High-resolution X-ray diffraction determination of the electron density of 1-(8-PhSC10H6)SS(C10H6SPh-8′)-1′ with the QTAIM approach: evidence for S4 σ(4c–6e) at the naphthalene peri-positions

An extended hypervalent S4 σ(4c–6e) system was confirmed for the linear BS-∗-AS-∗-AS-∗-BS interaction in 1-(8-PhBSC10H6)AS–AS(C10H6BSPh-8′)-1′ (1) via high-resolution X-ray diffraction determination of electron densities. The presence of bond critical points (BCPs; ∗) on the bond paths confirms the nature and extent of this interaction. The recently developed QTAIM dual functional analysis (QTAIM-DFA) approach was also applied to elucidate the nature of the interaction. Total electron energy densities Hb(rc) were plotted versus Hb(rc) − Vb(rc)/2 for the interaction at the BCPs, where Vb(rc) represents the potential energy densities at the BCP. The results indicate that although the data for an interaction in the fully optimized structure corresponds to a static nature, the data obtained for the perturbed structures around it represent the dynamic nature of the interaction in QTAIM-DFA. The former classifies the interaction and the latter characterises it. Although AS-∗-AS in 1 is classified by a shared shell interaction and exhibits weak covalent character, AS-∗-BS is characterized as having typical hydrogen-bond nature with covalent properties in the region of the regular closed shell interactions. The experimental results are supported by matching theoretical calculations throughout, particularly for the extended hypervalent E4 σ(4c–6e) (E = S) interaction.


Introduction
Recent research in our laboratory has been concerned with linear s-type interactions higher than s(3c-4e), which is the classical three-center four-electron s type bonds/interactions. 1 We refer to such interactions as extended hypervalent s(mc-ne) (4 # m; m < n < 2m). 2-7 The s(4c-6e) interaction is the rst to be studied. A  2), 4 (Se, S: 3) 4 and (Se, Se: 4) 2 ] as determined by X-ray crystallographic analysis (see Fig. 2 for the structure of 1 (S, S) determined by the high-resolution X-ray crystallographic analysis). Scheme 1 illustrates the structures of 1-4. A substantial number of compounds containing the s(4c-6e) interaction have been reported. 6, 8,9 Benzene substituents in the 1,2-positions, naphthalene substituents in the 1,8-positions and related systems serve as good spacers for the formation of these interactions. 2-4,10-12 It has been strongly suggested that s(4c-6e) interactions play an important role in the development of high functionalities in materials and also in key processes of biological and/or pharmaceutical activities. 2-4,6-12 Fig. 1 shows the molecular orbitals of E 4 s(4c-6e), which is exemplied in the case of Cl 4 2À (E ¼ Cl). The central A E-A E distance in B E/ A E-A E/ B E should be shorter than the A E/ B E distances in s(4c-6e) even if A E ¼ B E. This expectation is supported by the optimized structure of E 4 2À (E ¼ Cl) (Fig. 1).
Scheme 1 Structures of 1-4. 6), (Se, S: 7) and (Se,Se: 8), aer preparation and structural determination of 8. 13 The static nature of A E 2 B E 2 s(4c-6e) has also been reported for 1-4 based on the observed crystal structures. [13][14][15][16] A E 2 B E 2 s(4c-6e) are also recognized as a form of chalcogen bonding. 17 Thus, the question of how the nature of A E 2 B E 2 s(4c-6e) can be established experimentally arises. The high-resolution X-ray diffraction determination of electron densities of 1 (S, S) would provide a rm basis for the real existence of S 4 s(4c-6e) in 1 (S, S). The quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA), which we proposed recently, 18-22 will support the experimental results by elucidating the dynamic and static nature of S 4 s(4c-6e) from the observed and/or optimized structures of 1 (S, S). It will be easily understood if the interactions can be dened by the corresponding bond paths (BPs) in QTAIM, but we must carefully use the correct terminology with the concept. 23 A basis set system that reproduces the observed structural parameters, particularly for the A E/ B E distances, r( A E/ B E), must be established.
