^{1,a)}

### Abstract

Molecular-dynamics simulations were carried out for the SPC, SPCE, TIP4P, and TIP5P models of water at 298 K. From these results we determine the following quantities: the absolute entropy using the two-particle approximation, the mean lifetime of the hydrogen bond, the mean number of hydrogen bonds per molecule, and the mean energy of the hydrogen bond. From the entropy calculations we find that nearly all contributions to the total entropy originates from the orientation effects. Moreover, we determine the contributions to the total entropy which originate from the first, second, and higher solvation shells. It is interesting that the limits between solvation shells are clearly visible. The first solvation shell contributes approximately to the total entropy; the second solvation shell contributes approximately , while contributions from the third and other solvation shells are very small, approximately in summary. This indicates that water molecules are strongly ordered up to 0.55-0.6 nm around the central water molecule, and beyond this limit the ordering diminishes. The results of calculations (entropy and hydrogen bonds) are compared with the experimental data for the choosing of the best watermodel. We find that the SPC and TIP4P models reproduce the best experimental values, and we recommend these models for computer simulations of the aqueous solution of biomolecules.

The molecular-dynamics calculations were carried out at the Academic Computer Center in Gdańsk. The author also wishes to thank Professor P. Bała (Nicholas Copernicus University, Faculty of Mathematics and Computer Science, Toruń, Poland) for providing the parallel version of GROMOS96 molecular-dynamics program used in this work.

I. INTRODUCTION

II. DETAILS OF SIMULATION PROCEDURE

III. RESULTS OF CALCULATIONS

A. The entropy calculations

B. Calculations of the energy and lifetime of the hydrogen bond

IV. DISCUSSION

### Key Topics

- Entropy
- 39.0
- Hydrogen bonding
- 32.0
- Hydrogen energy
- 9.0
- Solvents
- 6.0
- Water energy interactions
- 6.0

## Figures

Plot of the dependence of the calculated absolute entropy on the simulation time.

Plot of the dependence of the calculated absolute entropy on the simulation time.

Probability as a function of elapsed time for single hydrogen bond in SPC water at .

Probability as a function of elapsed time for single hydrogen bond in SPC water at .

(a) Contributions and calculated according to Eqs. (8) and (9) as a function of the radius ; (b) absolute entropy of the SPC water calculated from Eqs. (2)–(4) as a function of radius ; and (c) molecule-molecule (between centers of mass) radial distribution function for SPC water. Total simulation time .

(a) Contributions and calculated according to Eqs. (8) and (9) as a function of the radius ; (b) absolute entropy of the SPC water calculated from Eqs. (2)–(4) as a function of radius ; and (c) molecule-molecule (between centers of mass) radial distribution function for SPC water. Total simulation time .

## Tables

Monomer geometry, Lennard-Jones parameters, and partial charges describing the water-water interactions.

Monomer geometry, Lennard-Jones parameters, and partial charges describing the water-water interactions.

Description of the results of entropy calculations for SPC water as a function of time using Eq. (5). deg—angle step, —simulation time, —number of collected, results, —fitted value of absolute entropy and std—average standard deviation of the results from the fitting line.

Description of the results of entropy calculations for SPC water as a function of time using Eq. (5). deg—angle step, —simulation time, —number of collected, results, —fitted value of absolute entropy and std—average standard deviation of the results from the fitting line.

Calculated values of the absolute entropy for various models of water. Calculations were carried out using the following steps of integration in Eq. (4): , ; for all the systems simulation time is equal to 60 ns.

Calculated values of the absolute entropy for various models of water. Calculations were carried out using the following steps of integration in Eq. (4): , ; for all the systems simulation time is equal to 60 ns.

Mean number of hydrogen bonds per water molecule ; mean lifetime of single hydrogen bond ; mean lifetime of hydrogen atom in the nonbonded state ; mean lifetime of water molecule in the bonded state and in the nonbonded state ; and mean energy of hydrogen bond (see text).

Mean number of hydrogen bonds per water molecule ; mean lifetime of single hydrogen bond ; mean lifetime of hydrogen atom in the nonbonded state ; mean lifetime of water molecule in the bonded state and in the nonbonded state ; and mean energy of hydrogen bond (see text).

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