 2.118 1.915 1.965 1.964 2.178 2.083 2.077 2.016 2.100 2.037 2.034 2.101 2.096 2.117 2.099 2.115 2.120

99.866 99.866 99.767 92.251 92.251 101.199 119.240 119.240 119.191 109.699 112.892 129.979 93.303 101.166 101.166 93.441 101.547 92.298 94.966 102.583 102.583 119.792 119.856 112.592 103.920 101.792 100.253 112.369 112.378 110.670 113.596 114.288 114.661 119.301 119.893 120.806 119.280 120.163 120.557 110.198 110.168 110.075 116.251 118.102 125.531 125.176 121.440 113.370 118.692 117.536 123.505 119.450 117.917 122.614 113.704 111.864 110.954 112.485 111.227 109.149

dMCd

2.447 2.448 2.453 2.275 2.276 2.276 2.326 2.329 2.330 2.473 2.473 2.475 2.468 2.416 2.241 2.494 2.239 2.251 2.440 2.411 2.319 2.411 2.325 2.315 2.430 2.434 2.469 2.426 2.465 2.461

TMMMNe

Egapf

Eeg

45.98

0.14

48.45

0.38

11.28

1.29

21.75

0.28

50.60

0.28

50.51

0.24

43.06

0.44

18.89

0.62

43.35

0.53

32.35

0.45

27.05

1.52

-9.854

0.048

1.43

-12.264

0.073

1.58

-10.165

34.195

0.53

-6.565

6.15

1.50

-11.089

0.73

1.49

-11.947

16.24

1.54

-10.110

0.96

1.56

-10.325

30.22

0.73

-8.651

31.99

0.51

-7.502

a Distance between two metal centers. b Distance between a metal and the nitrogen center. c Angle enclosed by the nitrogen and two metal centers. d Closest distance between a metal center and a fullerene cage carbon center. e Torsion angle between the three metal centers and the nitrogen center. f Energy gap. g Embedding energy, defined as energy release upon encapsulation of GdxM3-xN into C80 (0 e x e 3, M ) Sc, Sm, Lu). All energies are in eV.

this effect quantitatively, we average over all C-C bond distances within the C6-C5 cage fragment closest to the considered metal atom. Adopting Sc3N@C80 as reference, we find the C-C distance expansion in M3N@C80 increased by 1.3% for M ) Sm, Gd, but only by 0.5% for M ) Lu. These size effects may be related to the experimental result of free core cluster rotation inside C80 for Sc3N16 and Lu3N,13 while

Computational Study on C80

J. Phys. Chem. C, Vol. 112, No. 15, 2008 5773

Figure 3. (a) Angle-integrated electronic density distribution F(r; Gd3N@C80) (upper panel) versus the fullerene radius r. (b) Difference distribution F(r; Gd3N@C80) - [F(r; C80) + F(r; Gd3N)] versus the radius r, where F(r; C80) and F(r; Gd3N) are defined in analogy to F(r; Gd3N@C80) (see text, III.B).

TABLE 2: Data Related to the Electron Transfer Analysis of GdxM3-xN@C80 (0 e x e 3, M ) Sc, Sm, Lu). The Symbols qi (i ) I, II, III, IV, V, VI) Refer to the Electron Difference Populations in Regimes I-VI, as Defined in Figure 3.

Figure 2. Structures prototypical for M3N@C80 with M ) Sm, Gd (a) and with M ) Sc, Lu (b).

rotation of Gd3N inside the cage is hindered, as established by Raman spectroscopy.17 In terms of the average distance between metal atom centers, the largest of the three M3N clusters included in this study is Sm3N. This species accommodates to the spatial constraints of the C80 cavity by contraction of the Sm-Sm distances, as documented in Table 1, undergoing the maximum geometric change upon inclusion into the fullerene among all core clusters compared here. For all systems investigated, the intermetal spacing in GdxM3-xN@C80 exceeds that in GdxM3-xN (0 e x e 3), with the exception of Sm3N and Sm2GdN. For the latter units, the embedded cluster deviates more strongly from planarity than the free species. Specifically, the Sm3N torsion angle, which we adopt as a measure for nonplanarity, increases from 21.7° to 40.0° upon encapsulation, where the latter value results from the combined effect of purely geometric adjustment to the cage structure and electron transfer. The torsion angle reduces as Sm3N is replaced by GdxSm3-xN, x ) 1, 2. As expected, the geometric properties of Gd2SmN are dictated by the Gd component, and the encapsulated cluster is flatter than the free unit. The crossover between the two opposing trends is found for the unit GdSm2N where incorporation into C80 has only minimal impact on the torsion angle. The overall tendency of the embedding energy, Ee, of GdxM3-xN (x ) 1-3) is impacted by the strain resulting from the combination of the two subsystems. From Table 1, the values of Ee for M3N change according to the sequence Ee(Sm3N) < Ee(Gd3N) < Ee(Lu3N) < Ee(Sc3N). Not only the core geometry

