First-Principles Models of Polymorphism of Pharmaceuticals: Maximizing the Accuracy-to-Cost Ratio

Accuracy and sophistication of in silico models of structure, internal dynamics, and cohesion of molecular materials at finite temperatures increase over time. Applicability limits of ab initio polymorph ranking that would be feasible at reasonable costs currently represent crystals of moderately sized molecules (less than 20 nonhydrogen atoms) and simple unit cells (containing rather only one symmetry-irreducible molecule). Extending the applicability range of the underlying first-principles methods to larger systems with a real-life significance, and enabling to perform such computations in a high-throughput regime represent additional challenges to be tackled in computational chemistry. This work presents a novel composite method that combines the computational efficiency of density-functional tight-binding (DFTB) methods with the accuracy of density-functional theory (DFT). Being rooted in the quasi-harmonic approximation, it uses a cheap method to perform all of the costly scans of how static and dynamic characteristics of the crystal vary with respect to its volume. Such data are subsequently corrected to agree with a higher-level model, which must be evaluated only at a single volume of the crystal. It thus enables predictions of structural, cohesive, and thermodynamic properties of complex molecular materials, such as pharmaceuticals or organic semiconductors, at a fraction of the original computational cost. As the composite model retains the solid physical background, it suffers from a minimum accuracy deterioration compared to the full treatment with the costly approach. The novel methodology is demonstrated to provide consistent results for the structural and thermodynamic properties of real-life molecular crystals and their polymorph ranking.


Computational setup
This section provides details on how individual components of the quasi-harmonic processing were combined to model finite-temperature and finite-pressure properties of the seven target crystal structures, which are depicted in Figure S1 and described in Table S1 and Table S2.
Table S3 provides details on the computational setup of the raw M1 and M7 quasi-harmonic approaches, whereas the remaining composite approaches M2 to M6 are described in Table S4.

Table S1
Experimental unit-cell parameters (given in Å and deg.) of the target crystal structures determined in the literature at reference temperature Tref (in K).

Table S4
Definition of the composite quasi-harmonic methods developed in this work along with the color-coding occurring throughout the methods validation in the main paper.Individual methods combine results obtained with DFTB3-D4/3ob (abbreviated here as DFTB) and PBE-D3(BJ)/PAW (abbreviated as PBE).b Calculation of a single optimized unit-cell volume only, corresponding to the minimum of a Eel(V) curve provided by the target method.c Whole raw Eel(V) curve shifted horizontally to place its minimum to the minimum coordinate observed for the target method.d Initial calculations of the phonons vs. volume trends.e Calculation of phonon characteristics at a single unit-cell volume only, typically corresponding to the minimum of the target Eel(V) curve.f Phonons vs. volume trends constructed using the target phonon reference at a single volume and Grüneisen parameters determined from the phonon source method.

Materials
Description of samples treated in this work is given in Table S5.They were used without any purification and their purity was verified by the van't Hoff method.

X-ray powder diffraction
Identity of the crystal forms was verified by X-ray powder diffraction (XRPD) and the related diffractograms were analyzed with the software HighScore Plus in combination with annually updated powder diffraction databases PDF4+ and PDF4/Organics.The XRPD analysis was performed using a θ-θ powder diffractometer X'Pert 3 Powder from PANalytical in Bragg-Brentano para-focusing geometry using wavelength CuKα radiation (λ = 1.5418Å, U = 40 kV, I = 30 mA).The samples were scanned at temperature (298.15 ± 3) K in the range of 5° to 50°2θ with a step size of 0.039°2θ and 0.7 s for each step.

