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Excitations Energy transfer occurring among an excited donor chromophore and potential acceptor chromophores has gained prime research interest owing to the highly efficient nature of the energy transferring process. One of the more popular approximation methods in simulating this energy transfer is the multi-site exciton full polaron transformation-based quantum master equation which has shown the ability to interpolate between weak and strong system bath coupling regimes. It has been shown that decay processes in many physical processes follow the well-known exponential decay laws with inverse power law behaviour at longer time scales. Conventional ohmic-like spectral density functions, model this behaviour well. However, it has been shown quantum mechanically that the long-term relaxation of such systems also has a significant inverse logarithmic term that is not captured by ohmic-like SDF models. Therefore, logarithmic decays and logarithmic factors are not rare in the literature with respect to excitations energy transfer. Recently introduced Ohmic-like spectral density function that can account for slight perturbations in the frequency domain has used these logarithmic factors to model this perturbation. Our objective of this paper is to study the energy transfer of a multi-site exciton system attached to an environment where these logarithmic perturbations could be experienced, with a full polaron based quantum master equation. Our results reveal that, when system bath coupling strength is larger the derived multi-exciton full polaron transformation-based quantum master equation is unable to simulate accurate dynamics where in some scenarios the well-known phenomena of infrared divergence occur. On the other hand, when the system bath coupling strength is weak, derived equation conveys better results. In addition, results show that smaller Ohmicity values can suffer from acute distortions even for a smaller logarithmic perturbation. Also, we show that when logarithmic perturbations are increased, damping characteristics of the energy transfer are also increased in general.
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