SUPPLEMENTARY INFORMATION An Empirical IR Frequency Map for Ester C=O Stretching Vibrations Sean C. Edington, Jennifer C. Flanagan, Carlos R. Baiz* Department of Chemistry, University of Texas at Austin 105 E. 24th St. Stop A5300, Austin TX 78712-1224 *cbaiz@cm.utexas.edu S1. Hydrogen Bond Analysis Hydrogen bonding (HB) populations were computed for the terminal oxygen atom, O T, and the solvent H atoms of interest for HB-donating solvents used to optimize the map: hexanol, ethanol, methanol, and D 2O, as well as the HB-donating solvents used to assess the map capabilities: isopropanol, butanol, diethylene glycol, and dioxane. All HB analysis used the analysis tools in GROMACS 4.5.3. 1 The HB definition consists of a 30 cutoff H-donor-acceptor angle and a 0.35 nm cutoff donor-acceptor radius. Hydrogen bond analyses were performed for each stored snapshot of the 10 ns trajectory. The trajectories were then split into 0, 1, and 2 HB sub-trajectories for analysis of the electrostatic parameters and fitting of the corresponding peaks in the experimental FTIR spectra as discussed in the main text. Once the trajectories were obtained, we computed a hydrogen bond autocorrelation function, R, plotted as a function of number of lag frames ( t m ) and defined as follows: N m1 R( t ) J ( t ) J ( t ) m nm n n0 (1) Where N is the total number of frames in the simulation, m is the autocorrelation lag in number of frames, and the angled brackets indicate an average over multiple 10 ps trajectories extracted from the long 10 ns MD trajectory. J are the fluctuations around the average number of hydrogen bonds ( J ) over the length of the short trajectories and are defined in Equation 2. N 1 J ( t ) J ( t ) J ( t ) n n n' N n' 1 (2)
Figure S1. Normalized hydrogen bond populations obtained from MD simulations and from the integrated experimental IR absorption peaks (see Table S1) Figure S1 shows a comparison between populations derived from MD simulations and populations extracted from the Lorentzian fits to the IR absorption spectra as shown in Table S1 below. Error bars represent error propagation resulting from a 95% confidence interval used in extracting the Lorentzian fit parameters to the experimental data. A key observation here is that population uncertainties in our experimental fit are small compared to the differences between experiment and simulation. This indicates that the simulated trajectories do not accurately reflect hydrogen bond populations, as the difference is outside the range of experimental or fitting error. This comparison demonstrates an obvious shortcoming to the force field used to simulate our trajectories, which is not unique to this work. Force fields fail not only at predicting hydrogen bonding population fractions as they compare to experiment, but many also fail to capture the correct trends in hydrogen bonding between solvents. Recently, Lange, et al 2 published an extensive evaluation of the performance of six atomistic force fields and found that all six poorly describe the hydrogen bonding environments in their physical systems as studied by NMR spectroscopy. Not only did simulated observables compare poorly with experiment, but they were also irreproducible on a force field to force field basis. Likewise, Paton and Goodman 3 found a similar shortcoming in their study of non-bonded interactions as predicted by several all-atom force fields, finding that the hydrogen bonding predictions of several organic molecules did not compare well to benchmark values found using more sophisticated ab initio values. Table S1. Experimental hydrogen bond population fractions and their associated errors extracted from the fits shown in Table S2. SOLVENT D 2O MEOH ETOH HEXOH NUMBER OF HYDROGEN BONDS POPULATION FRACTION (%) ABSOLUTE FIT ERROR (%) 1 20.5 3.2 2 79.5 9.3 0 35.9 5.9 1 56.9 1.6 2 7.2 1.1 0 37.3 3.3 1 36.2 1.9 2 26.6 1.8 0 40.2 2.9 1 38.9 1.3 2 20.8 1.3
Hydrogen bond time autocorrelation functions (Figure S2) show an initial fast decay within the first 200 fs, followed by a slower relaxation in the picosecond regime - except in D 2O, where the correlation relaxes completely within the 2 ps window. Non-exponential relaxation of hydrogen bonds in water has been reported previously in similar MD simulations. 4 In light of these observations, we opted not to extract the exact timescales given that it is unlikely to reproduce experimental values. One could use twodimensional infrared spectroscopy, as demonstrated by Zheng and Fayer and more recently by Paglai et al, to study this phenomenon. Such studies may be used to help improve hydrogen bonding models in the future. 5-6 Figure S2. Hydrogen bond time autocorrelation functions computed using the model described in Equation 1. structure and fast dynamics of proteins. 