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Chem Sci
Chem Sci
SC
CSHCBM
Chemical Science
2041-6520
2041-6539
The Royal Society of Chemistry

39156932
d4sc03219e
10.1039/d4sc03219e
Chemistry
A new computational methodology for the characterization of complex molecular environments using IR spectroscopy: bridging the gap between experiments and computations†
† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4sc03219e

https://orcid.org/0000-0001-9538-4032
Sepulveda-Montaño Laura X. a
https://orcid.org/0000-0001-9968-362X
Galindo Johan F. b
https://orcid.org/0000-0002-4752-7024
Kuroda Daniel G. a
a Department of Chemistry, Louisiana State University Baton Rouge Louisiana 70803 USA dkuroda@lsu.edu

b Department of Chemistry, Universidad Nacional de Colombia Sede Bogotá Bogotá 111321 Colombia
13 8 2024
11 9 2024
13 8 2024
15 35 1444014448
17 5 2024
8 8 2024
This journal is © The Royal Society of Chemistry
2024
The Royal Society of Chemistry
https://creativecommons.org/licenses/by/3.0/ This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. You can use material from this article in other publications without requesting further permissions from the RSC, provided that the correct acknowledgement is given.
The molecular interactions and dynamics of complex liquid solutions are now routinely measured using IR and 2DIR spectroscopy. In particular, the use of the latter allows the determination of the frequency fluctuation correlation function (FFCF), while the former provides us with the average frequency. In turn, the FFCF can be used to quantify the vibrational dynamics of a molecule in a solution, and the center frequency provides details about the chemical environment, solvatochromism, of the vibrational mode. In simple solutions, the IR methodology can be used to unambiguously assign the interactions and dynamics observed by a molecule in solution. However, in complex environments with molecular heterogeneities, this assignment is not simple. Therefore, a method that allows for such an assignment is essential. Here, a parametrization free method, called Instantaneous Frequencies of Molecules or IFM, is presented. The IFM method, when coupled to classical molecular simulations, can predict the FFCF of a molecule in solutions. Here, N-methylacetamide (NMA) in seven different chemical environments, both simple and complex, is used to test this new method. The results show good agreement with experiments for the NMA solvatochromism and FFCF dynamics, including characteristic times and amplitudes of fluctuations. In addition, the new method shows equivalent or improved results when compared to conventional frequency maps. Overall, the use of the new method in conjunction with molecular dynamics simulations allows unlocking the full potential of IR spectroscopy to generate molecular maps from vibrational observables, capable of describing the interaction landscape of complex molecular systems.

The new instantaneous frequency method presented here can be integrated with molecular dynamics simulations to link the classical atomistic representation of the system to its vibrational observables.

Division of Chemistry 10.13039/100000165 CHE-175135 National Science Foundation 10.13039/100000001 CHE-175135 pubstatusPaginated Article
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pmcIntroduction

Complex liquid solutions are multi-component systems with intricate molecular arrangements arising from the diverse interactions among the components in the mixture. Due to the large number of contributions to the potential energy surface (PES), complex molecular systems typically exhibit nanoscopic heterogeneities, especially in cases where the solution contains molecules with contrasting chemical moieties, such as polar and non-polar.1 Therefore, the complex and non-ideal behaviour of the liquid creates challenges associated with its characterization, both experimentally and computationally. Moreover, the liquid state of the mixture allows its molecular components to diffuse freely (translate and rotate), resulting in a chemical environment that varies as a function of time. Consequently, one can characterize the structure and dynamics of the complex solution to indirectly assess the PES since these two properties are governed by its energy landscape (Fig. 1).

Fig. 1 Use of vibrational observables to study the PES and chemical environment of a molecular system.

The development of methods that can generate a map of intermolecular forces based on the dynamics and interactions of each component in the mixture has been a long-standing goal for understanding and later tailoring complex molecular systems. Experimentally, the complete characterization of complex solutions requires the use of techniques capable of resolving the individual interactions occurring in the multicomponent system. Among the various experimental methods commonly used to characterize the molecular structure of solutions, one can find NMR, UV-vis, fluorescence, Raman and IR spectroscopies as well as scattering techniques. For example, NMR has been successfully applied to study the diffusion of species in complex solutions, the molecular structure of DNA and RNA in live human cells,2 and the isomerization dynamics in ionic liquids.3 However, NMR spectroscopy lacks the required time resolution to characterize solutions undergoing ultrafast dynamics with characteristic times faster than nanoseconds, such as liquids at room temperature, and yields averaged signals for these processes.4 UV-vis and fluorescence spectroscopies have also shown potential for the analysis of micellar systems,5 for probing the chemical environment of hydrocarbons,6 and for exploring the air/liquid interphases.7 Notwithstanding the capabilities of these two spectroscopies, they are limited by the number of substrates with responses in the UV-vis spectral range, which significantly reduces the number of complex solutions that can be analysed with them.

