Solvophobicity-directed assembly of microporous molecular crystals

Dense packing is a universal tendency of organic molecules in the solid state. Typical porous crystals utilize reticular strong intermolecular bonding networks to overcome this principle. Here, we report a solvophobicity-based methodology for assembling discrete molecules into a porous form and succeed in synthesizing isostructural porous polymorphs of an amphiphilic aromatic molecule Py6Mes. A computational analysis of the crystal structure reveals the major contribution of dispersion interaction as the driving force for assembling Py6Mes into a columnar stacking while the columns are sterically salient and form nanopores between them. The porous packing is facilitated particularly in solvents with weak dispersion interaction due to the solvophobic effect. Conversely, solvents with strong dispersion interaction intercalate between Py6Mes due to the solvophilic effect and provide non-porous inclusion crystals. The solvophobicity-directed polymorphism is further corroborated by the polymorphs of Py6Mes-analogues, m-Py6Mes and Ph6Mes.

O rganic molecules tend to form a dense crystal with minimal void volume so that the molecules therein can maximize the intermolecular interactions between the adjacent molecules [1][2][3] . The synthesis of a porous crystal thus requires a tailored molecular design to overcome this universal tendency. To this end, established porous crystals, such as metal-organic frameworks, typically employ organic linkers featuring multiple adhesive functional groups that can bind with each other to form a reticular framework [4][5][6][7][8] .
A fundamental question here is whether it is really unfeasible to assemble nonfunctional discrete molecules in a sparse manner.
Although this question appears contradictory to the abovedescribed tendency toward dense packing, there actually exist a handful of successful examples [9][10][11][12][13][14][15][16][17][18][19][20] . Organic zeolites are a wellknown class of such compounds that can uptake/release guest solvent molecules efficiently, and selectively depending on the geometry and chemical affinity, yet organic zeolites are not truly porous materials because their pores readily collapse upon removing the guests [21][22][23][24] . More recently, several organic crystals that can retain vacant pores have been developed [9][10][11][12][13][14][15][16][17][18][19][20] . These compounds spontaneously assemble into a porous packing despite the fact that the packing is sustained only by weak interactions, including C-H···X bonds, π-π stacking, halogen bonds, and van der Waals (vdW) forces, whose bonding strength are much less than the conventional hydrogen bonding (15-60 kJ mol −1 ) 25 . These porous molecular crystals are intriguing not only fundamentally but also practically because of their distinct solution processability, structural flexibility, and selfhealing ability, which are largely prohibited in the conventional porous crystals [17][18][19][20] . However, it still remains unexplored how one can drive the discrete molecules to assemble sparsely 1,26 . Moreover, with the existing compounds, crystallization solvent and procedure have to be carefully designed. Otherwise, the porous molecular crystals readily collapse into a densely packed polymorph, which further prohibits their development. In fact, most of the reported stable porous molecular crystals were found by chance except those composed of intrinsically porous molecular cages [27][28][29] .
Previously, we reported a porous molecular crystal Py open ·MeCN composed of a D 3h -symmetric amphiphilic aromatic compound Py 6 Mes ( Fig. 1a) 18,20 . Py 6 Mes assembled together via multiple C-H···N bonds to form a molecular framework with onedimensional micropores (Fig. 2a), which can maintain its porous architecture up to 202°C. Although further heating ended up with the collapse of the pores, the resultant nonporous polymorph Py close spontaneously self-healed back into Py open ·MeCN upon exposure to vapor of MeCN at ambient temperature. We anticipated that Py open ·MeCN, featuring excellent thermal stability and compositional simplicity, could serve as a highly promising platform for investigating how discrete molecules assemble into a porous form. Along this line, we also reported, in the previous report, a plausible molecular assembly mechanism for Py open based on its four types of polymorphs 18 . However, the available crystallographic data were limited at that period and, thus, we could not establish a reliable and general design strategy toward porous molecular crystals.
