Theoretical investigation of C1–C4 hydrocarbons adsorption and separation in a porous metallocavitand

The purification of light hydrocarbons is one of the most important chemical processes globally which consumes substantial energy. Porous materials are likely to improve the efficiency of the separation process by acting as regenerable solid adsorbents. To investigate such translational systems, the underlying mechanism of adsorption in the porous materials must be taken into account. Herein we report the adsorption and selective separation of C1–C4 hydrocarbons in the coinage metal-based macrocyclic metallocavitand Pillarplex, which exhibits excellent performance in the adsorption of CH4 at the ambient conditions with a binding energy of −17.9 kcal mol−1. In addition, the endohedral adsorption of C2–C4 hydrocarbon is impressive. The CH4, C2H4, C3H4, and 1,3-butadiene have potential uptake of 2.57, 4.26, 3.60, and 2.95 mmol g−1, respectively at ambient conditions are highest from their respective isomers. Selective separation of C1–C4 hydrocarbons is studied using ideal adsorption solution theory demonstrating its potential for one-step purification of C1–C3 hydrocarbons.


Introduction
The paramount interest in fossil fuels continues in the petrochemical and automobile industry despite their adverse effect on the environment. 1,2 Using clean energy technology rather than fossil fuels and capturing greenhouse gases are the translational method to mitigate global warming. 3 Natural gas (NG), mainly composed of CH 4 can swap the demand for fossil fuels due to its abundance, high energy density, low CO 2 emission, and higher gure of merit for on-board applications. 4,5 The other varying components of NG are C 2 H 6 , C 3 H 8 , and C 4 H 10 are used as the basic feedstock in the petrochemical industry, thus it is essential to separate these hydrocarbons (HCs) from CH 4 for absolute utilization. 2 Conventional methods of adsorption using activated carbons, zeolites, and separation by cryogenic distillation are energy-intensive processes and require harsh working conditions such as high pressure and/or low temperature. 6 Therefore, a high throughput cost-effective storage media is required for optimal adsorption and separation of these HCs.
Molecular recognition supramolecular chemistry sets a new paradigm to study the adsorption and selective separation of guest molecules via the host-guest mechanism. The cucurbit[n] uril (n = 5, 6,7,8,10) and pillar[n]arene (n = 5,6) are versatile macrocyclic molecules and ideal hosts in the supramolecular domain. 7,8 Nau et al. studied the C1-C6 HCs within cucurbit [6] urils (CB [6]) for gas sensing and reveals that CB [6] is ideal for isobutene and cyclopentane adsorption. 9 Coskun et al. studied the propane/methane separation using pillar [5]arene based conjugated microporous polymer via host-guest chemistry and observed the facile separation of propane from the natural gas mixture. 10 So porous crystals of [2+3] imide based organic cage (NKPOC-1) and their HC adsorption phenomenon were investigated by Zhang et al. reveal the a-phase of NKOPC-1 selectively adsorbs propyne over propylene and propane at 298 K/1 bar condition. 11 However, such organic hosts are restricted in large-scale employment due to their troublesome synthetic separation, purication, and post-synthetic modications. 12 Other than organic hosts, metal-organic frameworks (MOFs) are profound against guest binding using the supramolecular binding approach. The higher storage density of acetylene over ethylene has been studied by Schröder et al. using functionalized MOF by supramolecular binding and separation approach. 13 Selective separation of C2-C4 HCs in the Zn 2 (sdc) 2 (bpe) (sdc = 4,4 ′stilbenedicarboxylate, bpe = 1,2-bis(4-pyridyl)ethane) MOF has been studied by Li et al., claimed that C2 HC has higher selectivity over C3 and C4. 14 Although MOFs are an attractive candidate for HCs capture and separation, their stability remains questionable. The limited stability against reactive species such as water is a major concern as they can debase the MOF during the in-service events. 15 The akin chemical properties, polarizability, and kinetic diameters of HCs (CH 4 , C 2 H 6 , C 3 H 8 , C 2 H 2 have kinetic diameters of 3.8, 4.4, 4.9, 3.3, 4.2Å respectively) coerce the complications for HC separations. 15,16 As all the light HCs are adsorbent dependent, it is imperative to develop suitable adsorbents for effective HCs separation. Early reports on metal coordinated cavitands, macrocycles, and cages are the awless supramolecular host with exceptional guest binding effect. 17,18 The coinage metal-based organometallic host has potential in the post-synthetic modication, simple synthetic pathway, tunable cavity, tailor-made pore surface, and high stability against air and water. 19 Pöthig and Altmann synthesized a well-dened tubular metallocavitand with Au(I) metal center; Pillarplex (PPX) analogous to pillar [5]arenes readily accommodate linear guests with high selectivity. 20 To address this challenge, we have investigated the adsorption of small HCs potentially with low carbon content (C1-C4) within the cavity of the PPX. Density functional theory (DFT) is employed to determine the electronic structure and stability of the system. The natural bond orbital (NBO) charge transfer method is used to explore the electronic transfer within the host-guest system. The nature of the interaction between HCs and PPX is analyzed using a non-covalent index (NCI). The individual components of binding energy are computed using the energy decomposition analysis (EDA). The maximum uptake of HCs is studied using the Grand canonical Monte Carlo (GCMC) simulation at various temperatures from 77-340 K and the pressure range from 0.1-10 bar. The isosteric heat of adsorption is computed to determine the thermodynamic stability of the complex. Further, the selectivity of HCs from their counterpart mixtures is studied using ideal adsorption Fig. 1 The optimized geometry of PPX and HC@PPX. The corresponding Au/H-interaction distances are shown. The distances are inÅ units. The grey, white, blue and yellow colour represents the carbon, hydrogen, nitrogen and gold atom, respectively. solution theory (IAST) for selective separation using PPX as a separator channel.

