DFT studies for the evaluation of amine functionalized polystyrene adsorbents for selective adsorption of carbon dioxide

Abstract

The interaction of carbon dioxide with four amine functionalized polystyrene based adsorbents was investigated by means of density functional theory (DFT). The structures of the adsorbents and CO₂–adsorbent complexes were optimized using the B3LYP/6-311++G(d,p) method. The interaction energies, equilibrium distances, charge transfer from the functionalized adsorbent to CO₂, highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) energy gap and thermochemical parameters of the complexes were evaluated. Weak intermolecular forces were responsible for the interaction between the active centers of functionalized adsorbents and CO₂ as confirmed from experimental studies. The interaction energies and vibrational frequencies confirmed stronger interaction of CO₂ towards imidazole functionalized polystyrene (PS-imidazole) followed by N-methylpiperazine loaded polystyrene (PS-piperazine) and were found to be the least for the bare adsorbent chloromethylated polystyrene (CMPS). Steric hindrance was found to play a major role in the case of dimethylamine (PS-DMA) and diethanolamine (PS-DEA) functionalized polystyrene during their interaction with CO₂. On the basis of the HOMO–LUMO energy gap and calculated density of states, a negligible change in the electronic properties of CO₂–adsorbent complexes was observed, indicating a physisorption process. The outcomes of the present theoretical studies are in good agreement with the experimental results and provide detailed insights for understanding the interaction of CO₂ with the active center of the functionalized adsorbent.

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1 Introduction

The concentration of carbon dioxide (CO₂) in the atmosphere has increased by about 30% in the last 50 years and is expected to increase over the next few decades as a result of anthropogenic fossil-fuel combustion.¹ Carbon dioxide is considered to be the major contributor to the greenhouse effect and is perceived to be responsible for global warming. Thus, the presence of excess CO₂ in earth's atmosphere has resulted in the gradual increase in temperature. Extensive efforts have been focused to develop efficient technologies for CO₂ capture, storage (sequestration) and utilization.^2,3

CO₂ capture by liquid amines (primary and secondary) are amongst the most commonly used processes.^1,4–6 However, the main drawbacks of the solvent based CO₂ absorption are high energy consumption for solvent regeneration accompanied by degradation of the amine leading to generation of waste, thus resulting in the capital loss.^1,4,7 Hence, adsorption is considered to be an alternative promising technology for separating CO₂ from gaseous mixtures due to its low energy requirement, easy operation and low maintenance.⁸ It involves binding of a molecule onto the solid surface by strong chemical or weak physical interactions or at times even both and adsorbent regeneration is carried out by either pressure or temperature swing cycles.^8–15 However, the development of low cost adsorbent with high CO₂ selectivity and adequate adsorption capacity under ambient conditions is an active area of research.¹⁶ The solid sorbents such as activated carbon,¹⁷ zeolites,¹⁸ zeolitic imidazole frameworks (ZIFs),¹⁹ single/multi-walled carbon nanotubes,¹ nanoporous silica-based molecular basket,²⁰ polymers^21–25 and metal–organic frameworks (MOFs)^1,7,10 have been used for adsorption of CO₂. The recent studies have focused on use of amine functionalized adsorbents for selective separation of CO₂ from flue gas mixtures.^{7,17,20,22–24,26–28} The incorporation of amine functionality on the surface of the adsorbent significantly increases CO₂ selectivity and uptake capacity because CO₂ is an acidic gas.²

