Theoretical Insight into Gate-Opening Adsorption Mechanism and

Article Cite This: J. Am. Chem. Soc. 2018, 140, 13958−13969

pubs.acs.org/JACS

Theoretical Insight into Gate-Opening Adsorption Mechanism and Sigmoidal Adsorption Isotherm into Porous Coordination Polymer Jia-Jia Zheng,†,‡ Shinpei Kusaka,† Ryotaro Matsuda,†,§ Susumu Kitagawa,*,† and Shigeyoshi Sakaki*,‡

Downloaded via UNIV OF LOUISIANA AT LAFAYETTE on October 29, 2018 at 15:49:09 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

Institute for Integrated Cell-Material Sciences, Kyoto University Institute for Advanced Study, Kyoto University, Yoshida Ushinomiya-cho, Sakyo-ku, Kyoto 606-8501, Japan ‡ Fukui Institute for Fundamental Chemistry, Kyoto University, Nishi-hiraki cho, Takano, Sakyo-ku, Kyoto 606-8103, Japan § Department of Chemistry and Biotechnology, Graduate School of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan S Supporting Information *

ABSTRACT: The gate-opening adsorption mechanism and sigmoidal adsorption isotherm were theoretically investigated taking CO2 adsorption into porous coordination polymers, [Fe(ppt)2]n (PCP-N, Hppt = 3-(2-pyrazinyl)-5-(4-pyridyl)1,2,4-triazole) and [Fe(dpt)2]n (PCP-C, Hdpt = 3-(2pyridinyl)-5-(4-pyridyl)-1,2,4-triazole) as examples, where the hybrid method consisting of dispersion-corrected DFT for infinite PCP and a post-Hartree−Fock (SCS-MP2 and CCSD(T)) method for the cluster model was employed. PCP-N has site I (one-dimensional channel), site II (small aperture to site I), and site III (small pore) useful for CO2 adsorption. CO2 adsorption at site I occurs in a one by one manner with a Langmuir adsorption isotherm. CO2 adsorption at sites II and III occurs through a gate-opening adsorption mechanism, because the crystal deformation energy (EDEF) at these sites is induced largely by the first CO2 adsorption but induced much less by the subsequent CO2 adsorption. Interestingly, nine CO2 molecules are adsorbed simultaneously at these sites because a large EDEF cannot be overcome by adsorption of one CO2 molecule but can be by simultaneous adsorption of nine CO2 molecules. For such CO2 adsorption, the Langmuir−Freundlich sigmoidal adsorption isotherm was derived from the equilibrium equation for CO2 adsorption. A very complicated CO2 adsorption isotherm, experimentally observed, is reproduced by combination of the Langmuir and Langmuir−Freundlich adsorption isotherms. In PCP-C, CO2 adsorption occurs only at site I with the Langmuir adsorption isotherm. Sites II and III of PCP-C cannot be used for CO2 adsorption because a very large EDEF cannot be overcome by simultaneous adsorption of nine CO2 molecules. Factors necessary for gate-opening adsorption mechanism are discussed on the basis of differences between PCP-N and PCP-C.

■

INTRODUCTION

To understand the gate-opening adsorption into PCPs at the molecular level, various theoretical studies have been carried out so far, as reviewed recently;33−37 some of them were based on thermodynamics38−43 and statistic mechanics.44−46 Monte Carlo and molecular dynamic (MD) simulations47−55 with classical force fields56−58 and ab initio MD simulation59 have been performed as well. Also, a vibrational spectrum study has been devoted to understand geometry relaxation by gas adsorption.60 However, our knowledge of the gate-opening adsorption mechanism has been still limited; for instance, we do not know in what case the gate-opening adsorption occurs (or does not occur) and what factor(s) is needed for the gateopening mechanism; though a flexible framework of PCP seems necessary for the gate-opening adsorption, it is not

Porous coordination polymers (PCPs) or metal−organic frameworks (MOFs)1,2 have attracted a lot of attention because of their significantly large potentials for gas storage, gas separation, molecular sensing, drug delivery, and so on.3−16 Some of them have a soft framework which exhibits a dynamic structural change triggered by external stimuli such as gas adsorption, light irradiation, and temperature change.17−20 In particular, gate-opening adsorption is of considerable interest because structural transformation induced by gas molecule adsorption enhances subsequent gas adsorption.21 Such behavior is useful for separating the gas molecule from a mixture containing several kinds of gas molecules with similar physicochemical properties such as CO/N2. This gate-opening adsorption mechanism is also interesting from the viewpoint of material science. Thus, a lot of efforts have been devoted to creating such PCPs.22−32 © 2018 American Chemical Society

Received: August 30, 2018 Published: September 28, 2018 13958

DOI: 10.1021/jacs.8b09358 J. Am. Chem. Soc. 2018, 140, 13958−13969

Article

Journal of the American Chemical Society always useful for the gate-opening mechanism.28 The other important issue to be discussed is the sigmoidal adsorption isotherm, which is often discussed in relation to the gateopening adsorption mechanism, because it completely differs from the usual Langmuir adsorption isotherm. The curve fitting of the sigmoidal adsorption isotherm with the Langmuir−Freundlich equation61,62 has been tried in many experimental works (for instance, see refs 25 and 28−30). However, we do not know the reason why the sigmoidal adsorption isotherm is observed in the case of the gate-opening adsorption mechanism. Though electronic structure theories based on density functional theory (DFT) and wave function theory have been applied to PCPs by the Sauer group,63−65 Truhlar group,66−77 Cramer/Gagliardi group,58,67,70,73,75−79 our group ,80−83 and some other groups,84−95 the gate-opening adsorption has not been investigated based on electronic structure theory except for one pioneering work of ab initio MD simulation on the breathing behavior by Düren and coworkers;59 see also review articles.34−36 In this theoretical work, we wish to elucidate the reason why the gate-opening adsorption mechanism works well in some of PCPs but not in others, what factors are important for the gateopening adsorption, and the reasons why the sigmoidal adsorption isotherm is experimentally observed in the gateopening adsorption but the Langmuir adsorption isotherm is seen in the usual gas adsorption. For such investigation, we selected here CO2 adsorption into [Fe(ppt)2]n (PCP-N, Hppt = 3-(2-pyrazinyl)-5-(4-pyridyl)-1,2,4-triazole, Scheme 1a) and

single-crystal X-ray diffraction analysis clearly indicated that the CO2 adsorption occurred at three different sites as a large cage (site I), small aperture next to the large cage (site II), and small pore around Fe2+ ions (site III),24 as shown in Scheme 1a. Geometry optimizations of PCPs with and without gas molecules were carried out using the DFT method under periodic boundary condition as implemented in the Vienna Ab initio Simulation Package (VASP 5.4.1).96,97 The Perdew− Burke−Ernzerhof DFT functional98 with Grimme’s “D3” dispersion correction99 (PBE-D3) was employed in these calculations. Plane wave basis sets with an energy cutoff of 500 eV were used to describe valence electrons, while core electrons were described by the projector-augmented-wave pseudopotentials.100,101 A Γ-point sampling for the Brillouin zone was used in all calculations. Both cell parameters and atomic positions were fully optimized until all atomic forces become smaller than 0.01 eV/Å. The binding energy (BE) was calculated here using the hybrid method like in previous work,64,65 because dispersion interaction plays a crucially important role in the adsorption of gas molecules into PCPs.81,90 In this method, the BE with the infinite system was calculated using DFT with the PBE-D3 functional. To incorporate better the dispersion interaction, we carried out MP2 and SCS-MP2 calculations using three cluster models of sites I, II, and III, named CMA, CMB, and CMC, respectively, as shown in Scheme 2. The dangling bonds in these cluster models were capped with hydrogen atoms. Since PCP-C is isostructural to PCP-N, these three adsorption sites were investigated similarly, where the relevant N atom of PCPN was replaced by a −CH group in PCP-C. The binding energy per one CO2 molecule with PCP was calculated at the PBE-D3 level using eq 1

Scheme 1. Primitive Unit Cells (PUCs) of PCP-N and PCPCa

BEPBE ‐ D3 = [EPBE ‐ D3(PCP ·nCO2 ) − EPBE ‐ D3(PCP)]/n − EPBE ‐ D3(CO2 )

(1)

where EPBE‑D3(PCP·nCO2) is the PBE-D3-calculated total energy of PCP with n adsorbed CO2 molecules and EPBE‑D3(PCP) and EPBE‑D3(CO2) are total energies of PCP and one CO2 molecule, respectively. The BEPBE‑D3 can be PBE‑D3 decomposed into the interaction energy EINT (H-G) between deformed CO2 molecules and deformed PCP PBE‑D3 framework, interaction energy EINT (G-G) between deformed CO2 molecules, and crystal deformation energy (EDEF) of the PCP framework, where the geometries of deformed PCP framework and deformed CO2 molecule are taken to be the same as those of the corresponding PCP and CO2 moieties in the PBE-D3-optimized PCP·nCO2 and H and G represent host (PCP) and guest (CO 2 molecule), respectively. Further correction by the SCS-MP2 method was made for the EPBE‑D3 (H-G) and EPBE‑D3 (G-G) as follows INT INT

a

The different moiety in structure between PCP-N and PCP-C is shown by green color.

its isostructural analogue [Fe(dpt)2]n (PCP-C, Hdpt = 3-(2pyridinyl)-5-(4-pyridyl)-1,2,4-triazole, Scheme 1b) as examples.24 These two PCPs experimentally showed interesting features: (i) the gate-opening CO2 adsorption was experimentally observed in the case of PCP-N, (ii) CO2 adsorption into PCP-N occurs with a very complicated unique adsorption isotherm, but (iii) a nongate-opening CO2 adsorption with a normal Langmuir-type adsorption isotherm occurs in the case of PCP-C despite the tiny difference between them.

