Non-equimolar discrete compounds in binary chiral systems of organic substances †

Since knowledge on the occurrence of non-equimolar discrete compounds in binary systems containing chiral molecules is very limited, this study reviews and systematizes the current state of investigating such systems and summarizes the results on two example systems studied in detail by the authors. In particular, the identification and verification of the non-equimolar discrete compounds compared to other discrete solid phases occurring in the two systems are discussed by presenting the results of related SCXRD, PXRD, TRPXRD, DSC, IR, and HSM studies. The (S)-malic acid–(R)-malic acid system has been found to contain non-equimolar 1 : 3 and 3 : 1 stable (S3R and SR3) and metastable (3S1R and 1S3R) discrete compounds, along with the equimolar compounds RSI and RSII (known monoclinic modifications) and the recently discovered RSIII modification. Polymorphic transformations of the discrete phases are debated, and the crystal structure of the stable compound S3R is identified (S. G. P1). The L-valine–L-isoleucine system has been stated to contain a non-equimolar 2 : 1 discrete compound, V2I, that could independently be proven by the ternary solubility diagram in water and its crystal structure solved (S. G. C2). The results obtained are discussed in conjunction with the findings reported in the literature. In order to systematize the variety of terms used for the description of discrete phases in binary chiral systems of organic substances, a systematization of equimolar and non-equimolar compounds based on chemical and crystallographic characteristics is proposed.


Introduction
When studying the limits of solid solutions and the polymorph diversity of organic compounds, several geometric and chemical factors are taken into account, such as dimensions, shape, and symmetry of a molecule, as well as the type of intermolecular bonding. [1][2][3] In the last decades, further geometrical (stereochemical) factorsthe molecule chirality and its configuration 4have been found to be essential for the analysis of molecular packing in crystal structures of enantiomeric compounds. 5,6 An avalanche-like growing interest in a rather abundant class of organic substances that contain chiral molecules is prompted by their numerous applications in the pharmaceutical industry, medicine, biochemistry [7][8][9][10][11] and even in geology, 12-16 where they are used, for example, for sediment rock dating; the last method is based on interrelations between levorotatory and dextrorotatory enantiomers in fossilized organic matter. 13,16 Industrial use and treatment of biochemically active chiral compounds requires development and improvement of synthesis techniques and also of methods for chiral resolution and Elena N. Kotelnikova Elena N. Kotelnikova is a Prof. in the Department of Crystallography at Saint Petersburg State University (SPSU). She received her PhD in 1982 and DSc in 1999, majoring in mineralogy and crystallography. She is a specialist in the crystal chemistry of paraffins, carboxylic acids, layered silicates, etc. She is the author and co-author of more than 120 papers. She is a Chairman of the Commission on Organic Mineralogy, a member of the Academic Council of the Russian Mineralogical Society, as well as a member of the Dissertation Council of SPSU. She is a laureate of the SPSU prize" For scientific research" and a holder of other awards. a Department of Crystallography, Saint Petersburg State University, discussed in detail by G. Coquerel. 6 However, all the diagrams presented there correspond to binary systems of the same group, viz. systems consisting of enantiomers of the same chemical compound.
In the published literature, there are sparse data on two other groups of binary systems containing chiral molecules. One group includes systems of diastereomers and the other systems of enantiomers of different compounds. Examples of our investigations of the solid phases existing in binary systems of the three above groups are summarized in Table 1.

Anton I. Isakov
Anton I. Isakov received his BSc in Geology (2011) and MSc in Molecular Geochemistry (2013) from the Crystallography Department of Saint Petersburg State University (St. Petersburg, Russia). He is a PhD student in the Crystallography Department of Saint Petersburg State University. He is currently researching equimolar and non-equimolar compounds as well as solid solutions formed in enantiomeric systems. His multidisciplinary research involves investigations of crystal chemistry, miscibility in solid state, thermal behavior, solubility, spectroscopic properties etc. of solids formed in the systems (S)-malic acid-(R)-malic acid and L-valine-L-isoleucine.

Heike Lorenz
Heike Lorenz is head of the crystallization research team at the Max Planck Institute for Dynamics of Complex Technical Systems and apl. Prof. at the Otto von Guericke University in Magdeburg (Germany). She obtained a Diploma in Chemistry from Freiberg University of Mining and Technology and completed her PhD (1993) and Habilitation (2004) at Magdeburg University. She was Chair of the Board Crystallization of Dechema/VDI-GVC's ProcessNet (2009)(2010)(2011)(2012)(2013)(2014) and is German Delegate to the EFCE Working Party on Crystallization since 2015. Her research interests include i.a. crystallization for separation and product design, and thermal analysis. She is author and co-author of more than 130 scientific papers. Fig. 1 Three basic types of phase diagrams characterizing binary systems formed by Sand R-enantiomers. At the top: diagrams of the systems containing a conglomerate (a), a racemic compound (b), and solid solutions (c). Subtypes 1, 2, and 3 of racemic compounds have melting points that lie above, are equal to, or lie below the melting points of the enantiomers; subtypes 1, 2, and 3 of the solid solutions are presented in the following order: a non-ideal solution having a maximum, an ideal solution, and a non-ideal solution having a minimum. 5 At the bottom: schematic representations of molecular packing in the equimolar phases corresponding to the diagrams above.
