Lennard-Jones Intermolecular Potentials for the Description of 6

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A: New Tools and Methods in Experiment and Theory

Lennard-Jones Intermolecular Potentials for the Description of 6-Membered Aromatic Heterocycles Interacting With the Isoelectronic CO and CS Molecules 2

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Ángel Vidal-Vidal, Carlos Silva López, and Olalla Nieto Faza J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b00375 • Publication Date (Web): 27 Mar 2019 Downloaded from http://pubs.acs.org on March 30, 2019

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The Journal of Physical Chemistry

Lennard-Jones Intermolecular Potentials for the Description of 6-Membered Aromatic Heterocycles Interacting With the Isoelectronic CO2 and CS2 ´ Angel Vidal-Vidal,† Carlos Silva López,† and Olalla Nieto Faza∗,‡ †Departamento de Qu´ımica Orgánica. Campus Lagoas-Marcosende, 36310, Vigo, Spain ‡Departamento de Qu´ımica Orgánica, Facultade de Ciencias, Universidade de Vigo. Campus As Lagoas, 32004, Ourense, Spain E-mail: [email protected] Phone: +34 9883 6888

Abstract We have generated Lennard-Jones potentials for the interaction between CX2 (X=O, S) and eleven nitrogen-doped benzene derivatives in different orientations at the M062X/def2-tzvpp level as tools to parametrize accurate force fields and to better understand the interaction of these greenhouse gases with heterocyclic building blocks used in the design of capture and detection systems. We find that the most favorable interactions are found between the carbon in CO2 and the main heterocycle in the ring in a parallel orientation, whereas the preferred interaction mode of CS2 is stablished between sulfur and the π density of the aromatic ring. The fact that the preferences for interaction sites and orientations of CO2 and CS2 are most of the times opposite helps in terms of ensuring the selectivity of these systems in front of this two isoelectronic

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compounds. The existence of very good linear correlations (R2 values very close to one) between the number of nitrogen atoms in the heterocyclic ring and the depth of the interaction potential wells, opens the door to the use of these results in generating coarse-grained potentials, or models with predictive power for use in the design of larger systems.

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Introduction

Over the past 50 years, the average global temperature has increased at the fastest rate recorded in history and this pace is increasing worryingly. This increase in global temperature is in part due to the high concentration of some gases in the atmosphere (CO2 , CS2 , CH4 , N2 O, etc.), which absorb solar radiation that has bounced off Earth’s surface (greenhouse effect). Among these, CO2 is one of the most important greenhouse gases because of the large amount of it that is liberated to the atmosphere by anthropogenic sources, although it does not have the largest greenhouse effect per mole or weight. 1,2 Other relevant pollutants with a very similar structure receive much less attention, such as the isoelectronic molecules CS2 and COS. Carbon disulfide can be converted to CO2 by up to five different mechanisms as was described by Rich et al. 3 One of this mechanisms involves the production of CO2 from CS2 via OCS by two sequential hydrolysis reactions producing two H2 S molecules, 4 the latter also being an atmospheric pollutant. Carbonyl sulfide is actually the predominant sulphur-bearing compound in the atmosphere, 5–7 and contributes to the formation of aerosol particles affecting also the global climate. 8 With the goal of remediation, different strategies for the capture and storage of CO2 , CS2 and OCS have been developed. Among them, covalent organic frameworks (COFs), 9–11 metal organic frameworks (MOFs), 12–16 zeolite 17–20 and zeolitic imidazolate frameworks (ZIFs), 21–23 are some of the most commonly used. These compounds in conjunction with ionic liquids, 24,25 polymers with light organic functional groups, 26–29 coordination polymers 30 or inorganic-organic interface composites, 31 have surpassed traditional ways of capturing 2


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those pollutants, however, new and more sophisticated methods are still needed. The a ` la carte design of new materials for the capture and storage of CO2 , or CS2 is a very active area that would greatly benefit from molecular simulation. 32–39 The contributions of computational chemistry to this field focus on the selective design of capture materials based on a rational manipulation of the intermolecular interactions that the greenhouse gases establish with different structural motifs of the material’s framework. Modelling the interactions of CX2 (X=O,S) with organic building blocks by means of accurate methods capable of efficient scalability is therefore a necessity in the field. This should also allow us to gain a deeper insight into how these systems behave at the molecular level. The use of large host molecules for the capture of pollutants, when combined with the presence of dominant multipolar interactions between the host and the guest, make for efficient capture devices, but also make simulating the capture process a challenging task. The sheer size of the systems currently used preclude their study via robust and accurate quantum methods. However, the use of more efficient approaches, like parametrized forcefields, is also problematic. We have recently shown great deficiencies of various force fields in the description of systems in which CO2 interacts with 5-member ring heterocycles, both in terms of their interaction potentials and in the calculation of binding energies. 40 As a result, if we want to correctly describe the guest-host chemistry for these linear molecules, specific interaction potentials are needed that take into account high order electrostatic moments but also dispersion and electron correlation effects. The study of the interaction of linear molecules (especially CO2 ) with different organic fragments is not new in the literature, both in terms of interaction potentials and the complexes that are formed. For example, Tang et al. carried out a systematic study on cation effects on the interactions between some nitrogen doped heterocycles of different character (carbenoid, neutral and anionic) and CO2 . 41 Boulmène et al. mapped the interaction potentials between different triazole isomers and CO2 analysing the effect of the angle and the intermonomeric separation distance. 42 Likewise, there are some thorough studies on the self

