Relaxation process of the self-trapping exciton inC60

Abstract

When C 60 is photoexcited, a self-trapping exciton ͑STE͒ is formed: The bond structure is distorted from symmetry I h to D 5d while the states A 1u and A 2u are pulled into the energy gap from highest occupied molecular orbital and lowest unoccupied molecular orbital, respectively. A dynamical scheme is employed to simulate the relaxation process of STE. The evolution of both bond structure and electronic states shows that the relaxation time to form STE is about 100 fs. It should be noted that this relaxation time is much shorter than that of charge transfer in C 60 . The origin for this large difference is discussed.

Dynamical Process of Excitation Fusion in Polymers

“…8,9 We can simulate the dynamic evolution of the bond structure. Since the period of lattice vibration τ 0 is about 4 × 10 -14 s, the time step τ should be much shorter than τ 0 , where we choose τ ) 1 fs(10 -15 s).…”

“…By using the Hellmann−Feynman theorem, we get With substitution of eq 7 into eq 5, the dynamic equation eq 6 can be solved numerically step by step. , We can simulate the dynamic evolution of the bond structure. Since the period of lattice vibration τ 0 is about 4 × 10 -14 s, the time step τ should be much shorter than τ 0 , where we choose τ = 1 fs(10 -15 s).…”

Effect of long-range electronic correlation on exciton in the conjugated polymers

“…In the tight-binding approximation, the eigen equation referring to the π electrons of the organic conjugated molecular system is [22] H e ∑ n Z σ µ,n |n >= ϵ σ µ ∑ n Z σ µ,n |n > (8) where µ means the molecular energy level index (or orbital index), ϵ σ µ is π electronic energy at molecular level µ and constitutes π electron energy spectrum of the molecular system. |n > is orthogonal Wannier state and |n >= C † nσ |0 >, here |0 > is vacuum state where there is no π electron in the site n. Z σ µ,n is stationary wave function belonging to the µth molecular energy level and located at the site n. H e is the electron part of the total Hamiltonian and given by…”

“…By self-consistently solving (8) and (10), we can obtain lattice configuration with the lowest total energy of system, charge density distribution, and energy spectrum which contains the long-range electron correlation effect because H e contains the long-range electron correlation Hamiltonian H c . Finally, we calculate the LREC energy E c of the exciton state from the HF approximation of H c [16]:…”

“…The self-trapped bound exciton will be dissociated under stronger electrical field and has contribution to the optical process [10]. People have studied properties of one-exciton state and two-exciton state in the conjugated polymers under applied electrical field along the polymer chain direction [7] [8] and also have studied polarizability of the single exciton [11] [12] using tight-binding model. However, there is one very important factor that did not have been considered analytically in those studies about the exciton states and the polarizability.…”