Exciton Dissociation in a Model Organic Interface: Excitonic State-Based Surface Hopping versus Multiconfigurational Time-Dependent Hartree

Quantum dynamical simulations are essential for a molecular-level understanding of light-induced processes in optoelectronic materials, but they tend to be computationally demanding. We introduce an efficient mixed quantum-classical nonadiabatic molecular dynamics method termed eXcitonic state-based Surface Hopping (X-SH), which propagates the electronic Schrödinger equation in the space of local excitonic and charge-transfer electronic states, coupled to the thermal motion of the nuclear degrees of freedom. The method is applied to exciton decay in a 1D model of a fullerene–oligothiophene junction, and the results are compared to the ones from a fully quantum dynamical treatment at the level of the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) approach. Both methods predict that charge-separated states are formed on the 10–100 fs time scale via multiple “hot-exciton dissociation” pathways. The results demonstrate that X-SH is a promising tool advancing the simulation of photoexcited processes from the molecular to the true nanomaterials scale.


Electronic Hamiltonian
In this study, we adopt the same 1D model of a fullerene-oligothiophene junction as used in Reference 1. In MCTDH, the total electron-nuclear Hamiltonian is composed of the kinetic (T1), the electronic (Ĥ el ) and the local electron-phonon (Ĥ MCTDH e-ph ) terms, (S1) In this study, both MCTDH and X-SH employ the same electronic Hamiltonian Ĥ el . Details of Ĥ el can be found in the main text (equations (2)- (5)).
MCTDH and X-SH differ in the treatment of the nuclear degrees of freedom and thus in the definition of the kinetic and local electron-phonon (Ĥ e-ph ) parts. 1 In MCTDH, is the nuclear kinetic energy operator in mass-and frequency-weighted coordinates.

Local electron-phonon coupling in X-SH
The energy of the neutral electronic ground state is calculated using the standard Generalized Amber Force Field (GAFF). 2 The energy of state XT n is calculated using suitably modified force field parameters for the excited state of the nth OT9 molecule and the standard GAFF force field parameters for the other molecules. The force field parameter for the excited state are based on the standard GAFF force field. Only the equilibrium bond lengths were changed so as to reproduce the reorganization energy obtained from DFT ground state and TDDFT excited state calculations on an isolated OT9 molecule in the gas phase (at CAM-B3LYP/6-31G(d,p) 3 level). The resultant reorganization energy for excitation of a single OT9 molecules is A similar approach was adopted to calculate the energy of state CS n . The force field was suitably modified to describe the C60 anion and the positively charged state of the nth OT9 molecule, and for all other molecules the default GAFF parameters were taken. Again, the force field parameters for the C60and OT9 + are based on the standard GAFF force field. Only the equilibrium bond lengths were changed so as to reproduce the reorganization energy obtained from DFT calculation for the neutral and charged isolated molecules in the gas phase (at B3LYP/6-31G(d,p) level 4-6 ), resulting in reorganization energies of 0.070 and 0.101 eV for C60 and OT9, The DFT bond displacements were scaled by factors of 0.99 and 0.82 to match the reorganization energies used in MCTDH, 0.069 and 0.068 eV.
(S10) (S11) The reorganization energy for charge separation (in the limit of infinite separation of OT and F) is 0.137 eV. We summarize all the reorganization energies and the values used in Reference 1 in Table S1.
We note that electrostatic interactions are not included in the force field description. The effective Coulombic interaction between the hole and the electron in the CS states is already included in the term. Van-der Waals interactions are modelled by standard Lennard-Jones terms and remain unchanged for the different electronic states.

Nuclear forces in X-SH
The nuclear forces on the active potential energy surface E a are expressed as ,

Thermal equilibrium populations in the X-SH approach
For the thermal equilibrium populations, we perform the simulations with a thousand trajectories on the lowest-lying state in the model system with Born-Oppenheimer approximation (without hops between states) and propagate each trajectory for 2 ps. The S5 equilibrium population P i for each diabatic state i is calculated using following equations at T = 300 K, where The w a is the weight of an adiabatic state a at each time step, where

The Energy Redistribution from the Normal Mode Analysis in the X-SH Approach
In the normal mode analysis, we adopt the procedures from literature. 8 In short, the massweighted Hessian matrix of OT9 molecule (S15) is diagonalized to obtain the eigenvectors with elements l ji . In the equation,   Figure S1. The Coulomb barrier at each site n applied in this study.