Scattering techniques, such as X-ray and neutron scattering, have also been used to characterize complex solutions such as deep eutectic solvents,1,8–10 ionic liquids,11–13 and solutions of proteins and DNA.14–16 These techniques provide structural information at the atomic level through the scattering profile. For a liquid sample, the peaks of the scattering profile contain different atomic contributions, requiring a nontrivial deconvolution to elucidate the structure from the data.17 To this end, the scattering experiments usually rely on molecular dynamics (MD) simulations to model and evaluate the different atomic contributions to each peak.9,12,13 Hence, the correct modelling of scattering data requires a good parameterization of the MD force field since two different atomistic models can generate the same scattering profile.18

An alternative characterization method for complex solutions relies on the use of vibrational spectroscopy, which includes both IR and Raman spectroscopies. By analysing the frequency shift of the vibrational bands in the IR or Raman spectrum, it is possible to probe the chemical environment.19–22 In either case, the vibrational bands are related to the molecular vibrational modes, either through the dipole (IR)23 or the polarizability (Raman)24 of the molecule; consequently, the bands change as a function of the molecular environment.

Normal modes are easily calculated from the motions in a potential energy surface, but the dipole moment associated with a vibrational transition is simpler than the equivalent polarizability tensor, which requires full electronic structure calculations.25,26 Hence, the changes in the Raman bands are often difficult to relate to specific molecular environments.

Normal modes are mathematical entities related to the diagonalization of the Hessian matrix (i.e., second derivatives of the PES at the minimum) and represent the motion of collections of atoms in a molecule. More importantly, the IR band can be understood in terms of normal modes using the dipole moment formalism.23 Similar to the PES, the normal mode frequencies (PES curvature) are highly dependent on the molecular speciation and environment (i.e., structure, temperature, pressure, molecular interactions, etc.).19,27,28 Therefore, the molecular environment of a molecule can be, and is, typically deduced from the central frequency of an IR band associated with a particular vibrational mode. In addition, the time evolution (dynamics) of the vibrational modes in a molecular system can be characterized using time resolved vibrational spectroscopy. Among the various possible time resolved methods, 2DIR spectroscopy is the most powerful for describing the dynamics of the system at thermal equilibrium using specific sets of atoms, such as carbonyl groups.29 Among other features, 2DIR spectroscopy measures the dynamics of the frequency-fluctuation correlation function (FFCF), or equivalently, the time scale at which the system loses its memory of a given molecular environment.27 In particular, the FFCF provides information about the interaction potential among the molecules through their dynamics.30 Moreover, the FFCF contains information about the various chemical environments through its amplitude term because it is the variance of the distribution of the frequencies (environments) sensed by the molecules in the sample.27

The use of 2DIR spectroscopy to characterize the molecular environments in a complex solution is also challenging due to the lack of prior knowledge of the chemical environment and interactions affecting the molecule under study. Thus, to obtain the location and interaction landscape of the molecular components via 2DIR spectroscopy, the modelling of the system using MD simulations is often required. However, the MD simulation does not directly provide the vibrational observables, and instead these are computed using the so-called frequency maps.

Frequency maps transform molecular coordinates into specific variables, such as electric fields, to obtain the instantaneous frequency of a molecule in the MD simulation.31 Hence, frequency maps have been instrumental in understanding and modelling vibrational spectroscopy data at a low computational cost. However, the applicability of this tool is generally limited to specific molecular systems for which the map was originally parametrized, and its extension to “new” chemical environments often requires further parametrization.32–35 Moreover, the intricacies in the theoretical description of complex molecular environments with nanoscopic heterogeneities do not always guarantee the access to such modelling and its transformation into vibrational observables, such as frequency shifts. In order to facilitate the experimental analysis of the IR spectroscopic data (IR position, line shape and dynamics), a new computational methodology is needed. In particular, this methodology should not only accurately translate molecular arrangements (environments) of highly heterogeneous molecular systems into frequency fluctuations but also be computationally efficient.

In this work, a new methodology (Instantaneous Frequencies of Molecules, IFM) is presented. This method uses a quantum mechanical method to compute the instantaneous frequencies of the molecules in a given molecular environment (Fig. 2). The exponential growth of computational power has allowed the direct use of ab initio quantum chemical and semiempirical methods to calculate frequencies. However, the proper description of the vibrational frequencies of a solvated molecule usually requires multiple solvation shells beyond the first one.31 Hence, a low cost computational method is needed to calculate the vibrational frequencies of such large systems, typically containing more than 100 atoms.

Fig. 2 Procedure followed for the development and testing of the IFM method.

GFN2-xTB is a new tight binding approach that uses multipole expansion and density-dependent dispersion fluctuation to describe electrostatic interactions.36,37 In particular, this semiempirical method is tailored to accurately compute the geometries, non-covalent interactions, and vibrational frequencies of molecular systems and has low computational cost.36,37 Furthermore, it has recently been shown that GFN2-xTB correctly predicts the vibrational solvatochromism of various molecular probes typically used in IR spectroscopy, depending only on the correct description of the solute and its chemical environment as defined by the classical force field.20 This makes IFM calculations fully transferable to complex molecular arrangements without the need of new parameterization, beyond the selection of an appropriate classical representation (i.e., force field).