Geometries and energetic
The coherent bond properties of optimized PPX with the experimental report authenticates the betting of the theoretical approach. The height and width of the PPX are 11.585Å (expt. 11.700Å) and 7.658Å respectively measured between the distance of Au-Au positioned opposite to each other as shown in Fig. S1. † The Au-Au distance is 3.190Å is congruent to the reported value (expt. 3.005Å). The existing distance evidence the aurophilic interaction where the Au(I) atoms are packed at a distance that is 0.130Å shorter than their van der Waals radii (Au: 1.66Å).
The depth of the cavity is 3.785Å longer than the analogous pillar [5]arene (7.800Å). 20 The structural resemblance with pillar [5]arene rationale PPX as a potential host and required further investigations.
The low carbon content HCs starting from CH 4 to C 4 H 8 (C1-C4) and their isomers are studied extensively using PPX to understand the adsorption behavior. The stable HC@PPX complex is discerned by swapping the position and orientation of HCs within the PPX using the B97D2/LanL2DZ level of theory. The potential stable structure is shown in Fig. 1. Since the reports on the gold phosphine complexes were established as the potential catalyst, much attention has been gained in recent times to its structural conformations. 21,22 It was found that the excellency of properties arises owing to Au/H-C distances which are remarkably short and even shorter than their van der Waals radii (2.86Å) as well as hydrogen bonds. 23 An investigation has been carried out comprising the Au/ H-C interactions. In CH 4 @PPX, The CH 4 resides closer to the Au atom with a distance of 3.033Å. C 2 H 2 was placed horizontally symmetrical fashion within the cavity with an Au/H-C distance of 2.937Å. C 2 H 4 and C 2 H 6 molecules are in the horizontally inclined position with multiple Au/H-C interactions and a noticeable bond length of less than 3Å is observed. In C3 HCs, Au/H-C interactions are impressive while in allene@PPX and C 3 H 8 @PPX some Au/H-C distances are found lesser than their van der Waals radii. C4 HCs are well buried inside the cavity of PPX and the majority of Au/H-C interactions are in the region of 2.721 to 3.054Å which pronounce a weak hydrogen bond type interaction. In isobutylene and isobutane, the Au/ H-C interactive distances are much lower compared to its isomers. The presence of such interactions inuences the polarization effect by altering the bond length of HCs within the cavity. Trivial changes in bond lengths are observed for all the encapsulated HCs and details are given in Table S1. † Upon entrapment of HCs, the structural deformation is observed in the PPX, where the Au-Au distance of HC@PPX gets reduced to some extent. Conversely, the Au-Au bond length in allene@PPX (0.019Å) and isobutane@PPX (0.055Å) is higher than that of PPX as shown in Table S2. † The unusual Au-Au bond length in allene and isobutane is due to its stronger Au/H-C interaction and the distance is 2.727 and 2.721Å, respectively which is lower than their van der Waal radii. Nonetheless, the N/H-C interactions can't be ignored which plays a crucial role in the HCs uptake via hydrogen bonding. Desiraju et al. established the N/H-C interaction as a hydrogen bond a weak one, largely electrostatic with a distance between 2.0-3.0Å and it depends upon the C-H acidity and the -N basicity. 24 In HC@PPX the more acidic p-character containing HCs such as allene (2. Notable interactions exist in the HC@PPX complex, it is obvious to prevail a structural distortion in both PPX and HCs. The deformation energy (DE) is calculated to determine the deformation of PPX upon complexation. The deformation energy (DE) is the energy difference between the total energy of the optimized guest and host molecule and energy aer the conformation deformation occurred during the encapsulation process. DE of host and guest is calculated as follows, where E(host) opt sp , E(guest) opt sp is the single point energy of the host and guest in the optimized complex, and E(host) opt , E(guest) opt is the energy of the optimized geometry of the host and guest, respectively.
