Quantum Master Equation Approach to the Second Hyperpolarizability of Nanostar Dendritic Systems

Abstract

We investigate the dynamic second hyperpolarizability (gamma) of nanostar dendritic systems using the quantum master equation approach. In the nanostar dendritic systems composed of three-state monomers, the multistep exciton states are obtained by the dipole-dipole interactions, and the directional energy transport, i.e., exciton migration, from the periphery to the core is predicted to occur by the relaxation between exciton states originating in the exciton-phonon coupling. The effects of the intermolcecular interaction and the exciton migration, i.e., exciton relaxation, on the gamma in the third-harmonic generation (THG) are examined in the three-photon off- and on- resonance regions using the two-exciton model. Furthermore, the method for analysis of spatial contributions of excitons to gamma is presented by partitioning the total gamma into the one- and two-exciton contributions. It turns out that the exciton relaxation between exciton states causes significant broadening of the spectra of gamma and their mutual overlap as well as the relative increase of two-exciton contributions in the nanostar dendritic system.

Mechanisms of Light Energy Harvesting in Dendrimers and Hyperbranched Polymers

“…Here, the interplay with advances in characterising the dynamics of photosynthetic systems is evident; notable examples include work by Scholes et al who deploy a generalized Förster approach for Monte-Carlo simulations [85,86]. A semi-empirical quantum chemical approach has been used by Wong et al [87], master equations are employed by several groups [88][89][90][91], and an extended Redfield approach, by Ishizaki and Fleming [92,93]. For the modelling of RET dynamics, specifically in dendrimers, significant methods include use of a Pauli master equation by Yeow et al [94], a mixed quantum/classical methodology by May et al [95,96], and non-adiabatic trajectories by Fernandez-Alberti et al [97].…”

“…Significantly, Monguzzi et al have reported energy up-conversion in a multi-component organic polymer at irradiances as low as 10 W m −2 , a level at which the low energy tail of the solar emission spectrum could be captured even without focusing optics [53]. Earlier reports of exceptionally high two-photon absorption cross-sections and enhanced third-order optical nonlinearity [54][55][56] have inspired many other suggestions for exploiting dendrimers in a range of applications extending well-beyond energy harvesting [57][58][59][60][61][62][63][64][65].…”

Development of Calculation and Analysis Methods for the Dynamic First Hyperpolarizability Based on the Ab Initio Molecular Orbital – Quantum Master Equation Method

“…The power of the fields is set to 100 MW/cm, which is strong enough to observe the longitudinal SHG signal, β zzz (−2ω;ω,ω). The relaxation factors Γ appearing in eqs and are neglected in this study because the effect of relaxation has been already discussed in our previous study, while we set the additional damping factor from the excited state to the ground state, Γ α1 = 0.01ω α . The time evolution of exciton RDM is calculated up to 3000 optical cycles.…”

Primary Photonic Processes in Energy Harvesting: Quantum Dynamical Analysis of Exciton Energy Transfer over Three-Dimensional Dendrimeric Geometries

“…40 Yeow et al developed a theoretical approach which employed the Pauli master equation to help understand time-resolved fluorescence anisotropy measurements that were made on a series of porphyrin-based dendrimers. 41 Nakando et al used a quantum master equation approach for modeling the second hyperpolarizability of nanostar dendrimers; 42 May et al employ a mixed quantum classical methodology to calculate rates of energy transfer in the pheophorbide-a DAB dendrimer, 43,44 and Fernandez-Alberti have used non-adiabatic trajectories to model energy transfer in dendrimeric units. 45 One of the authors of the current paper (Andrews) and collaborators have recently developed an adjacency matrix approach that has been used to model the multi-step flow of energy in light-harvesting dendrimers.…”