Growth Pattern, Stability, and Properties of Complexes of C₂H₅OH and nCO₂ (n = 1–5) Molecules: A Theoretical Study

Abstract

This work is dedicated to theoretically investigate the formation process of C₂H₅OH···nCO₂ (n = 1–5) complexes and to shed light on the nature of interactions formed under the variation of CO₂ concentration. It is found that CO₂ molecules tend to locate around the polarized −OH group to interact with the lone pairs of the O atom. The interaction of ethanol with three CO₂ molecules (C₂H₅OH···3CO₂) induces the most stable structure in the sequence considered. The atoms in molecules (AIM), NCIplot, and natural bond orbital (NBO) analyses point out that the O_ethanol···C_CO2 tetrel bond overcomes hydrogen, chalcogen, and CO₂···CO₂ tetrel-bonded interactions and mainly contributes to the strength of C₂H₅OH···nCO₂ (n = 1–5) complexes. All intermolecular interactions in the examined complexes are weakly noncovalent, and their positive cooperativity is evaluated to be slightly weaker than that of CO₂ pure systems. SAPT2+ and molecular electrostatic potential (MEP) calculations indicate that the electrostatic force is the main factor underlying the attractive interplay in the complexes of C₂H₅OH and CO₂.

1. Introduction

The usage of supercritical carbon dioxide (scCO₂) was early discovered with extensive applications in nanomaterials, chemical engineering, food science, and pharmaceuticals.^1,2 Besides the understanding of thermodynamic, kinetic, and critical properties of scCO₂ reactions, the solubility and intermolecular interactions involving scCO₂ are the research subfields that attract great scientific attention because of practical applications.³⁻⁹ Comprehensive insight into the interactions involving CO₂ at the molecular level has an important influence on improving technological applications based on scCO₂. Numerous studies on complexes of organic molecules and CO₂ were conducted to unveil the nature of intermolecular interactions between these molecules.⁹⁻¹⁷ The >C/S=O···C tetrel bond was addressed as the bonding feature of binary complexes formed by carbonyl/sulfoxide compounds and CO₂.^9,11,17 This feature was also investigated for larger complexes with 2–3 CO₂ molecules.^16,18

Many experimental investigations showed that the addition of a small amount of cosolvents into the scCO₂ solvent resulted in an increase in the solubility of the solutes.¹⁹⁻²¹ In particular, some alkanes were added to scCO₂ to dissolve the nonpolar compounds, whereas functional organic compounds or H₂O were used for the polar ones.²²⁻²⁴ Alcohols including methanol, ethanol, and propanol were extensively used as cosolvents to improve both solubility and selectivity processes.^21,24,25 According to Hosseini et al., the presence of alcohols as a cosolvent affects the shape of complexes formed, in which each alcohol has a different impact on the aggregation of CO₂ around the drugs.²⁴ The solubility of Disperse Red 82 and modified Disperse Yellow 119 increases substantially up to 25-fold by adding 5% of ethanol cosolvent to the scCO₂.²⁵ Vapor–liquid equilibria and critical properties of the CO₂···ethanol binary mixture were experimentally investigated using a variety of experimental techniques and equipment.²⁶⁻²⁹ Becker et al. reported that the addition of CO₂ to pure ethanol leads to a decrease of interfacial tension and the adsorption of CO₂ enhances with the increasing mole fraction of CO₂ in the liquid phase.²⁶

From another perspective, the behavior and origin of weak interactions such as hydrogen, tetrel, chalcogen, and halogen have been widely studied due to their considerable influence on crystal packing, material structures, and biological systems.³⁰⁻³⁶ Besides the experimental and large-scale modeling studies of solute–solvent mixtures, a combined investigation of intermolecular interactions and ethanol solvation in scCO₂ helps to clarify the dissolution process and to understand its solubility for efficient and advanced applications. The great attention on binary complexes of methanol/ethanol and CO₂ was reflected through a number of articles involved.^12,37−42 From the theoretical viewpoint, the primary intermolecular interaction in the C₂H₅OH···CO₂ complex was proposed to be the Lewis acid–base interaction or electron donor–acceptor one.^12,37,38 For the aggregation of CO₂ around ethanol, molecular dynamics simulations of the ethanol···64CO₂ system under supercritical conditions showed the higher probability of CO₂ around the oxygen lone pairs.³⁸ Some stable structures of ethanol with 1–4 and 6 molecules of CO₂ were proposed;⁴⁰ however, the growth mechanism of stable C₂H₅OH···nCO₂ structures under addition of CO₂ molecules and geometric behaviors, energetic characteristics, and bonding features of these complexes have not been reported yet. To shed light on these unclear points, we increased the size of these complexes by adding 1–5 CO₂ guests to the ethanol host molecule and systematically investigated the growth pattern of geometry and all of the important changes of stability and electronic properties of intermolecular interactions.

