Diabat method for polymorph free energies: Extension to molecular crystals

Abstract

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.

Pharmaceutical Digital Design: From Chemical Structure through Crystal Polymorph to Conceptual Crystallization Process

“…[135][136][137] A diabat free energy variant of LSMC makes further use of the exact Zwanzig-Bennet relationship 138,139 between free energy diabats. 140 This new method shows promising precision and efficiency for polymorphs of atomic systems, 141 as well as molecular systems 142 (requiring only two unbiased MD simulations in some cases). Our application to carbamazepine demonstrated precision at a level ±0.01 kcal mol -1 (±0.04 kJ mol -1 ) in computed free energy differences with just 5 ns of computing time per polymorph pair.…”

“…Our application to carbamazepine demonstrated precision at a level ±0.01 kcal mol -1 (±0.04 kJ mol -1 ) in computed free energy differences with just 5 ns of computing time per polymorph pair. 142…”

Pharmaceutical Digital Design: From Chemical Structure through Crystal Polymorph to Conceptual Crystallization Process

“…The use of a reference model system, namely the Einstein crystal, − coupled with free energy perturbation (FEP) or thermodynamic integration (TI), provides an alternative method. These methods and some of their modifications have been implemented in MD packages. − Some inherent errors in calculating relative free energies are removed by using the Lattice Switch Monte Carlo (LSMC) method, which has mainly been used in atomic solids. − A further enhancement using the exact Zwanzig-Bennett relationship shows promise. − Application to carbamazepine demonstrated precision at a level of ±0.01 kcal mol –1 (±0.04 kJ mol –1 ) in computed free energy differences with just 5 ns of computing time per polymorph pair . All of these methods are described in greater detail in Sections S2 and S3.…”

Emerging quantum computing algorithms for quantum chemistry

“…These observations call for the accuracy of first-principles quantummechanical approaches, the use, and refinement of many-body dispersion methods, and efficient configuration space exploration, making the computational characterization of molecular crystals one of the most difficult and yet highly important in molecular chemistry. 119,[122][123][124] 4 | QUANTUM ALGORITHMS FOR CHEMISTRY…”

“…The energy differences between polymorphs are typically within 0.5 kcal/mol or less and the structural differences between polymorphs govern their physical properties and functionality. These observations call for the accuracy of first‐principles quantum‐mechanical approaches, the use, and refinement of many‐body dispersion methods, and efficient configuration space exploration, making the computational characterization of molecular crystals one of the most difficult and yet highly important in molecular chemistry 119,122–124 …”