Molecular Dynamics Simulations of CO 2 Molecules in ZIF-11 Using Refined AMBER Force Field

Nonbonding parameters ofAMBER force field have been refined based on ab initio binding energies of CO 2 −[C 7 H 5 N 2 ] − complexes. The energy and geometry scaling factors are obtained to be 1.2 and 0.9 for ε and σ parameters, respectively. Molecular dynamics simulations of CO 2 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 themolecular distribution plots simulations indicate that all hydrogen atoms are favored binding site of CO 2 molecules. One slight but notable difference is that CO 2 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.


Introduction
The increase in carbon dioxide (CO 2 ) 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 CO 2 emission.The cost-effective and scalable technologies to capture and store CO 2 are now of great interest [1][2][3][4][5][6][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 CO 2 capture, due to their potential applications in separation processes, catalysis, and gas storage [8][9][10][11][12][13][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 CO 2 out of the atmosphere in hot energyproducing environments like power plants due to their exceptional chemical and thermal stabilities and nontoxic crystals [17][18][19].The ZIF-11 is one of ZIFs which exhibits the RHO topology.It is composed of Zn 2+ ion clusters linked by dipotic benzimidazolate ([C 7 H 5 N 2 ] − ) ligands with chemical formula Zn[C 7 H 5 N 2 ] 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 nonbonding 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 CO 2 in ZIF-11.Since some investigations show that the imidazolate organic linker is most favored adsorption site of guest molecules [17][18][19], by assumption the interactions between CO 2 and ZIF-11 frameworks are almost contributed by interactions between CO 2 molecule and [C 7 H 5 N 2 ] − 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.

Models of CO 2 and ZIF-11
Framework.In this study, a geometrical structure of [C 7 H 5 N 2 ] − is cut directly from ZIF-11 framework [15] and is not theoretical optimized (see Figure 1).The linear rigid model of CO 2 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 [C 7 H 5 N 2 ] − 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 Zn 2+ was fixed to be +2.The force fields and simulations atom types and their corresponding atomic partial charges are shown in Table 1.

Single Point Energies of CO
is defined on the basis of the supermolecular approach according to where (), (), and () are the total energy of complex, the energy of CO 2 molecule, and the energy of [C 7 H 5 N 2 ] − , 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 CO 2 -[C 7 H 5 N 2 ] − complexes are generated by varying positions and orientations of CO 2 molecule around [C 7 H 5 N 2 ] − (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.

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 CO 2 molecules in ZIF-11 framework system as follows: The intramolecular energy,  bonded , 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][29][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, i 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][32][33], with   = (    )1/2 and   = (  +  )/2.Formula ( 6) can be transformed into where  = 4   12  and  = 4   6  , respectively.

Molecular Dynamics Simulations of CO 2
Molecules in ZIF-11.All MD simulations are performed using DL POLY (version 2.20) package [34] in canonical ensemble (NVT) for 9 CO 2 molecules in the ZIF-11 frameworks (see Figure 3).The simulations box with a cubic length of 57.52 Å, subject to periodic boundary conditions, consists of 2 × 2 × 2 unit cells of ZIF-11, which contains at least 9 full cages (see Figure 3).This corresponds to a loading of about one CO 2 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 CO 2 in the ZIF-11 using sAMBER force field, respectively.

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 Δ  , Δ AMBER , and Δ sAMBER energies of CO 2 -[C 7 H 5 N 2 ] − 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.

Molecular Dynamics Simulations of CO 2 Molecules in
Rigid ZIF-11 Framework.The radial distribution functions (RDFs) are used to measure the distribution of intermolecular distances between CO 2 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 CO     (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 m 2 /s) of obtained selfdiffusion coefficient of CO 2 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 CO 2 from natural gases.

Conclusion
Several single point interaction energies of CO 2 -[C 7 H 5 N 2 ] − 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 CO 2 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 CO 2 molecules and also other flexible force fileds of ZIF-11.Several simulations such as varying number of CO 2 molecules in the framework and mixing CO 2 molecules with other natural gases molecules are of great interest.

Figure 2 :Figure 3 :
Figure 2: The possible configurations of CO 2 -[C 7 H 5 N 2 ] − complexes used to determine the ab initio binding energies.

Figure 7 :Figure 8 :
Figure 7: The position distributions of CO 2 molecules in ZIF-11 framework from (a) SIM I, (b) SIM II, and (c) SIM IV simulations, respectively.

Table 1 :
The simulation and AMBER force field atom types and their corresponding partial charges of [C 7 H 5 N 2 ] − and CO 2 molecules.

Table 3 :
The parameters   and   of AMBER force field.

Table 4 :
The parameters   and   (kcal/mol) that are obtained from the AMBER and sAMBER force fields.