molecule

qI

qII

qIII

qIV

qV

qVI

Gd3N@C80 Gd2ScN@C80 GdSc2N@C80 Sc3N@C80 Gd2LuN@C80 GdLu2N@C80 Lu3N@C80 Gd2SmN@C80 GdSm2N@C80 Sm3N@C80

-0.955 -0.941 -0.995 -0.805 -0.920 -0.806 -0.736 -0.859 -1.023 -1.014

0.152 0.175 0.159 0.108 0.190 0.216 0.172 0.096 0.258 0.026

-0.406 -0.419 -0.423 -0.450 -0.429 -0.477 -0.504 -0.410 -0.399 -0.314

1.230 1.228 1.264 1.153 1.187 1.103 1.095 1.228 1.150 1.325

-0.201 -0.220 -0.269 -0.184 -0.203 -0.189 -0.191 -0.213 -0.201 -0.211

0.180 0.172 0.275 0.180 0.177 0.167 0.177 0.160 0.221 0.190

but also the stability of the core in C80 can be fine-tuned by mixing different lanthanide elements. The embedding energies of GdxM3-xN, 0 e x e 3, with M ) Sc, Sm, are found to interpolate between those of the homogeneous clusters Gd3N and M3N. The significantly lower stability of Sm3N@C80 as compared to M3N@C80 with M ) Sc, Gd, Lu is also reflected by the energy gap (Egap) values found by our DFT computation and shown in Table 1. Although the respective results for the latter systems are close to each other, ranging from 1.43 to 1.58 eV, the energy gap for Sm3N@C80 is drastically lower at Egap ) 0.53 eV. It is interesting that the energy gaps for the mixed metal composites GdxSm3-xN@C80 (x ) 1,2) increase in approximate proportion with the Gd fraction in the core cluster. This observation emphasizes once more that the properties of GdxM3-xN@C80 may be sensitively manipulated by the core cluster choice. Our result for Egap (Gd3N@C80), namely 1.52 eV, is compatible with previous computation32 as well as experiment,17 which determined this quantity as 1.75 eV. III.B. Electronic Density Rearrangement. Formally, six electrons are transferred from GdxM3-xN (0 e x e 3, M ) Sc, Sm, Lu) to C80, as has been pointed out explicitly for the systems Sc3N16 and Gd3N.32 Because of backdonation18 and covalency effects, however, the net charge localized on the C80 cage of M3N@C80 (M ) Sc, Gd) is substantially lower than the limit of -6e. Population analysis allows for a relative assessment of

5774 J. Phys. Chem. C, Vol. 112, No. 15, 2008

Wu and Hagelberg

TABLE 3: Magnetic Properties of GdxM3-xN and GdxM3-xN@C80 (0 e x e 3, M ) Sc, Sm, Lu)a molecule

M(1)

M(2)

M(3)

N

mb

2 mtot (au)c

∆Ed

26 24 10 8 3 1 1 20 8 22 17 19 3 12 10 17 8 24 10 22 8 10 8 22 1 1 16 6 1 15 8 1 8 10 6 20 4 18 8

25 23 9 8 3 1 0 19 7 21 16 18 2 11 9 16 7 23 9 21 7 9 7 21 0 0 15 5 0 14 7 0 7 9 5 19 3 17 7

0 86 302 426 0 181 0 0 52 529 0 4 202 0 15 0 0 0 306 0 77 132 0 4 0 0 0 2 0 8 0 0 0 0 49 73 0 10 92