Therefore, this paper is concerned with the observation of the existence of S 4 s(4c-6e) in 1 (S, S) based on the data obtained from high-resolution X-ray diffraction determination of electron densities. The real existence of S 4 s(4c-6e) in 1 (S, S) was conrmed by theoretically elucidating the nature of S 4 s(4c-6e) with QTAIM-DFA. The nature of the interactions was determined by employing the criteria proposed previously when applying QTAIM-DFA to typical chemical bonds and interactions. QTAIM-DFA and the criteria are explained in the ESI in Scheme S1 and S2, Fig. S1 and eqn (S1)-(S6). † The basic concept of the QTAIM approach introduced by Bader 24-26 is also surveyed, which enables us to analyze the nature of chemical bonds and interactions. 27 High-resolution X-ray crystallographic measurement of 1 (S, S) Single crystal high-resolution data (sin(q/l max ) ¼ 1.08Å À1 ) were collected at 100(2) K on a Rigaku FRE+ equipped with VHF Varimax confocal mirrors, an AFC10 goniometer and an HG Saturn724+ detector using Mo-Ka radiation (l ¼ 0.71075Å). The Crystal Clear 3.1 soware 34 was used for data collection and CrysAlisPro 35 for data reduction and Gaussian absorption correction. SORTAV 36 was used to average and merge the sets of intensities. The crystallographic CIF le (CCDC-1811040) is provided in the ESI. † The crystal structure was solved using direct methods and least-squares independent atom renement (IAM) was carried out with the SHELX-2014 (ref. 37) soware package. All nonhydrogen atoms were rened with anisotropic displacement parameters, while all hydrogen atoms were calculated at theoretical positions with U iso ¼ 1.2 (see Fig. 2 for the crystal structure of 1 (S, S) and the crystal data and renement details in Table S1 of the ESI †). This model served as the initial point  for the aspherical atom renement, which was implemented using the Hansen-Coppens formalism 38 as implemented in the XD2016 program. 39 According to this formalism, electron density in a crystal is divided into three components as expressed in eqn (1): where, the rst term is the spherically averaged free-atom Hartree-Fock core contribution, r core , with population parameter P c . The second term is the spherically averaged free atom Hartree-Fock normalized to one electron valence contribution, r valence , with population parameter P v , modied by the expansion/contraction parameter k. The third term represents the deviation of the valence density from spherical symmetry modied by the expansion/contraction parameter k 0 . The deformation is expressed by a density normalized Slater-type radial function R 1 ðk 0 l rÞ modulated by the density normalized, real spherical harmonics angular functions d lmAE (r/r) dened on local axes centered on the atoms and with population parameters P lmAE .
R 1 ðk 0 l rÞ is given by eqn (2), where n(l) $ 1 obeys Poisson's electrostatic equation and values for a l are estimated from the Hartree-Fock optimized single-x exponents of the valence orbital wave function calculated for free atoms. Scattering factors for C, H and S were derived from the wave functions tabulated by Clementi and Roetti. 40 As shown in the literature, the use of default values of n(l) ¼ (4,4,4,4) and a l for second-row atoms (P, S) may lead to ambiguous results. 38,41 Thus, several models described previously 42,43 were tested and nally n(l) ¼ (4,4,6,8) values were used. An identical set of n(l) was used to rene the experimental data of another hypervalent sulfurnitrogen species 44,45 as well as in experimental studies of Lcysteine. 46 The a l parameter was kept constant at 3.851a o À1 . 47 Initially, only the scale factor was rened for all data. Next, accurate positional and displacement parameters for all nonhydrogen atoms were obtained from the high order renement (sin(q/l) > 0.7Å À1 ), while positional and isotropic displacements for hydrogen atoms were rened using low-angle data (sin(q/l) < 0.7Å À1 ). Due to the unavailability of neutron data, all C-H distances were xed to the averaged distances from neutron studies 48 (e.g., d Carom-H ¼ 1.083Å). During the next stages of renement, monopole, dipole, quadrupole, octupole and hexadecapole populations were rened with the single expansion/contraction k parameter in a stepwise manner. The expansions over the spherical harmonics were truncated at the hexadecapolar level [l max ¼ 4] for the sulfur-bonded atoms ( A S, B S, C i , /) and at the octupolar level [l max ¼ 3] for the remaining carbon. Hydrogen atoms were represented by the bond directed