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. 2024 Apr 12;128(16):4021–4032. doi: 10.1021/acs.jpcb.4c00582

Variation of Activation Volume as an Indicator of the Difference in Clusterization Phenomenon Induced by H-Bonding and F−Π Stacking Interactions in Enantiomers and a Racemate of Flurbiprofen

Paulina Jesionek †,‡,*, Barbara Hachuła †, Karolina Jurkiewicz §, Patryk Włodarczyk ∥, Marek Hreczka ∥,⊥, Kamil Kamiński §, Ewa Kamińska ‡,*
PMCID: PMC11056992  PMID: 38608273

Abstract

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In this paper, X-ray diffraction (XRD), differential scanning calorimetry (DSC), broadband dielectric (BDS), and Fourier transform infrared (FTIR) spectroscopy supported by molecular dynamics (MD) simulations and quantum chemical computations were applied to investigate the structural and thermal properties, molecular dynamics, and H-bonding pattern of R-, S-, and RS-flurbiprofen (FLP). Experimental data indicated various spatial molecular arrangements in crystalline forms of examined systems, which seemed to disappear in the liquid state. Surprisingly, deeper analysis of high-pressure dielectric data revealed unexpected variation in the activation volume of pure enantiomers and a racemate. MD simulations showed that it is an effect of the clusterization phenomenon and a higher population of small associates in the former samples. Moreover, theoretical consideration exposed the particular role of unspecific F−Π interactions as a driving force underlying local molecular arrangements of molecules in the liquid and the crystal lattice of R-, S-, and RS-FLP.

1. Introduction

In recent years, enantiomers, also called optical isomers or chiral molecules, have been the subject of intensive research in biology, chemistry, physics, and pharmaceutical sciences.1−10 These systems are indistinguishable from each other regarding most physicochemical properties, such as chemical formula, melting points, or glass-transition temperature (Tg), except for the direction of their refraction of plane-polarized light6 or circular dichroism.11 Nevertheless, many papers have demonstrated that despite such strong similarity of enantiomers, they can vary significantly in their biological, toxicological, as well as pharmacodynamic, and pharmacokinetic properties.6,8,12−23

One of the groups of active pharmaceutical ingredients (APIs), where chirality seems to be an important aspect that is systematically and thoroughly studied from physical, chemical, and pharmaceutical perspectives, are 2-arylpropionic acids, the so-called profens.24−36 The presence of a carboxylic moiety capable of forming hydrogen (H)-bonds in the close vicinity of the chiral carbon atom makes the situation very interesting since chirality can influence spatial molecular organization, self-assembly phenomenon, etc. This supposition was positively verified by studying, e.g., the H-bond pattern in the crystalline pure R- and S-enantiomers of flurbiprofen (FLP) and the racemic (RS) mixture. Namely, in the former systems, the chain-like organization of the molecules was found, while in the latter, dimeric structures were preferred.27 Interestingly, the case seems to be much different in the supercooled liquid state. Molecular dynamic (MD) simulations carried out by Ottou Abe et al.34 on ibuprofen (IBP) showed that the population of H-bonded (HB) aggregates, as well as the proportion of cyclic vs linear dimers, are comparable for pure S-enantiomer and the RS-racemate. Moreover, it is worth mentioning the investigations by Adrjanowicz et al., which revealed that structural (α)-relaxation times, as well as diffusion of pure S-enantiomer and RS-racemate of ketoprofen (KTP), are very similar around the Tg.36 Herein, one can also briefly refer to the studies on the chiral compound from a different group, i.e., N-acetyl-α-methylbenzylamine (strictly R(+) and S(−) enantiomers, conglomerates at various enantiomeric excesses (ee) and the racemic mixture (ee = 0%)). It was presented that also the time scales of α-relaxation (and other processes detected in BDS spectra, i.e., Debye, β, and γ), as well as their temperature dependences, are insensitive to chirality. However, factors such as glass-forming ability and the recrystallization of heterochiral arrangements turned out to be chirality-dependent.37

