Nonadiabatic molecular dynamics under adiabatic representation

<sec>In this paper, we develop a nonadiabatic molecular dynamics method based on Su-Schriffer-Heeger (SSH) Hamiltonian, and this method is widely used to study the photoexcitation dynamics and polaron motion in conjugated polymers. However, in this method, the time-dependent Schrödinger equation has so far been solved in a diabatic representation, also known as site representation. In order to provide a deeper insight into the nonadiabatic molecular dynamics method, we solve the time-dependent Schrödinger equation in an adiabatic representation. The new method can directly provide the important information about the strength of nonadiabatic couplings between different molecular orbitals in the excited-state relaxation process, helping us to predict the electron and energy transfer within or between polymer chains.</sec><sec>Solving the time-dependent Schrödinger equation in an adiabatic representation is much more complicated, it is mainly because we need to calculate the nonadiabatic couplings between different molecular orbitals. In this paper, the detailed formula derivation and actual calculation process of the nonadiabatic molecular dynamics method in an adiabatic representation are given. Using this new method, we simulate three photoexcitation processes in a conjugated polymer chain, HOMO→LUMO, HOMO–1→LUMO+1 and HOMO–2→LUMO+2. We analyze in detail the time evolutions of lattice configuration for these three photoexcitation processes, and compare these results with those obtained by diabatic representation (site representation) showing that the results obtained from these two representations are consistent with each other.</sec>