Hypervalency in Organic Crystals: A Case Study of the Oxicam

Article pubs.acs.org/JPCA

Hypervalency in Organic Crystals: A Case Study of the Oxicam Sulfonamide Group Christian Tantardini,†,‡,⊥ Elena V. Boldyreva,†,‡,∥ and Enrico Benassi*,†,§ †

Novosibirsk State University, Pirogova 2, Novosibirsk 630090, Russian Federation Institute of Solid State Chemistry and Mechanochemistry SB RAS, Kutateladze 18, Novosibirsk 630128, Russian Federation § Scuola Superiore Normale, Piazza dei Cavalieri 7, Pisa 56126, Italy ‡

S Supporting Information *

ABSTRACT: The theoretical charge density of the active pharmaceutical ingredient piroxicam (PXM) was evaluated through density functional theory with a localized basis set. To understand the electronic nature of the sulfur atom within the sulfonamide group, a highly ubiquitous functional group in pharmaceutical molecules, a theoretical charge density study was performed on PXM within the framework of Bader theory. Focus is on developing a topological description of the sulfur atom and its bonds within the sulfonamide group. It was found that sulfur d-orbitals do not participate in bonding. Instead, the existence of a strongly polarized (“ionic”) bonding structure is found through a combined topological and natural bonding orbital analysis. This finding is in stark contrast to longheld theories of the bonding structure of organic sulfonamide and has important implications for the parametrization of calculations using classical approaches.

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INTRODUCTION The sulfonamide group is one of the most widespread chemical groups found in pharmaceutical compounds, present in antibacterials, antiprotozoals, antifungals, nonsteroid antiinflammatories (NSAID), nonpeptidic vasopressin receptor antagonists, and translation initiation inhibitors.1−5 More recently, sulfonamide-containing compounds were shown to be useful as anticancer agents, antiviral HIV protease inhibitors, and in treating Alzheimer’s disease.6−8 In accordance with valence bond theory (VBT), the S−O interaction of the sulfonamide group is often described as being a double bond, thus necessitating that the sulfur atom be hypervalent.9,10 Within VBT, hypervalent atoms violate the octet rule11 through hybridization of the dnsp3 orbitals,9,10 but recent calculations have suggested that d-orbital contributions are artifacts of polarization functions in the selected basis set.12−23 Most recently, the S−O bond in inorganic compounds was shown using Bader theory to be a highly polarized covalent bond24 without requiring that the S atom violate the octet rule.11 That said, many compounds that are not classified as being hypervalent under the VBT criteria may be deemed hypervalent within the definition proposed by Musher.25 A particularly prominent family of sulfonamide-containing compounds are the oxicams, a well-known class of NSAIDS.26−34 Oxicams are selective inhibitors for COX-2 and are known to bind to two different target sites.35−37 In the first the sulfonamide oxygens are believed to form a weak hydrogen bond with the backbone oxygen of Ala-527, while in the second the oxicam is believed to interact with a hydrophobic pocket.35−37 There have been numerous computational efforts to deduce the nature of this © 2016 American Chemical Society

interaction, mainly based on classical simulations. These calculations require careful parametrization of molecular parameters, and thus a thorough understanding of molecular structureparticularly for bonding groupsis needed. Previous works have suggested the S−O bond in similar molecules to be more complex than previously believed.17,23 Thus, obtaining a complete understanding of the sulfonamide electronic structure in pharmaceutical molecules is crucial. This work employs a detailed topological analysis of the S−O bonding structure present in piroxicam [PXM; Figure 1], through the framework of Bader’s quantum theory of atoms in molecules (QTAIM).38−40 In recent years, a related topological tool, the source function (SF), was shown to give a feasible description of subtle electron-delocalization effects that determinate the molecular and crystal properties41−51 and recently was also extended to plane waves (PW) to study periodic systems.52 Its combination with traditional QTAIM analysis offers unique means to clarify the electronic structure of sulfonamide.