The behavior of the enantiomers and racemates was also studied at high pressure. It was shown that it is possible to separate pure enantiomers from the racemic mixture after crystallization of the latter systems in the liquid phase at high compression.38−40 However, such an approach can be effective only when both chiral molecules are denser than the racemate.41 The other interesting high-pressure studies on racemates (profens) were performed by Adrjanowicz et al.26,36 They indicated that there is only a small difference in the structural dynamics of the S-enantiomer of KTP and the racemic (RS) mixture under various temperature and pressure conditions. As a consequence, the pressure coefficient of the glass-transition temperature (dTg/dp = 0.193 and 0.200 K/MPa, respectively), as well as the activation volume of both systems, were almost the same.36 Furthermore, isochronal crystallization (τα = const) at high pressure revealed that the S-enantiomer of KTP forms crystals much faster with respect to the racemic mixture.36 A different scenario was noted in the case of IBP. Koperwas et al.42 assigned the observed discrepancy (i.e., a greater slowing down of crystallization in the case of pure S-isomer compared to the racemate) to a distinct impact of compression on the solid–liquid interfacial free energy of both systems.

This review presents the results of structural, spectroscopic, thermal, and dielectric studies carried out at ambient and elevated pressure on R- and S-enantiomers of FLP and their racemic mixture. The purpose of these studies, supported by molecular dynamics (MD) simulations and density functional theory (DFT) computations, was to answer the question of whether there are differences in molecular organization via H-bonds in pure enantiomers and the racemate in the crystalline and supercooled liquid states. If so, what do they result for? Moreover, the intention was to verify if the atomic structure, thermal properties, and ambient and high-pressure molecular dynamics of neat R- and S-FLP are similar to those of RS-FLP.

2. Experimental Section

2.1. Materials

R- and S-FLP, as well as their racemic mixture (RS-FLP) with a purity higher than 98%, were supplied by MedChemExpress and Acros Organics Chemicals, respectively, and used without further purification.

2.2. Methods

2.2.1. X-ray Diffraction (XRD)

XRD patterns of crystalline and molten FLP samples were collected on a Rigaku Denki D/Max Rapid II diffractometer equipped with a 2D image plate detector and a rotating Ag anode. Incident radiation was monochromatized, and the wavelength of the beam was λKα1,α2 = 0.5608 Å. The temperature was controlled by an Oxford Cryostrem system. Samples were measured in borosilicate glass capillaries, and the background from the empty capillary was subtracted.

2.2.2. Fourier Transform Infrared (FTIR) Spectroscopy

FTIR spectra of crystalline samples of racemic and chiral forms of FLP were recorded with a Nicolet iS50 spectrometer (Thermo Scientific) equipped with an attenuated total reflectance (ATR) accessory in the 4000–400 cm–1 region at 293 K. They were obtained with 16 scans and a resolution of 4 cm–1. The spectra were also collected on a Nicolet iS50 spectrometer coupled with a Pike GladiATR module at 403 K. The measurements were taken with 16 scans and a resolution of 2 cm–1 in the wavenumber range of 4000–400 cm–1.

2.2.3. Differential Scanning Calorimetry (DSC)

Calorimetric experiments were performed using a Mettler-Toledo DSC apparatus equipped with a liquid nitrogen cooling accessory and an HSS8 ceramic sensor with 120 thermocouples. The instrument was calibrated for temperature and enthalpy using indium and zinc standards. The samples were placed in sealed aluminum crucibles (40 μL), then heated above their melting temperatures, quenched, and scanned at the rate of 10 K/min well above the respective melting points.

2.2.4. Broadband Dielectric Spectroscopy (BDS)

Isobaric measurements of the complex dielectric permittivity ε*(ω) = ε′(ω) – iε″(ω) (frequency range from 10–2 to 106 Hz) were performed using a Novocontrol α dielectric spectrometer equipped with α impedance analyzer with an active sample cell. The samples were placed in a parallel-plate cell made of stainless steel (diameter: 15 mm; gap: 0.1 mm with Teflon spacer), mounted inside a cryostat, and kept under dry nitrogen gas flow during measurements. The temperature control was provided by a Quatro cryosystem with temperature stability better than 0.1 K. Measurements were carried out after fast cooling the liquid to the glassy state and were done in the temperature range from 298 to 203 K.

