Abstract
Nonbonding parameters of AMBER force field have been refined based on ab initio binding energies of CO2–[C7H5N2]− complexes. The energy and geometry scaling factors are obtained to be 1.2 and 0.9 for and parameters, respectively. Molecular dynamics simulations of CO2 molecules in rigid framework ZIF-11, have then been performed using original AMBER parameters (SIM I) and refined parameters (SIM II), respectively. The site-site radial distribution functions and the molecular distribution plots simulations indicate that all hydrogen atoms are favored binding site of CO2 molecules. One slight but notable difference is that CO2 molecules are mostly located around and closer to hydrogen atom of imidazolate ring in SIM II than those found in SIM I. The Zn-Zn and Zn-N RDFs in free flexible framework simulation (SIM III) show validity of adapting AMBER bonding parameters. Due to the limitations of computing resources and times in this study, the results of flexible framework simulation using refined nonbonding AMBER parameters (SIM IV) are not much different from those obtained in SIM II.
1. Introduction
The increase in carbon dioxide (CO2) in Earth’s atmosphere is a subject of worldwide attention as being the cause of global warming. Human activities such as combustion of fossil fuels (coal, oil, and natural gas) in power plants, automobiles, and industrial facilities are main sources of CO2 emission. The cost-effective and scalable technologies to capture and store CO2 are now of great interest [1–7]. The low energy requirement technologies based on adsorption processes are highlighted as promising methods, stimulating recent works to investigate suitable adsorbent materials. Metal-organic frameworks (MOFs) are a class of nanoporous materials that are promising candidates for CO2 capture, due to their potential applications in separation processes, catalysis, and gas storage [8–14]. Zeolitic imidazolate frameworks (ZIFs) are subclass of MOFs, in which positive metal ions such as Zn, Co, and Cu are linked by ditopic imidazolate ligands [15, 16]. Some ZIFs are attracted as materials which are used to keep the emissions of CO2 out of the atmosphere in hot energy-producing environments like power plants due to their exceptional chemical and thermal stabilities and nontoxic crystals [17–19]. The ZIF-11 is one of ZIFs which exhibits the RHO topology. It is composed of Zn2+ ion clusters linked by dipotic benzimidazolate ([C7H5N2]−) ligands with chemical formula Zn[C7H5N2]2 [15] (see Figure 1).
The high-throughput methods can be successfully applied to the development a robust synthesis protocol for several ZIFs in short time [20]. Computer models and simulations can be used to rapidly screen and develop promising ZIFs with large savings in experimental time and cost [9]. There are some computer simulations where bonding and non-bonding parameters of general force fields such as AMBER are applied [21]. This is one of well-known force fields that supplies reliable intramolecular force constants within the organic linker; however it is not developed directly for the system of MOFs or ZIFs as in this study.
In this study, the protocol to refine and validate molecular interactions was obtained from general force fields in order to meet both accuracy and time saving for using in specific system like adsorption of CO2 in ZIF-11. Since some investigations show that the imidazolate organic linker is most favored adsorption site of guest molecules [17–19], by assumption the interactions between CO2 and ZIF-11 frameworks are almost contributed by interactions between CO2 molecule and [C7H5N2]− groups. Nonbonding parameters obtained from AMBER force field are refined using ab initio data corresponding to the calculated partial atomic charge. The bonding parameters of AMBER force field are also adapted to represent the flexible framework of ZIF-11. Molecular dynamics simulations of rigid and flexible frameworks are done in order to validate the parameters.
2. Material and Methods
2.1. Models of CO2 and ZIF-11 Framework
In this study, a geometrical structure of [C7H5N2]− is cut directly from ZIF-11 framework [15] and is not theoretical optimized (see Figure 1). The linear rigid model of CO2 molecule is taken from [22] with C–O bond length of 1.16 Å and O–C–O bond angle of 180°. The partial atomic charges of [C7H5N2]− were computed according to the Merz-Singh-Kollman scheme [23, 24] and then further refined these ESP charges to so-called RESP charges using an Antechamber package [21, 25] with a total charge of −1, while the partial charge of the Zn2+ was fixed to be +2. The force fields and simulations atom types and their corresponding atomic partial charges are shown in Table 1.