2. Results and Discussion

2.1. Structural Pattern of the C₂H₅OH···nCO₂ (n = 1–5) Complexes

The stable configurations and geometric parameters of C₂H₅OH···nCO₂ (n = 1–5) complexes at the MP2/6-311++G(2d,2p) level are presented in Figure 1a,b. The dashed lines in Figure 1a,b represent the intermolecular interactions, which are taken from AIM topological analysis. The molecular graphs of some complexes are provided in Figure S1 of the Supporting Information (SI), with the aim of finding out intermolecular interactions formed. The existence of bond critical points (BCPs) is considered to be the indicator for the formation of interactions. From Figure 1a,b, it can be observed that the geometries adopted by interactions between ethanol and nCO₂ molecules are consistent with Saitow et al.’s work,⁴⁰ who reported that the high attractive energy of ethanol in scCO₂ was driven by the large negative charge on the oxygen atom of ethanol (O8). Values of ρ(r), ∇²(ρ(r)), and H(r) at BCPs of intermolecular interactions are summarized in Table S1 of SI. These values lie in the ranges of 0.003–0.013, 0.012–0.052, and 0.001–0.002 au, respectively, indicating that all interactions formed are weakly noncovalent.⁶⁹

Figure 1.

(a) Optimized structures of C₂H₅OH···nCO₂ (n = 1, 2). (b) Optimized structures of C₂H₅OH···nCO₂ (n = 3, 4, 5).

For binary complexes, two types of geometries are observed: (i) tetrel-bonded model (1A-anti/gauche) and (ii) hydrogen-bonded one (1B-anti/gauche). In particular, the anti and gauche structures are formed from the corresponding anti and gauche isomers of ethanol, which are distinguished by the orientation of the OH bond with respect to the CCO plane. The anti conformer of ethanol is predicted to be more stable than the gauche one by 0.5 kcal·mol^–1 at CCSD(T)/aug-cc-pVTZ.⁴³ The O8···C_CO2 distances of 1A-anti and 1A-gauche are very close to those in previous studies.^38,37 The calculated rotational constants of these structures are given in Table 1. Our predicted rotational spectra of 1A-anti fit well with the experimental data (cf. Table 1), as previous studies did.^12,37,38,40

Table 1. Rotational Constant and Vibrational Frequencies of the OH Group of Isolated Ethanol and C₂H₅OH···nCO₂ Complexes.

	A (MHz)	B (MHz)	C (MHz)		νOH (cm–1)	intensity (10–40·esu2·cm2)
1A-anti	6090.39	1721.79	1365.04	C2H5OH	3881	38.1
1A-gauche	5989.29	1706.24	1526.29	1A-anti	3876	42.6
1B-anti	18475.91	0807.35	0781.04	2A-anti	3866	42.9
1B-gauche	8652.14	1024.63	0951.94	3A	3857	124.1
Exptl38	6128.02	1677.25	1340.85	4A	3852	164.5
				5A	3858	127.8

When the number of CO₂ molecules increases, multiple interactions between C₂H₅OH and CO₂ molecules are observed. Indeed, six ternary structures are determined to be the minima on potential energy surfaces (PESs) of C₂H₅OH···2CO₂. Previous studies suggested the 2A-anti complex as the minima for the C₂H₅OH···2CO₂ system,^38,40 while the gauche conformer and other four ternary complexes have not been reported so far. As shown in Figure 1a, 2A-anti and 2A-gauche are the rearrangements of corresponding conformers of C₂H₅OH and two CO₂ molecules via two O8···C tetrel bonds and C–H···O hydrogen bonds. It is worth noting that two CO₂ in 2A are oriented to associate with two electron lone pairs of the oxygen atom O8 in C₂H₅OH. This result confirms the geometrical arrangements reported previously using molecular dynamics simulations.³⁸ The 2B–D structures are mainly formed via O–H···O hydrogen bonds, whereas three components in 2E associate as layers from C₂H₅OH to the first CO₂ and next to the remaining CO₂.