For dielectric studies at elevated pressure, a high-p chamber with a special homemade flat parallel capacitor was used. Thin Teflon spacers were employed to maintain a fixed distance between the plates. Each sample capacitor was sealed and mounted inside a Teflon capsule to separate it from the silicon liquid (a pressure-transmitting medium). Pressure was measured using a Nova Swiss tensometric meter with a resolution of 1 MPa. In turn, the temperature was adjusted with a precision of 0.1 K by means of a refrigerated and heated Huber circulator. Measurements of complex dielectric permittivity were performed in the same frequency range as in the case of measurements carried out at p = 0.1 MPa. It should be noted that each dielectric experiment (including sample preparation) was repeated three times. For more detailed information about the BDS technique (both ambient and high-pressure studies), see refs (43−45)

2.2.5. Molecular Dynamics (MD) Simulations

Molecular dynamics simulations were performed in the Gromacs 2023 package46−50 using a Gromos 54a751 force field. The topology for both FLP molecules was created by an online automated topology builder (ATB).52−54 Starting geometry was generated by Packmol.55 In the case of the S-enantiomer, it was 500 S-FLP molecules, while in the case of the racemate, it was 250 of S- and 250 of R-molecules. After the initial geometry optimization, two subsequent equilibrating simulations were performed. They were carried out in the NPT (constant temperature, constant pressure) ensemble, where the v-rescale and c-rescale were used as thermostat and barostat, respectively. The pressure was set in both simulations to 1 bar, while the temperature was set to 400 K in the first simulation and 293 K in the second simulation. The final production run was done as a 10 ns simulation in the NPT ensemble with p = 1 bar and T = 293 K using the same type of thermal and pressure control. The analysis of the production runs was performed using the Travis package,56−58 which enabled the provision of all needed RDFs, ADFs, and HB topologies. The histogram of the cluster sizes was obtained by the use of the Gromacs “clustsize” routine.

2.2.6. Density Functional Theory (DFT) Calculations

DFT computations were carried out in the ORCA 5.0.4 package.59−63 The starting geometry for calculating the R-S Π-stacking interaction was obtained from a cif file for the racemate. Then, the chirality of one molecule was changed by switching the H and OH group positions to form S–S Π-stacking interacting molecules. The geometry optimization was performed at the B97M-D4/6-31G(2d,2p) level of theory. The starting geometry of the dimers with linear HBs was created in a few steps. In the first step, the molecular dynamics algorithm in orca was employed to obtain 100 random dimeric structures by performing simulation at T = 293 K and saving xyz file after each 0.1 ps of simulation (where total time was 10 ps). All saved geometries were optimized in the xtb semiempirical method, and then, the 20 most energetically stable forms were optimized in the DFT method on the B97M-D4/6-31G(2d,2p) level of theory. The interaction energies were calculated as a difference between the energy of the optimized dimer and the sum of the energy of isolated molecules, according to the equation

2.2.6. 1

where Eint is the interaction energy, ET is the total energy of the entire complex, and Ei is the energy of every isolated molecule forming the complex.

All of the energies were calculated at the B97/6-311G(2df,2pd) level of theory using additional D4 corrections.

