Transferred Hyperfine Interaction between a Tetrahedral Transition

Feb 22, 2010 - Computational modelling of inorganic solids. Elaine Ann Moore. Annual Reports Section "A" (Inorganic Chemistry) 2011 107, 459 ...
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J. Phys. Chem. C 2010, 114, 4749–4755

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Transferred Hyperfine Interaction between a Tetrahedral Transition Metal and Tetrahedral Lithium: Li6CoO4 Dany Carlier,* Michel Me´ne´trier, and Claude Delmas ICMCB-CNRS, UniVersite´ de Bordeaux, IPB-ENSCBP, 87 aV. Schweitzer, 33608 Pessac cedex, France ReceiVed: NoVember 30, 2009; ReVised Manuscript ReceiVed: January 25, 2010

Li6CoO4 presents an antifluorite-type structure, with both the Co and Li ions in tetrahedral oxygen coordination. 7 Li MAS NMR shows remarkably different shifts (+885 and -232 ppm) for the two different crystallographic types of Li. In order to assign the signals and to understand the mechanisms whereby the electron spins on the e orbitals of Co2+ ions (e4 t23 electronic configuration) are transferred toward the two different types of Li with opposite polarization, we have carried out GGA and GGA+U calculations of the electronic structure using the VASP code. Spin density maps in selected planes of the structure reveal (as expected) that lobes of the t2 orbitals point toward the faces of the CoO4 tetrahedra and can thus overlap with the neighboring Li(2) through empty square pyramidal sites. As concerns Li(1), a mechanism is evidenced where the (filled) e orbitals of Co2+ are polarized by the electron spins in the t2 ones. These polarized e orbitals overlap with Li(1) through the common edge of the tetrahedra. The relative magnitude of the experimental shifts for the two types of Li are however not fully reproduced by the calculations, and the influence of the U parameter as well as of the pseudopotential method used is discussed. Introduction The transfer of some electron spin density from a transition metal to the site of the lithium nucleus governs the Li NMR shift (the so-called Fermi contact shift) in lithium transition metal oxides, as extensively reviewed by Grey et al.1 In an attempt to better understand the mechanisms that govern such a transfer, we studied earlier selected compounds for which we modeled the distribution of electron spin density by DFT calculations and correlated this with the measurement of the Li NMR shifts, to analyze the mechanisms of the interaction.2 When both the transition metal and Li are in octahedral oxygen coordination, a clear picture emerges from these studies, as summarized in Table 1. For edge and/or corner-sharing connectivity of the octahedra in such compounds, the possible orbital overlaps between the transition metal and Li are either direct (as is the case for the t2g orbital pointing to the common edge of edge-sharing octahedra, see Figure 1a) or via the p orbitals of oxygen (as is the case for the eg* orbitals overlapping with the p orbitals of oxygen, that in turn overlap with the s orbital of Li in a corner-sharing octahedron, i.e., with a 180° M-O-Li geometry, see Figure 1b). When the d orbitals of the transition metal carry electron spins, the two situations described above lead to a polarity-conserving delocalization of some of the electron spin density toward Li. The latter therefore feels an additional magnetization, and its NMR signal is affected by a positive Fermi contact shift. Now, when the t2g orbital is fully occupied, we also showed that it can be polarized by electron spins in the eg* orbital and that direct overlap of this polarized t2g orbital with Li in an edge-sharing octahedron can transfer a negatively polarized spin density, leading to a negative Fermi contact shift for this Li atom. The other case where a negative Fermi contact shift can arise is that of a transition metal with electron spins only in the t2g orbital, which can polarize the bonding counterpart of the (empty) eg* orbital. This polarized * Corresponding author: phone, +33 (0) 5 40 00 35 69; fax, +33 (0) 5 40 00 27 61; e-mail, [email protected].