Here, we report a molecular strategy for synthesizing isomorphic porous molecular crystals from various organic solvents. Through a detailed computational investigation, we reveal the major contribution of dispersion force in the assembling process of the constituent Py 6 Mes molecules into a porous manner. Following this understanding, we crystalize Py 6 Mes and succeed in synthesizing porous polymorphs in solvents with less dispersion interaction due to the solvophobic effect (Fig. 1b). In contrast, solvents with larger dispersion interaction provide nonporous inclusion crystals due to the solvophilic effect. Newly synthesized Py 6 Mes analogs, m-Py 6 Mes (Fig. 1a) and Ph 6 Mes, also show consistent solvophobicity-directed polymorphism.

Results and discussion
Energy decomposition analysis of Py open ·MeCN. To gain insight into how a discrete molecule assembles into a porous form, we focus on Py open ·MeCN, whose crystal structure was previously identified 18 . In Py open ·MeCN, Py 6 Mes stacks with each other to form a one-dimensional column along the twofold screw axis (crystallographic b-axis, Fig. 2c). The polar pyridine rings and the nonpolar benzene and mesitylene rings are spatially segregated in the column to form a polar shell and a nonpolar interior (Fig. 2b). We conduct a computational calculation of the intermolecular interactions between the adjacent Py 6 Mes molecules in Py open ·MeCN. Pair interaction energy decomposition analysis (PIEDA) 30 is performed for this purpose by using the fragment molecular orbital (FMO) 31 method at the RI-MP2 level of theory with 6-31 + G(d) basis set (Supplementary Fig. 23 and Supplementary Table 15, see "Methods" for the details of the computational methods). A negative value represents an attractive interaction. E vdW , E ES , and E CT + mix respectively represent   (Fig. 2c) at the expense of the energetic gain obtained from the intercolumnar packing along the crystallographic a-and c-axes. As expected from the richness of C-H···N bond, dispersion interaction is the major attractive contribution in the crystal, especially along the crystallographic aand b-axes (Fig. 2d). Electrostatic interaction as well as dispersion interaction is prominent along the crystallographic c axis (Fig. 2d). Altogether, dispersion interaction occupies 60.9% of the total attractive energy of -134.3 kcal mol −1 in Py open ·MeCN (Supplementary Table 15).
Subsequently, we conducted computational investigation into the effect of polarity of the crystallization solvents, which has been considered as an essential parameter for predicting the polymorphism. We calculate the total system energy of Py open on the assumption that the constituent Py 6 Mes molecules are surrounded by MeOH, CHCl 3 , acetone, toluene, and dichloroethane, respectively, which are available in GAMESS program 32 . As summarized in Supplementary Table 16, the porous architecture is stabilized more as the polarity of the surrounding solvent increases, yet the change in stabilization energy from the surrounding environment estimated by the polarized continuum model method is relatively small in comparison with the energetic gain from dispersion force. Overall, the porous assembly of Py 6 Mes is sustained dominantly by the dispersion forces together with the stabilization by the polarity of the surrounding media.
Crystallographic analysis of polymorphs of Py 6 Mes. Based on the understanding obtained from the calculation, we crystalize Py 6 Mes from a series of common organic solvents, and analyze their crystal structures with the aim to control the intra-and intercolumnar stacking of Py 6 Mes. As a typical recrystallization procedure, saturated solution of Py 6 Mes is poured into a small glass vial, which is loosely sealed with a cap and stood at 25°C for several days to allow the mother solvent to sluggishly evaporate. In the previous report, we utilized MeCN, 2-propanol (iPA), tetrahydrofuran (THF), and CHCl 3 as the crystallization solvents of Py 6 Mes. Here, we additionally utilize MeOH, EtOH, butyronitrile (BN), EtOAc, acetone, 1-chloropropane (PrCl), 1-butanol (BuOH), toluene, CH 2 Cl 2 , dimethylsulfoxide (DMSO), and γbutyrolactone (GBL) as the crystallization solvents.
