Comparative density functional theory–density functional tight binding study of fullerene derivatives: effects due to fullerene size, addends, and crystallinity on band structure, charge transport and optical properties

Abstract

We present a systematic comparative density functional theory-density functional tight binding study of multiple derivatives of C60 and C70 with different addends, in molecular as well as solid state. In particular, effects due to fullerene size, type and number of addends, and of crystallinity on band structure, charge transport, and optical properties are investigated. These are important, in particular, for rational selection of fullerene derivatives as acceptor and electron transport layers in organic as well as planar inverted perovskite solar cells. We find that by the choice of type and number of addends, one can modulate the LUMO within 0.4 eV. Changes in the HOMO can reach 0.7 eV. Substituting C70 for C60 results in destabilization of the HOMO by about 0.1 eV for indene and quinodimethane addends and by a less significant amount for PCBM addends. The effect of C70-C60 substitution on the LUMO is of similar magnitude. A more significant change in HOMO-LUMO energy is seen for the aryl addends. On the other hand, all C70 based molecules have strong visible absorption. For most addends, the crystal packing leads to a stabilization of both the LUMO and HOMO by about ∼0.2 and ∼0.1 eV, respectively, vs. single molecules. When using bis-addends, it is also possible to enhance the visible absorption. Electron and hole transport rates are computed to vary vastly depending on the addends chosen; specifically, we compute that indene and quimodimethane addends can enhance charge transport rates while the aryl addend is predicted to result in substantially smaller mobilities of electrons and holes, vs. PCBM. Furthermore, the -CH and bisaddend addition can significantly enhance the charge transfer rates for the PCBM addend.

Effect of Nuclear Motion on Charge Transport in Fullerenes: A Combined Density Functional Tight Binding—Density Functional Theory Investigation

“…The PBE functional (Perdew et al, 1996) was used for transfer integral calculations for computational efficiency (Baumeier et al, 2010). We previously showed (Pal et al, 2017) that this approach results in electron transfer rate for C60 in good agreement with available experimental and computational data reported elsewhere (Günes et al, 2007;Grzegorczyk et al, 2010;Ferguson et al, 2011;Nardes et al, 2012Nardes et al, , 2014Arntsen et al, 2013;Pelzer et al, 2017).…”

“…Density Functional Theory (DFT) (Hohenberg and Kohn, 1964;Kohn and Sham, 1965) calculations on molecules and dimers for calculating the transfer integral were performed in Gaussian 09 (Frisch et al, 2016) using the 6-31+g(d,p) basis set. The G and reorganization energy were calculated as described in the previous work (Pal et al, 2017). Namely, G estimated from the difference in the redox potentials of the neutral and charged systems:…”

“…While addends to the buckyball have to be employed in OSCs to control the BHJ morphology (PCBM is the famous example), bare C60 and C70 [or their mix (Lin et al, 2018)] work well in PSCs (Brédas et al, 2009;Ameri et al, 2013). Fullerenes with addends can also be used in PSCs to control film morphology and band alignment with the perovskite and they also have a significant effect on the charge transport (Pal et al, 2017).…”

“…Critical electronic properties of fullerenes in these applications include band alignment with the organic donor or the perovskite, which determines charge separation rate at the interface, and the electron transport rate in bulk and across grain boundaries. The band alignment is controlled by the position of the LUMO (lowest unoccupied molecular orbital), which is centered on the buckyball, even when addends are used (Pal et al, 2017). The LUMO must be lower in energy than the LUMO of the organic donor or the conduction band minimum (CBM) of the perovskite, to provide sufficient driving force for charge separation, where the charge transfer rate can be approximated with the Marcus equation:…”

“…This can have significant effects on charge separation, especially in interfaces with small driving forces designed for high voltage, as well as on bulk charge transport, via Equation (1). Further, molecular units in organic solids such as fullerenes, which are bound by van der Waals (vdW) forces, can be relatively mobile (Pal et al, 2017). This is expected to have a drastic effect on the overlap integral.…”