Anharmonic and Quantum Fluctuations in Molecular Crystals: A First-Principles Study of the Stability of Paracetamol.

Molecular crystals often exist in multiple competing polymorphs, showing significantly different physicochemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful form, a real challenge due to the combinatorial search space, and the complex interplay of subtle effects that work together to determine the relative stability of different structures. Here we take a comprehensive approach based on different flavors of thermodynamic integration in order to estimate all contributions to the free energies of these systems with density-functional theory, including the oft-neglected anharmonic contributions and nuclear quantum effects. We take the two main stable forms of paracetamol as a paradigmatic example. We find that anharmonic contributions, different descriptions of van der Waals interactions, and nuclear quantum effects all matter to quantitatively determine the stability of different phases. Our analysis highlights the many challenges inherent in the development of a quantitative and predictive framework to model molecular crystals. However, it also indicates which of the components of the free energy can benefit from a cancellation of errors that can redeem the predictive power of approximate models, and suggests simple steps that could be taken to improve the reliability of ab initio crystal structure prediction.

[1]  A. Tkatchenko,et al.  Role of dispersion interactions in the polymorphism and entropic stabilization of the aspirin crystal. , 2014, Physical review letters.

[2]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[3]  Free energy calculations for a flexible water model. , 2011, Physical chemistry chemical physics : PCCP.

[4]  Alexandre Tkatchenko,et al.  Collective many-body van der Waals interactions in molecular systems , 2012, Proceedings of the National Academy of Sciences.

[5]  A. Tkatchenko,et al.  Wavelike charge density fluctuations and van der Waals interactions at the nanoscale , 2016, Science.

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  V. Barone,et al.  Toward reliable density functional methods without adjustable parameters: The PBE0 model , 1999 .

[8]  J E Kipp,et al.  The role of solid nanoparticle technology in the parenteral delivery of poorly water-soluble drugs. , 2004, International journal of pharmaceutics.

[9]  D. Manolopoulos,et al.  An efficient ring polymer contraction scheme for imaginary time path integral simulations. , 2008, The Journal of chemical physics.

[10]  Mariana Rossi,et al.  Stability of Complex Biomolecular Structures: van der Waals, Hydrogen Bond Cooperativity, and Nuclear Quantum Effects. , 2015, The journal of physical chemistry letters.

[11]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[12]  S. Kashino,et al.  The orthorhombic form of p-hydroxyacetanilide , 1974 .

[13]  Miranda L. Cheney,et al.  Effects of Crystal Form on Solubility and Pharmacokinetics: A Crystal Engineering Case Study of Lamotrigine , 2010 .

[14]  Michele Parrinello,et al.  Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach , 2005, Comput. Phys. Commun..

[15]  A. Michaelides,et al.  Quantum nature of the hydrogen bond , 2011, Proceedings of the National Academy of Sciences.

[16]  Shumin Zhu,et al.  International Journal of Pharmaceutics , 2015 .

[17]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

[18]  I. Bruno,et al.  Cambridge Structural Database , 2002 .

[19]  Thomas E. Markland,et al.  Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges. , 2016, Chemical reviews.

[20]  Claire S. Adjiman,et al.  Towards crystal structure prediction of complex organic compounds – a report on the fifth blind test , 2011, Acta crystallographica. Section B, Structural science.

[21]  M. Haisa,et al.  The Monoclinic Form of p‐Hydroxyacetanilide , 1976 .

[22]  M. Neumann,et al.  Can crystal structure prediction guide experimentalists to a new polymorph of paracetamol , 2009 .

[23]  Thomas E. Markland,et al.  Unraveling quantum mechanical effects in water using isotopic fractionation , 2012, Proceedings of the National Academy of Sciences.

[24]  Michele Ceriotti,et al.  i-PI: A Python interface for ab initio path integral molecular dynamics simulations , 2014, Comput. Phys. Commun..

[25]  Richard J. Needs,et al.  Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice , 2015, 1508.02969.

[26]  Tejender S. Thakur,et al.  Significant progress in predicting the crystal structures of small organic molecules--a report on the fourth blind test. , 2009, Acta crystallographica. Section B, Structural science.