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interaction in the carbon dioxide dimer making the analytical representation of the 4D potential energy surface computed with high-quality ab-initio calculations and also some other works involving MP2 and Symmetry-Adapted Perturbation Theory (SAPT) calculations also at high computational levels. 43–48 Some of the more stable complexes that form CO2 with a simple organic molecules have also been studied. 49–53 In the field of CO2 and CS2 interactions with heterocycles and related molecules the work of Ibon Alkorta and coworkers must be highlighted. Their contributions in this area are focused on the characterization of exotic interactions such as tetrel bonds stablished between these polluting gases and different heterocyclic molecules such as azoles 54–56 or nitrogen heterocyclic carbenes (NHCs). 57–60 This type of secondary interactions can be established due to the existence of a positive electrostatic potential region on the carbon atom of the CO2 molecule called σ-hole and negative electron density of electron donating groups such as the nitrogen atoms of the heterocycles. In CO2 one sigma-hole is found placed in the carbon atom with a maximum value of the molecular electrostatic potential (Vs,max ) of +1.17 eV whereas in CS2 , two different sigma holes are present, one in the same position as in CO2 , that is in the carbon atom with Vs,max =+0.17 eV, and the other one located in each sulphur atom with an electrostatic potential of +0.63 eV, which can lead to the apparition of two types of intermolecular interactions with the lone pair of a nucleophilic nitrogen: a tetrel bond (N-C) or a chalcogen bond (N-S). These sigma-holes can be appreciated in the electrostatic potentials of CO2 and CS2 in Figure 1. Until now, however, there are few systematic studies, if any, that take into account the interaction of CO2 , and especially CS2 , with various organic molecules taking into account the interaction potentials of these molecules in different orientations. For that reason, in the present work we report a systematic study comparing the interaction of the isoelectronic molecules CO2 and CS2 with N-substituted six-membered ring heterocycles using high-level DFT calculations. Throughout the study, multiple orientations of the CX2

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-1.00·10-2 𝑉𝑠𝑚𝑎𝑥=1.17 𝑒𝑉

𝑉𝑠𝑚𝑎𝑥=0.17𝑒𝑉

𝑉𝑠𝑚𝑎𝑥=0.63 𝑒𝑉

CO2

CS2

1.00·10-2

Figure 1: Representation of the molecular electrostatic potential (MEP) of CO2 (left) and CS2 (right) where the maximum values of the MEP (Vs,max ) (in eV) have been highlighted. CO2 has a σ-hole on the carbon atom whereas CS2 has three regions in which a σ-hole is present: the carbon atom and two regions located in the sulphur atoms opposite to the C=S bonds. MEP are shown on a 0.0004 density isosurface with extreme values of ±1.00·10−2 eV; negative values are displayed in red and positive in blue. (X=O,S) molecules with respect to the heterocyclic systems are considered and the intermolecular interaction curves are computed and subsequently parametrized according to a Lennard-Jones potential. Among the spatial arrangements analyzed, all possible hydrogen interactions in two limit orientations (parallel and perpendicular dispositions with respect to the plane defined by the heterocycle) as well as diverse profiles of interaction between the X and C atoms of the CX2 molecule with the main heteroatom of the heterocycle have been taken into account.

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Computational methods

Density Functional Theory in the Kohn-Sham formulation as implemented in Gaussian 09 61 was used to describe the interaction between CX2 (X=O,S) molecules and the eleven 6membered ring heterocycles shown in Figure 2. All calculations were performed in the gas

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phase with dense pruned integration grids (99 radial shells and 590 angular points per shell) using the hybrid-meta GGA functional M06-2X in combination with Ahlrich’s triple-ξ quality basis set, including extra polarization functions, def2-TZVPP. 62,63 This basis set uses 2p1 d polarization for H, and 2d1 f for atoms B-Ne and Al-Ar. When modelling systems in which weak non-covalent interactions are present, several DFT benchmarks pointed out the necessity of considering dispersion terms and also long range correlation effects, 50,51 thus our choice of functional. M06-2X provides good results for the study of hydrogen bonds, H-π, π- π and electrostatic interactions both in neutral and charged dimeric systems. 49,64 In addition, we recently showed its good performance on the study of the structure, topology and spectroscopic characterization of carbon dioxide complexed with 5-membered ring heterocycles. 52 Furthermore, in another recent study we showed the excellent quality/cost ratio of the results obtained with M06-2X for small heterocyclic systems containing N, O and S atoms interacting with CO2 . 40 N

N

N

N

N

N

Benzene

6N0-I

N

N

N

N

Pyridine

Pyridazine

Pyrimidine

Pyrazine

1,2,3-triazine

6N1-I

6N2-I

6N2-II

6N2-III

6N3-I

N

N

N

N

N 1,2,4-triazine

6N3-II

N

N

N

N N

N N

N

N

N

N

N

N

1,3,5-triazine 1,2,3,4-tetrazine 1,2,4,5-tetrazine 1,2,3,5-tetrazine

6N3-III

6N4-I

6N4-II

6N4-III

Figure 2: Representation of the chemical structure of the 11 systems that will be studied in this work. Together with the IUPAC nomenclature, the notation that will be used throughout the discussion is included.

