{'fraction_non_alphanumeric': 0.025291647223518433, 'fraction_numerical': 0.012599160055996267, 'mean_word_length': 4.434077079107505, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Potassium bromide, KBr/{\epsilon} : New Force Field

The correct description of the ionic interaction and stable equilibrium of the simulations of biomolecular structure, dynamics, folding, catalysis, and function, an accurate model of the monovalent ions is very important. The force field needs to reproduce coincident many properties of ions, like their structure, solvation, and moreover both the interactions of these ions with each other in the crystal and in solution and the interactions of ions with other molecules. Using a similar strategy employed in the parameterization of the NaCl/epsilon , in this paper, we first propose a force field for the Potassium Bromide, the KBr/epsilon. This new model is compared with the experimental values of cristal density and structure for the salt and the density, the viscosity, the dielectric constant and the solubility in the water solution for a range of concentrations. Next, the transferability, of this new model KBr/epsilon and the NaCl/epsilon, is verified by creating the KCl/epsilon and the NaBr/epsilon models. The strategy is to employ the same parameters obtained for the NaCl/epsilon and for the KBr/epsilon force fields. The two new models derived are also compared with the experimental values for the density, the viscosity, the dielectric constant and the solubility in the water solution for a range of concentrations.


Introduction
The potassium Bromide salt shows a number of applications in medicine particularly in the metabolic regulation. 1 The potassium levels influence multiple physiological processes, including 1-3 the cellular-membrane potential, the propagation of action potentials in neuronal, in the muscular, and in the cardiac tissue. Recent studies suggest that bromine is necessary for tissue development [4][5][6] and is relevant in the antiparasitic enzyme in the human immune system.
The salt interaction with the biological system is quite complex and experiments even though very important are unable to isolate the properties of the individual moleculemolecule interaction. Therefore, one strategy to understand the interaction of the KBr with other molecules is the use of simulations. The crucial step in the simulations is to construct an appropriated force field for the interaction potential between the ions. The usual method is to fit the parameters of the model with the experimental results for the density and for the structure for the real system at one determined pressure and temperature. Then, the results obtained for thermodynamic and dynamic properties with the model are compared with experiments. Following this procedure, atomistic models for KBr have been proposed. 7 Unfortunately, even though capable of reproducing the density of the system at 298K and 1bar the current models fail in reproducing other properties such as the the dielectric constant of the solution in water, the viscosity and the solubility.
Recently we proposed a new model for Sodium Chloride, 8 the NaCl/ε, which is able to reproduce not only the density, but the dielectric constant, the viscosity and the solubility of this salt in aqueous solution, as well as, the density of the pure system at different temperatures. The idea of adjusting the model to give the experimental dielectric constant of the pure system and of the water solution at 1bar and 298K is inspired by the recent need to understand the behavior of salt in surfaces and confined geometries and in the solubility where the dielectric discontinuity plays quite a relevant role. [9][10][11] The remaining of the paper goes as follows. In the section 2 the new model, the KBr/ε, is introduced and the TIP4P/ε water model was reviewed. Section 3 summarizes the simulation details and the results are analysed in Section 4. Conclusions are presented in the section 5.

The Models
The KBr/ε Model The ions of the salt are modeled as spherical particles interacting through the potential where r i j is the distance between ions i and j, q i is the electric charge of ion i, ε 0 is the permitivity of vacuum, ε i j is the Lennard-Jones energy that is used as energy scale and σ i j is the distance between the ions, used as length scale.
For the interaction between the ions and the water molecules , the Lorentz-Berteloth rule is employed, 15 namely For the KBr/ε model the Lennard-Jones (LJ) energy, ε i j = ε LJ ,and the distance scale, Recently a new model for the NaCl, the NaCl/ε, was proposed. In this system, a screening for the Coulombic term was introduced. 16 The original assumption was to include effects due to water polarization by adding to a rigid model a screening term. 8,16 Here we addapt this proposition for the KBr salt model. Then the screening parameter becomes λ i = λ C .
Therefore, our interaction potential of the ions has three parameters, namely λ C , σ LJ and ε LJ to be adjusted with experimental data for each ion. These parameters are selected so the KBr/ε force field reproduces the experimental value for the density of the crystal in the face centred cubic phase at the 298 K of temperature 7,18 and 1 bar. These procedure allows for a number of possible parameters values. This degeneracy is broken by selecting the subset that also gives the radial distribution function, g(r), which gives the appropriate behavior of the salt crystal at 298 K of temperature and 1 bar of pressure.
The next step is this reduction in the parameter space is to select the set of values that also gives the proper density and the dielectric constant in the mixture of the salt with water 18 at 298 K of temperature and 1 bar of pressure. These last step was done using a solution with 4 molal of salt concentration and the TIP4P/ε water model . The final result for the force field for the KBr/ε model is shown in the Table 1.
The division by 2 in this equation accounts for a pair of ions and M H 2 O =18 g mol −1 . The figure 3 gives the value of the molality for each point of calculus where k B is the Boltzmann constant and T the absolute temperature. The dielectric constant is obtained for long simulations at constant density and temperature or at constant temperature and pressure. The shear viscosity is obtained using the autocorrelation function of the off-diagonal components of the pressure tensor P αβ according to the Green-Kubo formulation,