For n = 3–4, the stable shapes of complexes are positioned out-of-plane of CO₂ (out-of-plane here means that the O-C-O axis of CO₂ does not lie on the CCO plane of C₂H₅OH) (cf. Figure 1b). Interestingly, all submolecules interact with one another to form cage structures. The complexes with 3CO₂ are obtained from the corresponding 2A-anti or 2A-gauche geometries with different positions of the third CO₂. For the conformers containing four CO₂ molecules, the fourth CO₂ molecule is likely to connect to neighbor CO₂ molecules rather than the C₂H₅OH as observed in the smaller complexes with ≤3CO₂ molecules. The same way is also found for stable structures with five CO₂ molecules. Complexes of ethanol with nCO₂ (n = 1–5) seem to be similar to other carbonyl-containing molecules, in which CO₂ molecules surround the functional groups (=O, >C=O, and −OH) of the host molecules.^16,44 From the optimized geometries, it is suggested that CO₂ prefers to orient around the −OH functional group to interact with the lone pair or negative region of O8 of ethanol.

2.2. Complex Stability and Changes of OH Stretching Frequency and Intensity under Variation of CO₂ Molecules

The energetic characteristics of the C₂H₅OH···nCO₂ (n = 1–5) complexes at MP2/aug-cc-pVTZ//MP2/6-311++G(2d,2p) are gathered in Table 2. The binding energies with zero-point energy (ZPE) and basis set superposition error (BSSE) corrections are generally negative, in the range between −4.6 kJ·mol^–1 of the 1B complex and −61.9 kJ·mol^–1 of the 5A one. Their stabilities increase in the order 1CO₂ < 2CO₂ < 3CO₂ < 4CO₂ < 5CO₂. It is proposed that the addition of CO₂ molecules leads to the stability enhancement of investigated complexes.

Table 2. Binding Energy (E_b) of C₂H₅OH···nCO₂ (n = 1–5) Complexes (in kJ·mol^–1) Calculated at the MP2/aug-cc-pVTZ//MP2/6-311++G(2d,2p) level of theory.

complexes	Eb	complexes	Eb
1A-anti	–11.4	3A	–38.2
1A-gauche	–10.7	3B	–35.6
1B-anti	–5.1	3C	–34.3
1B-gauche	–4.6	4A	–48.6
2A-anti	–23.9	4B	–47.9
2A-gauche	–23.6	5A	–61.9
2B	–22.1	5B	–59.7
2C	–17.0
2D	–12.5
2E	–16.2

As shown in Table 2, the binding energies of 1A-anti and 1A-gauche complexes are −11.4 and −10.7 kJ·mol^–1, respectively. These values are more negative than those of hydrogen-bonded structures by 5.6–6.8 kJ·mol^–1. Hence, the tetrel-bonded model is the energy-favorable structure of C₂H₅OH···1CO₂ in comparison with the hydrogen-bonded one, which is consistent with the previous static analyses.^37,40−42 Both anti isomers are found to be more negative than the gauche ones by 0.5–0.7 kJ·mol^–1. Thus, the anti-type geometry corresponds to the characteristic structure for ethanol complexes that exhibits large attractive energy. The electron density at BCPs adopted from AIM calculations is considered as a diagnostic of bond strength, in which a larger ρ(r) value means a stronger strength and vice versa, for the same type of interaction.^45,46 The ρ(r) values at BCP of the O8···C tetrel bond in 1A-anti and 1A-gauche are 0.010 and 0.011 au, respectively (ca. Table S1 of SI). Nevertheless, 1A-anti is reinforced by a C=O···C1 secondary tetrel bond with ρ(rc) at a BCP of 0.004 au. Therefore, the slightly higher stability of 1A-anti as compared to 1A-gauche is due to an additional role of the C=O···C1 tetrel bond. For comparison with some previous reports, the interaction of CO₂ with ethanol is weaker than that with carbonyl/sulfoxide compounds, approximating to that with methanol, methylamine, and obviously stronger than alkanes such as methane, ethane and ethylene.^{6,8−10,16,40}