7-10 S2. Lorentzian Fits of the measured absorption spectra Measured IR absorption spectra are fit to a lineshape of the type: Despite the shortcomings of the MD simulations in capturing the underlying thermodynamics and kinetics of hydrogen bonding, the electrostatic map presented here remains largely independent of these effects. We show in Figure 11 (main text) that computed lineshapes are minimally affected by hydrogen bond exchange, which lessens the need for accurate hydrogen bond predictions in this context. Furthermore, we do not suggest that this map will be able to predict IR spectra directly from MD simulations. Rather, we are pursuing development of this map as a means to interpret experimental lineshapes given an underlying ensemble, similar to how amide I maps are currently used to obtain insight into the A( ) n 2 (3) n n 1 n where a represents the amplitude of the individual peaks within the normalized spectrum, Ω the peak centers and Γ the Lorentzian widths (half-width at half-maximum). Table S2 shows the parameters extracted from the fits. Errors shown reflect the uncertainties associated with each parameter's 95% confidence interval. We note the low fitting-associated uncertainty in line centers and linewidths, which is approximately 0.1 cm -1 in the vast majority of cases and under 1 cm -1 in all cases. Though we believe these values underestimate the uncertainty associated with fitting parameters in some cases, most notably those in D 2O and diethylene glycol, they nonetheless reflect the high quality of the converged fits and indicate their suitability as accurate representations of the experimental data. Fit quality is also reflected by parameter agreement across multiple fits. For example, spectra taken in the non-methanol alcohols display a high degree of line center uniformity across all hydrogen bond ensembles: the line centers all fall within 0.4 cm -1 of one another in the 2-HB case, within 0.6 cm -1 of one another in the 1-HB case, and within 1.7 cm -1 of one another in the 0-HB case. The spectral features in methanol fall a
significantly outside these intervals, but it is clear that this variation is due to actual changes in the methanol solvation environment (Figure 2, main text) and not fit-associated uncertainty. A high degree of uniformity is also apparent in the half-widths at half-maximum determined through the fitting procedure. Most (15 of 24) fit linewidths fall within 2.5 cm -1 of one another and nearly all (21 of 24) fall inside a 5 cm -1 interval. The widths outside this interval (in D 2O and diethylene glycol) are clearly due to physical changes in the solvation environment and are not artifacts of the fitting procedure. Table S2: Extracted parameters from the Lorentzian fits (Equation 3) to measured IR absorption spectra (plots shown Figure 2 of the main text). Lorentzian Fit Parameters D2O 0.07 1724.7 12.2 0.25 1703.3 13.6 Ethanol 0.33 1744.6 5.7 0.25 1726.8 7.4 0.14 1714.2 9.4 Methanol 0.29 1748.6 6.1 0.31 1730.0 9.0 0.04 1706.1 8.0 Hexanol 0.39 1745.9 5.4 0.28 1727.2 7.2 0.11 1714.0 10.0 Terahydrofuran 0.86 1741.6 5.2 Acetonitrile 0.80 1735.9 6.3 DMSO 0.65 1732.6 6.6 Diethyl ether 0.74 1745.7 5.5 Isopropanol 0.28 1746.3 5.7 0.35 1727.4 7.1 0.12 1714.0 9.1 Butanol 0.34 1745.5 5.5 0.28 1727.1 7.0 0.13 1714.4 10.1 Dioxane 0.93 1739.0 5.3 Diethylene glycol 0.43 1738.1 7.1 0.19 1719.4 13.9 Lorentzian Fit Errors D2O 3.2E-3 0.6 0.8 3.0E-3 0.2 0.2 Ethanol 2.3E-3 < 0.1 < 0.1 4.9E-3 0.1 0.2 5.0E-3 0.3 0.3 Methanol 3.0E-3 < 0.1 0.1 2.3E-3 < 0.1 0.2 2.4E-3 0.5 0.8 Hexanol 1.7E-3 < 0.1 < 0.1 3.5E-3 < 0.1 0.1 3.3E-3 0.3 0.3 Tetrahydrofuran 2.8E-3 < 0.1 < 0.1 Acetonitrile 4.1E-3 < 0.1 < 0.1 DMSO 4.6E-3 < 0.1 < 0.1 Diethyl ether 2.4E-3 < 0.1 < 0.1 Isopropanol 2.5E-3 < 0.1 < 0.1 2.5E-3 < 0.1 0.1 2.9E-3 0.3 Butanol 1.8E-3 < 0.1 < 0.1 4.0E-3 < 0.1 0.2 3.7E-3 0.3 0.3 Dioxane 4.4E-3 < 0.1 < 0.1 Diethylene glycol 6.5E-3 < 0.1 0.2 4.5E-3 0.5 0.5
Table S3: Extracted parameters from the Lorentzian fits (Equation 3) to calculated IR absorption spectra. Lorentzian Fit Parameters D2O 6.58 1730.9 10.3 6.40 1718.9 10.6 Ethanol 8.14 1742.1 8.5 6.64 1727.5 10.7 6.89 1710.6 10.2 Methanol 8.91 1739.6 7.4 6.70 1726.9 10.4 7.16 1709.5 9.5 Hexanol 8.59 1745.7 8.1 7.19 1728.5 9.9 7.70 1710.9 9.1 Terahydrofuran 9.12 1743.1 7.5 Acetonitrile 8.05 1739.2 8.5 DMSO 6.97 1737.3 10.1 Diethyl ether 9.77 1746.2 7.0 Isopropanol 7.96 1742.2 8.7 6.76 1729.2 10.6 6.61 1709.2 10.7 Butanol 7.69 1743.9 9.4 6.78 1729.1 10.6 6.53 1710.4 10.9 Dioxane 7.08 1741.3 10.1 Diethylene glycol 7.46 1738.3 9.1 5.45 1726.9 13.3 Lorentzian Fit Errors D2O 4.55E-2 < 0.1 0.1 4.36E-2 < 0.1 0.1 Ethanol 1.50E-1 0.1 0.2 7.09E-2 0.1 0.2 5.73E-2 < 0.1 0.1 Methanol 1.33E-1 0.1 0.2 9.66E-2 0.2 0.2 1.09E-1 0.2 0.2 Hexanol 2.34E-1 0.2 0.4 1.16E-1 0.2 0.2 1.32E-1 0.2 0.2 Tetrahydrofuran 1.04E-1 < 0.1 0.1 Acetonitrile 8.64E-2 < 0.1 0.1 DMSO 9.73E-2 0.1 0.2 Diethyl ether 1.33E-1 < 0.1 0.1 Isopropanol 1.84E-1 0.2 0.3 1.06E-1 0.2 0.2 9.27E-2 0.1 0.2 Butanol 2.10E-1 0.3 0.4 1.31E-1 0.2 0.3 1.22E-1 0.2 0.3 Dioxane 1.26E-1 0.2 0.3 Diethylene glycol 1.33E-1 0.2 0.3 8.31E-2 0.2 0.3
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