Approaching the Quantitative Description of Enantioselective Adsorption by Density Functional Theory Means

The applications of enantiopure organic compounds range from medicine to green agrochemistry. Their racemic or enantioselective synthesis permits their acquisition beyond the extraction from life forms. However, these procedures need chiral resolution steps to achieve the required degrees of enantiomeric purity. Many research endeavors are addressed at finding chiral materials, which are able to separate the enantiomers by their selective adsorption upon. Transition metal chiral surfaces have been found to reach enantiomeric excess degrees of purity outperforming surfaces of naturally existing chiral materials. Future research can be driven by high-throughput computational screening, given that the employed methodology is able to discern the subtle enantiomeric differences of free energies of adsorption. The capabilities of density functional theory methods are evaluated here on the textbook case of d/l-aspartic acid adsorption on chiral Cu(3,1,17)R&S metal surfaces. Results show that dispersive forces ar...


Introduction
The existence of pure enantiomers is crucial in life forms, from amino acids conforming enzymes to cell membrane or other metabolic proteins, which are, almost exclusively, present in their levorotatory (L) enantiomeric form. Furthermore, deoxyribonucleic acid (DNA) helixes are given in only one mirror image, due to their conformation based exclusively on the dextrorotatory (D) D-2-deoxyribose. Even sugars are exclusively metabolized on the D-form.
Because of this, homochirality is considered a hallmark of life on Earth, 1 being of paramount importance when dealing with pharmaceuticals, where, very often, only one enantiomeric form of a compound is the essential active ingredient in a medicine. 2 This prompted the socalled chiral switch in pharmacy, but has spread over other fields, including green agrochemistry by enantiopure pesticides, 3 insect plague control in agriculture, 4 and even food and fragrance industries. 5,6 Given these important fields of application, there are great worldwide research efforts aimed at obtaining enantiopure compounds, typically isolated from life form feedstocks.
There have been large advances in the asymmetric synthesis by homogeneous catalysis, inferring chirality to common chemicals by chiral inducers, prochiral reactants, and/or chiral organometallic catalysts. [7][8][9] This asymmetric synthesis, either enantiospecific or racemic, requires further steps to separate the enantiomeric compounds from the reaction medium and the employed catalyst, as well as for the enantiospecific separation, so as to reach the sought degrees of purity. The enantioselectivity success is quantified according to the enantiomeric excess (ee), and most commonly achieved by high-performance chromatographic and electromigrating techniques using pure chiral selector solid phases. 10 Research has been devoted at finding naturally chiral solid surfaces of minerals for such chiral resolution steps, although they typically display ee values of 1-2%, 10% at most, 11 with higher performances achieved by organic crystals chiral surfaces. 12 One particularly appealing field of research is oriented at using chiral surfaces of catalytically active materials, in the quest of finding materials able carry out the enantioselective asymmetric synthesis by heterogeneous catalysis, thus benefitting from easier separation steps and a facile regeneration and recycling of the catalyst. However, another large share of research is focused on the solidstate separation of racemic mixtures of enantiomers, either isolated form life sources or nonenantiospecifically synthesized. A paramount work was achieved by Yun and Gellman, who showed that naturally chiral metal surfaces can yield ee values much higher than mineral surfaces, as demonstrated for Cu (3,1,17) R&S surfaces, displaying an enantioselective adsorption of D/L-aspartic acid with an ee of 39 ± 3%. 13 A later study revealed that such ee of a gas stream could be auto-amplified even on an achiral surface by a molecular preferential enantiospecific aggregation, as shown for D/L-aspartic acid on Cu(111). 14 Despite there have been examples in the literature concerning enantioselective adsorption, 15 even reaction on chiral metal surfaces, 16 the still nowadays challenge is to unfold the origins of the enantioselective chemical adsorption, hampered by the difficulty of distinguishing two adsorbed enantiomers, due sometimes to the tiny differences of the Gibbs free energies of adsorption for both enantiomers. Experimentally, this has been achieved using radioisotopes of a given enantiomer, 13,17 although the procedure is costly and cumbersome. Indeed, this is an aspect where ab initio simulations on materials surface models could easily high-throughput screen a large number of situations, in order to determine the very nature of enantioselectivity, even to select possible candidates for maximizing the ee.
There exist landmark examples of such detailed studies, typically employing Density Functional Theory (DFT), 18 although here the challenge is to be able to accurately quantify the subtle differences of a few hundreds of eV in the Gibbs free adsorption energies of the different enantiomers.
For instance, one can take L-alanine as a reference case, where DFT simulations have appointed the preferential adsorption of L-alanine on Cu(3,1,17) S over D-Alanine by 0.03 eV/cell -2.89 kJ mol -1 /cell-at a moderate coverage, 19 as obtained using the Perdew-Wang (PW91) exchange-correlation functional. 20 A later study showed an amplified preferential adsorption at a full coverage adlayer situation of enantiopure phases of L,L-alanine on Cu(3,1,17) S over the racemic D,L-alanine on Cu(3,1,17) S situation by 0.091 eV/cell -8.78 kJ mol -1 /cell; note here that the L,L-notation implies enantiopure surface phases composed of Lenantiomer, and D,L-racemic phases composed of co-adsorbed D-and L-enantiomers.
However, isotopically labelled L-alanine adsorption revealed a racemate surface phase with no measurable enantiospecificity. 21 This discrepancy could only be met with DFT simulations using the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional 22 -an exchangecorrelation functional similar to PW91-accounting for dispersive forces through the Grimme D2 approximation, 23 revealing that the adlayer racemic phase is 0.01 eV/cell -0.96 kJ mol -1 /cell-more stable than the enantiopure L,L-alanine phase, and by that, underlining the key role played by dispersive forces, biasing this non-enantiospecific, racemic adsorption.
The open question mark is whether such DFT simulations accounting for dispersive forces are at a stage of accurately quantifying the small differences of free energies of adsorption as found in the literature. Thus, at variance with the D,L-alanine racemic adsorption case, here we address the enantiospecific adsorption of D/L-aspartic acid on Cu(3,1,17) R&S , assessing first whether DFT is able to reproduce the experimentally observed enantiomeric preferential adsorption, and, secondly, to determine the simulations accuracy in sizing the distinct free energies of adsorption, ΔΔG ads , measured of being 3.15 ± 0.29 kJ mol -1 . 13 The experimentally observed preference was found for D-aspartic acid over L-aspartic acid on Cu(3,1,17) S , and could be detected by first saturating the Cu(3,1,17) S chiral surface with isotopically labelled L-aspartic acid, *L-Asp, at 400 K. Later, the system was exposed D-aspartic, D-Asp, at 460 K, which displaced the adsorbed *L-Asp until reaching an equilibrium between the adsorbed and gas phases. The kinetics of replacement allowed the authors stating the molecular adsorption and the adsorption preference of D-aspartic acid over L-aspartic acid on Cu(3,1,17) S . 13 In the present computational study attention is paid to other aspects possibly affecting the enantiospecific adsorption as discussed in the literature, such as the role of the molecular side chains, 24

