Fig. 3: Decomposition of the configurational probability density distribution of the “special pair” moiety of proton in water. | Nature Communications

Fig. 3: Decomposition of the configurational probability density distribution of the “special pair” moiety of proton in water.

From: Unveiling the intermediate hydrated proton in water through vibrational analysis on the 1750 cm−1 signature

Fig. 3

a The 2D probability density (PD) distribution in 0.01 M HCl, which is extracted and mapped onto a coordinate space defined by \({R}_{{{{{\rm{O}}}}}_{1}{{{{\rm{H}}}}}^{*}}\) and \({R}_{{{{{\rm{O}}}}}_{2}{{{{\rm{H}}}}}^{*}}\), the distances between the excess proton (H*) and its two adjacent oxygen atoms (O1 and O2) of flanking water molecules (assuming \({R}_{{{{{\rm{O}}}}}_{1}{{{{\rm{H}}}}}^{*}} < {R}_{{{{{\rm{O}}}}}_{2}{{{{\rm{H}}}}}^{*}}\)). b The three 2D Gaussian-type fitting functions are assigned to Zundel-like (blue), Intermediate (yellow) and Eigen-like (green) configurations. The black lines illustrate the contour plot of the sum of the three types. c The absolute error (AE) distribution of the 2D Gaussian-type fitting, defined as the difference between the probability density distribution and the sum of the three 2D Gaussian-type fitting functions. The unit of root mean square error (RMSE) and AE is Å−2.

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