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2.1

Parameterization of the computed potentials

The potential energy surface has been sampled by calculating different intermolecular interaction profiles between CX2 and the heterocycles under study. We have selected a series or limit spatial dispositions, which are expected to maximize a given type of interaction. It must be remembered that the interactions involving the sigma-holes are markedly directional. The selected interaction modes are: CX2 interacting with the π electron density of the heterocycle, the interaction of the carbon atom of CX2 with the lone pair of one of the heteroatoms on the heterocycle, the interaction of one of the X atoms of CX2 with one nitrogen atom on the heterocycle and also the hydrogen bond interaction between the CX2 and each one of the hydrogens on the rings (Figure 3). For each of these interaction types, we have sought both a maximum and minimum interaction configuration, thus ensuring a fully characterized energy profile for each interacting mode. Any intermediate spatial arrangement should be within this range of energies. The profiles explored span internuclear distances from 2 to 10 ˚ A in 0.5 ˚ A increments. In order to better characterize the region in which attractive and repulsive interactions are balanced, a more dense array of points is sampled around the minimum of the curve (in 0.25 ˚ A increments) to obtain a total of twenty two points per profile. The intermolecular interaction potential plots are built considering a relative energy versus distance approach, where the largest separation distance (in this case 10 ˚ A) is attributed zero energy. Taking the energy of this 10 ˚ A point as the asymptotic value of the curve produces negligible errors (of the order of 0.1 kJ/mol). To parameterize the intermolecular interaction potentials between CX2 X C X N CX2 - π density

X C X

N

C(CX2) - lone pair

X C X

X(CX2) - lone pair

C H

X C X

hydrogen bond

Figure 3: Representative examples of the interaction types included in this work. and the N-doped 6-membered ring heterocycles considered in this work, a classical Lennard7



Jones potential with fixed 6/12 exponents is employed. The only adjustable parameters are therefore the potential well depth, , and the zero intercept, σ. For the parametrization of the potentials obtained, we have followed the same procedure described for the study of the interaction between CO2 and thirty 5-membered ring heterocycles derived from pyrrole, furan and thiophene. 40

2.2

Description of the heterocycles considered

The systems considered in this study are represented in Figure 2: benzene and 10 heterocycles built through doping the benzene structure with nitrogen atoms. The heteroatom colored in pink is considered the main heteroatom in the study of the interactions in which a nitrogen atom is involved directly. In order to avoid propagating long IUPAC names in the discussion, a simpler naming scheme is presented in Figure 2: 6NA-B where 6 means that the system is a six-membered ring heterocycle, that is doped with A N atoms (A is 0 for the parent benzene system), and B is a Roman numeral which arbitrarily helps to differentiate between positional isomers of a given system.

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Results and Discussion

We will analyze the interaction between CX2 molecules and eleven six-membered ring cycles including benzene and ten heteroaromatic systems generated by substituting CH groups in benzene by nitrogen atoms. These heterocyclic rings, apart from being found in commonly studied structures such as MOFs, ZIFs or COFs, are fundamental building blocks in the gas capture systems that we are developing. They have numerous interaction points and at each of these interaction points various orientations can be considered, a complex situation that led us to take into account a series of different representative configurations and obtain the corresponding rigid intermolecular interaction potential energy curves. This work will be divided into three blocks according to the different families of inter-

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actions that can be found in these systems (see Figure 3): the first block deals with the interactions between CX2 and the π electron density; the second with the interaction of CX2 with the main heteroatom on the heterocycle, and the third one with the interactions through hydrogen bonding. With them we cover a wide range of interactions, which can be used to describe almost any situation found in the absorption/adsorption of CX2 in a supramolecular structure containing these heterocyclic fragments.

3.1

Interactions with the heterocyclic backbone: π electron density

Two possible limit-case arrangements can be envisioned for this kind of interaction: one in which CX2 is oriented perpendicularly to the plane defined by the ring, and only one of the X atoms of the CX2 molecule interacts with the π electronic density (Figure 4 A); and another in which the main axis of the CX2 molecule is parallel to the molecular plane of the heterocyclic fragment (Figure 4 B). In this parallel configuration the carbon atom in CX2 is placed directly on top of the geometrical center of the ring. 65 A

B

Perpendicular

Parallel

Figure 4: Spatial disposition of the fragments involving interaction of CX2 X= O,S with the π electron density of the cycles studied (perpendicular, A, and parallel, B, orientations are considered). For CO2 in perpendicular orientation we find σ values in the 3.798-4.131 ˚ A range (see Table 1). The average values for 0N, 1N, 2N 3N and 4N systems are 4.131, 4.042, 3.967, 3.924, 9


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

6N0-I 4.131 -1.161


10 6N0-I 2.908 -9.118 6N0-I 3.303 -5.845

(CO2 ) σP arallel ( ˚ A) P arallel (kJ/mol)

(CS2 ) σP arallel ( ˚ A) P arallel (kJ/mol)

6N1-I 6N2-I 6N2-II 6N2-III 6N3-I 6N3-II 6N3-III 6N4-I 3.234 3.225 3.226 3.182 3.214 3.176 3.217 3.162 -6.503 -6.435 -6.124 -7.005 -6.485 -6.700 -5.803 -6.695

6N1-I 6N2-I 6N2-II 6N2-III 6N3-I 6N3-II 6N3-III 6N4-I 2.944 2.948 2.945 2.996 2.956 2.937 2.935 3.071 -6.640 -5.509 -5.648 -3.606 -4.905 -2.374 -4.708 -1.632

6N4-II 3.168 -6.497

6N4-II 3.106 -1.277

6N4-II 2.953 -4.159

6N1-I 6N2-I 6N2-II 6N2-III 6N3-I 6N3-II 6N3-III 6N4-I 6N-4-II 4.042 3.967 3.970 3.964 3.894 3.982 3.896 3.798 3.798 -1.819 -2.779 -2.782 -2.861 -3.911 -3.876 -3.766 -5.148 -4.998

6N0-I 6N1-I 6N2-I 6N2-II 6N2-III 6N3-I 6N3-II 6N3-III 6N4-I ˚ σP erpendicular ( A ) 2.808 2.839 2.879 2.871 2.868 2.921 2.909 2.902 2.961 P erpendicular (kJ/mol) -11.160 -9.206 -7.347 -7.470 -7.460 -5.625 -5.746 -5.912 -4.030

(CS2 )

(CO2 ) σP erpendicular ( ˚ A) P erpendicular (kJ/mol)

6N-4-III 3.172 -6.196

6N-4-III 3.094 -1.407

6N-4-III 2.952 -4.105

6N4-III 3.802 -5.020

Table 1: Compilation of σ (in ˚ A ) and (in kJ / mol) parameters for the interaction potentials between CX2 (X= O,S) molecules and the heterocycles considered in this study in perpendicular and parallel spatial arrangements. (See Figure 4).