Gd3N

7.65

7.67

7.78

-0.064

Sc3N

0.43

0.47

0.60

-0.0069

Lu3N Sm3N

0 5.96

0 5.96

0 6.06

0 -0.082

Gd2ScN

7.56

7.59

0.32

-0.038

GdSc2N

7.72

0.82

0.72

-0.028

Gd2LuN GdLu2N Gd2SmN

7.53 7.09 7.58

7.55 -0.016 7.60

0.15 -0.012 6.16

-0.031 -0.019 -0.057

GdSm2N

7.22

6.08

6.08

-0.043

Gd3N@C80

7.05

7.06

-7.06

-0.016

Sc3N@C80 Lu3N@C80 Sm3N @C80

0 0 5.22

0 0 5.23

0 0 5.24

0 0 -0.195

Gd2ScN@C80

7.06

-7.06

0.00015

-0.0041

GdSc2N@C80 Gd2LuN@C80 GdLu2N@C80 Gd2SmN @C80

7.06 7.06 7.05 7.07

-0.0050 -7.06 -0.053 7.06

-0.0048 0.00034 -0.054 -5.25

-0.014 -0.0031 -0.014 0.024

GdSm2N@C80

-7.09

5.23

5.26

-0.119

a The values under the entries M(i), i ) 1-3 and N are obtained by integration of the magnetic moment density within a spherical volume around a metal or the nitrogen center of the respective trimetallic nitride cluster. The integration radii are chosen as the valence radii of the corresponding atoms. For units involving Gd complexed with Sc or Sm, as well as for Sm3N and Sm3N@C80, isomers of different spin multiplicities are included. For each system, the values of M(i), i ) 1-3 and N refer to the multiplicity of highest stability, as indicated by the relative energy ∆E, given in the last column. b Spin multiplicity. c mtot ) Total magnetic moment. d Energy difference with respect to the isomer found most stable, in meV.

the electron transfer in different metallofullerenes by comparing effective cage charges on Cn for GdxM3-xN@Cn for any given n. A more detailed model of the transfer process is obtained by inspecting the intramolecular electron density rearrangement. Essential information about this effect can be derived from the difference between the radial electron density distribution of the metallofullerene and the sum of the corresponding distributions for the trimetallic cluster and the fullerene in isolation from each other, where the latter quantities, F(r; GdxM3-xN), 0 e x e 3, and F(r, C80), are evaluated at the geometries that they adopt in the combined system at equilibrium. Figure 3a shows the results of this treatment for Gd3N@C80. The density F(r; Gd3N@C80), as found by integration of F(x) over the angular variables, is displayed along with the two distributions F(r; C80) and F(r; Gd3N)), while Figure 3b shows the difference F(r; Gd3N@C80) - [F(r; C80) + F(r; Gd3N)]. Plausibly, the density distribution of the metallofullerene is dominated by two maxima that correspond to the Gd3 subsystem and the C80 shell. The density difference distribution (Figure 3b) is characterized by alternating maxima and minima, which reflect electron density gain and loss, respectively. The highest maximum separates the two troughs that emerge in the regime of the Gd3 ring and the C80 enclosure. The integral over this peak, taken between the

two bounding zeros of the distribution, yields a measure for the amount of electron displacement from the fullerene shell as well as the trimetallic component of the core into a covalent intermediate region where bonds are formed between these cluster constituents. The upper limit of this regime is naturally given by the crossing radius, Rc, between the functions F(r; C80) and F(r; Gd3N@C80). The electronic charge concentration in the covalent range causes a slight polarization effect that induces a rapidly damped oscillation between intervals of charge increase and reduction for radii beyond Rc. It is instructive to compare the integrals of the difference distribution in the covalent region for the various metallofullerenes treated in this study. In the case of Gd3N@C80, integration over this region yields a population of 1.23. Adopting this result as a reference value, we find a reduction of 6.3 and 11% when going from the Gd3N core to Sc3N and Lu3N, respectively. For Sm3N, in contrast, the covalent population is enhanced by 7.7%. The former result is consistent with the experimental observation of motional averaging in the case of M3N@C80 (M ) Sc, Lu),13,16 but not of Gd3N@C80 (see above). III.C. Magnetic Properties of Free Core Clusters and Metallofullerenes. For Gd3N, stable isomers with four different spin multiplicities were identified. As can be seen from Table

Computational Study on C80

Figure 4. Energy eigenvalues versus number of eigenstates for Gd3N (upper panel) and Sm3N (lower panel). The black squares refer to the majority spin, the red triangles to the minority spin values. In both panels, the Fermi energy is equated with E ) 0.