TABLE 1: Summary of the Electron Spin Transfer Mechanism from Our Previous Work, When Both the Transition Metal and Li Are in Octahedral Oxygen Coordination2

bonding eg orbital can then transfer a density of electron spin with negative polarization to the Li with a 180° M-O-Li geometry. Of course, if the antibonding eg* orbital were also to contain electron spins, then the delocalization from these spins with positive polarization toward the Li with 180° M-O-Li configuration would by far supersede the small amount of negatively polarized spin transferred from the polarized bonding eg orbital with the same symmetry. We also addressed a case where Li resides in tetrahedral oxygen coordination next to a transition metal in octahedral coordination (namely, the spinel LiNi2O4).3 In such a case, DFT modeling showed that the d orbitals of oxygen adopt a tilted orientation compared to the case where both ions reside in octahedra, in such a way that electron spins in the eg* orbitals of the transition metal can still transfer (although to a lesser extent) some electron spin density with positive polarization to the Li in the neighboring corner-sharing tetrahedron by delo-

10.1021/jp911364w  2010 American Chemical Society Published on Web 02/22/2010

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Figure 1. Possible orbital overlaps between the transition metal and Li in octahedral site sharing an edge with a 90° M-O-Li geometry (a) or a corner with a 180° M-O-Li geometry (b). Possible orbital overlaps between the transition metal in octahedral site and Li in tetrahedral one sharing a corner with a 120° M-O-Li geometry (c).

calization via the oxygen, despite the 120° M-O-Li configuration (Figure 1c). In this paper, we address the more complicated case where both the transition metal and Li reside in tetrahedral oxygen coordination, such as in the antifluorite-type Li6CoO4. This compound was characterized as a positive electrode material in Li cells by Narukawa et al.,4 and its magnetic and optical properties were reported by A. Mo¨ller.5

Carlier et al. were obtained with a 1 µs pulse duration corresponding to about 45° flip of the macroscopic magnetization. First-order phasing of the signal was used due to loss of the beginning of the FID during the dead time (8 µs), with a spline correction of the baseline to eliminate the sin x/x distortion thus introduced. Hahn echo spectra were obtained using a refocusing delay corresponding to one rotor period (33-100 µs) with a 2 µs 90° pulse length. The recycle time (1 s) was checked to allow full relaxation of the signals except for the minority impurity signal at 0 ppm. The spectrum width was 1 MHz, and the number of scans was 512. The 0 ppm external reference was a 1 M LiCl aqueous solution. First-principles calculations were performed using density functional theory (DFT) in the Generalized Gradient Approximation GGA (PBE)6 and GGA+U with the Projector Augmented Wave (PAW) method7 as implemented in the Vienna Ab Initio Simulation Package (VASP).8 A plane wave cutoff energy of 500 meV and a 6 × 6 × 6 k-points grid were used for all cells in order to get the total energy to be converged by less than 5 meV/unit cell. The structure was relaxed and the final energy of the optimized geometry was recalculated so as to correct for the changes in basis during relaxation. Previous studies showed that the GGA method allows a better simulation of magnetic interactions and Jahn-Teller distortions than the LDA method.9 The DFT+U method (LDA+U or GGA+U) allows treating more accurately the electronic structure of strongly correlated systems, such as transition metal or rare earth containing materials.10,11 In many DFT+U studies, the value used for the “on site” electron-electron repulsion (U) parameter is chosen in order to match the calculated and experimental band gaps or by analogy with other studies in literature involving similar ions and spin configurations. In our study, Dudarev’s approach was used in order to perform the GGA+U. In this method, the parameters U and J (exchange interaction) are not entered separately as only the difference (U - J) is meaningful. It, therefore, allows a single parameter to be entered that will be called Ueff ) U - J. Because no experimental gap was measured for Li6CoO4, Ueff ) 3 eV was used here for the 3d levels of Co. The aim of comparing GGA and GGA+U calculations was to evidence the effect of electron localization on the predicted spin transferred on the Li nucleus even if Ueff may be overestimated. In our calculations, the spins of the transition metal ions are assumed to be aligned with the applied magnetic field at 0 K. To plot the partial spin density of state and to evaluate the amount and polarization of spin on the lithium and cobalt nuclei, the integration was done in a sphere around each nucleus using ionic radii given by the Shannon tables. Spin density integration and spin density map were performed from the ouput of the VASP code with the Convasp code.12 Further details on the method used can be found in ref 2.