Phase behavior study
The phase behavior was investigated with a heat-flux differential scanning calorimeter (TA DSC2500, TA Instruments, USA) whose temperature and enthalpy calibration was performed using peak areas of melting endotherms and onset melting temperatures of 1,3-difluorobenzene (Sigma-Aldrich, molar purity 0.9995), n-octane (Supelco, molar purity 0.997), indium, tin (both from a set of calibration substances for temperature and heat calibration of DSC, H. K. Cammenga, GEFTA, molar purities >0.9999), distilled and demineralized water (Millipore RQ, France, molar purity 0.9999), naphthalene (Aldrich 99+%, purified by zone refining, molar purity 0.9999), and benzoic acid (NIST SRM 39j, vacuum-dried, molar purity 0.9999) for several respective heating rates.Note that 1,3-difluorobenzene should be used as a DSC calibration standard with caution as it has two polymorphs with close melting points. 8ot stated otherwise, the results presented were obtained at a heating rate of 5 K min −1 .
Sample loads of 5 to 10 mg were determined by an analytical balance with a readability of 0.01 mg, which was periodically calibrated.The overall molar purity of the samples was determined from the DSC thermograms using the van't Hoff method.Onset slope used for correction for the nonzero heating rate was determined as an average from calibration measurements for water, naphthalene, indium, and tin.The estimate of the standard uncertainty of molar purity x is u(x) = 0.15(1−x).

Heat capacity measurements
The heat capacity measurements were carried out in the temperature range from 240 to 350 K using a Tian-Calvet calorimeter Microcalvet (SETARAM, France) employing the continuous heating method 9 with a three-step methodology. 9The following steps were performed to obtain the heat capacity of a sample: i) measurement of the sample, ii) measurement of the reference material (synthetic sapphire, NIST standard reference material No. 720), and iii) measurement with both cells empty (so-called blank experiment).A detailed description of the performance of the Microcalvet calorimeter and calibration results are provided in ref. 10

Thermodynamic data obtained in this study
In the following text, an alternative notation of individual polymorphs is used.As explained in Table S6, notation crI is equivalent to FFA1 in discussion relevant for flufenamic acid, and crIII is equivalent to STZ3 in the context of sulfathiazole.

Phase behavior of flufenamic acid
Flufenamic acid has a complex phase behavior, which has been extensively studied and is relatively well described, 4 except for few issues.Perhaps the most critical is the inconsistency between Table 6.1 and Figure 6.1 in the SI of ref. 4 , which are in conflict with respect to order of melting temperatures of forms II and III.Based on comparison with our results and previous literature, [11][12] it seems that form III melts lower than I and II.At the same time, it has a higher melting enthalpy than form I, which means that the forms are enantiotropic and at low temperatures, form III should become thermodynamically stable, as confirmed in ref. 12 .runs), which slightly lowers the achievable uncertainty of the DSC results.In case of fast cooling, the sample has not crystallized completely and a glass transition could be observed at 283.1 ± 0.4 K at a heating rate of 5 K min −1 .) 427 (ref. 14) 415.5 (ref. 15) 4.9 (ref. 15) crV d ~434 6.6 ± 0.3 STZ5 = crV Annealed at 435 K l 469.0 ± 0.3 28.8 ± 0.8 469.7 (ref. 15) 31.6 (ref. 15) STZ1 = crI Annealed at 470 K l 474.2 ± 0.3 28.0 ± 0.8 475.0 (ref. 15) 474 (ref. 13) 27.9 (ref. 15) STZ4 = crIV e Recrystallized from water (ref.e Form IV with about 15 % of phase III according to XRPD.Small amount of residual water (wH2O = 0.0002) was detected by a eutectic peak close to 273 K.
The "as received" form of flufenamic acid was I. Form III was prepared by melting the material at 433 K and left to cool to room temperature spontaneously.According to XRPD, this sample contained 13% of form I. Upon heating in DSC, the same sample exhibited an endothermal solid-solid transition before melting as form I, which is in agreement with the enantiotropic relationship of phases III and I.Other phases were not successfully prepared in larger amounts, only within the DSC experiments.Form II (identified based on its melting temperature and enthalpy) was observed to crystallize in some runs with slow cooling of the melt.Some other forms were observed during the experiments (probably V and VI), but they could not be unambiguously identified because of close melting temperatures and fusion enthalpies with form IV. The typical thermograms observed for flufenamic acid including some runs with concomitant occurrence of more forms are visualized in Figure S2.Melting