The applicability of the IFM method for vibrational spectroscopy is tested on a molecular system composed of N-methylacetamide (NMA) in different solvents, ranging from simple to complex. NMA was selected because of its amide I vibrational mode, which is highly sensitive to the chemical environment, as evidenced by its solvatochromic frequency shifts in different solvents.38–40 In addition, as a model peptide unit, NMA has been extensively studied both experimentally and computationally. From a theoretical perspective, there are now many MD simulation studies dedicated to the solvation structure and dynamics of this molecule and some provide frequency maps to correlate with vibrational dynamics studies.32,41–44 From an experimental perspective, the vibrational dynamics of NMA has been thoroughly investigated using time resolved vibrational spectroscopy,32,33,41,45–47 making it an excellent reference for the IFM method. To this end, the following systems have been selected: NMA in heavy water (D2O), chloroform (CLF), dimethylsulfoxide (DMSO), tetrahydrofuran (THF), and toluene (TOL), as well as mixtures of DMSO and THF and of DMSO and D2O. The suitability of the computational methodology combining MD simulations and the IFM method (MD-IFM) was evaluated by computing and comparing with experimental data the vibrational frequency shifts (solvatochromism), the FFCF dynamics (solvent motions), and the amplitudes of the frequency fluctuations (distribution of environments) of NMA in different molecular environments.

Methods

The experimental measurements to test the IFM method in the present work include linear and non-linear IR spectroscopy. The procedures and specifications can be found in the ESI.†

The schematic computational methodology for the IFM calculation is described in Fig. 2. However, a brief description is given in the following sections, and an example of the code used here can be found free of charge at https://github.com/dkurodalab/IFM.

Molecular dynamics

MD simulations were carried out for the systems of NMA in D2O, CLF, DMSO, THF, TOL, DMSO : THF (1 : 3), and DMSO : D2O (1 : 1). In the first and last cases (D2O and D2O : DMSO (1 : 1) as solvents), the hydrogen atom attached to the nitrogen atom of NMA was replaced by a deuterium. Solvent boxes of 40 Å with or without the solute were built using PACKMOL.48 The quality of the force field was evaluated from the densities determined from an MD simulation in the pure system. MD simulations were performed using the AMBER 18 computational package.49 For water and all the other solvents, the TIP3P model and Generalized Amber Force Field (GAFF) were used, respectively.50 The NMA molecule was parameterized with the ff14SB force field.51 The MD simulation was performed by starting with an energy minimization, followed by a heating step from 0 to 300 K over 20 ps; the production run was carried out for 250 ps in the NPT ensemble after an equilibration run of 20 ns. A time step of 0.5 fs was used for all simulation stages. For the NMA/TOL system, a 1 ns production run was performed to accomplish the necessary averaging in the FFCF calculation.

Frequency calculations and FFCF

Snapshots were selected every 50 fs from the MD production run and subsequently trimmed to the number of solvation shells needed for optimization and frequency calculations. At least two solvation shells were selected in each case, as they are sufficient to yield reliable frequency values (see the ESI†). To preserve the distribution of states from the MD, the geometry energy minimizations were performed only for the NMA molecule embedded in the selected solvation shells using the GFN2-xTB package. The geometry optimization and frequency calculations were carried out at the GFN2-xTB level of theory. The central frequencies for the amide I normal mode of NMA in different solvents represent the intensity weighted average. Note that the selection of GFN2-xTB semiempirical method is based on the low computational cost when compared to other ab initio methods, such as DFT (see the ESI†).

The FFCF was calculated from the instantaneous amide I frequencies over time: C(t) = δω(t)δω(0), where δω(t) is the delta between the frequency at time t and the average frequency (ω(t)–〈ω〉).27 The correlation time (τc) was obtained by modelling the calculated FFCF with the Kubo formalism (i.e., the bi-exponential decay function, see the ESI† for the fits of all molecular systems). The amplitude of the fluctuations was obtained by analysing the frequency distributions with Gaussian profiles.27

Results and discussion

The IFM method predicts Gaussian distributions for the amide I frequencies of NMA in different solvents, consistent with the stochastic motions of the molecular environment (see the ESI†).52 Because of the nature of the amide I vibrational mode, these distributions contain information about the molecular environment through their central frequencies; i.e., solvatochromism.28,43,53 The central frequencies predicted by the IFM method correctly reproduce the experimental solvatochromic shift of NMA amide I mode in different solvents including mixtures. Moreover, a linear relationship is observed between the computed and experimental values (Fig. 3). A linear model of frequencies also shows that the IFM method overestimates their values by ∼60 cm−1. This deviation from experimental values is associated with the semiempirical method.20 A Pearson correlation coefficient (R2) of 0.874 is observed, indicating not only the strong linear correlation between the predicted and experimental frequency values but also the suitability of the IFM model for computing instantaneous frequencies. Notably, the NMA/TOL system deviates significantly from the linear trend. The linear model without NMA–toluene has a significantly better predictive power (i.e., R2 increases to 0.990, see the ESI†). Note that the deviation in the prediction of the vibrational solvatochromism of amide I of NMA in toluene is likely due to a deficiency in the force field describing toluene in the MD simulation and not in the method. This assertion based on the GFN2-xTB method correctly characterizes other complex solvents, such as DMSO : D2O, where various and competing interactions are found.28,45,54–58

Fig. 3 Solvatochromic shift for the NMA amide I mode in different solvents calculated through the IFM method vs. experimentally through FTIR (data points). Linear fit correspond to the red line.