Experimental Section

Results and Discussion

Li6CoO4 was prepared by reacting stoichiometric amounts of Li2O and CoO in a sealed Ni tube under Ar. The tube was heated under Ar to 650 °C at a 2 °C/mn rate, kept at this temperature for 15 h, and then quenched in water. The X-ray diffraction (XRD) pattern was recorded using a Siemens D5000 powder diffractometer with the Cu KR radiation and a graphite diffracted beam monochromator, from 10° to 80° (2θ) with a 0.02° step and a 2 s counting time by step. 7 Li NMR spectra were recorded at 116 MHz using a Bruker AVANCE 300 spectrometer and a Bruker 2.5 mm MAS probehead at spinning speeds up to 30 kHz. Single pulse spectra

The XRD pattern of Li6CoO4 (Figure 2) confirmed that Li6CoO4 with tetragonal P42/nmc space group, matching exactly the pattern reported by Luge et al.,13 was obtained with the presence of traces of LiCoO2. The structure of Li6CoO4 was reported by Luge et al.: in the unit cell (a ) 6.536 Å and c ) 4.654 Å), Co, Li(1), Li(2), and O occupy respectively the 2a, 8f, 4d, and 8 g atomic positions.13 The structure of Li6CoO4 is shown in Figure 3a. It exhibits CoO4 tetrahedra and two different types of Li ions, characterized by different connections of their LiO4 tetrahedra with the CoO4 ones Figure 3b. The Li(1)O4 tetrahedron shares one edge and two corners with CoO4

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Figure 2. XRD pattern of Li6CoO4. Asterisk indicates the position of the diffraction peaks of the LiCoO2 impurity.

Figure 4. 7Li MAS NMR spectra of Li6CoO4 recorded using a single pulse sequence at different spinning rates: (νR ) 20 kHz and 30 kHz) (a). A 20 kHz spectrum with the position of the isotropic resonances (b).

Figure 3. Structure of Li6CoO4 with the Li ions represented either as atoms or as LiO4 tetrahedra (a). The two lithium ions’ local environments (b).

tetrahedra, while the Li(2)O4 tetrahedron shares only its four corners with four CoO4 tetrahedra. 7 Li MAS NMR spectra of Li6CoO4 for two spinning speeds (30 and 20 kHz) are shown in Figure 4a. The spectra are clearly composed of two lines with their respective set of spinning sidebands. A minor trace of diamagnetic Li probably corresponding to LiCoO2 can also be observed close to 0 ppm. The isotropic positions for the two signals are unambiguously those shown on the figure, taking into account the fact that faster

spinning also causes a temperature rise of the rotor due to the friction of the stronger drive gas flow, in such a way that the Fermi contact shifts decrease in absolute value due to the decrease in magnetic susceptibility to which it is proportional (Figure 4a). The values given in Figure 4b are those measured at a 20 kHz spinning speed, while those measured at 30 kHz are 824 and -215 ppm, respectively. The relative difference between the shifts at the two spinning speeds is therefore 7.5% for the positively shifted signal and 7.4% for the negatively shifted one, which confirms our assignment. The relative magnitude of the signals requires a caveat. The spectrum shown was obtained using a single pulse sequence with a relatively short pulse (1 µs) corresponding to approximately a 45° flip angle of the magnetization. It is clear that the dead time of the spectrometer (8 µs with the current probehead) leads to a loss of the very beginning of the FID, corresponding to the broad part of the signals. Using a Hahn echo-type sequence indeed allows us to refocus on the electron-nucleus dipolar interaction that causes the width of the signals. This leads to a spectrum with a coalescence of the base of the individual spinning sidebands (as shown in Figure 5). However, the excitation range of the echo sequence is clearly too narrow for the present spectrum, leading to an artificial narrowing of the total spectrum. Furthermore, the relatively long echo delay (50 µs) when synchronized to 20 kHz spinning can also lead to significant loss of observation in echo mode

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Figure 5. 7Li MAS NMR spectrum of Li6CoO4 recorded with a rotorsynchronized Hahn echo (2 µs 90° pulse) sequence at 20 kHz spinning rate.