dipole. Finally, a single k 0 parameter was rened for all non-hydrogen atoms. Chemically and symmetry related atoms were constrained to share the same expansion/ contraction (k/k 0 ) parameters. Throughout, the multipole renement expansion/contraction parameters (k/k 0 ) of all hydrogen atoms were xed to values k ¼ 1.20 and k 0 ¼ 1.20. This procedure was repeated several times in a block renement until satisfactory convergence was achieved. Chemical constraints for similar atoms were applied at the initial stages of the renements. These constraints were gradually released and the nal model was chemically unconstrained. The electron neutrality condition was imposed on the molecule for the entire renement. Final multipole renement led to a featureless residual density map (Fig. S4 in the ESI †). The overall residual density aer multipole renement with all high order data was À0.24 # V 2 and r # 0.25 eÅ À3 . The multipolar renement details are shown in Table S1 in the ESI. † For further details, see Table S2 in the ESI. †

Methodological details used for calculations
Calculations were performed using the Gaussian 09 program package. 49 Compound 1 (S, S) was optimized with the 6-311+G(d) basis set for S and the 6-31G(d,p) basis sets for C and H. Herein, we refer to this basis set system as A (BSS-A). The Møller-Plesset second order energy correlation (MP2) level was applied to the calculations. 50 The structural parameters optimized with MP2/BSS-A (r( A S, A S) ¼ 2.0730Å and r( A S, B S) ¼ 2.9874Å) were very close to the observed values (r obsd ( A S, A S) ¼ 2.0559(5)Å and r obsd:av ( A S, B S) ¼ 2.9852Å), respectively. Compounds 1-4 were similarly optimized with MP2/BSS-A, where the 6-311+G(d) basis sets were applied to S and/or Se with the 6-31G(d,p) basis sets for C and H. The deformation density map for 1 (S, S) was computed using the Multiwfn program. 51 The QTAIM functions were calculated using the Gaussian 09 program package 49 with MP2/BSS-A. The results were analyzed with the AIM2000 program. 52 Normal coordinates of internal vibrations (NIV) obtained by frequency analysis were employed to generate the perturbed structures. 20,21 A k-th perturbed structure (S kw ) was generated by the addition of the normal coordinates of the k-th internal vibration (N k ) to the standard orientation of a fully optimized structure (S o ) in the matrix representation as shown in eqn (3). The coefficient f kw in eqn (3) was determined to satisfy eqn (4) for an interaction in question. The perturbed structures generated with NIV correspond to the structures in the zero-point internal vibrations, where the interaction distances in question are elongated or shortened to the values given in eqn (4), where r and r o stand for the distances in the perturbed and fully optimized structures, respectively, with a o the Bohr radius (0.52918Å). 16,17,52 N k signicant to ve decimal places was used to predict S kw .
/2 was plotted for data from ve points of w ¼ 0, AE0.05 and AE0.1 in eqn (4) in QTAIM-DFA. Each plot for an interaction was analyzed using a regression curve assuming the cubic function in eqn (5)

Results and discussion
High-resolution X-ray diffraction determination of electron densities for 1 (S, S) Fig. 2 shows the crystal structure of 1 (S, S) determined by highresolution X-ray crystallographic analysis and Table 1 shows selected bond distances, angles and torsional angles. The r obsd ( A S, A 0 S) and r obsd:av ( A S, B S) values were determined to be 2.0559 (8) S is larger than 150 , which is the cut-off value we propose to determine the linearity of these interactions. Accordingly, the B S/ A S-A 0 S/ B 0 S interaction can be well described by the S 4 s(4c-6e) model. Fig. 3 depicts the valence electron density map in the 3b). The deformation density map in the A 0 S A SC 1 plane for 1 (S, S) and the magnied map around the B Fig. 3c and d, respectively. The positive Laplacian map in the A 0 S A SC 1 plane for 1 (S, S) and the magnied map around the B Fig. 4a and b, respectively. The BCPs around B S-*-A S-*-A 0 S-*-B 0 S in 1 (S, S) are expected to be located in the negative area of V 2 r b (r c ). Fig. 5 illustrates the molecular graph of 1 (S, S), which was determined by high-resolution X-ray crystallographic analysis. All the BCPs are detected as expected, including those around B S-*-A S-*-A 0 S-*-B 0 S in 1 (S, S). Two pairs of BPs with BCPs are also detected for the weaker interactions, which are very close to those drawn theoretically and therefore discussed in the theoretical section.