To further assess the suitability of the computational methodology (MD-IFM), the FFCF was computed from the instantaneous frequencies predicted by the IFM method. Assuming a Kubo stochastic model,27 the FFCF includes both correlation times (τc) and amplitude of frequency fluctuations (Δ) of the form: c(t) = ∑iΔi2e−t/τci. The computed τc as a function of the chemical environment also shows a linear relationship with the experimental values (Fig. 4, Table 1, and the ESI†). In general, the predicted correlation times are in reasonable agreement with the experiments. In addition, NMAD/D2O is a particularly well studied system and has frequency maps to predict the amide I mode (e.g. the electric field and electrostatic potential models).56 Comparison of the new method with the previously reported results from frequency maps shows very similar results. Specifically, the correlation time obtained from frequency maps was ∼0.75 ps,56 while the new method based on GNF2-xTB predicted a value of 0.82 ps. A similar result is obtained for the NMA/DMSO system, where τc values of 1.6 ps and of 1.3 ps are predicted from the frequency map and the new method, respectively. In contrast, NMA in CLF presents different correlation times for the FFCF dynamics when computed using either frequency maps28 or the new method. In this case, the frequency map and the new method predicts τc values of 2.9 ps and of 1.6 ps, respectively; while the experimental result is 1.9 ps.28 Hence, it appears that the new method has a smaller error than the frequency map, which is likely due to the IFM method taking into account more detailed interactions affecting the frequency of the amide I mode, such as weak hydrogen bonds.20

Fig. 4 Correlation times calculated from the IFM method vs. the experimental values determined from 2DIR (data points). Linear fit corresponds to the red line.

Central frequencies, correlation times, and fluctuation amplitudes determined from the IFM method, experimentally, and from frequency maps

Solvent	Ṽ (cm−1)	τ c (ps)	Δ (cm−1)	
IFM	Exp.	MD-IFM	Exp.	Freq. maps	IFM	Exp.	Freq. maps28	From IR	
D2O	1680	1623	0.82 ± 0.03	1.2 (ref. 64)	0.76,56 0.75 (ref. 56)	20.9 ± 0.3	19.75,28 9 (ref. 63)	17a	8.2	
CLF	1712	1669	1.6 ± 0.7	1.9 ± 0.1	2.9 (ref. 28)a	12.1 ± 0.3	13.57 (ref. 28)	8.8a	7.7	
DMSO	1712	1668	1.3 ± 0.2	1.7 ± 0.1	1.6 (ref. 28)a	10.95 ± 0.08	11.55 (ref. 28)	7.8a	6.1	
THF	1727	1684	1.02 ± 0.06	1.5 ± 0.1	N/A	9.1 ± 0.1	N/A	N/A	3.1	
TOL	1747	1686	1.06 ± 0.07	1.6 ± 0.2	N/A	7.0 ± 0.2	N/A	N/A	3.4	
DMSO : THF	1721	1676	1.9 ± 0.1	2.0 ± 0.2	N/A	10.2 ± 0.1	N/A	N/A	6.1	
DMSO : D2O	1696	1646	3.8 ± 0.2	3.1 ± 0.3	N/A	14.6 ± 0.2	N/A	N/A	11.1	
a Averaged value.

The goodness of the MD-IFM method for computing instantaneous frequencies was also further supported by computation of NMA amide I in other chemical environments. For example, the method predicts τc values of 1.02 ps and 1.06 ps for the NMA/THF and NMA/TOL systems, respectively, which are in good agreement with the experimental values of 1.5 ps (NMA/THF) and 1.6 ps (NMA/TOL). Overall, the use of the new method in single solvents allows us to demonstrate not only the validity of the MD-IFM method for predicting the dynamics of the FFCF when compared to other methods but also the transferability of the IFM method to different solvents without the need for modification or reparametrization.

The adequate predictions made by the MD-IFM method allow us to extend its application to complex molecular systems, such as mixtures of solvents. To this end, two different mixtures were selected: DMSO : THF (1 : 3 molar ratio) and DMSO : D2O (1 : 1 molar ratio). These two particular systems represent solvents with competitive dipole–dipole interactions as well as hydrogen bond and picosecond dynamics.28,40,56,59,60 The characteristic time of the FFCF for the amide I vibrational mode in these two solvents was found to be 1.9 ps (DMSO : THF) and 3.8 ps (DMSO : D2O), which are in very good agreement with the observed experimental values of 2.0 and 3.2 ps, respectively (see Fig. 4, Table 1, and the ESI†).

These last two cases are particularly important because of the complexity of the molecular environment or, analogously, the chemical interaction landscape. The selected molecular landscapes make it particularly challenging to parametrize a single frequency map capable of representing specific probes in various solvents. Consequently, a single frequency map is usually not capable of describing the solvatochromism of a probe on both the individual solvents and their mixtures when the solvents are very different. This is the case for DMSO and D2O, where not only the hydrogen bond donating and accepting capabilities are changed but also their dipoles. The correct description of both single solvents and mixtures provides strong support for the broad applicability of the new methodology in complex environments.31,61 Overall, it is shown that the IFM-MD methodology can be applied to compute with good agreement with the experiment not only the vibrational solvatochromism of molecules in solution (R2 = 0.874, Fig. 3) but also the FFCF decorrelation times (R2 = 0.976, Fig. 4). More importantly, this is achieved without any additional parameterization or modelling beyond the MD simulation force field.