and R-enantiomers of the ethanolamine salt of 3-chloromandelic acid (E3ClMA) is an example of a eutectic system with partial miscibility between the components. 24,25 The system of malic acid Sand R-enantiomers belongs to the type 2 systems showing different polymorphs of the racemic compound and limited solid solutions. [26][27][28][29] Moreover, the system is complicated by the presence of two non-equimolar discrete compounds, S : R = 1 : 3 and 3 : 1. 29 The system of Land D-enantiomers of threonine is a eutectic system free from solid solutions. 30 Two shown systems of the second group are formed by diastereomers of the same compound. D-and L-allo-diastereomers of threonine form a eutectic system, 31 where, in contrast to the L-and D-threonine system, the eutectic point must be shifted from the equimolar composition. Land L-allo-diastereomers of threonine show full miscibility in the solid state, 32,33 and the phase diagram is asymmetric due to different components' melting points/solubilities. 32 The third groups' system studied consists of enantiomers of different compounds: L-valine and L-isoleucine. This system is characterized by the occurrence of a non-equimolar discrete compound Val : Ile = 2 : 1 and limited solid solutions. 34,35 Polymorphism of enantiomers and their equimolar compounds is rather common among chiral systems. 6 However, the systems (S)-malic acid-(R)-malic acid and L-valine-Lisoleucine show relatively rarely reported additional phase behaviours as limited solid solutions and, in particular, nonequimolar discrete compounds. Both, as well as literature data concerning these and similar systems, will be presented in this paper. A discrete compound as used here is a solid phase with fixed stoichiometry (equimolar or not but stoichiometric) having a crystal structure different from the compound components and, hence, clearly differs from solid solutions.
The paper is structured as follows. After introducing in section 2 the materials and experimental methods used in our own studies, in section 3, the systems of enantiomers of the same compound containing non-equimolar discrete phases are reviewed and followed by a detailed discussion of the (S)-malic acid-(R)-malic acid example. Section 4 refers to the systems of enantiomers of different compounds containing equimolar and non-equimolar discrete solid phases with a special emphasis on the L-Val-L-Ile system. For both exemplary systems, particular focus is set on discrete compounds described recently. In section 5, a systematization of the discrete compounds occurring in binary chiral systems of organic substances is suggested. Finally, the main results are summarized, and conclusions are drawn.

Materials
System 1: (S)-malic acid-(R)-malic acid. The starting reactants were Sand R-enantiomers and racemates of the RSI modification with 98% purity, which are available from Merck Schuchardt OHG, Hohebrunn, Germany. The reactants were used for preparing samples of quenched mixtures and growing samples of different compositions from aqueous, ethanol, acetone, and isopropanol solutions. The sample preparation techniques are described in detail elsewhere. [27][28][29] System 2: LĲ+)-valine-LĲ+)-isoleucine. The starting substances were L-valine and L-isoleucine with a 99% purity, which are available from Alfa Aesar, Massachusetts, USA, as well as deionized water as solvent. These reactants were used for sample preparation by means of isothermal evaporation and cooling techniques, as well as grinding of mixtures with various compositions. The sample preparation techniques are described in detail elsewhere. 34,35

Experimental techniques
High-performance liquid chromatography (HPLC). An analytical HPLC system equipped with a Phenomenex Chirex 3126 column was used. System 1: The material was dissolved in distilled water (1 wt%) and analyzed under the following conditions: eluent − 5 mM CuSO 4 at pH 3.2 (acetic acid), flow  The system of enantiomers of different compounds

Enantiomers of different compounds
This journal is © The Royal Society of Chemistry 2017 rate − 0.5 mL min −1 , injection volume − 2 μL, temperature − 25°C, wavelength − 254 nm. 29 System 2: The material was dissolved in distilled water (up to 0.2 wt%) and analyzed using the following conditions: eluent − 2 mM aqueous CuSO 4 solution/MeOH 85/15 (v/v), flow rate − 0.5 mL min −1 , injection volume − 5 μL, temperature − 25°C, wavelength − 280 nm. 34 Differential scanning calorimetry (DSC). System 1: For the melting temperature measurement, a SETARAM DSC 131 unit (France) was employed. Helium purge gas flow was 20 mL min −1 . About 10 mg of the substance were studied in closed aluminum crucibles at a heating rate of 1 K min −1 in the range of 30-150°C. 29 Melting temperatures were taken from the extrapolated onset temperatures of the melting peaks.
Powder X-ray diffractometry (PXRD). System 1: Measurements were performed using a Bruker D2 Phaser diffractometer (Germany) applying Cu Kα radiation and collecting data in 2θ range of 5-45°with a step of 0.02°. 29 System 2: Measurements were carried out at an X'Pert Pro diffractometer (PANalytical GmbH, Germany) using Cu Kα radiation and an X'Celerator detector in a 2θ range of 3-40°with a step size of 0.017°. 34 The diffraction patterns obtained for both systems were processed using a STOE WinXPOW software package.
