^{1,a)}and Branka M. Ladanyi

^{1,b)}

### Abstract

A molecular dynamics simulation study of structural and dynamical properties in liquid mixtures of formamide and water is presented. Site-site radial pair distribution functions, local mole fractions, pair energy distributions, and tetrahedral orientational order are the quantities analyzed to investigate the local structure in the simulated mixtures, along with a review of the intermolecular structure in terms of the distribution of hydrogen bonds. Our results indicate that there is a substitution of formamide molecules by water in the hydrogen bonds and a formation of a common hydrogen bond network. By analyzing the extent of tetrahedral order in the liquid as a function of composition, it is observed that whereas the tetrahedral network of liquid water is progressively lost by increasing the formamide concentration, the water structure within the first coordination shell is preserved and somewhat enhanced. The hydrogen-bond mean lifetimes were estimated by performing a time integration of the autocorrelation functions of bond occupation numbers. The lifetimes associated with hydrogen bonds between water, formamide, and interspecies pairs are found to increase with increasing formamide concentration. The lifetimes of the water hydrogen bonds show the largest variations, supporting the picture of an enhancement of the water structure among the nearest neighbors within the first coordination shell. We have used two different force field models for water, SPC/E [J. C. Berendsen *et al.*, J. Phys. Chem.91, 6269 (1987)] and TIP4P/2005 [J. L. F. Abascal and C. Vega, J. Chem. Phys.123, 234505 (2005)]. Our results for structural and dynamical properties yield very small differences between those models, the TIP4P/2005 predicting a slightly more structured liquid and, consequently, exhibiting a slightly slower translational and librational dynamics.

Financial support from the National Science Foundation Grant No. CHE 0608640 is gratefully acknowledged.

I. INTRODUCTION

II. POTENTIAL MODELS AND SIMULATION DETAILS

III. LOCAL STRUCTURE

A. Radial pair distribution functions

B. Pair energy distributions

C. Tetrahedral order

D. Distribution of H bonds

IV. DYNAMICS

A. Translational dynamics

B. Rotational dynamics

C. Hydrogen-bond lifetimes

V. CONCLUSIONS

### Key Topics

- Hydrogen bonding
- 99.0
- Correlation functions
- 17.0
- Molecular dynamics
- 14.0
- Trajectory models
- 12.0
- Bond formation
- 11.0

## Figures

Formamide-formamide site-site radial distributions for and atom pairs pertaining to distinct molecules.

Formamide-formamide site-site radial distributions for and atom pairs pertaining to distinct molecules.

Water-water site-site radial distributions for O–O, O–H, and H–H atom pairs. Note different scales on axes.

Water-water site-site radial distributions for O–O, O–H, and H–H atom pairs. Note different scales on axes.

Formamide-water site-site radial distributions for , , and site pairs.

Formamide-water site-site radial distributions for , , and site pairs.

(a) Local mole fractions of FA (, solid lines) and water (, dot-dashed lines) as a function of , for the mixtures studied. The thickest and thinnest lines correspond to and , respectively; the intermediate lines correspond to intermediate compositions. The horizontal dashed lines at , 0.4, 0.6, and 0.8 are plotted for comparison. (b) Parameter obtained for the compositions studied.

(a) Local mole fractions of FA (, solid lines) and water (, dot-dashed lines) as a function of , for the mixtures studied. The thickest and thinnest lines correspond to and , respectively; the intermediate lines correspond to intermediate compositions. The horizontal dashed lines at , 0.4, 0.6, and 0.8 are plotted for comparison. (b) Parameter obtained for the compositions studied.

Pair energy probability distributions, considering only the four nearest neighbors of a given molecule, for (a) FA-FA pairs, (b) W-W pairs, (c) FA surrounded by closest W neighbors, and (d) W surrounded by closest four FA molecules.

Pair energy probability distributions, considering only the four nearest neighbors of a given molecule, for (a) FA-FA pairs, (b) W-W pairs, (c) FA surrounded by closest W neighbors, and (d) W surrounded by closest four FA molecules.

Distribution of the tetrahedral order parameter, , for (a) FA-FA pairs, (b) W-W pairs, (c) FA with respect to the closest four W neighbors, and (d) W with respect to its closest FA molecules. The inset in panel (b) shows computed for the water molecules that have all four nearest neighbors inside the first coordination shell, that is, . The area under each curve is normalized to unity.

Distribution of the tetrahedral order parameter, , for (a) FA-FA pairs, (b) W-W pairs, (c) FA with respect to the closest four W neighbors, and (d) W with respect to its closest FA molecules. The inset in panel (b) shows computed for the water molecules that have all four nearest neighbors inside the first coordination shell, that is, . The area under each curve is normalized to unity.

Distribution of tetrahedral order parameter, : comparison between SPC/E and TIP4P/2005 potential models for water, for (a) W-W pairs and (b) FA-W pairs. The curves corresponding to FA mole fractions , 0.4, 0.2, and 0.0 have been offset vertically by , , , and , respectively.

