Superintermolecular orbitals in the ${\mathrm{C}}_{60}$-pentacene complex

We report a group of unusually big molecular orbitals in the ${\mathrm{C}}_{60}$-pentacene complex. Our first-principles density-functional calculation shows that these orbitals are very delocalized and cover both ${\mathrm{C}}_{60}$ and pentacene, which we call superintermolecular orbitals (SIMOs). Their spatial extension can reach 1 nm or larger. Optically, SIMOs are dark. Different from ordinary unoccupied molecular orbitals, SIMOs have a very weak Coulomb and exchange interaction. Their energy levels are very similar to the native superatomic molecular orbitals in ${\mathrm{C}}_{60}$and can be approximately characterized by orbital angular momentum quantum numbers. They have a distinctive spatial preference. These features fit the key characters of charge-generation states that channel initially bound electrons and holes into free-charge carriers. Thus, our finding is important for ${\mathrm{C}}_{60}$-pentacene photovoltaics.

Figure 1

Light first strikes the ${\mathrm{C}}_{60}$-pentacene complex and creates a singlet, followed by singlet fission into triplets. But electrons and holes have to dissociate from each other to become free charge carriers. The central question is what the channel states are for charge generation in organic solar cells. We show that the superintermolecular orbitals may offer an answer.

Figure 2

Superintermolecular orbitals in ${\mathrm{C}}_{60}$-pentacene for the edge-on configuration (left) and face-on configuration (right). We show one representative $1p$ SIMO for each configuration; $1p$ SIMO has orbital number 205.

Figure 3

Coulomb and exchange matrix elements between pairs of states in native ${\mathrm{C}}_{60}$. There are 3081 elements. The magnitude of matrix elements is proportional to the radius of circles, and all the Coulomb elements are rescaled by multiplying by 0.15. Since the matrix is symmetric, the upper triangle shows the Coulomb integral, while the lower triangle shows the exchange integral.

Figure 4

Coulomb and exchange matrix elements between pairs of states. The magnitude of matrix elements is proportional to the radius of circles. Since the matrix is symmetric, the upper left triangle shows the Coulomb integral, while the lower right triangle shows the exchange integral. The largest Coulomb integral (4.51 eV) is from LUMO+1 (orbital number 175) localized on Pc, and the smallest (0.43 eV) is among $1f$ SIMOs (orbital numbers 226 and 228). The exchange integrals are shown by small red circles and are extremely small.

Figure 5

Top: Energy-level comparison between SIMOs of ${\mathrm{C}}_{60}$-pentacene and SAMOs of ${\mathrm{C}}_{60}$. The energy in $1s$ states is similar. A small splitting is noticed in the $1p$ state. The $1d$ state has the largest shift of 0.16 eV due to an overlap in the $d$ orbitals. Change in $1f$ is small. Bottom: Wave function of $1d$ SIMO (left) and wave function of $1f$ SIMO (right).