Phase behavior of sulfathiazole
Sulfathiazole was previously shown to form five crystal structures and the ways for their preparation were described. 15According to our observations, sulfathiazole abruptly decomposes in liquid form at temperatures above approximately 445 K.When the melt is cooled to lower temperatures, the decay stops, but the sample was never observed to crystallize.
The observed glass transition temperatures varied between 329 and 346 K for various samples, probably depending on their purity.The lower results would be in agreement with the Beaman-Kauzmann rule with Tg/Tm ≈ 0.69, but not the higher ones.We assume, that because of the instability of the melt, it not possible to determine the glass transition temperature of sulfathiazole accurately with the conventional technique.
The "as-received" form of sulfathiazole was crIII, which is supposedly thermodynamically stable at the room temperature.Unlike in the literature reports, form III transformed to crV upon heating at around 435 K.The large peak of quantitative transformation was accompanied with two minor peaks, which might either mean that the sample does not recrystallize directly from III to V, but through a sequence of several transformations, or that these correspond transformations of trace forms contained in the sample to crV or to crI.Upon additional cooling, form crV incongruently melts at 469.0 ± 0.3 K and gives form I, which melts at 474.2 ± 0.3 K.
Preparation of a larger amount of form V was attempted by annealing the material at 455 K, but the XRPD analysis corresponded to a mixture of V and I.Because of the incongruent melting, it is not possible to verify or refute the concomitant occurrence of V and I in the DSC experiments.On the other hand, the peak of III-V transformation has a regular shape, which suggests a simple recrystallization process.Because of their close fusion enthalpies, it is not definite if forms I and V are monotropic or enantiotropic, but at least at elevated temperatures, form V is less stable than I and a spontaneous recrystallization may proceed between the two forms.Larger amount of form I was prepared by annealing the material at 470 K and according to XRPD, the sample was crystallographically pure, although it turned slightly grey because of thermal decomposition.
Form IV was prepared according to the procedure suggested by Abu Bakar et al. 15 , by cooling recrystalization from water.Crystal stucture of the prepared sample was verified by XRPD with a possible contamination by 15% of form III, as is common according to the literature. 13DSC experiments with this sample showed very similar behaviour as form III did.The sample recrystallized to form V showing three peaks, of which the largest was located at lower temperature than in case of form III and was also slightly smaller.Forms III and IV are thus very close both from the crystallographic and thermodynamic point of view.
The typical observed thermograms are visualized in Figure S3.Phase-transition temperatures and enthalpies of the observed forms are compared with the literature in Table S6.

Heat capacities
Heat capacities of forms of flufenamic acid and sulfathiazole that were successfully prepared in larger amounts are given in Table S7.According to the XRPD analysis, form III of flufenamic acid contained about 13% of form I and form IV of sulfathiazole about 15 % of form III. Since heat capacities of these concomitant forms are practically identical, no corrections were performed.In one experiment, heat capacities of mixture of forms V+I of flufenamic acid were determined.According to XRPD analysis performed six days later, the composition was 56% of form I and 44% of form V. The heat capacities of form V in Table S7 were calculated by linear extrapolation with the assumption that this composition was constant.However, the sample more probably continuously recrystallized from form V to more stable form I and the real heat capacity of form V can be in between the datasets labeled 'form I+V' and 'form V'.
The experimental heat capacities were represented with a polynomial equation, the parameters of which are given in Table S8.Heat capacities of form I and form III of flufenamic acid are compared in Figure S4.Form III has steeper temperature dependence of the heat capacity curve, which correlates with the assumption that the two phases are enantiotropic.
Heat capacities of different forms of sulfathiazole are compared in Figure S5.Forms III and IV that have similar crystallographic patterns and close melting properties have also equal heat capacities within the uncertainty of the measurement.Form I of sulfathiazole that is enantiotropic with respect to forms III and IV and has a significantly higher fusion entropy also exhibits higher heat capacity over the whole range of temperatures.At high temperatures, the heat capacity curves approach each other and should intersect around 383 K (I and III) or 405 K (I and IV), which is still below the observed III-I and IV-I transition temperatures.This observation is again in agreement with the enantiotropic relationship between forms I and III and forms I and IV.Form V of sulfathiazole was only studied in a mixture with form I, and there is a lower level of certainty about its heat capacities.Its heat capacities seem to be lower than that of form I, but higher than that of form III and IV.As in the case of form I, they seem to intersect with heat capacities of forms III and IV at elevated temperatures.