Results
The KBr/ε Model The parameters for KBr/ε model were selected to reproduce the density of the crystal at the The Table 4 shows a comparison of the values obtained for the the density, the Lattice Energy and the Lattice Crystal for the KBr/ε model, for the experiments, 18 for the Joung-Cheatham, 7 the JC force field, and for the force field parametrized with SPC/E water, the JC S3 model. 17 Our model gives good agreement with the experiments 18 in the density of the crystal and the Lattice Constant, but is 13% far from the reproduction of the Lattice Energy.
The figure 3 illustrates the the dielectric constant versus molal concentration for the KBr/ε model with the TIP4P/ε water, for the experiments, 18 JC S3 17 and JC T 4 7 models.
The molal concentration imployed to parametrize the KBr/ε is shown with a purple circle.
The result shows that our model gives a good agreement with the experiments.
In the figure 4 shows the density versus salt concentration for the experiments, 18 for the   KBr/ε, for the JC S3 17 and for the JC T 4 7 models. The results are consistent with the fact that the models were parametrize to give the correct density value.
In addition to thermodynamic properties, the transport was also evaluated.

The KCl/ε Model
Since both NaCl/ε and KBr/ε models have been already parametrized, we test the transferability of these two force fields as follows. Instead of fitting the parameters for the KCl from experiments, the parameters for the K are taken from the KBr/ε given in the Table 1 while the parameters for the Cl are taken from the NaCl/ε model. 8 The parameters for the KCl are summarized in the Table 6. It is important to notice that no additional parameterization was needed for obtaining the KCl/ε model.  −3 , that is the same as the experimental data. 18 The radial distribution for K-K, Cl-Cl and K-Cl is illustrated in the Figure 7 and it shows a peak at 3.08 in agreement with the experiments. 18  Table 7, is also in accordance with the experimental values. 18 The Lattice Energy (LE), however, it is 16.5% far from the reproduction of the Lattice Energy. This difference was present in the NaCl/ε and KBr/ε and models. Next, the KCl/ε in the water TIP4P/ε performance is tested for a number of properties.

The NaBr/ε Model
The consistency of the new force fields is now checked by creating the NaBr/ε model employing the parameters for Br and Na, shown in the table 9, extracted from the force fields for the KBr/ε and NaCl/ε models respectively. The radial distribution for Na-Na, Br-Br         The figure  at diluted concentration also shown in the figure. When the concentration is increase there is a difference between the value that reproduces the NaBr/ε with TIP4P/ε of 13.5% at 6.1m, compared to experimental value and the JC S3 with respect to the experimental value is 55.3 percent and the JC T 4 is 71.4 percent at the same experimental concentration of 6.1m. It is important to note that the result with the new force field NaBr/ε describes the curvature of the shear viscosity. Exp. TIP4P/ε + NaBr/ε TIP4P/Ew + NaBr-JC T4 SPC/E + NaBr-JC S3 Figure 15: Viscosity versus molal concentration of the salt at temperature and pressure at room conditions.The black line is the experimental data 18 and the blue filled diamond are the results for our model.   Figure 17: Solubility of the atomistic models

Conclusions
In this paper the force field, the KBr/ε, was introduced. The model reproduces the density of the crystal and structure, as well as the thermodynamic and dynamic properties of the solution with the TIP4P/ε model for water at different molal concentration.
The model, particularly reproduces the dielectric constant of the solution what is a property not well represented in other atomistic models. In order to test the KBr/ε and the NaCl/ε models, the same parameters for the isolated ions were employed in the construction of the KCl/ε and of the NaBr/ε models. In the construction of these two new models not there was an additional parameterization. The results of the density, the dielectric constant, the viscosity and the solubility of the KCl/ε and of the NaBr/ε models reproduces well the experiments. Since all the models give a very robust result for the dielectric constant, we believe that they are suitable for studying confined systems and can be used to study ionic channels.