Introducing Prism[4]arene: A Macrocycle with Enantiomerically Resolvable Inherent Chirality and Intriguing Chiroptical Properties

Abstract

This study presents the first report of an inherently chiral prismarene with resolved enantiomers. Prism[4]­arenes, synthesized via a thermodynamic template approach using a tailor-made selective cation, effectively maintain their chirality due to their strained macrorings and narrow annuli, which prevent the flipping of naphthalene rings. The solid-state structure of the synthesized PrS­[4] ^iPe revealed a racemic crystal composed of all-pR and all-pS enantiomeric pairs, forming supramolecular polymeric chains of homochiral molecules interlinked by intermolecular host–guest interactions. Both enantiomers were resolved by using chiral high-performance liquid chromatography (HPLC), and their chiroptical properties were thoroughly investigated. Configurational assignment was achieved through time-dependent density functional theory (TDDFT) computations alongside electronic circular dichroism/ultraviolet–visible (ECD/UV–vis) spectral analysis. Notably, the circularly polarized luminescence (CPL) properties exhibited a significant dissymmetry ratio of 0.008 for these prism[4]­arenes, due to electric and magnetic dipole transition moments both directed along the cylinder axis. Furthermore, the ability of PrS­[4] ^iPe to achieve enantioselective recognition with chiral ammonium guests was demonstrated.

Introduction

The design and synthesis of macrocycles have been a significant challenge in supramolecular chemistry for decades. , Researchers have devoted considerable efforts to creating artificial systems that mimic natural molecules like proteins and enzymes. , Among them, macrocyclic arenes with deep cavities, − chiral structures, and peculiar (chiro)­optical properties have emerged as particularly attractive biomimetic hosts due to their potential applications across various fields. ,

Additionally, from the perspective of emissive chiroptical spectroscopies, such as circularly polarized luminescence (CPL), there has been considerable interest in macrocycles with strong CPL responses, which is beneficial for sensing and electro-optical applications. − Notably, examples have been reported by Sato and Fukunaga, who described macrocycles exhibiting chirality in their cylindrical molecular structures, resulting in extremely large dissymmetry factors associated with circularly polarized light. Prismarenes ,,− (Figure ) represent a novel class of macrocycles constituted of methylene-bridged 2,6-dialkoxynaphthalene units, featuring distinctive deep cavities. Recently, there has been a surge of research focused on the synthesis and investigation of the supramolecular properties of these intriguing compounds. − To date, the synthesis of prismarenes comprising five and six naphthalene units (PrS­[5] ^R and PrS­[6] ^R in Figure ) has been reported. ,,−

1.

(a) Chemical drawings of the prism­[n]­arene family, highlighting various members. (b, c) Flipping-induced inversion of planar chirality (FIIPC) in prismarenes by oxygen-through-the-annulus passage. (b) FIIPC mechanism inhibited in prism[4]­arene (this work). (c) FIIPC active in prism[5]­arene.

Prismarenes display planar chirality of naphthalene moieties established by the curvature of the macroring (Figure ). , Each 2,6-dialkoxynaphthalene ring can adopt one of two configurations, referred to as pR and pS (Figure ), with the most stable isomers being the homochiral all-pR/all-pS. These conformational isomers are capable of interconverting by oxygen-mediated concerted rotations of the naphthalene units through the annulus (Figure c). ,,

Notably, the all-pS and all-pR enantiomers of permethylated prismarenes (PrS­[5] ^R and PrS­[6] ^R in Figure ) can interconvert via this mechanism, a process that occurs rapidly on the NMR time scale. ,, However, the presence of long substituents or branched alkyl groups at both rims of prism[5]­arenes slows down inversion without completely hindering it. This is particularly evident considering that, while cyclohexylmethyl groups are sufficiently large to enable enantiomeric separation of pillar[5]­arene macrocycles without racemization, they still allow the passage of naphthalene units in prism[5]­arenes. These considerations clearly indicate that resolving prismarene enantiomers is challenging due to the large ring size of the prismacyclic structure.

However, successfully blocking the planar chirality in these macrocycles would be highly beneficial, as it would pave the way for numerous applications, especially in materials chemistry and chiral sensing. − Among macrocycles with stable chirality, Ogoshi and colleagues have recently demonstrated that 2-benzofuranyl groups are sufficiently large to induce stable chirality in pillar[5]­arene molecules. An additional example of conformationally stable chiral macrocycles is provided by Chen, who reported the synthesis of octopus[3]­arenes. Most recently, Cai and colleagues have developed a water-soluble macrocycle exhibiting chiral stability with effective enantioselective recognition properties. In 2020, Wang and colleagues reported an intriguing example of inherently chiral tetraazacalix[4]­aromatics. These new macrocycles exhibited stable chirality, along with pH-triggered, switchable circular dichroism, and circularly polarized luminescence.

Finally, Chuan-Feng Chen previously reported the synthesis of anthracene-based planar chiral macrocycles, termed pagod[4]­arene, which are formed from four 2,6-dimethoxyanthracene units. These macrocycles exhibit stable planar chirality due to the narrow cavity that impedes the interconversion of the two enantiomers via the oxygen-through-the-annulus passage.

Therefore, to achieve the goal of impeding the racemization of prismarenes, we restricted the size of the cavity by reducing the number of monomers in the macrocycle. In this work, we achieved the synthesis of the first racemic prismarene, which can be resolved into its individual enantiomers, allowing investigation of enantiospecific recognition and chiroptical properties of this class of chiral macrorings.

In detail, we demonstrated that a thermodynamically templated macrocyclization, ,, facilitated by a tailor-made templating agent, allows the isolation of the first example of prism[4]­arene from the reaction mixture.

The racemic PrS­[4] ^iPe was characterized by NMR and single-crystal X-ray diffraction. The two enantiomers of prism[4]­arene were separated using chiral high-performance liquid chromatography (HPLC), and their chiroptical properties, i.e., electronic circular dichroism (ECD) and circular polarized luminescence (CPL), were investigated.

Density functional theory (DFT) calculations of ECD and CPL enabled us to determine the absolute configurations and conformational properties of the macrocycle in both the ground and excited states. Finally, we investigated the chiral recognition capabilities of this novel macrocycle.

