Anthracenyl polar embedded stationary phases with enhanced aromatic selectivity. Part II: A density functional theory study

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Anthracenyl polar embedded stationary phases with enhanced aromatic selectivity. Part II: A density functional theory study Mélanie Mignot a , Benjamin Schammé a , Vincent Tognetti b,∗ , Laurent Joubert b , Pascal Cardinael a , Valérie Peulon-Agasse a,∗ a b

Normandie Univ., Laboratoire SMS-EA3233, Univ. Rouen, F-76821, Mont Saint Aignan, France Normandie Univ., COBRA, UMR 6014 & FR 3038, Univ. Rouen, INSA Rouen, CNRS, 1 rue Tesnière, F-76821, Mont-Saint-Aignan, Cedex, France

a r t i c l e

i n f o

Article history: Received 17 May 2017 Received in revised form 28 August 2017 Accepted 30 August 2017 Available online xxx Keywords: High-performance liquid chromatography Aromatic stationary phase Polar embedded group Steric selectivity Molecular modeling Density functional theory Chemical interactions Energy decompositions

a b s t r a c t New polar embedded aromatic stationary phases (mono- and trifunctional versions) that contain an amide-embedded group coupled with a tricyclic aromatic moiety were developed for chromatographic applications and described in the first paper of this series. These phases offered better separation performance for PAHs than for alkylbenzene homologues, and an enhanced ability to differentiate aromatic planarity to aromatic tridimensional conformation, especially for the trifunctional version and when using methanol instead of acetonitrile. In this second paper, a density functional theory study of the retention process is reported. In particular, it was shown that the selection of the suitable computational protocol allowed for describing rigorously the interactions that could take place, the solvent effects, and the structural changes for the monofunctional and the trifunctional versions. For the first time, the experimental data coupled with these DFT results provided a better understanding of the interaction mechanisms and highlighted the importance of the multimodal character of the designed stationary phases: alkyl spacers for interactions with hydrophobic solutes, amide embedded groups for dipole-dipole and hydrogen-bond interactions, and aromatic terminal groups for ␲-␲ interactions. © 2017 Elsevier B.V. All rights reserved.

1. Introduction Polar-embedded phases have become increasingly popular in reversed-phase liquid chromatography (RP-LC). These phases are primarily hydrophobic but have hydrophilic polar groups incorporated in the ligand structure. Various chromatographic selectivities can be obtained as a result of the type of polar embedded group (PEG) (i.e. amide, urea, carbamate, ether or sulphonamide moieties) and the length and type of the alkyl group of the ligand. Compared to the commonly used octadecyl stationary phases, polar-embedded phases provide several advantages such as good peak shapes for basic compounds [1], excellent compatibility with highly aqueous mobile phases [2], and very often, original selectivities [3]. Polar-embedded group (PEG) poly-aromatic stationary phases can offer various types of interaction. The precise determination of their 3D structure is necessary to understand their chromatographic behavior. This can be achieved theoretically by using molecular modeling tools, such as molecular mechanics, or semi-

∗ Corresponding authors. E-mail addresses: [email protected] (V. Tognetti), [email protected] (V. Peulon-Agasse).

empirical methods, which have already been used to elucidate the structures of conventional stationary phases. In this paper, density functional theory (DFT) [4] was used, which improves upon the classic solute modeling and docking [5–10] approaches by introducing a full quantum description of the system. Hence, one of the purposes of this paper is to propose and assess a robust DFTbased computational protocol to model the involved compounds in order to cast more light on the experimental results. The developed methodology was notably designed so that it is enough general and applicable in the future to a wide variety of phases and analytes. To this aim, this article focuses on the DFT description of a new generation of polar embedded aromatic stationary phases, whose synthesis and complete characterization (microscopy, elemental analysis, thermogravimetry, infrared spectroscopy, 1 H, 13 C, 29 Si CP/MAS NMR) were the target of previous studies [11,12] and of the first paper of this series [13]. In this work, a fine-tuned DFT approach to the retention in chromatographic systems with chemically bonded phases is proposed. Importantly, their chromatographic properties include the evaluation of their selectivity towards the homologous series of alkylbenzenes as well as different congeners of polycyclic aromatic hydrocarbons (PAHs). These solutes are indeed good probes to investigate the aromatic and

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shape selectivity. The influence of the type of organic modifier of the mobile phase and of the ligand functionality on the retention will be thus closely analyzed.