It is derived from the data that central frequencies and correlation times of the amide I mode in different solvents are not correlated (R2 = −0.192, see the ESI†). This result demonstrates that the two vibrational observables are independent and that both are needed to obtain a correct description of the molecular system. However, the central frequencies and correlation times are not sufficient to completely determine the molecular environment observed by a molecule. A good example of the ambiguity in determining the molecular environment from vibrational observables can be seen in the cases of NMA/DMSO and NMA/CLF. In these two systems, the central frequencies for the amide I mode (1712 cm−1 for both) and the correlation times (1.3 ± 0.2 and 1.6 ± 0.7 ps, respectively) are similar. Therefore, these predictions, while accurate, are not sufficient to determine the chemical environment of the studied molecule and require a third observable.

Thus far, only the central frequencies and correlation times have been used to assess the molecular environment of a molecule using IR spectroscopy. Another important parameter that defines the line shape of a vibrational transition is the amplitude of the frequency fluctuations. This vibrational observable contains information about the ensemble of molecular environments that the molecule can observe thermally. Consequently, the amplitudes of frequency fluctuations (Δ) are strongly dependent on the chemical nature of the system.27 Experimentally, these amplitudes are obtained by modelling the FTIR and 2DIR spectra.62 Particularly, the computed amplitudes are found to be 12.1 ± 0.3, 10.95 ± 0.08 and 20.9 ± 0.3 cm−1 for NMA in CLF, DMSO and D2O, respectively, and compare very well with those derived from the experiment: 13.57 cm−1, 11.55 cm−1, and 19.75 cm−1, respectively.28

Nonetheless, it is important to note that the NMA in D2O experimental Δ has been reported by others to be 9 cm−1.63 Therefore, it was excluded from the overall analysis of the frequency fluctuation amplitude.

The IFM-based amplitudes of the remaining systems were compared with the experimental values by using a more approximate method to compute the fluctuation amplitudes from the FTIR and 2DIR spectra.62 The experimental amplitudes, Δ, show a good agreement with those obtained by the IFM method (Fig. 5 and Table 1). The correlation between the experiment and computation is very good, as seen by the linear correlation between the experimental and computed values (R2 = 0.882). Interestingly, the amplitude for the NMA/TOL system has the largest deviation from the linear trend observed for the other samples. In the case of NMA/TOL, the result is not surprising, given that the method is not particularly good at predicting the vibrational solvatochromism of the same system, as previously shown. Nonetheless, the high Pearson correlation coefficient between the experimental and computation amplitudes indicates that the IFM-based method predicts reasonably well the amplitudes of the frequency fluctuations in different systems. More importantly, the strong correlation between the experiment and theory shows that the IFM method captures more detailed interactions, which directly translates into more accurate frequency fluctuations, even when compared to other maps.

Fig. 5 Frequency fluctuation amplitudes (Δ) calculated by the IFM vs. determined from the IR spectra (data points). Linear fit corresponds to the red line. Star (*) NMA in the D2O Δ value was not included into the fit.

Overall, it was demonstrated that the method based on the IFM frequencies produces a reliable prediction of the solvatochromism (ω0), dynamics (τc) and distribution of environments (Δ) from different samples without the need for reparametrization, which is usually required when using frequency maps. These metrics, obtained for a molecule (NMA) solvated in pure solvents and their mixtures, describe the effect of the dynamics and interactions of the molecular environment on the investigated molecule. Therefore, the method presented here allows unambiguous assignment of experimental observables in the vibrational spectra (linear and non-linear), unlocking the full potential of vibrational observables to create molecular maps capable of describing the interaction landscape of complex molecular systems.

Conclusions

A new method for frequency calculation is presented. This method takes advantage of the existing and new computational tools (MD simulations and semi-empirical methods), as well as of current computational power to obtain the frequencies of solvated molecules in large clusters. The new methodology in conjunction with MD simulations allows us to determine vibrational solvatochromism, dynamics, and distribution of environments. The new method is successfully tested on a well-studied system: N-methylacetamide in polar solvents and their mixtures. In addition, the transferability of the method to more complex binary solutions was examined. The correct description of the vibrational solvatochromism in both simple and complex chemical environments shows the utility of the method to predict the location of a probe in a solution. Moreover, it is observed that the combination of frequencies, decorrelation times and fluctuation amplitudes is sufficient to fully characterize a specific system. The use of such a tool is particularly important for vibrational spectroscopy to unlock the full potential of the IR methodology when probing highly heterogeneous environments.

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Author contributions

L. X. S.-M.: methodology, data curation, validation, formal analysis, investigation, writing – original draft, visualization; J. F. G.: methodology, writing – original draft, writing – review and editing, supervision; D. G. K.: conceptualization, methodology, writing – review and editing, resources, supervision, project administration, funding acquisition.

Conflicts of interest

There are no conflicts to declare.