Result and Discussion

Templated Synthesis of Prism[4]­arenes

To date, the tetramer prism[4]­arene has not been observed during the macrocyclization process involving 2,6-dialkoxynaphthalene units. Our previous research demonstrated that the main factors which direct the product distribution of prism­[n]­arene cyclooligomers are the solvent, the alkoxy groups, and the presence of templates. ,,, For example, prism[5]­arene are preferentially formed in halogenated solvents, such as 1,2-dichloroethane (DCE), particularly when templating agents like DABCO cations are utilized. , The formation of prism[6]­arene is significantly enhanced, reaching 75–90%, when cyclohexane is used as the solvent and the alkyl chains are of suitable size and length to facilitate effective self-filling of the hexamer’s cavity (typically ethyl and propyl). In our systematic study on the investigation of the effects of these factors, when 2,6-bis­(isopentyloxy)­naphthalene 1a underwent macrocyclization with paraformaldehyde, trifluoroacetic acid (TFA), in cyclohexane solution (Scheme ), the desired PrS­[4] ^iPe was obtained with a yield of 5% (Table ). Additionally, chromatographic purification and spectrometric analysis identified linear oligomers as well as a complicated mixture of other prismarene cyclooligomers.

1. Tailor-Made Template Synthesis of Prism[4]­arenes.

1. Synthesis of PrS­[4] ^R (R = iPe and EtCy) from Starting Monomers (1a,b in Scheme ) and Templating Agents (2–5)⁺ as Chloride Salts, along with Binding Constant Values (K _ass, M^–1) Determined by ¹H NMR Experiments (See the SI for Details; Mean Values of Three Measurements, Estimated Errors <15%,).

templating agent (G + )	R	PrS[4] R (yield %)	K assG+@ PrS[4] R
–	iPe	5
2 +	iPe	20	45,000
3 +	iPe	5	125
4 +	iPe	4	4200
5 +	iPe	4	5600
2 +	EtCy	15	1000

^aCalculated by integrating the free and complexed ¹H NMR signals of the host.

^bCalculated using a ¹H NMR competition experiment with methoxy-prism[5]­arene as a competitive host.

^cGuest 2 ⁺ was tested also with I^– and Br^– as counterions, but no significant differences in yield were observed.

The high-resolution Fourier transform ion cyclotron resonance (FT-ICR) mass spectrum confirmed the molecular mass of PrS­[4] ^iPe , with an observed molecular ion peak at m/z of 1248.8354, matching the calculated value of 1248.8352 for [M]⁺. Detailed one-dimensional (1D) and two-dimensional (2D) NMR analyses (SI) demonstrated that all naphthalene rings of PrS­[4] ^iPe are interconnected at their 1,5-positions, exhibiting D ₄ symmetry. This structural arrangement was further confirmed by X-ray crystallographic analysis (vide infra). The ¹H NMR spectrum (Figure e, 600 MHz, 298 K, CD₂Cl₂) of PrS­[4] ^iPe displayed an aromatic AX system at 8.19 and 6.89 ppm (J = 9.0 Hz), a singlet attributable to the methylene bridges at 4.68 ppm, and an AB system at 4.20 and 4.10 ppm associated with diastereotopic OCH₂ groups (Figure e). Moreover, ultraviolet–visible (UV–vis) and emission spectra were recorded (SI, dichloromethane, 25 °C). Absorption spectrum shows three bands at 237, 286, and 352 nm and exhibits a fluorescence maximum at λ_em= 385 nm (fluorescence quantum yield ϕ = 0.23). With these results in hand, the objective was to identify an effective templating guest that could enhance the yield of prism[4]­arenes during the macrocyclization process. , Given the smaller cavity of prism[4]­arene compared to its pentameric and hexameric counterparts (see Figure and the Solid-State Studies section), the study focused on the complexation abilities toward axle-type dialkylammonium and tetraalkylammonium ions 2 ⁺ –5 ⁺ (Scheme ).

2.

(a) Schematic illustration of the complexation between PrS­[4] ^R and ammonium guests; (b–e) ¹H NMR spectra (CD₂Cl₂, 600 MHz) of: (b) a 1:1 mixture of PrS­[4] ^iPe and 5 ⁺ at 233 K (4.56 mM), with assignments delineated in (h); (c) a 1:1 mixture of PrS­[4] ^iPe and 4 ⁺ at 298 K (4.00 mM), with assignments shown in (g); (d) a 1:1 mixture of PrS­[4] ^iPe and 2 ⁺ at 298 K (2.67 mM), with assignments depicted in (f); (e) PrS­[4] ^iPe at 298 K. (f–h) Cartoon representations of the endo-cavity complexes G ⁺ @PrS­[4] ^iPe .

3.

Representation with molecular surface of DFT-optimized structures at B97D3/SVP/SVPFIT level of theory of: (a) PrS­[4] ^iPe , (b) 2 ⁺ @PrS­[4] ^iPe , (c) 3 ⁺ @PrS­[4] ^iPe , and (d) 5 ⁺ @PrS­[4] ^iPe complexes in side view (top) and top view (bottom).

In accordance with a standardized protocol, , we conducted ¹H NMR spectroscopic investigations to evaluate the binding affinity of PrS­[4] ^iPe with the selected cations 2 ⁺ –5 ⁺ as barfate salts (BArF^– in Scheme ).

When 2 ⁺ as a barfate salt was mixed in equimolar ratios with PrS­[4] ^iPe in a CD₂Cl₂ solution, the ¹H NMR spectra of both the host and guest (Figure d) exhibited significant changes, indicating the formation of the endo-cavity complex 2 ⁺ @PrS­[4] ^iPe . The ¹H NMR spectrum of 2 ⁺ @PrS­[4] ^iPe (Figure d) exhibits two aromatic signals at 8.32 and 6.99 ppm (Δδ = 1.33 ppm), and diastereotopic hydrogens of OCH ₂ groups were found at 4.24 and 4.13 ppm. The rod-like 2 ⁺ cation is threaded through the central cavity of PrS­[4] ^iPe , forming a pseudo[2]­rotaxane architecture (Figure b). This structure was confirmed by 1D and 2D NMR analyses (SI). In particular, the ¹H NMR spectrum (Figure d) shows signals at negative chemical shifts, which can be assigned to guest 2 ⁺ . Specifically, broad signals at −0.74, −1.35, and −2.25 ppm are attributed to the ⁺NH₂ group and the CH₂ groups in the β and α positions, respectively. In the HSQC spectrum, the β and α signals at −1.35 and −2.25 ppm correlate with carbon signals at 26.3 and 44.0 ppm (SI).

