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Combining MOSCED with molecular simulation free energy calculations or electronic structure calculations to develop an efficient tool for solvent formulation and selection

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Abstract

Solubility parameter based methods have long been a valuable tool for solvent formulation and selection. Of these methods, the MOdified Separation of Cohesive Energy Density (MOSCED) has recently been shown to correlate well the equilibrium solubility of multifunctional non-electrolyte solids. However, before it can be applied to a novel solute, a limited amount of reference solubility data is required to regress the necessary MOSCED parameters. Here we demonstrate for the solutes methylparaben, ethylparaben, propylparaben, butylparaben, lidocaine and ephedrine how conventional molecular simulation free energy calculations or electronic structure calculations in a continuum solvent, here the SMD or SM8 solvation model, can instead be used to generate the necessary reference data, resulting in a predictive flavor of MOSCED. Adopting the melting point temperature and enthalpy of fusion of these compounds from experiment, we are able to predict equilibrium solubilities. We find the method is able to well correlate the (mole fraction) equilibrium solubility in non-aqueous solvents over four orders of magnitude with good quantitative agreement.

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Notes

  1. Recall that \(\ln \frac{f_{2}^\mathrm{S}}{f_{2}^{0}}=\frac{1}{R T}\left( {\mu _{2}^\mathrm{S}} -{\mu _{2}^{0}}\right).\)

  2. Note that while Eqs. 5 and 6 are written for calculating the infinite dilution activity coefficient of component 2 in 1, an equivalent expression may be written for component 1 in 2 by switching the subscript indices.

  3. It is useful to put the calculation of the solvation free energy using the SMD and SM8 solvation model in the context/language of a conventional molecular simulation free energy calculation. The free energy of solvation is computed as the change in free energy of coupling/decoupling a single solute molecule to solution. When coupling/decoupling a single solute molecule when performing a molecular simulation free energy calculation, the SMD and SM8 calculations assume that the simulation box is approximately the same size when the solute is fully coupled and fully decoupled. This may equivalently be expressed as the change in free energy of taking a single solute molecule from an ideal gas phase (or vacuum) to solution at the same concentration. Additionally, note that in the SMD and SM8 solvation model the solvent is modeled as a continuum; the value of \(N_{1}\) in Eq. 8 is therefore not of importance.

  4. Note that TraPPE-EH does parameterize aniline in ref. [71]. We chose not to use the N LJ parameters from aniline because it is a primary amine, and it was previously shown in ref. [92] that there is an appreciable change in LJ parameters in going from a primary to secondary amine. Also, in ref. [92], the primary amide LJ parameters are the same as the primary amine (i.e., only the charges change). Therefore, we took the secondary amide LJ parameters for N to be the same as for a secondary amine. The H has LJ parameters of 0 in primary and secondary amines and primary amides. The LJ parameters for H in a secondary amide were therefore taken to also be 0 in the present study.

  5. The alkyl groups (CH\(_{3}\), CH\(_{2}\) and CH) were modeled as a single united-atom pseudoatom as a result of the parameterization of the TraPPE-EH force field for n-alkanes which places the LJ site for a hydrogen atom at the center of the corresponding bond [14], and the complication of implementing such a model in a molecular dynamics framework. Note that for the CH group attached to the hydroxyl group in ephedrine, we used CH LJ parameters as in 2-propanol [15]. These differ slightly from the LJ parameters for a CH group for a branched alkane [55]. (The value of \(\sigma\) is smaller).

  6. The exception to this is the value for water which MOSCED doubles (\(v_1=36\) cm\(^3\)/mol) to obtain better agreement with experiment when predicting infinite dilution activity coefficients. We use the value of \(v_1=18\) cm\(^3\)/mol when computing reference solvent normalized activity coefficients using our SMD and SM8 solvation free energies.

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Acknowledgements

C.E.C., J.R.P, and E.J.O. are thankful for financial support through the Undergraduate Summer Scholars (USS) program through the Office of Research for Undergraduates at Miami University. B.T.R., C.E.C. and R.T.L. gratefully acknowledge financial support from the Miami University College of Engineering and Computing. G.G.N., L.F.S. and A.K.P.B. gratefully acknowledge financial support through the Brazil Scientific Mobility Program, sponsored by CAPES and CNPq. Computing support was provided by the Ohio Supercomputer Center and Miami University’s Research Computing Support group.

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    Authors and Affiliations

    1. Department of Chemical, Paper and Biomedical Engineering, Miami University, Oxford, OH, 45056, USA

      Courtney E. Cox, Jeremy R. Phifer, Larissa Ferreira da Silva, Gabriel Gonçalves Nogueira, Ryan T. Ley, Elizabeth J. O’Loughlin, Ana Karolyne Pereira Barbosa, Brett T. Rygelski & Andrew S. Paluch

    2. Departamento de Engenharia Química, Universidade Federal de São João del-Rei, CEP: 36420-000, Ouro Branco, MG, Brazil

      Larissa Ferreira da Silva & Gabriel Gonçalves Nogueira

    3. Instituto de Ciência e Tecnologia, Universidade Federal dos Vales do Jequitinhonha e Mucuri, CEP: 39100-000, Diamantina, MG, Brazil

      Ana Karolyne Pereira Barbosa

    Authors
    1. Courtney E. Cox
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    2. Jeremy R. Phifer
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    3. Larissa Ferreira da Silva
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    4. Gabriel Gonçalves Nogueira
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    5. Ryan T. Ley
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    6. Elizabeth J. O’Loughlin
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    7. Ana Karolyne Pereira Barbosa
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    8. Brett T. Rygelski
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    9. Andrew S. Paluch
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    Corresponding author

    Correspondence to Andrew S. Paluch.

    Additional information

    Courtney E. Cox, Jeremy R. Phifer, Larissa Ferreira da Silva, Gabriel Gonçalves Nogueira, Ryan T. Ley, Elizabeth J. O’Loughlin, Ana Karolyne Pereira Barbosa, Brett T. Rygelski contributed equally to this work.

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    Cox, C.E., Phifer, J.R., Ferreira da Silva, L. et al. Combining MOSCED with molecular simulation free energy calculations or electronic structure calculations to develop an efficient tool for solvent formulation and selection. J Comput Aided Mol Des 31, 183–199 (2017). https://doi.org/10.1007/s10822-016-0001-6

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    • DOI: https://doi.org/10.1007/s10822-016-0001-6

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