Supplementary Material

SC-015-D4SC03219E-s001

L. X. S.-M. and D. G. K. acknowledge the financial support from the National Science Foundation (CHE-175135) and the computer time from the High Performance Computing Center at Louisiana State University and the Louisiana Optical Network Initiative (LONI). D. G. K. would like to thank LSS, his work has been a tremendous inspiration to him.
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References

Cui Y. Rushing J. C. Seifert S. Bedford N. M. Kuroda D. G. Molecularly heterogeneous structure of a nonionic deep eutectic solvent composed of n-methylacetamide and lauric acid J. Phys. Chem. B 2019 123 3984 3993 10.1021/acs.jpcb.8b11732 30978021
Yamaoki Y. Kiyoishi A. Miyake M. Kano F. Murata M. Nagata T. Katahira M. The first successful observation of in-cell NMR signals of DNA and RNA in living human cells Phys. Chem. Chem. Phys. 2018 20 2982 2985 10.1039/C7CP05188C 29022027
Clark R. Nawawi M. A. Dobre A. Pugh D. Liu Q. Ivanov A. P. White A. J. Edel J. B. Kuimova M. K. McIntosh A. J. The effect of structural heterogeneity upon the microviscosity of ionic liquids Chem. Sci. 2020 11 6121 6133 10.1039/D0SC02009E 32874514
Bryant R. G. The NMR time scale J. Chem. Educ. 1983 60 933 10.1021/ed060p933
Sabaté R. Gallardo M. de la Maza A. Estelrich J. A spectroscopy study of the interaction of pinacyanol with n-dodecyltrimethylammonium bromide micelles Langmuir 2001 17 6433 6437 10.1021/la010463y
Narayan B. Nagura K. Takaya T. Iwata K. Shinohara A. Shinmori H. Wang H. Li Q. Sun X. Li H. The effect of regioisomerism on the photophysical properties of alkylated-naphthalene liquids Phys. Chem. Chem. Phys. 2018 20 2970 2975 10.1039/C7CP05584F 28952630
Rubia-Payá C. De Miguel G. Martín-Romero M. T. Giner-Casares J. J. Camacho L. UV–Vis Reflection–Absorption Spectroscopy at air–liquid interfaces Adv. Colloid Interface Sci. 2015 225 134 145 10.1016/j.cis.2015.08.012 26385430
Manasi I. Schweins R. Ma K. Edler K. J. Nanostructure in Amphiphile-Based Deep Eutectic Solvents Langmuir 2023 39 16776 16784 10.1021/acs.langmuir.3c02105 37965899
Malik A. Kashyap H. K. Heterogeneity in hydrophobic deep eutectic solvents: SAXS prepeak and local environments Phys. Chem. Chem. Phys. 2021 23 3915 3924 10.1039/D0CP05407K 33543176
Sakuragi M. Tsutsumi S. Kusakabe K. Deep eutectic solvent-induced structural transition of microemulsions explored with small-angle X-ray scattering Langmuir 2018 34 12635 12641 10.1021/acs.langmuir.8b02565 30251861
Murphy T. Atkin R. Warr G. G. Scattering from ionic liquids Curr. Opin. Colloid Interface Sci. 2015 20 282 292 10.1016/j.cocis.2015.10.004
Kashyap H. K. Santos C. S. Annapureddy H. V. Murthy N. S. Margulis C. J. Castner Jr E. W. Temperature-dependent structure of ionic liquids: X-ray scattering and simulations Faraday Discuss. 2012 154 133 143 10.1039/C1FD00059D 22455018
McGrogan A. Lafferty J. O'Neill L. Brown L. Young J. M. Goodrich P. Muldoon M. J. Moura L. Youngs S. Hughes T.-L. Liquid Structure of Ionic Liquids with [NTf2]− Anions, Derived from Neutron Scattering The Journal of Physical Chemistry B 2024 128 3220 3235 10.1021/acs.jpcb.3c08069 38520396
Larsen A. H. Wang Y. Bottaro S. Grudinin S. Arleth L. Lindorff-Larsen K. Combining molecular dynamics simulations with small-angle X-ray and neutron scattering data to study multi-domain proteins in solution PLoS Comput. Biol. 2020 16 e1007870 10.1371/journal.pcbi.1007870 32339173
Gräwert T. W. Svergun D. I. Structural modeling using solution small-angle X-ray scattering (SAXS) J. Mol. Biol. 2020 432 3078 3092 10.1016/j.jmb.2020.01.030 32035901
Yamamoto S. Kono F. Nakatani K. Hirose M. Horii K. Hippo Y. Tamada T. Suenaga Y. Matsuo T. Structural characterization of human de novo protein NCYM and its complex with a newly identified DNA aptamer using atomic force microscopy and small-angle X-ray scattering Front. Oncol. 2023 13 1213678 10.3389/fonc.2023.1213678 38074684
Soper A. K. The radial distribution functions of water as derived from radiation total scattering experiments: Is there anything we can say for sure? Int. Scholarly Res. Not. 2013 2013 279463
Head-Gordon T. Hura G. Water structure from scattering experiments and simulation Chem. Rev. 2002 102 2651 2670 10.1021/cr0006831 12175263