SCS ‐ MP2:PBE ‐ D3 E INT (H‐G) PBE ‐ D3 SCS ‐ MP2 PBE ‐ D3 = E INT (H‐G) + E INT (CMX) − E INT (CMX)

(2)

■

SCS ‐ MP2:PBE ‐ D3 E INT (G‐G)

MODELS AND COMPUTATIONAL DETAILS Scheme 1 shows primitive unit cells (PUCs) of PCP-N and PCP-C; see Figure S1 in the Supporting Information for the conventional unit cell consisting of three PUCs. In PCP-N,

PBE ‐ D3 SCS ‐ MP2 = E INT (G‐G) + E INT ([CO2 ]n ) PBE ‐ D3 − E INT ([CO2 ]n )

13959

(3) DOI: 10.1021/jacs.8b09358 J. Am. Chem. Soc. 2018, 140, 13958−13969

Article

Journal of the American Chemical Society

Scheme 2. Cluster Models (CMs) and Small Cluster Models (SCMs) Employed for MP2 and CCSD(T) Calculations, Respectivelya

a

The small cluster models were used to calculate the interaction energy between CO2 and each fragment in CMs at the MP2, SCS-MP2, and CCSD(T) levels.

two CO2 molecules in the [CO2]n cluster, respectively; see Scheme 2 for details of SCMXi (X = A, B, or C). Though eqs 4 and 5 are similar to the ONIOM method,102 they are not exactly the same, because the correction is made for several layers in the ONIOM but made for pairs herein. This type of pairwise correction is highly reliable when the correction was made for dispersion interaction.103 MP2, SCS-MP2, and CCSD(T) calculations of cluster models were performed using the GAMESS104 and Gaussian 09105 programs, respectively. The resolution of identity (RI) approximation106 was employed in MP2 calculations. Dunning’s correlation-consistent aug-cc-pVDZ basis sets107,108 were used with appropriate auxiliary basis functions109,110 for RI approximation, where a set of diffuse functions was removed from the H atom. In MP2, SCS-MP2, and CCSD(T) calculations, the basis set superposition error (BSSE) was corrected using the counterpoise method.111 Details of MP2 and SCS-MP2 calculations for the cluster model are presented in the Supporting Information (p S3). Enthalpy change for gas molecule adsorption was evaluated by calculating vibrational frequencies of free and adsorbed CO2 molecules, where vibrations of the PCP framework were neglected because it is likely that vibrational frequencies of framework are influenced little by gas adsorption. For evaluating the enthalpy of the free CO2 molecule, translational, rotational, and vibrational movements were counted, while only vibrational movements were counted in evaluating enthalpy of CO2 cluster in PCPs because translation and rotational movements are almost frozen in the CO2 cluster in PCPs; strictly speaking, they are changed to vibrational modes with very small frequencies. The final adsorption enthalpy (ΔHads) is calculated with eq 6

where the superscript X of CM is A, B, or C representing the cluster model for site I, II, or III, respectively, and EINT([CO2]n) is the interaction energy of the [CO2]n cluster whose geometry was taken to be the same as that in the PBED3-optimized crystal structure. The CO2 binding energy at the SCS-MP2 level is represented by eq 4 SCS ‐ MP2 BE SCS ‐ MP2:PBE ‐ D3 = BEPBE‐D3 + E INT (CMX) PBE‐D3 X − E INT (CM ) SCS ‐ MP2 PBE ‐ D3 + E INT ([CO2 ]n ) − E INT ([CO2 ]n )

(4)

The CCSD(T) was employed to make further correction of the SCS-MP2-calculated CO2 binding energy. Because these cluster models are still too large to perform CCSD(T) calculation, we made pairwise correction of the correlation energy by CCSD(T) using such small cluster models as SCMAi, SCMBi, and SCMCi (i = 1−18 for CMAii, 1−7 for CMBi, and 1−4 for CMCi), as shown in Scheme 2, where the geometry of each fragment in the small cluster model was taken to be the same as that in the PBE-D3-optimized structure (Scheme 2). On the basis of the above definition, the CCSD(T)-correction term ΔBECCSD(T) is evaluated by eq 5 n

ΔBE CCSD(T) =

CCSD(T) SCS ‐ MP2 ∑ [EINT (i) − E INT (i)] i CCSD(T) SCS ‐ MP2 + E INT ([CO2 ]n ) − E INT ([CO2 ]n )

(5)

ECCSD(T) (i) INT

ESCS‑MP2 (i) INT

where and represent CCSD(T)- and SCS-MP2-calculated interaction energies of CO2 in small cluster models SCM A i , SCM B i , and SCM C i and ECCSD(T) ([CO2]n) and ESCS‑MP2 ([CO2]n) represent the sum INT INT of CCSD(T)- and SCS-MP2-calculated interaction energies of 13960


Article


computational method is discussed in p S4 in the Supporting Information. In PCP-C, essentially the same CO2 adsorption structures were optimized in sites I, II, and III (Figure S1) despite the fact that a significantly large difference in CO2 adsorption was experimentally observed between PCP-N and PCN-C, as mentioned above. These similarities and differences will be discussed below in relation to the gate-opening CO2 adsorption. CO2 Adsorption into PCP-N; Difference in Binding Energy among Sites I, II, and III. The binding energy of one CO2 molecule with PCP-N was evaluated at each site, as shown in Table 1. PBE-D3- and SCS-MP2:PBE-D3-calculated

ΔHads = BE SCS ‐ MP2:PBE ‐ D3 + ΔBE CCSD(T) + ΔZPVE + ΔEthermal − RT

(6)

where ΔZPVE, ΔE , and RT represent changes in zeropoint vibration energy, thermal energy, and PV term by gas adsorption, respectively. thermal

■

RESULTS AND DISCUSSION We started this study by investigating CO2 adsorption structures in PCP-N and PCP-C and then evaluated CO2 binding energies and adsorption enthalpies. On the basis of those computational results, we discussed the gate-opening adsorption and the unique adsorption isotherm observed in PCP-N. Structures of PCP-N and PCP-C with and without CO2 Molecule(s). Both the optimized cell parameters and the Fe− N distances of PCP-N without any guest molecule agree well with experimental values, as shown in Figure 1a and 1b; see

Table 1. Binding Energy (BE, kcal mol−1) of CO2, Interaction Energy (EINT, kcal mol−1) between CO2 and Framework,a and Crystal Deformation Energy (EDEF, kcal mol−1) When One CO2 Molecule Is Adsorbed into PCP-Nb BESCS‑MP2:PBE‑D3+ΔBECCSD(T) BESCS‑MP2:PBE‑D3 BEPBE‑D3 EPBE‑D3 DEF ESCS‑MP2:PBE‑D3 (H-G) INT

site I

site II

site III

−6.51 −5.41 −7.37 0.35 −5.75

−2.30 −1.21 −2.94 4.82 −6.04

−4.52 −3.16 −4.03 4.55 −7.71

a

Stabilization energy between deformed CO2 and PCP-N, where geometries of CO2 and PCP-N were taken to be the same as those in PCP-N with CO2 molecules. bTable S2 shows details.

binding energies decrease in the order of site I > III > II, but MP2:PBE-D3-calculated binding energy decreases in the different order of site III > I > II (Table S2 in SI). Because of this difference between MP2:PBE-D3- and SCS-MP2:PBED3-calculated binding energies, CCSD(T) correction was further made. BESCS‑MP2:PBE‑D3+ΔBECCSD(T) is almost the same as BEMP2:PBE‑D3+ΔBECCSD(T) and decreases in the order of site I > III > II like the SCS-MP2:PBE-D3 computational results. Also, the RMS error from CCSD(T)-corrected BE is much smaller in the SCS-MP2:PBE-D3-calculated values than in the MP2:PBE-D3-calculated ones; see Table S2 in the Supporting Information. Thus, the SCS-MP2:PBE-D3-calculated values are used in the discussion hereinafter.112 To understand the reason(s) why the binding energy of one CO2 molecule is larger at site I than at sites II and III, the binding energy was analyzed by using the interaction energy (EINT) between CO2 and the framework and the crystal deformation energy (EDEF) of the PCP-N framework, where the CO2 deformation energy is not discussed because it is negligibly small. The ESCS‑MP2:PBE‑D3 is similar between sites I INT and II but moderately larger at site III. On the other hand, the EPBE‑D3 is significantly smaller at site I than at sites II and III. DEF Consistent with the small crystal deformation energy at site I, the lattice vectors change much less by the CO2 adsorption at site I than at sites II and III (Table S3). It is concluded that the smallest crystal deformation energy at site I is the reason why the CO2 binding energy is the largest at site I; the ESCS‑MP2:PBE‑D3 is 0.29 and 1.96 kcal mol−1 more negative at INT sites II and III, respectively, than at site I, but the EPBE‑D3 is DEF 4.47 and 4.20 kcal mol−1 larger at sites II and III than at site I. Thus, the CO2 binding energy is the largest at site I and decreases in the order of site I > III > II. In summary, the CO2 adsorption occurs first at site I rather than at sites II and III because the CO2 binding energy at site I is larger than those at sites II and III for the same CO2 loading.