Temperature-resolved powder X-ray diffractometry (TRPXRD). System 1: A STOE diffractometer (Germany) (Cu Kα radiation) provided with high-temperature equipment was used in an air atmosphere. The temperature variation was from room temperature to the substance decomposition point with a temperature step of 2-10°C. 27

, This work
Single crystal X-ray diffractometry (SCXRD). Systems 1 This work and 2: 34 A diffractometer, Agilent Technologies Super-Nova (USA), with Cu Kα radiation was used at a temperature of 100 K. The structure was solved by direct methods and re-fined by means of the SHELX program incorporated in the OLEX2 program package.
Infrared spectroscopy (IR). System 1: A Bruker ALPHA FT-IR-spectrometer (Germany) equipped with a Platinum-ATR-sampling module was used for the analysis of solid samples. This work Hot stage microscopy (HSM). System 1: A Linkam LTS 420 hot stage (UK) combined with a Zeiss Axioskop microscope (Germany) was applied. Samples prepared on a microscope glass slide were continuously heated from room temperature to the substance melting point at 2 K min −1 heating rate. The temperature was held constant at certain temperatures to observe the changes in the sample behaviour.
3. Systems of enantiomers of the same compound containing nonequimolar discrete phases

Overview
A list of enantiomeric systems, which are found to contain equimolar, as well as non-equimolar discrete compounds («anomalous racemates»), is presented in Table 2. Published data on the formation of non-equimolar discrete compounds in chiral systems is not always reliable, in particular, when the study is only based on melting point/ DSC analyses, and the crystal structure of the compounds is not deciphered. A brief description of some systems is presented below.
β-hydro-di-γ-benzoylamino-butyric acid. M. Bergmann and M. Lissitzin 51 were the first (in 1930) to introduce the concept of so-called "anomalous racemate". In the research, 51 they tried to separate enantiomers of β-hydro-di-γ-benzoylamino-  butyric acid via rapid crystallization from a highly supersaturated aqueous solution containing both enantiomers in the ratio of about 1 : 2. They found that the homogeneous precipitate obtained via such crystallization has a unique optical activity value. Its angle of optical rotation [α] D was +/−7.2°, while the same parameter for the enantiomers was +/−22°. On this basis, they stated that the compound in question could crystallize in the racemic form and two additional compounds 1 : 2 and 2 : 1. Quite recently (2015), A. A. Bredikhin et al. 52 proved in a reinvestigation via IR spectra, SCXRD and PXRD analysis, and solubility data that no additional compounds exist in the system. Taking this into account, we did not include the system in Table 2. Naringenin. Furthermore, Table 2 does not include the system of naringenin enantiomers, which was studied by P. J. Cox et al. 53 The authors synthesized racemic naringenin via recrystallization of the precursor substance from an ethanol solution. They detected the micro-inhomogeneity of a crystal of racemic composition. Despite the fact that its crystal structure corresponds to that of the racemate, the crystal is a combination of two types of unit cells; those of the 1st type are populated with Rand S-molecules in proportions of 77.5% and 22.5%, while the proportions in the 2nd type unit cells are 22.5% and 77.5%, respectively. These proportions roughly correspond to compositions of S : R = 3 : 1 and 1 : 3. The authors 53 assumed that the matter analyzed was a solid solution. Later, J. E. Tabora et al. 21 mentioned that the existence of unit cells with 1 : 3 and 3 : 1 populations in the crystal structure of racemic naringenin can be indirect evidence of the presence of 1 : 3 phases in the system. In our opinion, this crystal structure can be regarded as a partially disordered racemate since the authors 21 showed it to be centrosymmetric (present authors' note: pseudo-centrosymmetric).
As a result, Table 2 contains 16 systems with nonequimolar discrete compounds of which we have knowledge. It should be mentioned that crystal structures of four of the listed compounds have not yet been clarified. 21,[36][37][38][39] For example, paper 21 reports the results of the crystallization of different mixtures of the 3-hydroxy-4-(2,4,5-trifluorophenyl) butanoic acid enantiomers from toluene solutions. In the ternary phase diagram, two additional eutonics and a maximum in-between were detected. The composition S : R = 1 : 3, corresponding to the maximum, showed both a unique melting point and X-ray powder pattern, leading to the conclusion that it is a discrete compound.
Thus, the compounds found in the systems discussed must be further investigated since a final conclusion can be drawn only after depicting their crystal structures. For this reason, the detection of such compounds can be considered completely valid only for 12 (ref. 29,[40][41][42][43][44][45][46][47][48][49][50] of the systems shown in Table 2. Among them, 1 : 2 and 1 : 3 compounds are reported for eight and three cases, respectively; for one system, a 1 : 5 compound is described. Beside our research on the malic acid system in section 3.2, two examples shall be briefly mentioned. R. G. Kostyanovsky et al. 41 determined crystal structures for two chiral compounds belonging to the group of bicyclic bis-lactam (BBL). There, compound BBL7 is composed of three different, independent homochiral chains: two of them comprising molecules of the same chirality, -R-R-R-, while the third contains molecules of chirality -S-S-S-. Therefore, it could be classified as a compound of an S : R = 1 : 2 type. A. A. Bredikhin et al. 49 studied the 3-(2-tert-butylphenoxy)propane-1,2-diol system and found an additional peak in the DSC curve for the composition with an S : R ratio close to 1 : 3. SCXRD analysis of that sample allowed identification of a discrete phase and its crystal structure.