For complexes with 2CO₂ molecules, 2A conformers display the approximate binding energies. The remaining complexes are less stable than 2A by roughly 1.5–7.7 kJ·mol^–1. The increasing stability of ternary complexes is estimated in the order of 2D < 2E < 2C < 2B < 2A-gauche ≈ 2A-anti. Combined with their geometries, the tetrel bonds between CO₂ and ethanol are still preferred in the case of 2CO₂ molecules. For comparison purposes, the geometrical and energetic calculations on complexes of (CO₂)_n (n = 2–3) were employed at the same level of theory in the present work. The minima and their binding energies were previously elucidated.⁴⁷⁻⁴⁹ The calculated binding energies for the minima of these complexes are −4.4 and −12.3 kJ·mol^–1 for (CO₂)₂ and (CO₂)₃, respectively. Both of them are less negative than those of relevant complexes between ethanol and 1, 2 molecules of CO₂ (1A-anti and 2A-anti). Hence, the solvent–solvent interactions between CO₂ molecules are obviously less stable than the solute–solvent ones between CO₂ and ethanol.

To evaluate the stability and role of interaction contributing to the strength of complexes of C₂H₅OH···nCO₂ (with n = 1, 2) as compared to those of the complexes of ethanol dimers, ethanol dimers with CO₂, computations on these complexes were performed at MP2/aug-cc-pVTZ//MP2/6-311++G(2d,2p) (details are given in the SI section). The ethanol dimer,⁵⁰⁻⁵⁴ which were studied using both theoretical and experimental approaches, are 9 kJ·mol^–1 more stable than the binary complexes of ethanol and CO₂. The reason for this is the stronger strength of the O–H···O hydrogen bond in ethanol dimers as compared to that of the C···O tetrel bond in C₂H₅OH···CO₂ complexes. For (ethanol)₂···CO₂ complexes, the stable configurations are presented in Figure S2 of SI. Their binding energies range from −16.6 to −17.9 kJ·mol^–1 at MP2/aug-cc-pVTZ//MP2/6-311++G(2d,2p), indicating that these complexes are more stable than those formed by interaction of ethanol with 2CO₂ molecules. It is noted that the tetrel and/or hydrogen bonds play an important role in stabilizing the complexes considered.

Going to 3CO₂ systems, their binding energies are significantly more negative than those of complexes involving 1,2CO₂ molecules. The 3A complex is the global minimum of the C₂H₅OH···3CO₂ system, while the 3C one is the most weakly bound complex with binding energies of −38.2 and −34.3 kJ·mol^–1, respectively. All stable structures of the 3CO₂ system found in this study are more stable than those reported by Kajiya and Saitow by around 1–6 kJ·mol^–1 in relative energy at 6-311++G(2d,2p).⁴⁰ The complexes of C₂H₅OH with 4, 5CO₂ have binding energies in the range of −47.9 to −61.9 kJ·mol^–1. This implies that the complex stabilization is enhanced when the CO₂ guest molecule is added to the previous ethanol host complex. The electron density at BCP of the C_CO2···O8 contact changes insignificantly when going from n = 1 to 5 (cf. Table S1). To evaluate the cooperativity in the ternary complexes of ethanol with 2CO₂ and compare with that of the (CO₂)₃ trimer, the cooperativity energies of 2A-anti and (CO₂)₃ were computed using the many-body procedure.⁵⁵ These values are estimated to be −7.8 and −8.6 kJ·mol^–1, respectively, indicating the larger positive cooperativity of the (CO₂)₃ trimer as compared to that of 2A-anti. The positive cooperativity contributes an amount of roughly 30% to the binding energy of 2A-anti; however, it increases up to 70% in the case of the (CO₂)₃ trimer. Accordingly, the positive cooperativity effect plays a vital role in the formation of the (CO₂)₃ trimer, and its contribution is much smaller in the binding of ethanol and 2CO₂ molecules. This finding of C₂H₅OH···nCO₂ (n = 1–5) complexes is consistent with the positive cooperativity in other complexes stabilized by tetrel bonds.^56,57 On the basis of the energy-preferred structures, the minimum structures follow an addition pathway in which the structure with nCO₂ is built from the previous one with (n – 1) CO₂. The geometric formation and energetic data also reveal the important role of the oxygen site of ethanol in attracting CO₂ molecules, as previously found in complexes of carbonyl compounds with CO₂.^16,44