Figure 1. Optimized crystal structure of PCP-N with 15 CO2 molecules at sites I, II, and III (a), Local coordination environment of Fe2+ center (b), and optimized CO2 adsorption structures at sites I (c), II (d), and III (e). Distances are given in Angstroms. In parentheses is the experimental value. Atom colors: Fe, dark yellow; O, red; N, blue; C, gray; H, white.

also Table S1 in the Supporting Information for details. In PCP-N fully occupied by 15 CO2 molecules, lattice constants a and c were calculated to increase by 0.51 and 0.60 Å, respectively, as shown in Table S1. These results indicate that structural expansion of PCP-N occurs upon CO2 adsorption, as observed experimentally.24 PCP-C has almost the same structure optimized without a CO2 molecule, as compared in Table S1. In this PCP-C, CO2 adsorption also induces structural expansion like that in PCP-N. No significant difference is observed in geometry between PCP-N and PCP-C. X-ray analysis displayed that CO2 adsorption occurred at three sites (I, II, and III in Scheme 1) in PCP-N.24 DFT calculations here indicate that CO2 molecules are found at those three sites, which agrees with the experimental result. As shown in Figure 1, the number of CO2 molecules in one PUC is calculated to be 6, 6, and 3 for sites I, II, and III, respectively. Six CO2 molecules form a hexamer cluster at site I (Figure 1c). However, CO2 molecules are separated well from each other at sites II and III (Figure 1d and 1e). Their geometries are essentially the same as those of experimental structures, while the optimized CO2−CO2 distance of the hexamer at site I is longer than in the experimental one; the reliability of the 13961


Article


Table 2. Binding Energy (BE, kcal mol−1) and Adsorption Enthalpy (ΔHads, kcal mol−1) of CO2 at Sites I, II, and III of PCP-N with Increase in CO2 Loadinga (A) CO2 molecule is adsorbed at site I no. (n) of CO2 molecules

1

2

3

−7.37 −7.74 −8.07 −5.41 −5.65 −5.71 −6.51 −6.81 −7.02 0.35 0.24 0.23 −5.75 −5.68 −5.44 0.00 −0.13 −0.51 −6.53 −6.90 −7.23 −4.57 −4.81 −4.87 −5.67 −5.97 −6.18 −5.71 to −6.45 (B) CO2 molecule is adsorbed at site II or III

BEPBE‑D3 BESCS‑MP2:PBE‑D3 BESCS‑MP2:PBE‑D3+ΔBECCSD(T) b EPBE‑D3 DEF SCS‑MP2:PBE‑D3 EINT (H-G)c SCS‑MP2 EINT (G-G)c ΔHPBE‑D3 ads ΔHSCS‑MP2:PBE‑D3 ads ΔHSCS‑MP2:PBE‑D3 +ΔBECCSD(T) ads d ΔHads(Expt.)

4

5

6

−8.37 −5.92 −7.29 0.21 −5.44 −0.68 −7.54 −5.09 −6.46

−8.62 −6.01 −7.50 0.20 −5.36 −0.85 −7.79 −5.18 −6.67

−8.87 −6.10 −7.73 0.17 −5.21 −1.05 −8.04 −5.26 −6.89

site II

site III

no. (n) of CO2 molecule

1

2

3

4

5

6

1

2

3

BESCS‑MP2:PBE‑D3 b EPBE‑D3 DEF SCS‑MP2:PBE‑D3 EINT (H-G)c SCS‑MP2 EINT (G-G)c

−1.21 4.82 −6.03 0.00

−3.38 2.74 −6.07 −0.05

−4.11 2.09 −6.14 −0.07

−4.52 1.76 −6.20 −0.08

−4.77 1.62 −6.31 −0.08

−5.09 1.48 −6.48 −0.09

−3.16 4.55 −7.71 0.00

−5.32 2.46 −7.77 −0.00

−6.06 1.85 −7.90 −0.01

a

Tables S4 and S5 show details. Adsorption enthalpy was evaluated at 298 K for comparison with the experimental results at 273−298 K. bEPBE‑D3 DEF represents the average crystal deformation energy of PCP-N per one CO2 molecule induced by CO2 adsorption at site I. cESCS‑MP2:PBE‑D3 (H-G) and INT (G-G) represent the stabilization energy between deformed CO2 and PCP-N and between CO2 molecules. dExperimental ΔHads was ESCS‑MP2 INT measured for adsorption of 1−4 CO2 molecules.24

Table 3. Binding Energy (BE, kcal mol−1) of CO2 at Sites II and III of PCP-N in the Presence Six CO2 Molecules at Site Ia site II

site III

no. (n) of CO2 molecules

1

2

3

4

5

6

1

2

3

BESCS‑MP2:PBE‑D3b c EPBE‑D3 DEF ESCS‑MP2:PBE‑D3 (H-G)d INT SCS‑MP2 EINT (G-G)d

1.20 7.52 −5.52 −0.80

−2.19 4.41 −5.76 −0.84

−3.33 3.34 −5.84 −0.82

−4.00 2.76 −5.92 −0.83

−4.41 2.37 −5.99 −0.80

−4.77 2.12 −6.04 −0.84

−0.62 7.46 −7.93 −0.15

−4.15 3.97 −7.96 −0.16

−5.26 2.95 −8.04 −0.16

a

Table S6 shows details. bBESCS‑MP2:PBE‑D3 represents the CO2 binding energy at sites II and III in the presence of six CO2 molecules at site I, which represents the average crystal deformation energy of is defined by BESCS‑MP2:PBE‑D3 = [E(PCP·(n + 6)CO2) − E(PCP·6CO2)]/n − E(CO2). cEPBE‑D3 DEF (H-G) represents the interaction energy between CO2 PCP-N per one CO2 molecule induced by CO2 adsorption at site II or III. dESCS‑MP2:PBE‑D3 INT and the PCP-N framework. ESCS‑MP2 (G-G) is the sum of the CO2−CO2 interaction energy at sites I, II, and III. INT

hand, the CO2−CO2 interaction energy gradually increases. Also, the crystal deformation energy EPBE‑D3 per one CO2 DEF molecule gradually decreases as the number of adsorbed CO2 molecules increases; for instance, the first CO2 adsorption induces a large amount of crystal deformation energy (35% of the total EPBE‑D3 at site I), but the adsorption of the second to DEF sixth CO2 molecules induces almost 22% to 2% of the total EPBE‑D3 DEF . The CO2 binding energy at sites II and III was calculated as a function of CO2 loading too, as shown in Table 2B. Like the CO2 adsorption at site I, the CO2 binding energy at site II becomes larger as the number of adsorbed CO2 molecules increases. However, the sum of the CO 2 −framework SCS‑MP2:PBE‑D3 (H-G) and CO2−CO 2 interaction energy EINT SCS‑MP2:PBE‑D3 interaction energy EINT (G-G) does not change very much. On the other hand, the crystal deformation energy EPBE‑D3 per one CO2 molecule decreases from 4.82 to 1.48 kcal DEF mol−1 when the number of adsorbed CO2 molecules at site II increases from 1 to 6. This means that the crystal deformation energy is large (4.82 kcal mol−1) for the first CO2 adsorption at site II but considerably decreases to 2.74 and 2.09 kcal mol−1 for the second and third CO2 adsorptions, respectively. As a result, the CO2 binding energy increases as the number of