2. Theory 2.1. On the choice of the theoretical method Because the use of quantum chemistry calculations still remains pretty rare in the chromatography community and because this paper is also intended for a wide audience in analytical chemistry, it could be informative to recall some general statements about molecular modeling. In brief, from a methodological aspect, any theoretical study can be divided into three successive steps: the selection of the computational protocol, the computation itself, and subsequent data processing. The first step involves the choice of the model system (which atoms are included) and its components (possible counterions or solvent molecules). The second step requires prior determination of the optimal method with respect to the available computer resources; in practice, it consists of defining the formulas for calculating the relevant energy (e.g., electronic energy, enthalpy, free energy). The third step is related to the extraction of a few pertinent numbers (among the thousands generated by the computation), called descriptors, which can explain the experimental results and provide guidelines for further experimental improvement. However these steps are somewhat entangled. Indeed, the size of the model system, for instance, is not chosen independently of the energy calculation method. Roughly speaking, one can rely on either classical mechanics (the realm of force fields) or on quantum chemistry. While full macromolecular systems can be handled by the first methods, only limited ones (typically hundreds of atoms) can be routinely treated by the latter. However, force fields are generally specialized (for instance, designed for a protein, sugar, or water) and often need to be reparametrized for special cases. One should then notice that the systems of interest here are challenging for force fields since they mix inorganic (silica) and organic fragments. Such a combination makes quantum chemistry presumably more reliable, to the obvious detriment of computational time. For this reason, only the end arm of the chromatographic system is generally modeled at the quantum level in the literature [5,6,8–10,14,15] Two notable but isolated exceptions are found in a recent work [16] where the full system was studied, taking advantage of GPU architecture, which requires still yet non-standard technology, and another study [9,16] where geometries were optimized at the MM3 semi-empirical level of theory, a level that cannot correctly describe the crucial noncovalent interactions of the dispersion type. Therefore, MM3 may produce satisfying results for the silica phase but will not be suitable to investigate its interactions with aromatic compounds. Neglecting the surface is certainly erroneous in the case of trifunctional phases, where the interactions between the three arms should be geometrically accommodated by the silica and are thus constrained. Moreover, solvent effects are generally not considered (the phase-solute adduct is viewed as a free molecule). In fact, many of the referenced studies reported calculations in the gas phase. Nevertheless, solvent effects are important for practical applications, an issue addressed here from a theoretical perspective. The only exceptions noticed [9,16] have used an implicit solvation approach. Let us recall that solvent effects can be introduced through an explicit (solvent molecules are described at the atomic level) or implicit (a continuum model [17] mainly accounts for the average electrostatic interaction with the solute) approach. The descriptions can be further mixed in a hybrid approach, which