The DE of PPX is higher than the HCs given in Table 1. The DE of PPX in allene@PPX (3.7 kcal mol −1 ) is the highest and C 4 H 8 @PPX (0.4 kcal mol −1 ) is the least among the studied system. The DE of PPX, in C 2 H 2 @PPX, is 1.1 kcal mol −1 and 0.2 kcal mol −1 higher than that of C 2 H 4 @PPX and C 2 H 6 @PPX and the ease of p electron transfer from HC to the metal center is C 2 H 2 > C 2 H 4 > C 2 H 6 . The PPX in C 3 H 8 @PPX exhibits DE of 1.6 kcal mol −1 is 1.2, 1.7, and 2.1 kcal mol −1 lower than that of C 3 H 6, C 3 H 4 , and allene, respectively due to the unavailability of p electrons. Owing to the presence of orthogonal cumulative p bonds in allene, its complex procures higher deformation. The unsaturated C 3 H 6 and C 3 H 4 amplify the signicant p-electron transfer to PPX resulting in higher deformation of PPX in the complex. In C4 isomers the DE of 1,2-butadiene is 0.6 kcal mol −1 higher than 1,3-butadiene and 2-butyne is 2.0 kcal mol −1 higher than 1-butyne. The Z-isomer of C 4 H 8 @PPX experiences 0.1 kcal mol −1 higher DE than the Eisomer. The DE of isobutylene@PPX and isobutane@PPX is 3.0 and 1.2 kcal mol −1 higher than C 4 H 8 @PPX and C 4 H 10 @PPX isomers, respectively. DE unveils the structural distortion of PPX is simulated by the unsaturated HC species. The DE of HCs in the HC@PPX complex is lesser than 1.0 kcal mol −1 . Isobutane undergoes maximum distortion with DE of 0.8 kcal mol −1 followed by C 4 H 8 (0.594 kcal mol −1 ) and C 2 H 2 is least given in Table S3. † As the maximum deformation occurs in guest C 4 H 8 , in its complex PPX deforms least. The higher distortion of isobutane is reected by its bulkier size and larger van der Waals sphere whereas the C 2 H 2 has the least due to its horizontal orientation within the cavity of PPX.
The binding energy (DE), BSSE, and ZPE corrected DE (DE + ZPE) are computed to determine the interaction strength between HC and PPX as given in Table 1. The DE is the energy difference between the HC@PPX and the sum of individual energy components of HC and PPX as expressed in eqn (1).
The DE value portrays the interaction of HCs within PPX as fairly high owing to its so interaction exerted between the Au(I) and HCs unravelled by the Pearson HSAB principle. The CH 4 molecule strongly binds to PPX with a DE value of −17.9 kcalmol −1 . The CH 4 uptake capacity of PPX is exceptionally higher than many of the reported systems such as MOF-5 (−4.51 kcal mol −1 ), 25 NI-MOF-74 (−7.78 kcal mol −1 ), 26 Cu 24 (m-BDC) 24 (−8.27 kcal mol −1 ), 27 TpPa1 COF (−5.39 kcal mol −1 ), 28 Graphdiyne (−5.18 kcal mol −1 ) 29 etc. The ultrahigh binding energy of CH 4 in PPX is due to the strong interaction between the 6s levels of Au(I) and 2a 1 orbital of CH 4 and the charge transfer through level hybridization from CH 4 to Au(I) and not via Au(I) unoccupied orbitals. 30 An upraised DE value of C2 HCs observed with a lowering in the percentage of s character unveils the stability of C 2 H 6 over C 2 H 2 and C 2 H 4 with DE of −32.9 kcal mol −1 is 10.7 and 4.4 kcal mol −1 higher than C 2 H 2 and C 2 H 4 respectively. The higher binding energy of the C 2 H 6 is due to the mixing of the occupied p − (CH 3 ) orbitals with the Au(I) orbitals resulting in an electron charge donation from C 2 H 6 to Au(I) and a partial deoccupation of the p − (CH 3 ). 31 The partial de-occupation is re-ected in the lowest unoccupied molecular orbital (LUMO) that is formed by the interaction of the occupied p − (CH 3 ) of ethane and unoccupied s-orbitals of Au(I). The C 2 H 4 stabilizes the p mode adsorption and strengthens the Au-C bond by readily balancing between donation and back-donation of electrons which strongly inuence the molecular adsorption. 32 The C 2 H 2 is oriented in such a fashion that it experiences interaction with the Au(I) p x orbital parallel to it via dative interaction by the Dewar-Chatt-Duncanson scheme resulting donation of lled p y orbitals of the ligands into the vacant s orbitals of the metal atoms and the back donation. 33 In a conned PPX region, the overlap of orbitals experiences repulsions, hence a steady decline in energy is observed. The binding energy of C2 HCs in PPX is higher than reported benchmark study such as PCN-245 (C 2 H 4 : C 2 H 6 : −5.5 kcal mol −1 : −6.5 kcal mol −1 ), 34 HKUST-1 (C 2 H 4 : −5.5 kcal mol −1 ), 35 IRMOF The DE value of C3 HCs is also remarkable where C 3 H 8 possesses maximum binding energy of −43.7 kcal mol −1 which is 13.3, 12.5 and 5.8 kcal mol −1 higher than of allene, C 3 H 4 , and C 3 H 6 , respectively. The absence of p-electron density in C 3 H 8 portrays higher DE value while the existence of orthogonal pelectron density in allene reduce the binding strength to −30.4 kcal mol −1 . The DE difference in allene/C 3 H 4 (0.8 kcal mol −1 ), allene/C 3 H 6 (7.5 kcal mol −1 ), C 3 H 4 /C 3 H 6 (6.7 kcal mol −1 ) is substantial enough for facile separation of individual C3 HCs from their respective mixtures. The obtain DE is substantially higher than that of CuBTC (C 3 H 8 : C 3 H 6 : −10.8 kcal mol −1 : −11.1 kcal mol −1 ), 43 Fe-MOF-74 (C 3 H 8 : C 3 H 6 : −9.9 kcal mol −1 : −14.3 kcal mol −1 ), 40 pyr@Cu-BTC (C 3 H 8 : C 3 H 6 : −8.7 kcal mol −1 : −11.6 kcal mol −1 ), 44 UiO-66 (C 3 H 8 : 9.9 kcal mol −1 ), 45 Cu-DTO (C 3 H 8 : C 3 H 6 : −14.0 kcal mol −1 : −33.5 kcal mol −1 ), 46 tpt-Mg-MOF-74 (C 3 H 8 : 8. 15 kcal mol −1 ), 47 WOFOUR-1-Ni (C 3 H 8 : C 3 H 6 : −11.9 kcal mol −1 : −11.3 kcal mol −1 ) 48 etc.