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and 3.799 ˚ A, respectively. Considering these averages, there is a linear reduction of the σ parameter (R2 =0.980) with respect to an increasing number of N atoms on the heterocycle. Something similar happens with the depth of the potential well, but in an opposite way: as we increase the degree of doping with nitrogens, the stability of the CO2 -heterocycle interaction increases. The average values for this interaction range from -1.161 kJ/mol in 6N0 to -5.055 kJ/mol in 6N4 systems passing through -1.819 kJ/mol, -2.807 kJ/mol and -3.551 kJ/mol for systems with 1, 2 and 3 nitrogen atoms, respectively. Again the evolution of the trend is remarkably linear (R2 =0.990). The value varies sharply (77.03 %) from the most to the least favorable interaction system. If CO2 is replaced by CS2 there is a remarkable change in the interactions, which affects both the sign of the trends and the LJ potential parameters σ and . In this case the evolution of the average value of the potential well depth is opposite to that found in CO2 (although in this case the variation is slightly lower: 63.28 %). While for the unsubstituted system (6N0-I) the average is -11.160 kJ/mol, for the tetrasubstituted system it is only -4.098 kJ/mol. These parameters increase in a strongly linear maner with respect to the number of N atoms in the system (R2 =0.999). The σ parameters for the interaction with CS2 range between 2.808 ˚ A, for the 6N0-I system and 2.955 ˚ A, for the 6N4 family, and, contrary to CO2 , they increase linearly (R2 =0.995) as the substitution with nitrogen atoms increases. When analyzing the interaction of CX2 with the π electron density of the heterocycles in parallel arrangement (Figure 4 B) there is a significant overlap between the electron density of the linear molecule with that of the heterocycle, especially at short distances. Since this interaction occurs mainly with atoms at positions 1 and 4 of the heterocyclic system and these atoms and their inmediate neigbors can be different (C or N), the scattering of data within each group of heterocycles is expected to be high. Despite this, some interesting trends could be found for average values. The distance at which the intermolecular interaction potential is zero for the parallel

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interaction in the CO2 molecule (Figure 4 B) ranges from 2.908 ˚ A, to 3.090 ˚ A while for CS2 it varies between 3.303 and 3.167 ˚ A. The slightly higher values for CS2 can be due to the larger van der Waals radius of sulphur. On the other hand, the average value for CO2 ranges from -9.118 kJ/mol for 6N0-I to -1.439 kJ/mol for the 6N4 family, decreasing with an increasing degree of substitution. It is in this orientation that the highest variation between the most and the less favorable system is found for CO2 : a total change of 7.679 kJ/mol (an 84.22% reduction with respect to the most stable system) makes the slope of this linear trend (R2 =0.979) the highest of all systems and orientations explored in this work. Due to these dramatic energy differences, it seems paramount to take this mode of interaction into account when designing capture structures or planing structural modifications in order to get more efficient structures. The evolution of for the CS2 molecule is slightly more complex. The least favorable in the perpendicular orientation is due to the 6N0-I system (-5.845 kJ/mol, 9.44 % lower than the average for the systems that have nitrogen atoms doping the structure). Contrary to the trends found so far, the evolution of this parameter with the degree of substitution is not linear, and displays a minimum 1 for the systems with 1 and 2 nitrogen atoms (6N1 and 6N2). We can conclude that, in average, stronger interactions are established with CS2 in both the parallel and perpendicular arrangements. Among them, the perpendicular orientation is the one that provides the deepest potential well for CS2 whereas CO2 favours the parallel configuration. The highest singular value is also obtained in the perpendicular orientation for carbon disulphide (-11.160 kJ/mol for 6N0). Although the linear molecules considered are isoelectronic, there are large differences in their interactions with the electronic density of the rings considered. 1

The term ”minimum” here refers to the minimum of the Lennard-Jones potential curve where the interaction energy of the rigid CX2 and azine fragments is plotted against the distance between the fragments for a given orientation. As in this work we are not performing geometry optimizations, every time from now on that this term is used will have the same meaning explained here.

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3.2

Interactions with the main heteroatom of the system

Due to the symmetry of the CX2 molecule there are two possibilities for the interaction with the main heteroatom of the aromatic molecule: this could be established through the central carbon atom or through the terminal X atom.