To understand in more detail the stability of complexes with the increasing number of CO₂ molecules, the binding energy per CO₂ (ΔE_n) is used as a scoring for the average strength of interactions formed by the C₂H₅OH host and nCO₂ guest molecules. The changes of ΔE_n with different basis sets are presented in Figure 2. The magnitude of ΔE_n values is estimated to decrease from n = 1 and get minima at n = 3, and then, it increases with n = 4 and 5. Let us consider the 3A structure, where two CO₂ molecules are located at the electron n-pair of oxygen and the last CO₂ molecule associates with O–H to form a hydrogen bond. In other words, the contribution of the O atom of ethanol gradually increases from n = 1 and gains the maximum with n = 3. The fourth and fifth CO₂ molecules tend to connect to other CO₂ molecules instead of ethanol to establish an ethanol:4, 5CO₂ system. It proves the potential ability of ethanol to bind with three molecules of CO₂.

Figure 2.

Binding energies per carbon dioxide.

The changes of the OH stretching mode along with the addition of CO₂ are also considered in Table 1. A red shift varying from 5 to 19 cm^–1 is observed in the stretching mode of the OH group in complexes compared to that of isolated C₂H₅OH. The ν_OH stretching mode of ethanol interacting with 1CO₂ molecule was previously reported to be lower than that of isolated ethanol and consistent with the experimental results.³⁷ For n = 2 and 3, the ν_OH stretching modes of C₂H₅OH···nCO₂ are found to be remarkably decreased by 9–10 cm^–1 as compared to the corresponding values with (n – 1)CO₂. The vibrational intensity also shows an increase, up to 126.4 (×10^–40·esu²·cm²). The intensity of OH mode is significantly enhanced from 42.9 at n = 2 to 124.1 (×10^–40·esu²·cm²) at n = 3. This result is another evidence for the relatively strong interactions of ethanol with 3 molecules of CO₂. Thus, from a solvent perspective, the concentration ratio of 1:3 between ethanol and scCO₂ is predicted to be a potential ratio for good solubility.

2.3. Intermolecular Interaction Analysis

NCI two-dimensional (2D) and three-dimensional (3D) plots of C₂H₅OH···nCO₂ (n = 1–5) complexes are shown in Figure 3. The low-density and low reduced gradient in the negative region of the λ₂ eigenvalue of all 2D plots demonstrate the weak and noncovalent attractive interactions between ethanol and CO₂ molecules. To further understand the difference of properties between tetrel and hydrogen bonds, 2D plots of 1A-anti and 1B-anti are considered. In two cases, the attractive interactions between C₂H₅OH and CO₂ are observed, which obviously dominate the repulsive interactions and are consistent with the results of Kajiya and Saitow.⁴⁰ The 2D plot of 1A-anti has a peak in the negative region of sign (λ₂)·ρ(r) with an electron density of about 0.01 au, confirming again the noncovalent attractive nature of the O8···C tetrel bond, which was also assessed from AIM analysis. The larger volume of gradient isosurface of 1A-anti describes a stronger strength of the O8···C tetrel bond as compared to the O–H···O hydrogen one of 1B-anti. Furthermore, as expected, the C1···O_CO2 bond is also detected via the isosurface between O of CO₂ and C of ethanol. From n = 1 to 3, the spikes expand in the negative region of sign(λ₂)·ρ(r), indicating the increase of the attractive interactions contributing to the stabilization of the corresponding complexes (cf. (a-d) of Figure 3). However, for complexes with n = 4–5, it is observed that the attractive spikes remain unchanged as compared to those of complex of 3CO₂ (cf. (e, f) of Figure 3). It confirms the higher stability of complexes with 3CO₂ in the sequence of 1–5 CO₂.