3, the stabilities of these four species correlate with their multiplicities. The Gd3N cluster with the maximum magnetic moment 1/2 25 au is preferred with a small but distinct energy margin of 0.09 eV over the unit with the second highest magnetic moment. We point out that the favored spin multiplicity of Gd3N draws a parallel between the magnetic structures of the latter system and the Gd2 molecule for which a spin multiplicity of 19 has been obtained.36 In both cases, the overall magnetic moment is determined by four polarized majority spin valence orbitals besides the ferromagnetically ordered localized 4f contributions of the Gd constituents. A ferromagnetic (FM) arrangement, involving parallel magnetic moments due to the Gd 4f shells, as realized in Gd2, is also found for Gd2MN with M ) Sc and Lu. For the units Gd2MN with M ) Sc and Lu, the multiplicity m ) 17 is preferred over m ) 19. This effect which is slight for M ) Sc and more pronounced for M ) Lu has been confirmed by additional computations for Gd2ScN using the P3PW91 potential29 in conjunction with a cep-121G basis set.30 The spin state of Gd2MN (M ) Sc, Lu) is thus not entirely governed by the Gd2 subunit. Molecular orbital analysis of Gd2ScN reveals a considerable degree of Gd(5d, 6s2) - Sc(3d, 4s2) hybridization in the unpaired alpha orbitals that are not of Gd(4f) character. A similar analysis was performed for the complex GdLu2N with multiplicities 8 and 10, where, from DFT computation with a plane wave basis, the former results with an advantage of 20 meV over the latter. In the preferred spin state of GdLu2N, the magnetic moment is entirely carried by the Gd(4f) subsystem. An analogous computation on the P3PW91/cep-121G level confirms this finding while yielding a considerably enhanced energy difference between the alternative multiplicities, namely 0.91 eV. For the free cluster Sm3N, three multiplicities were identified, with m ) 20 as the most stable among them. In contrast to Gd3N, Sm3N displays a considerable amount of lanthanide 4f hybridization with the p states of the nitrogen atom, as revealed by molecular orbital analysis. This apparent opposition between these two trimetallic nitrides is based on a similarity between them. For atomic Sm as well as Gd, the preferred state of oxidation is +3. In the case of Gd3N, the 4f orbitals occupy a well-defined band of about 0.3 eV width, with minimal contributions due to N or other Gd orbitals. The 4f contingent of Sm3N, in contrast, extends over an interval of approximately

J. Phys. Chem. C, Vol. 112, No. 15, 2008 5775 1.0 eV, involving significant nitrogen p population admixtures. This is illustrated in Figure 4 where the energy eigenvalues of the Kohn-Sham eigenstates are plotted versus the eigenstate number for Gd3N (upper panel) and Sm3N (lower panel). While the Gd(5d1, 6s2) electrons interact with the N(2p3) electrons to form the Gd3-N bond, this function is performed by a Sm(4f1, 6s2) subsystem in the case of Sm3N. Here we neglect a rather slight d electron fraction that emerges from promotion from 6s2 to 5d1 and amounts, by natural orbital analysis,37 to an average of 0.18 for the spin alpha and of 0.13 for the spin beta population. The resulting magnetic structure of Sm3N is closely related to that of Gd3N. The localized contribution of each Sm 4f shell to the overall magnetic moment is effectively 5 au. The preferred multiplicity of Sm3N results from FM ordering of the three Sm atoms, augmented by four spin-polarized valence electrons, in precise analogy to Gd3N. The same construction principle is obeyed in the case of the mixed species Gd2SmN and GdSm2N. The obtained groundstate multiplicities are consistent with the assumption of a localized 4f shell magnetic moment of 1/2 5 au (1/2 7 au) for each Sm (Gd) atom. The magnetic properties of the pure trimetallic nitrides differ considerably from those of the respective metallofullerenes. The changes due to encapsulation can be summarized into two key features: The magnetic moments of GdxM3-xN@C80 (0 e x e 3, M ) Sc, Sm, Lu) are (a) localized and (b) reduced as compared to those of GdxM3-xN. Both observations are clearly substantiated by the entries of Table 3. In what follows, we comment on both items. Focusing on (a), we notice that a sizable portion of the magnetic moment expectation value of the various GdxM3-xN (0 e x e 3, M ) Sc, Sm, Lu) species is delocalized. This conclusion can be drawn by integrating the computed equilibrium spin density for each atomic constituent over a spherical volume centered at the nucleus and determined by the ionic radius of the considered atom. The results of this procedure are shown in Table 3 for all investigated isomers along with their overall magnetic moments, mtot. Averaging the difference between mtot and the sums of the individual components over the pure core clusters, we arrive at a delocalized contribution of 8.4%. This figure drops to 0.55% as the metallofullerenes are considered. This observation is plausible because the magnetism of the latter is carried almost entirely by the 4f shell of Gd, as may be seen from the individual magnetic moments of all Gd containing composites. The strong decrease of the delocalized admixture to the overall magnetic moment as one goes from the pure trimetallic nitride to the metallofullerene partly rationalizes feature (b). More importantly, however, the free core clusters exhibit a marked tendency toward ferromagnetic (FM) ordering, whereas the antiferromagnetic (AFM) phase is preferred by their metallofullerene counterparts in most cases considered here. The latter finding agrees with the earlier theoretical assessment of the most stable Gd3N@C80 isomer32 by Lu et al. The AFM and the FM alternative of Gd3N@C80 are very close in total energy, being separated only by the small margin of 4 meV, as reported previously in ref 32. From a recent theoretical investigation of solid GdN,38 small lattice parameter changes may exert a strong impact on the magnetic structure of this compound. Although this result can neither be extended from periodic systems to the clusters studied here nor from Gd to Sm, it is remarkable that the Sm3N@C80 ground state realizes an FM scheme. Although the FM and the AFM state of Sm3N@C80 may, in view of their small energy separation, be described more properly as near-degenerate, the slight preference