Table S7
Experimental heat capacities of flufenamic acid and sulfathiazole (in J K −1 mol − c According to the XRPD, sample of form IV of sulfathiazole contained up to 15 % of form III. Since heat capacities of form III and IV are practically identical, no corrections were performed.Small amount of residual water (wH2O = 0.0002) was detected through a eutectic peak close to 273 K. d According to the XRPD performed six days later, the mixture contained 56% of form I and 44% of form V.
e Calculated from experimental heat capacities of form I and mixture (I+V) in previous columns.(ibuprofen).The calculation results were scaled by a constant factor below the lower limit of measurements (240 K for FFA1 and STZ3, 260 K for STZ4, and 216 K for IBURS1and IBUS) to match the experimental value at the minimal temperature, enabling a smooth joint of the two data sets as depicted in Figure S6.Absolute entropy profiles were then constructed via essential thermodynamic integration, assuming that there is zero residual entropy for these materials at 0 K.Given pseudo-experimental heat capacities are listed in Table S9 and entropies in Table S10.

Table S9
Pseudo-experimental a isobaric heat capacities of selected polymorphs of the target molecular crystals (in J K −1 mol −1 ).   a Data are based on scaling the PBE-D3/PAW results (M7) by a factor ξ (given in Figure S6) to match the raw experimental data (at the lower edge of the experimental range).

Polymorph ranking
Experimental data on heat capacities and solid-solid and/or solid-liquid phase transition temperatures and enthalpies determined in this work were used to calculate profiles of the Gibbs energy change ΔI α Gm 0 (T), corresponding to transitions from the high-temperature polymorphs FFA1 and STZ1 to different phases.Figure S7 and Figure S8 also compare the current ranking with that arising from literature data on phase behavior of flufenamic acid and sulfathiazole, respectively.
Our results agree qualitatively well with the literature for flufenamic acid, both confirming that phases FFA1 and FFA3 are the most stable at high-temperatures and ambient-temperatures.The most significant difference is the position of the triple point temperature of crI and crIII.
According to the fusion enthalpies and melting temperatures observed in this work and in literature, 4 it should occur at around 260 K and 340 K, respectively.The difference is obviously given by the long temperature extrapolation, which exemplified the uncertainties in the experimental data.An enantiotropic phase transition of form III to form I at 315.2 K was described. 12The triple point temperature must therefore be below 315 K, since the solid-solid transition can superheat noticeably (as e.g. in this work, where it was observed at 356 K, see Table S6), but may not occur below the equilibrium temperature.Mutual stability of forms III and I at 298 K thus remains unclear.
For sulfathiazole, very small differences among individual polymorphs make it difficult to establish a definite ranking of their stability.Whereas the phase STZ1 is clearly the hightemperature structure, current experimental uncertainties admit that either STZ3 of STZ4 is the most stable modification at ambient-temperatures. The most beneficial clue to prioritize one of the possibilities is the identity of the commercial form.Forms III and IV crystallize concomitantly in most cases, 15 but pure form III is commercially available, which renders very improbable that a pure metastable form, which is obtainable only with severe difficulties, would be distributed.On the other hand, slow recrystallization from the concomitant mixture of III and IV to the more stable form may easily occur during the storage and expedition.Stability ranking based on our experimental data (Figure S8a) is thus more probable.
To derive the polymorph differences in terms of enthalpy and Gibbs energy in Table 2 and in Figure S7 and Figure S8, only experimental phase transition temperature and enthalpy data were used.Operating range of the employed calorimeters does not enable to cover the whole interval from 300 K up to the melting temperatures.Furthermore, heat capacities of both polymorphs within the ranked polymorph pairs are very similar (for STZ), or the higher-energy polymorph could not be prepared in a sufficient quantity to measure its heat capacity reliably (for FFA).However, we incorporated the expected uncertainties of the measured heat capacities to estimate the overall uncertainty associated to the temperature adjustment of ΔH and ΔG terms to 300 K.