Figure 3.

NCIplots of C₂H₅OH···nCO₂ (n = 1–5) complexes (gradient isosurface of s = 0.65): (a, b) tetrel and hydrogen models of the C₂H₅OH···1CO₂ binary complex; (c–f) NCIplot of the most stable configurations of C₂H₅OH···nCO₂ (n = 2–5) complexes at the MP2/6-311++G(2d,2p) level of theory.

To identify the characteristics of intermolecular interactions and evaluate the strength of interactions, the NBO calculations were conducted at the ωB97X-D/aug-cc-pVTZ level of theory. The charge of C₂H₅OH unit, orbital interactions, and their donor–acceptor stabilization energies (E⁽²⁾) are collected in Table 3. The other intermolecular components found in the NBO analysis with the E⁽²⁾ values lower than 0.5 kJ·mol^–1 are not discussed here.

Table 3. NBO Analysis of C₂H₅OH···nCO₂ (n = 1–5) Complexes at ωB97X-D/aug-cc-pVTZ.

complexes	chargea (me)	orbital interactions	E(2) (kJ·mol–1)
1A-anti	2.44	n(O8) → π*(C10–O12)	6.0
		π(C10–O12) → σ*(C1–H3)	1.1
1A-gauche	3.45	n(O8) → π*(C10–O11)	7.3
1B-anti	–0.38	n(O11) → σ*(O8–H9)	3.7
1B-gauche	–3.03	n(O11) → σ*(O8–H9)	8.1
2A-anti	4.49	n(O8) → π*(C10–O12)	5.7
		n(O8) → π*(C13–O14)	5.4
		n(O11) → π*(C13–O14)	1.6
		n(O15) → π*(C10–O12)	3.0
		n(O14) → σ*(C1–H3)	0.5
2A-gauche	5.61	n(O8) → π*(C10–O12)	5.6
		n(O8) → π*(C13–O14)	7.4
		n(O11) → π*(C13–O14)	2.0
		n(O15) → π*(C10–O12)	2.1
3A	5.11	n(O8) → π*(C10–O11)	8.6
		n(O8) → π*(C13–O15)	5.9
		n(O17) → σ*(O8–H9)	6.7
		n(O12) → π*(C13–O15)	3.1
		n(O12) → π*(C16–O18)	2.6
		n(O14) → π*(C16–O18)	2.8
4A	4.98	n(O8) → π*(C10–O11)	9.7
		n(O8) → π*(C13–O15)	8.0
		n(O17) → σ*(O8–H9)	4.5
		n(O12) → π*(C13–O15)	2.3
		n(O12) → π*(C16–O18)	3.2
		n(O14) → π*(C16–O18)	4.0
		n(O15) → π*(C19–O20)	2.1
		n(O21) → π*(C10–O11)	3.4
5A	2.72	n(O8) → π*(C10–O11)	8.0
		n(O8) → π*(C13–O15)	6.8
		n(O12) → π*(C13–O15)	3.3
		n(O12) → π*(C16–O18)	3.1
		n(O14) → π*(C16–O18)	3.4
		n(O14) → π*(C19–O20)	3.1
		n(O17) → σ*(O8–H9)	2.5
		n(O17) → π*(C19–O20)	3.9
		n(O17) → π*(C22–O24)	2.0

^aCharge of C₂H₅OH unit.