Dependence of CO2 Binding Energy on CO2 Loading in PCP-N. Because in total six, six, and three CO2 molecules were observed experimentally at sites I, II, and III, respectively,24 we evaluated the binding energy for 1−6 CO2 molecules at sites I and II and for 1−3 CO2 molecules at site III. As shown in Table 2A, the adsorption enthalpy (ΔHads) at site I was evaluated to be from −5.67 to −6.46 kcal mol−1 at the SCS-MP2:PBE-D3 level with CCSD(T) correction for adsorptions of 1−4 CO2 molecules. This computational result agrees well with the experimental value (from −5.71 to −6.45 kcal mol−1) measured for adsorption of 1−4 CO2 molecules, indicating that this computational method is reliable.112 It should be noted that the calculated adsorption enthalpy at site I increases from −5.67 to −6.89 kcal mol−1 as the number of adsorbed CO2 molecules increases from 1 to 6 (Table 2A). To elucidate the reason, we evaluated several important energy components such as the CO2−framework interaction energy SCS‑MP2:PBE‑D3 E INT (H-G), CO 2 −CO 2 interaction energy SCS‑MP2 EINT (G-G), and crystal deformation energy EPBE‑D3 DEF . As the number of adsorbed CO2 molecules increases from one to six, the CO2−framework interaction energy ESCS‑MP2:PBE‑D3 (HINT G) moderately decreases, indicating that this term does not contribute to the increase in binding energy. On the other 13962


Article


Table 4. Binding Energy (BE, kcal mol−1) of CO2 at Sites I, II, and III of PCP-C in the Absence and Presence of Six CO2 Molecules at Site Ia

adsorbed CO2 molecules increases. Similar results are observed in the CO2 adsorption at site III (Table 2B). In summary, the CO2 binding energy and adsorption enthalpy increase with the increase in the number of adsorbed CO2 molecules because at site I the CO2−CO2 interaction energy increases but the crystal deformation energy per one CO2 molecule decreases and at sites II and III the CO2−CO2 interaction energy changes little but the crystal deformation energy per one CO2 molecule decreases. Continuous Adsorption of 15 CO2 Molecules in PCPN. Because in total 15 CO2 molecules are found experimentally in PCP-N, we investigated the adsorption of 15 CO 2 molecules. The considerably larger BE at site I than at sites II and III (Tables 1 and 2) indicates that 1−6 CO2 molecules are adsorbed first at site I, and then the seventh CO2 molecule is adsorbed at either site II or site III in the presence of six CO2 molecules at site I. However, the binding energy of the CO2 molecule is positive (repulsive) at site II and very small at site III, as shown in Table 3. These very small binding energies arise from the large crystal deformation energy EPBE‑D3 of sites DEF II and III in the presence of six CO2 molecules at site I (Table 3); note that the CO2−framework interaction energy (H-G) differs little between the absence and ESCS‑MP2:PBE‑D3 INT the presence of CO2 molecules at site I. This means that the presence of six CO2 molecules at site I makes the PCP-N structure less flexible to suppress the CO2 adsorption at sites II and III. However, the CO2 binding energy significantly increases (becomes more negative) from 1.20 to −4.77 kcal mol−1 at site II and from −0.62 to −5.26 kcal mol−1 at site III as the number of adsorbed CO2 molecules increases (Table 3). As a result, the sum of binding energies of six CO2 molecules at site II becomes negative and that at site III also becomes significantly values, indicating negative and overcomes the sum of EPBE‑D3 DEF that simultaneous adsorption of six CO2 molecules at site II and that of three CO2 molecules at site III can occur. The SCS‑MP2:PBE‑D3 (H-G) CO2−framework interaction energy EINT moderately increases and the CO2−CO2 interaction energy ESCS‑MP2:PBE‑D3 (G-G) is almost constant with an increase in the INT number of adsorbed CO2 molecules at both sites II and III. per one CO2 However, the crystal deformation energy EPBE‑D3 DEF molecule significantly decreases as the number of adsorbed CO2 molecules increases, suggesting that the framework is already distorted enough by the first CO2 adsorption at sites II and III, and therefore, the next CO2 molecule can be adsorbed at sites II and III without a large energy loss by crystal deformation. This is the reason why the binding energy increases with the increase in CO2 loading at sites II and III. In conclusion, adsorption of one CO2 molecule at sites II and III is difficult to occur, but simultaneous adsorptions of six and three CO2 molecules is possible to occur at sites II and III, respectively. This phenomenon corresponds to the gateopening gas adsorption mechanism. CO2 Adsorption into PCP-C. In PCP-C, one N atom of the pyrazinyl ligand is replaced by one CH group. Because PCP-C is isostructural to PCP-N, this PCP-C has three possible adsorption sites for CO2 like PCP-N, as shown in Scheme 1b. We first evaluated the CO2 binding energy at these three sites in the absence of the CO2 molecule at another site. As shown in Table 4, the CO2 binding energies at all of these sites are smaller than those of the corresponding sites in PCPN (Tables 2 and 3), indicating that PCP-C is less effective for CO2 adsorption than PCP-N. For site I, the crystal

PCP-Cb no. (n) of CO2 molecules BESCS‑MP2:PBE‑D3d e EPBE‑D3 DEF ESCS‑MP2:PBE‑D3 (H-G)f INT SCS‑MP2 EINT (G-G)f

PCP-C·6CO2c

site I

site II

site III

site II

site III

6 −4.55 0.22 −3.37 −1.06

6 −2.00 3.89 −5.82 −0.07

3 −2.12 5.68 −7.79 −0.01

6 −0.27 6.23 −5.71 −0.78

3 −0.15 7.83 −7.82 −0.16

a

Table S7 shows details. bCO2 molecules are adsorbed at sites I, II, or III without any other CO2 molecule at other site. cSix CO2 molecules are adsorbed at site I. dBESCS‑MP2:PBE‑D3 represents CO2 binding energy, which is defined by BESCS‑MP2:PBE‑D3 = [E(PCP·nCO2) − E(PCP]/n − E(CO2) for PCP-C and by BESCS‑MP2:PBE‑D3 = [E(PCP· (n + 6)CO2) − E(PCP·6CO2)]/n − E(CO2) for PCP-C with six CO2 molecules at site I. eEPBE‑D3 represents average crystal deformation DEF energy of PCP-C per one CO2 molecule induced by CO2 adsorption. f SCS‑MP2:PBE‑D3 EINT (H-G) represents the interaction energy between CO2 and the PCP-C framework. ESCS‑MP2 (G-G) is the interaction energy INT between CO2 molecules.

deformation energy is comparable between PCP-C and PCP-N. This is reasonable because CO2 adsorption at this site does not induce significant geometry distortion in both of these PCPs. However, the CO2−framework interaction energy is smaller in PCP-C than in PCP-N by 1.84 kcal mol−1 per one CO2 molecule at the SCS-MP2:PBE-D3 level, leading to the smaller binding energy of CO2 in PCP-C. For sites II and III, the CO2−framework interaction is similar between PCP-C and PCP-N. This is reasonable because the local environment of sites II and III is similar between these two PCPs. However, it is noted that the crystal deformation energy by CO2 adsorption is much larger in PCP-C than in PCP-N, leading to the smaller CO2 binding energy in PCP-C than in PCP-N; the crystal deformation energies for sites II and III are 3.89 and 5.68 kcal mol−1 in PCP-C, respectively (Table 4), and 1.48 and 1.85 kcal mol−1 in PCP-N (Table 2A). Because the SCS-MP2:PBE-D3-calculated binding energy decreases in the order of site I ≫ III ≈ II, it is likely that CO2 adsorption occurs first at site I in PCP-C like in PCP-N and then CO2 adsorption starts to occur at site II or III after site I is fully occupied by six CO2 molecules. Therefore, we evaluated the CO2 binding energy at sites II and III in the presence of six CO2 molecules at site I. As shown in Table 4, the total binding energies for six and three CO2 molecules at sites II and III are very small (−0.27 and −0.15 kcal mol−1 at site II and III, respectively). It is likely concluded that the CO2 molecule is hardly adsorbed at sites II and III when site I is occupied by six CO2 molecules. The CO2−framework interaction energy ESCS‑MP2:PBE‑D3 (HINT G) and the CO2−CO2 interaction energy ESCS‑MP2:PBE‑D3 (G-G) INT at sites II and III are similar between the absence and the presence of six CO2 molecules at site I. However, the crystal deformation energy EPBE‑D3 is significantly large when six CO2 DEF molecules are adsorbed at site I. It is 5.68 and 7.83 kcal mol−1 for sites II and III, respectively, as shown in Table 4. This result clearly shows that the flexibility of PCP-C is significantly reduced by the CO2 occupation at site I, and it is the main reason for the difficulty in CO2 adsorption at sites II and III. In conclusion, CO2 adsorption occurs at site I of PCP-C but does not at sites II and III in the presence of six CO2 molecules at site I, because the crystal deformation energy is very large. 13963


Article

Journal of the American Chemical Society This result is consistent with the experimental report that CO2 adsorption quantity is much less in PCP-C than in PCP-N.24 Stepwise Adsorption Isotherm in PCP-N and Typical Langmuir-Type Isotherm in PCP-C. It is important to elucidate the reason why the stepwise adsorption isotherm was observed in CO2 adsorption into PCP-N and whether or not this stepwise isotherm is related to the gate-opening adsorption mechanism in PCP-N. The CO2 molecule can be gradually adsorbed in a one by one manner at site I because the crystal deformation energy is moderate and the interaction energy of one CO2 molecule is enough to overcome the crystal deformation energy (Table 2A). This situation is shown in Scheme 3a. This adsorption

θ=

K (p /p0 ) 1 + K (p /p0 )

(8)

where p0 is the standard pressure (101.325 kPa). Equation 8 is essentially the same as the Langmuir adsorption. At sites II and III, adsorption of one CO2 molecule is difficult to occur because EINT of one CO2 molecule is not enough to overcome the large EDEF, as shown in Scheme 3b (left). However, EINT of simultaneous adsorption of more than one CO2 molecule can overcome the EDEF, as discussed above. This situation is schematically shown in Scheme 3b (right). Because the averaged CO2 binding energy is similar between sites II and III when six and three CO2 molecules are adsorbed at sites II and III, respectively (Table 3), it is likely that in total nine CO2 molecules can be simultaneously adsorbed at sites II and III. Its equilibrium equation is represented by eq 9

Scheme 3. Relation between Gas Adsorption and EINT/EDEF.