Densities of crystals
Density data were searched for all target materials in the Cambridge Structural Database.There are multiple entries for all the structures, except IBURS2 polymorph.Figure S9 to Figure S11 depict that although there are crystal structures resolved at more than one temperature, the interlaboratory scatter of the unit-cell volume and related crystal densities can be significant.
Therefore, we performed interpolations of the crystal densities with a cubic polynomial only for structures where data were available at least for three distinct temperatures, all consistently following a clear trend.That scenario was fulfilled only for IBURS1, STZ3, and STZ4, for which we were also able to derive experimental information on thermal expansivities.Data points outlying by more than 3 kg m -3 from the cubic interpolation were omitted.In a similar way, variable-pressure density data were interpolated for IBURS1.Note that for the sake of consistency of the thermal expansivity or isothermal compressibility data, it is safer to use multiple data points determined on a single apparatus over a wide temperature or pressure range, rather than data points at multiple conditions each obtained on a different apparatus.
Pressure dependent data for IBURS1 and their interpolation is given in Figure S12.

Components of QHA
Experimental data on heat energy -volume curves Eel(V) for polymorphs which are not shown in Figure 3 in the main paper are depicted in Figure S13.Additional characteristics of all the computed Eel(V) are given in Table S11.S14.0] Such a better performance of DFTB for modeling the stretch modes can be traced to its parametrization strategy. 21 this context, it is difficult to assess the accuracy of the predicted frequencies of any O-H and N-H stretching modes in our target crystals that vary by hundreds of cm −1 upon using either   A typical fast decay of the Grüneisen parameters, decreasing from units for the low-frequency lattice modes towards zero for the intramolecular modes can be observed in Figure S16.A detailed look reveals that PBE-D3/PAW yields somewhat lower Grüneisen parameters than DFTB3-D4 for the low-frequency modes.PBE-D3/PAW also captures negative values of the Grüneisen parameters for the O-H and N-H stretching modes, which is a consequence of the hydrogen bonding. 22The DFTB3-D4 method also yields a larger scatter of results.In this context, attention should be paid to the magnitude of the ΔV0 off-set.In cases of large ΔV0, M1 phonon calculations should be performed over a sufficiently broad volume interval that extends to the V0 PBE value to maximize the chances for a sensible phonon extrapolation.In this work, we evaluated the DFTB Grüneisen parameters for each phonon mode from a fit over at least six crystal volumes.
Phonon dispersion was fully accounted for in all considered crystal volumes in the DFTB calculations.Ratio of the Helmholtz vibrational energies obtained with and without the phonon dispersion (including its volume dependence), was then used to scale the Helmholtz energies computed from the Grüneisen-extrapolated PBE frequencies.
Characteristics of the vibrational Helmholtz energies Avib(V) at 300 K with respect to crystal volume are given in Table S13 to enable validation of the newly developed composite M4 model with raw methods M1 and M7.

Figure S16.
Grüneisen parameters that can be used to extrapolate phonon frequencies of the target molecular crystals.Values determined from fits over phonon frequencies explicitly calculated using PBE-D3/PAW (purple) for 5 crystal volumes and using DFTB3-D4/3ob (red) for at least 6 crystal volumes.

Table S13
Comparison of Avib values (in kJ mol −1 ) at 300 K, their first derivatives (in J cm −3 ) and second derivatives (in J mol cm −6 ) with respect to the molar volume calculated using the raw M1 (DFTB3-D4/3ob) and M7 (PBE-D3/PAW) methods and their composite M4 approach.All data were evaluated for the volumes corresponding to the minima of the respective Eel(V) curves.