As the quest for the development of CO₂-specific adsorbent is continuously increasing, the use of computational studies has become an indispensable tool for understanding the parameters which govern CO₂–adsorbent interactions at the molecular level. Panda et al. performed computational studies with a series of ZIFs using different 4,5-functionalized imidazole units, viz., –CH₃, –OH, –Cl, –CN, –CHO and –NH₂ by applying Universal Force Field (UFF).¹⁹ The symmetry and polarizability of the functional group exhibited significant influence on CO₂ uptake. MOF,^1,7,10 CNT¹ and zeolites¹⁸ have also been investigated to predict the selective CO₂ adsorption using ab initio calculations. Thakur et al. theoretically studied the adsorption of CO₂ on graphene surface and reported π interaction of CO₂ with the electron rich benzene ring.²⁹ Hussain et al. performed ab initio calculations to study the affinity of CO₂ towards 20 naturally occurring amino acids and also proposed amino acids as alternatives to chemical dissolution of CO₂.³⁰ Baei et al. theoretically studied the interaction of CO₂ with B₁₂N₁₂ nanoclusters using DFT calculations and reported interaction energy of −2.30 kcal mol⁻¹ on physisorption.¹² Valenzano et al. reported 1 : 1 adsorption complex of CO, N₂, and CO₂ with the Mg²⁺ adsorption site of Mg-MOF-74 by weak (dispersion) interactions.¹¹

Extensive efforts are being directed from a variety of fields including polymer technology to search better CO₂ capturing materials.^{21–25,31–33} The surface properties of the polymer can easily be tailored with different organic or inorganic ligands. After functionalization of the polymer surface, the accessibility of the amine to capture CO₂ is the most important factor to be considered during adsorption. Primary^22–24 and secondary amine^22,23 functionalized polymeric adsorbents have already been used for CO₂ capture which result in the formation of carbamate species. The regeneration of such adsorbents involve energy intensive temperature swing process.^22,24,34 However, tertiary amines (in the absence of moisture) do not support formation of carbamate and thus bind CO₂ by physical interactions only.²⁸ Recently, Khot et al. carried out CO₂ sorption studies with tertiary amine functionalized polystyrene as well as with bare polystyrene.⁸ The amine functionality is covalently attached to the macroporous surface of polymeric adsorbent after the bead formation. Hence, the surfaces of the pores are expected to be available for adsorption and a molecule like CO₂ diffuses through the pores of the adsorbent beads. Further, these amines are neither mobile nor there will be any loss of functionality from the surface during the adsorption and desorption process.

The current work includes theoretical studies of these tertiary amine functionalized adsorbents for interaction with CO₂. Since quantum mechanical calculations involving the entire polymeric structure would be difficult and computationally expensive, only the amino functional group covalently attached to the repeating structure of the polymer viz. styrene moiety, was taken for the current study. The calculations were carried out with the objective to gain fundamental insights into equilibrium geometry of the adsorbents and the complexes, interaction energy, charge transfer, band gap, vibrational frequencies and understand the dominant factors responsible for CO₂ complexation. This study is expected to be useful for future designing of CO₂ specific adsorbents.

2 Computational methodology

The DFT studies were performed using Gaussian 09 package³⁵ for investigating the structural and electronic properties during interaction of CO₂ with functionalized adsorbent as well as with the bare polymer, chloromethylated polystyrene (CMPS). The functional considered is Becke's three parameter-Lee–Yang–Parr correlation B3LYP^4,5,7 with 6-311++G(d,p)^5,36,37 basis set. The geometry optimization of the adsorbents, free CO₂ and the CO₂–adsorbent complexes was carried out without imposing any initial symmetry restriction. In order to find the most stable equilibrium structure for CO₂–adsorbent complex, several initial guess structures were considered based on the position of CO₂ close to the electron rich sites of the adsorbent and only the minimum energy structures are further studied. The stationary points were characterized as no imaginary frequencies were obtained during Hessian calculations.

Corrections to the interaction energy for all the complexes were evaluated by considering the basis set superposition error (BSSE) with counterpoise correction (CPC) calculation.^4,11 Natural population analysis using the Natural Bond Order (NBO) method was performed.⁴ The charge transfer (Q_T) from the donor atoms of the amine loaded adsorbents to CO₂ during the interaction was evaluated by summing up the electrostatic potential (ESP) charges on CO₂ molecule.³⁰ To compare the calculated vibrational frequencies with the experimental values, the calculated frequencies were scaled using a factor of 0.964 ± 0.023.³⁷ The contribution of a group to a molecular orbital was calculated by Mulliken population analysis (MPA). The density of states (DOS) spectra were created by convoluting the molecular orbital information, allowing identification of amine and CO₂ centered orbitals with Gaussian curves of full width at half maximum (FWHM) = 0.3 eV. The DOS diagrams for all the adsorbents and the complexes presented in this work were obtained using the Multiwfn program.³⁸

