Strong electron correlation plays an important role in the determination of double ionization energy, which is required for removing or adding two electrons, particularly in small-sized systems. Starting from the state-of-the-art GW approximation, we evaluate the particle-particle ladder diagrams up to the infinite order by solving the Bethe-Salpeter equation of the T-matrix theory to calculate the double-ionization energy spectra of atoms and molecules (Be, Mg, Ca, Ne, Ar, Kr, CO, C(2)H(2), Li(2), Na(2), and K(2)) from first principles. The ladder diagrams up to the infinite order are significant to calculations of double-ionization energy spectra. The present results are in good agreement with available experimental data as well as the previous calculations using, e.g., the configuration-interaction method.

The vacuum space inside carbon nanotubes offers interesting possibilities for the inclusion, transportation, and functionalization of foreign molecules. Using first-principles density functional calculations, we show that linear carbon-based chain molecules, namely, polyynes (C(m)H(2), m = 4, 6, 10) and the dehydrogenated forms C(10)H and C(10), as well as hexane (C(6)H(14)), can be spontaneously encapsulated in open-ended single-walled carbon nanotubes (SWNTs) with edges that have dangling bonds or that are terminated with hydrogen atoms, as if they were drawn into a vacuum cleaner. The energy gains when C(10)H(2), C(10)H, C(10), C(6)H(2), C(4)H(2), and C(6)H(14) are encapsulated inside a (10,0) zigzag-shaped SWNT are 1.48, 2.04, 2.18, 1.05, 0.55, and 1.48 eV, respectively. When these molecules come inside a much wider (10,10) armchair SWNT along the tube axis, they experience neither an energy gain nor an energy barrier. They experience an energy gain when they approach the tube walls inside. Three hexane molecules can be encapsulated parallel to each other (i.e., nested) inside a (10,10) SWNT, and their energy gain is 1.98 eV. Three hexane molecules can exhibit a rotary motion. One reason for the stability of carbon chain molecules inside SWNTs is the large area of weak wave function overlap. Another reason concerns molecular dependence, that is, the quadrupole-quadrupole interaction in the case of the polyynes and electron charge transfer from the SWNT in the case of the dehydrogenated forms. The very flat potential surface inside an SWNT suggests that friction is quite low, and the space inside SWNTs serves as an ideal environment for the molecular transport of carbon chain molecules. The present theoretical results are certainly consistent with recent experimental results. Moreover, the encapsulation of C(10) makes an SWNT a (purely carbon-made) p-type acceptor. Another interesting possibility associated with the present system is the direction-controlled transport of C(10)H inside an SWNT under an external field. Because C(10)H has an electric dipole moment, it is expected to move under a gradient electric field. Finally, we derive the entropies of linear chain molecules inside and outside an open-ended SWNT to discuss the stability of including linear chain molecules inside an SWNT at finite temperatures.

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The structure of carbon nanotubes constitutes graphene sheets that are rolled to form cylinders with extremely small diameters. It is interesting to investigate the interaction between single-walled carbon nanotubes and an Fe atom because such nanotubes are fabricated with the aid of metal catalysts (Fe, Co, etc). Using an ab initio program DMol 3 , we have calculated the total energy of a system of (10,0) nanotube incorporated with an Fe atom. We have determined the most stable position of Fe near the entrance of the nanotube and the potential map for that position.