Furthermore, C4 HCs and their ten isomers are investigated as their contributions to the natural gas mixtures cannot be ignored. C 4 H 10 interacts strongly with an effective binding energy of −54.7 kcal mol −1 whereas the binding strength of 2butyne is least (−38.4 kcal mol −1 ). The notable energy difference of 6.3 kcal mol −1 between C 4 H 10 and C 4 H 8 is ideal for the mainstream separation of their mixture. 1,3-butadiene (−43.8 kcal mol −1 ) exhibits higher binding strength than 1,2 butadiene (−42.6 kcal mol −1 ) and the binding energy of 1butyne is −42.2 kcal mol −1 is 3.8 kcal mol −1 higher than 2butyne. The energy difference between E-C 4 H 8 /Z-C 4 H 8 and isobutane/Isobutylene is noteworthy. In general, the binding energy values of HC@PPX are higher than the ever-studied system. Hence, PPX can be a good material for selective adsorption and separation of light HCs. To reduce the errors associated with total binding energy, BSSE and ZPE corrected binding (DE + ZPE) energy values are taken into account and no such perceived changes are noticed.
To explore the stability of PPX + HC / HC@PPX inclusion complex, Gibbs free energy (DG) has been computed for HC@PPX. The DG value for all the studied complexes is found to be negative, proclaiming HC@PPX is exergonic. The higher DH reveals the stability of the system is enthalpy driven. The calculated DG and DH values are given in Table 1 Table S3. † Both the DG and DH values are the least for CH 4 @PPX while the maximum for C 4 H 10 @PPX. Noteworthy DG values in C2 and C3 suggest PPX as a material of interest for C2/ C3 HCs separation. A trivial DG value is observed in C4 HCs, Thus the separation of C4 HC needs an external potential.
To understand the effect of the inter-ligand and cooperativity within the cavity, for example, we have considered some of the p-bonded molecules. It is noticed that the PPX host accommodates only two HC within the cavity while the third one residing the open face of the PPX. Within the cavity C 2 H 2 , C 2 H 4 , allene, C 3 H 4 , 1-butyne, and 2-butyne experience p/p interaction at a distance of 3.189, 3.340, 3.364, 3.280, 3.506 and 3.405Å respectively. The large size of C 3 H 6 , and other C4 HC dimers exerted by CH/p interactions. The CH/p distance in C 3 H 6 is 2.781Å whereas in 1,2-butadiene, 1,3-butadiene, 2-butyne, C 4 H 8 , (E)-C 4 H 8 , (Z)-C 4 H 8 and isobutylene, the distance is 3.022, 2.799, 2.526, 2.743, 2.517, 2.743 and 2.513Å respectively. The p interaction impetus the enhanced adsorption of HCs within the conned cavity.
The cooperative effect is an interesting factor in host-guest supramolecular interaction; therefore, we have computed the cooperative adsorption binding energy (CABE) and adsorption binding energy (ABE). The CABE is calculated by taking out the HC from the PPX host cavity, and single point calculations were carried out with the same orientations as obtained from the PPX cavity and the ABE is evaluated by relaxing the structure obtained from the HC@PPX complex. The ABE of HC@PPX is higher than the CABE value which suggests a cooperative interaction exists in the host-guest system. The CABE, ABE, and C-C bond distance of relax and constrained dimer is shown in Fig. S2. † The relax dimer bond distance is higher than the constrained dimer which claims the cooperative interaction engendered within PPX. C 3 H 4 , 1-butyne, 2-butyne, and (E)-C 4 H 8 exhibit higher cooperativity interaction with an energy value of 5.1, 6.5, 6.0, and 8.4 kcal mol −1 . Thus, it is well observed that the HCs adsorption within the PPX is asserted by the cooperative effect.
Natural gas sweetening is another stumbling block to the industrial separation of natural gas and acidic gas such as CO 2 , and H 2 S. Hence we have studied CO 2 and H 2 S adsorption by PPX using B97D2/LanL2DZ level of theory. The DE of CO 2 and H 2 S is −17.6 and −21.9 kcal mol −1 respectively while CH 4 , C 2 H 6 , C 3 H 8 and C 4 H 10 is −17.9, −32.9, −43.7 and −54.7 kcal mo, respectively. The DE of an alkane is higher than acidic gas, thus alkane is the superior adsorbate over CO 2 and CS 2 . The DG 298 value for CO 2 , H 2 S is −9.0 and −10.0 kcal mol −1 whereas CH 4 , C 2 H 6 , C 3 H 8 and C 4 H 10 are −8.4, −19.6, −28.6 and −38.9 kcal mol −1 , respectively. Hence it will be difficult to separate CH 4 in presence of an excessive amount of CO 2 and CS 2 as the complexation is exergonic and the complexation will be CO 2 @PPX and CS 2 @PPX instead of CH 4 @PPX. The C2-C4 hydrocarbon separation can be easily separated in the presence of CO 2 and CS 2 as the substitution reaction undergoes endergonic.