TABLE 2: Optimized Structural Parameters Obtained by the GGA and GGA+U Calculations Given in Comparison with the Experimental Ones from Reference 13 a (Å) c (Å) V (Å3) dLi(1)-O (Å) dLi(2)-O (Å) dCo-O (Å)

GGA

GGA+U

exptl13

6.555 4.663 200.39 1.975 (×2) 2.109 (×2) 1.903 (×2) 1.974 (×2) 1.995 (×4)

6.569 4.674 202.54 1.972 (×2) 2.116 (×2) 1.913 (×2) 1.977 (×2) 2.005 (×4)

6.536 (1) 4.654 (1) 198.82 1.963 (×2) 2.113 (×2) 1.894 (×2) 1.969 (×2) 1.996 (×4)

depending on the T2 relaxation time of the two signals. Therefore, both types of NMR signal acquisition lead to significantly nonquantitative spectra. In these conditions, the relative magnitude of the two signals cannot be used to assign them to the two crystallographic types of Li even though the multiplicity of Li(1) is twice that of Li(2). The importance of the local geometry in the mechanism of the Fermi contact interaction1–3,14 is particularly well illustrated in this compound, since the isotropic shifts recorded for the two types of Li in the structure are remarkably different. To understand the mechanisms whereby some density of electron spins is transferred so differently from the (identical) Co tetrahedra to the two different types of Li, we have carried out DFT calculations of the electronic structure of Li6CoO4, and first extracted the magnitude and sign of the spin density transferred on the sites of the two Li in order to assign each signal to the right Li. Then we have extracted spin density maps in carefully selected planes to elucidate the mechanisms of the spin transfer. GGA and GGA+U methods were both used. Our earlier calculations of the spin transfer on Li nucleus in layered transition metal oxides were carried out only with the GGA method. Here, we also performed GGA+U calculations, since it appears to better model the properties of several oxides, as discussed in the Experimental Section. Table 2 gives the relaxed cell parameters of the tetragonal P42/nmc space group obtained by the GGA and GGA+U methods in comparison with the experimental ones.13 One can notice that the geometry optimization performed with the GGA method gives closer agreement with the experimental data. However, since the experimental values are obtained at room temperature, whereas calculations are done at 0 K, this agreement cannot be considered as a better accuracy of the calculation without U. Figures 6 and 7 show the spin density of state calculated for Li6CoO4 with the GGA and GGA+U methods, respectively. The total spin density of state and the one projected on the different 3d orbitals of Co2+ ions are represented respectively in (a) and (b). For GGA calculations, the total DOS (Figure 6a) shows a real separation (1 eV) between levels that have a

Figure 6. Total (a) and Co (b) spin density of state calculated for Li6CoO4 with the GGA method. (c) Expansion of the Co “up spin” DOS region of the orbitals just below the Fermi level.

strong oxygen p orbital identity and levels, just below the Fermi level, that have a strong 3d Co orbital identity. Above the Fermi level a 0.56 eV band gap is calculated which is in agreement with the |∆t| ) 0.53 eV evaluated by Mo¨ller for [CoO4]6-.5 The partial DOS calculated on Co (Figure 6b) are in agreement with the spin configuration expected for Co2+ ions in a tetrahedral environment, i.e., e4 t23. Nevertheless, one can notice that the three t2 orbitals are not equivalent and neither are the e orbitals: (i) the dxy level is located at higher energy than the dxz and dyz ones for the spin up and spin down levels; (ii) the e levels are closer in energy, but still, the dx2-y2 level is located at slightly higher energy that the dz2 one in both spin up and spin down levels. These differences can be understood from the structure of Li6CoO4 that does not exhibit regular CoO4 tetrahedra. Whereas the Co-O distances are equivalent, the O-Co-O angles are not. In Figure 8, the local geometry around Co is

Lithium Transition Metal Oxides

Figure 7. Total (a) and Co (b) spin density of state calculated for Li6CoO4 with the GGA+U method.