is sometimes compulsory to explain subtle conformational differences [18]. For the energy calculation procedure, almost all past studies [5,6,8–10,14,15,19–23] employed the still popular global hybrid B3LYP exchange-correlation functional (one recent counterexample is the use of the more modern M06 in [24]). Nonetheless, this twenty-four-year-old venerable functional is known to be inaccurate for noncovalent interactions, particularly those stemming from van der Waals dispersion forces [25]. For instance, B3LYP is unable to predict a stable structure for helium, methane, and benzene dimers. This failure, which is now well documented [26], makes it unsuitable when ␲-stacking is at stake. In addition to the functional issue, a basis set should be cautiously chosen. Quite unexpectedly, the minimal STO-3G basis set is still in use in the chromatography community for describing noncovalent interactions [19–21], but it is obviously too small to produce any converged results. On the contrary, recent studies made use of high quality basis-sets [27–29], but remaining focused on small model systems. Finally, in the literature, the results are usually rationalized in terms of atomic charges (the use [5] of the Mulliken scheme, while fast, is strongly discouraged since it is not physically motivated and shows spurious basis set convergence) and molecular electrostatic potentials (MEPs). This last tool, which is meaningful to account for charge-controlled interactions (whereas Fukui functions and their extensions should be used in the case of orbital control) [30] or for noncovalent interactions involving the so-called ␴-hole paradigm [31–33], cannot reveal dispersion-controlled interactions because dispersion is a (correlation) non-electrostatic effect. Complementary tools should thus be considered when ␲-stacking occurs. Eventually, such descriptors can be finally incorporated into a statistical approach within Quantitative structure-retention relationship (QSRR) approaches, which allow for the prediction of new chromatography systems through in-silico design (see refs. [9,24,34–37] for some recent examples of this chemometrics screening procedure). This comparative literature survey should help understanding the upgrade of the common computational protocols. Based on all these previous points, our current specifications for a trustable computational approach are the following: a quantum description of the trifunctional phase and of its interactions with aromatic molecules, which includes solvent effects and which describes ␲-stacking in a reliable way. To this aim, we consider the gas phase, implicit solvent [through the polarizable continuum model (PCM)], and hybrid implicit-explicit [explicit microsolvation consisting of two solvent molecules immerged in PCM that can form hydrogen bonds with the phase, perturbing the internal Hbonds network] calculations on a system including a silica surface (Si3 O7 H5 moiety) that will be allowed to relax during the geometric optimization performed with a modern exchange-correlation functional. However, the fact that the silica bulk could restrain some of these moves will not be considered. 2.2. Descriptors from quantum calculations For the sake of brevity, the discussion was restrained to the sole energetic features that can be extracted from the calculations. But other quantities, such as structural and advanced electronic properties and vibrational data (infrared spectra could for instance be generated by our approach) can be determined. However, even if this study was only focused on energies, some important concepts must be clarified. To beginning with our typology, when dealing with the interaction between molecules M1 and M2 , different energies can be evaluated: the first is the DFT “binding energy” defined by Eq. (1): bind EM = E DFT (M1 ...M2 ) − E DFT M1 ...M2 (M1 ) − E DFT M1 ...M2 (M2 ), ...M 1

2

(1)

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Fig. 1. (a). View of the optimized structure for the interaction between naphthacene and the trifunctional stationary phase with two explicit methanol molecules immerged in a methanol implicit continuum. Atoms circled in blue are described by the 6–311 + +G(d,p) basis set, those in green by STO-3G, and the remaining by 6–31G(d). (b). View of the optimized structure for the interaction between naphthacene and the trifunctional phase with two explicit acetonitrile molecules immerged in an acetonitrile implicit continuum. Atoms shown as balls and sticks are treated at the MP2 level (high-level layer), while atoms in the wireframe format are described by DFT (low-level layer). Color code: H in white, C in grey, N in blue, O in red, and Si in turquoise. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

where the DFT energies of molecules M1 and M2 are evaluated at the geometries that M1 and M2 adopt in the optimized M1 · · ·M2 complex. When these two energies are calculated on the optimized free A and B molecules, one evaluates the “complexation energy” in Eq. (2) (the fragments might never adopt an arrangement close to their most stable conformation during the separation process, making in some cases this reference state irrelevant):

M2 , while the second describes the energy reorganization inside each fragment (e.g., the energetic (de)stabilization of each atom within the fragment–a contribution that cannot be described by usual force fields—and the variation of the bond strengths inside each moiety upon complex formation; see refs [41] and [42] for a detailed discussion). These interactions are mainly noncovalent, elec , and so they can be divided into (“classical”) electrostatic,EM ...M

compl EM ...M 1 2

“dispersion contribution”, EM

=E

DFT

DFT DFT (M1 ) − EM (M2 ). (M1 ...M2 ) − EM 1 2 compl 1 ...M2

bind The difference between EM and EM ...M deform

1

2

(2)

is the “deformation

energy” of M1 and M2 ,EM ...M , that is required to form the stable 1 2 complex. Adding the vibrational zero-point energy (ZPE) to Eq. (2) provides the “complexation Gibbs energy at 0 K”: compl0K 1 ...M2

GM

= E DFT +ZPE (M1 ...M2 ) − EM1 DFT +ZPE (M1 ) − EM2 DFT +ZPE (M2 ).