CO2 adsorption at sites II&III; 9 CO2 + PCP V PCP ·(CO2 )9 (9)

For the CO2 adsorption at sites II and III, therefore, the coverage θ at a given pressure can be represented by eq 10 θ=

K (p /p0 )9 1 + K (p /p0 )9

(10)

This eq 10 is the same as the Langmuir−Freundlich equation, θ = K(p/p0)ν/[1 + K(p/p0)ν] (ν = larger than 1). Equations 9 and 10 clearly indicate that the parameter ν represents the number of gas molecules simultaneously adsorbed at the adsorption site; this relationship provides the physical meaning of the parameter ν. Total CO2 adsorption quantity Nads(CO2) is represented by the sum of coverages of θI and θII&III 9θ y i 6θ Nads(CO2 ) = Nsatjjjj I + II&III zzzz 15 15 { k

where Nsat is the saturated adsorption amount (214.0 cm3/g for CO2 adsorption in experiment). To calculate the adsorption isotherm, the Gibbs energy o change (ΔGads ) for CO2 adsorption must be evaluated. Because CO2 adsorption occurs at sites II and III after six CO2 molecules are adsorbed at site I, as discussed above, the ΔGoads values for sites II and III were evaluated in the presence of six CO2 molecules at site I.113 As shown in Table 5, ΔGoads is much larger (more positive) in PCP-C than in PCP-N. In particular, the ΔGoads value is considerably large (positive) for CO2 adsorption at sites II and III in PCP-C. The largely positive ΔGoads indicates that the CO2 adsorption does not occur at sites II and III in PCP-C, as schematically shown in Scheme 3c. Using these ΔGoads values and eq 11, we calculated the CO2 adsorption isotherms in PCP-N and PCP-C. However, the calculated CO2 adsorption amount was much smaller than the experimental one (Figures S3 and S4). This is not unreasonable because ΔGoads for gas adsorption in PCPs/ MOFs is often underestimated,64,65 as follows; in general, the rotational and translational degrees of freedom (DOFs) are considered to be frozen in adsorbed gas molecule, but strictly speaking, some of those rotational/translational DOFs are not completely frozen in an adsorbed gas molecule. Therefore, the ΔGoads value is underestimated if the rotational/translational DOFs are assumed to be completely frozen, and it is reasonable to increase the ΔGoads value for CO2 adsorption

does not show any unique feature, and therefore, it follows the usual equilibrium equation (eq 7) CO2 adsorption at site I; CO2 + PCP V PCP ·CO2

(11)

(7)

The equilibrium constant K is represented by the Gibbs energy change for adsorption through K = exp(−ΔGoads/RT). CO2 coverage θ at given pressure P can be represented by eq 8 for the CO2 adsorption at site I using the equilibrium constant K 13964


Article


Table 5. Adsorption Enthalpy Change (ΔH°, kcal mol−1), Entropy Change (TΔS°, kcal mol−1), and Gibbs Energy Change (ΔG°, kcal mol−1) of CO2 at Sites I and II&III in PCP-N and PCP-Ca PCP-N no. (n) of CO2 molecules ΔHoads −TΔSoads ΔGoads

PCP-C

site I

site II&IIIb

site I

site II&IIIb

6 −7.18 (−7.38/−7.58)c 6.14 (5.87/5.38) −1.04 (−1.51/−2.20)

9 −5.95 (−6.15/−6.35) 6.17 (6.00/5.40) 0.22 (−0.15/−0.96)

6 −5.30 (−5.50/−5.69) 5.26 (−5.25/−4.94) −0.04 (−0.25/−0.75)

9 −3.14 (−3.34/−3.55) 7.05 (6.50/5.75) 3.91 (3.16/2.20)

a T = 195 K. CCSD(T) correction was made here; see also footnote 113. bSix CO2 molecules are already adsorbed at site I. The binding energy is calculated by BE=[E(PCP·(n+6)CO2)−E(PCP·6CO2)]/n−E(CO2), where n = 9 because nine is the maximum number of CO2 molecules at sites II and III. cThese values are calculated by conserving one (before slash) or two (after slash) rotational degrees of freedom of adsorbed CO2 molecule.

by 1.0−1.5 kcal mol−1 if one or two rotational DOF(s) remain in the CO2 molecule adsorbed in PCPs (Table 5);64,65 see discussion on p S17 in the Supporting Information. As shown in Figure 2a, the calculated CO2 adsorption isotherms in PCP-

and II&III. As shown in Figure 3, the CO2 adsorption at site I contributes mostly to the first adsorption step without a

Figure 3. Calculated CO2 adsorption isotherms at sites I and II&III in PCP-N at 195 K. Adsorption Gibbs energy change was increased by 1.5 kcal mol−1.

sigmoidal curve and the CO2 adsorption at sites II and III contributes to the second isotherm with a sigmoidal curve. These results indicate that the sigmoidal adsorption isotherm is related to the gate-opening adsorption. The characteristic feature of eq 10 can be understood by considering the second-order derivatives of eqs 8 and 10 (see p S5 for details); when ν = 1 (CO2 adsorption at site I), the second-order derivative of eq 8 is always smaller than zero, indicating that the isotherm does not show an inflection point. This means that the adsorption amount gradually increases following the Langmuir-type adsorption isotherm. On the other hand, the inflection pressure (Pinf) is represented by ln Pinf = ln p0 − (1/ν)ln[(ν + 1)K/(ν − 1)] when ν is larger than 1. In such case, the sigmoidal adsorption isotherm is presented. These results clearly indicate that simultaneous adsorption of more than one gas molecule is the reason for the sigmoidal adsorption isotherm. Because the ν value of the Langmuir− Frendlich adsorption isotherm represents how many molecules are simultaneously adsorbed into PCP, as discussed above, the ν value of the Freundlich-type isotherm is experimental evidence showing how many gas molecules are adsorbed simultaneously to PCPs/MOFs. Because eq 10 with ν = 9 reproduced well the experimental adsorption curve, it is reasonable to conclude that nine CO2 molecules are simultaneously adsorbed at sites II and III of PCP-N; actually X-ray analysis showed the presence of nine CO2 molecules at sites II and III.24 The above discussion means that the sigmoidal adsorption isotherm can be presented even when the gate-opening adsorption does not work. Actually, the sigmoidal adsorption

Figure 2. Calculated CO2 adsorption isotherms at 195 K in (a) PCPN and (b) PCP-C. Black lines represent experimental isotherms; blue and red lines represent isotherms calculated by increasing the adsorption Gibbs energy change by 1.0 and 1.5 kcal mol−1, respectively. Inset represents the expansion at the low-pressure region.