Figure 8. Distortion of the CoO4 tetrahedral in the Li6CoO4 structure. The two different values of the O-Co-O angles (calculated and experimental) are given.

given. One can see that the CoO4 tetrahedra are flattened along the c axis, therefore reinforcing the overlap of the orbitals in the xy plane (dxy and dx2-y2) with the oxygen p orbitals and weakening the overlap of the dxz and dyz and dz2 with the p oxygen orbitals. Because the t2 and even the e orbitals in Figure 6b are antibonding levels, an increase of the overlap between 3d Co and 2p O orbitals induces a shift of the levels toward higher energy as observed for dxy and dx2-y2. The dxy level is more affected than the dx2-y2 one because it implies a stronger overlap with oxygen 2p orbitals in the tetrahedral geometry. The use of the U term in the GGA+U calculations induces an increase of the band gap above the Fermi level to 2.2 eV (Figure 7a), which may be too high for a Co2+ in a tetrahedral site. Nevertheless, the use of the U term on the Co d orbital causes a lowering in energy of the occupied t2 and e levels and

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Figure 9. (a) Integrated net spin in spheres with various r radii around the Li(1) and Li(2) nuclei as a result of the GGA and GGA+U calculations for Li6CoO4. (b) Net spin values calculated with GGA and GGA+U in a 0.6 Å radius sphere around Li(1) and Li(2) nuclei.

a stronger mixing with the p-like ones, whereas the unoccupied levels rise in energy. No clear separation is any more observed between the levels that have a strong oxygen p identity and levels that have a strong 3d Co identity. Moreover, the use of U in the calculations induces a stronger contribution of the 3d Co orbitals in the bonding e and t2 levels located around -5 eV versus the Fermi level energy (Figure 7b). This should therefore induce different spin transfer on the Li ions as will be discussed below. For both GGA and GGA+U calculations, the net spin was integrated in spheres around the Li nucleus with variable radius size. Figure 9a shows the resulting curves for the two Li sites. As the NMR shift is mainly due to the presence of electronic spin on the nucleus in s orbitals, we are more interested in evaluating the electronic spin in a sphere with small radius size that involves the s Li orbitals. In both GGA and GGA+U calculations, the electronic spin transfer on Li(2) is positive and relatively strong, whereas the spin transfer on Li(1) is negative and relatively weak. In Figure 9b the net spin value obtained for a 0.6 Å radius sphere corresponding to the Li+ ionic radius in tetrahedral coordination is given. From the resulting electron spin calculated on the two Li sites, we can unambiguously assign the two NMR signals, since opposite spin polarizations are obtained in both GGA and GGA+U calculations for the two Li sites, in agreement with the sign of the experimental NMR contact shifts. The +885 ppm signal is therefore assigned to

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the Li(2) site for which a positive spin was calculated and the -232 ppm signal is assigned to the Li(1) site for which a negative spin was calculated. Note, however, that the relative magnitude of the calculated spin densities does not scale with the magnitude of the NMR shifts. Since the shift is proportional to the electron spin density at the nucleus, the ratio between the shifts should be identical to the ratio between the spin densities for the two Li sites. Although the calculations obviously refer to a zero kelvin state, whereas the NMR experiments are carried out at room temperature, one would expect the electron spin density transferred on the two Li to vary identically (i.e., keeping the same ratio) with temperature, since this quantity first linearly depends on the net polarization of the electron spins on the single Co2+ ions. Experimentally the Li(2)/Li(1) shift ratio is close to 3.8 (in absolute value), whereas spin densities calculated with GGA in a 0.6 Å sphere yield a much larger ratio of 14.8. With the U term, i.e., when localizing more the 3d orbitals, the calculated spin transfer on the two Li sites is weaker than for GGA calculation as expected, and the Li(2)/Li(1) absolute spin ratio is lower (12.2). It appears, thus, that localization of the 3d orbitals does not affect similarly the transfer on the two lithium nuclei: the transfer on Li(2) is relatively more lowered than that on Li(1) (Figure 9b). In order to understand the origin of the opposite sign of the shifts for Li(1) and Li(2), we tried to visualize all the different spin transfer mechanisms from Co2+ to each Li that can occur in the Li6CoO4 structure, either though space or via the oxygen 2p orbitals by drawing spin density maps in a number of selected planes. Only those where significant transfer was observed are discussed to explain the different shift signs for the two Li sites. Figure 10a thus shows the spin density map calculated with the GGA method (the GGA+U calculation leads to qualitatively similar spin density maps) in the xy plane for z ) 0.25, since the main transfer mechanisms occur in this plane. Figure 10b shows this plane in the structure. Note that only the Co2+ and Li(1) atoms are really located in the z ) 0.25 plane and that the Li(2) are located slightly above and below at z ∼ 0.20 and z ∼ 0.30. The oxygen ions are represented here in order to visualize the CoO4 tetrahedra, but they do not belong to the z ) 0.25 plane, they are located much further from that plane at z ∼ 0.04 and z ∼ 0.46. The Co2+ ions have a (dx2-y2)2 (dz2)2 (dxz)1 (dyz)1 (dxy)1 electronic state as seen on the DOS (Figures 6b and 7b). The single spin located in the dxy orbital is clearly seen in Figure 10a, as the single electron in the (xy) plane is located in an orbital with lobes that point toward faces of the CoO4 tetrahedra (conversely, the e type orbitals for a tetrahedral coordination lead to lobes pointing toward the middle of the edges of the tetrahedron).15 As seen in Figure 10, this dxy orbital thus points directly (across an empty square-pyramidal site) toward the Li(2) site and therefore a delocalization mechanism from Co dxy to Li s is possible through space as represented in Figure 11a (the trace of the z ) 25 (a,b) plane used in Figure 10 is also shown). The direct overlap between these two orbitals leads to a strong transfer on Li s of an electron spin with similar polarization than the one on Co 3d, i.e., positive. As seen in Figure 11a, Li(2) is surrounded by two Co2+ ions that can transfer such a positive spin density. On the opposite, no direct transfer by a delocalization mechanism can occur for the Li(1) site (Figure 11b). The negative spin transfer is thus due to a polarization mechanism: the t2 electron spins polarize the paired electrons in the e orbital that points toward Li(1) through the common edge and overlaps with it, thus leading to a positive spin near the transition metal and to a negative one further, i.e., on the Li s orbital (Figures 10a and 11b).