(3)

Using statistical thermodynamics, one can evaluate the temperature and entropy contributions at 298.15 K under atmospheric pressure (standard conditions), affording the “standard Gibbs complexation energy”: ◦ compl

GM

1 ...M2

◦

◦

= GM

◦

(M1 ...M2 ) − GM1 (M1 ) − GM2 (M2 ). 1 ...M2

(4)

therm is Then, the “thermal contribution to complexation”,GM ...M ◦ compl

compl 0K

1

2

defined as the difference between GM ...M and GM ...M . It is an 1 1 2 2 important quantity since temperature can have a significant impact on selectivity. Because our thermodynamic corrections are based on the quantum harmonic oscillator model valid at stationary point on the potential energy surface, our static approach cannot define “binding Gibbs energies”. However, the binding energy in Eq. (1) can be further explored, as it can be exactly split into two physical counterparts (Eq. (5) within the interaction quantum atoms (IQA) framework [38–40]:



bind EM ...M = 1



2

atomsA ∈ M1 atomsB ∈ M2





int EAB + Eintra

(5)



E int

M1 ...M2

The first right-hand side term corresponds to the sum of the interaction energy between each atom in M1 with each atom in

disp . 1 ...M2

1

2

At the smallest approximation

elec is given by the “point-charge (pc) contribution”, while order, EM ...M disp

1

2

EM ...M can be evaluated from Grimme’s D2 pair-potential scheme, 1 2 according to the following equations (Eq. (6)) (in atomic units):

⎧   qA qB pc ⎪ EM ...M = ⎪ ⎪ 1 2 RAB ⎨ A ∈ M1 B ∈ M2

disp ⎪ ⎪ E ≈− ⎪ ⎩ M1 ...M2

 

A ∈ M1 B ∈ M2

fAB

C6A C6B .

(6)

R6 AB

An alternative for evaluating dispersion energy is to perform bindMP2 second-order Møller-Plesset (MP2) calculations. Let us call EM 1 ...M2 the binding energy between the two fragments obtained at this bindHF the energy obtained by replacing the MP2 step level and EM 1 ...M2 with the Hartree Fock (HF) step. As a first approximation, one can assume that the dispersion energy is equal to the second-order perdispMP2 bindMP2 − E bindHF were turbation energy. Accordingly, EM ...M as EM M1 ...M2 1 2 1 ...M2 defined, a strategy used in ref [43]. Note that, in practice, a full MP2 calculation was not performed, but a QM/QM’ extrapolation was used, as described at the end of the computational details section. Henceforth, the interaction process between two moieties will disp be described by six “imbricated” energetic descriptors: EM ...M , deform

◦ compl

1

2

bind therm , G ,EM ...M ,GM ,which will be computed for EM M1 ...M2 1 ...M2 1 2 1 ...M2 three environment models (gas phase, PCM, PCM-explicit hybrid). Both their magnitude (which enables us to determine the interaction nature) and their variation within a given compound family are of interest and are potentially not equivalent. For instance, one of these energy components could be of high magnitude but relatively constant in the dataset, so that it will account for coordination but not for discrimination. Conversely, if one small quantity varies

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Table 1 Energy decomposition for the interaction between the selected functional phases and the benzene molecules at the B97-D DFT level of theory with various solvent models. All values in kcal/mol. pc

Entry

Phase

Solvent

EM

1 2 3 4 5

tri-PEG-anthra tri-PEG-anthra tri-PEG-anthra tri-PEG-anthra tri-PEG-anthra

None PCM CH3 OH PCM CH3 CN PCM CH3 OH + 2 CH3 OH PCM CH3 CN + 2 CH3 CN

−0.50 −0.43 −0.43 −0.50 −0.59

1 ...M2

significantly from one compound to the other, it will provide less insight into the interaction nature but may be valuable to explain selectivity. In this paper, the aim is to find the energy components that correlate the most to the experimental log(k) values.