3 Results & discussion

3.1 Molecular electrostatic potential analysis of the adsorbents

The calculated molecular electrostatic potential surface (MESP) of the optimized structures of the four amine functionalized adsorbents along with CMPS at DFT-B3LYP level are shown in Fig. 1. MESP measures the electrostatic potential onto the isoelectron density surface and simultaneously displays electron and nuclei distribution which provides a good understanding of the relative polarity within the molecule.³⁹ In Fig. 1, the red color refers to the high electron density region (negative ESP) while the blue colored region refers to the positive ESP within the adsorbent. Out of the four amines, imidazole is a heterocyclic aromatic amine consisting of two ‘N’ atoms. Out of two ‘N’ atoms, one has sp² and other has sp³ character, while the remaining three aliphatic amines (N-methylpiperazine, dimethylamine (DMA) and diethanolamine (DEA)) contain only sp³ nitrogen. For imidazole functionalized polystyrene (PS-imidazole), maximum electron density is localised over the sp² nitrogen atom (Fig. 1(A)). In N-methylpiperazine (PS-piperazine) and dimethylamine (PS-DMA) functionalized polystyrene, the nitrogen center is electron rich (Fig. 1(B)) and (Fig. 1(C)), respectively. In diethanolamine functionalized polystyrene (PS-DEA), the electron density is found to spread more over the ‘O’ atom of hydroxyl groups rather than ‘N’ of amine (Fig. 1(D)). In the case of CMPS (Fig. 1(E)), the electrons are more localised over the chlorine atom as compared to π-electron rich benzene ring as confirmed from ESP studies. Amongst all the functionalized adsorbents, the electron density lies over either ‘N’ or ‘O’ atoms of the amine and thus, poses suitable sites for preferential adsorption CO₂ over other adsorption site viz. the phenyl ring.

Fig. 1 B3LYP/6-311++G(d,p) calculated mapped electrostatic potential (MESP) surface of PS-imidazole (A), PS-piperazine (B), PS-DMA (C), PS-DEA (D) and CMPS (E). The C, N, O, Cl and H atoms are depicted by , , , , respectively. Red, green, and blue represent negative, zero, and positive values (au), respectively.

3.2 Study of CO₂–adsorbent complexes: structure and stability

The equilibrium geometries of CO₂–adsorbent complexes are given in Fig. 2. The degree of interaction between CO₂ and the adsorbents was investigated by calculating the interaction energy ΔE_noCPC as given by eqn (1).

ΔE_noCPC = TE_complex − (TE_adsorbent + TE_CO2) (1)

where TE is the total energy of the molecule. The calculated values of ΔE are negative (Table 1), indicating that adsorption of CO₂ is exothermic on all the adsorbents. To understand fully the matrix effect phenomena, the interaction of CO₂ with bare CMPS adsorbent was also performed as the phenyl ring of the polystyrene backbone is present as the competitive adsorption site in all the functionalized adsorbents. For the amine functionalized adsorbents, PS-imidazole shows relatively stronger interaction with CO₂ followed by PS-piperazine, PS-DMA, PS-DEA, while CMPS shows the weakest interaction. The calculation of interaction energy between two chemical species is significantly affected by Basis Set Superposition Error (BSSE).⁴ Note that the B3LYP contribution to the interaction energy not corrected for the counterpoise method (ΔE_noCPC), and the BSSE correction, add up to give the final corrected interaction energy (ΔE_CPC) as given by eqn (2).

ΔE_CPC,corr = ΔE_noCPC + BSSE (2)

Fig. 2 Optimized structures of PS-imidazole + CO₂ (A), PS-piperazine + CO₂ (B), PS-DMA + CO₂ (C), PS-DEA + CO₂ (D), and CMPS + CO₂ (E) complexes. The calculated values of d₁, d₂, d₃ and θ are given in Table 2.