The complexation process between 2 ⁺ and PrS­[4] ^iPe occurs slowly on the NMR time scale. The association constant (K _ass) for the formation of the 2 ⁺ @ PrS[4] ^iPe complex was determined through an NMR competition experiment against the previously characterized PrS­[5] ^Me , yielding a value of 4.5 × 10⁴ M^–1 (Table and SI).

Comparable spectral features were found in the ¹H NMR spectrum of the 3 ⁺ @PrS­[4] ^iPe complex (SI). The signals of guest ion 3 ⁺ , threaded within the macrocyclic cavity, experienced shielding effects, resulting in negative chemical shift values. Specifically, the ⁺NMe signal was observed at 2.96 ppm, while the α–CH₂ signal appeared at −2.24 ppm, as confirmed by COSY and HSQC experiments (SI). A binding constant of 125 M^–1 was calculated for the formation of the 3 ⁺ @PrS­[4] ^iPe complex (Table ), which is significantly lower than that for the 2 ⁺ @PrS­[4] ^iPe complex.

This indicates that the interaction between the 3 ⁺ cation and the PrS­[4] ^iPe host is weaker than that of the 2 ⁺ cation. This reduced binding affinity may stem from the steric hindrance introduced by the N­(Me)₂ group (Figure c) within the cavity of prismarene, which can limit the accessibility and optimal fitting of the 3 ⁺ cation within the host structure.

Notably, PrS­[4] ^iPe exhibits no conformational changes upon endo-cavity complexation with guests 2 ⁺–5 ⁺. In contrast, larger prism[5]­arene typically undergoes conformational adaptation during complexation with cationic guests, as evidenced by ¹H NMR studies. , For example, the spacing Δδ between the aromatic doublets shifts from approximately 1.2 ppm in the free prism[5]­arene PrS­[5] ^R to 1.6 ppm when complexed G ⁺@PrS­[5] ^R , indicating an induced fit process to accommodate the guest. , Comparatively, the Δδ of the aromatic protons of the complexed PrS­[4] ^iPe in the G ⁺ @PrS­[4] ^iPe complex remains identical to that of the free macrocycle PrS­[4] ^iPe (about 1.3 ppm). This result suggests that the rigid structure of PrS­[4] ^iPe does not experience significant conformational changes upon guest threading (see the comparison between panels (a) and (b) of Figure , top view). These structural features invoke Cram’s preorganization principle, indicating that the internal cavity of the prism[4]­arene host exhibits a high degree of preorganization, thereby facilitating the complexation of suitable guest molecules.

Upon addition of one equivalent of the diethylammonium guest 4 ⁺ as a barfate salt to a CD₂Cl₂ solution of PrS­[4] ^iPe , the ¹H NMR spectrum (Figure c) of the resulting mixture exclusively displayed signals corresponding to the 4 ⁺ @ PrS[4] ^iPe complex. Signals were observed at −1.73 and −0.94 ppm, corresponding to the CH₃ and CH₂ protons of the guest, respectively. Additionally, a signal at −0.13 ppm was observed for the ⁺NH₂ group. A binding constant of 4200 M^–1 was calculated for the complexation of 4 ⁺ , which is significantly higher than that observed for the complexation of 3 ⁺ . This result confirms that prism[4]­arene prefers rod-shaped linear guests.

The ¹H NMR spectrum in Figure b highlights the complexation of butylbenzylammonium 5 ⁺ , resulting in the formation of 5 ⁺ @PrS­[4] ^iPe . Specifically, confirmed by the DFT-optimized structure of the 5 ⁺ @PrS­[4] ^iPe complex, illustrated in Figure d, the butyl chain is deeply embedded within the cavity of PrS­[4] ^iPe . Meanwhile, the bulky benzyl moiety is located externally, in contact with the rim, facilitating C–H···π interactions with the isopentyl groups. The interlocking of the benzyl group among the isopentyl chains likely restricts the rotational freedom of guest 5 ⁺ within the cavity of PrS­[4] ^iPe , which may explain the presence of diastereotopic signals for the β–H of 5 ⁺ , as depicted in Figures b and d. A binding constant of 5600 M^–1 was calculated for the formation of 5 ⁺ @PrS­[4] ^iPe , which is comparable to that of 4 ⁺ @PrS­[4] ^iPe (Table ).

Natural Bond Orbital (NBO) and Noncovalent Interaction (NCI) calculations , were conducted on the 2 ⁺ –4 ⁺ complexes utilizing the B97D3/SVP/SVPFIT level of theory (see the SI). The dipentylammonium cation 2 ⁺ establishes CH···π and ⁺N–H···π interactions with PrS­[4] ^iPe , contributing 72 and 14% to the total interaction energy, respectively. According to the DFT-optimized structures presented in Figure , calculations indicate that 2 ⁺ occupies 92% of the internal volume upon complexation. In comparison, the volumes occupied by the 3 ⁺ , 4 ⁺ , and 5 ⁺ cations are 60, 52, and 59%, respectively. The NBO analysis of the 3 ⁺ @PrS­[4] ^iPe complex reveals a similar proportion of CH···π interactions; however, the cation’s ⁺N···π interactions account for only 1%. The presence of the N–Me group in 3 ⁺ hinders the optimal fitting of the axis within the cavity, thereby limiting the access of the positively charged nitrogen.

Based on the data presented in Table , the dipentylammonium cation 2 ⁺ appears to be the best candidate as a template for the directed synthesis of PrS­[4] ^iPe .

In cyclohexane as solvent, 2,6-bis­(isopentyloxy)­naphthalene 1a (5.0 mM) was reacted with paraformaldehyde and trifluoroacetic acid (TFA) in the presence of 1 equiv of the dipentylammonium 2 ⁺ as chloride salt. The reaction progress was monitored by thin-layer chromatography (TLC). After 22 h, the reaction was quenched by adding a saturated aqueous solution of sodium bicarbonate (NaHCO₃). Following standard workup procedures and chromatographic purification, PrS­[4] ^iPe was obtained with a yield of 20%, along with a mixture of linear oligomers, and a complex mixture of other prismarene compounds. The macrocyclization in Scheme was also conducted in the presence of 2 ⁺ as I^– or Br^– salts (Table ). No significant differences in yields were observed with the iodide or bromide salt of 2 ⁺ (Table ). To confirm the hypothesized relationship between the affinity of 2 ⁺ –5 ⁺ for PrS­[4] ^iPe quantified as the binding constant values for their prismarene complexes (Table )and their efficiency as templates, which is assessed through macrocyclization yield, we also conducted reactions using the cations 3 ⁺ –5 ⁺ (see Table ).