Some of the non-protic solvents (EtOAc, CH 2 Cl 2 , and toluene) successfully give crystalline precipitates of Py 6 Mes that are applicable for the single-crystal X-ray diffraction structure analysis. Crystallographic information and the symbols of the resultant crystals are summarized in Table 1 and Supplementary  Tables 1-3  Inclusion molecular crystals Py VDW ·CH 2 Cl 2 and Py VDW ·C 7 H 8 are obtained, respectively, from CH 2 Cl 2 and toluene. Py VDW ·CH 2 Cl 2 ( Fig. 3a and Supplementary Fig. 10) belongs to a space group of C2/c, in which eight non-disordered CH 2 Cl 2 molecules pack together with four molecules of Py 6 Mes in a unit cell. The H atoms in CH 2 Cl 2 make a short contact with a N atom in Py 6 Mes (2.594 Å; Fig. 3b). Py 6 Mes molecules form C-H···N contacts (2.583 and 2.500 Å) with each other along with several C-H···H contacts. Py VDW ·C 7 H 8 ( Fig. 3c and Supplementary  Fig. 11) belongs to a space group of P-1, in which four toluene molecules pack together with four Py 6 Mes molecules in a unit cell. The guest toluene molecules form C-H···π contacts and a π-π stacking with Py 6 Mes (Fig. 3d, e). Py 6 Mes molecules form eight C-H···N contacts with each other along with C-H···π contacts and π-π stackings.
Precipitates obtained in other solvents are analyzed by PXRD due to the difficulty in synthesizing diffraction-quality single crystals ( Supplementary Fig. 8). BN solution of Py 6 Mes affords a porous crystal that is isomorphic to Py open , while the crystals obtained from other solvents (acetone, PrCl, BuOH, DMSO, and GBL) are not isomorphic to Py open . The single-crystal structures, PXRD profiles, and the physical properties of the crystallization solvents (relative permittivity and Hansen parameters 34 ) are summarized in Supplementary Table 14 along with those of mesitylene, benzene, and pyridine as the components of Py 6 Mes.
It is worth noting that isomorphic porous crystals were obtained from a variety of solvents (MeCN, iPA, BN, and EtOAc) that are seemingly irrelevant with each other, in terms of the polarity or hydrogen bonding capability. This is in clear contrast with the previously reported porous molecular crystals that were basically sensitive to the crystallization solvents or crystallization procedures 1 .
Hansen solubility parameter and polymorphism. Relative permittivity (ε) has often been regarded as the primal parameter for the prediction of the solute-solvent interactions. However, the tendency in polymorphism of Py 6 Mes toward ε is indistinct (Supplementary Table 14). We presume that, based on the results from the computational analysis, the capability of forming the dispersion interaction may govern the polymorphism. To prove  this theory, we focus on Hansen parameters, which are the empirical values of the strength of dispersion (δ D ), polar (δ P ), and hydrogen bonding cohesion parameters (δ H ). Besides the conventional utility for the prediction of the solubility of organic polymers, Hansen parameters have recently been applied for the prediction of polymorphism of some pharmaceutical molecules 35,36 . We apply this method to the polymorphism of Py 6 Mes. The crystallization solvents and Py 6 Mes components are plotted in the Hansen space according to their three coordinates of δ D , δ P , and δ H (Fig. 4 and Supplementary Table 14). The Py 6 Mes components (green spheres in Fig. 4a) feature large δ D and relatively small δ P and δ H . MeCN, BN, EtOAc, and iPA (red spheres in Fig. 4a) feature small δ D and moderate or large δ P and δ H . Highly polar solvents (MeOH and EtOH, black spheres in Fig. 4a) locate at the opposite corner from the Py 6 Mes components. The other solvents (blue spheres in Fig. 4a) locate between the red and green spheres.
The geometrical distance in the Hansen space represents the solubility or affinity of given two substances. In line with this conventional understanding, the plot in Fig. 4a shows an explicit dependence on the distance from the Py 6 Mes components. Solvents that are close to the Py 6 Mes components yield nonporous polymorphs (blue spheres in Fig. 4a), while solvents that locate far from the Py 6 Mes components are poor in solubility (black spheres in Fig. 4a). The remaining slightly affinitive solvents yield the porous crystals (red spheres in Fig. 4a).
