Short-lived memory in multidimensional spectra encodes full signal evolution

Abstract

Ultrafast multidimensional spectroscopies are powerful tools that can access charge and energy flow in complex materials, shifting chemical kinetics, and even many-body interactions in correlated matter. However, current implementations typically involve complex apparatuses and long averaging times. As a result, these methods have been limited to detailed mechanistic investigations of a few samples, precluding the broad characterization of molecular systems and/or the optimization of material ones. For example, converging the statistical noise in 2D spectra becomes exponentially expensive with increasing waiting times, and extended laser exposure heightens the probability of sample degradation. We address this fundamental challenge by developing a new technique, the spectral generalized master equation (GME), that enables one to employ short-waiting time 2D spectra to determine the full evolution of 2D spectra over arbitrary waiting times with high temporal resolution. In addition to reducing the cost of experiments by multiple orders of magnitude, our approach accurately removes statistical noise, reducing the need for time averaging, while circumventing the increasing convergence costs with longer waiting times. We provide a rigorous theoretical footing for the spectral GME and demonstrate its applicability on theoretically generated and experimentally measured 2D electronic and 2D infrared spectra. We anticipate that this advance has the potential to enable the investigation of systems that are too delicate for study with current multidimensional spectroscopies and accelerate the progress of 2D spectroscopy-based microscopies that can offer highly resolved excitation dynamics with spatial resolution over heterogeneous environments.

Figures (5)

• Figure 1: Schematic representation of 2D spectroscopy with the spectrum divided across $t_2$ into regions according to the spectral GME. Our primary discovery is that 2D spectroscopy exhibits short-lived memory, that one can extract this memory from experiment directly to construct the dynamical propagator, and that this propagator can be used to predict the full evolution of the 2D spectrum using only its early-time data.
• Figure 2: Applicability of the spectral GME to simulated 2DES data of a model nonadiabatic energy transfer dimer. 2D spectra span a $80 \times 80$ spectral grid with $\delta \omega_1 = \delta \omega_2 = 10$ cm$^{-1}$ and were sampled at a timestep of $\delta t_2 = 48$ fs. (a) Snapshot of the 2D spectrum at $t_2=48$ fs highlighting the 3 pixels to visualize spectral evolution in (b). We highlight pixels located at indices $[(20,53), (53, 20), (53, 53)]$ to monitor both diagonal and off-diagonal spectral features. (b) Spectral evolution of the selected pixels along $t_2$. Squares correspond to benchmark simulation data up to $t_2=720$ fs. The dashed grey line is the chosen GME cutoff, $\tau_ \mathcal{U}$. The dotted grey line is the known time-nonlocal memory decay timescale for the multitime response function from previous work.Sayer2024 Inset shows the error plot which, together with the visual agreement contextualizing the error value, justifies $\tau_ \mathcal{U} \simeq 336$ fs. We employ an SVD truncation threshold of $\xi = 10^{-10}$ and $\tau_ \mathcal{U} =t_u$ for this system. As such, the spectral GME spectrum contains 22 singular values at $t_2 = 0$ fs, and uses only the first 7 frames up to the $\tau_ \mathcal{U} =336$ fs cutoff. (c) Comparison of 2D spectra at $t_2=720$ fs obtained from the simulation benchmark (top) and spectral GME prediction (bottom).
• Figure 3: Applicability of the spectral GME to experimental 2DES of a Cy3-Cy5 dimer separated by six nucleotides on DNA origami and originally characterized experimentally in Ref. Hart2021. 2D spectra span a $111 \times 111$ spectral grid with $\delta \omega_1 = \delta \omega_2 = 52.25$ cm$^{-1}$ and were sampled at variable timesteps, including $1$ ps, $2.5$ ps, $5$ ps, and $25$ ps. (a) 2D spectrum of Cy3-Cy5 in the visible range at $t_2=1$ ps. We highlight points at indices $[(27, 27), (51, 51), (51, 74), (40, 27)]$ as these span the full range of pixel intensities. (b) Comparison of 2D spectra at $t_2=600$ ps obtained from the experimental benchmark (left) and spectral GME prediction (right). (c) Spectral evolution of the selected pixels along $t_2$ on logarithmic time axis. Grey region represents the data used to construct $\langle\bm{ \mathcal{U} }_\infty(\delta t_2)\rangle$, and circles are the spectral GME predictions, which we evolve out to $3500$ ps to capture the equilibration timescale. Inset: Spectral evolution on a linear time axis. (d) Root mean squared error heat map. The purple diamond represents the choice of parameters shown in (c) while the white diamond denotes the global minimum error. Based on this plot, we choose $t_u=50$ ps, $\tau_ \mathcal{U} =200$ ps and $\xi=1$, and construct our spectral GME propagator using the data sampled with a timestep of $\delta t_2 = 25$ ps. We choose the parameterization $\langle \mathcal{U} \rangle_{2, 6}$ because it requires significantly less data while maintaining comparable accuracy to the global minimum.
• Figure 4: Applicability of the spectral GME to experimental 2DIR data of the dicyanamide (DCA) vibrational probe in a model ionic liquid electrolyte widely studied in battery science. These 2D spectra span a $64 \times 64$ spectral grid with $\delta \omega_1 = \delta \omega_2 = 3$ cm$^{-1}$ and were sampled at a timestep of $\delta t_2 = 100$ fs. (a) 2DIR spectrum of room temperature ionic liquid mixture [BMIM]$_x$[DCA]$_y$[BF$_4$]$_{1-x-y}$ in the IR at $t_2=0$ ps. We highlight pixels located at $[(5, 13), (9, 13), (13, 13), (13,42)]$ to survey a range of time dependence and intensities. (b) Comparison of 2D spectra at $t_2=11.5$ ps obtained from the experimental benchmark (left) and spectral GME prediction (right). (c) Spectral evolution of the selected pixels along $t_2$. Grey region represents the data used to construct $\langle \bm{\mathcal{U}} _\infty(\delta t_2)\rangle$, the circles denote the spectral GME predictions. The inset shows the dynamics of the bleach signal (purple pixel) that crosses zero. (d) Root mean squared error heatmap showing the sum of only the four tagged pixels at all predicted time points, normalized by the number of predicted time points. The point marked by a black diamond represents the choice in panel (c) and is the global minimum. Consequently, we choose $t_u=0.8$ ps, $\tau_ \mathcal{U} =1.4$ ps, and $\xi=0.01$.
• Figure 5: Applicability of the spectral GME to capture the evolution of the central line slope (CLS) of 2DIR data of the N3 dye undergoing spectral diffusion. We interrogate the evolution of the CLS for two spectral features at $\omega_1=2100$ cm$^{-1}$ and $2125$ cm$^{-1}$, with $\omega_3=2133$ cm$^{-1}$ for both features, corresponding to the symmetric and antisymmetric $\mathrm{C}\equiv\mathrm{N}$ stretches in N3. Insets show both the reference experimental (left) and the spectral GME-predicted (right) CLSs for the selected spectral features. We apply modest linear interpolation to double the number of pixels along each frequency axis, mirroring experimental processing steps for the center line slope. For the result without interpolation, see Fig. S7.