N agree well with the experimental result. It should be emphasized that the stepwise adsorption isotherm could be reproduced well by the calculation. For CO2 adsorption in PCP-C, the adsorption isotherm was successfully reproduced well by increasing the ΔGoads by 1.0− 1.5 kcal mol−1 (Figure 2b). In this case, no stepwise curve could be observed, which is consistent with the experimental result.24 This is true because CO2 adsorption does not occur at sites II and III (Figure S5) due to the largely positive ΔGoads value (Table 5). Relation between the Sigmoidal Adsorption Isotherm and the Gate-Opening Adsorption Mechanism. To understand the relationship between the stepwise adsorption isotherm and the gate-opening mechanism, we separately evaluated the CO2 adsorption isotherms at sites I 13965


Article


sites II and III. Because of the larger CO2 binding energy at site I than at sites II and III, six CO2 molecules are adsorbed first at site I (adsorption of six CO2 molecules is the maximum). In the presence of six CO2 molecules at site I, adsorption of one CO2 molecule cannot occur at sites II and III in both PCP-N and PCP-C, because the adsorption energy of one CO2 is not enough to overcome the large EDEF; see Scheme 3b and 3c. However, the EDEF per CO2 molecule significantly decreases as the number of adsorbed CO2 molecules increases in PCP-N. In other words, the adsorption of the first CO2 molecule gives rise to a large EDEF, but the subsequent adsorption of CO2 molecules does not increase EDEF very much. Therefore, the adsorption energy by nine CO2 molecules (this is the maximum) at sites II and III can overcome the EDEF in PCP-N. This adsorption corresponds to our understanding of the gate-opening mechanism because the first CO2 adsorption induces most of the crystal deformation to make subsequent CO2 adsorption feasible; see Scheme 3b. The gate-opening adsorption, however, does not occur in PCP-C because the considerably large EDEF cannot be overcome by the CO2 adsorption energy even if nine CO2 molecules are adsorbed (adsorption of nine CO2 molecules is the maximum at sites II and III); see Scheme 3c. These results show the important factors for the gate-opening gas adsorption into PCP, as follows: (i) Adsorption of one gas molecule cannot occur because a large EDEF is not overcome by EINT by one gas molecule. (ii) EDEF per one gas molecule decreases as the number of adsorbed gas molecules increases. (iii) In such case, simultaneous adsorption of more than one gas molecule can occur if the sum of adsorption energies overcomes total EDEF. However, (iv) if EDEF is so large that simultaneous adsorption of more than one gas molecule cannot overcome EDEF, gas adsorption does not occur, indicating that for the gate-opening gas adsorption EDEF must be smaller than EINT of simultaneous adsorption of maximum gas molecules. The complicated stepwise CO2 adsorption isotherm of PCPN was reproduced well by the computational results. It consists of the usual Langmuir-type adsorption isotherm at site I and the Langmuir-Frendlich type sigmoidal one at sites II and III. The simultaneous adsorption of nine CO2 molecules at sites II and III of PCP-N is the origin of the sigmoidal CO2 adsorption isotherm because the adsorption equilibrium is represented by eq 10. This means that when the gate-opening mechanism allows the simultaneous adsorption of more than one gas molecule, a sigmoidal adsorption isotherm is presented. However, a sigmoidal adsorption isotherm can be presented even without the gate-opening adsorption if more than one gas molecule is adsorbed simultaneously to PCP. The other important conclusion is the meaning of the ν value of the Langmuir−Freundlich adsorption isotherm. It represents the number of gas molecules simultaneously adsorbed into PCP. If the sigmoidal curve is analyzed well, one can know experimentally how many gas molecules are simultaneously adsorbed into PCP.

isotherm was experimentally reported recently in CO adsorption into FeII-based PCP through a nongate-opening adsorption mechanism.114 In the CO2 adsorption into PCP-N, however, the sigmoidal adsorption isotherm arises from the gate-opening adsorption, as follows: As discussed above and also shown in Scheme 3b (left), adsorption of one CO2 molecule at sites II and III cannot occur because the adsorption energy of one CO2 molecule cannot overcome the large crystal deformation energy. However, the crystal deformation energy at the first CO2 adsorption is large but the crystal deformation energy per one CO2 molecule decreases as the number of adsorption CO2 molecules increases (Table 3). Therefore, when nine CO2 molecules are adsorbed simultaneously at sites II and III, the sum of CO2 adsorption energies can overcome the total crystal deformation energy. In other words, the first CO2 adsorption induces most of crystal deformation and the second and third CO2 adsorptions induce smaller crystal deformation energy. Important Factor(s) for Gate-Opening Adsorption Mechanism. On the basis of the above computational results, we will discuss here what factors are needed for the gateopening adsorption mechanism. Characteristic features of the CO2 adsorption into PCP-N and PCP-C are summarized as follows. (i) a CO2 molecule is gradually adsorbed at site I in both PCP-N and PCP-C, because the crystal deformation energy is negligibly small. This is the case of Scheme 3a. (ii) When site I is fully occupied by six CO2 molecules, adsorption of one CO2 molecule cannot occur at sites II and III of both PCP-N and PCP-C because adsorption of one CO2 molecule cannot overcome the large crystal deformation energy. This is the case of Scheme 3b (left). (iii) However, simultaneous adsorption of six and three CO2 molecules at sites II and III in PCP-N can occur because the crystal deformation energy is overcome by adsorption of these CO2 molecules. This is the case of Scheme 3b (right). (iv) This is possible because the crystal deformation energy per one CO2 molecule decreases with the increase in the number of adsorbed CO2 molecules; in other words, the EDEF by one CO2 molecule is large, but it does not increase very much by the subsequent CO2 adsorption. (v) In the case of PCP-C, the gate-opening adsorption cannot occur because the crystal deformation energy is so large at sites II and III that it cannot be overcome by simultaneous adsorption of nine CO2 molecules at sites II and III (adsorption of nine CO2 molecules is maximum at sites II and III). This is the case of Scheme 3c. On the basis of the above features, the gate-opening adsorption to flexible PCPs is possible when the crystal deformation energy is large by the adsorption of one gas molecule, it decreases as the increase in gas molecules adsorbed into PCP, and the total deformation energy is overcome by simultaneous adsorption of many gas molecules. In such case, the sigmoidal adsorption isotherm is observed.

■

CONCLUSIONS The gate-opening adsorption mechanism and sigmoidal adsorption isotherm were theoretically investigated with the hybrid SCS-MP2:PBE-D3 method, employing CO2 adsorption into flexible PCP-N and its rigid analogue PCP-C as examples. The calculated CO2 binding energy decreases in the order of site I > III > II in both PCP-N and PCP-C because the interaction energy between CO2 and the PCP framework is similar among these sites but the crystal deformation energy (EDEF) by the adsorption at site I is much smaller than those at

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.8b09358. Details of MP2 and SCS-MP2 calculations, comparison among structural parameters of an isolated CO2 hexamer optimized with various methods, potential energy 13966


Article


■

surfaces of CO2−CO2 and CO2−pyrazine interactions at various levels of theory, details of binding energy, additional calculated adsorption isotherms and discussion, and coordinates (in POSCAR format used in VASP calculations) of optimized CO2 adsorption structures at different sites and loading in PCP-N and PCP-C (PDF) PCP_nCO2 optimized with the PBE-D3 method (TXT)