Specifically, when 2,6-bis­(isopentyloxy)­naphthalene 1a was subjected to macrocyclization under the conditions outlined in Scheme , the isolation of PrS­[4] ^iPe in the presence of template 3 ⁺ yielded only 5% (Table ). This yield is significantly lower than that achieved with template 2 ⁺ and is comparable to the yield observed when the reaction was conducted without any template. Similarly, low yields of PrS­[4] ^iPe were observed in the presence of the templating agents 4 ⁺ and 5 ⁺ (Table ), which exhibit a lower affinity for the prismarene PrS­[4] ^iPe compared to 2 ⁺ . Therefore, only guest 2 ⁺ shows a significant template effect, while all the other guests, having a binding affinity at least 1 order of magnitude lower, show no template effect in the synthesis (Table ). These findings indicate that in the thermodynamically driven macrocyclization of prismarenes, the design of the templating agent should be based on its binding affinity for the macrocycle. Finally, the cation 2 ⁺ was effective as templating agent even in the macrocyclization of 2,6-bis­(2-cyclohexylethoxy)­naphthalene 1b. When 1b was reacted with paraformaldehyde in the presence of TFA in cyclohexane and 2 ⁺ ·Cl^– as templating agent the reaction afforded PrS­[4] ^EtCy with a yield of 15% (Table ).

Solid-State Studies

Single crystals suitable for X-ray diffraction (XRD) analysis were obtained through the slow evaporation of a methanol/dichloromethane solution containing PrS­[4] ^iPe .

While the prismarene molecules lie on C ₂ crystallographic symmetry axes which pass through opposite methylene bridges, the prism[4]­arene skeletons show pseudo D ₄ point symmetry (Figure a,b). Therefore, all of the naphthalene units of each molecule have the same planar chirality. The centrosymmetric crystal is composed of a racemic mixture of all-pR and all-pS enantiomeric pairs (Figure e). The pseudo D ₄ point symmetry of the scaffold is stabilized by eight weak intramolecular C–H···O hydrogen bonds (C···O distances ranging from 3.05 to 3.22 Å, SI), involving the hydrogen atoms of the equivalent 4 and 8 naphthalene positions pointing toward the oxygen lone pair of the neighboring alkoxy groups.

4.

Top view (a) and side view (b) of the solid-state structure of PrS­[4] ^iPe . The molecule is shown as a capped stick representation inside its van der Waals surface. (c) Geometric characteristics of the internal cavity of PrS­[4] ^iPe : void volume (V), opening (B), and contact surface area (A). (d) Linear homochiral polymeric assembly of PrS­[4] ^iPe , formed by the mutual threading of isopentyl chains. Each cavity hosts two isopentyl threads from adjacent prismarenes. The central molecule (brown) is shown as a capped stick representation inside its transparent van der Waals surface, to aid visualization of the threaded isopentyl chains of the adjacent molecules (cyan). (e) Crystal packing of PrS­[4] ^iPe enantiomeric pairs: all-pR (cyan) and all-pS (green), as viewed along the 3̅-axes. (f) Detail of one enantiomeric pair.

The crystal packing shows the formation of supramolecular polymeric chains composed of homochiral PrS­[4] ^iPe molecules (Figure d). In particular, the PrS­[4] ^iPe macrocycles form a linear homopolymeric assembly along the c-axis by mutual threading of isopentyl chains inside the cavity of adjacent prismarenes, related by translation of the unit cell and therefore with the same planar chirality (Figure d). The hexagonal arrangement of these linear homochiral polymeric assemblies along the rotoinversion 3̅-axes is characterized by the alternate disposition of all-pR and all-pS chains (Figure e). The prism[4]­arene scaffold shows only a small deviation from a regular square prism, as indicated by the dihedral angles between the mean planes of the naphthalene rings.

These angles are 93 and 96° for the naphthalene moieties related by symmetry (SI), while the two angles between the independent naphthalene moieties are 86°. This deformation, with two opposite dihedral angles being obtuse and two being acute, is apparent in the two diagonal distances between the opposite methylene bridges, which are 9.24 and 8.86 Å (SI).

All naphthalene planes are slightly bent (with a dihedral angle of 9–10° between the mean planes of the two fused aromatic rings) outward from the cavity, forming a saddle-like deformation. The distances between the adjacent methylene bridges, which represent the base of the prism, are 6.36 and 6.44 Å (SI).

The surface area, A, and volume, V, of the regular square prism enclosed by the aromatic walls of PrS­[4] ^iPe have been evaluated based on the geometrical method reported in a previous paper (Figure c and SI). In particular, the volume V of the regular square prism enclosed by the macrocycle was calculated as the product of the area of the square base B, which represents the cavity opening, and the geometric height (SI). In addition, the potential contact surface area, A, was calculated as the total internal area of the four rectangular prism faces (Figure c). The calculated internal volume of 87 ų for the prism[4]­arene scaffold is approximately 1/3 of the volume enclosed by prism[5]­arene (255 ų) and less than 1/5 of that of prism[6]­arene (490 ų). This volume is also less than half of the enclosed volume of the analogous pagoda[4]­arene based on 2,6-dialkoxylanthracene (206 ų). The cavity opening, B, is strictly related to the number of monomers in the macrocycle. Thus, prism[4]­arene shows a narrower opening (9.3 Ų) than prism[5]­arene and prism[6]­arene (27.3 and 52.4 Ų, respectively). Interestingly, the comparison with the analogous anthracene tetramer, pagoda[4]­arene, shows that the smaller enclosed volume of the naphthalene derivative, prism[4]­arene is mainly due to the smaller opening of the cavity (19.1 Ų in pagoda[4]­arene), while the depth of the cavity is similar (9.35 and 10.78 Å in prismarene and pagodarene, respectively). Another important geometric feature is the potential contact surface area A, derived from the total area of the rectangular prism faces. In this case, the prism[4]­arene also exhibits a smaller potential contact area (114 Ų) than the other macrocycles evaluated: prism[5]­arene (186 Ų), pagoda[4]­arene (188 Ų), and prism[6]­arene (252 Ų).