In general, second-order energies of n(O8) → π*(C=O) are significantly higher than those of other delocalization processes, revealing the decisive role of the O8···C_CO2 tetrel bond from an orbital perspective. For complexes of 1CO₂, E⁽²⁾(n(O8) → π*(C=O)) values of 1A-anti and 1A-gauche are estimated to be 6.0 and 7.3 kJ·mol^–1, respectively. An additive contact from a nucleophilic section π(C=O) to an electrophilic one σ*(C–H) of the 1A-anti complex is found with an E⁽²⁾ of 1.0 kJ·mol^–1. Furthermore, the second-order interactions of n(O8) → π*(C=O) are significantly higher than those of n(O11) → σ*(O8–H9) by 2.3–3.3 kJ·mol^–1. This emphasizes the dominant role of the C···O8 tetrel bond relative to that of the O8–H9···O11 hydrogen bond in stabilizing the complexes investigated.

For the most stable complexes, the positive charge values of the C₂H₅OH unit are observed, indicating that a fraction of electronic charge is transferred from the C₂H₅OH host to the CO₂ guest molecule (cf. Table 3), in line with the attractive factor of the O site of ethanol. As a consequence, C₂H₅OH behaves as an electron donor (Lewis base), while CO₂ molecules prefer to be electron acceptor (Lewis acid) upon complexation. A small charge transfer is observed, and the electrostatic force is expected to drive intermolecular interactions.

2.4. Role of Physical Energetic Components

To further explore the contribution of the different energetic components to the total stabilization energy of the complexes, the SAPT2+ calculations are performed to separate the interaction energy into exchange, electrostatic, induction, and dispersion terms as given in Figure 4. A significantly large role of the attractive electrostatic term is observed in comparison with induction and dispersion terms. It is speculated that the electrostatic component acts as a prime contributor of 49–57% to the binding of C₂H₅OH···nCO₂ complexes. The dispersion force also provides a large percentage of 35–38% to the overall stabilization, while the contribution of induction energy is only 10–12%.

Figure 4.

Contributions (%) of different energetic components to stabilization energy at MP2/aug-cc-pVDZ.

The molecular electrostatic potential (MEP) is also an important tool to determine intermolecular interactions. The MEPs of monomers are displayed in Figure 5, where red regions correspond to the maximal negative potentials and blue regions indicate positive ones. Values of charges at the surface of monomers are represented by different colors, with the potentials increasing in the following order: red < orange < yellow < green < blue. All negative potentials are associated with the oxygen atoms, while the positive potentials are mainly located at C of CO₂ and H atoms of C₂H₅OH. It is accounted for the formation of the O···C=O, O–H···O, and C–H···O contacts in C₂H₅OH···nCO₂ (n = 1–5) complexes. It is worth noting that the C atom of CO₂ and the O atom of C₂H₅OH possess the maximum of positive and negative potentials, respectively, compared to other locations in corresponding monomers. These results prove that the bonding feature of C₂H₅OH···nCO₂ (n = 1–5) systems is the O_ethanol···C_CO2 tetrel bond and all intermolecular interactions are mainly held by the electrostatic attraction.

Figure 5.

MEP surface of monomers at MP2/aug-cc-pVTZ.

3. Conclusive Remarks

Based on the high-level computations on C₂H₅OH···nCO₂ (n = 1–5) systems, seventeen stable structures are found, in which CO₂ molecules preferentially solvate around −OH of ethanol as the solvation site. The obtained results are in agreement with previous studies of the equilibrium configurations of small complexes (n = 1–2); however, the stable geometries of larger complexes with n = 3–5 are discovered for the first time and exhibit an increasing trend of stability. A growth pattern in geometry is found that the stable complexes are formed based on the structures of (n – 1) CO₂ ones when adding a CO₂ molecule, with an exception of n = 5.

The binding energies with ZPE and BSSE corrections range from −4.6 to −61.9 kJ·mol^–1 at MP2/aug-cc-pVTZ//MP2/6-311++G(2d,2p) for the complexes investigated. It is noted that the binding of C₂H₅OH with 3 CO₂ molecules has a remarkable stability, which is expected for the good solubility of ethanol in the scCO₂ solvent at ratio 1:3.