Table 1 Calculated values of uncorrected adsorbent–CO₂ interaction energy (ΔE_noCPC), ΔE_BSSE, BSSE-corrected energy (ΔE_CPC,corr), zero point vibrational energy Δ(ZPE), finite-temperature translational/rotational/vibrational contributions ΔE_T/R/V, entropic contribution (TΔS), and free-energy of adsorption at 303 K and 1 bar (ΔG), calculated at B3LYP/6-311++G(d,p) (all energy terms are given in kJ mol⁻¹)

Adsorbents	ΔEnoCPC	ΔEBSSE	ΔECPC,corr	Δ(ZPE)	ΔET/R/V	TΔS	ΔG	ΔG^a
a Interaction between Lewis base, pentafluoro phenolate anion and CO2, ΔE = −23.1 kJ mol^−1 and the distance between the oxygen of the anion and ‘C’ of CO2, 2.43 Å (Teague et al.).^4
PS-imidazole	−12.80	0.95	−11.85	1.67	5.74	−24.18	17.25	12.7
PS-piperazine	−8.24	1.58	−6.66	2.41	5.94	−28.56	30.25
PS-DMA	−6.57	1.49	−5.08	2.78	6.02	−30.38	34.10
PS-DEA	−4.22	1.55	−2.67	3.13	6.18	−30.56	37.19
CMPS	−3.56	1.51	−2.05	3.24	6.29	−30.77	38.26

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The smaller values of ΔE_CPC,corr implies that CO₂ experiences weak van der Waals interaction with the adsorbent, thus it is identified as physical in nature.^2,40 The thermal and entropic contributions were considered to calculate the free energy of the system which is given by eqn (3),⁴

ΔG = ΔE_CPC,corr + Δ(ZPE) + ΔE_T/R/V – RT − TΔS (3)

where, Δ(ZPE) is the change in zero point vibrational energy, ΔE_T/R/V is the finite-temperature translational, rotational, and vibrational contributions to the total energy, TΔS is the entropic contribution to the change in free energy (ΔG) at T = 303 K and P = 1 bar.

The enthalpic contributions to ΔE were indicative of the specific interactions, but the entropic factors seem to negate the advantage of specific interactions. The ΔG values for the functionalized and the bare adsorbent is positive indicating that the interaction between the adsorbent and CO₂ is weak as the complexes are destabilized by entropic effects and hence the gas phase reaction is unfavorable at 303 K and 1 bar. A positive change in free energy, however, should not be taken as a sufficient reason for not pursuing a potentially useful reaction involving CO₂, the kinetics might indeed be favorable. Hence to achieve significant adsorption, increasing the pressure and/or lowering the temperature may enhance the binding of CO₂ with amine functionality. The optimized parameters (ΔE and distances between the interacting centers) from the current study are comparable to the positive free energy results reported by Teague et al.⁴ (Table 1).

The experimental investigations of CO₂ adsorption on these four functionalized adsorbents executed by Khot et al.⁴¹ confirmed the physical nature of adsorption. Also, the IR frequencies of the adsorbents after CO₂ adsorption showed no changes in the C–N stretching frequency towards 1609 cm⁻¹ and the asymmetric stretching (ν₃) of CO₂ (2349 cm⁻¹), indicating no carbamate and bicarbonate formation.⁸ An improved adsorption of CO₂ on the amine functionalized adsorbents was observed by Khot et al.⁸ during the experimental studies performed by increasing the pressure (∼40 bar). Thus, the above methodology correctly predicts the presence of physisorbed CO₂ on amine functionalized polystyrene.

