Journal of Chemistry

Volume 2013 (2013), Article ID 415027, 10 pages

http://dx.doi.org/10.1155/2013/415027

Research Article

Molecular Dynamics Simulations of CO₂ Molecules in ZIF-11 Using Refined AMBER Force Field

W. Wongsinlatam¹ and T. Remsungnen1,2

¹The Applied Mathematics Research Group (AMRG), Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

²Faculty of Applied Science and Engineering, Nong Khai Campus, Khon Kaen University, Nong Khai 43000, Thailand

Received 1 August 2013; Accepted 8 September 2013

Academic Editor: Hakan Arslan

Copyright © 2013 W. Wongsinlatam and T. Remsungnen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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).

Figure 1: The topologies of ZIF-11, [C₇H₅N₂]⁻, and CO₂.

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.

Table 1: The simulation and AMBER force field atom types and their corresponding partial charges of [C₇H₅N₂]⁻ and CO₂ molecules.

Simulation atoms
AMBER model
RESP charges ()

C1
CR
0.582

N
NA
−0.901

C2
CC
0.400

C3
CA
−0.367

C4
CA
−0.279

H1
HC
0.001

H3
HA
0.200

H4
HA
0.155

Zn²⁺
Zn²⁺
2.000

C
C
0.596

O
O
−0.298

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.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Figure 2: The possible configurations of CO₂–[C₇H₅N₂]⁻ complexes used to determine the ab initio binding energies.

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.

Table 2: The AMBER force field parameters for ZIF-11 flexible framework.

Bond potential: =

Bond type
(kcalmolÅ⁻²)
(Å)

Zn–N
157.0
2.011

C1–H1
734.0
1.080

C1–N
954.0
1.343

C2–C2
1,024.0
1.375

C2–N
844.0
1.385

C2–C3
1,036.0
1.371

C3–C4
938.0
1.400

C3–H3
734.0
1.080

C4–H4
734.0
1.080

C4–C4
938.0
1.400

Bending potential:

Angle type
(kcalmol⁻¹·rad⁻²)
(degree)

C2–C3–C4
126.00
120.00

C3–C4–C4
126.00
120.00

N–C1–N
140.00
120.00

N–C1–H
70.00
120.00

C1–N–C2
140.00
120.00

N–C2–C3
140.00
132.80

C2–C3–H3
70.00
120.00

H3–C3–C4
70.00
120.00

C3–C4–H4
70.00
120.00

H4–C4–C4
70.00
120.00

N–C2–C2
140.00
120.00

N–Zn–N
70.48
109.48

Zn–N–C1
97.36
128.33

Zn–N–C2
64.95
126.40

C2–C3–C4
126.00
120.00

C3–C4–C4
126.00
120.00

Dihedral:

Dihedral type
(kcal·mol⁻¹)

(degree)

C1–N–C2–C2
5.40
2.0
180.0

C3–C2–C2–C3
0.00
2.0
0.0

N–C2–C2–C3
21.50
2.0
180.0

Zn–N–C1–H1
9.30
2.0
180.0

C2–N–C1–H1
9.30
2.0
180.0

Zn–N–C2–C2
5.60
2.0
180.0

N–C2–C2–N
21.50
2.0
180.0

N–C2–C3–H3
21.50
2.0
180.0

N–C2–C3–C4
21.50
2.0
180.0

C2–C2–C3–C4
0.00
2.0
180.0

C2–C2–C3–H3
21.50
2.0
180.0

C2–C3–C4–H4
14.50
2.0
180.0

C2–C3–C4–C4
14.50
2.0
0.0

H3–C3–C4–H4
14.50
2.0
180.0

H3–C3–C4–C4
14.50
2.0
180.0

C3–C4–C4–H4
14.50
2.0
180.0

H4–C4–C4–H4
14.50
2.0
180.0

Improper:

Improper type
(kcal·mol⁻¹·rad⁻²)
(degree)

C4–C4–C3–H4
2.2
180

C3–C4–C2–H3
2.2
180

C2–C2–C3–N
2.2
180

C1–N–N–H1
2.2
180

N–Zn–C1–C2
2.2
180

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.

Table 3: The parameters and of AMBER force field.

AMBER

Types

CR
1.9080
0.0860

NA
1.8240
0.1700

CC
1.9080
0.0860

CA
1.9080
0.0860

HC
1.4870
0.0157

HA
1.4590
0.0150

Zn
1.9600
0.0125

C
1.9080
0.0860

O
1.6612
0.2100

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).

(a)

(b)

Figure 3: The ZIF-11 framework used as the simulations cell; (a) and (b) are both side views that represent the full caves (big grey balls) within the framework.

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.

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

Atom
Force field

AMBER
sAMBER

C

C1
3279886
1062
1941479
855

N2, N3
3530476
1306
2060296
1044

C4, C5
3279886
1062
1941479
855

C6, C7, C8, C9
3279886
1062
1941479
855

H10
344616
225
188575
174

H11, H12, H13, H14
304980
209
165897
161

Zn
1470963
439
498532
280

O

C1
2297573
1111
1420611
914

N2, N3
2427317
1354
1479780
1106

C4, C5
2297573
1111
1420611
914

C6, C7, C8, C9
2297573
1111
1420611
914

H10
217704
223
124434
176

H11, H12, H13, H14
191163
207
108610
163

Zn
1470963
462
498532
269

(a)

(b)

(c)

(d)

Figure 4: The comparison between (–), (- -), and (––) energies of some CO₂–[C₇H₅N₂]⁻ complexes.

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].

(a)

(b)

(c)

(d)

Figure 5: The obtained (a) C1-CO₂, (b) C3-CO₂, (c) C4-CO₂, and (d) H1-CO₂ RDFs of SIM I (—X–C, ––X–O) and SIM II (– –X–C, X–O) when X=C1, C3, C4, and H1, respectively.

(a)

(b)

(c)

(d)

Figure 6: The obtained (a) H3-CO₂, (b) H4-CO₂, (c) N-CO₂, and (d) Zn-CO₂ RDFs of SIM I (—X–C, ––X–O) and SIM II (– –X–C, X–O) when X=H3, H4, N, and Zn, respectively.

(a)

(b)

(c)

Figure 7: The position distributions of CO₂ molecules in ZIF-11 framework from (a) SIM I, (b) SIM II, and (c) SIM IV simulations, respectively.

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.

(a)

(b)

Figure 8: The Zn-Zn and Zn-N RDFs of ZIF-11 frameworks obtained from SIM I (- -), SIM III (--), and SIM IV (-◊-), respectively.

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.

(a)

(b)

(c)

(d)

Figure 9: The obtained (a) C1-CO₂, (b) C3-CO₂, (c) C4-CO₂, and (d) H1-CO₂ RDFs of SIM IV (—X–C, – –X–O) when X=C1, C3, C4, and H1, respectively.

(a)

(b)

(c)

(d)

Figure 10: The obtained (a) H3-CO₂, (b) H4-CO₂, (c) N-CO₂, and (d) Zn-CO₂ RDFs of SIM IV (—X–C, – –X–O) when X=H3, H4, N, and Zn, respectively.

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.

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