3. Results and Discussion

The first stage of research was to characterize the atomic structure of the examined systems. According to previous studies, three polymorphic forms (I, II, and III) of RS-FLP have been reported. However, only the crystal structures of forms I and III have been solved.64−66 In both polymorphs, the dimerization of enantiomers through the carboxylic acid group and a similar molecular conformation were recognized, except that in form III, the position of the F atom is disordered over two positions related by a 180° rotation of the F-substituted ring. Based on the diffraction pattern presented in Figure 1a, it was possible to identify the polymorphic form of crystalline racemic FLP as form I. It is characterized by triclinic P1 space group and unit cell parameters: 5.8164(2), 9.3136(4), 12.7480(5)Å, 73.136(4), 83.117(3), 72.982(4)° and is the thermodynamically stable form under ambient condition, and hence used in the clinic. In turn, the crystal structure of R- and S- enantiomers at the same conditions was identical but different from that of racemic FLP, which can be deduced from the following XRD patterns in Figure 1a. This crystal structure has also been reported for the R-isomer—as orthorhombic P212121 space group and unit cell lengths: 5.6535(3), 13.2097, 16.0709 (5)Å.67 It was shown that in such crystal lattice, FLP molecules interacting via H-bonding create chains along the a-axis.67,68 One can assume that an analogous structural motif occurs for the crystalline sample of the S-isomer based on a similar diffraction pattern. Thus, the main difference between the crystal structures of racemic mixture and R-, S-FLP may be related to the spatial organization of molecules and their interaction through H-bonds with neighboring molecules. In the case of the liquid structure upon melting, the diffraction patterns presented in Figure 1b did not exhibit apparent variations between the chiral and racemic forms.

Figure 1.

Figure 1

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XRD patterns of racemic FLP and both (R and S) enantiomers in the (a) crystalline (T = 293 K) and (b) molten (T = 403 K) states. Panels (c, d) show the corresponding FTIR spectra of the same phases in the wavenumber region of 3800–400 cm–1. In the insets of panel (c), the structures of R- and S-FLP are presented.

The different spatial arrangement of the molecules in the crystalline lattice of racemate and pure enantiomers is also well captured in infrared spectra measured in a wide wavenumber range of 3800–400 cm–1 (please see Figure 1c). As can be seen, the spectra show the most significant differences in their band contours in the regions corresponding to the vibrations of the groups involved in the association process, i.e., stretching vibration of the H-bonded (HB) hydroxyl (νO–H 3500–3000 cm–1), carbonyl (νC=O 1800–1640 cm–1), carboxylic (νC–O 1280–1240 cm–1), and aliphatic (νC–H 3000–2400 cm–1) moieties as well as out-of-plane deformation of O–H group (γO–H 980–930 cm–1).69 It should also be noted that the IR spectrum of racemic FLP exhibits a typical dimeric structure of the νO–H band consisting of the shorter-wave branch (3500–2750 cm–1) of higher intensity and the longer-wave component (2750–2200 cm–1) of lower intensity. In contrast, the νO–H band of R-FLP is essentially characterized by a single broad signal, shifted toward higher frequencies relative to RS-FLP. Moreover, in a lower wavenumber range of the RS-FLP spectrum, an intense and sharp peak at 1694 cm–1 due to the stretching vibration of the carbonyl group (νC=O) is observed. On the other hand, the νC=O band of R- and S-FLP has a doublet structure consisting of two components (1728 and 1691 cm–1). The peak at 1258 cm–1 in the infrared spectrum of the racemic FLP is assignable to the C–O stretching and C–O–H deformation vibrations, while for R- and S-FLP, no signal at this frequency occurs. Instead of that, a peak at 1270 cm–1 is detected. A broad, medium-intensity band due to out-of-plane O–H deformation in the RS-FLP spectrum can be observed at 957 cm–1. In the case of both enantiomers, this peak has a very weak intensity.

As can be seen in Figure 1d, all of these spectral differences related to various spatial arrangements of the molecules in pure enantiomers and the racemate disappear after the sample’s melting, and the spectra of the three examined systems are identical. Moreover, one can postulate that melting of R- or S- FLP destroys the chain-like arrangement of the molecules as the spectrum of liquid samples closely resembles that of the crystalline racemic FLP (Figure S1 in the Supporting Information). Thus, the broad structure and shape of the νO–H band after melting are maintained, and the positions of the peaks are similar to those in the racemic FLP crystals. Only the νC=O band is slightly shifted to the higher wavenumbers (1708 cm–1) for molten samples relative to that in the crystalline RS-FLP (1694 cm–1). This fact may suggest that the HB dimers, with a relatively similar geometry to those in the crystal lattice, exist in the liquid forms of studied R-, S-, and RS-FLP.