Chiral Resolution, Determination of Absolute Configuration, and Chiroptical Properties of Prism[4]­arene

Starting from the racemic mixtures of PrS­[4] ^iPe and PrS­[4] ^EtCy , we proceeded to separate their enantiomers using HPLC on a cellulose phenyl carbamate (OD) chiral stationary phase (SI and Figure ). When rac-PrS­[4] ^iPe was separated onto the chiral column, the chromatogram (Figure S75) revealed two distinct peaks of equal area, confirming that rac- PrS­[4] ^iPe consisted of an equimolar mixture of all-pS-PrS­[4] ^iPe and all-pR-PrS­[4] ^iPe (Figure ). We isolated both fractions and measured their optical rotations in dichloromethane. The first eluted fraction exhibited a specific rotation of [α]_D = −14.9° (c = 1.1 mg·mL^–1), while the second showed [α]_D = +15.0° (c = 1.1 mg·mL^–1). Furthermore, ECD analysis of these isolated fractions produced mirror-image spectra (Figure c), providing additional evidence that the resolution of the enantiomers was successfully achieved, and no subsequent racemization occurred. The racemization of (−)-PrS­[4] ^iPe and (+)-PrS­[4] ^iPe was not observed even when their solution in cyclohexane was heated to 70 °C for 48 h (Figure S75). Analogously, the resolution of rac-PrS­[4] ^EtCy was efficiently achieved by chiral HPLC (Figure S76). Both fractions of rac-PrS­[4] ^EtCy were separated and collected.

5.

Representation of the X-ray molecular structures of (a) all-pS-PrS­[4] ^iPe and (b) all-pR-PrS­[4] ^iPe . (c) Experimental ECD (top trace) and UV (bottom trace) spectra of (−)-PrS­[4] ^iPe (blue, first eluted) and (+)-PrS­[4] ^iPe (red, second eluted) and TDDFT/CAM-B3LYP/6–311G­(d,p) computed ECD (top trace) and UV (bottom trace) spectra for all-pS-PrS­[4] ^iPe (dashed Black). (d) Experimental ECD (top trace) and UV (bottom trace) (−)-PrS­[4] ^EtCy (blue, first eluted) and (+)-PrS­[4] ^EtCy (red, second eluted).

The first eluted showed a specific rotation of [α]_D = −4.1° (c = 2.0 mg·mL^–1), while the second eluted showed [α]_D = +4.0° (c = 2.0 mg·mL^–1). ECD analysis of these isolated fractions also produced mirror-image spectra (Figure d). The ECD spectra recorded in the 180–400 nm wavelength range show several Cotton effects (CEs) that are very similar for both PrS­[4] ^iPe and PrS­[4] ^EtCy compounds (Figure c,d). For (−)-PrS­[4] ^iPe , at high wavelength, a negative band is visible at 364 nm followed by a weaker positive one at 335 nm, a weak negative one at 311 nm, and a positive band at 296 nm.

However, the main features of the spectrum are at lower wavelengths, with the two very strong CEs at 245 nm (negative) and 229 nm (positive), followed by the negative one at 184 nm. As expected, the ECD of the second eluted (+)-PrS­[4] ^iPe enantiomer is a mirror image of the (−)-PrS­[4] ^iPe spectrum.

The enantiomers of PrS­[4] ^EtCy exhibit ECD spectra that are nearly superimposable with the corresponding enantiomers of PrS­[4] ^iPe with the same [α]_D sign. As we have previously demonstrated for PrS­[5] ^R and PrS­[6] ^R prismarenes, the main observed bands can be ascribed to three distinct couplet features generated by exciton coupling between the long- and short-axis polarized transitions of naphthalene chromophores centered at 345, 269, and 228 nm, respectively (Figures S88 and S89).

The CE at higher energy is associated with the π–π* transitions of HOMO −2, −5, −6 to LUMO, +2, +4, and +5 of the naphthalene chromophores (Figure S90, Tables S4 and S5). Accordingly, application of the Harada-Nakanishi exciton chirality rule to the higher-energy long-axis polarized transition of the naphthalene chromophore at 228 nm can allow absolute configuration assignment to the macrocycle enantiomers (SI). In fact, we have previously shown that a negative couplet (negative at lower-energy and positive at higher-energy Cotton effect) can be associated with the all-pS enantiomer and a positive couplet with the all-pR enantiomer (Figures S88 and S89). Therefore, the first eluted enantiomers (−)-PrS­[4] ^iPe and (−)-PrS­[4] ^EtCy , both displaying a negative couplet at around 230 nm, are expected to have an all-pS absolute configuration. This preliminary configurational assignment was further supported by TDDFT computations of [α]_D and ECD/UV–vis spectra on pS-PrS­[4] ^iPe (SI). The starting geometry for TDDFT calculations on PrS­[4] ^iPe was retained by coordinates of the crystal structure and optimized at the DFT/B3LYP/6–311G­(d,p)/gas-phase level of theory. A computed [α]_D value of −23.9° was obtained for all-pS-PrS­[4] ^iPe at the DFT/B3LYP/TZVP level of theory, in agreement with [α]_D of the levorotatory first eluted enantiomer. The TDDFT/CAM-B3LYP/6–311G­(d,p)/gas phase computed ECD spectrum for all-pS-PrS­[4] ^iPe (Figure c, black dashed trace), was also in good agreement with the experimental, particularly in reproducing the most intense negative couplet at 237 nm, and thus confirming the all-pS-PrS­[4] ^iPe absolute configuration for the first eluted (−)-PrS­[4] ^iPe enantiomer. The less intense negative couplet at 346 nm is also well reproduced in terms of negative CE intensities but not so well in terms of wavelength position, mostly due to intrinsic limitations of the CAM-B3LYP functional. The structural and spectral similarity between the two resolved prismarenes can also allow the assignment of the absolute configuration for the PrS­[4] ^EtCy enantiomers.

Circularly Polarized Luminescence of Prism[4]­arenes

CPL spectra in Figure have been recorded for both eluted enantiomers of PrS­[4] ^EtCy and PrS­[4] ^iPe in 4.5 × 10^–4 M hexane solutions in 2 mm cuvette, with a homemade apparatus using an excitation wavelength of 345 nm. Spectra in Figure are reported after normalization of the corresponding fluorescence band. The two compounds show quite similar CPL features with practically the same intensity.

6.