[27]  T. Halgren.  Merck molecular force field. I. Basis, form, scope, parameterization, and performance of MMFF94 , 1996, J. Comput. Chem..

[28]  L. Daemen,et al.  Polymorphism of paracetamol: a new understanding of molecular flexibility through local methyl dynamics. , 2014, Molecular pharmaceutics.

[29]  A. Tkatchenko,et al.  Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. , 2009, Physical review letters.

[30]  G. Day,et al.  Static and lattice vibrational energy differences between polymorphs , 2015 .

[31]  Teter,et al.  Separable dual-space Gaussian pseudopotentials. , 1996, Physical review. B, Condensed matter.

[32]  Joost VandeVondele,et al.  Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases. , 2007, The Journal of chemical physics.

[33]  VINCENT ZOETE,et al.  SwissParam: A fast force field generation tool for small organic molecules , 2011, J. Comput. Chem..

[34]  S. Grimme,et al.  Accurate Modeling of Organic Molecular Crystals by Dispersion-Corrected Density Functional Tight Binding (DFTB). , 2014, The journal of physical chemistry letters.

[35]  F. Allen.  The Cambridge Structural Database: a quarter of a million crystal structures and rising. , 2002, Acta crystallographica. Section B, Structural science.

[36]  L. Blair.  A prediction. , 1995, Hospitals & health networks.

[37]  Michele Ceriotti,et al.  Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei. , 2012, Physical review letters.

[38]  Ross H McKenzie,et al.  Effect of quantum nuclear motion on hydrogen bonding. , 2014, The Journal of chemical physics.

[39]  Miss A.O. Penney.  (b) , 1974, The New Yale Book of Quotations.

[40]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[41]  J. R. Helliwella,et al.  Acta Crystallographica Section B: Structural Science , 2005 .

[42]  Matthias Scheffler,et al.  Ab initio molecular simulations with numeric atom-centered orbitals , 2009, Comput. Phys. Commun..

[43]  J. Bauer,et al.  Ritonavir: An Extraordinary Example of Conformational Polymorphism , 2001, Pharmaceutical Research.

[44]  M. Scheffler,et al.  Impact of vibrational entropy on the stability of unsolvated peptide helices with increasing length. , 2012, The journal of physical chemistry. B.

[45]  Many-body dispersion interactions in molecular crystal polymorphism. , 2012, Angewandte Chemie.

[46]  J. Gauchi,et al.  Polymorphism of paracetamol: relative stabilities of the monoclinic and orthorhombic phases inferred from topological pressure-temperature and temperature-volume phase diagrams. , 2005, Journal of pharmaceutical sciences.

[47]  L. Christophorou.  Science , 2018, Emerging Dynamics: Science, Energy, Society and Values.

[48]  A. Tkatchenko,et al.  Accurate and efficient method for many-body van der Waals interactions. , 2012, Physical review letters.

[49]  G. Day,et al.  The prediction, morphology, and mechanical properties of the polymorphs of paracetamol. , 2001, Journal of the American Chemical Society.

[50]  Michele Ceriotti,et al.  Efficient methods and practical guidelines for simulating isotope effects. , 2012, The Journal of chemical physics.

[51]  Mariana Rossi,et al.  Inverse Temperature Dependence of Nuclear Quantum Effects in DNA Base Pairs , 2016, The journal of physical chemistry letters.

[52]  A. Tkatchenko,et al.  Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem. , 2012, The Journal of chemical physics.

[53]  Matthew J. Rosseinsky,et al.  Crystal Growth & Design , 2011 .

[54]  A. Tkatchenko,et al.  Understanding molecular crystals with dispersion-inclusive density functional theory: pairwise corrections and beyond. , 2014, Accounts of chemical research.

[55]  V Kapil,et al.  Accurate molecular dynamics and nuclear quantum effects at low cost by multiple steps in real and imaginary time: Using density functional theory to accelerate wavefunction methods. , 2015, The Journal of chemical physics.

[56]  Alderley Park,et al.  Pharmaceutical Research , 1957, Canadian journal of comparative medicine and veterinary science.

[57]  Giovanni Bussi,et al.  Colored-Noise Thermostats à la Carte , 2010, 1204.0822.