Results of QHA
Comparison of the experimental data on molar volumes with the results calculated in this work, which are not shown in Figure 5 in the main document, are depicted in Figure S17.Calculated molar volumes at selected temperatures are given in Table S14.Analysis of the anisotropy of the target crystals is given in Figure S18 and Figure S19.Calculated absolute entropies for all the target crystals at 300 K are listed in Table S15 and their comparison with the pseudoexperimental data is depicted in Figure S20.Analysis of the agreement of individual models with the reference M7 in terms of the first derivatives of Gibbs energy is given in Figure S21.
Calculated isobaric heat capacities for all the target crystals at 300 K are listed in Table S16 and their mutual comparison is depicted in Figure S22 (except for IBURS1, which is shown in

Figure S22
. Isobaric heat capacities of selected target crystal phases at zero pressure calculated using individual formulations of the quasi-harmonic approximation M1 to M7 (colored lines, see Figure 2 in the main paper for explanation), and experimental reference data (gray diamonds).Dashed lines are optionally used to make multiple overlapping curves visible.

Figure S1 .
Figure S1.Illustration of target crystal structures of model APIs used for validation of computational methods throughout this work.

a
Initial construction of the entire Eel(V) curve.
. Based on the calibration measurements, the combined expanded uncertainty Uc( o ,m p C ) (at the 0.95 level of confidence) of the heat capacity measurements with the given methodology was estimated to be Uc(

Figure S2 .
Figure S2.Typical thermograms observed for flufenamic acid.Starting form: , "as received" material -form I, , form II, , form III (or its mixture with form II), , form V, , form IV, , mixture III+I, , mixture VI+II.All experiments are recorded at a heating rate of 5 K min −1 , except for form V (olive line) and mixture III+I (cyan line), which are at 10 K min −1 and were scaled by a factor of 1/2 for clarity.

Figure S3 .
Figure S3.Typical thermograms observed for Sulfathiazole.Starting form: , "as received" material -form III, , form I, , form IV, , form V. All experiments are recorded at a heating rate of 5 K min −1 , except for form V (green line), which is at 10 K min −1 .

Figure S6 .
Figure S6.Illustration of the development of pseudo-experimental isobaric heat capacities (Est) based on scaling the PBE-D3/PAW results (M7) by a factor ξ to match the raw experimental data (Exp) at 240 K (the lower edge of the experimental range).Note that ξ is kept constant below 240 K but it becomes slightly temperature dependent above 240 K to account for the contributions to Cp from the thermal expansion.

Figure S7 .
Figure S7.Experimental polymorph ranking for flufenamic acid: a) according to data observed in this work; b) according to phase transition parameters from the literature. 4Legend: , liquid, , form I, , form II, , form III.

Figure S8 .
Figure S8.Experimental polymorph ranking for sulfathiazole: a) according to data observed in this work; b) according to phase transition parameters from the literature. 15Legend: , liquid, , form I, , form II, , form III, , form IV.

Figure S9 .
Figure S9.Experimental density data for two crystal forms of ibuprofen at ambient pressure, all culled from the respective CSD entries.A cubic fit of the variable-temperature density data showing consistency (full symbols) is depicted for IBURS1.

Figure S10 .
Figure S10.Experimental density data for two crystal forms of flufenamic acid, all culled from the respective CSD entries.

Figure S11 .
Figure S11.Experimental density data for two sulfathiazole crystal forms, all culled from the respective CSD entries.Cubic fits of the variable-temperature density data showing consistency (full symbols) are depicted.

Figure S12 .
Figure S12.Experimental density data for crystalline ibuprofen at 296 K, all culled from the respective CSD entries.A cubic fit of the variable-pressure density data showing consistency (full symbols) is depicted.
DFTB or PBE methods.Precise positions of the respective phonon signals are strongly affected by the intensity of hydrogen bonding in crystals.Since the enantiopure IBUS exhibits O-H modes at lower wavenumbers than the racemic IBURS1 phase, one can assume from the PBE phonon frequencies that the hydrogen bonding between the carboxyl groups is stronger in the former structure.Similarly, stretch modes of the O-H donors in flufenamic acid are red-shifted with respect to the stretch modes of the N-H donors.For the larger unit cell of STZ3, phonon signals are more split in a more complex way than for STZ4.Hydrogen bonds of the imino N-H1 donors are predicted to be somewhat stronger in STZ3, whereas those of the amino N-H2 donors are stronger in STZ4.