The observed trend in interaction energies can be well correlated to the distance between C_CO2–donor atom of the functionalized adsorbent (d₁). PS-imidazole which exhibits the strongest interaction with CO₂ has the lowest C_CO2–N_amine distance (2.8533 Å), followed by PS-piperazine (2.9933 Å) and PS-DMA (3.1346 Å). This is because the planar structure of imidazole experiences less steric hindrance allowing the sp² nitrogen atom to move closer to the ‘C’ of CO₂ as compared to PS-piperazine and PS-DMA. In the case of PS-DEA, due to the inaccessibility of the ‘N’, electron deficient ‘C’ of CO₂ interacts with the electronegative –OH groups of DEA. The ‘O’ atoms of CO₂ strongly interact with the electropositive ‘H’ atoms of the alcoholic group thus leading to the formation of a hydrogen bonded structure.⁴² However with CMPS, CO₂ exhibits π-quadrupolar interaction with the π-electron rich phenyl ring. In CMPS–CO₂ complex, CO₂ is parallel to the ring but slightly displaced from the centre of mass of phenyl ring.^25,43

The interaction between CO₂ and the donor atom of the amine functionality leads to varying degrees of distortion in carbon dioxide molecule as well as the interacting centers of the adsorbents. The calculated bond length of free CO₂ is 1.1608 Å, which is comparable to the experimental bond length (1.161 Å).⁴⁴ On analyzing the structure of adsorbed CO₂, we see lengthening of the C=O bond which is closer to the active center (d₂ − d₀) in all systems when compared to the free CO₂ bond length (1.1608 Å) while, the C=O bond farther away from the active center (d₃) is shortened in all the adsorbents (d₃ − d₀). Summing up the two C=O bond lengths (d₂ and d₃), yields the overall length (l) of the CO₂ molecule, which can be used in determining elongation of the molecule (l − l₀) after interaction, for all the adsorbents. PS-imidazole and PS-piperazine display a higher increase in bond length of physisorbed CO₂ as compared to that with PS-DMA and PS-DEA (Table 2) owing to the strong interaction with CO₂. Also, the bond lengths of amine functional group changes during the complexation. The C_amine–donor atom bond lengths before and after complexation are listed in Table 3.

Table 2 Bond distances^a between the adsorbent–CO₂ complexes, the distortions in CO₂ bond lengths and bond angle after complexation and charge transfer to CO₂ (Q_T)

Adsorbents	d1	d2	d3	(d2 − d0) × 10^3	(d3 − d0) × 10^3	(l − l0) × 10^3	θ (deg)	QT
a All distances are given in Å. d0 = 1.1608 Å (C=O bond length of unadsorbed CO2). d2 and d3 are C=O bond length of physisorbed CO2. l0 = 2 × d0 = 2.3216 Å (bond length of CO2 before interaction). l = d2 + d3 (bond lengths of CO2 after interaction).
CMPS		1.1615	1.1602	0.72	−0.60	0.12	179.54
PS-imidazole	2.8533	1.162	1.1607	1.47	−0.01	1.46	176.05	−0.009
PS-piperazine	2.9933	1.1616	1.1615	0.80	0.75	1.55	176.74	−0.012
PS-DMA	3.1346	1.1613	1.1609	0.55	0.15	0.70	177.53	−0.005
PS-DEA	2.9013, 2.2023, 2.7061	1.1616	1.1599	0.84	−0.90	−0.06	178.06	−0.011

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Table 3 Comparison of calculated bond lengths of the amine functionalized adsorbents (before and after complexation) (all distances are given in Å)

Adsorbents	Bonds	Before complexation	After complexation
PS-imidazole	C(11)–N(12)	1.3137	1.3157
PS-piperazine	C(20)–N(24)	1.4623	1.4662
	C(21)–N(24)	1.4638	1.4669
	C(25)–N(24)	1.4539	1.4571
PS-DMA	C(9)–N(10)	1.4635	1.4706
	C(11)–N(10)	1.4581	1.4611
	C(12)–N(10)	1.4565	1.4601
PS-DEA	O(15)–H(35)	0.9618	0.9626
	O(16)–H(36)	0.9618	0.9641
	C(12)–O(15)	1.4387	1.4413
	C(14)–O(16)	1.4251	1.4275

