Magnetic ordering in abruptly compressed FCC fullerite S.S.Moliver

1. Magnetic ordering in abruptly compressed FCC fullerite S.S.Moliver State University of Ulyanovsk, Russia Grant-in-aid 08-03-97000 from Rus. Basic Res. Foundation. The nature of magnetic ordering in carbon materials stays an unresolved problem of experimental, theoretical, and simulation research [Kvyatkovskii O.E., et al. Phys. Rev. B. 72, 214426 (2005)] Search of atomic displacements, bringing minimum to the ground many-electron term, in such a complicated case, as fullerite, demands to analyse the picture of chemical bonds, arising and changing during the search itself. Recent studies confirm this difficulty once more: [Zipoli F., Bernasconi M. Phys. Rev. B. 77, 115432 (2008)]

2. Structure model of the high-pressure tetrahedral FCC close packing with [r5+r5] contacts of unbroken C60s. Open-shell restricted Hartree-Fock-Roothaan MO LCAO approximation for configurations t2, t4, t6. Large-unit-cell model of the crystal: [Moliver S.S., Rozhetskin D.D. Fullerenes, Nanotubes, and Carbon Nanostructures. 16(5-6), 517 (2008)] V W U W V

3. The open shell of nb MOs has occupancy f, hence, different determinants j are taken into spectroscopic sum. Single-determinantal closed-shell RHF (a) expression is appended with the open-shell (b) one. Coefficients A depend upon that term, or that "diagonal Slater sum", which is taken for the self-consistent calculation.

4. Self-consistent MO LCAO calculation is an eigen-problem, based on the Fock matrix F, constructed by density-matrix projection method [McWeeny]. Three density matrices (close-, open-, and virtual-shell) are used at every iteration of the self-consistensy loop.

5. Those terms and diagonal sums, which have AI=0, are accessible for ROHF approximation. For example, 3T term of t2 multiplet (1-st line) can be calculated either independently, or as a member of diagonal sum (5-th line).

6. Improoved strategy of searching atomic shifts, bringing minimum to the total energy. 1) All pentagons are equivalently distorted by vectors U (atom 1), V (atoms 2-3), and W (atoms 4-5). 2) Each distortion is represented by normal modes: t – torsion, p – pentagonal, and b – breathing. 3) X"=t+p+b, Y"=-t+p+b, Z"=-2p+b U, V, W=(X",Y",Z")R 4) p and b were varied separately for each distortion, while t was taken the same, as a final effort to tune inter-fullerene contact without destroying intra-fullerene coordinations.

7. Self-consistent total energies of configurations t6 (closed-shell insulator model), t4, t2 (open-shell-multiplet metal model) were calculated independently. Absolute energy is -6.8 eV/atom (vdW value -5.6).

8. Energy minimum (page 7) In room-temperature Th-FCC-C60 inter-fullerene distance R enables van-der-Waals cohesion of rotating fullerenes. Decreasing R, we arrive to the covalent cohesion limit Rcov=2R60+r5≈16.3 au, when [2+2] cycloaddition may appear (numerical values fit our INDO parametrization of carbon systems, RvdW=20.9 au, R60=7.21 au, r5=2.845 au). At R<Rcov those atomic displacements, which provide covalent bonding, can be simulated by MO LCAO calculations. Besides, only atomic structures with "correct covalent coordinations", are accessible for the closed-shell approximation, while the open-shell RHF allows more wide range of chemical structures (with partially occupied antibonding MOs). Our strategy was: to vary p and b modes of U, V, W, at a given R, in order to find energy minimum of t4, and to define a valley of "correct covalent coordinations" in many-parameter space. Within so found manifold of displacements other electron configurations were calculated, giving a not-suggested result: very close total energies of insulating t6 and magnetic t2 states.

10. Torsion mode (page 9) The valley of "correct covalent coordinations" narrows as R decreases, arriving to the limit of fullerene cage destruction. It is rather wide at intermediate values Rmin<R<Rcov, where torsion mode opens additional channel to the total-energy decrease. Taking reasonable values for t and R, we have found again optimal p and b modes of all displacements with large energy lowering. This result appends figure 9 with dashed lines, meaning an optimal route to the FCC covalent high-pressure structure. When the fullerenes are bringing closer, in order to support "correct covalent coordinations": atoms shift up and down the fullerene surface, while pentagons of the surface rotate as a whole. Covalent-minimiun distortions: dist.modepmodeb R=15.68 au modet=0 U -0.0016 +0.0380 atom 1 stays 3-coordinated V +0.0080 +0.0054 atoms 2-3 are 4-coordinated W -0.0058 -0.0250 [2+2]-like coordination of atoms 4-5 page 11 shows contact area between two fullerenes

12. Conclusion If some abrupt compression of fullerite can bypass topo-chemical high-pressure polymerization, the conducting FCC phase becomes possible as one of «3D polymer states». High-symmetry chemical bonds organization, tetrahedral FCC-close-packed fullerite, enables metallic electron configuration, where spin-triplet correlation may bring energy gain. Spin-triplet ordering in this phase is predicted by quantum chemistry, which cannot solve, whether this ordering is ferro- or antiferromagnetic. Fullerene's cage distortion in compressed FCC structure does not break the tetrahedral symmetry and the equivalence of the adjacent-fullerene contacts [r5+r5]. Abrupt compression, together with optical stimulation of torsion vibrations (IR absorbance, or Raman scattering), may transform FCC fullerite into metallic and magnetic 3D phase.

13. About two methods of quantum chemistry DFT: electron band structure and density of states are calculated self-consistently, as well as the occupation of the bands by a fixed number of electrons. It is unknown in the beginning, whether the output will be insulator or metal, and there is no independent test for both possibilities. This contradicts the DFT methodology to apply different E[n] to metals and insulators. MO LCAO: the 0-th approximation MOs can present any electron configuration. The choice of certain open-shell term means certain combination of determinants. Thus, self-consistent fields are different in cases of metalic and insulator occupancies.