2.2. Single Point Energies of CO2–[C7H5N2]− Complexes
The binding energy, , of a CO2–[C7H5N2]− complex is defined on the basis of the supermolecular approach according to where , , and are the total energy of complex, the energy of CO2 molecule, and the energy of [C7H5N2]−, respectively. The binding energy without basis set superposition error (BSSE) correction of a complex is defined as where denotes the total energy of the complex AB calculated with the full basis set of the complex. The and denote the total energies of the monomers and , each calculated with its basis sets, respectively. The counterpoise BSSE corrected binding energy [26] is represented by where , , and denote the total energy of complex, the energy of monomer , and the energy of monomer which are computed using the union of the two basis sets of monomer and , respectively.
Several structures of CO2–[C7H5N2]− complexes are generated by varying positions and orientations of CO2 molecule around [C7H5N2]− (see Figure 2). Then their corresponding binding energies without and with BSSE correction were calculated at level of HF/6-31G* using Gaussian 09 package [27]. These energies are used as data for refinement nonbonding parameters of AMBER force field.
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2.3. The Parameters of the Intramolecular and Intermolecular Interactions
In this study, the functions in the AMBER force field which is known to be reliable for biomolecules and organic species are adopted to represent CO2 molecules in ZIF-11 framework system as follows: The intramolecular energy, , includes bond stretching and bending and proper and improper torsional potentials: The parameters used to describe the flexibility of ZIF-8 framework from previous studies [28–30] are adopted for ZIF-11 framework in this study and are summarized in Table 2.
The AMBER force field describes the nonbonding interaction of two atom sites, and with Lennard-Jones parameters and the following formula
The Lorentz-Berthelot mixing rules were applied to obtain the cross-interactions parameters and (see Table 3) between different atom types, and [31–33], with and . Formula (6) can be transformed into where and , respectively.
2.4. Molecular Dynamics Simulations of CO2 Molecules in ZIF-11
All MD simulations are performed using DL_POLY (version 2.20) package [34] in canonical ensemble (NVT) for 9 CO2 molecules in the ZIF-11 frameworks (see Figure 3).
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The simulations box with a cubic length of 57.52 Å, subject to periodic boundary conditions, consists of unit cells of ZIF-11, which contains at least 9 full cages (see Figure 3). This corresponds to a loading of about one CO2 molecule per unit cell. The precision of Ewald summation for long length dispersion force had been set to 0.0001. In order to maintain a constant temperature of 300 K, the Nosé-Hoover thermostat with a relaxation time and time step of 0.001 ps was applied along the whole simulations. The simulations were equilibrated for 1,000,000 time steps (1 ns), and then further simulations of 1 ns were carried out in order to provide data for structural and dynamical properties evaluation. There are four simulations in this study and denote as SIM I, SIM II, SIM III, and SIM IV for the rigid framework simulations using original AMBER force field, the rigid framework simulations using sAMBER force field, the flexible framework simulations for free ZIF-11, and the flexible framework simulations for CO2 in the ZIF-11 using sAMBER force field, respectively.
3. Results and Discussion
3.1. Obtained Refined Parameters
By using the BSSE corrected ab initio binding energies as data to refine the AMBER parameters, the energy and geometry scaling factors are obtained to be 1.2 and 0.9 for and , respectively. The consequence and parameters for original and scaled parameters are summarized in Table 4 while Figure 4 shows the comparison between , , and energies of CO2–[C7H5N2]− complexes. The results show that all and parameters of scaled AMBER are less than those obtained from original AMBER but the total binding energy is more close to the ab initio data. Then only the sAMBER parameters are used in the flexible framework simulation.