To verify the eventual differences or similarities in the phase transitions and thermal properties of the crystal and liquid samples, calorimetric measurements were performed. In Figure 2, DSC curves recorded on heating the crystalline (inset) and glassy (main panel) samples at the rate of 10 K/min are presented. As can be seen in the inset, there is one strong endothermic process at T = 384.6 K and T = 385.3 K for R- and S-enantiomer, respectively, as well as at T = 388.1 K for a racemate, related to the melting of the crystalline samples. It should be mentioned that the obtained values of the melting temperature (Tm) stay in good agreement with those published in the literature (Tm = 385 K for S-FLP29 and Tm = 388 K for RS-FLP70). Further cooling without any sign of crystallization, followed by heating of the vitrified samples, reveals the presence of one visible glass transition as well as an exothermic peak at around 320 K (a racemate) or 325 K (both enantiomers), corresponding to the cold crystallization. Importantly, the glass-transition temperatures (Tg) of all examined samples are very similar (Tg = 267.9 ± 1.0, 268.1 ± 1.0, and 267.4 ± 1.0 K, for R-, S-, and RS-FLP, respectively). Moreover, the heat capacity jumps at the Tg are close to each other (ΔCp = 0.373, 0.357, and 0.375 J g1– K–1, for R-, S-, and RS-FLP, respectively).

Figure 2.

Figure 2

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DSC thermograms obtained during heating of the crystalline (inset) and glassy (main panel) R-, S, and RS-FLP at a rate of 10 K/min. Tg values were determined as the midpoint of the heat capacity increment, while Tm values were obtained from the maximum of the endothermic peaks.

Subsequently, having the results of previous investigations in mind, the molecular dynamics of R-, S-, and RS-FLP at ambient and elevated pressure (p) conditions were followed using the BDS technique. Figure 3a–c presents dielectric loss spectra of all samples collected at p = 0.1 MPa and in a wide range of temperatures (T), both above and below the Tg. In the supercooled liquid phase (T > Tg), two characteristic processes can be identified in the spectra of pure FLP enantiomers and the racemic mixture. The first one, whose source is charge transport of ionic impurities, is the dc-conductivity (σdc), while the second one, located at higher frequencies (f), is a structural (α)-relaxation related to cooperative motions of all molecules in the examined samples. As illustrated, both processes shift toward lower values of f with a decreasing T. In turn, in the glassy state (T < Tg), one well-visible secondary relaxation, labeled β, is observed in dielectric loss spectra for all investigated systems.

Figure 3.

Figure 3

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Dielectric loss spectra measured for R-FLP (a), S-FLP (b), and RS-FLP (c) at ambient pressure in a wide temperature range, above and below the Tg. A comparison of dielectric spectra obtained at different thermodynamic conditions (T, p), close to Tg, is shown for R, S, and RS-FLP (d). They were normalized with respect to the maximum of dielectric loss (ε″max).

To determine relaxation times of the structural (α) process, dielectric data collected at p = 0.1 MPa and T > Tg were fitted using the Havriliak–Negami (HN) function71

3. 2

where σdc is the dc-conductivity, ε0 is the vacuum permittivity, ω̅ is an angular frequency (ω̅ = 2πf), ε∞ is the high-frequency limit permittivity, Δε is the dielectric relaxation strength, τ is the HN relaxation times, and α and β are the shape parameters that represent the symmetric and asymmetric broadening of given relaxation peaks. Then, using the expression given in a book by Kremer and Schönhals,43

3. 3

τα have been recalculated from τ. To describe the T-dependencies of τα (see Figure S2 in the Supporting Information) at 0.1 MPa, the Vogel–Fulcher–Tammann (VFT) equation72−74 was applied. Subsequently, based on the VFT fits, the Tg (defined as a T at which τα = 100 s) for pure enantiomers and the racemic mixture was estimated. It should be noted that the obtained values (Tg = 263.1 ± 1.0, 263.4 ± 1.0, and 261.9 ± 1.0 K for R-, S-, and RS-FLP, respectively) do not differ significantly from each other and are only a few Kelvins lower when compared to those estimated from the DSC technique (see Figure 2). At first sight, one can get the impression that the relaxation time at the vitrification point is different when we analyze dielectric and calorimetric data. However, it is a common observation reported in the literature for many systems that is predominantly related to a difference in the heating rates applied during both experiments.