5776 J. Phys. Chem. C, Vol. 112, No. 15, 2008 for the FM state in this case is in opposition to the AFM order of Gd3N@C80. This observation might be related to the geometric difference between the core clusters of the two metallofullerenes, as Sm3N adopts a more compact structure in C80 than Gd3N. The latter species, however, prefers FM ordering as a free cluster, exhibiting a more compressed equilibrium geometry than that found in the encapsulated case. In GdSm2N@C80, the Gd 4f magnetic moment opposes the orientation of the two Sm magnetic moments that are parallel, resulting in the magnetic moment mtot ) 1/2 3 au for the complex as a whole. For Gd2SmN@C80, an arrangement of two ferromagnetically ordered Gd atoms and an antiparallel Sm atom give rise to mtot ) 1/2 9 au. IV. Conclusions The geometric, energetic, electronic, and magnetic properties of GdxM3-xN@C80 (x e 3; M ) Sc, Sm, Lu) have been investigated by DFT using a GGA + U approach in conjunction with a plane wave basis set. Within this group of metallofullerenes, equilibrium structures, stabilities, and ground-state spin multiplicities vary greatly with the choice of the GdxM3-xN core cluster. The tendency toward trimetallic nitride planarization is confirmed for M ) Sc, Lu, but some core clusters involving Sm deviate from this rule. In particular, because of the geometric adjustment of Sm3N to the C80 cavity, the encapsulated Sm3N system is found to be more compact than the free. The specific combination of metal elements in GdxM3-xN determines the degree of core cluster planarity. By inspection of the GdxM3-xN@C80 charge density distribution as a function of the fullerene radius, it was shown that a covalent region emerges between the cage and the core cluster as a result of electron displacement from either subsystem. This effect is less pronounced for metallofullerenes M3N@C80 for which motional averaging has been established by experiment (M ) Sc, Lu) than for the remaining cases (M ) Sm, Gd). Gd and Sm are seen to prefer the same state of oxidation, +3, in the free trimetallic nitride systems and their encapsulated counterparts, implying a localized magnetic moment of 1/2 5 au on each Sm constituent. Analyzing the magnetic structure of the studied composites, we found that for M ) Sc, Sm, Lu, the 4f magnetic moments of the free clusters GdxM3-xN (x ) 1-3) organize according to an FM scheme. For Sc, Lu, this changes to AFM ordering upon encapsulation into C80. For Sm3N@C80, however, FM order appears to be favored. As a result of interest for the potential use of GdxM3-xN@C80 as MRI contrast agents, the localized 4f magnetic moments of these species do not exclusively display AFM ordering. Depending on the nature of the chosen lanthanides, FM ordering is possible, as realized in the case of Sm3N@C80. Although this configuration involves a stable species with extremely high magnetic moment and is thus favorable for MRI application, it should be noted that the FM and AFM isomers of GdxM3-xN@C80 (0 e x e 3; M ) Sc, Sm, Lu) are, as a rule, separated from each other by only small energy differences in the regime of a few millielectronvolts. This near-degenerate situation, implying frequent transitions between the AFM and FM states, is associated with enhanced proton relaxivity33,38 and could be advantageous for MRI spectroscopy. The present study is to be continued in two directions. First, the investigation of trimetallic nitride core clusters in terms of their structural, electronic, and magnetic characteristics will be extended to a larger group of lanthanide elements. Second, organic ligands will be added to the metallofullerenes considered

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