Electronic charge transfer
Natural bond orbital (NBO) analysis has been performed to articulate the charge transfer between the host-guest system. An apparent charge transfer is discerned from guest HCs to PPX and the ease of charge transfer increases with the HCs size. The signicant charge transfer is observed in C4 HCs, C 3 H 6, and C 3 H 8 of ca. 0.10-0.13 e − while for other complexes is ca. 0.10 e − . CH 4 (0.05 e − ) and C 2 H 2 (0.04 e − ) experience very lower e − transfer due to their smaller size. Further illustration proclaims a metal to ligand (HCs) e − transfer (MLCT) exhibits during the complexation process. The MLCT is in the range of 0.01-0.03 e − and it's obvious the back donation of p-electron from the bonding molecular d-orbital of metal to the empty antibonding p* orbital of ligands. The charge transfer values are given in Table S3. † In the complexation, the predominant charge transfer obtains from HCs to PPX.

Energy decomposition analysis
Energy decomposition analysis (EDA) has been accomplished by considering PPX and HC as interacting fragments are provided in Fig. 3 and their corresponding energy and percentage of contribution are given in Table S4. † The dispersion (DE disp ) term is the major contributor of ca. 45.8-61.4% to the total interaction. Regardless, the electrostatic (DE elct ) of ca. 22.5-34.1% and orbital (DE orb ) of ca. 15.1-20.1% contribute signicantly to the total binding energy of the stabilized complex. As expected, the higher DE disp of CH 4 @PPX is owing to its zero-eld dipole and quadrupole moment, instigating the induced dipole interaction between CH 4 and the charged portal of PPX. Similarly, C2 HCs exhibit zero eld-dipole but unveil positive quadrupole moment and higher polarizability than the former one engenders induced dipole interaction. All C3 HCs experienced a permanent dipole moment except allene, claiming strong dipole-dipole interaction between the HCs and PPX, hence exhibiting notable DE elct interaction compared to other HCs. The presence of acidic hydrogen in allene possibly forms the hydrogen bonding interaction with the -N-centered pyrazole portal of PPX. Therefore, the contribution of DE elct (34.3%) is the highest among the studied HCs, which reects the higher DE orb (19.9%) and lower DE disp (45.8%) term. In C4 HCs, 1,2butadiene, 1-butyne, C 4 H 8 , (Z)-C 4 H 8 , isobutylene, and isobutane interact with the PPX by dipole-dipole interaction due to permanent dipole moment, hence their DE elct term ca. 27.8-34.0% from their isomers (ca. 26.0-27.6%). Isobutane and isobutylene experienced weak hydrogen bonding resulting DE elct , of 34.0 and 32.6% and the DE disp term is 47.9 and 48.8% respectively is the lowest among the studied system. 2-Butyne, (E)-C 4 H 8 interaction with PPX is purely dispersive like ca. 58%. All-inclusive analysis reveals the combined effect of DE disp and DE elct are major factors for HC@PPX stabilization. Although the orbital interaction is trivial but can't be neglected and the contribution of DE orb is ca. 15.1-20.1% and stronger interactions are perceived in the complexes containing the acidic hydrogen ligands.

Noncovalent interaction
NCI index deciphered the noncovalent interaction in the HC@PPX system as shown in Fig. 4. The presence of green surfaces between HCs and PPX highlights the van der Waals type in nature. The increasing size of the green surface enhances van der Waals interaction and increasing HC size strengthens the van der Waal's contact. The spattered red plot in the imidazole/pyrazole ring center depicts the strain produced by the ring current. The blue color surfaces claim the hydrogen bonding interaction in the stabilized system, according to the presently used color coding scheme. A significant H-bonding is visualized in the allene, isobutylene and isobutane entrapped complex. Furthermore, the plots of reduced density gradient s versus sign (l 2 )r elucidate better insight into the specic types of interaction present in the complex. Extremely low density, low gradient, and moderately low density and low gradient troughs with a negative sign (l 2 )r values indicate the presence of attractive dispersion and Fig. 3 The results of EDA consider the guest HC as one fragment and PPX as another at the B3LYP-D3/TZ2P/ZORA level of theory. The percentage contribution of attractive interaction to the total binding energy is inset in the figure. hydrogen bonding interactions, respectively. Contrary, a low gradient trough appearing in the positive region of sign (l 2 )r conveys the repulsive interactions produced by ring strain. The superimposed plots are shown in Fig. S3, † where PPX moieties are designated by blue color and complexes, are portrayed in red color. In every system, an additional narrow spike is observed at slightly negative sign (l 2 )r values around −0.005 a.u. implies the interaction is dispersive.

GCMC analysis
The gravimetric uptake of C1-C4 HCs at 77-340 K/0.1-10 bar has been investigated using the PPX host. At 273, 298, and 340 K and 1 bar, CH 4 adsorption has been 3.51, 2.37, and 1.33 mmol g −1 and at 10 bar the adsorption values are 5.41, 4.81, and 3.69 mmol g −1 , respectively. The CH 4 follows type-1 adsorption isotherm and increasing temperature reduces CH 4 uptake whereas high pressure induces higher CH 4 adsorption. At 77 K the adsorption of CH 4 is 5.60 mmol g −1 at 1 bar and 7.31 mmol g −1 at 10 bar pressure.