3. 2 The system (S)-malic acid-(R)-malic acid 3.2.1 History. The system of malic acid enantiomers has been investigated over decades. One of the four carbon atoms forming the malic acid C 4 H 6 O 5 molecule includes a chiral center. As already mentioned, it is a representative of the chiral systems containing a racemic compound, 54 and it is also remarkable for being an example of the combination of a few complications discussed in the work. 6 For example, the RS compound can crystallize in various polymorphic modifications. The data on the crystal structure and diffraction spectra of the two monoclinic modifications of RS-malic acid (designated as RSI and RSII in the following), as well as the malic acid enantiomers, are available from the Cambridge Structural Database (CSD) 55 and the International Centre for Diffraction Data (ICDD). 56 In the crystal structures of the S-enantiomer and racemic compounds RSI and RSII, malic acid molecules form chains with neighbour molecules in the chains being linked by hydrogen bonds. [57][58][59][60] This is a common arrangement for dicarboxylic acids, such as terephthalic, 61 succinic 62 and adipic 62 acids.
In addition to the racemic compound, the presence of "anomalous racemates" in the malic acid system was firstly reported in paper. 37 The authors studied some enantiomeric compositions using HSM and plotted the phase diagram. Besides the maximum corresponding to the racemic compound (RSI, the only modification known at that time), they found additional inflexion points of the liquidus line at compositions S : R = 3 : 1 and 3 : 1. They also found that the sample crystallized from aqueous solution with the composition S : R = 1 : 3 was characterized by a unique diffraction pattern. Later, the authors of other work 63 discovered a second monoclinic polymorph of the racemic compound (RSII). They assumed that the inflexions of the liquidus line discovered by previous authors resulted from the intersections of two liquidus lines belonging to the different polymorphs of the racemic compound, which, consequently, could not be proof of the anomalous racemates existence. For many years, this point of view has prevailed. Later, H. Kaemmerer et al. 26 carried out experiments to verify that the racemic forms RSI and RSII are monotropically related. They showed that the lower melting form RSII undergoes a polymorphic phase transition to RSI by storage at room temperature. The DSC data also This journal is © The Royal Society of Chemistry 2017 proved monotropy in accordance with the heat-of-fusion rule. 64 DSC and DTA studies on Sand RS-malic acid have been also reported by other authors. 65 3.2.2 Phase relations in the system based on PXRD, TRPXRD, IR-spectroscopy, DSC and HSM investigations Phase diversity in the (S)-malic acid-(R)-malic acid system. The system of malic acid enantiomers appeared to be more complex than it seemed before. Firstly, along with the known monoclinic modifications RSI and RSII, a third modification of the racemic compound RSIII can be formed. Secondly, in addition to the equimolar compound RS, non-equimolar discrete phases with the ratio S : R = 3 : 1 and 1 : 3 occur that thirdly, can crystallize as stable S 3 R (SR 3 ) and metastable 3S1R (1S3R) modifications. Moreover, the discovery of additional discrete phases necessitated further adjusting the limits of solid solutions in this system. Equimolar discrete compounds. PXRD studies of samples of the racemic compounds crystallized from various solvents showed 27 that the polymorphic diversity of the RS compound depends, first of all, upon the crystallization medium and the crystallization rate (ESI: † Table 1). The influence of some other crystallization conditions is discussed in details in the paper. 27 Phase distribution of the crystallization products according to the crystallization time (ESI: † Table 1) correlates with estimation of the stability of the various phases based on DSC data.
Non-equimolar discrete compounds. A PXRD study of samples with an enantiomer ratio of S : R = 3 : 1 (1 : 3) allowed the determination of stable S 3 R (SR 3 ) and metastable modifications 3S1R (1S3R) of 3 : 1 and 1 : 3 discrete compounds in the system. 66 As for the racemic compound, the diversity of the polymorphic modifications of these compounds depends upon the crystallization medium and the crystallization rate (ESI: † Table 1). The presence of the non-equimolar discrete phases in the system was also confirmed by IR-spectroscopy, DSC and HSM studies. We obtained IR spectra of the malic acid equimolar and nonequimolar compounds in the area of 4000-400 cm −1 . Fig. 2a and b show the IR spectra of S-enantiomer, racemic compounds RSI and RSII and non-equimolar S 3 R and 3S1R discrete phases in the diagnostic ranges of 3600-3300 cm −1 and 1740-1630 cm −1 . It can be seen that each of the phases S, RSI, RSII, SR 3 , and 3S1R, of malic acid has its own spectrum that allows for the use of IR-spectroscopy for their identification. The results for the known racemic and enantiomer phases agree with data reported in the works 26,63 and do not contradict other literature findings. 