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3.2. Molecular Dynamics Simulations of CO2 Molecules in Rigid ZIF-11 Framework
The radial distribution functions (RDFs) are used to measure the distribution of intermolecular distances between CO2 molecules and the framework of ZIF-11. All RDFs for rigid simulations (see Figures 5 and 6) show notable difference between both simulations, that is, in SIM II, the CO2 molecules lie closer to the [C7H5N2]− groups than those obtained from SIM I. The smallest distance is found of about 2.5 Å with a first peak of about 3.0 Å in H1-O RDF (see Figure 5(d)) of SIM II, while these distances are increased by about 0.9 Å in H1-O RDF of SIM I. This makes sense, since the energies and the geometrical parameters of sAMBER are stronger and shorter than those of original AMBER. The favorite adsorption sites of CO2 molecules are found at H3 and H4 positions in SIM I, while all hydrogen atoms (H1, H3, and H4) are equally favored in SIM II. One can say that CO2 molecules are found more located around H1 in SIM II than those found in SIM I. The distribution plots in Figure 7 indicate that in both simulations, all CO2 molecules are located only in one pore along the whole simulation times. In addition, CO2 molecules in SIM II obtained a bit wider distribution than those in SIM I. The self-diffusion coefficients of CO2 molecules are obtained as m2/s and m2/s in SIM I and SIM II, respectively, being less than those obtained in ZIF-8 [18, 35], ZIF-68, and ZIF-69 [19].
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3.3. Molecular Dynamics Simulations of CO2 Molecules in Flexible ZIF-11 Framework
The flexibility of the framework is modeled by AMBER force field with the RESP partial atomic charges. The free framework simulation (SIM III) had been done first. The RDFs of Zn-Zn and Zn-N of ZIF-11 frameworks (see Figure 8) are plotted in comparison to those obtained from XRD data (SIM I). The results show that the flexible model can remain the main structure of the frameworks without collapsing during the whole simulations. This indicates the validity of the flexible model at least for NVT ensembles that used in this study. Moreover the CO2-framework interactions models in SIM IV simulation have no significant effect on the main flexible structure of the framework.
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The RDFs of ZIF-11 framework and CO2 molecules are shown in Figures 9 and 10. The oriented structure of CO2 molecules in ZIF-11 obtained from flexible framework simulation is similar to those obtained from rigid framework simulations (SIM II). Slight difference can be obtained in the distribution plot (see Figure 7) which indicates that H1 is more favorable binding site than H3 and H4. The distributed areas which obtained from the flexible simulation (Figure 7(c)) are smaller than those obtained from the rigid simulations (Figures 7(a) and 7(b)). This corresponding to almost zero value (less than 10−14 m2/s) of obtained self-diffusion coefficient of CO2 in flexible framework. It is difficult to point here that this value is realizable or not. However some previous work [18] convinces that ZIF-11 framework is promising to use for separate CO2 from natural gases.
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4. Conclusion
Several single point interaction energies of CO2–[C7H5N2]− complexes are calculated and this data was used in the processes of modifying the general AMBER force field. The method of calculations at HF/6-31G* gives large BSSE which needs to be corrected in order to have accurate binding energies. The rigid framework simulations, SIM I and SIM II, give similar results; that is, all hydrogen sites are favored binding site but CO2 molecules are found more located around H1 in SIM II than those found in SIM I. Due to the limited time and computer resources, we success only a flexible simulations for testing parameters both intramolecular and intermolecular interactions. However the results which obtained from flexible simulations are not much different from those obtained from rigid framework simulations. The distribution plots are slightly different which indicates that H1 is more favorable binding site than H3 and H4. Until now this study is one of the successful works on flexible ZIF-11.
In further works, one should focus to try some other both rigid and flexible models of CO2 molecules and also other flexible force fileds of ZIF-11. Several simulations such as varying number of CO2 molecules in the framework and mixing CO2 molecules with other natural gases molecules are of great interest.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
The authors would like to thank the Higher Education Research Promotion and National Research University Project of Thailand, Office of Higher Education Commission, through the Advanced Functional Materials Cluster of Khon Kaen University.