CPL spectra of: (top) (−)-PrS­[4] ^iPe (blue), (+)-PrS­[4] ^iPe (red), and TD-DFT/M06/6–311g­(d,p) computed for all-pS-PrS­[4] ^Me model molecule (dashed); (bottom) CPL spectra of (−)-PrS­[4] ^EtCy (blue) and (+)-PrS­[4] ^EtCy (red). CPL has been plotted after normalizing the fluorescence signal recorded with the same apparatus. Excitation wavelength: 345 nm.

The sign of the CPL band correlates with the sign of the longest-wavelength ECD, as expected in all cases when the first excited state is similar in geometry and electronic properties to the ground state. The dissymmetry ratio for CPL, g _lum = ΔI/I = 2­(I _L – I _R)/(I _L + I _R), is about 0.008 (reaching 0.01 at 375 nm), comparable to g _abs of the first ECD band. The value is relatively high for an organic compound in the case of electric dipole-allowed transitions and is significantly higher than the value of 0.002 reported for prism[5]­arenes. , Such a high CPL dissymmetry ratio value can be ascribed to the D ₄ symmetry of the chromophoric system. In fact, the first chiral molecular square with D ₄ symmetry reported in the literature also has a significantly high g _abs. Furthermore, exceptionally high dissymmetry ratios have been reported for [4]­cyclochrysene derivatives with D ₄ symmetry by Sato and Fukunaga. This was attributed to “cylindrical chirality” responsible for generating a strong magnetic dipole transition moment. In this context, our newly synthesized prism[4]­arenes represent active chromophores with D ₄ symmetry. To simulate the CPL spectra, we conducted the TD-DFT analysis on a simpler PrS­[4] ^Me (see Figures S91–S95).

The model compound PrS­[4] ^Me reproduces very well the observed ECD on the two molecules, thus confirming that the pendants do not play any significant role in the low-energy bands of the spectrum (see Figure S92).

After optimization of ground and excited state at M06/6–311G­(d,p) level, we conclude that the first bright (i.e., symmetry allowed) transition is an A1→A2 transition both for absorption and emission (see Figure S95), with negative rotational strength for all-pS configuration. Ground and excited state structures are quite similar, which requires a low value of the Stokes shift, as observed (17 nm), and quite similar electronic level sequence, dipole and rotational strengths, and configuration interaction pattern. The bright transitions present parallel (antiparallel) electric and magnetic dipole transition moments and are directed along the cylinder axis, like the A1→A2 transition, or perpendicular to it (in this case with degeneracy, see Table S7).

Chiral Recognition Properties of Prism[4]­arenes

With these results in hand, the chiral recognition , abilities of prism[4]­arene were investigated (Table ). To determine the affinity of racemic PrS­[4] ^iPe for enantiopure ammonium guests, ¹H NMR titration experiments were conducted using the guests as their barfate salts (6–9 in Figure ).

2. Binding Constant Values (K _ass, M^–1) Determined by NMR Experiments (SI) and Chiral Selectivity Ratio Calculated by HR-MS Spectrometry Experiments.

guest	Kass G+@ PrS[4] iPe	chiral selectivity R L/R D
6 2+	1900	2.01
7 +	40,000	1.22
8 +	290	0.94
9 +	690	0.70

^aCalculated by integrating the free and complexed ¹H NMR signals of the host.

^bCalculated using a ¹H NMR competition experiment with methoxy-prism[5]­arene as a competitive host.

7.

Chemical drawings of enantiopure chiral guests G investigated in this study and barfate counterion (BArF^–).

The selected guests comprised the dicationic ethyl ester of the amino acid Lysine 6 ²⁺, a chiral primary ammonium cation 7 ⁺, a secondary aliphatic ammonium cation 9 ⁺, and a secondary ammonium cation with an aromatic group 8 ⁺ (Figure ). We began our investigation of the chiral binding affinity with (l)-lysine ethyl ester 6 ²⁺ . Complexation studies in CD₂Cl₂ of rac-PrS­[4] ^iPe with (S)-6 ²⁺ revealed endo-cavity complexation of the −CH₂CH₂CH₂CH₂NH₃ ⁺ moiety within the PrS­[4] ^iPe (see the SI and DFT structures in Figure a,e).

8.

DFT-optimized structure of complexes obtained at B97D3/SVP/SVPFIT level of theory of (a) (S)-6 ^{2 +} @pS-PrS­[4] ^iPe , (b) (S)-7 ⁺ @pS-PrS­[4] ^iPe , (c) (S)-8 ⁺ @pS-PrS­[4] ^iPe , and (d) (S)-9 ⁺ @pS-PrS­[4] ^iPe . Gradient RDG isosurfaces (0.25) for the noncovalent interaction (NCI) regions of (e) (S)-6 ^{2 +} @pS-PrS­[4] ^iPe , (f) (S)-7 ⁺ @pS-PrS­[4] ^iPe , (g) (S)-8 ⁺ @pS-PrS­[4] ^iPe , and (h) (S)-9 ⁺ @pS-PrS­[4] ^iPe . Normalized percentages of the intact (S)@pR (blue) and (S)@pS (red) complexes, plotted against collision energy in the center-of-mass frame: (i) 6 ^{2 +} @pS-PrS­[4] ^iPe , (j) 7 ⁺ @pS-PrS­[4] ^iPe , (k) 8 ⁺ @pS-PrS­[4] ^iPe , (l) 9 ⁺ @pS-PrS­[4] ^iPe .

This was evidenced by NMR signals exhibiting negative chemical shifts between 0 and −2.5 ppm (SI). An apparent binding constant of 1900 M^–1 was determined for the complexation of (S)-6 ^{2 +} with rac- PrS­[4] ^iPe in CD₂Cl₂. Analysis of the 1D and 2D NMR spectra revealed considerable difficulty in distinguishing the signals of the two (S)-6 ^{2 +} @pR-PrS­[4] ^iPe and (S)-6 ^{2 +} @pS-PrS­[4] ^iPe diastereomers. This isochronicity is likely favored by the conformational rigidity of the prismarenic framework.