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COMPUTATIONAL METHODS Atomic positions were optimized using PW density functional theory (DFT), and all lattice constants were held at their experimental values. The PW86PBE53,54 exchange-correlation function was used in combination with the exchange-hole dipole moment (XDM)55−57 dispersion correction, employing Received: October 24, 2016 Revised: December 6, 2016 Published: December 8, 2016 10289

DOI: 10.1021/acs.jpca.6b10703 J. Phys. Chem. A 2016, 120, 10289−10296

Article

The Journal of Physical Chemistry A

calculations. The integration grid for the electronic density for topological analyses was set to 150 radial shells and 974 angular points. For the remaining calculations, the integration grid was set at 99 radial shells and 590 angular points. Convergence criteria of the self-consistent field was set to 1 × 10−12 for RMS change in the density matrix and 1 × 10−10 for maximum change in the density matrix. Convergence criteria for optimizations were set to 2 × 10−6 bohr for maximum force, 1 × 10−6 bohr for RMS force, 6 × 10−6 bohr for maximum displacement, and 4 × 10−6 bohr for RMS displacement. An initial topological search for bond critical points (BCPs) was performed along the bond paths between sulfur and its directly bonded atoms, and the charge density (ρ) in each BCP was compared between the different theoretical approaches. The SF % values coming from sulfur and its directly bonded atoms were also analyzed and compared across the series of computational methods. It is clear, Table E.S.I.2, that the quality of results is independent of the method used. DFTbased approaches are therefore sufficient to accurately describe the topology of sulfonamide-containing molecules. Crystallographic data were taken from the Cambridge Crystallographic data Centre (CCDC; reference code: BIYSEH0673) and employed as an initial geometrical guess for the quantum chemical calculations. Condensed and gas-phase calculations were performed using Quantum Espresso v5.474 and Gaussian G09.D1,75 respectively. For the Bader analysis, a modified version of the PROAIMV software76,77 was used.

Figure 1. PXM molecule coming from crystal structure.

damping factors a1 = 0.6836 and a2 = 1.5045. The fully optimized structure differs from the experimental structure with root-mean-square (RMS) less than 2%,validating the DFT approach used. Subsequently, the resulting molecular structure was extracted and investigated using a localized basis set (LBS) for the isolated gas-phase molecule. Calculations were performed across a range of DFT functionals to ensure a reliable description of the system: B3LYP,58 CAM-B3LYP,59 M06-2X,60 PBE,53,61 PBE0,62 LC-ωPBE,63−65 and ωB97XD.66 The same investigation was also performed by means of the second-order Møller−Plesset perturbation theory (MP2).67−71 The 6-31+G** basis set was used in all cases. Among all tested functionals, the B3LYP functional proved to be the more robust method for this system (see E.S.I.5 table). To increase the accuracy of the subsequent Bader analysis, a PROAIM72 wave function was calculated with B3LYP/6-311+G** for the isolated gas-phase molecule. As the basis functions (or orbitals) decay exponentially with distance from the core, the extraction of a single molecule from the crystal structure is reasonable. Any perturbation from the weak noncovalent interactions is negligible. By accepting these negligible errors, it becomes possible to employ an LBS for the study of charge density; thus, the results obtained here are directly relatable to the solid state. Loss of core−shell information by implementation of a pseudopotential can lead to erroneous results when core− shell electrons are explicitly involved in the process being investigated. A test molecule, methanesulfonamide (IUPAC name; Figure E.S.I.1) was used to compare QTAIM results from a DFT and coupled cluster (CC) based approach. Because of the size of the PXM molecule, a full CC-based approach is unfeasible; thus, assessing the accuracy of computationally affordable method is necessary. PROAIM wave functions were generated in vacuum using a 6-311+G** LBS using the B3LYP hybrid DFT functional, as well as the coupled cluster for single and double excitation (CCSD), and quadratic configuration integration for single and double excitation (QCISD)