Computational Details
The DFT optimizations have been carried out within the Generalized Gradient Approximation (GGA), specifically, using the PBE functional, 22 known to be one of the most accurate in describing, in average terms, transition metal bulks and surface properties, 28,29 and normally a work horse functional for the adsorption of enantiomeric molecules on transition metal surfaces. 21 Following previous successful works, 21 dispersive forces were described through the Grimme D2 correction. 23 The Vienna Ab initio Simulation Package (VASP) suite, exploiting periodic boundary conditions, has been used for this purpose, 30 employing a plane-wave basis set with a kinetic energy cutoff of 415 eV for the valence electron density, which delivers converged energy results with variations below 0.01 eV -0.96 kJ mol -1 /cell-, according to tests with increased kinetic cutoff energies. This reduced energy change is stressed throughout the study so as to define the limits of numerical accuracy of the presently DFT simulations.
The atomic core electron density has been described by the Projector Augmented Wave (PAW) method. 31 The optimizations have been carried out with an electronic convergence criterion of 1·10 -6 eV, and stopped when forces acting on the relaxed atoms were all below 0.01 eV Å -1 . All calculations were carried out in a non spin-polarized fashion, although spin-polarization tests revealed no surface magnetization, neither for the pristine  (001) terraces. The rotation along the upwards substituent bond axis by 120º offers three different adsorption conformations per upward substituent. Note as well that the adsorption is considered here distinguishing the two sides of the kinked step, this is, considering two options for the (001) terrace, namely with a molecular chiral C substituent facing the lower-terrace (LT) or the upper-terrace (UT). Altogether, the total number of sampled conformations is 24 per enantiomer.
The site notation used here is different from the n_A_x notation defined previously by Rankin and Sholl,33 and is adapted to the aforementioned sampling analysis. In detail, is defined as D/L-R 1 -S 1 -R 2 -S 2 -R 3 -S 3 , where considered R 1 -R 3 are the substituents of the chiral C atom of the aspartic acid (-H, -NH 2 , -COOH, or -CH 2 COOH) in contact with the Cu(3,1,17) S chiral surface sites S 1 -S 3 (2 and 3, combined with either LT or UT, see Figure 1). The fourth substituent is always considered pointing towards the vacuum region. Merely by this, the enantiomers and adsorption modes are already unequivocally defined, although for clarity the L and D tags are added defining whether the L-or D-aspartic acid enantiomer is considered. Figure 2 the initial example of the D-NH 2 -2-COOH-3-CH 2 COOH-UT case.

See in
The adsorption energy of D/L-aspartic acid on the Cu(3,1,17) S chiral surface, E ads , is defined as where the isolated L-aspartic acid energy, E L-Asp , was calculated Γ-point placed in an asymmetric cell of 12×13×14 Å dimensions, ensuring 10 Å of vacuum in between periodically repeated cells and variations below 0.01 eV when using larger cells. Note that the same reference is used for D-aspartic acid adsorption as E D-Asp = E L-Asp , as explained above.