(16) Horcajada, P.; Serre, C.; Maurin, G.; Ramsahye, N. A.; Balas, F.; Vallet-Regi, M.; Sebban, M.; Taulelle, F.; Férey, G. J. Am. Chem. Soc. 2008, 130, 6774. (17) Horike, S.; Shimomura, S.; Kitagawa, S. Nat. Chem. 2009, 1, 695. (18) Ferey, G.; Serre, C. Chem. Soc. Rev. 2009, 38, 1380. (19) Schneemann, A.; Bon, V.; Schwedler, I.; Senkovska, I.; Kaskel, S.; Fischer, R. A. Chem. Soc. Rev. 2014, 43, 6062. (20) Chang, Z.; Yang, D. H.; Xu, J.; Hu, T. L.; Bu, X. H. Adv. Mater. 2015, 27, 5432. (21) Kitaura, R.; Seki, K.; Akiyama, G.; Kitagawa, S. Angew. Chem., Int. Ed. 2003, 42, 428. (22) Seo, J.; Bonneau, C.; Matsuda, R.; Takata, M.; Kitagawa, S. J. Am. Chem. Soc. 2011, 133, 9005. (23) Sato, H.; Kosaka, W.; Matsuda, R.; Hori, A.; Hijikata, Y.; Belosludov, R. V.; Sakaki, S.; Takata, M.; Kitagawa, S. Science 2014, 343, 167. (24) Ma, Y.; Matsuda, R.; Sato, H.; Hijikata, Y.; Li, L.; Kusaka, S.; Foo, M.; Xue, F.; Akiyama, G.; Yuan, R.; Kitagawa, S. J. Am. Chem. Soc. 2015, 137, 15825. (25) Mason, J. A.; Oktawiec, J.; Taylor, M. K.; Hudson, M. R.; Rodriguez, J.; Bachman, J. E.; Gonzalez, M. I.; Cervellino, A.; Guagliardi, A.; Brown, C. M.; Llewellyn, P. L.; Masciocchi, N.; Long, J. R. Nature 2015, 527, 357. (26) Bon, V.; Kavoosi, N.; Senkovska, I.; Muller, P.; Schaber, J.; Wallacher, D.; Tobbens, D. M.; Mueller, U.; Kaskel, S. Dalton Trans. 2016, 45, 4407. (27) Taylor, M. K.; Runcevski, T.; Oktawiec, J.; Gonzalez, M. I.; Siegelman, R. L.; Mason, J. A.; Ye, J.; Brown, C. M.; Long, J. R. J. Am. Chem. Soc. 2016, 138, 15019. (28) Foo, M. L.; Matsuda, R.; Hijikata, Y.; Krishna, R.; Sato, H.; Horike, S.; Hori, A.; Duan, J.; Sato, Y.; Kubota, Y.; Takata, M.; Kitagawa, S. J. Am. Chem. Soc. 2016, 138, 3022. (29) Li, L.; Lin, R. B.; Krishna, R.; Wang, X.; Li, B.; Wu, H.; Li, J.; Zhou, W.; Chen, B. J. Am. Chem. Soc. 2017, 139, 7733. (30) Lin, R. B.; Li, L.; Wu, H.; Arman, H.; Li, B.; Lin, R. G.; Zhou, W.; Chen, B. J. Am. Chem. Soc. 2017, 139, 8022. (31) Carrington, E. J.; McAnally, C. A.; Fletcher, A. J.; Thompson, S. P.; Warren, M.; Brammer, L. Nat. Chem. 2017, 9, 882. (32) Sen, S.; Hosono, N.; Zheng, J.-J.; Kusaka, S.; Matsuda, R.; Sakaki, S.; Kitagawa, S. J. Am. Chem. Soc. 2017, 139, 18313. (33) Coudert, F. X.; Boutin, A.; Jeffroy, M.; Mellot-Draznieks, C.; Fuchs, A. H. ChemPhysChem 2011, 12, 247. (34) Yang, Q.; Liu, D.; Zhong, C.; Li, J.-R. Chem. Rev. 2013, 113, 8261. (35) Odoh, S. O.; Cramer, C. J.; Truhlar, D. G.; Gagliardi, L. Chem. Rev. 2015, 115, 6051. (36) Coudert, F.-X.; Fuchs, A. H. Coord. Chem. Rev. 2016, 307, 211. (37) Fraux, G.; Coudert, F.-X. Chem. Commun. 2017, 53, 7211. (38) Coudert, F.-X.; Jeffroy, M.; Fuchs, A. H.; Boutin, A.; MellotDraznieks, C. J. Am. Chem. Soc. 2008, 130, 14294. (39) Neimark, A. V.; Coudert, F.-X.; Boutin, A.; Fuchs, A. H. J. Phys. Chem. Lett. 2010, 1, 445. (40) Boutin, A.; Coudert, F.-X.; Springuel-Huet, M.-A.; Neimark, A. V.; Férey, G.; Fuchs, A. H. J. Phys. Chem. C 2010, 114, 22237. (41) Pera-Titus, M. J. Phys. Chem. C 2011, 115, 3346. (42) Bousquet, D.; Coudert, F.-X.; Boutin, A. J. Chem. Phys. 2012, 137, 044118. (43) Vanduyfhuys, L.; Rogge, S.; Wieme, J.; Vandenbrande, S.; Maurin, G.; Waroquier, M.; Van Speybroeck, V. Nat. Commun. 2018, 9, 204. (44) Dunne, L. J.; Manos, G. J. Stat. Mech.: Theory Exp. 2015, 2015, P05008. (45) Dunne, L. J.; Manos, G. Dalton Trans. 2016, 45, 4213. (46) Simon, C. M.; Braun, E.; Carraro, C.; Smit, B. Proc. Natl. Acad. Sci. U. S. A. 2017, 114, E287. (47) Ghoufi, A.; Maurin, G. J. Phys. Chem. C 2010, 114, 6496. (48) Zang, J.; Nair, S.; Sholl, D. S. J. Chem. Phys. 2011, 134, 184103.

AUTHOR INFORMATION

Corresponding Authors

*[email protected] *[email protected] ORCID

Shinpei Kusaka: 0000-0001-7718-4387 Susumu Kitagawa: 0000-0001-6956-9543 Shigeyoshi Sakaki: 0000-0002-1783-3282 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the PRESTO (Grant No. JPMJPR141C) and ACCEL (Grant No. JPMJAC1302) projects of the Japan Science and Technology Agency (JST) and JSPS KAKENHI Grant-in-Aid for Young Scientists (B) (Grant No. 25870360), JSPS KAKENHI Grant-in-Aid for Scientific Research “Soft-Crystal” (No. 18H04513), Challenging Exploratory Research (Grant No. 25620187), and Specially Promoted Research (Grant No. 25000007). We are thankful to the Institute for Molecular Science (Okazaki, Japan) for performing some of the calculations with the computer systems.

■

REFERENCES

(1) Kondo, M.; Yoshitomi, T.; Matsuzaka, H.; Kitagawa, S.; Seki, K. Angew. Chem., Int. Ed. Engl. 1997, 36, 1725. (2) Li, H.; Eddaoudi, M.; Groy, T. L.; Yaghi, O. J. Am. Chem. Soc. 1998, 120, 8571. (3) Kitagawa, S.; Kitaura, R.; Noro, S. Angew. Chem., Int. Ed. 2004, 43, 2334. (4) Kitagawa, S.; Matsuda, R. Coord. Chem. Rev. 2007, 251, 2490. (5) Morris, R. E.; Wheatley, P. S. Angew. Chem., Int. Ed. 2008, 47, 4966. (6) Czaja, A. U.; Trukhan, N.; Müller, U. Chem. Soc. Rev. 2009, 38, 1284. (7) Murray, L. J.; Dincă, M.; Long, J. R. Chem. Soc. Rev. 2009, 38, 1294. (8) Li, J.-R.; Kuppler, R. J.; Zhou, H.-C. Chem. Soc. Rev. 2009, 38, 1477. (9) Sumida, K.; Rogow, D. L.; Mason, J. A.; McDonald, T. M.; Bloch, E. D.; Herm, Z. R.; Bae, T.-H.; Long, J. R. Chem. Rev. 2012, 112, 724. (10) Suh, M. P.; Park, H. J.; Prasad, T. K.; Lim, D.-W. Chem. Rev. 2012, 112, 782. (11) Li, J.-R.; Sculley, J.; Zhou, H.-C. Chem. Rev. 2012, 112, 869. (12) Liu, J.; Thallapally, P. K.; McGrail, B. P.; Brown, D. R.; Liu, J. Chem. Soc. Rev. 2012, 41, 2308. (13) Wu, H.; Gong, Q.; Olson, D. H.; Li, J. Chem. Rev. 2012, 112, 836. (14) Lin, Z.-J.; Lü, J.; Hong, M.; Cao, R. Chem. Soc. Rev. 2014, 43, 5867. (15) Halder, G. J.; Kepert, C. J.; Moubaraki, B.; Murray, K. S.; Cashion, J. D. Science 2002, 298, 1762. 13967