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RESULTS AND DISCUSSION The atomic valence shell has been amply studied for the atoms composing sulfonamide, and variations in their charge density have been correlated to their atomic behavior. Within the framework of the valence shell charge concentration (VSCC),39 it is typical to consider the function L(r) = −∇2ρ. Maximum critical points (CPs) in L(r) therefore correspond to local accumulations of charge density, whereas minimum CPs indicate local depletions of charge density. If a maximum CP sits along a bond path,39 it can be described as a bond maximum (BM), whereas all other maximum CPs are nonbonding maxima (NBM).39 It follows that a study of the CP structure within an atomic valence shell can offer an initial indication as to the nature of its bonding structure. In this study, the analysis was done for all atoms of the sulfonamide group in PXM, with particular focus on the atoms bonded to sulfur: two oxygen atoms, O1 and O2, a nitrogen atom, N1, and a carbon atom, C1 [Figure 2]. Note that all calculations referred to in the following text relate to gas-phase electron densities. Interpretation of the location of these CPs through the framework of molecular orbital theory then allows identification of the atomic hybridization state. As expected, all four atoms bonded to S1 have a BM along their respective bond paths.39 VSCC analysis for N1 revealed three BMs, with the N1 nucleus sitting above their plane. Within the framework of VBT, this CP construction is consistent with three hybridized sp2 orbitals. Two NBMs are also found on opposite faces of the above-mentioned BM plane, indicating the residual lone pair of the nonhybridized pz orbital. This assignment of N1 hybridization is consistent with that found previously in planar SNx.78 The C1 nucleus belongs to an aromatic system; thus, the lack of NBMs for its pz orbital is not surprising and is due to delocalization of these electrons throughout the π-interaction 10290


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1) CP is found in the proximity of the VSCC region, opposite the BM. This (3,−1) CP has a value of ∇2ρ ≃ − 2.79 e/bohr5 comparable to that of the other values of ∇2ρ at the NBMs; it is therefore indicative of important charge density concentration [Figure 2]. A (3,−1) CP of ∇2ρ indicates a curvature of the surface of atomic basin39 giving an information on sphericity of VSCC region opposite the BM.39 The distribution of CPs within the VSCC of each oxygen atom, Figure 2C, is consistent with both the presence of a double covalent bond and with a strongly polarized (“ionic”) S−O interaction. The latter respecting the octet rule, avoiding the involvement of sulfur d-orbitals as previously suggested by Schmøkelet et al.24 and Ponec et al.79 for related inorganic compounds. Thus, a more sophisticated topological investigation was required. It is worth noting that regardless of the d-orbital involvement, the sulfur atom studied here is hypervalent within the extended definition provided by Musher,25 where it is classified as an HV1-type hypervalent species. This contrasts the alternative Pauling definition,9 which requires participation of d-orbitals; a definition by which the sulfur atom remains nonhypervalent. Having obtained a general overview of the bonding structure through VSCC analysis, it becomes noteworthy to delve deeper into the structure of individual bonds. Analysis of the ellipticity39 ε along each bond path can be used to validate the traditional picture obtained through VSCC. Defined as

Figure 2. (A) Picture of VSCC CPs of atoms bonded to sulfur atom into PXM sulfonamide group: NBM (turquoise). BM (gray), and in addition the BCP (purple). (B) Enlargement of O1 with values of charge density, ρ (e/bohr3), Laplacian of charge density, ∇2ρ(e/ bohr5); at CPs, the (3,−1) is in blue.(C) L(r) function map cut in the O2−S1−O1 plane of the PXM molecule. Dotted blue lines mark a positive L(r) function, whereas solid red lines mark regions of negative L(r).

with the closest pz orbitals of the aromatic system.39 Both O1 and O2 have two NBMs, sitting nearly perpendicular to the SO2 plane. An oxygen atom that is bonded via a double covalent bond to another atom must be sp2 hybridized. For such a case, one expects two NBMs corresponding to the other sp2 hybridized orbitals, each containing a pair of electrons. The repulsion between the nonhybridized p-electron and the lone pairs is reduced on formation of the π-bond, and the lone pairs sit nearly perpendicular to one another, rather than the 120° expected for sp2 hybridization. In addition, this sp2-hybridized oxygen atom should have one BM along the double covalent bond corresponding to the other hybridized sp orbital. In PXM, a BM and two NBMs are observed and located ca. 0.35 Å from the two oxygen nuclei (i.e., within the valence shell), and a (3,−

ε = (λ1/λ 2) − 1

(1)

where λ1 and λ2 are the eigenvalues of the Laplacian of charge density normal to the bond path, the ellipticity describes a bond’s deviation from sphericity. This value can be used to discern the bond order of selected interactions. In particular, as the ellipticity approaches 0, there is a high level of sphericity, indicating a single or triple bond. In contrast, large deviations from 0 are indicative of double-bond structure and should be expected for the S−O bond structure proposed in the literature.6−27 Surprisingly, the ellipticity across each S−O bond sits close to 0 for each S−O BCP, significantly less than what would be expected for a double bond32 (see E.S.I.6 Figure).

