| Abstract [eng] |
Optical spectroscopy experiments are an essential tool for probing the properties of molecular systems. An important class of experimental methods belongs to the domain of Stark spectroscopy, whereby the conventional absorption, fluorescence, or even two-dimensional spectroscopy experiments are performed with an additionally applied external static electric field. Specifically, the Stark fluorescence (and, similarly, absorption) spectrum is defined as the difference of two spectra: one registered with an externally applied electric field, and one without it. In particular, these experiments provide a way of identifying and parametrising the charge-transfer (CT) states that play an essential role in the process of photosynthesis. Interpretation of experimental data, however, is no trivial task due to the interweaving of various effects that occur in real systems. The first theoretical model that has been proposed for analysing the Stark spectroscopy data is due to Liptay, but some authors have questioned the applicability of this model because the parameters obtained from the fit were unphysical in certain cases. A number of new methods for simulations of spectroscopic signals have been developed, which, however, is only targeted at Stark absorption experiments. No attempts to simulate Stark fluorescence spectra using a microscopic theory have been made so far, and the present study is the first work in this direction. The aim of this work is to simulate the Stark fluorescence spectra of model molecular systems and determine how the presence of CT states influences the shapes of the spectra. In the process, we check whether the Liptay formalism yields results consistent with those obtained using a numerically exact method. Additionally, we apply the quantum-classical theory to the calculations of the Stark fluorescence spectra to find whether such an approach could be used in cases when the system does not allow for a numerically exact treatment. The calculations are performed by applying the theory of open quantum systems, whereby the molecular system is divided into the electronic subsystem and the vibration bath. The spontaneous emission is treated from the perspective of quantum electrodynamics, and the Stark fluorescence spectra are calculated as the Fourier image of the dipole–dipole correlation function. Formally exact results are obtained using the Hierarchical Equations Of Motions (HEOM) approach, which, however, is only applicable for a specific class of systems and scales unfavourably as the subsystem size increases. These issues are circumvented by applying the Forward-Backward Trajectory Solution (FBTS) of the quantum-classical Liouville equation. In the first part of the work, the Stark fluorescence spectra of systems consisting of two molecular-excitation states are simulated. Then, systems where one of the states is a CT state are analysed. After that, spectra of systems with two molecular-excitation states and one CT state are investigated. In the final part of the work, an analytical analysis of a two-level system placed in an external electric field is performed. The results of the calculations provide an explanation for the changes of the total fluorescence yield that are observed in the spectra. The conclusions of the work are: (1) The presence of charge-transfer states in the system may cause a change of the total fluorescence yield in an external electric field: an increase if the energy of this state is the lowest in the system, or a reduction if its energy is the highest among all states. (2) The quantum-classical FBTS method may be applied for simulating the Stark fluorescence spectra if the subsystem–bath coupling strength does not exceed the strength of the resonance coupling (λ /J ≲ 1). (3) The Liptay formalism does not allow for an estimation of the magnitude of the specific effects caused by the presence of charge-transfer states in the system. |