Given the difficulty in distinguishing the two diastereomeric complexes using 1D and 2D NMR in solution, we employed MS/MS techniques in the gas phase, utilizing soft ionization methods, specifically, electrospray ionization (ESI). This approach facilitated a detailed analysis of the gas-phase stability and chiral recognition of guests 6–9 with PrS­[4] ^iPe . ,, The high-resolution electrospray ionization Fourier transform ion cyclotron resonance (HR ESI-FT-ICR) mass spectrum (Figure S37) of an equimolar mixture of rac-PrS­[4] ^iPe and 6 ^{2 +} in CH₂Cl₂ displayed a molecular ion peak at m/z 712.4947, consistent with the molecular formula of the complex (SI). To further investigate the relative stability of the (S)-6 ²⁺@all-pS-PrS­[4] ^iPe complex (Figure a) in comparison to the (S)-6 ²⁺@all-pR-PrS­[4] ^iPe diastereoisomeric complex in the gas phase, collision-induced dissociation (CID) experiments were conducted at collision energies ranging from 0.1 to 0.4 eV for each PrS­[4] ^iPe enantiomer (Figure ). , An equimolar solution of all-pS-PrS­[4] ^iPe (or all-pR-PrS­[4] ^iPe ) and (S)-6 ²⁺ in dichloromethane was prepared, and collision experiments were conducted by isolating the complex and subjecting it to collisions at different energies.

As illustrated in Figure i, the normalized percentage of the intact complex was plotted against the collision energy in the center-of-mass frame. (S)-6 ²⁺@all-pS-PrS­[4] ^iPe exhibited greater resistance to dissociation compared to the (S)-6 ²⁺@all-pR-PrS­[4] ^iPe complex. Specifically, while 50% of the (S)-6 ²⁺@all-pR-PrS­[4] ^iPe complex dissociated at 0.21 eV, only 7% of the (S)-6 ²⁺@all-pS-PrS­[4] ^iPe complex fragmented under the same conditions. To estimate the ability of all-pR-PrS­[4] ^iPe and all-pS-PrS­[4] ^iPe to discern the chirality of l-lysine methyl ester, we have calculated the R _chiral ratio (R _L/R _D). Here, R _L is defined as I _{[(S)‑6 ⁺⁺@all‑pS‑PrS[4] ^iPe ]}/ I _{[all‑pS‑PrS[4] ^iPe ]} and R _D as I _{[(S)‑6 ⁺⁺@all‑pR‑PrS[4] ^iPe ]}/ I _{[all‑pR‑PrS[4] ^iPe ]} (I = signal intensity in mass spectra). , An R _chiral value approaching 1 indicates a diminished capacity for chiral recognition, while values greater than or less than 1 suggest relatively high chiral recognition capability. Mass spectra for equimolar solutions (1 × 10^–4 mol/L) of l-lysine methyl ester and all-pS-PrS­[4] ^iPe , and l-lysine methyl ester and all-pR-PrS­[4] ^iPe were analyzed, yielding an R _chiral of 2.01 (Table ). Thus, in agreement with the results of the CID experiments, the R _chiral measurements also indicate that the binding strength of the (S)-6 ²⁺@all-pS-PrS­[4] ^iPe is greater than that of (S)-6 ²⁺@all-pR-PrS­[4] ^iPe .

Density functional theory (DFT) calculations (B97D3/SVP/SVPFIT level of theory, Figure a,e) show that the (S)-6 ^{2 +} @all-pS-PrS­[4] ^iPe complex is more stable than the (S)-6 ^{2 +} @all-pR-PrS­[4] ^iPe by 1.31 kcal/mol. Specifically, a stronger H2N⁺–H···O^prismarene H-bond interaction (NH···O distance of 2.7 Å, angle of 173°) was identified in the (S)-6 ^{2 +} @all-pS-PrS­[4] ^iPe complex, in comparison to the (S)-6 ²⁺ @all-pR-PrS­[4] ^iPe complex (NH···O distance = 2.8 Å, angle = 161°). NBO analysis corroborated this, showing that hydrogen bonding interaction contributed 29% of the total interaction energy in the (S)-6 ^{2 +} @all-pS-PrS­[4] ^iPe complex, compared to 17% in the (S)-6 ^{2 +} @all-pR-PrS­[4] ^iPe . The molecular model shows that the ester group is significantly outside the cavity (Figure a).

With these results in hand, we investigated the chiral recognition abilities of simpler and smaller (S)-7 ⁺. The addition of one equivalent of (S)-7 ⁺ to a dichloromethane solution of racemic PrS­[4] ^iPe resulted in significant changes in their ¹H NMR spectra. The observed upfield shift of the guest’s ⁺N–CH₂ signal to 1.00 ppm (see the SI) indicates the formation of the (S)-7 ⁺@PrS­[4] ^iPe complex. In contrast, no significant chemical shift change was observed for the CH₃ and CH₃CH₂ protons, indicating that this portion of the chain remains outside the cavity (see Figure b). In the ¹H NMR spectrum of the equimolar rac-PrS­[4] ^iPe /(S)-7 ⁺ mixture, the signals for the free host were absent. The apparent binding constant for the complexation of rac-PrS­[4] ^iPe in CD₂Cl₂ with (S)-7 ⁺ was determined to be 40000 M^–1 via a competition experiment using PrS­[5] ^Me . The HR ESI-FT-ICR mass spectrum (Figure S41) of an equimolar mixture of PrS­[4] ^iPe and 7 ⁺ in CH₂Cl₂ displayed a molecular ion peak at m/z 1336.9503, which aligns with the molecular formula of the complex. Gas-phase collision-induced dissociation (CID) and R _chiral ratio for the diastereoisomeric complexes reveal that the (S)-7 ⁺@all-pS-PrS­[4] ^iPe complex is only slightly more stable than the (S)-7 ⁺@all-pR-PrS­[4] ^iPe complex (Figure j). Specifically, 50% dissociation of (S)-7 ⁺@all-pR-PrS­[4] ^iPe occurred at 0.47 eV, while approximately 45% of (S)-7 ⁺@all-pS-PrS­[4] ^iPe dissociated under the same conditions. This translates to a R _chiral value of 1.22 (Table ). DFT calculations (Figure b) show that the (S)-7 ⁺ @all-pS-PrS­[4] ^iPe complex is more stable than (S)-7 ⁺ @all-pR-PrS­[4] ^iPe by 1.10 kcal/mol, confirming the generally greater stability of the (S)@all-pS complexes.

