Single-particle motions in liquid water

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Abstract
A physical picture of the single‐particle motions in liquid water is developed as a generalization of the relaxing cage concept that has been employed to describe the single‐particle motions in classical monatomic liquids. In the generalized picture, the solid‐like cage that surrounds a given water molecule in the liquid at short times is assumed to exhibit several normal modes whose frequencies are essentially the same as those at resonance positions in the frequency spectrum of ice Ih. The coupling of these modes to all of the other normal modes in ice via a Hamiltonian that destroys the symmetry of the lattice is considered to be a principal cause of the decay of the resonance modes that produces the differences between the frequency spectra for ice and liquid water. A perturbation–theoretic method is applied to solve the classical equation of motion for the center‐of‐mass velocity of an H20 molecule in the liquid, as a formal representation of the physical picture developed. This approach produces an expression for the velocity autocorrelation function that is identical with the well known three‐pole approximation if the cage surrounding a molecule in the liquid exhibits only one normal mode. In the general case of several cage normal modes, the model in its simplest form produces an expression for the velocity autocorrelation function that is a weighted sum of three‐pole approximation terms, one for each cage normal mode. A numerical calculation using 18 observed resonance frequencies in the ice Ih density of states results in a frequency spectrum and velocity autocorrelation function that agree well with molecular dynamics estimates.

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