Figure S14 .
Figure S14.Overview of densities of phonon states calculated for geometries corresponding to the minimum of the Eel(V) curve for the target polymorphs of ibuprofen (IBU), flufenamic acid (FFA) and sulfathiazole (STZ).Data in red and purple stand for results of PBE-D3/PAW (M7) and DFTB3-D4/3ob (M1) methods, respectively.

Figure 7
Figure 7 in the main text).Calculated coefficients of isobaric thermal expansion for all target materials except IBURS1 (given in Figure 7 in the main text) are depicted in Figure S23.Analysis of the agreement of individual models with the reference M7 in terms of the first derivatives of Gibbs energy is given in Figure S24.

Figure S17 .
Figure S17.Equilibrium molar volumes for selected target crystal phases at zero pressure calculated using individual formulations of the quasi-harmonic approximation M1 to M7 (colored lines, see Figure2in the main paper for explanation), and experimental reference data (gray diamonds).

Figure S18 .
Figure S18.Comparison of thermal expansion of unit cells of target crystal structures in the directions of individual lattice vectors.Data represent relative prolongation of individual unitcell parameters upon heating from 100 K up to the ambient conditions.Results shown for literature experimental data (sources referenced in Figures S9 to S12) and three selected computational models (M1, M4, M7) adopted in this work.

Figure S19 .
Figure S19.Comparison of thermal expansion of the target crystal structures in terms of the difference of their linear expansion coefficients in the crystallographic directions of minimum and maximum thermal expansion.

Figure S20 .
Figure S20.Absolute entropies of selected target crystal phases at zero pressure calculated using individual formulations of the quasi-harmonic approximation M1 to M7 (colored lines, see Figure2in the main paper for explanation), and pseudo-experimental reference data (gray diamonds).Dashed lines are optionally used to make multiple overlapping curves visible.

Figure S21 .
Figure S21.Absolute average deviations (AAD) of molar volumes (Vm) and absolute entropies (Sm) at 300 K and zero pressure calculated using individual formulations of the quasi-harmonic approximation (M1 to M6, see Chyba! Nenalezen zdroj odkazů.for explanation) from the results of the M7 model.Standard deviations of the errors of calculated properties that were observed for individual target crystal structures are depicted as error bars to illustrate scatter of computational errors yielded by the considered methods.

Figure S23 .
Figure S23.Isobaric thermal expansivity coefficients of selected target crystal phases at zero pressure calculated using individual formulations of the quasi-harmonic approximation M1 to M7 (colored lines, see Figure2in the main paper for explanation), and experimental reference data (gray diamonds -rigorously derived from variable-temperature experimental data for STZ3 and STZ4; gray dashed lines -tentative estimate from two literature data points).Colored dashed lines are optionally used to make multiple overlapping curves visible.

Figure S24 . 5 .
Figure S24.Absolute average deviations (AAD) of isobaric molar heat capacities (Cp,m) and isobaric thermal expansion coefficients (αp) at 300 K and zero pressure calculated using individual formulations of the quasi-harmonic approximation (M1 to M7, see Figure2for explanation) from the results of the M7 model.

Figure S25 .
Figure S25.Gibbs energy change ΔG related to the phase transition between the target polymorphs of RS-ibuprofen, flufenamic acid and sulfathiazole.Experimental data and their expanded uncertainties are depicted with gray lines and shaded areas, respectively.Single-point MP2C-F12/aug-cc-pVDZ refinement of proximate pair interaction energies within a 8 Å cutoff distance in the crystal lattice and a MP2/aug-cc-pVDZ refinement of the monomer energies were applied in all cases of the solid colored lines (with respect to DFTB3 energies for M1, and with respect to PBE elsewhere).Results of raw PBE-D3/PAW and DFTB3-D4/3ob electronic energies without this refinement are given with dashed colored lines.