The adsorption isotherm plot of 298 K is shown in Fig. 5(a) while the 77, 273, and 340 K are shown in Fig. S4(a), S5(a), and S6(a), † respectively. The adsorption is higher at 77 K due to the lowering of intermolecular repulsion between the CH 4 molecule. 340 K results decrease in CH 4 uptake, this can be attributed to high temperature favors the CH 4 in the free gaseous state rather than adsorbed state, and also in high temperature the pore volume of the substrate decreases rendering lower adsorption. Fig. 4 The noncovalent interaction plot of pristine host PPX and the HC encapsulated PPX. The green, blue and red color code represents the van der Waal, hydrogen bonding attractive interaction while red color depicts repulsive interactions.
The uptake of C 2 H 6 (3.0-4.1 mmol g −1 ) is high compared to its isomers in the low-pressure region (298 K/0.1-1 bar). At high pressure, the C 2 H 4 adsorption is prominent followed by C 2 H 6 and C 2 H 2 . The gravimetric uptake of C 2 H 2 , C 2 H 4, and C 2 H 6 are 2.80, 4.26, and 4.22 mmol g −1 respectively at ambient conditions while at 10 bar the uptake increases to 4.37, 4.74, and 4.50 mmol g −1 respectively. At 77 K/1 bar the uptake varies C 2 H 2 > C 2 H 4 > C 2 H 6 whereas at 273 K the adsorption strength is C 2 H 4 > C 2 H 6 > C 2 H 2 up to 4 bar and thereaer C 2 H 4 > C 2 H 2 > C 2 H 6 . The 340 K is contrary to 273 K i.e. C 2 H 6 > C 2 H 4 > C 2 H 2 . This reveals at low-temperature the uptake of unsaturated HC is more effective whereas at high temperatures the C 2 H 6 adsorption is signicant. The adsorption isotherms plot of C2 HC at ambient condition is shown in Fig. 5(a) while Fig. S4(a), S5(a), and S6(a), † represents the isotherm plot of 77, 273, and 340 K respectively.
A type-IV adsorption isotherm has been observed for allene shows signicant uptake of 3.76 mmol g −1 at 298 K/2 bar whereas other C3 isomers exhibit type-I at 298 K. At ambient conditions, the uptake of allene, C 3 H 4 , C 3 H 6, and C 3 H 8 is 3.51, 3.60, 3.57 and 3.12 mmol g −1 , respectively are shown in Fig. 5(b), increasing pressure up to 1.5 bar results higher allene uptake followed by C 3 H 4 , C 3 H 6, and C 3 H 8 . The gravimetric capacity of C 3 H 8 is lower than other C3 isomers due to a larger kinetic diameter of 4.9Å. At 77 K [ Fig. S4(b) †], the adsorption isotherm of C 3 H 4 is moderately higher than allene with increasing pressure and C 3 H 6 adsorption is notably higher than C 3 H 8 . At STP [ Fig. S5(b) †] the allene uptake is very high and high pressure portrays the C 3 H 4 and allene have an equal propensity for adsorption. Thus, 273 K and 0.1-4 bar could be the ideal setup for selective adsorption of C3 HCs. The adsorption of allene (3.29 mmol g −1 ), C 3 H 4 (3.20 mmol g −1 ), and C 3 H 6 (3.33 mmol g −1 ) swing trivially at 340 K [ Fig. S6(b) †], and the uptake of C 3 H 8 (2.90 mmol g −1 ) is lowest. Increasing pressure reduces the C 3 H 6 adsorption while inducing allene uptake. Unusual behavior is observed in C 3 H 4 uptake capacity at a highpressure and overall range of temperature which coincides with the allene adsorption isotherm. This can be explained by the activation of p-bond of allene and alkyne by Au(I) attributed to relativistic effects. Though Au(I) is coordinated with the electron-rich NHC groups which propel the p-activation more signicantly with C 3 H 4 rather than allene in high-pressure regions.
C4 HC uptake by PPX is in the ideal range, the highest adsorption is observed for 1,3-butadiene and isobutane is least at ambient condition and 1,2-butadiene follows type-IV adsorption while others are of type-I shown in Fig. 5(c). A preference analysis of C 4 H 10 , isobutane, 1,3-butadiene and isobutylene over other C4 HCs is investigated owing to its presence in the natural gas mixture. At ambient setup, the uptake capacity of C 4 H 10 , isobutane, 1,3-butadiene, and isobutylene are 2.32, 1.93, 2.95, and 2.36 mmol g −1 , respectively. The remaining HC adsorption is in the ideal range. Except for 1,3butadiene (3.08 mmol g −1 ), other HCs do not have notable uptake in cryogenic condition/1 bar as shown in Fig. S4(c). † An unrelieved uptake of HC has been observed at ambient and STP conditions [ Fig. S5(c) †]. At 340 K/1 bar, the adsorption of 1,2-butadiene is high and with increasing pressure, the isobutylene shows steep growth in the adsorption as shown in Fig. S6(c). † The other C4 HC uptake strength is monotonous due to their equal kinetic diameter. Thus, the simulation study reveals that PPX might be a good candidate for the capture of C1-C4 HC under ambient conditions. Further, we have performed the density distribution of the center of mass of HC molecules in GCMC simulation as shown in Fig. S7. † The results from GCMC simulation at ambient condition indicate that the guest HC molecules lies at the center and also adhere to the outer open site of PPX due to the presence of the -N atom in the imidazolylidene motif. C1 and C2 HC show higher density coverage than C3 and C4 due to smaller size and lower kinetic diameter. The thermodynamic view of HC adsorption using PPX at 298 K has been determined using the isosteric heat of adsorption (Q st ) and is shown in Fig. 6.
