Molecular volume calculation using AM1 semi-empirical method toward diffusion coefficients and electrophoretic mobility estimates in aqueous solution

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Abstract

Diffusion coefficients and electrophoretic mobility are two important physicochemical parameters used in mass transport phenomenon studies. The volume of the solute is required to determine or estimate these parameters. Classical methods, such as the LeBas method are commonly used. However, although valid, this method may represent a boring and time-consuming task, depending on the nature and number of compounds to be calculated. In this study, the volumes of a series of neutral and charged substances of the main functional groups present in organic molecules, amino acids, drugs and diverse compounds, such as cytosine and glucose, were calculated according to the LeBas method (VM) and the AM1 semi-empirical method, VW(AM1). The latter showed to be statistically coincident with the former. Employed as a pure value or corrected by the LeBas molar volume, the AM1 molecular volume was also demonstrated to estimate the diffusion coefficients in infinite aqueous dilution within an acceptable average error, according to the Othmer–Thakar, Wilke–Chang and Hayduk–Laudie methods, as well as the electrophoretic mobility of charged substances, such as carboxylates and protonated amines. According to these results, the AM1 method was seen to be statistically valid to calculate molecular volume. Many advantages in the construction of most diverse structures were noted, as well as a reduction in time and an increase in the quality of the information, when run on molecular modeling software.

Introduction

Diffusion is a fundamental phenomenon in several physical and chemical processes, representing the natural movement of neutral or charged species in solution [1], [2]. The diffusion coefficient in liquids is an important parameter to understand the complex processes of mass transportation [3]. However, the experimental determination of diffusion coefficients can be considered difficult, time-consuming, besides being costly. In fact, diffusion coefficients of many organic species in aqueous medium are not determined and this also occurs for newly developed and launched compounds in the market [1]. As such, several empirical methods for the estimation of diffusion coefficients in aqueous phase, considering infinite dilution and being based on molecular size indicators, have been developed [1], [2], [3], [4], [5], [6], [7], [8], [9]. Three of these methods are introduced as follows:Othmer&Thakar[4],Dw=14×105ηw1.1VM0.6Wilke&Chang[5],Dw=7.4×108(xM)0.5TηwVM0.6Hayduk&Laudie[6],Dw=13.3×105ηw1.14VM0.589where Dw is the diffusion coefficient of the solute in water (cm2 s−1); ηw is the viscosity of water (cP) at the required temperature (ηw=0.8937 at 25 °C) [1], M is the molar mass of water (g mol−1), T the temperature (K), x the association parameter of water, and VM is the molar volume of the solute (cm3 mol−1) [1], [4], [5], [6]. These methods are based on the Stokes–Einstein relation, in which the diffusion coefficient is proportional to the absolute temperature and inversely proportional to the viscosity of the solvent. Moreover, these methods consider molecules as spheres and the correspondent molar volume has shown a logarithmical proportionality with Dw in which the slope of the equation corresponds to the exponent of VM [4], [5], [6]. Classically, the molar volumes are values at the normal boiling point estimated by the atomic contributions of LeBas [10].

Diffusion coefficient estimates can be useful and applicable in various interesting fields, such as electrochemical techniques employed for elucidation of reaction mechanisms of organic compounds involving electron transfer. Normally, the Dw value varies between 10−5 and 10−6 cm2 s−1 and it is present in the equations of current–voltage developed for the electrochemical methods. Thus, the limiting current registered is frequently used as an indicator for the number of electrons involved in the electrochemical process [11], [12].

The electrophoretic mobility (μ0) is another parameter that can be estimated from volume of solute. Fu and collaborators [13] demonstrated the factors that govern the μ0 of protonated amine (Eq. (4)) and carboxylate (Eq. (5)) derivatives. The molecular volume (Å3) and the constant dissociation of the ionized groups are the fundamental factors for μ0 estimation, both related to friction and dielectric hydrodynamics of electrolytic speciesμ0=7.8×103VW0.62+0.66pKb

μ0=6.8×103VW0.62+0.66pKa

The intrinsic mobility of an ion refers to the mobility of the fully ionized form of a molecule. The discussion presented by Fu and collaborators [13] is restricted to the prediction of intrinsic mobility at infinite dilution, which eliminates problems related to solution conditions such as ionic strength and ion association.

Several ways in which the volume of the molecule may be estimated [7], [14], [15] could be expressed by molar volume (cm3 mol−1) or molecular volume (Å3). The Bondi method, which assumes the knowledge of bond distances, bond angles, and intermolecular van der Waals radii, is the most popular for both calculations [15]. Recently, calculation of the molar and/or molecular volumes has been facilitated with the computer assistance [13], [16], [17], [18], [19].

Molecular modeling has been introduced as a valuable methodology for scientific research providing useful tools for the analysis and estimate of the physicochemical parameters and/or biological activity [20]. However, recent studies have shown divergences regarding the validity of the application of molecular modeling software for molecular volume calculation. According to some researchers, although the results obtained using molecular modeling are valid, they are dependent on the software [18], while others consider the purchase of specific software for such purposes expensive [19].

This paper reports a statistical analysis of molecular volume calculated by AM1 semi-empirical method, employing the classical additive method as a reference. The final purpose was to find an acceptable and more available molecular volume calculation to be used in the estimate of diffusion coefficients (Dw) and electrophoretic mobility (μ0) in infinite aqueous dilution.

Section snippets

Calculation of molecular volumes

Non-electrolytic compounds were selected for the diffusion coefficient study, while electrolytic compounds were employed for the electrophoretic mobility study. Table A1 shows 147 neutral compounds, including aliphatic, aromatic, heteroaromatic and representative species of the major chemical classes, besides several substances present in the biological systems, such as amino acids, sugars, hormones and nucleotides and some drugs. The electrolytic compounds (Table B1) were represented by seven

Non-electrolyte species

The correlation established by Eq. (8) and used as the theoretical reference for the calculated volumes is presented in Fig. 1. The empirical correlation between VM values and VW(AM1) showed excellent linear fit (R=0.993), enabling the determination of the molar volume, VM, from the volumes calculated by AM1 using the equation:VM=1.06(±0.0048)VW(AM1)

The validity of Eq. (10) was observed using the VM for the Dw prediction. Fig. 2 shows the relationship between Dw(exp) and Dw values in a

Conclusion

The volume of the solute is required for calculating physicochemical parameters, such as diffusion coefficients and electrophoretic mobility, being the LeBas method usually employed. In this method, the molar volume is calculated throughout the total sum (additive method) of the increments constituting the molecule. However, although the major increments representing the organic compounds are described by LeBas, it is necessary to infer values for some molecules, particularly heteroaromatic

Acknowledgements

We thank FAPESP for the financial support (process no. 01/01192-3 and 03/10763-0) and for the posdoctor fellowship to M. A. La-Scalea (process no. 01/09418-0), Capes-Prodoc for the fellowship to C.M.S. Menezes (process no. 00019-03-8).

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