Hydrogen bonding autocorrelation functions

H-bonds. The relaxation time of hydrogen bonds is characterized by the hydrogen bond autocorrelation function [58,59]... 

Figure 2.5 (a) Hydrogen bond autocorrelation function C(I) when q = 0.6e (solid Unes), 0.8 e (dashed lines) and 1.0 e (dotted lines) for within-monolayer H-bonds (black line) and between-monolayer-droplet H-bonds (red line), (b) Average relaxation time x of within-monolayer H-bonds (black line) and between-monolayer-droplet H-bonds (red hne) vs. q. 

Fig. 6 Intermittent Cinit) hydrogen bond autocorrelation functions obtained from calculations (a) with the hydrogen bond criteria that the distance of the hydrogen bond donor and acceptor atom is lower than the sum of the Van der Waals radii and the angle a(C2-H2-Y) is larger than 160° and (b) with the distance criterion reduced to 90% of the sum of the Van der Waals radii...

Figure 3. Hydrogen and oxygen velocity autocorrelation function from two-body MCY with vibrations allowed (MCYL), and computed infrared spectrum for intramolecular bending modes and bond stretching.

The linear response theory [50,51] provides us with an adequate framework in order to study the dynamics of the hydrogen bond because it allows us to account for relaxational mechanisms. If one assumes that the time-dependent electrical field is weak, such that its interaction with the stretching vibration X-H Y may be treated perturbatively to first order, linearly with respect to the electrical field, then the IR spectral density may be obtained by the Fourier transform of the autocorrelation function G(t) of the dipole moment operator of the X-H bond ... 

Here, t/(f) is the reduced time evolution operator of the driven damped quantum harmonic oscillator. Recall that representation II was used in preceding treatments, taking into account the indirect damping of the hydrogen bond. After rearrangements, the autocorrelation function (45) takes the form [8]... 

It has been shown that the autocorrelation function (46) is the limit situation in the absence of damping of the autocorrelation function of the hydrogen bond within the indirect damping [8]. It must be emphasized that this autocorrelation function does not require for computation any particular caution because of its analytic character. Thus, it may be considered as a numerical reference for the computation involving representation I or III. 

The autocorrelation function of the hydrogen bond within the effective Hamiltonian expression of the standard approach takes the form... 

Thus, effects of the surfaces can be studied in detail, separately from effects of counterions or solutes. In addition, individual layers of interfacial water can be analyzed as a function of distance from the surface and directional anisotropy in various properties can be studied. Finally, one computer experiment can often yield information on several water properties, some of which would be time-consuming or even impossible to obtain by experimentation. Examples of interfacial water properties which can be computed via the MD simulations but not via experiment include the number of hydrogen bonds per molecule, velocity autocorrelation functions, and radial distribution functions. 

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