Natural Bond Orbital (NBO) analysis (Figure f) indicates that approximately 70% of the total interaction energy of the complex between 7 ⁺ and PrS­[4] ^iPe arises from CH···π and van der Waals interactions (Figure f). NBO calculations suggest significant contributions from the interactions of the chiral center with the aromatic cavity of PrS­[4] ^iPe . In particular, the CH group of the chiral center exhibits slightly stronger CH···π interactions in the (S)-7 ⁺ @all-pS- PrS­[4] ^iPe complex (10% of the total interaction energy) compared to the (S)-7 ⁺ @all-pR- PrS­[4] ^iPe complex (7% of the total interaction energy). In the (S)-7 ⁺ @all-pS- PrS­[4] ^iPe complex, the CH···π interaction of the ⁺NCH₂ group contributes approximately 26% of the total interaction energy. The interaction angles (⁺NCH···π) differ significantly, measuring 129.4° in (S)-7 ⁺ @all-pS-PrS­[4] ^iPe versus 106.3° in (S)-7 ⁺ @all-pR- PrS­[4] ^iPe , indicating a stronger and more directional interaction in the (S)-7 ⁺ @all-pS- PrS­[4] ^iPe complex. The CH₃ and ethyl groups interact primarily through van der Waals forces, remaining peripheral, whereas the NH₃ ⁺ group is deeply embedded within the aromatic cavity (Figure b,f).

The chiral recognition properties of PrS­[4] ^iPe toward the secondary ammonium cation with the phenyl group (S)-8 ⁺ in CD₂Cl₂ were also studied using NMR analysis, which indicated endo-cavity complexation of the pentyl chain within the PrS­[4] ^iPe cavity (Figure c). An apparent binding constant of 290 M^–1 was calculated for the formation of the complex. In the ¹H NMR spectrum (SI) of the equimolar (S)-8 ⁺ /PrS­[4] ^iPe mixture, the pentyl chain protons of 8 ⁺ displayed significantly shielded signals with chemical shifts at −2.27, −1.34, −0.09, 1.10, and 1.60 ppm (corresponding to the α, β, γ, δ, and ε protons, as identified by COSY and HSQC). 1D and 2D NMR studies (Supporting Information), corroborated by DFT calculations (Figure c,g), indicate that the chiral center of 8 ⁺ resides outside the PrS­[4] ^iPe cavity. CID investigations revealed that 50% of the (S)-8 ⁺ @all-pR-PrS­[4] ^iPe complex dissociates at 0.26 eV, while 31% of the (S)-8 ⁺ @all-pS-PrS­[4] ^iPe complex undergoes fragmentation under the same conditions. DFT calculations (Figure c) indicate that the (S)-8 ⁺ @all-pS-PrS­[4] ^iPe complex is slightly more stable than (S)-8 ⁺ @all-pR-PrS­[4] ^iPe by 0.51 kcal/mol. Analysis of mass spectra for equimolar solutions (1 × 10^–4 mol/L) of (S)-8 ⁺ and (S)-8 ⁺ @all-pS-PrS­[4] ^iPe /(S)-8 ⁺ @all-pR-PrS­[4] ^iPe yielded an R _chiral value very close to unity (Table ).

NMR spectroscopic analysis of the secondary aliphatic ammonium cation (S)-9 ⁺ reveals endo-cavity complexation of its linear moiety, evidenced by α-CH₂ and α-CH chemical shifts at −2.24 and 3.19 ppm, respectively. The sec-butyl group remains outside the cavity (Figure d). The (S)-9 ⁺/rac-PrS­[4] ^iPe apparent binding constant is 690 M^–1. As shown in Figure h, the (S)-9 ⁺ @all-pR-PrS­[4] ^iPe complex exhibits marginally greater dissociation resistance than its counterpart, (S)-9 ⁺@all-pS-PrS­[4] ^iPe , with approximately 50 and 55% dissociation observed at 0.33 eV, respectively. This is supported by a calculated R _chiral value of 0.7 (Table ), indicating a slight preference for the (S)-9 ⁺ @all-pR-PrS­[4] ^iPe complex. The DFT calculations (Figure d,h) show a negligible energy difference between the two diastereomeric complexes (0.06 kcal/mol).

Regarding the chiral recognition properties of this new PrS­[4] ^iPe macrocycle, the results indicate a preference toward the formation of S-(guest)@all-pS-PrS­[4] ^iPe complexes. Interestingly, the highest stereoselectivity has been observed for amino acid derivative 6 ²⁺ , which could lead to specific biological applications of this new member of the prismarene family.

Conclusions

In this study, we report for the first time inherently chiral prismarenes with resolvable enantiomers PrS­[4] ^iPe and PrS­[4] ^EtCy . Prism[4]­arenes were synthesized through a thermodynamic template approach using a tailor-made selective cation, designed for the prism[4]­arene cavity. The prism[4]­arene scaffold, characterized by its narrow annulus, effectively prevents the flipping of the naphthalene rings observed for the other members of the prismarene family (PrS[5] and PrS[6]), thereby exhibiting persistent conformational chirality. The solid-state structure of this new macrocycle revealed that the centrosymmetric crystal of PrS­[4] ^iPe is composed of a racemic mixture of all-pR and all-pS enantiomeric pairs. The crystal packing demonstrates the formation of supramolecular polymeric chains of homochiral PrS­[4] ^iPe molecules in the solid state.

The enantiomers were successfully isolated using chiral HPLC, and their chiroptical properties were thoroughly investigated. Configurational assignment was carried out through TDDFT computations of [α]_D and ECD/UV–vis spectra. The circularly polarized luminescence (CPL) properties of these new prism[4]­arenes were also explored, yielding a dissymmetry ratio for CPL of 0.008. This value is notably high for an organic compound exhibiting electric dipole-allowed transitions. The correlation between the g _lum value and the molecular structure underscores the significance of the D ₄ symmetry of the chromophore. This distinctive attribute is essential for generating a strong magnetic dipole transition moment and an intense associated rotational strength. Finally, the chiral recognition properties of the prism[4]­arene toward chiral enantiopure guests were assessed using NMR and gas-phase techniques, specifically, HR-ESI-FT-ICR mass spectrometry and MS/MS methods. Interestingly, the formation of S-(guest)@all-pS-PrS­[4] ^iPe complexes is favored, and the most significant enantioselective recognition was observed for the (S)-Lysine derivative. The results presented here could pave the way for the development of new chiral materials with intriguing chiroptical properties based on prism[4]­arene.

The data underlying this study are available in the published article and its Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.5c04512.

• Detailed synthetic procedures, complexation studies, NMR and HR MS spectra, and details of calculations (PDF)

The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.

The authors declare no competing financial interest.