3.2.1

Interactions C(CX2 )-Heteroatom

The two limit orientations in this group are illustrated in Figure 5. In the first spatial arrangement, called IPCH (Figure 5 A), the CX2 molecule is coplanar with respect to the heterocyclic system, allowing the X atoms to interact with positions adjacent to the main heteroatom. Depending on the nature of these adjacent atoms, significant differences in the potential well depth () are expected between different isomers. In the second interaction mode, called PPCH (Figure 5 B), the CX2 molecule lies in a perpendicular plane with respect to the ring structure. This arrangement involves fewer contact points between the fragments which should translate in reduced differences in the Lennard-Jones parameters between the different isomers of the same family of compounds. A

B

IPCH

PPCH

Figure 5: Spatial disposition of the fragments involving interaction of the carbon atom of CX2 X= O,S molecule with the main heteroatom of the cycles considered. Subfigure A corresponds to the IPCH disposition where both fragments (CX2 and the heterocycle) are placed in the same plane, whereas in the PPCH spatial arrangement the CX2 main axis is perpendicular to the plane defined by the heterocyclic ring. (See text for more information). The σ and values obtained for the IPCH and PPCH interaction modes can be found in 13


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6N0-I 6N1-I 6N2-I 6N2-II 6N2-III No min 2.398 2.411 2.435 2.434 No min -12.675 -11.895 -11.290 -11.070


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6N0-I 3.462 -2.932

6N0-I 3.554 -2.047

(CS2 ) σIP CH ( ˚ A) IP CH (kJ/mol)

(CS2 ) σP P CH ( ˚ A) P P CH (kJ/mol)

6N1-I 2.909 -4.395

6N1-I 2.786 -6.527 6N2-I 2.906 -3.980

6N2-I 2.773 -6.225 6N2-II 6N2-III 2.934 2.919 -4.062 -4.110

6N2-II 6N2-III 2.809 2.799 -6.212 -6.181

(CO2 ) 6N0-I 6N1-I 6N2-I 6N2-II 6N2-III ˚ σP P CH ( A ) No min 2.218 2.289 2.244 2.250 P P CH (kJ/mol) No min -21.490 -16.660 -20.120 -19.555

(CO2 ) σIP CH ( ˚ A) IP CH (kJ/mol)

6N3-I 2.928 -3.157

6N3-I 2.824 -4.485

6N3-I 2.335 -14.750

6N3-I 2.459 -10.255

6N4-I 2.495 -8.695

6N4-III 6N-4-II 2.496 2.488 -8.940 -8.945

6N3-II 6N3-III 2.912 2.953 -3.759 -3.911

6N3-II 6N3-III 2.784 2.825 -5.906 -6.044

6N4-I 2.926 -3.571

6N4-I 2.798 -5.827

6N4-III 6N-4-II 2.930 2.931 -3.503 -3.008

6N4-III 6N-4-II 2.801 2.841 -5.617 -4.130

6N3-II 6N3-III 6N4-I 6N4-III 6N-4-II 2.234 2.265 2.365 2.360 2.242 -14.900 -18.800 -12.934 -13.350 -20.120

6N3-II 6N3-III 2.446 2.473 -10.420 -9.980

Table 2: Compilation of σ (in ˚ A ) and (in kJ / mol) parameters for the interaction potential between CX2 and the heterocycles considered in this study in IPCH and PPCH spatial arrangements.


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Table 2. In general, for the IPCH spatial arrangement, CO2 establishes stronger interactions compared to CS2 . For systems featuring nitrogen atoms in their structure, the average value of is almost double for CO2 than for the analogous interactions with carbon disulfide (10.793 kJ/mol, for systems with CO2 vs. -5.851 kJ/mol for systems with CS2 ). Within the values collected in Table 2, the interaction with the parent benzene molecule (6N0 system) stands out. For CO2 no minimum could be found whereas for CS2 this minimum is shallow (less than 3 kJ/mol). The larger size and polarizability of sulfur could be responsible for this weak interaction. If the average values of both σ and are analyzed for the CO2 molecule, a perfect linear fit could be found (R2 =0.999). However, the trends point in opposite directions: while for σ, the average value increases with the increasing degree of substitution with nitrogen atoms, for values decrease with substitution. In the case of CS2 , the average values of , as discussed above, are significantly lower, ranging between -6.527 and -5.191 kJ/mol in the 6N1 and 6N4 groups. The evolution of σ and is also strongly linear (R2 =0.929 for σ and R2 =0.969 for ). Disregarding the anomaly of 6N0, for the heterocycles with nitrogen atoms in their structure the trends are the same as in the case of CO2 : σ increases and decreases with increasing substitution with nitrogen. The effect of the adjacent groups is well illustrated in the 6N2-III (2 CHs), 6N2-I (1 N, 1 CH) and 6N3-I (2 Ns) systems. In this family, interactions with both CO2 and CS2 result in decreasing following the sequence: 6N2-I, 6N2-III and 6N3-I (individual values for the potential depth well being -11.895, -11.070 and -10.255 kJ/mol for CO2 and -6.225, -6.181 and -4.485 kJ/mol for CS2 , respectively). In view of these results the most favorable IPCHtype interaction is formed with a system containing adjacent CH and N fragments, followed by a ring with two adjacent CH groups. The least stable situation is found in the system featuring three consecutive nitrogen atoms. The difference in energy between the parameter of the most and least favorable systems in terms of adjacent groups is ∼1.7 kJ/mol. The interaction of CX2 with 6N0 in the PPCH spatial arrangement, is very similar: there is no minimum with CO2 while with CS2 a shallow potential well with a depth of -2.047

15



Page 16 of 34

kJ/mol is obtained. Due to the off-plane spatial arrangement the sulfur atoms in PPCH do not interact with the ring, hence the reduced parameter. In this spatial arrangement the potential well depths obtained for CO2 are remarkable, ranging from -21.490 kJ/mol for 6N1 to -15.468 kJ/mol for the 6N4 family. The decrease of the parameter is linear (R2 =0.947) as well as the increase of the σ parameter (R2 =0.975) from 2.218 ˚ A in 6N1 to 2.322 ˚ A in the 6N4 set. One of the possible causes for such deep potential wells is the stabilizing tetrel bond interaction that could be formed between the positive partial charge of the carbon atom of CO2 and the negative partial charge on the nitrogen atom with which it interacts. However, in the case of CS2 , the reduced electronegativity of sulfur translates into a less positively charged carbon atom and the interaction becomes less favorable, hence the significant energy differences.