Enantioselective Adsorption
The obtained adsorption energies, either gained from PBE or PBE-D2 optimizations, are listed in Table 1. Notice that some values are not reported, belonging to cases where the adsorption lead to a molecular disaggregation, not observed in the experiments, 13 or to a weak adsorption conformation (physisorption), also not detected in the experiments. 13 In this last sense, conformations with a difference in adsorption energy with respect the most stable situation higher than 100 kJ mol -1 have been disregarded. The results in Table 1 show enantiomeric preferences, in accordance to experiments, 13 but, when considering PBE results, the preference is for L-aspartic acid instead of the experimentally observed D-preference. 13 Explicitly, the most stable situation is the L-H-2-NH 2 -3-COOH-LT case, while the closest situation in energetic stability preference for D-aspartic acid is the D-COOH-2-H-3-CH 2 COOH-LT, with a difference in adsorption energies, ΔE ads , of 22.82 kJ mol -1 /cell. This energetic stability preference is well beyond the above-commented present numerical accuracy of ~0.98 kJ mol -1 /cell, and also beyond the DFT accuracy of ~10 kJ mol -1 .
Therefore, the results do not seem to be computationally or theoretically biased, allowing its later discussion. In the case of the D-aspartic acid, the enantiomer is quite located over the kinked step region, on the UT side. Actually, the interaction is as strong as to slightly bend the molecular framework, allowing the interaction of -CH 2 COOH, -COOH, and -NH 2 groups with the 2, 3, and step ledge positions, respectively. As happened with L-aspartic acid enantiomer, the final three-point contact adsorption differs from the initially sampled D-COOH-2-CH 2 COOH-3-NH 2 -UT position, here involving a lateral displacement and a rotation of the molecule along the -H group axis. Although not apparently critical, it is worth highlighting that there exist intermolecular hydrogen bonds on both L-and D-aspartic acid enantiomers, as found also for other amino acids adsorbed on chiral metal surfaces. 37 In the L-aspartic acid case, there are two, one O···H in between -COOH and -CH 2 COOH groups of vicinal molecules, and another H···N in between -COOH and -NH 2 groups as well, with 2.015 and 1.712 Å lengths, respectively. In the case of D-aspartic acid, there is only one H···N hydrogen bond in between -COOH and -NH 2 groups, with a bond length of 1.865 Å, see Figure S3 in the SI.
A further aspect to consider is whether the distinct adsorption energies for the L-and D-aspartic enantiomers are affected by the ZPE or the experimental conditions, and to what extent. However, the commented experimental reference is based on differences of Gibbs free energies of adsorption, ΔΔG ads , obtained at an equilibration temperature of 460 K, and averaged over different flux ratios of gas phase D-and L-aspartic acid mixtures. 13 Here, ΔΔG ads has been approximated based on the Ab Initio Thermodynamics (AIT) approach. 38   seems clear as well that vibrational aspects of the adsorbed enantiomers, these are, the ZPE correction and the vibrational free energy, are key at trying to quantitatively determine the ΔΔG ads , and, ultimately, the ee performance of the metal chiral surface.

Recognition by Surface Science Techniques
As a last point, the possible distinction of both D/L-aspartic acid enantiomers on the Cu(3,1,17) R&S chiral surfaces is analysed well beyond the previously employed STM imaging, 18 as regularly applied on other species in the past, or the TPD or TPR mediated differentiation of the adsorption strengths. 13 Here we evaluated the quantitative XPS or Photoemission Electron Spectroscopy (PES) detection of such adsorbates, being an extended procedure to characterize and quantify adsorbates in surface science. 39 The Binding Energies  Figure S4 of the SI. On Figure S4 one sees that the PBE upright conformations imply four distinguishable C atoms (a-d), but the similitudes in between L-and Denantiomers would prevent their sole unequivocal identification. The same seems to apply to O 1s signals (e-h), where there would be two overlapped signals in the middle spectrum region. Only N 1s would permit discerning in between the adsorbed L-and D-aspartic acid enantiomer, being their shift in between BEs (ΔBEs) of ~0.5 eV.
However, when dealing with the likely flat adsorption conformations of D/L-aspartic acid as obtained from PBE-D2 optimizations, the situation changes, see Figure 5. In principle, for both enantiomers, the C 1s spectra would have three signals instead of four, with the two highest BE peaks overlapped. The matching between enantiomers is also found for the N 1s

Conclusions
Here the capabilities of modern DFT methods in describing enantioselective adsorption processes are put at stakes, with the ultimate aim of determining whether they are suitable for qualitative or quantitative predictions of enantiomeric resolution on chiral metal surfaces. To this end, the enantioselective adsorption of D/L-aspartic acid on chiral Cu(3,1,17) R&S metal surface is taken as an exemplary textbook case, whose enantiomer difference in Gibbs free energy of adsorption, ΔΔG ads , is known to be of 3.15 ± 0.29 kJ mol -1 . 13 The systematic adsorption of D-and L-aspartic acid enantiomers, carried out on a Cu ( where L-and D-enantiomers signals are spaced by 110 cm -1 , allowing its discrete characterization.

Notes
The authors declare no competing financial interest.     Colour coding as in Figure 2.