Formation of S 4 s(4c-6e) in 1 (S, S) conrmed based on experimental background The electron distributions can be clearly observed in Fig. 3. The valence electron density map of 1 (S, S) seems to dene (threedimensional) saddle points of r(r) between A S and B S and between A 0 S and B 0 S of 1 (S, S) and the typical saddle point between A S and A 0 S (see Fig. 3a or b). Each saddle point of r(r) between the adjacent S atoms in B S/ A S-A 0 S/ B 0 S should correspond to a BCP on a BP in 1 (S, S) (see also Fig. 5). The enhanced charge density at B S directs toward to the depleted area at A S extending over the backside of the A S-A 0 S bond, as shown in Fig. 3c and d. This shows the contribution of the CT interaction of the n p ( B S)/s*( A S-A 0 S) form. Similar phenomena can be found between B 0 S and A 0 S-A S, which show the CT interaction of the n p ( B 0 S)/s*( A 0 S-A S) form. Such degenerated CT interactions should be analyzed as S 4 s(4c-6e) of the n p ( B S)/s*( A S-A 0 S)) n p ( B 0 S) form, which must be the driving force for the formation of S 4 s(4c-6e) as proposed by our group. The valence electron density maps and the deformation density maps around the B S/ A S-A 0 S/ B 0 S interaction, as shown in Fig. 3, strongly support the formation of linear S 4 s(4c-6e) of the n p ( B S)/s*( A S-A 0 S)) n p ( B 0 S) type in 1 (S, S) based on the experimental treatment. As shown in Fig. 4, three VSCCs (valence shell charge concentrations) appear at each S atom in the B S A S A 0 S ( B 0 S) plane of 1 (S, S). A pair of VSCCs on A S and B S is beginning to merge with each other, which conrms the presence of the A S/ B S interaction. The A 0 S/ B 0 S interaction is similarly conrmed through almost merging between the VSCCs on A 0 S and B 0 S. These results together with the original A S-A 0 S bond also conrm the formation of S 4 s(4c-6e) in 1 (S, S). The linearity of the VSCCs is not very good, which would affect the BPs between the atoms. The differences between the lengths of the BPs (r BP ) and the straight-line distances (R SL ) (Dr BP ¼ r BP À R SL ) are less than 0.0010Å and 0.012-0.013Å for A S-A 0 S and A S/ B S (and A 0 S/ B 0 S), respectively, in 1 (S, S). Therefore, each of the B S/ A S-A 0 S/ B 0 S interactions in 1 (S, S) can be approximated to a linear interaction.
The BCPs on BPs around B S/ A S-A 0 S/ B 0 S in 1 (S, S) are clearly specied in the molecular graph drawn experimentally in Fig. 5 together with that expected for 1 (S, S). Some QTAIM parameters were experimentally determined at the BCPs around B S/ A S-A 0 S/ B 0 S in 1 (S, S) (see the observed values for the QTAIM parameters and that evaluated theoretically with MP2/ BSS-A employing the observed structure of 1 (S, S) in Table 2). Although the A S-A 0 S bond in 1 (S, S) is experimentally classied by the regular CS (r-CS) interactions, the A S/ B S and A 0 S/ B 0 S interactions are shown to exist just on the border area between the pure CS (p-CS) and r-CS interactions (see, Fig. 5 and Table 2).   The values evaluated theoretically employing the observed structure of 1 (S, S) reproduced the experimentally obtained values accurately except for (ħ 2 /8m)V 2 r b (r c ) (¼ H b (r c ) À V b (r c )/2), H b (r c ) and k b (r c ) (¼ V b (r c )/G b (r c )) at the BCP of the A S-A 0 S bond although this deviation does not seem to be very severe. However, the difference in (ħ 2 /8m)V 2 r b (r c ) (¼ H b (r c ) À V b (r c )/2) will greatly affect the classication of A S-A 0 S since the signs are opposite to the values predicted experimentally and the value calculated employing the observed structure of 1 (S, S).
Theoretical basis for the nature of S 4 s(4c-6e) in 1 (S, S) Structure of 1 (S, S) optimized at the MP2 level. Compound 1 (S, S) was optimized with MP2/BSS-A, retaining C 2 symmetry. Table 1 shows selected predicted bond distances, angles and  E), the optimized overall structure of 1 (S, S) can be considered to satisfy the criterion since the A E/ B E interactions are the principle concern for S 4 s(4c-6e).