3.2.2

Interactions X(CX2 )-Heteroatom

We have studied this interaction mode through two limit relative dispositions named IPOH and PPOH. The former (Figure 6 A) is based on a collinear arrangement of the CX2 molecule with the heteroatom of the heterocycle. In the latter (Figure 6 B) the CX2 molecule is placed perpendicularlly to the heterocycle both in terms of the Nd XC bond angle and CNd XC dihedral angle. A

B

IPOH

PPOH

Figure 6: Spatial disposition of the fragments involving interaction between the X atom of the CX2 X= O,S molecule and the main heteroatom of the cycles considered. In order to facilitate the visualization of the interactions stablished, a red dotted line has been included. 16


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In the IPOH spatial orientation there is no minimum for the interaction between CO2 and any of the heterocyclic systems considered in this study. For CS2 , however, energy minima can be found in the intermolecular interaction profiles for all systems, with an average value of 7.120 kJ/mol. The potentials that feature no minimum, asymptotically apprach zero at longer distances, but they neverthelss display small relative energy values across the entire range studied. The existence of a minimum in the case of CS2 and not in CO2 may origin in the existence of a σ-hole in sulfur that stabilizes the S · · ·N interaction. Systems with 1 and 2 nitrogen atoms in their structure have higher values (-9.052 kJ/mol and -7.808 kJ/mol, respectively), while systems with 3 and 4 nitrogens display shallower minima (3N =-6.473 kJ/mol and 4N =-5.147 kJ/mol). The values decrease with increasing substitution with nitrogen atoms following a strong linear trend. The σ values vary between 2.685 ˚ A, for 6N1, to 2.849 ˚ A, for the 6N4 system, showing again a remarkable linear behaviour (R2 =0.996) with respect to the degree of substitution with nitrogen atoms. The PPOH interaction mode features potentials with minima for both CO2 and CS2 molecules. The average value of based on the number of atoms that substitute the structure is always greater for CO2 . While these values range between -3.680 kJ/mol (6N1) and -2.442 kJ/mol (6N4 system) for CO2 , in CS2 they vary between -2.030 kJ/mol (6N1) and -1.137 kJ/mol (6N4 family). In both cases a reduction of is observed when increasing the number of nitrogen atoms doping the structure. Furthermore, these trends are again stronly linear, with correlation coefficients R2 =0.988 and R2 = 0.995 for CO2 and CS2 , respectively. The σ parameter also evolves linearly as in the previous cases: between 2.852 ˚ A and 2.944 ˚ A (R2 =0.973) in the case of CO2 and between 3.206 ˚ A and 3.348 ˚ A (R2 =0.995) for the CS2 molecule.

3.3

Interactions by hydrogen bond

In this last section we will focus on hydrogen bonding (HB) interactions that can be established between the CX2 molecules with the different hydrogen atoms present on the hetero17


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18 6N1-I 2.685 -9.052

(CS2 ) σIP OH ( ˚ A) IP OH (kJ/mol)

6N0-I -

6N2-I 2.844 -3.593

6N2-II 6N2-III 2.906 2.906 -3.055 -2.966

6N3-I 2.843 -3.380

6N3-II 6N3-III 2.896 2.965 -2.925 -2.505

6N4-I 2.966 -2.259

6N4-III 6N-4-II 2.968 2.898 -2.293 -2.773

6N2-I 2.744 -7.910

6N2-I 3.241 -1.655 6N2-II 6N2-III 2.753 2.752 -7.839 -7.674

6N2-II 6N2-III 3.255 3.251 -1.783 -1.762

6N3-I 2.803 -6.246

6N3-I 3.314 -1.125

6N3-II 6N3-III 2.799 2.793 -6.434 -6.739

6N3-II 6N3-III 3.284 3.295 -1.414 -1.601

6N4-I 2.848 -5.174

6N4-I 3.327 -1.281

6N4-III 6N-4-II 2.843 2.857 -5.297 -4.969

6N4-III 6N-4-II 3.338 3.378 -1.224 -0.907

6N1-I 6N2-I 6N2-II 6N2-III 6N3-I 6N3-II 6N3-III 6N4-I 6N4-III 6N-4-II No min No min No min No min No min No min No min No min No min No min No min No min No min No min No min No min No min No min No min No min

6N1-I 3.206 -2.030

6N0-I -

6N1-I 2.852 -3.680

(CS2 ) 6N0-I ˚ σP P OH ( A ) P P OH (kJ/mol) -

(CO2 ) σIP OH ( ˚ A) IP OH (kJ/mol)

(CO2 ) 6N0-I σP P OH ( ˚ A) P P OH (kJ/mol) -

Table 3: Compilation of σ (in ˚ A ) and (in kJ/mol) parameters for the interaction potential between CX2 and the heterocycles considered in this study in IPOH and PPOH spatial arrangements.