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Further, CO₂ molecule undergoes nonlinear distortion, and the calculated deviation of ∠O–C–O from its linear geometry (180°) in the adsorbed state is relatively small, ∼1–5° (Table 2). The extent of bending of CO₂ during complexation is generally considered to be a measure of the basicity of the amine.⁴ Amongst the amine functionalized adsorbents, PS-imidazole and PS-piperazine reveal maximum change in the ∠O–C–O bond angle as compared to PS-DMA and PS-DEA, which justifies superior contact with the former adsorbents. CMPS which shows the least interaction with CO₂ at atmospheric pressure exhibits the lowest bent of ∠O–C–O (179.54°) as compared to the functionalized adsorbents (Table 2). Thus, the extent of distortion of CO₂ from the linear geometry and shorter C_CO2–donor atom distances (d₁) can be correlated to stronger CO₂–adsorbent interactions.

3.3 Charge transfer to CO₂ from the adsorbent

To understand the electronic effects taking place during the interaction of CO₂ with the adsorbents, the charge transfer (Q_T) to CO₂ from amine functionalized adsorbent was investigated and the values are listed in Table 2. For all the CO₂–adsorbent complexes, negative Q_T indicates charge flow from the lone pair of electronegative atoms of the amine functional group to CO₂ which is consistent with Lewis type acid–base interaction.³⁰ Maximum charge transfer occurs in PS-piperazine followed by PS-DEA, PS-imidazole and least for PS-DMA. In PS-piperazine, due to the positive inductive effect (+I) of the –CH₃ group attached to ‘N’ as well as the chair conformation of the ring makes access for interaction of CO₂ with the active center viz., electron rich ‘N’ atom easier and thus maximum electrons are transferred to CO₂. In case of PS-DEA, the ‘N’ atom is sterically hindered due to the presence of two ethylene groups which results in the inaccessibility of ‘N’ towards CO₂. This causes weak intermolecular hydrogen bonding with ‘O’ of CO₂ and thus maximum electronic charge is transferred from ‘O’ of alcoholic group to CO₂ resulting in higher Q_T value.

3.4 Vibrational frequency analysis

The change in bond lengths of the interacting species, asymmetric distortion of CO₂ as well as change in atomic charges after complexation results in a corresponding change of the dipole moment. These changes significantly affect the vibrational frequencies of the interacting centers.^45,46 The vibrational spectral analyses of the interactive centers (‘C’ of CO₂ and ‘donor atom’ of amine functionalized adsorbent) before and after complexation as well as the asymmetric stretching vibration of CO₂ (v₃) are given in Table 4.

Table 4 Comparison of simulated and experimental IR frequencies of CO₂–amine functionalized adsorbents (before and after complexation)

Adsorbents	Bonds	Before (cm^−1)	After (cm^−1)
			C-donor atom	ν3^a	ν3^b	ν3^c	Δν3
							Exp.	Cal.
a Calculated frequency of C=O.b Calculated frequency of C=O multiplied with the scaling factor (0.964).c Experimental frequency.^8d Simulated frequency of CO2.^46
CO2	C=O			2420	2333	2349^d	—	—
PS-imidazole	C(11)–N(12)	1535	1537	2413	2326	2335	14	7
PS-piperazine	C(20)–N(24)	1219	1221	2411	2324	2336	13	9
PS-DMA	C(9)–N(10)	1115	1116	2415	2328	2348	1	5
PS-DEA	O(15)–H(35), C(12)–O(15)	3315, 1039	3345, 1043	2420	2333	2348	1	0