This trend can be decomposed into the basic elements by focusing on the projections of the Hansen space onto the δ D δ P -, δ D δ H -, and δ P δ H -planes (Fig. 4b-d). As shown in Fig. 4d, the polymorphic tendency barely correlates with δ P and δ H of the crystallization solvents. On the other hand, δ D describes the polymorphic tendency reasonably (Fig. 4b, c and Supplementary  Table 14), namely, Py 6 Mes crystalizes into the porous form when the crystallization solvent can partially dissolve Py 6 Mes, but is not affinitive with Py 6 Mes especially in terms of the strength of the dispersion force.
We also analyze the intermolecular short contacts and crystal packing efficiency of the single crystals, with the aim to reveal the detailed solute-solvent interactions. The egoistic C-H···N and C-H···π contacts per one Py 6 Mes molecule are summarized in Table 1. In the solvents with small δ D , Py 6 Mes facilitates multiple C-H···N and C-H···π contacts with each other, while solvents with large δ D suppress the egoistic contacts by intercalating between Py 6 Mes molecules as shown in Py VDW ·CH 2 Cl 2 and Py VDW ·C 7 H 8 (Fig. 3a, c) (Table 1). Namely, solvents with large δ D are affinitive with Py 6 Mes and allow the Py 6 Mes to assemble into a dense packing by intercalating between Py 6 Mes (solvophilic crystallization), while solvents with small δ D are segregated from Py 6 Mes due to the solvophobicity and facilitate the columnar assembly of Py 6 Mes although the intercolumnar packing is not dense (solvophobic crystallization).
Polymorphism of m-Py 6 Mes and Ph 6 Mes. The δ D -dependent solvophilic/solvophobic crystallization is further corroborated by the polymorphs of m-Py 6 Mes and Ph 6 Mes (Figs. 1a, b and 5). Meta-substituted hexapyridyl mesitylene derivative m-Py 6 Mes was newly synthesized by sequential Suzuki-Miyaura couplings of pyridineboronic acid, dibromo aniline, and triiodomesitylene (for details, see Supplementary Methods). Tri(terphenyl) mesitylene, Ph 6 Mes, was newly synthesized by Suzuki-Miyaura coupling reaction of terphenylboronic acid and triiodomesitylene (for details, see Supplementary methods). The molecular structure of the resultant m-Py 6 Mes and Ph 6 Mes are unambiguously assigned by means of 1 H-and 13 C-NMR spectroscopies, elemental analysis, and high-resolution mass spectrometry ( Supplementary  Figs. 1-7).
We crystalize m-Py 6 Mes in the same way as Py 6 Mes in MeCN, EtOAc, iPA, and CHCl 3 to obtain diffraction-quality single crystals. Their crystal packing diagrams and crystal structure information are shown in Fig. 3f-j and Table 2, respectively. Nonporous inclusion crystals are obtained when solvents with large δ D (iPA and CHCl 3 ) are utilized (Fig. 3f, h, and Supplementary Figs. 14 and 15). The inclusion crystal obtained from iPA (m-Py VDW ·iPA) belongs to a space group of P-1. The constituent m-Py 6 Mes molecules form multiple C-H N and C-H···π contacts with each other along with a solvophilic C-H···N contact with a guest iPA molecule (Fig. 3g). The inclusion crystal with CHCl 3 (m-Py VDW ·CHCl 3 ) belongs to a space group of P-1. The constituent m-Py 6 Mes molecules form three C-H···N bonds with each other along with solvophilic C-H···N (Fig. 3i) and C-H···π contacts with guest CHCl 3 molecules.