2.3. Computational details All calculations were performed using the Gaussian 09 package [44]. The DFT calculations were performed with the dispersioncorrected B97D exchange-correlation functional [45], which has two main advantages: it is fast since it does not require the evaluation of non-local exact exchange, and it is designed to correctly account for van der Waals interactions. It was used in conjunction with the following basis set combination, depicted in the left part of Fig. 1: atoms involved in hydrogen bonds (these are the two intramolecular bonds involving the amide groups within the trifunctional fragment and the two intermolecular bonds with the solvent) are described by 6–311 + +G(d,p), while, to save time, the butyl linkers (that have mainly structural and steric effects) are treated by STO-3G. The 6–31G(d) basis set is used for the remaining atoms (a maximum of 2973 primitive Gaussian functions are used to solve the Kohn-Sham (KS) equations). Implicit solvation is described by the conductor polarizable continuum model (CPCM [46] with default parameters), which provides values that are as accurate as more recent implementations (like Gaussian 09’s default IEFPCM) for common isotropic solvents but is computationally less time-consuming. All structures were fully optimized without symmetry constraints, and the nature of the obtained stationary points was further confirmed by vibrational analyses (only real harmonic frequencies for minima). Standard formulas from statistical mechanics were used to compute the thermodynamic corrections. Because they are based on the ideal gas model, they however lead to overestimation of the entropic effects for molecules in solution. To circumvent this drawback, several groups have proposed scaling the obtained values for the rotational and the translational entropies (that are reduced in condensed phases). In accordance with previous papers and with our own experience, the scaling factor of 0.65 was used [47–49]. This correction is actually made compulsory by the fact that, when the scaling factor was taken equal to 1.0, the calculated complexation Gibbs energies were found positive, indicating that the coordination is endothermic. Conversely, this is no longer the case when 0.65 is chosen, in agreement with the experimental results. Finally, the binding energies are not corrected from the basis set superposition errors because Boys-Bernardi’s counterpoise protocol is not available within PCM. Point-charge contributions to the electrostatic interaction were evaluated using atomic charges fitted on the molecular electrostatic potential by the ChelpG formalism [50]. Noncovalent index (NCI) analysis was performed using the NCIplot software [51]. Finally, ONIOM-type calculations were conducted within a twolayer QM/QM’ approach (see Fig. 1b) to estimate the dispersion contribution to the binding energy in a full ab initio way. The highlevel layer was defined as the one including the mobile phase and the three anthracyl groups of the stationary phase, which was

disp 1 ...M2

bind EM ...M

EM

therm GM ...M

GM

−14.39 −14.70 −14.70 −14.88 −15.00

−8.15 −8.03 −8.03 −8.01 −8.14

0.24 0.28 0.28 0.28 0.32

5.18 5.73 5.75 5.34 5.25

−1.73 −1.16 −1.14 −1.33 −1.34

1

2

deform 1 ...M2

◦ compl

EM

1

2

1 ...M2

described at the MP2 level of theory with the 6–31G(d) basis set (note that frozen cores were used; despite the small basis set, such calculations required large memory and hard disk space), while the remaining system was treated at the B97D/6–311 + +G(d,p) DFT level. These QM/QM’ calculations were performed in a single-point manner on the geometries optimized at the previous DFT level. Fig. 1 shows the largest systems under consideration (174 atoms), where one can identify two explicit methanol molecules (a) and two acetonitrile ones (b) in their optimized geometries. 3. Results and discussion Having these theoretical tools in hand, the first focus was the benzene interaction with the stationary phase. Table 1 shows the values for the energy components presented above. The comparison of entries 1 and 2 in Table 1 shows that the gas phase and solvent models produced significantly different ◦ compl therm results (particularly for GM and GM ...M ). However, as 1 ...M2 1 2 shown by entries 2 and 3, the implicit solvent calculations could not differentiate methanol from acetonitrile because the energies were almost identical. This was not surprising since the two solvents have very similar PCM parameters (εr = 35.7 for CH3 CN and 32.6 for CH3 OH) and since the C6 coefficients in Eq 6 are solvent-independent. Accordingly, the difference in the absolute self-consistent field (SCF) energy of the optimized trifunctional phase in the two PCM solvents was found equal to 0.1 kcal/mol, which explains why the relative energies are almost the same. Therefore, explicit solvent molecules should be considered and were expected to produce slightly different results since the H· · ·O hydrogen bonds in methanol and the H· · ·N hydrogen bonds in acetonitrile were present. This was corroborated by entries 4 and 5, although the differences remained small. As expected, the highest energy contribution stems from dispersion (approximately −15.0 kcal/mol). Let us recall that there are several van der Waals geometries for adducts built on aromatic cycles. For instance, for the benzene dimer [52], the two main categories are parallel (the most stable being called “displaced”, where the two cycles are not exactly on top of each other) and T-shaped [53]. As shown in the top of Fig. 2, benzene interacts in a T-shaped fashion with the trifunctional phase. This can be explained by the fact that the intramolecular hydrogen bonds inside the stationary phase preclude the intercalation of benzene between two anthracyl groups. This did not occur for the monofunctional phase (which is saturated with hydroxyl groups). As depicted in the lower part of Fig. 2b, benzene “slipped” but was not fully parallel to the anthracyl group because one methanol solvent molecule hindered the corresponding face. Once having established the required level of theory, the C6 H5 R alkylbenzene series with R = H, CH3 , C2 H5 , C3 H7 , and C4 H9 was considered; the results are presented in Table 2. The modeling is not realistic for longer alkyl chains because the C6 H5 -R molecule would be larger than the phase width, meaning that it could significantly interact with another trifunctional moiety. This effect can be modeled using a periodic approach that assumes homogeneous grafting (with high coverage) on the silica surface, an assumption