In C1/C2 HC, the Q st of CH 4 and C 2 H 2 are constant over the entire pressure range (0.1-10 bar) whereas C 2 H 4 and C 2 H 6 increase slowly from 0.1-1 bar and aerward remain constant. The increasing Q st value depicts the adsorbate interaction with the PPX and lateral interaction between the adsorbate molecules which is corroborated by the DFT and cooperative binding study. The constant Q st portrays the adsorption that occurs in the energetically homogenous adsorbent which is due to the effect of capillary condensation in the mesoporous material. The onset of capillary condensation results in constant Q st induced by connement within the pore network. Akin to C 2 H 4 and C 2 H 6 , C3 and C4 HCs exhibit the increase in Q st value from 0.1-1 bar enunciates the adsorbate-adsorbent interaction and constant from 1-10 bar attributed by capillary condensation.

Ideal adsorption solution theory
The potential separation of C1-C4 HCs has been investigated using ideal adsorption solution theory (IAST) for equimolar components. At the ambient setup, the selectivity of C2H6 is higher than its counterpart C2 isomers as shown in Fig. 7(a). However, at 273 K the C 2 H 4 separation is more facile shown in Fig. S8(a). † C 2 H 2 selective separation is very much pronounced irrespective of temperature and pressure. The selectivity difference between allene and C 3 H 4 is minor at 298 K and is notable at STP under high pressure shown in Fig. S8(b). † At ambient conditions the selectivity between C 3 H 6 and C 3 H 8 is distinguishable. However, in 273 K all C3 HCs can be easily separable by applying moderate to high pressure and the selectivity is allene > C 3 H 4 > C 3 H 6 > C 3 H 8 . The selectivity of C3H6 is preferred over other C3 HCs at a higher temperature of 340 K [ Fig. S9(b) †]. Lower temperature and high pressure will be facile for allene separation whereas high temperature leads C 3 H 6 with effective selectivity from its isomers. The selectivity of C4 hydrocarbon is quite lower than C1-C3 HCs. At ambient conditions, the separation of 2-butyne from its isomers is a bottleneck whereas at STP [ Fig. S8(c) †] the separation is favorable. 2-10 bar/298 K and 0.1-2 bar/273 is the ideal range for the 2-butyne/1-butyne selective separation. The selectivity of isobutane is least in all conditions. The order of selectivity at 298 K/2-10 bar is 2-butyne > 1-butyne > 1,3-butadiene > 1,2butadiene > (Z)-C 4 H 8 > (E)-C 4 H 8 z C 4 H 8 > C 4 H 10 z isobutylene > isobutane. The adsorption selectivity is mainly attributed to pore shape, guest size, temperature, and internal surface functionality of pores in the PPX. 298 K, 273 K, and 340 K are ideal temperature conditions for the selective separation of C2, C3, HCs. For C4 HCs more external pressure is required.
The adsorption of C3 HCs is steady as compared to the other reported results. The C 3 H 4 adsorption is less studied and only MFM-300(In) 62 adsorption capacity is 6.30 mmol g −1 which is higher than PPX. The C 3 H 6 adsorption in PPX is 3.57 mmol g −1 is higher than PCN-207-FA (2.17 mmol g −1 ), 66 UMCM-151(3.07 mmol g −1 ), 51 MOF-801(3.50 mmol g −1 ). 67 The C 3 H 8 adsorption in PPX is 3.12 mmol g −1 , moreover, the reported MOFs show promising C 3 H 8 adsorption compared to the PPX. Although the uptake of C3 HCs in PPX is quite low but the selectivity is well noticeable. The C4 HC uptake is more propitious and it is observed that the uptake capacity of (E)-C 4 H 8 , (Z)-C 4 H 8 , 1,3-butadiene, C 4 H 8 , isobutylene, C 4 H 10 , and isobutene using PPX is higher than the M-Gallate (M = Ni/Mg/Co), 68

Computational details
The metallocavitand PPX is a well-dened tubular cavity made up of octanuclear N-heterocyclic carbene complex of Au(I) have been explored in this study. The crystal structure obtained from ref. 20 is further investigated to understand the electronic effect and adsorption properties. The geometry of PPX and HCs entrapped PPX (HC@PPX) has been optimized at B97D2/ LanL2DZ level of theory. 74,75 The subsequent harmonic vibrational analysis reveals the existence of real frequency in the structure belonging to minima on the potential energy surface (PES). We have computed zero-point energy corrected binding energy (DE + ZPE) and basis set superposition error (BSSE) at the same level of theory. The standard counterpoise method proposed by Boys and Bernardi has been adopted for the BSSE correction. 76 The natural bond orbital (NBO) analysis has been performed at the B3LYP-D3/Def2-TZVP level of theory to determine the electronic charge transfer within the host-guest complex. 74,77 All the calculations are computed using the Gaussian 09 program package. 78 The energy decomposition analysis (EDA) has been carried out using dispersion corrected hybrid functional B3LYP-D3 with triple-zeta two polarization function TZ2P implemented in the ADF (2017) program. [79][80][81][82] Zeroth order relativistic approximation (ZORA) method has been incorporated for computation as gold exhibits a large relativistic effect. 83 In EDA, the fragment-based computations are invoked to treat PPX as one fragment and the guest molecules are other fragments. The total energy is decomposed into four major energy components viz. electrostatic (E elct ), dispersion (E disp ), orbital (E orb ), and the Pauli term (E pau ). The former three energy terms are attractive while the latter one is repulsive. The E elct term represents the classical electrostatic interaction that exists between the two charged species namely host and guest aer complexation. E disp term arises due to the electronic uctuation between two adjacent molecules attributed to temporary dipoles in the complex. E orb is the orbital interactions initiated by the overlapping of occupied and unoccupied atomic orbitals of the host-guest system. The E pau is the Paulis repulsive term exerted by the overlapping of an identical quantum number between the two interacting fragments.