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The simulated frequency values are slightly higher than the experimental values which is due to the fact that the experimental values are anharmonic frequencies while the calculated values are harmonic frequencies.⁴⁷ Hence, the calculated vibrational frequencies of CO₂ (v₃) are compared with experimentally determined FTIR frequency values⁸ of physisorbed CO₂ after multiplying with the scaling factor (Table 4). Increase in the C=O bond length of CO₂ results in decrease in v₃ (red shift).⁴⁶ As mentioned earlier, PS-imidazole and PS-piperazine show a considerable increase in bond length of CO₂ and thus result in the higher v₃ shift as compared to PS-DMA and PS-DEA, respectively. A fairly consistent trend is observed between experimental and DFT calculated v₃ values.⁸ The stretching frequency of C(11)=N(12) bond in PS-imidazole exhibited a 2 cm⁻¹ shift on complexation with CO₂. Similarly, the C(20)–N(24) symmetrical stretching shifted from 1219 to 1221 cm⁻¹ in PS-piperazine, while only 1 cm⁻¹ shift in C(9)–N(10) symmetrical stretching was observed for PS-DMA adsorbent. However, in PS-DEA adsorbent the electron rich oxygen center (O(15)) polarizes more on complexation as indicated by increase in its symmetric stretching frequency (C(12)–O(15) exhibits 4 cm⁻¹ while O(15)–H(35) reveals 30 cm⁻¹ shift).

3.5 HOMO–LUMO and density of states (DOS) studies

The calculated frontier molecular orbital (FMO) energies of CO₂ closely matches the reported value obtained at B3LYP/6-31+G* level.⁴⁸ The band gap (E_b) is calculated by using eqn (4) and the FMO energies are reported in Table 5.

Band gap (E_b) = E_LUMO − E_HOMO (4)

Table 5 The calculated values of HOMO–LUMO energies (eV) of the adsorbents, the band gap before and after complexation of CO₂ (E_{b,uncomplexed} and E_b,complex, respectively) on functionalized adsorbent and stability of complex (%∆Eg)

Molecule	HOMO	LUMO	Eb,uncomplexed	Eb,complex	%ΔEg
a B3LYP/6-31+G* level.^48
CO2	−10.50	−0.537	9.963, (9.909)^a
PS-imidazole	−6.371	−0.849	5.522	5.586	0.56
PS-piperazine	−5.630	−0.452	5.178	5.273	0.32
PS-DMA	−5.999	−0.457	5.542	5.691	0.30
PS-DEA	−5.867	−0.569	5.298	5.082	−0.04

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On analysing the FMO's of the adsorbents, the HOMO of PS-imidazole is the most stable followed by PS-DMA > PS-DEA and least is for PS-piperazine. Further, the HOMO's of all the adsorbents are more stable as compared to the LUMO of CO₂. Since CO₂ is electrophilic in nature, the HOMO of the adsorbent reacts with the LUMO of CO₂ molecule.⁴⁹

The molecules which exhibit a large HOMO–LUMO gap are considered as hard molecules and are relatively more stable than soft molecules which have a small HOMO–LUMO gap.⁵⁰ To understand the interactions taking place during the adsorption of CO₂, the total and partial density of states (TDOS and PDOS, respectively) of the CO₂–adsorbent systems were determined and were compared with the TDOS of adsorbents without CO₂ (Fig. 3). During the interaction of CO₂ with the functionalized adsorbent, the electronegative donor atoms of the adsorbent attract the electron deficient ‘C’ of CO₂ increasing the band gap which leads to stabilization of system, except in the case of PS–DEA–CO₂ complex (Table 5). For the PS–imidazole–CO₂ complex (Fig. 3(a)), the red curve (PDOS of imidaole fragment) is high and nearly approaches the black line (TDOS of complex) in the region of −6.8 to −6.1 eV. Hence it can be concluded that imidazole moiety has significant contribution towards HOMO. In contrast, the LUMO is mostly localized on the styrene moiety as there is no such clear contribution of imidazole or CO₂ fragments found in the PDOS diagram. However, for the remaining amine functionalized adsorbents, the % contribution of amine towards HOMO decreases indicating lesser overlap between the amine and electron deficient ‘C’ of CO₂. The PDOS of CO₂ in the LUMO for PS-piperazine (Fig. 3(b)) occurs at slightly higher energy than PS-DEA (Fig. 3(d)), PS-DMA (Fig. 3(c)) and CMPS (Fig. 3(e)). However, the difference is very small (0.01–0.02 eV). The HOMO's of the adsorbent–CO₂ complexes are shown in the Fig. 4.