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Fig. 2. (a) View of the optimized structure of the interaction between benzene and the trifunctional stationary phase with two explicit methanol molecules immerged in a methanol implicit continuum. (b) View of the optimized structure for the interaction between benzene and the monofunctional phase with two explicit methanol molecules immerged in a methanol implicit continuum. Color code: H in white, C in grey, N in blue, O in red, and Si in turquoise. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Table 2 Energy decomposition for the interaction between the trifunctional phase and C6 H5 -R and polycyclic aromatic molecules at the B97-D DFT level of theory. All values in kcal/mol. System

Solvent

C6 H5 -R (alkylbenzenes) R = CH3 PCM CH3 OH + 2 CH3 OH PCM CH3 OH + 2 CH3 OH R = C2 H5 PCM CH3 OH + 2 CH3 OH R = C3 H7 PCM CH3 OH + 2 CH3 OH R = C4 H9 PCM CH3 CN + 2 CH3 CN R = CH3 R = C2 H5 PCM CH3 CN + 2 CH3 CN PCM CH3 CN + 2 CH3 CN R = C3 H7 PCM CH3 CN + 2 CH3 CN R = C4 H9 Polycyclic (PAHs) PCM CH3 OH + 2 CH3 OH Naphthalene PCM CH3 OH + 2 CH3 OH Anthracene PCM CH3 OH + 2 CH3 OH Naphthacene PCM CH3 CN + 2 CH3 CN Naphthalene PCM CH3 CN + 2 CH3 CN Anthracene PCM CH3 CN + 2 CH3 CN Naphthacene

pc

disp 1 ...M2

bind EM ...M

EM

therm GM ...M

GM

−0.58 −0.72 −0.76 −0.66 −1.23 −1.36 −1.46 −1.52

−16.56 −16.93 −17.14 −17.19 −16.26 −17.33 −17.88 −17.92

−8.69 −8.70 −8.60 −8.38 −9.10 −9.23 −9.55 −9.37

0.37 0.34 0.31 0.28 0.60 0.50 0.70 0.69

6.34 5.77 3.34 3.47 6.24 4.37 5.75 6.29

−0.66 −1.48 −4.01 −3.80 −1.16 −3.59 −2.19 −1.39

−0.15 −0.07 0.03 0.13 0.06 0.13 0.21 0.29

−0.55 −0.75 −0.58 −1.09 −1.57 −1.68

−18.81 −20.62 −26.47 −17.20 −22.06 −25.60

−9.52 −10.31 −12.54 −8.98 −11.49 −12.37

0.31 0.60 2.01 0.53 0.80 0.91

5.76 5.66 4.73 5.12 6.12 6.21

−2.34 −2.92 −5.08 −2.42 −4.36 −4.12

0.15 0.62 1.14 0.23 0.52 0.89

1 ...M2

that is however arguable from the experimental point of view. On the other hand, the explicit quantum treatment of a second trifunctional fragment is precluded by the associated computational cost. The polycyclic aromatic molecules, such as naphthalene, anthracene, and naphthacene were then considered. The results are presented in Table 2.