The real-space visualization of interaction has been studied using the NCI index which identies noncovalent interactions solely based on electron density and its derivatives. 84 NCI index is based on the 2D plot of reduced density gradient (RDG), s as a function of electron density r(r): The plot where RDG value approaches zero is identied as the noncovalent region. 84 Analysis of electron density determines the binding strength of interacting molecules. However, both attractive and repulsive interactions have a positive correlation with electron density in the corresponding region. 85 A real space function sign (l 2 ) multiplied by electron density r(r) is indeed to dene the attractive and repulsive term where the curvature l 2 is the second eigenvalue of the Hessian density matrix. 86 A negative and positive value of l 2 is identied as strong attractive and repulsive interactions respectively while for van der Waals interaction the value of l 2 approaches to zero. 86,87 Multiwfn program has been used to compute the NCI index whereas Chemcra for the gradient isosurface visualization, where the color codes decide the value of sign (l 2 )r(r). 88,89 Blue and green color represents the attractive hydrogen bonding and van der Waals interaction whereas red color depicts the repulsive strain ensure by steric crowding.
Grand canonical Monte Carlo (GCMC) simulation has been carried out to determine the maximum HCs uptake capacity of PPX at an adsorption temperature of 77, 273, 298, and 340 K and pressure from 0.1 to 10 bar. For each simulation 1 × 10 5 GCMC cycles were used for equilibration and 1 × 10 5 cycles were used to assess the ensemble average properties. The simulations were performed using the sorption module of Material Studio. 90,91 The universal force eld (UFF) parameter has been used to describe the interatomic interaction with a cut-off distance of 12.5Å has been used for all Lennard-Jones interactions. 92 Long-range electrostatic interactions were computed using the Ewald summation method. 93 The simulation has been carried out in a 1 × 1 × 2 supercell with imposed periodic boundary conditions in all directions.
The adsorbate uptake capacity using PPX crystal obtained from the GCMC simulation is further utilized for the computation of selective separations. Langmuir adsorption isotherm model has been used to examine the selectivity of individual gas components over multi-component using ideal adsorption solution theory (IAST). 94 where P is the pressure of the bulk gas at equilibrium, q is the saturation loading The separation of the mixture is carried out at 298 K temperature and the data over the pressure range tted more precisely with an R 2 value of 0.99.

Conclusions
In summary, Au(I) coordinated microporous metallocavitand host, PPX has been investigated for potential HCs adsorption and separation. C1-C4 light HCs have been taken into consideration owing to their availability in the natural gas mixture. DFT study unveils facile adsorption of HCs at ambient conditions with extraordinary binding strength. All the complexes are stable at ambient conditions and the complexation is enthalpy driven. CH 4 , C 2 H 6 , C 3 H 8 , and C 4 H 10 are the leading adsorbents with unprecedented binding energy from their respective isomers. The energy difference between the C 2 H 2 /C 2 H 4 , C 2 H 2 / C 2 H 6 , allene/C 3 H 6 , C 3 H 4 /C 3 H 6 , C 4 H 8 /C 4 H 10 is strong enough for selective separation from their isomers. EDA discerns the nature of interactions that are dominated by dispersion (45.8-61.4%) followed by electrostatic (22.5-34.3%) and orbital (15.1-20.1%) terms which are further corroborated by the NCI index. GCMC simulation predicts the gravimetric uptake of CH 4 , C 2 H 4 , C 2 H 6 , C 3 H 4 , C 3 H 6 , and 1,3-butadiene is very high at 298 K and pressure range up to 10 bar. The magnitude of Q st reveals the high affinity of HCs to the pore volume of the adsorbents and the existence of adsorbate-adsorbate interaction unveils the binding cooperativity. The results of GCMC and Q st corroborated with the DFT and cooperative effect study. The IAST claims that 298 K, 273 K, and 340 K are ideal temperature conditions for the selective separation of C 2 H 6 , allene, and 1butyne from their respective isomers. This work provides an elegant example of N-heterocyclic carbene (NHC) based Au(I) metallocavitand for the HCs separation and effectively more sophisticated porous material can be designed based on these concepts.

Conflicts of interest
There are no conicts to declare.