Whittall I. R. McDonagh A. M. HAMPHREY M. Samoc M. Organometallic complexes in nonlinear optics I: second-order nonlinearities ChemInform 1998 29 199830303 10.1002/chin.199830303
Sepulveda-Montaño L. X. Galindo J. F. Kuroda D. G. Infrared Spectroscopy of Liquid Solutions as a Benchmarking Tool of Semiempirical QM Methods: The Case of GFN2-xTB J. Phys. Chem. B 2023 7955 7963 10.1021/acs.jpcb.3c03174 37676972
Romei M. G. von Krusenstiern E. V. Ridings S. T. King R. N. Fortier J. C. McKeon C. A. Nichols K. M. Charkoudian L. K. Londergan C. H. Frequency changes in terminal alkynes provide strong, sensitive, and solvatochromic Raman probes of biochemical environments J. Phys. Chem. B 2022 127 85 94 10.1021/acs.jpcb.2c06176 36538691
Bagchi S. Fried S. D. Boxer S. G. A solvatochromic model calibrates nitriles' vibrational frequencies to electrostatic fields J. Am. Chem. Soc. 2012 134 10373 10376 10.1021/ja303895k 22694663
Wilson E. B. , Decius J. C. and Cross P. C. , Molecular vibrations: the theory of infrared and Raman vibrational spectra, Courier Corporation, 1980
Szymanski H. A. , Raman spectroscopy: theory and practice, Springer Science & Business Media, 2012
Lee S. Y. Placzek-type polarizability tensors for Raman and resonance Raman scattering J. Chem. Phys. 1983 78 723 734 10.1063/1.444775
Nafie L. A. Theory of Raman scattering Pract. Spectrosc. 2001 28 1 10
Hamm P. and Zanni M. , Concepts and methods of 2D infrared spectroscopy, Cambridge University Press, 2011
DeCamp M. DeFlores L. McCracken J. Tokmakoff A. Kwac K. Cho M. Amide I vibrational dynamics of N-methylacetamide in polar solvents: The role of electrostatic interactions J. Phys. Chem. B 2005 109 11016 11026 10.1021/jp050257p 16852342
Bakker H. Skinner J. Vibrational spectroscopy as a probe of structure and dynamics in liquid water Chem. Rev. 2010 110 1498 1517 10.1021/cr9001879 19916491
Kwac K. Cho M. Two-color pump – probe spectroscopies of two-and three-level systems: 2-dimensional line shapes and solvation dynamics J. Phys. Chem. A 2003 107 5903 5912 10.1021/jp034727w
Baiz C. R. Błasiak B. Bredenbeck J. Cho M. Choi J.-H. Corcelli S. A. Dijkstra A. G. Feng C.-J. Garrett-Roe S. Ge N.-H. Vibrational spectroscopic map, vibrational spectroscopy, and intermolecular interaction Chem. Rev. 2020 120 7152 7218 10.1021/acs.chemrev.9b00813 32598850
Małolepsza E. Straub J. E. Empirical maps for the calculation of amide I vibrational spectra of proteins from classical molecular dynamics simulations J. Phys. Chem. B 2014 118 7848 7855 10.1021/jp412827s 24654732
Wang L. Middleton C. T. Zanni M. T. Skinner J. L. Development and validation of transferable amide I vibrational frequency maps for peptides J. Phys. Chem. B 2011 115 3713 3724 10.1021/jp200745r 21405034
Mesele O. O. Thompson W. H. A “universal” spectroscopic map for the OH stretching mode in alcohols J. Phys. Chem. A 2017 121 5823 5833 10.1021/acs.jpca.7b05836 28715218
Edington S. C. Flanagan J. C. Baiz C. R. An Empirical IR Frequency Map for Ester C=O Stretching Vibrations J. Phys. Chem. A 2016 120 3888 3896 10.1021/acs.jpca.6b02887 27214642
Bannwarth C. Ehlert S. Grimme S. GFN2-xTB—An accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions J. Chem. Theory Comput. 2019 15 1652 1671 10.1021/acs.jctc.8b01176 30741547
Bannwarth C. Caldeweyher E. Ehlert S. Hansen A. Pracht P. Seibert J. Spicher S. Grimme S. Extended tight-binding quantum chemistry methods Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021 11 e1493
Mukherjee P. Kass I. Arkin I. T. Zanni M. T. Structural disorder of the CD3ζ transmembrane domain studied with 2D IR spectroscopy and molecular dynamics simulations J. Phys. Chem. B 2006 110 24740 24749 10.1021/jp0640530 17134238
Fang C. Senes A. Cristian L. DeGrado W. F. Hochstrasser R. M. Amide vibrations are delocalized across the hydrophobic interface of a transmembrane helix dimer Proc. Natl. Acad. Sci. U. S. A. 2006 103 16740 16745 10.1073/pnas.0608243103 17075037
la Cour Jansen T. Knoester J. A transferable electrostatic map for solvation effects on amide I vibrations and its application to linear and two-dimensional spectroscopy J. Chem. Phys. 2006 124 044502 10.1063/1.2148409 16460180
Ham S. Kim J.-H. Lee H. Cho M. Correlation between electronic and molecular structure distortions and vibrational properties. II. Amide I modes of NMA–n D 2 O complexes J. Chem. Phys. 2003 118 3491 3498 10.1063/1.1536980