Figure 3. Profiles of L(r) along the S−O1 (black) and S−O2 (red) bonds within PXM. The dots marks the position of the BCP. 10291


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atomic basin with LS(r′) > 0 donates charge density. The presence of a sulfur valence shell that depletes charge density from the BCP alongside an oxygen valence shell that donates charge density to the same BCP reflects an “ionic” interaction.42,46−48 It is evident from QTAIM atomic charges that there is a sizable charge separation between the S (+2.84) and O atoms (−1.27 and −1.25 for O1 and O2, respectively). It can thus be suggested that formal charges of S2+ and O1− can be assigned and are in agreement with the closed-shell interaction suggested by Cioslowski and Surjan for little test molecules containing sulfone and sulfoxide groups.19 We note that this confirms the initial VSCC interpretation, which was based solely on the geometric distribution of electron density. Further, to avoid any doubts about the nature of the S−O interaction, a gedankenexperiment, in line with those of Schmøkelet et al.,24 was performed. The variation of SF% and the delocalization indices at the BCP were monitored as a function of S−O bond length. The delocalization index δ(I,J) correspond to number of electron pairs that interact between atomic basins I and J.40 Tables 2 and 3 show the SF% values for S1 and O1 (2) atoms calculated at the S−O BCP as a function of d(S···O). With increasing S−O bond distance, SF% contribution of sulfur increases, whereas that for oxygen decreases. Instead, on decreasing the S−O distance, the opposite occurs. Following the delocalization index as a function of bond distance reveals an increase in electron exchanging between the S and O atoms on elongating the S−O bond. Instead, a decrease of electron exchange between the oxygen atoms is observed on decreased S−O bond distance. The picture described by this test agrees with a strongly polarized (“ionic”) S−O interaction, where sulfur adopts a positively charged state and where oxygen adopts a negatively charged state. On decreasing the S−O internuclear distance, oxygen contribution to the BCP increases and that of sulfur decreases. This likely stems from a reduction in the polarity of the bond on shortening. In case of double covalent bond, with the increasing S−O bond distance the atoms lose the capability to share electrons, and both their delocalization index δ(S, O) and SF% values correspondingly decrease. On the contrary, when the bond is compressed, the delocalization index δ(S, O) and SF% values increase. The covalent behavior described before is due to synergistic bonding interactions of a σ-bond and π-bond, with overlap between the S−O pπ−pπ orbitals. This derives from the fact that, in a shared shell interaction, the increase of bond strength is associated with a decrease of bond distance.39 An S− O ionic interaction, demonstrated through Bader analysis, is indeterminate as to the role of d-orbital contributions. The presence of an S−O ionic interaction does not inherently exclude the ability of sulfur to expand its valence shell. Thus, to complete the investigation natural bond orbital analysis81−86 (NBO) was performed, showing a d-orbital contribution of less than 2% for S. This minor contribution is a computational artifact, resulting from addition of polarization functions in the basis set (Figure 5; see E.S.I.6 for the complete NBO analysis). Through a combination of Bader analysis and NBO calculations, it is clear that the S−O interactions in the common organic sulfonamide group display a highly polarized (what is commonly defined as ionic) character, with no participation of d-orbitals.