67 Phase relationships in the (S)-malic acid-(R)-malic acid system. The TRPXRD method showed that the racemic phases RSI and RSIII do not undergo polymorph transformations until the substances reached their melting points at 124°C and 123°C, respectively. However, heating a sample of an RSI + RSIII mixture resulted in a homogenization at 110-123°C to form RSI and the subsequent melting of the latter at 124°C. In addition, a slurry experiment where a RSI + RSIII mixture was slurried in an acetonitrile solution for 1 month also showed RSI to be stable and RSIII to be metastable. Upon heating, the RSII phase transforms into RSI at a temperature of 106-108°C. The experiments confirmed stability of the RSI phase, the obvious metastability of RSII, and the less obvious metastability of RSIII at ambient temperature. Fig. 3 shows the DSC melting curves for the three racemic phases and the non-equimolar S : R = 3 : 1 modifications of malic acid. The melting temperatures increased in the order 3S1R, S 3 R, RSII, RSIII, RSI. Based on the heat-of-fusion rule, 64 the monotropic relationships between the polymorphs RSI, RSII and RSIII of the racemic compound as well as the polymorphs S 3 R and 3S1R of the non-equimolar discrete compounds could be proven (Fig. 3). Thermomicroscopic (HSM) investigations of the S-enantiomer, racemic compounds RSI and RSII, physical mixtures of enantiomers S + R with the proportions of 1 : 1 and 1 : 3 for the components, and the non-equimolar discrete compounds S 3 R and 3S1R were performed (ESI: † Fig. 1). Close to the DSC results, the heating of the enantiomer and racemates RSI and RSII did not lead to any noticeable changes until melting of the substances. Instead of powders, in experiments with a 1 : 1 physical mixture of enantiomers S + R, we used two homochiral crystallites obtained by quenching the melt of the corresponding enantiomers (ESI: †  Fig. 1a). The interaction between the enantiomers starts at the contact area of the two grains and leads to the formation of racemic compound. This correlates with the fact that the crystallization of a melt containing two enantiomers provides the compound RSII (ESI: † Table 1). Experiments with the 3 : 1 physical mixture (S + R) were run with powders (ESI: †  Fig. 1b). They resulted in the formation of the discrete compound that finally melts. After recrystallization, a crystallite was taken, which was the metastable discrete phase 3S1R, and analyzed (ESI: † Fig. 1c). A visible transformation of the metastable into the stable phase, 3S1R → S 3 R, was not observed. The substance melted and recrystallized after removal of the heat.
The thorough study of the malic acid system resulting in identification of various modifications of the equimolar and non-equimolar discrete phases as well as the limits of solid solutions in two of the systems 28 facilitates compiling a schematic representation of the phase diagram (Fig. 4). It is based on the data obtained by the PXRD, TRPXRD, DSC, HSM, IR, and SCXRD methods mentioned. The given melting points originate from both the DSC and TRPXRD results. The limits of solid solutions were allocated using the results of a PXRD study of molten mixtures (ESI: † Fig. 2). When compared with the known diagrams of the second type 5,21 (see Fig. 1), the diagram of the malic acid system is very complex with the following characteristics. 1) The racemic compound can form three polymorphic modifications, with two of them already known 26,58-60,63,65 (RSI and RSII), and the third one (RSIII) discovered by the present authors. 27 2) Non-equimolar discrete compounds with the ratio S : R = 3 : 1 and 1 : 3 (ref. 29) are formed in the system. 3) The non-equimolar discrete compounds can crystallize in stable (S 3 R and SR 3 ) and metastable (3S1R and 1S3R) modifications. 4) Studies of the detected discrete phases allow determination of the areas of solid solutions in this system, which are found in the vicinity of all the discrete phases. 28  This journal is © The Royal Society of Chemistry 2017 3.2.3 Crystal structure of compound S 3 R. Definitive confirmation of the existence of non-equimolar discrete compounds in the system became possible after determining the crystal structure of the stable compound S 3 R. A single crystal with the S : R ratio of 75 : 25% obtained from an acetonitrile solution via an isothermal evaporation method was studied by means of SCXRD. The crystal structure data and structure refinement of the compound are presented in ESI: † Table 2.
The powder X-ray diffraction pattern calculated using the structural data (ESI: † Fig. 3a) is consistent with the experimental diffractogram of the stable compound S 3 R (ESI: †  Fig. 3b) and differs from the pattern of the metastable compound 3S1R (ESI: † Fig. 3c). ESI: † Table 3 shows the triclinic cell parameters of the compound S 3 R in comparison to the other discrete phases in the system. Fig. 5 presents the crystal structure of the compound S 3 R in projections on the planes ab (a), bc (b), and ac (c). It might be described as an arrangement of molecular chains of two types. Chains of the first "enantiomeric" type are composed of molecules of the same chirality -S-S-S-S-, while chains of the second "racemic" type include alternating molecules of both chiralities -S-R-S-R-.
ESI: † Fig. 4 shows projections of the crystal structures of racemate RSI, racemate RSII, S-enantiomer, and compound S 3 R onto the ab and bc planes. The most interesting for analysis of these crystal structures are their projections on the ac plane depicted in Fig. 6. It can be seen that the neighbor molecules within the chains are interlinked via hydrogen bonds in all the crystal structures of RSI (Fig. 6a), RSII (Fig. 6b), S (Fig. 6c), and S 3 R (Fig. 6d). For a convenient description, two opposite edges of the molecules will be designated here as a "head" and a "tail", where the head is the end of the molecule, which is closer to the side OH group, while the opposite end is, correspondingly, the tail.