The weakly noncovalent nature of intermolecular interactions between C₂H₅OH and CO₂ molecules is elucidated by means of different approaches including AIM, NBO, and NCI. It is found that the positive cooperativity between the noncovalent interactions in C₂H₅OH···2CO₂ is slightly weaker than that of (CO₂)₃ pure systems. With the addition of CO₂ molecules, the C···O tetrel bond overwhelming the C/O–H···O hydrogen bonds is still retained as the bonding characteristic and mainly contributes to the strength of C₂H₅OH···nCO₂ complexes. SAPT2+ and MEP results present the major role of electrostatic energy overcoming the dispersion and induction terms in stabilizing the complexes. These findings are expected to be useful for understanding ethanol solvation in scCO₂.

4. Computational Methods

In this work, the geometric structures of complexes were optimized using second-order Moller–Plesset perturbation theory⁵⁸ (MP2) in combination with the 6-311++G(2d,2p) basis set. The initial geometries with a given n were built by considering all possible arrangements of the (n – 1) ones and addition of one more CO₂ molecule.

The frequency calculations were performed after the geometrical optimizations to check whether the obtained structures are energetic minima on potential energy surfaces (PESs) and to compute the zero-point energy (ZPE). The binding energy (E_b) was calculated using the MP2 method in conjunction with different basis sets including 6-311++G(2d,2p) and aug-cc-pVXZ (X = D, T) based on the supramolecular method.⁵⁹ These values are defined as the difference in total electronic energy between the optimized complexes and the sum of two optimized monomers. The MP2 treatment that takes electron correlation into account in concert with these large basis sets has demonstrated their accuracy for noncovalent bonds in a number of studies.⁶⁰⁻⁶² The basis set superposition error (BSSE) using the counterpoise procedure⁶³ was also applied to evaluate the binding. To investigate the stability of these complexes with respect to the number of CO₂ molecules, the binding energy per CO₂ molecule (ΔE_n, n is the number of CO₂ molecules) was calculated for the most stable structures of different complex sizes using the equation

The atoms in molecules (AIM) approach⁶⁴ was applied to find evidence for formed interactions via the bond critical points (BCPs) and their local properties. Data of these analyses are taken from the AIMall package.⁶⁵ To be more specific, the positive values of Laplacian (∇²ρ(r)) and electron energy density (H(r)) imply that the kinetic electron energy density (G(r)) is greater than the potential electron energy density (V(r)) and hence such interactions are characterized as closed shell or noncovalent in nature. To further identify the noncovalent behaviors, interactions between carbon dioxide and ethanol were assessed with the noncovalent interaction index (NCIplot) at MP2/6-311++G(2d,2p). NCIplot is an effective tool to detect noncovalent interactions in the real space based on electron density and reduced gradient density (s).^66,67 The value of sign(λ₂)ρ(r) is used as an effective indicator to distinguish the interactions: sign(λ₂)ρ(r) > 0 indicating a repulsive interaction (nonbonding), sign(λ₂)ρ(r) < 0 meaning an attractive interaction (bonding), and a value close to zero implying a very weak, van der Waals interaction. The natural bond orbital (NBO) theory along with the NBO 5.G program⁶⁸ was employed to quantitatively evaluate the charge transfer interactions between individual orbitals and the unit charges.⁶⁹ In this study, NBO analyses were performed with the ωB97X-D functional in conjunction with the Dunning aug-cc-pVTZ basis set. This functional is used instead of MP2 because the second-order perturbation energy is only generated by a well-defined one-electron Hamiltonian operator. The molecular electrostatic potential (MEP)⁷⁰ of isolated monomers was plotted at the MP2/aug-cc-pVTZ level. All quantum calculations mentioned above were carried out via the Gaussian09 package.⁷¹

The contribution of physical components including exchange, electrostatic, dispersion, and induction terms to the stability of complexes was determined based on the symmetry-adapted perturbation (SAPT) approach⁷² because the nature of interactions could be revealed through the percentage of each one. SAPT2+ calculations were performed using density-fitted integrals, MP2 natural orbital approximation, and the aug-cc-pVDZ basis set via the PSI4 program.⁷³

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c00948.

• Topological geometries of stable complexes plotted at MP2/6-311++G(2d,2p); selected parameters at BCPs of intermolecular interactions taken from calculations by means of the AIMALL package; detail of calculations and results on ethanol dimers and (ethanol)₂···CO₂ complexes (PDF)

The authors declare no competing financial interest.