This simple analysis of bond symmetry only allows one to refute the possibility of a covalent double bond; however, confirmation of the bond nature requires deeper investigation. As shown by Bader (1990)39 and Espinosa (2002),80 by studying the profile of L(r) along the S1−O1 and S1−O2 bond paths, and with knowledge of BCP location, one can deduce considerable information as to the nature of the S−O bonds. The profiles of L(r) highlight the valence shell structure of each atom, and the S−O1 and S−O2 BCPs are located within the sulfur valence shell [Figure 3]. This corresponds to charge transfer from the sulfur to the oxygen atomic basin, defined as the region of space belonging to an atom. This, in addition to L(r) values of −0.998 and −0.957 e/bohr5 at the S1−O1 and S1−O2 BCPs, respectively, strongly supports a closed-shell interaction. The small asymmetry between the results of S1− O1 and S1−O2 is likely attributed to the differences in the geometries of these two bonds coming from PW atomic optimization within the crystal of these two bonds (see E.S.I.5 picture with the bond distances to three decimal places order into sulfonamide group). The updated model proposed through consideration of L(r) analysis offers a possible alternative to the S−O bonding structure, supporting the existence of a strongly polarized (“ionic”) interaction. To ensure consistency in this new model, calculation of the SF is necessary.41,42 Within the framework of QTAIM, the SF offers a means through which to decompose a BCP into contributions from individual atoms. In doing this, it becomes possible to build a more physical picture of the sulfurbased interactions in PXM. The difference of percentage contribution between directly bonded sulfur and oxygen atoms to their BCP is 17.47% and 17.56% for S1−O1 and S1−O2 BCPs, respectively. Such a large difference suggests an “ionic” nature of the S−O1 and S−O2 bonds. The two oxygen atoms contribute more to the S1−N1 BCP than the S1−C1 BCP, Table 1, and are likely due to the increased polarization of the Table 1. SF% Contributions at the BCPs of Atoms Bonded at S within the PXM Crystal Structure at the Equilibrium bond

ρ, e/bohr3

S

O1

O2

N

C

tota

S− O1 S− O2 S− N1 S− C1

0.294 08

32.99

50.46

7.03

2.36

0.92

93.77

0.293 47

32.83

7.03

50.39

2.42

0.90

93.56

0.229 92

34.56

8.21

8.33

37.33

1.14

89.58

0.209 99

33.82

6.28

6.29

2.00

37.03

85.42

a

tot is the total SF% values from the SF% values of atoms reported in this Table.

former. The S1−N1 bond is a highly polarized covalent bond, as indicated by SF% values, consistent with the literature.13 Instead the S1−C1 covalent bond is only slightly polarized. The considerable electron sharing of C1 density into the aromatic ring makes C1 unable to participate in the sulfonamide bonding system. The influence of O1 to its BCP and to the S1−O2 BCP (and O2 on its BCP and on the S1−O1 BCP) is clear by consideration of the local source (LS; Figure 4).40,41 These plots show the local effect of a generic point r′ to point r. Sulfur and oxygen basins participate in opposite ways to their BCPs: the valence shell of the sulfur atomic basin with LS(r′) < 0 depletes charge density, whereas the valence shell of the oxygen 10292


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Figure 4. LS(r′) maps cut in the O2−S1−O1 plane of the PXM molecule evaluated on S−O1 BCP (left) and S−O2 BCP (right). Dotted blue lines mark negative LS(r′), whereas solid red lines mark regions of positive LS(r′). The BCP is marked with a black dot.

Table 2. SF%, Charge Density (ρ), Delocalization Indexes δ(S,O1) and δ(O1,O2), and QTAIM Atomic Charge Q(O1) Contributions to the S−O1 BCP of Sulfonamide Group into PXM at the Equilibrium (in Italics), Shortened and Elongated Bond Distance distance

ρ, e/bohr3

S1

O1

O2

δ(S,O1)

δ(O1,O2)

Q(O1)

1.41 1.43 1.45 1.47 1.49

0.308 32 0.298 67 0.293 47 0.285 55 0.277 56

34.03 34.58 34.73 35.36 36.24

52.58 51.98 50.70 49.91 49.19

7.29 7.14 6.88 6.70 6.50

1.110 1.129 1.148 1.168 1.188

0.248 0.242 0.236 0.231 0.226

−1.328 −1.299 −1.270 −1.238 −1.205

Table 3. SF%, Charge Density (ρ), Delocalization Indexes δ(S,O2) and δ(O1,O2), and QTAIM Atomic Charge Q(O2) Contributions to the S−O2 BCP of Sulfonamide Group into PXM at the Equilibrium (in Italics), Shortened and Elongated Bond Distance distance