1

2

deform 1 ...M2

◦ compl

EM

EM

1

2

1 ...M2

log(k)

It was found that the electrostatic pc contribution was always stabilizing (all values are negative) but very low in absolute value in all cases, less than 0.8 kcal/mol for methanol and less than 1.6 kcal/mol for acetonitrile (with roughly pc, CH3 CN ≈ 2E pc, CH3 OH ). The variation was not monotonic with EM M1 ...M2 1 ...M2 respect to the alkyl chain length in the first case. As a

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Fig. 3. (a) Experimental log(k) values with respect to the theoretical values (in kcal/mol). (b) values with respect to (in kcal/mol). The linear regression lines are shown in red. (F-value = 149 for (a) and = 405 for (b)), and the 95% confidence interval is represented in orange. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

providing the following coefficient of determination (R2 ) values: pc disp deform bind ), 0.73 (EM ...M ), 0.01 0.18 (EM ...M ), 0.91 (EM ...M ), 0.89 (EM ...M 1

2

1

2 ◦ compl

1

2

1

2

therm ), 0.52 and (G ). The fact that dispersion showed (GM M1 ...M2 1 ...M2 the highest correlation follows from our previous statements. One may wonder whether better models can be built using more degrees of freedom. To this aim, bilinear regressions were investidisp gated using EM ...M and one of the other components. The highest 1

2

deform . Similarly, the best bilin1 ...M2 therm , with R2 = 0.92. involved GM 1 ...M2

R2 value (0.93) was obtained with EM bind EM 1 ...M2

ear regression with Nonlinear fitting (polynomial, logarithmic, exponential) were also disp considered, based on EM ...M , but no significant improvement was 1 2 obtained with only a few parameters. Therefore, the best monolinear regression was used (with the energy in kcal/mol): disp , 1 ...M2

log(k) = −1.73 − 0.11EM Fig. 4. Experimental log(k) values with respect to the molecular mean polarizability values (in bohr3 ) with methanol as solvent. The linear regression line (F-value = 1913) is shown in red, and the 95% confidence interval is represented in orange. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

◦ compl

bind therm , and G consequence,EM ,GM were not monotonic M1 ...M2 1 ...M2 1 ...M2 in methanol, in contrast to the increasing log(k) values. Moreover, the deformation energy was almost constant and negligible (less than 0.4 kcal/mol), so only the dispersion contribution (always increasing due to the cumulative effect of the C6 -pair potentials) followed the experimental trend for both solvents. The same conclusions (non-monotonic variations of several energy components, dispersion contribution of approximately −20 kcal/mol, binding energies of −10 kcal/mol) could be drawn for the polycyclic (naphthalene, anthracene, naphthacene) aromatic compounds. As expected, the increase of the dispersion contribution was enhanced with respect to the alkylbenzene cases since 6-membered rings establish stronger van der Waals interactions than alkyl chains. One can now consider whether this semi-quantitative analysis can be used for prediction. All the 16 log(k) values reported in Table 2 were considered: 8 values in methanol solvent (the trifunctional phase interacting with benzene, methylbenzene, ethylbenzene, propylbenzene, butylbenzene, naphthalene, anthracene and naphthacene) and the corresponding 8 values with acetonitrile as the organic modifier. Linear regressions between these values and the 6 energy components were investigated,

(7)

which is represented in Fig. 3a. disp Subsequently, as EM ...M appeared to be the key to predict1 2 ing the experimental results, unprecedented post-HF calculations were performed in a QM/QM’ fashion (see computational details) to assess the quality of this simple pair-potential model by comparing it to an ab initio approach based on the quantum wave function and dispMP2 not on empirical correction, providing EM ...M reference values. 1

2

disp 1 ...M2

A strong linear correlation was found (R2 = 0.97) between EM dispMP2

and EM ...M (see Fig. 3b). This benchmark validated the chosen 1 2 Grimme-type simple approach to the dispersion interaction energy contribution. It also proved that no significant improvement could be expected from higher (and much more time-consuming) levels of theory. In a way, the performance of our quite simple model is actually quite surprising since it was based on an optimized static structure. However, the retention time is intrinsically a dynamic (kinetic) parameter. The fact that it can be approached quite successfully by static DFT calculations was not a priori obvious. Three other remarks about this model are in order. The first is that it does not involve temperature dependence. This means that new regression parameters should be determined if log(k) is measured at a different temperature. The second is related to the solvent issue. While the differences between methanol and acetonitrile in disp the EM ...M values remained small within the alkylbenzene fam1 2 ily, a significant difference was observed for the largest system: −26.47 kcal/mol for methanol compare to −25.60 kcal/mol for acetonitrile, which could explain why the retention was more intense