Additionally, extensive high-pressure BDS investigations under isobaric and isothermal conditions were carried out. In Figure 4, representative dielectric loss spectra collected for pure enantiomers and a racemic FLP at constant p and various T > Tg (panels a,c,e), as well as at constant T and indicated p < pg, where pg is a glass-transition pressure (panels b,d,f), are shown. Similar to the ambient pressure studies, except for the dc-conductivity, a structural (α)-relaxation peak (whose maximum moves toward lower f with decreasing T or increasing p), as well as one secondary (β)-relaxation, are observed in the spectra of all examined substances.

Figure 4.

Figure 4

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Representative dielectric loss spectra measured for R-, S-, and RS-FLP at isobaric (panels (a), (c), (e)) and isothermal (panels (b), (d), (f)) conditions.

In Figure 3d, the normalized dielectric spectra measured for R-, S-FLP, and RS-FLP at ambient and high p, and T close to Tg (the maxima of α-peaks near 1 Hz) were compared. As can be seen, for all investigated samples, the position of α- and secondary (β)-relaxation peaks is the same at various combinations of T and p, which means the fulfillment of the isochronal α- and β-superpositioning (the rule, whose confirmation has been reported for many HB systems75−78). However, it can also be observed that for both FLP enantiomers, the left-hand side of α-dispersion broadens with compression, indicating the violation of the so-called temperature pressure superpositioning (TPS).79 This effect is more pronounced for the R-isomer. Surprisingly, in the case of the racemic FLP, the TPS is satisfied (the width of the structural relaxation remains unchanged under various T and p conditions).

As the further part of the in-depth analysis of the molecular dynamics of R-, S-FLP, and RS-FLP, BDS data shown in Figure 4 were analyzed using the superposition of two HN functions (eq 2). Then, the obtained τα (also those determined from ambient-p experiments) were plotted as a function of T and p in Figure 5 and then analyzed with the use of the modified Avramov equation80

3. 4

where τ∞ is a relaxation time at extremely high T, τg = τ(Tg), Tr is a reference temperature lying close to the Tg, Cp0 is a specific heat capacity, C is an additional adjustable parameter, and Π is a constant with the dimension of pressure, while α0 and β are exponential parameters defined as

3. 5
3. 6

where Z is the degeneracy of the system, αp is a volume expansion coefficient at 0.1 MPa, and Vm is a molar volume. In Table S1 in the Supporting Information, the parameters of eq 4 determined from the global numerical fitting procedures (Figure 5) are presented.

Figure 5.

Figure 5

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Structural relaxation times of R- (a), S- (b), and RS-FLP (c) plotted versus temperature (T) and pressure (p). Purple, orange, and blue areas represent surface fits to the modified Avramov eq (eq 4).

Subsequently, two quantities, which define the sensitivity of the α-process to compression, i.e., the pressure coefficient of the glass-transition temperature (dTg/dp) and the activation volume (ΔVα), were estimated. To determine the former one, Tgs obtained for both enantiomers and the racemic FLP by applying the following expression proposed by Avramov81

3. 7

with the same values of the parameters Cp0, Π, β, and α0 as those appearing in eq 4, were presented as a function of pressure (Figure 6a). Interestingly, dTg/dps obtained from this plot are almost the same for all examined systems (dTg/dpR-FLP = 240 ± 12 K/GPa, dTg/dpS-FLP = 247 ± 12, K/GPa, and dTg/dpRS-FLP = 248 ± 12 K/GPa) and signify a high sensitivity of the structural relaxation to pressure. Note that somewhat lower values of this parameter have been previously reported for the two other APIs from the profens’ group—ibuprofen (dTg/dp = 195 K/GPa)82 and ketoprofen (dTg/dp = 200 K/GPa).26

Figure 6.

Figure 6

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Tg plotted as a function of pg (a). Dependence of the activation volume for the α-process (ΔVα) versus Tg/T (b).

