Three-dimensional electron momentum densities of graphite and fullerene: a comparison

Abstract

We report on the three-dimensional electron momentum densities (EMD) of graphite and fullerene obtained by a so-called (,e) experiment, i.e. the coincident detection of an inelastically scattered hard x-ray photon with its recoil electron. A monochromatized flux of 1012 photons s-1 at 150 keV from the high-energy x-ray wiggler beamline of the ESRF was directed onto thin graphite or fullerene targets. Comparison with a pseudopotential and a full-potential linear muffin-tin orbital calculation in the case of graphite is made. Inclusion of electron correlation via the Lam-Platzman correction is discussed. The experimental EMD of C60 shows stronger electron delocalization in the `buckyball' compared to graphite, which is supported by theory.

Recent Results from (γ, ϱγ) and Compton Spectroscopy

“…The most remarkable difference in the EMDs of graphite and C 60 is the increased density of C 60 compared to graphite at small momenta [16]. The bending of the graphite basal planes to form the buckyball induces a hybridization of wavefunctions with s-character with those of the π-electrons, which results in a charge transfer from the interlayer region into the shell of the C 60 spheres [17].…”

“…This kind of delocalization results apparently in an enhancement of the EMD at small momenta. A comparison of one-dimensional cuts through the EMD of fullerene with either the FP-LMTO for graphite or the molecular C 60 calculation showed that experiment could not distinguish between both theories within error bars [16]. To improve the statistics we have summed all coincidence events for a constant p z -value.…”

Anisotropy of the electron momentum density of graphite studied by(γ,eγ)and(e,2e)spectroscopy

“…Since in all three theories the EMD was obtained by the Fourier transform of the Kohn-Sham pseudo-wave-functions, the so-called Lam-Platzman correction 98 has been applied though its contribution is vanishingly small. 30 Whereas for both the PP and FP-LMTO approximations the azimuthal and spherical average have been obtained by angular integration of the 3D-EMD, in case of the MAPW calculation the special direction method has been applied. Evidently, FP-LMTO and MAPW ͑with a tendency of MAPW to be superior to FP-LMTO in case of the LPA foil͒ describe the data better than PP, a fact which has also been recognized by Metz et al 30 atomic core has been added.͒ But we also observe that the often cited deficiency of a PP calculation of not reproducing the wave function oscillations near the nuclei and therefore to underestimate the EMD at large momenta, 94 is not significant for the comparison with our data.…”

“…30 Whereas for both the PP and FP-LMTO approximations the azimuthal and spherical average have been obtained by angular integration of the 3D-EMD, in case of the MAPW calculation the special direction method has been applied. Evidently, FP-LMTO and MAPW ͑with a tendency of MAPW to be superior to FP-LMTO in case of the LPA foil͒ describe the data better than PP, a fact which has also been recognized by Metz et al 30 atomic core has been added.͒ But we also observe that the often cited deficiency of a PP calculation of not reproducing the wave function oscillations near the nuclei and therefore to underestimate the EMD at large momenta, 94 is not significant for the comparison with our data. The discrepancy between our data and PP is not due to an underestimate of high momentum components-and therefore a reduction of intensity at small momenta due to charge conservation-but due to a different slope of experiment and theory.…”

“…[27][28][29] In this paper we report on the EMD of graphite obtained by (␥,e␥) and (e,2e) experiments. In contrast to earlier investigations, 30,31 the main emphasis of this paper is the study of EMD anisotropies and their comparison with band structure theories. Both experimental techniques obtain results for the EMD.…”