Role of Dispersion Interactions in the Polymorphism and Entropic Stabilization of the Aspirin Crystal

Aspirin has been used and studied for over a century but has only recently been shown to have an additional polymorphic form, known as form II. Since the two observed solid forms of aspirin are degenerate in terms of lattice energy, kinetic effects have been suggested to determine the metastability of the less abundant form II. Here, first-principles calculations provide an alternative explanation based on free-energy differences at room temperature. The explicit consideration of many-body van der Waals interactions in the free energy demonstrates that the stability of the most abundant form of aspirin is due to a subtle coupling between collective electronic fluctuations and quantized lattice vibrations. In addition, a systematic analysis of the elastic properties of the two forms of aspirin rules out mechanical instability of form II as making it metastable.

Figure 1

(Top) The unit-cell structures of form-I (left) and form-II (right) aspirin (acetylsalicylic acid). The $\mathbf{b}$ direction is perpendicular to $\mathbf{a}$ and $\mathbf{c}$. (Bottom) View of form-I (left) and form-II (right) aspirin showing the different interlayer hydrogen-bonding motifs.

Figure 2

Phonon density of states for forms I (top) and II (bottom) of aspirin with the DFT-PBE functional in combination with a pairwise (TS) and many-body (MBD) description of vdW interactions. Gaussian broadening of $10{\mathrm{cm}}^{-1}$ is used in this plot. The shaded region highlights the difference in low-frequency phonon modes.

Figure 3

A low-frequency vibrational mode in (a) form-I aspirin as calculated with $\mathrm{PBE}+\mathrm{MBD}(\omega =33{\mathrm{cm}}^{-1})$ and (b) form-II aspirin as calculated with $\mathrm{PBE}+\mathrm{MBD}(\omega =64{\mathrm{cm}}^{-1})$. The vectors indicate the direction and relative magnitude of each atom’s motion. The black lines indicate the unit cells.

Figure 4

Spherical plots of the Young’s modulus of form I and form II aspirin as determined by using DFT-calculated elastic constants. For form I, the $e_2$ and $e_3$ axes are parallel to the $b$ and $c$ lattice vectors, with $e_1$ being perpendicular to $e_2$ and $e_3$. To aid comparison, the form-II elastic constants have been rotated around the $e_1$ axis to make the common, central aspirin dimers of the two forms overlap (cf. Fig. 1).