On the other hand, ΔVα for all examined systems (FLP enantiomers and the racemate), usually defined as45

3. 8

was determined at different T directly from the surface fit of the modified Avramov approach. The plot presenting ΔVα versus Tg/T is shown in Figure 6b. Notably, the values of this parameter calculated for pure enantiomers at Tg (Tg/T = 1) were very close and equal to 377 ± 23 and 385 ± 23 cm3/mol for R- and S-FLP. In turn, surprisingly, ΔVα obtained for the racemic mixture is clearly lower (ΔVα = 337 ± 20 cm3/mol) in comparison to the values obtained for both isomers. This unexpected variation in ΔVα between pure FLP enantiomers and racemate indicates that the local spatial arrangement of the molecules in the liquid state of these systems may not be the same. Hence, some memory of the crystalline molecular arrangement, although not detectable with the experimental techniques applied in our studies, survived upon melting and in the vicinity of the Tg. To confirm this hypothesis, in-depth molecular dynamics (MD) simulations in the supercooled liquid state of S- and RS-FLP were performed.

The final simulations (after the initial equilibration) of FLP systems were taken at ambient pressure and a temperature of 293 K. The first analysis was related to the clusterization effect by H-bonds. It was found that hydrogen-bond-based clusters are more abundant in the enantiomeric system than in the racemate. Moreover, the difference in the total clusters, although noticeable, is relatively small. As presented in the histogram in Figure S3 in the Supporting Information, there is only a 0.5% difference in the overall amount of HB clusters. Nevertheless, a more significant difference can be found in their distribution. In the case of the S-isomer, there is a higher population of low-molecular-weight clusters (dimer to tetramer). The percentage of low-molecular HB clusters (2–4 molecules) equals 56% in the enantiomer and 44% in the racemate.

In both systems, there is also a small population of cyclic dimers and trimers. As illustrated in Figure 7, showing the detailed topology of H-bonds, cyclic dimers constitute 13 and 9% of all dimers in the S-isomer and RS-racemate, respectively. In the case of trimers, more abundant cyclic structures occur in the racemic mixture (18% of all trimers in RS versus 9% of all trimers in the S-enantiomer).

Figure 7.

Figure 7

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Topology of the most abundant H-bonds between two flurbiprofen molecules that can be found in the supercooled systems. T1.1, T1.2, and T1.3 are the most abundant dimer topologies, while T2.1–T2.4 are the most abundant trimer topologies.