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cycles. This is a highly directional interaction that is energetically relevant in very specific distance ranges; however it plays a crucial role in some capture systems for these gases. As in the previous sections, we have analysed two limit interactions, which we named IPHB and PPHB. These spatial arrangements are depicted in Figure 7. Both are analogous to the interacting modes studied in the previous section (PPXH and IPXH), but now a C—H group is replacing the role of the heteroatom. The first one is therefore a colinear arrangement (IPHB) whereas in the second mode (PPHB) the CX2 is biorthogonal in terms of bond and dihedral angles. A

IPHB

B

PPHB

Figure 7: Spatial arrangements used in the study of hydrogen bond interactions between one of the X atoms of the CX2 molecule and the different hydrogen atoms of the heterocycles. Each configuration has been marked with a dotted red line to highlight the interaction. These two orientations called IPHB and PPHB are calculated for each of the non-equivalent (by symmetry) hydrogen types. The heterocycles included in our study have different hydrogen atom types depending on the symmetry of the system. We have therefore included in this study all posible unique interactions, thus obtaining 19 different approaches for which the two different spatial arrangements illustrated in Figure 7 were analyzed. The different types of hydrogen atoms are represented in Figure 8 using a colour code that, for the sake of readability, will be also employed in the table summarizing the interaction parameters (Table 4). In the IPHB spatial arrangement it is striking that the CS2 molecule has no minimum in intermolecular interaction potentials in more than half of the systems. In systems where 19



Page 20 of 34

H H H

H

H

H

H

N

H H

H

H

6N0-I

6N1-I H

N

H

N

N H

H

N

H

H

H

H

6N2-I

6N2-II

H

N

H

H

N

H

6N2-III H

N

N

N

H

H

H

N

H

N

N

N H

H

N H

N

H 6N3-I

6N3-II

6N3-III

H H

N

H

N

N N

N N

N N

N

H N

N

H N

H 6N4-I

6N4-II

6N4-III

Figure 8: Representation of the eleven heterocycles under study highlighting the candidates for hydrogen bonding. A color key is used to mark different hydrogens according to their environment (symmetry makes those hydrogens with the same color equivalent): red, green and pink. it does have a minimum, the depth of the potential well () is very small, for instance, the 6N0-I system with an of -0.330 kJ/mol. These results contrast with those obtained in the case of CO2 . The values range there from -1.520 kJ/mol (6N0-I system) to -4.030 kJ/mol in one of the systems doped with four nitrogen atoms. In this case, average values become more negative as the degree of substitution with nitrogen atoms increases, following a linear trend with a correlation coefficient of 0.980. In view of the results reported in Table 4, it is important to highlight the great influence that the type of hydrogen atom has on the values obtained. For example, if we take the three systems that have three different hydrogen atoms (6N1-I, 6N2-II and 6N3-II), the great influence of the hydrogen considered is clearly

20


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observed. The values vary between the hydrogen atoms with the most and less favorable interaction a 12.9% in the 6N1-I system, a 5.97% in the 6N2-II and a 24.5% in the 6N3-II system. As expected, the hydrogen bond for CO2 is less favorable in the PPHB than in the colinear arrangement, since hydrogen bonds are remarkably directional. In this case the values are significantly reduced and lie between -0.683 kJ/mol in the most favorable system and -0.012 kJ/mol in the least favorable one. Even with these small figures, the average value of as a function of the number of nitrogen atoms doping the structure of the heterocycle varies in a stronly linear maner (R2 =0.995) between -0.660 kJ/mol in the 6N0 system and -0.147 kJ/mol in the systems with 4 nitrogen atoms. The interacting profiles for the CS2 molecule show the completely opposite behaviour. Instead of decreasing, the values of the potential well depth in the PPHB interaction increase with the degree of doping. Again, the presence of a σ-hole in the interacting sulfur atom radically changes the interacting abilities of the system. The average values of the potential well depth evolve linearly (R2 =0.951) but following the inverse trend just mentioned with respect to that shown for the CO2 molecule. This trend for the values indicates that the complexed systems become more stable by increasing the degree of substitution with nitrogen atoms. The average values of this parameter range between -1.498 kJ/mol for the 6N0 system and -2.393 kJ/mol in the 6N4 family. The larger polarizability and the presence of σ-holes in sulphur explain the stronger interactions and the opposite trend. These holes in larger atoms allow an attractive and directional interaction with negative electron density regions such as those in anions, π electron-rich density areas or lone pairs in Lewis bases. 54–56,66–68

4

Conclusions

In this work we have computationally studied the interaction of two isoelectronic greenhouse gases, CO2 and CS2 , with a comprehensive set of nitrogen-doped benzene derivatives, with

21


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22

σP P HBCS2 ( ˚ A) P P HBCS2 (kJ/mol)

σP P HBCS2 ( ˚ A) P P HBCS2 (kJ/mol)

σP P HBCO2 ( ˚ A) P P HBCO2 (kJ/mol)

σP P HBCO2 ( ˚ A) P P HBCO2 (kJ/mol)

σIP HBCS2 ( ˚ A) IP HBCS2 (kJ/mol)

σIP HBCS2 ( ˚ A) IP HBCS2 (kJ/mol)

σIP HBCO2 ( ˚ A) IP HBCO2 (kJ/mol)

σIP HBCO2 ( ˚ A) IP HBCO2 (kJ/mol)

