ВРАЩЕНИЯ ЯКОБИ В ОБРАТНОЙ ЗАДАЧЕ НАХОЖДЕНИЯ ПАРАМЕТРОВ ВИБРОННОЙ СВЯЗИ В УСЛОВИЯХ РЕЗОНАНСА

We have found an exact solution to the task of determination of the energies of the non-perturbed states ai and vibronic coupling matrix elements bi that describe the vibronic analogue of the complex Fermi resonance, using the experimental data represented by the energies ek (obs) and the transition intensities Ik (obs) (k = 1, 2, …, n) in an observed absorption spectrum. The algorithm consists of two stages. At the first stage, the Jacobi rotations are used to construct a similarity transformation X with the requirement (X1k)2 = Ik (obs) that corresponds to the condition that there is only one non-perturbed «bright» state. At the second stage, the algebraic eigenvalue problem for the matrix Xdiag({ek (obs)})X –1 is employed to find ai and bi values.Найдено точное решение задачи определения из экспериментальных данных (энергий ek (obs) и интенсивностей переходов Ik (obs) наблюдаемого спектра поглощения, k = 1, 2, …, n) энергий невозмущенных состояний αi и матричных элементов вибронной связи bi, описывающих вибронный аналог сложного резонанса Ферми, n ≥ 3. В первой части алгоритма используются элементарные вращения Якоби для построения преобразования подобия X с требованием для элементов первой строки матрицы X (X1k)2 = Ik (obs), в соответствии с тем, что только одно невозмущенное состояние является «светлым». Во второй части для нахождения величин αi и bi решается алгебраическая проблема собственных значений матрицы Xdiag({ek (obs)})X –1

Solvent Polarity Effect on Nonradiative Decay Rate of Thioflavin T

It has been established earlier that fluorescence quantum yield of thioflavin T (ThT)a probe widely used for amyloid fibrils detectionis viscosity-dependent, and photophysical properties of ThT can be well-described by the fluorescent molecular rotor model, which associates twisted internal charge transfer (TICT) reaction with the main nonradiative decay process in the excited state of the dye. Solutions of ThT in a range of polar solvents were studied using steady-state fluorescence and sub-picosecond transient absorption spectroscopy methods, and we showed that solvent effect on nonradiative transition rate <i>k</i>_nr cannot be reduced to the dependence on viscosity only and that ∼3 times change of <i>k</i>_nr can be observed for ThT in aprotic solvents and water, which correlates with solvent polarity. Different behavior was observed in alcohol solutions, particularly in longer <i>n</i>-alcohols, where TICT rate was mainly determined by rotational diffusion of ThT fragments. Quantum-chemical calculations of S₀ → S₁ transition energy were performed to get insight of polar solvent contribution to the excited-state energy stabilization. Effect of polar solvent on electronic energy levels of ThT was simulated by applying homogeneous electric field according to the Onsager cavity model. Static solvent effect on the excited-state potential energy surface, where charge transfer reaction takes place, was not essential to account for experimentally observed TICT rate differences in water and aprotic solvents. From the other side, nonradiative decay rate of ThT in water, ethylene glycol, and aprotic solvents was found to follow dynamics of polar solvation <i>k</i>_nr ∼ τ_<i>S</i>^–1, which can explain dependence of the TICT rate on both polarity and viscosity of the solvents