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Fig. 5. (a) NCI plot: selected reduced density gradient isosurface (s = 0.5 a.u.) showing noncovalent interactions. (b) View of the molecular electrostatic potential mapped on the 0.001 isodensity surface. Atomic units and a color code (red: negative, blue: positive values) are used. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

disp

in the first case. Furthermore, the EM ...M gap between anthracene 1 2 and naphthacene was larger in methanol (−5.9 kcal/mol) than in acetonitrile (-3.54 kcal/mol), which is another clue to understand the enhanced selectivity for PAHs. However, one should remain cautious with such a simple analysis since it is not fully valid for the smallest molecules, for which the solvent effects are too subtle to be rationalized by the current model. The third one stems from the well-known links between dispersion and polarizability (evidenced by Debye’s model or by the Casimir-Polder formula for instance). For such reason, the PCM mean molecular polarizability (defined as one third of the trace of the static polarizability tensor and denoted ˛) ¯ of all solutes was computed and assessed the ability of this descriptor to predict log(k) values. Interestingly, high R2 values (0.99) were obtained. However, due to the fact that polarizabilities in PCM methanol and in PCM acetonitrile are almost identical, two models had to be built (where polarizability values are given in bohr3 , see Fig. 4 for the corresponding plot in the methanol case):



log(k)CH3 OH = −0.62 + 0.0053˛ ¯ CH3 OH log(k)CH3 CN = −0.22 + 0.0033˛ ¯ CH3 CN

.

(8)

For completeness, other standard electronic descriptors (frontier molecular orbital energies) were considered in the methanol case: the KS HOMO energy (R2 = 0.92), the KS LUMO energy (R2 = 0.84), and the HOMO-LUMO gap (R2 = 0.88), but they showed to be less correlated to log(k) than the mean polarizability. Finally, it is sometimes useful to have a graphical representation of the involved interactions. In the case of van der Waals complexes, this can be achieved using the popular noncovalent index (NCI) [54,55] as represented in Fig. 5a. The green layers are characteristic of dispersion interactions and were found to be present inside the stationary phase between the anthracyl groups and in the interaction region between the mobile and the stationary phases, revealing the clear T-shape fashion. This figure also shows that the naphthacene moiety is slightly corrugated, accounting for the nonnegligible deformation energy observed in this particular case. This energy loss is then compensated by a higher absolute dispersion interaction contribution. If interested in charged analytes, it would be instead more relevant to analyze the molecular electrostatic potential. Because it is linked to the local polarity of the molecule, it has already been used to locate the lipophilic/lipophobic or hydrophilic/hydrophobic

regions. For the trifunctional phase, it is represented in Fig. 5b, which shows that it is anisotropic. Let us recall that zones with negative (positive) values are prone to bind cationic (anionic) species. Interestingly, the two faces of the trifunctional phase are not equivalent: the right upper part is negative (blue-orange color), while the right bottom part is positive (green-blue color). From this viewpoint, this system exhibits an interesting “Janus character”.

4. Conclusion Density functional theory can be applied to retention solutes in chromatography with chemically bonded phases. A modern functional/basis set combination was used to accurately describe the structure of the trifunctional phase. The overall structure (silanol, alkyl chain, PEG and aromatic units) was considered using a validated quantum chemical formalism. With the structure elucidated, the impact of modifications inside the stationary phase skeleton on the separation behavior was investigated through a parallel evaluation of the experimental data, such as the retention factors for PAHs and alkylbenzenes. For the first time, the experimental data coupled with the DFT results indicated that the new polar embedded aromatic stationary phases presented a particular ability to recognize aromatic solutes. Additionally, solvent effects were taken into account. Because of the similar constant permittivity of acetonitrile and methanol, the PCM approach could not explain the better selectivity for PAH homologues than alkylbenzenes and the enhancement of this trend when using methanol instead of acetonitrile as the organic modifier. The latter issue was partly solved for the largest molecules by an additional explicit microsolvation model for acetonitrile and methanol. From a chromatographic point of view, the combination of aromatic and polar embedded groups (mono-PEG-anthra and triPEG-anthra) led to stationary phases with hydrophobic properties and aromatic selectivity that could be modulated by adjusting the organic modifier type. The DFT results nicely matched the chromatographic results, providing a better understanding of the interaction mechanisms and highlighting the importance of the multimodal character of the designed stationary phases: alkyl spacers for interactions with hydrophobic solutes, amide embedded groups for dipole-dipole and hydrogen-bond interactions, and aromatic terminal groups for ␲-␲ interactions.

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