In the crystal structures of racemate RSI, S-enantiomer and compound S 3 R, the neighbor molecules have "head-to-head, tail-to-tail" connections. Molecules of different chiralities are characterized by the same conformation in the case of RSI chains and "racemic" chains of S 3 R. Alternatively, molecules of the same chirality in the case of enantiomer chains and "enantiomeric" chains of S 3 R are characterized by two conformations; this allows interlinking of such molecules. The crystal structure of RSII contains "head-to-tail" arrangements of molecules. As for RSI, the molecules are also characterized by different chiralities and by the same conformation.
In the crystal structures of all the malic acid compounds, the hydrogen bonds between neighbor molecules are conducted by the edge COOH groups. Two COOH groups belonging to neighbor molecules form carboxylic dimers (dimer ring). The differences in H-bond topography between various compounds (RSI, RSII, S, and S 3 R) are due to the number of such contacts linking the molecules of the neighbor chains. In the case of RSI (Fig. 6a), there is an alternating number of H-bonds that connect the carboxylic rings corresponding to the neighbor chains. Carboxylic rings forming four contacts alternate with those forming six contacts. In Fig. 6, the contacts connecting the carboxylic dimers, as well as the contacts forming the dimers, are shown by the blue dashed lines. In  the case of RSII (Fig. 6b), there are no hydrogen bonds between the neighbor chains. In the case of the S-enantiomer (Fig. 6c), only half of the carboxylic rings are connected to those of a neighbor chain. There are five H-bonds per one ring. Moreover, there are two H-bonds on both sides from the ring that connect the pendant OH groups of the molecules corresponding to the neighbor chains. The contacts are shown by green dashed lines. In the case of S 3 R (Fig. 6d), there are rings of four types. This is due to molecular chains of two types alternating in the crystal structureenantiomeric and racemic. In the enantiomeric chains, there are alternating dimers with three and two contacts with the neighbor chains. In the racemic chains, there are alternating dimers forming two and four such contacts.
For convenience, the crystal structures described are schematically shown in Fig. 7(a-d). The use of different colors enables distinguishing Sand R-enantiomer molecules, and the OH groups are indicated to recognize the "tails" and the "heads" of the molecules. The molecule shape reflects its conformationa straight shape corresponds to the "racemic" conformation, while the slanted shape corresponds to the "enantiomeric" conformation. This representation shows the principle packing of molecular chains of two types in the crystal structure of the compound S 3 R. The crystal structure is a combination of the racemate RSI chains and S-enantiomer chains.

Systems of enantiomers of different compounds containing equimolar discrete phases
In the available literature, there are a considerable number of publications reporting systems composed of enantiomers of different compounds. Some of these systems belong to the type two (see Fig. 1) since their equimolar compositions are discrete compounds. Fifteen examples of such systems are presented in Table 3, 36,[68][69][70][71][72][73][74][75][76][77][78][79][80] and for ten of the related compounds, the crystal structures were determined using SCXRD. Almost all the represented enantiomeric molecules have only one chiral center, the exceptions being (−)-dilactic acid, (+)-2,4-dimethylglutaric acid and tartaric acid molecules with two equal chiral centers, i.e., the carbon atoms with the chiral centers have the same substituents. 70 The most interesting for our discussion are three systems: L-malic acid-L-tartaric acid, 78 L-malic acid-D-tartaric acid 79 and D-valine-L-isoleucine, 80 while malic acid and L-valine-Lisoleucine are, in turn, the subjects of our studies (see Table 1).
The first two systems differ from each other only in the type of chirality of tartaric acid as the second component. It should be noted that malic and tartaric acids have noncoinciding directions of rotation for the polarized light plane, which are LĲ−) and DĲ+) for malic acid and LĲ+) and DĲ−) for tartaric acid. The configuration difference of the tartaric acid molecule is reflected in the structure of the resulting binary compounds. The compound formed in the L-malic acid-Dtartaric acid system has the space group P2 1 , while the one in the L-malic acid-L-tartaric acid system is characterized by the space group P1. The schematic representations of the molecular packing in the equimolar compounds of the above systems and selected discrete phases in the system of malic acid enantiomers are shown in Fig. 7(e and f) and (a-d), respectively. The third system, D-valine-L-isoleucine, differs from the one we studied only in having a different chirality in valine. This discrepancy determines the differences in the molecular compositions of the discrete compounds formed in the corresponding systems. A comparative analysis of their crystal structures is given in section 4.2.
L-Malic acid-D-tartaric acid system (Fig. 7e) is denoted L-D′. In the molecular chains of the LD′ binary compound of this system, the malic acid molecules only have the "racemic" conformation. In contrast to the chain arrangements in malic acid RSI and RSII (Fig. 7a and b), the neighbor chains are shifted relative to each other by one molecule in the direction  of their elongation. This shift results in the molecules having a staggered arrangement (Fig. 7e). The tartaric acid molecule contains two side OH groups, while malic acid only has one. Hence, the neighbor molecular chains in the crystal structure of tartaric acid form more hydrogen bonds than the chains in the crystal structure of the malic acid racemate RSI.
L-Malic acid-L-tartaric acid system (Fig. 7f) is denoted L-L′. Similar to the LD′ compound, in the molecular chains of the LL′ discrete compound, the malic acid molecules only have the "racemic" conformation, and the neighbor chains are shifted, forming a staggered arrangement. The difference is that the "heads" of the malic acid molecules in the neighbor chains of the binary compound LL′ are directed to the same direction (Fig. 7f), while in the LD′ compound, they face the opposite sides (Fig. 7e).

