CLS Next Gen: Accurate Frequency–Frequency Correlation Functions from Center Line Slope Analysis of 2D Correlation Spectra Using Artificial Neural Networks

Abstract

The center line slope (CLS) observable has become a popular method for characterizing spectral diffusion dynamics in two-dimensional (2D) correlation spectroscopy because of its ease of implementation, robustness, and clear theoretical relationship to the frequency−frequency correlation function (FFCF). The FFCF relates the frequency fluctuations of an ensemble of chromophores to coupled bath modes of the chemical system and is used for comparison to molecular dynamics simulations and for calculating 2D spectra. While in the appropriate limits, the CLS can be shown to be the normalized FFCF, from which the full FFCF can be obtained, in practice the assumptions that relate the CLS to the normalized FFCF are frequently violated. These violations are due to the presence of homogeneous broadening and motional narrowing. The generalized problem of relating the CLS to the FFCF is reanalyzed by introducing a new set of dimensionless parameters for both the CLS and FFCF. A large data set was generated of CLS parameters derived from numerically modeled 2D line shapes with known FFCF parameters. This data set was used to train feedforward artificial neural networks that act as functions, which take the CLS parameters as inputs and return FFCF parameters. These neural networks were deployed in an algorithm that is able to quickly and accurately determine FFCF parameters from experimental CLS parameters and the fwhm of the absorption line shape. The method and necessary inputs to accurately obtain the FFCF from the CLS are presented.

Identical Water Dynamics in Acrylamide Hydrogels, Polymers, and Monomers in Solution: Ultrafast IR Spectroscopy and Molecular Dynamics Simulations

“…The FFCF is the probability that the vibrational probe with a frequency at time t = 0 has the same frequency at a later time, averaged over all the frequencies in the inhomogeneously broadened absorption line shape. ,, The complete FFCF is typically described with the Kubo model , where C ω ( t ) is the normalized FFCF, and the frequency fluctuation, δω ( t ) = ω­( t ) – ⟨ω⟩, is the difference between the instantaneous frequency at time t and the average frequency, ω­( t ) and ⟨ω⟩, respectively, while Δ i and τ i are the amplitude of the frequency fluctuation and the time constant of the i th decay pathway, respectively. If a pathway is in the motionally narrowed limit, Δ i τ i ≪ 1, then it contributes to the homogeneous line width, Γ = 1/ πT 2 , which is the result of ultrafast fluctuations, i.e., pure dephasing processes, as well as the vibrational lifetime and orientational relaxation.…”

Ultrafast Dynamics and Liquid Structure in Mesoporous Silica: Propagation of Surface Effects in a Polar Aprotic Solvent

“…The FFCF can be calculated by simultaneously fitting the CLS­( T w ) and the linear absorption spectrum. ,, While FFCFs can be calculated from the spatially averaged measurements on the pore samples (Table ), it is not straightforward to decompose the FFCF by distance because there are no distinctive core and shell contributions to the observed linear spectra; the spectra for all pore sizes were identical and barely different from the bulk spectrum. The near identity of the bulk and pore spectra was also observed for SeCN – in D 2 O …”

“…The full FFCF, which has the same time constants as the CLS­( T w ), was determined from the CLS­( T w ) and the linear absorption spectrum using the recently developed CAFE program. CAFE employs artificial neural networks to quickly and accurately obtain the FFCF parameters, producing results that are accurate for spectral diffusion components in both the homogeneous and inhomogeneous limits …”

Observing Multiexciton Correlations in Colloidal Semiconductor Quantum Dots via Multiple-Quantum Two-Dimensional Fluorescence Spectroscopy

“…While positive peak tilts were previously observed in 2Q spectra of semiconductor quantum wells and a laser dye, we here observe, in contrast, a negative peak tilt in 3Q 2D spectra. One of the great strengths of 2D spectroscopy, which we want to exploit in the following, is its ability to probe frequency–frequency correlation functions. − We sought to model the origin of this peak tilt by a simple response-function calculation (Figure e). For the sake of simplicity, we only modeled the feature with the largest magnitude in the 1Q–3Q spectrum, which we mainly attribute to the excited triexciton |X 3 X 3 X 3 ⟩.…”