Suppressing sampling noise in linear and two-dimensional spectral simulations

Abstract

We examine the problem of sampling noise encountered in time-domain simulations of linear and two-dimensional spectroscopies. A new adaptive apodization scheme based on physical arguments is devised for suppressing the noise in order to allow reducing the number of used disorder realisations, but introducing only a minimum of spectral aberrations and thus allowing a potential speed-up of these types of simulations. First, the method is demonstrated on an artificial dimer system, where the effect on slope analysis, typically used to study spectral dynamics, is analysed. It is, furthermore, tested on the simulated two-dimensional infrared spectra in the amide I region of the protein lysozyme. The cross polarisation component is investigated, particularly sensitive to sampling noise, because it relies on cancelling of the dominant diagonal spectral contributions. In all these cases, the adaptive apodization scheme is found to give more accurate results than the commonly used lifetime apodization scheme and in most cases better than the gaussian apodization scheme.

Two-dimensional infrared spectroscopy of neat ice Ih

“…This may be related to the lifetime of 700 fs used here based on previous estimations, 21,61 while recent experimental data suggested a lifetime of the OD-stretch as low as 480 fs. 62 As the lifetime affects the anisotropies very little and the lifetime used in the simulations is mainly included as an apodization function 30,63 to get smooth spectra we chose the lifetime used in the previous simulations of the absorption spectra. 22 The two dominant bleach/stimulated emission peaks exhibit the same trend in theory and experiment that the high frequency one is narrower in particular along the detection axis than the low frequency peak.…”

Assessing Spectral Simulation Protocols for the Amide I Band of Proteins

“…In this way, time-evolution matrices, U , for each excitation manifold are obtained for the delays between the interactions at times denoted τ 0 –τ 4 . This allows one to calculate the linear response function governing the linear absorption: Similarly, the third-order response functions related to the Feynmann diagrams in Figure are given by ,, The response functions are multiplied with exponential apodization functions corresponding to a vibrational lifetime of 1.8 ps. , The linear absorption is then obtained by a Fourier transform of eq with respect to τ 01 , while a two-dimensional Fourier transform with respect to the coherence times ( t 1 = τ 10 and t 3 = τ 32 ) of eq provides the 2DIR spectra, respectively. These coherence times were varied from 0 to 2.16 ps.…”

“…To provide the benchmark, we need to determine the similarity between experimental and theoretical line shapes. We achieve this through the calculation of the spectral overlap , where I (ω i ) is the intensity of the theoretical spectra at a given frequency ω i , for which the frequencies were shifted to maximize the overlap, while I ref (ω i ) is the intensity of the experimental spectra for the same frequencies. A cubic spline interpolation was used, in order to determine the simulated spectral intensities at the same frequencies as experiment .…”

“…48,94 The linear absorption is then obtained by a Fourier transform of Eq. 4 with respect to τ 01 , while a two-dimensional Fourier transform with respect to the coherence times (t 1 = τ 10 and t 3 = τ 32 ) of Eq.…”

Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala

“…To incorporate information from multiple experiments and generalize the refinement method to arbitrary spectral line shapes, we apply a Bayesian framework using the spectral overlap function defined in Eq. 3 as the new refinement metric (91). The Bayesian framework is naturally suitable for updating the posterior probability distribution when given new experi-mental information, and constraints need not be matched exactly.…”