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Figure 10. (a) Calculated spin polarization density map in the (a,b) plane at z ) 0.25 plane of the Li6CoO4 structure from GGA calculations. Color and black and white regions indicate respectively positive and negative spin densities. (b) Visualization of the z ) 0.25 (a,b) plane. Note that O atoms of the CoO4 tetrahedra (not in this plane) are also shown with their z coordinate in order to visualize those polyhedra and that Li(2) is not exactly located in the z ) 0.25 plane.

Concluding Remarks The polarization of the calculated spin density on the two Li ions compared to the sign of the experimental NMR shifts recorded leads to an unambiguous assignment. However, the relative magnitude of the calculated spin densities does not scale with the magnitude of the NMR signals. Besides, the spin density map clearly shows that Li(2) lies within a zone of positively polarized transferred electron spin density, while the situation is less clear for Li(1) that appears to lay at the boarder of two zones with opposite polarization of electron spin density. Integration of the spin density on the latter shows that the negatively polarized density is predominant. This situation suggests that the calculation either underestimates some contribution of negatively polarized spin density or overestimates the contribution of positively polarized spin density (or both). As recalled in the introduction, a negatively polarized spin density contribution has to involve a polarization mechanism, whereby a fully occupied orbital can be polarized by a spincarrying orbital, and the resulting negatively polarized part of

Lithium Transition Metal Oxides

J. Phys. Chem. C, Vol. 114, No. 10, 2010 4755 mechanism is missed by the calculation (note that spin density maps in planes containing Co, O, and Li did not reveal significant transfer pathways), and a reasonable assumption is that such a mechanism would involve core orbitals which are indeed not well taken into account in the present pseudopotential and plane wave based calculations. Improvement of the methodology is therefore currently underway along these lines. Acknowledgment. The authors would like to thank Re´gion Aquitaine (2007/2013 CPER Contract: 2.3.1-08012000) for financial support, M3PEC for computing facilities, and Cathy Denage for the technical assistance. References and Notes

Figure 11. Electron spin transfer mechanisms from Co2+ to Li(2) (a) or to Li(1) (b) s orbital. The dashed line indicates the position of the z ) 0.25 (a,b) plane chosen for the plot of the electron spin density map in Figure 10.

the former can overlap with Li(1). In the present case, the calculation has indeed shown such a polarization of the fully occupied e orbitals of Co and a direct transfer of the resulting negatively polarized electron spin density to Li(1) through the common edge of the tetrahedral, but this mechanism can be underestimated in the resulting spin density actually transferred onto Li. Another possibility is that an altogether different

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