Fig. 3 The density of states of uncomplexed adsorbents (left, TDOS) and CO₂–adsorbent complexes (right, TDOS and PDOS) of PS-imidazole (a), PS-piperazine (b), PS-DMA (c), PS-DEA (d), and CMPS (e). The curves corresponding to TDOS and PDOS are given by black line, red line for fragment 1 and blue line for fragment 2, respectively.

Fig. 4 HOMO's of CO₂ with PS-imidazole (A), PS-piperazine (B), PS-DMA (C), PS-DEA (D), and CMPS (E) complexes.

The stability of the complex is measured in terms of %ΔE_g which is defined by eqn (5)

The values of E_b,complex and %ΔE_g are reported in Table 5. As the band gap E_b,complex increases after complexation, the ability of the adsorbent to attract CO₂ increases, which indicates increased stability of the system.⁴⁰ The above discussion is in trend with the values of %ΔE_g which is highest for PS-imidazole and lowest for PS-DEA. Since the HOMO of all the complexes presents no contribution from interacting CO₂ molecule, the interactions are considered as physisorption process.

The current work involves the use of specific amines which are loaded on polystyrene and are highly selective in its interaction with CO₂. The quadrupole moment of CO₂ (4.3 × 10⁻³¹ C m²) induces strong and specific Lewis acid–base type interactions with the functionalized adsorbents.⁸ In these complexes, the ‘C’ of CO₂ behaves as an electron acceptor and the ‘N or O’ of the amine as the donor. The above studies indicate PS-imidazole to be a superior adsorbent for complexing with CO₂ possessing ΔE of −11.85 kJ mol⁻¹ and shortest C_CO2–N_amine distance (2.8533 Å). The objective of the current study was to understand the interaction and binding of CO₂ with amine functional group at the molecular level. The above study highlights the molecular level information about charge transfer, FMO contribution and vibrational frequency analysis occurring during complexation. The results indicate that the CO₂–amine interaction is mainly of physisorption augmented by hydrogen bond type chemical interactions. As a result, the CO₂ is adsorbed reversibly on these adsorbents and its desorption can be facilitated by thermal/pressure swing for regeneration as studied by Khot et al.⁸ This study aims at understanding the interaction and binding types of CO₂ with amine functionalized adsorbents which can provide useful guidance for the designing of newer ligands for CO₂ selective adsorption.

4 Conclusions

We investigated the interaction of CO₂ on amine functionalized adsorbents containing tertiary nitrogen at the DFT level. The electrostatic interactions were responsible for the complexation of CO₂ with the adsorbents. PS-imidazole shows the strongest interaction with CO₂ (ΔE = −11.85 kJ mol⁻¹) followed by PS-piperazine > PS-DMA and least for PS-DEA as evident from the interaction energies and distance between C_CO2–donor atom of the adsorbent (d₁). H-bonding between –OH groups of DEA and ‘O’ of CO₂ occurs as ‘N’ atom of DEA is sterically hindered. During complexation, there is considerable elongation of the C=O bond closer to the interacting center while the C=O farthest from the donor atom of the adsorbent experiences shortening. The calculated vibrational frequency values clearly indicate that CO₂ is slightly distorted from its linear shape in the complex and these calculated frequencies exhibit good correlation with experimental values. Further the analysis of thermodynamical parameters, HOMO–LUMO and DOS studies suggest weak interaction between CO₂ and adsorbents indicating physisorption process. These simulation studies involving parameters of interaction energy, partial charges and vibrational spectral analysis suggest the use of imidazole loaded polystyrene as a suitable adsorbent selective for CO₂ capture. The above molecular level studies help in designing of newer moieties for efficient CO₂ capture systems.

Acknowledgements

We acknowledge the financial support for computational amenities provided by Indo-EU DST-AMCOS (Dept. of Science and Technology-Advanced Material for Computational Studies) project.

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