Based on the data obtained from MD simulations, one can suppose that the higher activation volume obtained from dielectric investigations for the pure enantiomers with regard to the racemate is a manifestation of the difference in clusterization pattern and a higher population of the di-, tri-, and tetramers in the former systems. As a consequence of that, there is a larger average cluster size in the enantiomer. Having that in mind, one can ask the question, what is a driving force underlying the formation of extensive clusters in a pure isomer? To address this question, the OH···O hydrogen bond energy between S–S and R–S molecules was calculated. It was found that the interaction energies (Eint) between S–S and R–S molecules are similar. The obtained value was equal to 105 and 100 kJ/mol for the former and latter systems, respectively. The calculated Eint is unusually high if only a single OH···O hydrogen bond is considered. It became clear that the conformation of linearly H-bonded two FLP molecules has additional Π-stacking aromatic rings. Moreover, due to the fluorine (F) atom connected with the ring, the strength of such interaction can be higher because of the particular case of Π-stacking, i.e., F–Π interaction. As this was found to be a concurrent interaction with the H-bonds, MD simulations were analyzed to show possible differences in Π-stacking conformations. It was achieved by plotting 2D maps of the radial distribution function (RDF) of ring atoms versus the angular distribution function (ADF) of ring plane vectors. In the right panel of Figure 8, the 2D map of intermolecular RDF between F and Cring (where Cring is the ring atom connected with the F atom) versus the ADF between F–Cring and F–Cring vectors, indicating significant differences in the Π-stacked structures, are presented. As can be observed, there are two possible Π-stacking formations. The first one is when aromatic rings with fluorine atoms are parallel to each other. In this scenario, the angle on the map is close to 180°, and the distance between the F and Cring atoms is approximately equal to 4 Å. The second possible arrangement is when both rings are antiparallel to each other. The angle on the map is then close to 0°, and the distance between F and Cring is approximately equal to 6 Å. It is visible that in the case of the RS-racemate, both arrangements, i.e., ordered parallel and antiparallel structures, are abundant. For the S-enantiomer, only parallel structures are detected, but in this case, there is a broader angle distribution, which means that in these structures, rings are not so well parallel aligned. This finding corresponds very well with the crystalline patterns of the R-S and S–S structures. The antiparallel alignment found in the racemate is the precursor of the F–Π interacting conformation, which can be easily found in the unit cell of triclinic R-S crystals (see Figure S4 in the Supporting Information for details). In the left panel of Figure 8, two structures of R-S and S-S dimers bonded exclusively by Π-stacking forces are shown. These structures were optimized by the density functional theory (DFT) method and presented as electron density with mapped electrostatic potential on their surface. The R-S unit is the same as that found in the crystal cell. The S-S unit was optimized from the initial R-S structure after switching the chirality of the asymmetric carbon in one molecule. As one can see, the R-S structure is perfectly symmetric, which is manifested in the zero dipole moment (μ = 0 D). In the case of the S-S conformation, there are visible distortions in the charge distribution and its symmetry. The dipole moment of S-S molecules is equal to 1.33 D. The F−Π stacking energy is equal to 55 and 50 kJ/mol in R-S and S-S systems, respectively. Therefore, in the case of S-FLP, as the enantiomeric molecules are unable to form symmetric F−Π structures, the system is dominated more by H-bonds, which further leads to the different crystalline structure (an orthorhombic structure in the case of the S-enantiomer). Moreover, as it was found that the energy of F−Π interaction is comparable to OH···O hydrogen bond, the bonding energy of linear dimer, where there are contributions of both types of interactions, is comparable to the bonding energy of cyclic dimer. This is the reason why both supercooled systems are dominated by the linear HB clusters and not seemingly more stable cyclic dimers.

Figure 8.

Figure 8

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Visualization of the F–Π interactions in RS- and S-FLP systems. In the left panel, the geometry and electrostatic potential of R-S and S–S non-HB dimers are presented. In the right panel, RDF vs ADF 2D maps are illustrated to show the abundance of parallel and antiparallel Π-stacking formations.

4. Conclusions

To summarize, the studies indicated much different molecular organization via H-bonds in pure enantiomers (long chains) and racemate (cyclic dimers) in the crystalline samples of flurbiprofen. However, once the crystalline lattice is destroyed, these differences vanish, as can be deduced from the experimental data. According to the collected diffractograms, thermograms, infrared, and dielectric spectra, enantiomers have properties identical with those of the racemate. However, a deeper analysis of dielectric data revealed an unexpected variation in the activation volume, which may be related to changes in the local molecular arrangement of these compounds. In fact, MD simulations confirmed this supposition, indicating a higher population of smaller supramolecular clusters in S-FLP with regard to the RS-FLP. Finally, it was also found that there are very specific and enormously strong F−Π interactions in the studied systems that may control local molecular arrangement in the crystalline and supercooled samples. The presented data contribute to a better understanding of the correlation among the structure, intermolecular interactions, and basic physical properties of the enantiomers and racemates.

Acknowledgments

This research was funded in whole by the National Science Centre (Poland), grant number: Opus 21 No. 2021/41/B/NZ7/01654. For the purpose of open access, the author has applied a CC-BY public copyright license to any author accepted manuscript (AAM) version arising from this submission.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpcb.4c00582.

  • Comparison of FTIR spectra of crystalline and molten RS-FLP, relaxation map for FLP enantiomers, and a racemate obtained from the analysis of ambient pressure BDS data, parameters of the modified Avramov eq (eq 4), as well as additional outcomes of MD simulations and DFT calculations (PDF)

The authors declare no competing financial interest.

Supplementary Material

jp4c00582_si_001.pdf (306.2KB, pdf)

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