Choi J.-H. Ham S. Cho M. Local amide I mode frequencies and coupling constants in polypeptides J. Phys. Chem. B 2003 107 9132 9138 10.1021/jp034835i
Kwac K. Cho M. Differential evolution algorithm approach for describing vibrational solvatochromism J. Chem. Phys. 2019 151
Bouř P. Keiderling T. A. Empirical modeling of the peptide amide I band IR intensity in water solution J. Chem. Phys. 2003 119 11253 11262 10.1063/1.1622384
Lin Y.-S. Shorb J. Mukherjee P. Zanni M. Skinner J. Empirical amide I vibrational frequency map: application to 2D-IR line shapes for isotope-edited membrane peptide bundles J. Phys. Chem. B 2009 113 592 602 10.1021/jp807528q 19053670
Karjalainen E.-L. Ersmark T. Barth A. Optimization of model parameters for describing the amide I spectrum of a large set of proteins J. Phys. Chem. B 2012 116 4831 4842 10.1021/jp301095v 22458674
Reppert M. Tokmakoff A. Electrostatic frequency shifts in amide I vibrational spectra: Direct parameterization against experiment J. Chem. Phys. 2013 138 04B603 10.1063/1.4798938 23574217
Martínez L. Andrade R. Birgin E. G. Martínez J. M. PACKMOL: a package for building initial configurations for molecular dynamics simulations J. Comput. Chem. 2009 30 2157 2164 10.1002/jcc.21224 19229944
Case D. A. , Darden T. , Cheatham T. , Simmerling C. L. , Wang J. , Duke R. E. , Luo R. , Crowley M. , Walker R. C. and Zhang W. , Amber 10, University of California, 2008
Wang J. Wolf R. M. Caldwell J. W. Kollman P. A. Case D. A. Development and testing of a general amber force field J. Comput. Chem. 2004 25 1157 1174 10.1002/jcc.20035 15116359
Maier J. A. Martinez C. Kasavajhala K. Wickstrom L. Hauser K. E. Simmerling C. ff14SB: improving the accuracy of protein side chain and backbone parameters from ff99SB J. Chem. Theory Comput. 2015 11 3696 3713 10.1021/acs.jctc.5b00255 26574453
Kubo R. A stochastic theory of line shape Adv. Chem. Phys. 1969 15 101 127 10.1002/9780470143605.ch6
Kwac K. Cho M. Machine learning approach for describing vibrational solvatochromism J. Chem. Phys. 2020 152 174101 10.1063/5.0005591 32384851
Krestyaninov M. A. Ivlev D. V. Dyshin A. A. Makarov D. M. Kiselev M. G. Kolker A. M. Complex investigation of H-bond in Water-N-methylacetamide system: Volumetric properties, DFT, IR, MD analysis J. Mol. Liq. 2022 119533 10.1016/j.molliq.2022.119533
Lawrence C. Skinner J. Vibrational spectroscopy of HOD in liquid D2O. III. Spectral diffusion, and hydrogen-bonding and rotational dynamics J. Chem. Phys. 2003 118 264 272 10.1063/1.1525802
Schmidt J. Corcelli S. Skinner J. Ultrafast vibrational spectroscopy of water and aqueous N-methylacetamide: Comparison of different electronic structure/molecular dynamics approaches J. Chem. Phys. 2004 121 8887 8896 10.1063/1.1791632 15527353
Chand A. Chowdhuri S. Effects of dimethyl sulfoxide on the hydrogen bonding structure and dynamics of aqueous N-methylacetamide solution J. Chem. Sci. 2016 128 991 1001 10.1007/s12039-016-1092-2
Schweitzer-Stenner R. Carson H. DiGuiseppi D. Probing the replacement of water by dimethyl sulfoxide in the hydration shell of N-methylacetamide by FTIR-spectroscopy Vib. Spectrosc. 2017 92 251 258 10.1016/j.vibspec.2017.08.003
DeFlores L. P. Ganim Z. Ackley S. F. Chung H. S. Tokmakoff A. The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide J. Phys. Chem. B 2006 110 18973 18980 10.1021/jp0603334 16986892
Galle Kankanamge S. R. Ma J. Mackin R. T. Leonik F. M. Taylor C. M. Rubtsov I. V. Kuroda D. G. Proving and Probing the Presence of the Elusive C–H⋯O Hydrogen Bond in Liquid Solutions at Room Temperature Angew. Chem. 2020 132 17160 17165 10.1002/ange.202006210
Oh K.-I. Baiz C. R. Empirical S= O stretch vibrational frequency map J. Chem. Phys. 2019 151
Kuroda D. G. Vorobyev D. Y. Hochstrasser R. M. Ultrafast relaxation and 2D IR of the aqueous trifluorocarboxylate ion J. Chem. Phys. 2010 132 044501 10.1063/1.3285265 20113043
Woutersen S. Pfister R. Hamm P. Mu Y. Kosov D. S. Stock G. Peptide conformational heterogeneity revealed from nonlinear vibrational spectroscopy and molecular-dynamics simulations J. Chem. Phys. 2002 117 6833 6840 10.1063/1.1506151
Ghosh A. Hochstrasser R. M. A peptide's perspective of water dynamics Chem. Phys. 2011 390 1 13 10.1016/j.chemphys.2011.07.018 22844177
