Yanting Wang, Nathan O. Hodas, Yousung Jung and R. A. Marcus

Phys. Chem. Chem. Phys., 2011, 13, 5388–5393 (DOI: 10.1039/c0cp02745f). Amendment published 1^st April 2011

The authors have provided the following information regarding corrections to some of the equations in their above article:

The corrected equations produce calculated ratios similar to those presented in Tables 2 and 3 of the article (see below), and the calculated magnitudes remain similar to the experimentally measured magnitudes of the A_eff’s in those tables. The method also provides a calculation, in agreement with experiment, of the average tilt angle of surface free OH bonds, number of free OH bonds, and the amplitudes and ratios of the A_eff’s, using the experimental linewidth Γ_q(14.5cm⁻¹) and an additional parameter, the cutoff angle of the free OH bonds. A fuller presentation of the results using long time trajectories, ensemble averages, and additional water models, will be described elsewhere.

The corrections are as follows: in eqn (3) an iω₂ is missing from the right hand side,¹ and in eqn (4) and (5) the exp(iω_qt), cos ω_qt and the sin ω_qt should read iω_qexp(i(ω₂ − ω_q)t), cos (ω₂ − ω_q)t and sin (ω₂ − ω_q)t. The leading minus sign in eqn (5) should be removed. On page 5390, the units of beta should read m⁴ V⁻¹ s⁻¹. In Tables 2 and 3 the title should have s⁻¹ instead of s and the expression containing should read , where N = (T − t)/δt. A corrected Table 2 is given below and shows a definite improvement over the previous results, in terms of less dependence on snapshot size.

Table 2. Mode amplitudes and their ratios calculated from MD simulations and comparison with the experimental values. A_eff has units 10⁻⁹ m² V⁻¹ s⁻¹.^a

^a Results of fitting the spectrum to a Lorentzian and correcting for experimental width.

¹ Using the standard quantum mechanical expression for containing a and an α(0), an integration by parts led to eqn (3), with the cited iω₂ term included. This ω₂ in the pre-exponential factor was replaced by its value at the peak, ω_q. A constant term from the integration by parts step is frequency-independent, forming part of the background, and is omitted. One then introduces a basis set for the oscillator q, only and being needed for the high frequency (3700 cm⁻¹) OH oscillator, and one notes that the depends on time as exp(−iω_qt). With the corrections noted above, eqn (4) and (5) then follow, from which we calculate a spectral response. Because Wei and Shen (2001) extracted the A_eff’s by fitting the experimentally measured spectrum with a Lorentzian, we fit our calculated spectrum to a Lorentzian to permit a comparison. To obtain the final results for the Aeff’s it was assumed that a total “signal strength” (in the form of ) was the same for the calculated and experimental models, giving where δC and γ are obtained from the Lorentzian fit to the MD calculations, , and Γ_q(14.5 cm⁻¹) is the experimental decay constant. The constant δC is the correlation function evaluated at t=0, where is the baseline of the plot. This δC is determined only by the equilibrium properties and is insensitive to the detailed dynamics, while the dynamics lie in Γ_q (and γ). Thus, when a single Lorentzian description and the above assumption are appropriate this method of analysis of the data separates the problem into an equilibrium part and a dynamical part.

The Royal Society of Chemistry apologises for these errors and any consequent inconvenience to authors and readers.

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