Article

Journal of the American Chemical Society (49) Chang, B. K.; Bristowe, P. D.; Cheetham, A. K. Phys. Chem. Chem. Phys. 2013, 15, 176. (50) Zheng, B.; Pan, Y.; Lai, Z.; Huang, K.-W. Langmuir 2013, 29, 8865. (51) Zhang, L.; Hu, Z.; Jiang, J. J. Am. Chem. Soc. 2013, 135, 3722. (52) Zhang, L.; Wu, G.; Jiang, J. J. Phys. Chem. C 2014, 118, 8788. (53) Witman, M.; Ling, S.; Jawahery, S.; Boyd, P. G.; Haranczyk, M.; Slater, B.; Smit, B. J. Am. Chem. Soc. 2017, 139, 5547. (54) Moghadam, P. Z.; Ivy, J. F.; Arvapally, R. K.; Dos Santos, A. M.; Pearson, J. C.; Zhang, L.; Tylianakis, E.; Ghosh, P.; Oswald, I. W.; Kaipa, U. Chem. Sci. 2017, 8, 3989. (55) Jawahery, S.; Simon, C. M.; Braun, E.; Witman, M.; Tiana, D.; Vlaisavljevich, B.; Smit, B. Nat. Commun. 2017, 8, 13945. (56) Vanduyfhuys, L.; Verstraelen, T.; Vandichel, M.; Waroquier, M.; Van Speybroeck, V. J. Chem. Theory Comput. 2012, 8, 3217. (57) Garcia-Perez, E.; Serra-Crespo, P.; Hamad, S.; Kapteijn, F.; Gascon, J. Phys. Chem. Chem. Phys. 2014, 16, 16060. (58) Lin, L.-C.; Lee, K.; Gagliardi, L.; Neaton, J. B.; Smit, B. J. Chem. Theory Comput. 2014, 10, 1477. (59) Chen, L.; Mowat, J. P.; Fairen-Jimenez, D.; Morrison, C. A.; Thompson, S. P.; Wright, P. A.; Düren, T. J. Am. Chem. Soc. 2013, 135, 15763. (60) Ryder, M. R.; Civalleri, B.; Bennett, T. D.; Henke, S.; Rudić, S.; Cinque, G.; Fernandez-Alonso, F.; Tan, J.-C. Phys. Rev. Lett. 2014, 113, 215502. (61) Kara, A.; Demirbel, E.; Tekin, N.; Osman, B.; Beşirli, N. J. Hazard. Mater. 2015, 286, 612. (62) Osman, B.; Ö zer, E. T.; Kara, A.; Yeşilova, E.; Beşirli, N. J. Porous Mater. 2015, 22, 37. (63) Tonigold, M.; Lu, Y.; Mavrandonakis, A.; Puls, A.; Staudt, R.; Möllmer, J.; Sauer, J.; Volkmer, D. Chem. - Eur. J. 2011, 17, 8671. (64) Sillar, K.; Sauer, J. J. Am. Chem. Soc. 2012, 134, 18354. (65) Kundu, A.; Piccini, G.; Sillar, K.; Sauer, J. J. Am. Chem. Soc. 2016, 138, 14047. (66) Verma, P.; Xu, X.; Truhlar, D. G. J. Phys. Chem. C 2013, 117, 12648. (67) Lee, K.; Isley, W. C., III; Dzubak, A. L.; Verma, P.; Stoneburner, S. J.; Lin, L. C.; Howe, J. D.; Bloch, E. D.; Reed, D. A.; Hudson, M. R.; Brown, C. M.; Long, J. R.; Neaton, J. B.; Smit, B.; Cramer, C. J.; Truhlar, D. G.; Gagliardi, L. J. Am. Chem. Soc. 2014, 136, 698. (68) Verma, P.; Maurice, R. M.; Truhlar, D. G. J. Phys. Chem. C 2016, 120, 9933. (69) Tang, B.; Huang, S.; Fang, Y.; Hu, J.; Malonzo, C.; Truhlar, D. G.; Stein, A. J. Chem. Phys. 2016, 144, 194702. (70) Lownsbury, J. M.; Santos-López, I. A.; Zhang, W.; Campbell, C. T.; Yu, H. S.; Liu, W.-G.; Cramer, C. J.; Truhlar, D. G.; Wang, T.; Hupp, J. T. J. Phys. Chem. C 2016, 120, 16850. (71) Gallington, L. C.; Kim, I. S.; Liu, W.-G.; Yakovenko, A. A.; Platero-Prats, A. E.; Li, Z.; Wang, T. C.; Hupp, J. T.; Farha, O. K.; Truhlar, D. G. J. Am. Chem. Soc. 2016, 138, 13513. (72) Liu, W.-G.; Truhlar, D. G. Chem. Mater. 2017, 29, 8073. (73) Platero-Prats, A. E.; League, A. B.; Bernales, V.; Ye, J.; Gallington, L. C.; Vjunov, A.; Schweitzer, N. M.; Li, Z.; Zheng, J.; Mehdi, B. L.; Stevens, A. J.; Dohnalkova, A.; Balasubramanian, M.; Farha, O. M.; Hupp, J. T.; Browning, N. D.; Fulton, J. L.; Camaioni, D. M.; Lercher, J. A.; Truhlar, D. G.; Gagliardi, L.; Cramer, C. J.; Chapman, K. W. J. Am. Chem. Soc. 2017, 139, 10410. (74) Zhang, W.; Ma, Y.; Santos-López, I. A.; Lownsbury, J. M.; Yu, H.; Liu, W.-G.; Truhlar, D. G.; Campbell, C. T.; Vilches, O. E. J. Am. Chem. Soc. 2018, 140, 328. (75) Wu, X.-P.; Gagliardi, L.; Truhlar, D. G. Phys. Chem. Chem. Phys. 2018, 20, 1778. (76) Ye, J.; Gagliardi, L.; Cramer, C. J.; Truhlar, D. G. J. Catal. 2018, 360, 160. (77) Bernales, V.; Ortuño, M. A.; Truhlar, D. G.; Cramer, C. J.; Gagliardi, L. ACS Cent. Sci. 2018, 4, 5. (78) Ortuño, M. A.; Bernales, V.; Gagliardi, L.; Cramer, C. J. J. Phys. Chem. C 2016, 120, 24697.

(79) Yang, D.; Bernales, V.; Islamoglu, T.; Farha, O. K.; Hupp, J. T.; Cramer, C. J.; Gagliardi, L.; Gates, B. C. J. Am. Chem. Soc. 2016, 138, 15189. (80) Deshmukh, M. M.; Sakaki, S. Theor. Chem. Acc. 2011, 130, 475. (81) Deshmukh, M. M.; Ohba, M.; Kitagawa, S.; Sakaki, S. J. Am. Chem. Soc. 2013, 135, 4840. (82) Hijikata, Y.; Sakaki, S. Inorg. Chem. 2014, 53, 2417. (83) Zheng, J.-J.; Kusaka, S.; Matsuda, R.; Kitagawa, S.; Sakaki, S. J. Phys. Chem. C 2017, 121, 19129. (84) Sagara, T.; Klassen, J.; Ganz, E. J. Chem. Phys. 2004, 121, 12543. (85) Sagara, T.; Klassen, J.; Ortony, J.; Ganz, E. J. Chem. Phys. 2005, 123, 014701. (86) Lee, T. B.; Kim, D.; Jung, D. H.; Choi, S. B.; Yoon, J. H.; Kim, J.; Choi, K.; Choi, S.-H. Catal. Today 2007, 120, 330. (87) Kuc, A.; Heine, T.; Seifert, G.; Duarte, H. A. Theor. Chem. Acc. 2008, 120, 543. (88) Kuc, A.; Heine, T.; Seifert, G.; Duarte, H. A. Chem. - Eur. J. 2008, 14, 6597. (89) Pianwanit, A.; Kritayakornupong, C.; Vongachariya, A.; Selphusit, N.; Ploymeerusmee, T.; Remsungnen, T.; Nuntasri, D.; Fritzsche, S.; Hannongbua, S. Chem. Phys. 2008, 349, 77. (90) Rubeš, M.; Grajciar, L.; Bludský, O.; Wiersum, A. D.; Llewellyn, P. L.; Nachtigall, P. ChemPhysChem 2012, 13, 488. (91) Supronowicz, B.; Mavrandonakis, A.; Heine, T. J. Phys. Chem. C 2013, 117, 14570. (92) Lee, K.; Howe, J. D.; Lin, L.-C.; Smit, B.; Neaton, J. B. Chem. Mater. 2015, 27, 668. (93) Mavrandonakis, A.; Vogiatzis, K. D.; Boese, A. D.; Fink, K.; Heine, T.; Klopper, W. Inorg. Chem. 2015, 54, 8251. (94) Ji, Y.; Ding, L.; Cheng, Y.; Zhou, H.; Yang, S.; Li, F.; Li, Y. J. Phys. Chem. C 2017, 121, 24104. (95) Hyeon, S.; Kim, Y.-C.; Kim, J. Phys. Chem. Chem. Phys. 2017, 19, 21132. (96) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15. (97) Kresse, G.; Furthmüller, J. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169. (98) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865. (99) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. J. Chem. Phys. 2010, 132, 154104. (100) Blöchl, P. E. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953. (101) Kresse, G.; Joubert, D. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758. (102) Chung, L. W.; Sameera, W. M. C.; Ramozzi, R.; Page, A. J.; Hatanaka, M.; Petrova, G. P.; Harris, T. V.; Li, X.; Ke, Z.; Liu, F.; Li, H. B.; Ding, L.; Morokuma, K. Chem. Rev. 2015, 115, 5678. (103) Deshmukh, M. M.; Sakaki, S. J. Comput. Chem. 2012, 33, 617. (104) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J. Comput. Chem. 1993, 14, 1347. (105) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, O.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J. Gaussian 09, revision D.01; Gaussian, Inc.: Wallingford, CT, 2013. 13968


Article

Journal of the American Chemical Society (106) Dunlap, B. I.; Connolly, J.; Sabin, J. J. Chem. Phys. 1979, 71, 3396. (107) Dunning, T. H., Jr J. Chem. Phys. 1989, 90, 1007. (108) Kendall, R. A.; Dunning, T. H., Jr; Harrison, R. J. J. Chem. Phys. 1992, 96, 6796. (109) Weigend, F.; Köhn, A.; Hättig, C. J. Chem. Phys. 2002, 116, 3175. (110) Hättig, C. Phys. Chem. Chem. Phys. 2005, 7, 59. (111) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553. (112) CCSD(T) calculation has a huge computational cost. The SCS-MP2:PBE-D3 successfully reproduces important features of binding energy calculated by the SCS-MP2:PBE-D3 with CCSD(T) correction such as the decreasing order of site I > III > II and the increasing order of BE with the number of adsorbed CO2; the SCSMP2:PBE-D3 method is also useful for discussion. (113) Here, CCSD(T) correction was made because accurate ΔG°ads is needed to reproduce the adsorption isotherm. (114) Reed, D. A.; Keitz, B. K.; Oktawiec, J.; Mason, J. A.; Runčevski, T.; Xiao, D. J.; Darago, L. E.; Crocellà, V.; Bordiga, S.; Long, J. R. Nature 2017, 550, 96.

13969


Theoretical Insight into Gate-Opening Adsorption Mechanism and

Recommend Documents