6N1-I 3.779 -1.712 6N3-I 3.677 -2.490

6N1-I 3.792 -1.487 6N3-I 3.679 -2.229

6N1-I 3.769 -1.764 6N3-II 3.702 -2.112

6N1-I 3.725 -0.420 6N3-II 3.665 -0.448

6N1-I 3.715 -0.456 6N3-I 4.450 -0.012

6N1-I 3.598 -0.683 6N3-I 3.785 -0.222

6N1-I 3.342 -2.033 6N3-II 3.266 -2.490 6N1-I 4.404 -0.139 6N3-II No min No min

6N1-I 3.362 -1.953 6N3-I 3.218 -3.360

6N1-I 6N1-I 4.424 4.371 -0.187 -0.169 6N3-I 6N3-I No min No min No min No min

6N1-I 3.352 -1.800 6N3-I 3.197 -3.236

6N2-I 3.768 -1.764 6N3-II 3.707 -2.101

6N2-I 3.805 -0.240 6N3-II 3.615 -0.437

6N2-I 4.404 -0.140 6N3-II No min No min

6N2-I 3.221 -3.053 6N3-II 3.186 -3.027

6N2-I 3.742 -1.821 6N3-II 3.712 -1.812

6N2-I 3.668 -0.281 6N3-II 3.775 -0.260

6N2-I No min No min 6N3-II No min No min

6N2-I 3.265 -2.490 6N3-II 3.216 -3.100

6N2-II 3.767 -1.468 6N3-III 3.719 -1.771

6N2-II 3.565 -0.667 6N3-III 3.615 -0.448

6N2-II No min No min 6N3-III No min No min

6N2-II 3.260 -2.296 6N3-III 3.198 -2.916

6N2-II 6N2-II 6N2-III 3.749 3.748 3.761 -1.973 -1.768 -1.708 6N4-I 6N4-II 6N4-III 3.622 3.636 3.637 -2.681 -2.249 -2.249


6N2-II 6N2-II 6N2-III 4.775 4.965 4.864 -0.022 -0.002 -0.016 6N4-I 6N4-II 6N4-III No min No min No min No min No min No min


Table 4: Parameters of the hydrogen bond interaction potentials for all the non-equivalent hydrogen atoms in the eleven heterocycles under study. The σ parameter (distance at which the interaction potential is zero) is shown in ˚ A, while the parameter that expresses the potential well depth () is expressed in kJ/mol. The type of hydrogen atom being defined is expressed as a colour as illustrated in Figure 8. The IPHB and PPHB labels accompanying each parameter refers to the spatial arrengements considered (Figure 7).


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the goal of helping the development of new capture materials through rational design. The interaction have been explored by the calculation of rigid energy profiles in a series of limit orientations which cover the main interaction modes between these fragments: CX2 with the π density in the ring (perpendicular and parallel), CX2 with the lone pair of a nitrogen in the heterocycle (through carbon both in a coplanar IPCH and perpendicular PPCH orientation , and through X, both in a coplanar IPXH and perpendicular PPXH orientation as well) and CX2 (through X) with all the non-equivalent hydrogens in each heterocycle (both in a collinear, IPHB and perpendicular, PPHB, orientation). These profiles have been fitted to a classical 12-6 Lennard-Jones potential, for which the (well depth) and σ (intercept at zero potential) parameters have been provided in the text. We find that for the interaction of CO2 with the π system on the heterocycle, the values of correlate linearly with the number of nitrogens on the ring (we average the of the isomers), and that the trends are opposite in the perpendicular and parallel orientations. Thus, the strogest interactions are found for 6N0-I when parallel and for 6N4-I when perpendicular, although interactions are generally stronger in parallel orientations (the systems with 4 nitrogen atoms are the exception). In the case of CS2 , the trends in the parallel orientation are not as clear, with a maximum interaction for the systems with two nitrogens. In the perpendicular orientation, trends are opposite to those found for CO2 with the largest interaction found for benzene. Here, in general, interactions are stronger in a perpendicular arrangement. For the interactions between CX2 and the main heteroatom in the ring, the deepest well is found for 6N1-I in all cases, although the preferred interacting site is the carbon (PPCH orientation) in CO2 and one of the sulfur atoms (IPOH orientation) in CS2 . Interactions are significantly stronger for the former molecule, and actually, the PPCH orientation is by far the preferred one in the case of CO2 , due to the strong electrophilicity of its carbon atom. We find again a linear correlation between the number of nitrogens and the average of the Lennard-Jones parameters (although the dispersion of the data for isomers is large),

23



with interactions decreasing with increased substitution in all systems. When CX2 interacts with the main heteroatom in the ring through X, interactions are significantly lower and for CO2 they don’t give raise to a stable complex in most cases. The exception is CS2 in the IPOH orientation, which provides the strongest interaction between nitrogen and CS2 because of the formation of a chalcogen bond. The analysis of hydrogen bonding between CX2 and the heterocycles provides interesting information in terms of the parametrization of force fields, since, although these interactions are much weaker than those found for other interaction modes, their contributions can easily add up and modulate the interaction energy when several heterocycles are included in the capture system. In this work we have generated Lennard-Jones potentials to parametrize force fields in detail and also to understand the interactions between CX2 and nitrogen-doped six membered heterocyclic rings and apply this knowledge to the design of capture or detection systems. We find that the most favorable interactions are found between the carbon in CO2 and the main heterocycle in the ring in a parallel orientation, whereas the preferred interaction mode of CS2 is stablished between sulfur and the π density of the aromatic ring. The fact that the preferences for interaction sites and orientations of CO2 and CS2 are most of the times opposite helps in terms of ensuring the selectivity of these systems in front of this two isoelectronic compounds. One of the most remarkable findings of this work, which was unexpected, is the existence of very good linear correlations (R values very close to one) between the number of nitrogen atoms in the heterocyclic ring and the depth of the interaction potential wells. Taking into account that the values used in these correlations are average values of all the isomers considered, these results could be very well used in the parametrization of more general, coarse-grained potentials, or the elaboration of general models with predictive power for use in the design of larger systems.

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Acknowledgement The authors thank the Centro de Supercomputación de Galicia (CESGA) for the generous allocation of computer time, and the Ministerio de Econom´ıa y Competitividad (MINECO, ´ VidalPCTQ2016-75023-C2-2-P) and Xunta de Galicia (ED431C 2017/70) for funding. A. Vidal is grateful to the Universidade de Vigo for a predoctoral fellowship.

Supporting Information Available Computed values for all the intermolecular potential profiles considered in this work. This material is available free of charge via the Internet at http://pubs.acs.org/.

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Lennard-Jones Intermolecular Potentials for the Description of 6

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