Monte Carlo Wavefunction Approach to Singlet Fission Dynamics of Molecular Aggregates.

Masayoshi Nakano,Takanori Nagami,Yasutaka Kitagawa,Kenji Okada,Ryohei Kishi,Takayoshi Tonami

doi:10.3390/molecules24030541

Abstract

We have developed a Monte Carlo wavefunction (MCWF) approach to the singlet fission (SF) dynamics of linear aggregate models composed of monomers with weak diradical character. As an example, the SF dynamics for a pentacene dimer model is investigated by considering the intermolecular electronic coupling and the vibronic coupling. By comparing with the results by the quantum master equation (QME) approach, we clarify the dependences of the MCWF results on the time step (Δt) and the number of MC trajectories (MC). The SF dynamics by the MCWF approach is found to quantitatively (within an error of 0.02% for SF rate and of 0.005% for double-triplet (TT) yield) reproduce that by the QME approach when using a sufficiently small Δt (~0.03 fs) and a sufficiently large MC (~105). The computational time (treq) in the MCWF approach also exhibits dramatic reduction with increasing the size of aggregates (N-mers) as compared to that in the QME approach, e.g., ~34 times faster at the 20-mer, and the size-dependence of treq shows significant reduction from N5.15 (QME) to N3.09 (MCWF). These results demonstrate the promising high performance of the MCWF approach to the SF dynamics in extended multiradical molecular aggregates including a large number of quantum dissipation, e.g., vibronic coupling, modes.

Highlights

Singlet fission (SF) is a photophysical process, where a singlet exciton state splits into two triplet excitons, and is known to be a very fast reaction process on time scales of pico- or subpico-seconds [1,2,3,4,5].One of the reasons is that the two triplet excitons created are firstly coupled and in a singlet state overall
We investigate the dependences of the accuracy of the results of SF dynamics (SF rate and TT yield) on time step and the number of Monte Carlo sample sizes (MC) trajectories using a pentacene dimer model, and discuss the applicability and performance of the Monte Carlo wavefunction (MCWF) approach to the SF dynamics for larger-size molecular aggregate systems
In order to clarify the performance of the MCWF approach by comparing with the quantum master equation (QME) results, we examine a pentacene dimer model with R = 3.5 Å and θ = 60◦ (N = 2 in Figure 1) [24,25], which indicate the intermonomer distance between the nearest neighbor carbon atoms in the zigzag edges, and the angle between the pentacene monomer plane and the longitudinal axis in parallel to the R

Summary

Introduction

Singlet fission (SF) is a photophysical process, where a singlet exciton state splits into two triplet excitons, and is known to be a very fast reaction process on time scales of pico- or subpico-seconds [1,2,3,4,5]. Due to solving the Schrödinger-type wave equation (not QME), a significant advantage of the MCWF approach lies in its small numerical efforts (the number of elements is proportional to NB ). This advantage is predicted to become marked when we investigate the dynamics in large-scale dissipative quantum systems, e.g., SF dynamics of oligomers with a large number of vibronic coupling modes. We investigate the dependences of the accuracy of the results of SF dynamics (SF rate and TT yield) on time step and the number of MC trajectories using a pentacene dimer model, and discuss the applicability and performance of the MCWF approach to the SF dynamics for larger-size molecular aggregate systems

Hamiltonian of a Linear Molecular Aggregate

Quantum Master Equation Approach and Monte Carlo Wavefunction Approach

Time-evolution

Findings

Concluding Remarks