ρ, e/bohr3

S1

O1

O2

δ(S,O2)

δ(O1,O2)

Q(O2)

1.41 1.43 1.45 1.47 1.49

0.307 46 0.297 92 0.289 02 0.285 04 0.277 12

33.81 34.40 35.06 35.27 36.08

7.29 7.14 6.98 6.69 6.50

52.55 51.96 51.31 49.85 49.12

1.121 1.140 1.160 1.180 1.200

0.248 0.242 0.236 0.231 0.226

−1.311 −1.282 −1.252 −1.220 −1.185

electronic contribution to chemical bonding. We stress that the aim of the present work is not to state whether the sulfur atom should be defined as hypervalent or not, which clearly depends on the definition one chooses. Instead, it is the aim of the present contribution to understand the valence shell structure of sulfur within an organic sulfonamide group and whether one must consider d-orbital participation conjectured by Pauling.9 The concept of hypervalency proposed by Musher25 continues to be valid also when d-orbitals are not involved in the bonding, as shown by Ponec et al.79 The participation of d-orbitals revealed through NBO analysis is artificial and the result of polarization functions being added in the basis set. In the present study, initial VSCC analysis suggests a traditional double covalent bond with an sp2-hybridized oxygen atom. This was subsequently disproven through a deepened topological analysis, supporting the possibility of a S−O ionic interaction. This refutes participation of d-orbitals. An analysis of L(r) function profiles along the S−O bond paths showed a BCP located within the sulfur valence shell, having a negative sign. The large differences of 17.47% (S−O1) and 17.56% (S−O2) between the respective SF% contributions of S and O are feasible for a closed-shell interaction. The QTAIM atomic charges show a high charge separation between S and O atoms. The gedankenesperiment of squeezing and elongating the S−O internuclear distance confirmed the existence of a highly polarized (ionic) bond. Furthermore, the NBO analysis allowed

Figure 5. Bond orbital composition for sulfur bonding into sulfonamide bonds: S1−N1, S1−C1, S1−O1, and S1−O2. The s(blue), p- (red), and d- (green) orbital contributions are shown. The d-polarization function leads to consistent d-orbital contribution to each bond.

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CONCLUSIONS The theoretical charge density of PXM was evaluated through DFT with LBS, allowing consideration of an all-electron system. This allowed consideration of the influence of each 10293


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us to discard the presence of sulfur d-orbitals in S−O bonds, showing only the presence of its s and p-orbitals. Thus, the picture of the S−O double covalent bond has been replaced by a new picture. Instead of involving d-orbitals, the sulfur atom donates one electron to each directly bonded oxygen atom, leaving the sulfur atom with a formal 2+ charge. The sulfonamide group is therefore not purely covalent as previously assumed but instead adopts an ionic-like structure. The sulfonamide group therefore has considerably larger charges than previously suspected, and parametrization for such groups is required for correct modeling of its interactions.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b10703. Illustrated test molecule, tabulated charge density and SF % values, tabulated SCF electronic energies, profiles of ellipticity, bond distances illustrated in sulfonamide group and associated VSCC with CPs of atoms bonded to S, tabulated NBO analysis (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Christian Tantardini: 0000-0002-2412-9859 Present Addresses ∥

E-mail: [email protected]. (E.V.B.) E-mail: [email protected]. (C.T.)

⊥

Author Contributions

The manuscript was written only through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding

C.T. and E.V.B. acknowledge financial support from Russian Ministry of Education and Science, Project No. 1828. E.B. thanks the Italian “Ministero per l’Università e la Ricerca Scientifica e Tecnologica” for fundings [FIRB 2013, RBFR13PSB6]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank A. A. L. Michalchuk for helping with editing and discussions. C.T. would like to thank Dr. G. Saleh, Dr. L. Lo Presti, and Dr. C. Gatti for useful discussions. This work was performed using the equipment of Siberian Supercomputer Center ICMMG SB RAS and “Supercomputing Center of the Novosibirsk State University” (http://nusc.nsu.ru).

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