Systems of enantiomers of different compounds containing non-equimolar discrete phases: the example of L-Val-L-Ile
We are aware of the existence of only three such systems containing non-equimolar discrete phases ( Table 4). Two of them have been studied by means of melting point measurements, 36,70 and both are cited in Table 3 since they also include equimolar compounds. According to work, 5 these systems tend to form non-equimolar discrete compounds because they involve 2,4-dimethylglutaric acid as a component. The crystal structures of the 1 : 3 discrete compounds have not been determined; their presence was indicated by additional inflexion points in the liquidus lines. Molecules constituting both systems have different chiralities. Each of the molecular components of the system (−)-dilactic acid-(+)-2,4-dimethylglutaric acid has two equal chiral centers, while the molecules of the system (+)-2-methylglutaric acid-(−)-2,4dimethylglutaric acid possess (with one and two) different numbers of chiral centers.
The principal feature distinguishing the L-valine-Lisoleucine system from those discussed above is the samethe L-chirality (configuration) of its components. The valine molecule has one chiral center; isoleucine contains two unequal chiral centers that differ from the (−)-dilactic and (+)-2,4-dimethylglutaric acid molecules, which have equal chiral centers (Table 4).
At least since 1933, 81 34 where most of our results for the L-Val-L-Ile system using HPLC (11 samples), PXRD (13 compositions), and SCXRD methods are published. First data obtained by TRPXRD was recently reported. 35 According to the PXRD data, the limits of solid solutions in the system L-Val-L-Ile are rather limited. The system has been found to contain a non-equimolar discrete compound V 2 I with the ratio Val : Ile = 2 : 1 (∼66 mol% Val). According to this, three areas of solid solutions (ss) originating from valine ssV (>70 mol% Val), isoleucine ssI (<10 mol% Val), and discrete compound ssV 2 I (60-68 mol% Val) were distinguished; also, two-phase regions were identified consisting of solid solutions ssI + ssV 2 I (10-60 mol% Val) and ssV 2 I + ssV (68-70 mol% Val). The results agree well with that obtained by independent HPLC studies. As shown in Fig. 8, the ternary phase diagram of the system L-Val-L-Ile-water contains a local solubility minimum that corresponds to the composition of ∼66 mol% Val and is positioned in-between two eutonics laying asymmetrically left and right from it. Such behavior of the solubility curve is characteristic for systems containing a binary discrete compound. 22,89 Although the absolute solubility data (obtained by different methods) differ slightly from each other, they clearly indicate the local solubility minimum close to the 2 : 1 Val : Ile composition and verify the presence of the related V 2 I compound in the system.
Crystal structure of compound V 2 I. Crystal structures of the system components, valine and isoleucine, are known. [90][91][92][93][94] The newly discovered non-equimolar discrete compound V 2 I has been studied by means of SCXRD.
The monoclinic cells of Val and Ile (space group P2 1 ) ( Fig. 9a and b) are characterized by two crystallographically independent positions of the molecules. [90][91][92][93][94] Molecules occupying both positions have the same conformation. The monoclinic cell of V 2 I (space group C2) (Fig. 9c) is characterized by four independent positions of the molecules, each of which have mixed populations, i.e., can be occupied by either a Val or Ile molecule. The parameter a of the V 2 I monoclinic cell is doubled in comparison to the corresponding parameters c of Val and Ile monoclinic cells (due to different unit cell orientations). The empirical formula of compound V 2 I calculated on the basis of structural data corresponds to the Val : Ile ratio of ∼60 : 40 and is practically confirmed by the composition of the sample studied (66 mol% Val). The calculated powder X-ray diffraction pattern shows good agreement with the experimentally obtained one. 34 Similar to the crystal structures of Val 90,92,94 and Ile, 91,93,94 the crystal structure of the discrete compound V 2 I is layered. Molecules in the three crystal structures are combined in H-bonded dimer molecules, and dimers form molecular layers also via H-bonds. The layers interact with each other by van der Waals forces. The Val and Ile dimers are elongated along the c axis, and the layers are connected by axes 2 1 . However, the dimers in the crystal structure of V 2 I are elongated along the a axis, and the layers are connected by axes 2 1 and 2. The difference in the azimuthal arrangement of the molecular layers can be seen easily if the doubled unit cell of Ile and the unit cell of V 2 I are compared (see ESI: † Fig. 5 and work 34 ).
Components of the system D-Val-L-Ile are known in the literature 80 and were mentioned before (Table 3). They differ from those of the system L-Val-L-Ile only by the configuration of the valine molecules. These systems exemplify the effect of the different chiralities of the molecules forming a binary system. In the first system, 80 an equimolar discrete compound VI (Val : Ile = 1 : 1) is formed, while in the second system, a non-equimolar discrete compound V 2 I (Val : Ile = 2 : 1) is formed. The crystal structures of both compounds are characterized by alternating azimuthally non-equivalent molecular   layers and by doubled unit cells including two layers in corresponding translation. Wherein, the compound VI crystallizes in the space group P2 1 , and the compound V 2 I in the space group C2. Schematic representations of the molecular packing in the crystal structures of Val, Ile, V 2 I, and VI are shown in Fig. 10 for comparison. Molecules with L-configuration and the coordinates y and y + 1/2 at the b axis of the unit cell are shown in blue and light blue colors, respectively; molecules with D-configuration are in green. Different shapes of the Val and Ile molecules reflect the fact that in comparison to Val, the edge H atom is replaced by a CH 3 group in Ile. The group is shown by an additional rear circle. Partial coloring of the circle in the case of V 2 I symbolizes the partial (33%) occupation of the site by a rear CH 3 group.