The crystals obtained from MeCN (m-Py VDW ·MeCN) and EtOAc (m-Py VDW ·EtOAc) are isomorphic with each other, featuring no apparent pores or guest solvent molecules (Fig. 3j, and Supplementary Figs. 12 and 13). The crystal packing mode is basically analogous to the nonporous polymorph Py close , which is obtained by thermal annealing of Py open (see our previous report 18 for the detailed synthetic and structural information). In m-Py VDW ·MeCN, the constituent m-Py 6 Mes molecules are solvophobically packed together to form five C-H···π contacts with each other in a unit cell. Moreover, 11 out of 12 pyridine rings in a unit cell form C-H···N bonds with the adjacent m-Py 6 Mes molecules.
Polymorphs of m-Py 6 Mes not only corroborate the δ Ddependency of Py 6 Mes polymorphs, but also tell us about the delicate energetic balance between Py close and Py open ·MeCN. Geometrically, Py 6 Mes can assemble into a dense packing as proved by Py close , m-Py VDW ·MeCN, or m-Py VDW ·EtOAc. However, unlike m-Py 6 Mes, the position of the N atoms is static upon the rotation of the pyridyl rings around the single bond, which is unfavorable for the formation of multiple C-H···N bonds  Crystal structure information of m-Py VDW ·MeCN, m-Py VDW ·EtOAc, m-Py VDW ·iPA, and m-Py VDW ·CHCl 3 together with relative permittivity (ε) 37 and the Hansen dispersion cohesion parameters (δ D ) 34 of the crystallization solvents. with each other. Therefore, Py 6 Mes may prefer to form a porous framework, in which Py 6 Mes can form multiple C-H···N and C-H···π contacts with each other at the expense of the packing efficiency.

Conclusion
In conclusion, we succeed in establishing a solvophobicity-based design strategy for the synthesis of porous molecular crystals and succeed in synthesizing porous molecular crystals by using various organic solvents. Typical procedure for the synthesis of single crystals of Py 6 Mes, m-Py 6 Mes, and Ph 6 Mes. A glass vial containing saturated solution of Py 6 Mes, m-Py 6 Mes, or Ph 6 Mes was placed at 25°C with a cap loosely fastened to allow the solvent to evaporate sluggishly until some precipitates emerged. The precipitates were poured onto paraffin oil and were picked up by a loop.
Computational analysis. The FMO method 31 using the second-order Møller-Plesset perturbation theory (MP2) with the resolution-of-the-identity (RI) approximation was used to elucidate the insight into the intermolecular energy between contact pairs of Py 6 Mes. Firstly, each molecule of Py 6 Mes was divided into four molecular fragments: F1, F2, F3 (1,3-di(pyridin-4-yl)benzene), and F4 (mesitylene) as shown in Supplementary Fig. 23c. The geometry optimization was then performed with the standard 6-31 + G(d) basis set implemented in GAMESS program package 32 . The molecular coordinates remained the same as the initial structure during the FMO calculation. Among the eight fragments of the contact pairs of Py 6 Mes ( Supplementary Fig. 23a, b), any two fragments (I and J) were subjected to the calculation of the interaction energy decomposition analysis (PIEDA, Supplementary Table 15) 30 . The total of the contributed energy terms (E total )) is given in Eq. (1).
where E ES is the classical electrostatic energy between Py 6 Mes, E CT + mix is the charge transfer energy with higher-order mixed terms energies, E vdW is the vdW dispersion energy, and E EX is the exchange repulsion between the adjacent fragments.
The total of the attractive energies (E att ) is given in Eq. 2.
The total system energies of Py open •MeCN in a series of organic solvents with different relative permittivity ε are calculated by the conductor-like polarizable continuum model method.

Data availability
The data that support the findings in this study are available within the article and its Supplementary Information and/or from the corresponding authors on reasonable request. The X-ray crystallographic data reported in this article is deposited at the Cambridge Crystallographic Data Center (CCDC) under deposition numbers of 2072485-2072491 and 2095190-2095195. These data can be obtained free of charge from The Cambridge Crystallographic Data Center via www.ccdc.cam.ac.uk/ data_request/cif. Received: 12 April 2021; Accepted: 6 August 2021;