Figure S26 .
Figure S26.Pair interactions calculated for proximate molecular pairs within the crystal lattices of two polymorphs of racemic ibuprofen using three quantum-chemical levels of theory.Data shown with respect to the distance d related to the closest atomic contact of the two molecules within a dimer.

Figure S27 .
Figure S27.Pair interactions calculated for proximate molecular pairs within the crystal lattices of two polymorphs of flufenamic acid using three quantum-chemical levels of theory.Data shown with respect to the distance d related to the closest atomic contact of the two molecules within a dimer.

Figure S28 .
Figure S28.Pair interactions calculated for proximate molecular pairs within the crystal lattices of two polymorphs of sulfathiazole using three quantum-chemical levels of theory.Data shown with respect to the distance d related to the closest atomic contact of the two molecules within a dimer.

Figure S29 .
Figure S29.Sensitivity analysis of the Gibbs energy change ΔG related to the phase transition between the target polymorphs of sulfathiazole.Experimental data are depicted with gray line.Colored lines represent results of raw PBE-D3/PAW quasi-harmonic ranking where the absolute molar entropy of phase STZ4 was artificially increased by given constant values.

Figure S30 .
Figure S30.Sensitivity analysis of the Gibbs energy change ΔG related to the phase transition between the target polymorphs of sulfathiazole.Experimental data are depicted with gray line.Colored lines represent results of raw PBE-D3/PAW quasi-harmonic ranking where the isobaric heat capacity of phase STZ4 was artificially scaled by given values.

Table S5
Sample descriptions.
a Thin-layer chromatography.b Determined from van't Hoff plot of the DSC measurements.Sulfathiazole decomposes upon melting, purity evaluated by the DSC should be considered a lower bound of the true value.c Assay by electrophoresis.
Transformation proceeds in three steps, the reported values correspond to the largest peak.It is not clear, if the minor peaks correspond to consecutive transformations through other forms or to transformations of trace forms to crV or to crI. d temperatures and fusion enthalpies of forms I, II and III are compared with literature in Table S6.Melting temperatures observed in this work are in good agreement with ref. 11, but they are about 1.5 K lower than in ref. 4. Since our calibration procedure comprises of seven compounds and the presented results are corrected for impurity content, it seems more probable that the systematic difference is introduced by the literature values.
According to the XRPD, sample of form III contained up to 13% of form I. Since heat capacities of form III and I are practically identical, no corrections were performed.
a The combined expanded (k = 2) uncertainty of the experimental heat capacity data is Uc = 0.006 b

Table S8
Parameters of equation 1 for isobaric heat capacity of the APIsDue to the from-below limited operating range of the Microcalvet calorimeter, we had to derive pseudo-experimental absolute entropies of the crystal phase from the raw experimental heat capacity and from the PBE-D3/PAW quasi-harmonic heat capacities.The experimental data were determined in this work (flufenamic acid and sulfathiazole) or taken from ref.16 Figure S4.Heat capacities of flufenamic acid experimentally determined in this work.Figure S5.Heat capacities of sulfathiazole experimentally determined in this work.

Table S10
Pseudo-experimental a absolute entropies of selected polymorphs of the target molecular crystals (in J K −1 mol −1 ) a

Table S11
Curvatures κ of calculated Eel(Vm) curves defined as the second derivatives of the energy with respect to the molar volume, evaluated at the minimum of the Eel(Vm) curve.

Table S12
Comparison of experimental unit-cell parameters with their counterparts belonging to optimized unit-cell geometries corresponding to minima of the respective Eel(Vm) curves.Raw data given in Å or degrees.Relative percentage deviations of calculated unit-cell parameters δi given for reader's convenience.Experimental data entries were collected at 90 to 100 K, always representing reference data relevant at the lowest available temperature.The only exception is the IBURS2 structure investigated at 258 K.