Deformation density map around B S-*-A S-*-A S-*-B S of 1 (S, S). The deformation density map was drawn theoretically on the B S A S A 0 S plane around the B S-*-A S-*-A 0 S-*-B 0 S interaction of 1 (S, S) in C 2 symmetry, similarly to the case of the experimental approach as shown in Fig. 6. The deformation density map shown in Fig. 6 is (very) similar to that shown in Fig. 3d. The enhanced charge density at B S also directs toward to the depleted area at A S extending over the backside of the A S-A 0 S bond, as shown in Fig. 6. In particular, the CT interaction of the n p ( B S)/s*( A S-A 0 S))n p ( B 0 S) type is also demonstrated theoretically by the deformation density map, which should be analyzed as linear S 4 s(4c-6e) as discussed above. The contribution of the CT interaction of the n p ( B E)/s*( A E-A E))n p ( B E) type in 1 ( A E ¼ B E ¼ S) was evaluated by the second order perturbation of the Fock matrix (E(2)) 56 with MP2/BSS-A, and also those for 2-4 ( A E, B E ¼ S and/or Se). The results are shown in Table S4 of the ESI. † The E(2) values of 13.2-26.1 kcal mol À1 were predicted for 1-4 depending on A E and B E, where s*( A E-A E) contributes much more than the case of n( B E). The S 4 s(4c-6e) nature of the linear S 4 interaction in 1 (S, S) as well as in A E 2 B E 2 s(4c-6e) in 2-4 ( A E, B E ¼ S and/or Se) are theoretically well established. Molecular graph, contour plot, and negative Laplacian around B S-*-A S-*-A 0 S-*-B 0 S in 1 (S, S). Fig. 7 shows the molecular graph, contour plot, and negative Laplacian map for 1 (S, S) calculated with MP2/BSS-A. All BCPs are detected as expected, including those around B S-*-A S-*-A 0 S-*-B 0 S in 1 (S, S). Similarly to the case of the experimental results, BCPs are also detected for the weaker interactions of A S-*-2 0 H with A 0 S-*-2 H and 3 H-*-p 0 C with 3 0 H-*-p C. The former may play an additional role in stabilising the linear B S-*-A S-*-A 0 S-*-B 0 S interaction, while the latter is likely to inuence the specic positions of the phenyl groups through the C Nap -H/p(C 6 H 5 S) interactions. As shown in Fig. 7b, the BCP on A S-*-A 0 S is located in the negative area of V 2 r b (r c ), while those on A S-*-B S are in the positive region. These results indicate that A S-*-A 0 S and A S-*-B S are classied by shared shell (SS) and closed shell (CS) interactions, respectively. Accordingly, these results clearly demonstrate the formation of S 4 s(4c-6e) in 1 (S, S) theoretically. As shown in Fig. 7, the BPs ( A S-*-B S) seem somewhat bent around A S. However, the differences between r BP and the corresponding R SL (Dr BP ¼ r BP À R SL ) are 0.001Å and 0.021Å for Dr BP ( A S, A 0 S) and Dr BP ( A S, B S), respectively, in 1 (S, S) (Table S3 of the ESI †). These results indicate that each of the B S/ A S-A 0 S/ B 0 S interactions in 1 (S, S) can also be approximated as a linear interaction theoretically. The Dr BP values in 5-8 have been discussed elsewhere. 11 The nature of the non-covalent E/E interaction was established for E ¼ S in 1 (S, S) both experimentally and theoretically in this study. The interaction becomes much stronger for E ¼ Se in 4 (Se, Se) based on the theoretical investigations. The results are in accordance with those reported recently 14-16 although the strength of S/S seems to change widely as the structure changes.
Application of QTAIM-DFA to A E 2 B E 2 s(4c-6e) ( A E, B E ¼ S, Se). The QTAIM functions of r b (r c ), H b (r c ) À V b (r c )/2, H b (r c ) and k b (r c ) (¼ V b (r c )/G b (r c )) were evaluated for A E-*-A E and A E-*-B E at the BCPs and Table 2 presents the values obtained. Table 2 also contains the frequencies (n) and force constants (k f ) corresponding to A E-*-A 0 E and A E-*-B E. Fig. 8 shows the plots of H b (r c ) versus H b (r c ) À V b (r c )/2 for the fully optimized data of 1-4 given in Table 2 together with those from the perturbed structures around the fully optimized structures; the perturbed structures were generated with NIV according to eqn (3) and eqn (4). The plots were analyzed according to eqn (S3)-(S6) in the ESI † and the QTAIM-DFA parameters of (R, q) and (q p , k p ) were obtained. Table 2 presents the (R, q) and (q p , k p ) values for A E-*-A E and A E-*-B E in 1-4.