Distribution of tetrahedral order parameter, : comparison between SPC/E and TIP4P/2005 potential models for water, for (a) W-W pairs and (b) FA-W pairs. The curves corresponding to FA mole fractions , 0.4, 0.2, and 0.0 have been offset vertically by , , , and , respectively.

Top scheme: H-bond definition (see text). (a) represents the fraction of FA molecules participating in H bonds with FA, (b) the fraction of water molecules forming H bonds with water, (c) the fraction of FA molecules forming H bonds with water, and (d) the fraction of water molecules participating in H bonds with FA. The different symbols correspond to different FA mole fractions, as indicated.

Top scheme: H-bond definition (see text). (a) represents the fraction of FA molecules participating in H bonds with FA, (b) the fraction of water molecules forming H bonds with water, (c) the fraction of FA molecules forming H bonds with water, and (d) the fraction of water molecules participating in H bonds with FA. The different symbols correspond to different FA mole fractions, as indicated.

Average number of H bonds between W-W (black squares) and W-FA (gray squares) per water molecule; and between FA-FA (black circles) and FA-W (gray circles) per FA molecule, as a function of FA mole fraction, . The curves with white symbols correspond to the total average number of H bonds per water (squares) and FA molecules (circles).

Average number of H bonds between W-W (black squares) and W-FA (gray squares) per water molecule; and between FA-FA (black circles) and FA-W (gray circles) per FA molecule, as a function of FA mole fraction, . The curves with white symbols correspond to the total average number of H bonds per water (squares) and FA molecules (circles).

Self-diffusion coefficients for FA (circles) and water (squares) as a function of FA mole fraction. The white circles are experimental data taken from Ref. 52. Black and gray symbols correspond to SPC/E and TIP4P/2005 potential models for water.

Self-diffusion coefficients for FA (circles) and water (squares) as a function of FA mole fraction. The white circles are experimental data taken from Ref. 52. Black and gray symbols correspond to SPC/E and TIP4P/2005 potential models for water.

TCF of the total angular velocity, , for (a) water and (b) formamide molecules, for the studied mixtures.

TCF of the total angular velocity, , for (a) water and (b) formamide molecules, for the studied mixtures.

(a) Short-time behavior of the water single dipole TCF, . The inset shows the decay of , corresponding to FA molecules, on a longer time scale. Panel (b) shows the water librational spectra, , for the compositions studied.

(a) Short-time behavior of the water single dipole TCF, . The inset shows the decay of , corresponding to FA molecules, on a longer time scale. Panel (b) shows the water librational spectra, , for the compositions studied.

Single-molecule orientational relaxation times for FA (dipole vector, left panel) and water (HH vector, right panel) as functions of composition, for SPC/E and TIP4P/2005 potential models. Experimental estimates for FA and water according to NMR measurements are taken from Ref. 58 and drawn with white symbols. The lines are just guides to the eye.

Single-molecule orientational relaxation times for FA (dipole vector, left panel) and water (HH vector, right panel) as functions of composition, for SPC/E and TIP4P/2005 potential models. Experimental estimates for FA and water according to NMR measurements are taken from Ref. 58 and drawn with white symbols. The lines are just guides to the eye.

Logarithm of H-bond lifetime autocorrelation functions, (a) and (b), for hydrogen bonds between FA-FA, W-W, and unlike FA-W molecules. The curves for W-W and FA-W have been shifted vertically by and for clarity. The different line types correspond to different FA mole fractions, as indicated. Note the different time scales in panels (a) and (b).

Logarithm of H-bond lifetime autocorrelation functions, (a) and (b), for hydrogen bonds between FA-FA, W-W, and unlike FA-W molecules. The curves for W-W and FA-W have been shifted vertically by and for clarity. The different line types correspond to different FA mole fractions, as indicated. Note the different time scales in panels (a) and (b).

## Tables

Intermolecular potential parameters and molecular geometry. Lennard-Jones parameters and are equal to zero for the three reported force fields.

Intermolecular potential parameters and molecular geometry. Lennard-Jones parameters and are equal to zero for the three reported force fields.

Total and partial number densities for the solutions studied, box length employed in each MD trajectory average temperature and excess internal energies of mixing obtained from simulations, along with experimental excess enthalpies. Energies are given in kJ/mol.

Total and partial number densities for the solutions studied, box length employed in each MD trajectory average temperature and excess internal energies of mixing obtained from simulations, along with experimental excess enthalpies. Energies are given in kJ/mol.

Mean lifetimes obtained for H bonds between species of the same and different kinds in FA-water mixtures, computed from the TCF of the occupation numbers, .

Mean lifetimes obtained for H bonds between species of the same and different kinds in FA-water mixtures, computed from the TCF of the occupation numbers, .

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