Systematization of discrete compounds formed in binary chiral systems of organic substances
The term "racemate" or "racemic modification" was introduced as early as the 2nd half of the 19th century after L. Pasteur's well-known experiments to describe an enantiomer mixture containing equimolar amounts of the components. However, this definition does not reveal the nature of the mixture itself. In the published literature, there are plenty of terms used for discrete phases in related systems, e.g., true racemates, false conglomerates, quasiracemates, anomalous racemates, anomalous quasiracemates, anomalous conglomerates, cocrystals, 1 : 1 complexes, and others. The importance of knowledge about the variety of solid phases in chiral systems (e.g., for pharmaceutical and food industries) as well as the great scope of acquired data made the following questions emerge: Which particular type of compound is implied when one of the above definitions is used? How do they relate to each other?
We have attempted to systematize the data on discrete compounds in such systems, and the results are compiled in Table 5. The systematization is not aimed at changing the terminology but clarifying what is exactly meant under the terms mentioned. To make the systematics viable, it is necessary to define the border lines covering the types of compounds that can be included.
First, it is applicable only to chiral compounds that are "true" organic substances (known to contain a selected number of chemical elements 95 ) and, therefore, excludes organometallic compounds. Second, the systematization is proposed only for compounds formed in true binary systems, i.e., substances composed of only two molecular species. That is why it does not encompass compounds containing solvent molecules. For example, E. Wachter et al. 96 97 Furthermore, attention should be paid to the term "cocrystals," which is frequently used in relation to pharmaceuticals with the potential to improve their physicochemical properties. 98 A broadly accepted definition of the term comprises substances composed of two or more neutral molecular components at definite stoichiometric amounts, which are characterized by structural homogeneity and the absence of solvate molecules in their crystal structure. 99,100 Therefore, related compounds include binary donor-acceptor complexes and crystals with hydrogen bonds. 99 Consequently, the term cocrystal has a rather broad definition, especially considering chiral and achiral compounds. Accordingly, only cocrystals containing chiral components and only two of them find proper positions in our systematization. This journal is © The Royal Society of Chemistry 2017

Summary
Information on non-equimolar discrete compounds in binary systems of chiral organic substances, which is available in the literature, has been reviewed and systematized, including the rate of occurrence of such systems and the current state of knowledge in the field. For the systems (S)-malic acid-(R)-malic acid and L-valine-L-isoleucine, as examples representing different types of binary systems, the crystal structures of the non-equimolar discrete compounds were analyzed on the basis of comprehensive experimental studies. The results obtained were compared with the data reported in the literature for these two and other similar systems. The (S)-malic acid-(R)-malic acid system was shown to form 1) an equimolar compound, which could occur in three modifications; two of these, the RSI and RSII modifications, have been known for some time, while the third form, RSIII, was discovered and described by the present authors, and 2) the non-equimolar stable (S 3 R and SR 3 ) and metastable (3S1R and 1S3R) compounds with ratios S : R equal to 3 : 1 and 1 : 3, correspondingly. Crystallization conditions resulting in the formation of a particular modification of both equimolar and non-equimolar compounds have been ascertained, and the polymorphic transformations between the discrete phases have been studied. The data obtained were used to plot a schematic representation of the system phase diagram. The (triclinic) crystal structure of the non-equimolar discrete compound S 3 R has been identified and compared to those of the S-enantiomer and the racemic compounds RSI and RSII. At present, information on the crystal structures of nonequimolar discrete compounds is available only for a dozen systems of enantiomers of the same compound of which we have knowledge (including our data).
For the L-valine-L-isoleucine system, the occurrence of a non-equimolar compound V 2 I with the Val : Ile ratio of 2 : 1 could be proven. The solubility diagram plotted for the ternary L-valine-L-isoleucine-water system exhibits two eutonics located on both sides from the local solubility minimum, which corresponds to the composition of compound V 2 I. The (monoclinic) crystal structure of the V 2 I compound has been determined and compared to those of the system components L-Val, L-Ile and the equimolar compound formed in the D-Val-L-Ile system. To the best of our knowledge, this is the only available information on the crystal structure of a non-equimolar compound in a system of enantiomers of different substances and, at the same time, the only example of a binary compound where these enantiomers are of the same chirality.
Based on the results of the study, a systematization of discrete compounds occurring in binary chiral systems of organic substances was proposed. This was motivated by the great scope of the acquired knowledge and the variety of terms used in the literature. The presented systematics define chemical and crystallographic characteristics of the discrete compounds that can be ascertained when using a particular term. To increase its applicability, the types of compounds covered with the systematization were defined. Of course, we do not consider this systematization as complete and allencompassing. New materials are steadily appearing that might fill the still empty places in the systematization table and support a deeper understanding of the structure-property relationships within the systems studied.