Nature of A S-*-A S and A S-*-B S in 1 (S, S) as dened by q and q p . The nature of A S-*-A S and A S-*-B S in 1 (S, S) was determined using the QTAIM-DFA parameters of (R, q) and (q p , k p ) with the standard values in Scheme S2 of the ESI † as a reference. The q values are for the classication of interactions, which can then be characterized by q p with R being used to sub-divide the covalent interactions. It is instructive to survey the criteria briey in relation to this study. The CS and SS interactions have values of 45 < q < 180 (0 < H b (r c ) À V b (r c )/2) and 180 < q < 206.6 (H b (r c ) À V b (r c )/2 < 0), respectively. The CS interactions are sub-divided into p-CS and r-CS for values of 45 < q < 90 (0 < H b (r c )) and 90 < q < 180 (H b (r c ) < 0), respectively. The q p value plays an important role in characterizing the interactions. In the p-CS region of 45 < q < 90 , when 45 < q p < 90 , the interactions will be vdW type character, while for 90 < q p < 125 , they will be typical HB (t-HB)-type without covalency (q p of 125 corresponds to q ¼ 90 ). 18-21 CT interactions will occur in the r-CS region, where 90 < q < 180 . The t-HB interactions with covalency (t-HBwc) appear in the range of 125 < q p < 150 (90 < q < 115 ). CT-MC (molecular complex through charge transfer) and CT-TBP (trigonal bipyramidal adduct through CT) type interactions will appear in the ranges of 150 < q p < 180 (115 < q < 150 ) and 180 < q p < 190 (150 < q < 180 ), respectively, although CT-TBP was not observed in this study. R provides a way to sub-classify the SS interactions, where the classical covalent SS chemical bonds are weak (Cov-w) when R < 0.15 au.
The (q, q p , R) values for A S-*-A S in 1 (S, S) are (187.9 , 197.5 , 0.0704 au), which is therefore classied as SS and predicted to have weak covalent nature (SS/Cov-w). Similarly, (q, q p , R) ¼ (93.1 , 117.8 , 0.0075 au) for A S-*-B S, which is therefore classi-ed as r-CS. The interaction is predicted to have t-HB-wc nature irrespective of q p ¼ 117.8 (<125 ) because the q value of 93.1 (>90 ) is superior to q p ¼ 117.8 (<125 ) [q p ¼ 125 corresponds to q ¼ 90 for typical interactions (see Scheme S2 of the ESI †)]. Therefore, A S-*-B S in 1 (S, S) is predicted to have r-CS/t-HB-wc nature overall. The nature of A E-*-A E and A E-*-B E was also predicted for 2-4. The A E-*-A E interactions in 2-4 have SS/Cov-w nature irrespective of the q p value of about 187 for 3 (Se, S) and 4 (Se, Se) since q values (larger than 180 ) are superior to the q p values in the classication. Although A E-*-B E in 2-4 are classied as r-CS interactions based on the criterion of 93 < q < 102 , they are predicted to be of t-HB-wc, t-HB-wc and CT-MC nature, respectively, based on the q p values. These results are summarized in Table 2.

Conclusion
The high-resolution X-ray diffraction determination of electron densities supported by a rigorous theoretical treatment was performed for 1 (S, S). The valence electron density map exhibits (three-dimensional) saddle points of r(r) between A S and B S and between A 0 S and B 0 S. Enhanced charge densities at B S and B 0 S direct toward to the depleted area around A S and A 0 S, respectively, and extend over the backside of the A S-A 0 S bond. The results demonstrate the formation of S 4 s(4c-6e) of the n p ( B S)/s*( A S-A 0 S))n p ( B 0 S) type. This is supported by the valence electron density map(s) and the deformation density maps in the region around B S/ A S-A 0 S/ B 0 S. A pair of VSCCs originating from A S and B S merge with each other conrming the presence of the A S/ B S interaction as well as those on A 0 S and B 0 S forming the A 0 S/ B 0 S interaction. These results together with the conventional A S-A 0 S bond conrm the formation of S 4 s(4c-6e) in 1 (S, S). The formation of S 4 s(4c-6e) is experimentally demonstrated clearly by BPs with BCPs in the molecular graph for B S/ A S-A 0 S/ B 0 S. The A S/ B S and A 0 S/ B 0 S interactions are observed on the border area between the p-CS and r-CS interactions. These experimental results are well supported and rationalised by complementary theoretical calculations.
The dual experimental-theoretical approach provides a solid basis for understanding the behavior of B E/ A E-A 0 E/ B 0 E of E 4 s(4c-6e) not only in 1 (S, S) but also in 2-4. This methodology has previously been applied to 2-(2-pyridylimino)-2H-1,2,4-thiadiazolo[2,3-a]pyridine, 57 for which the behavior of N-E-N s(3c-4e) (E ¼ S, Se and Te) was claried. Compilation of these results makes it possible to conrm the real existence and chemistry of hypervalent and extended hypervalent interactions.

Conflicts of interest
The authors declare no conict of interest.