QTAIM Dual Functional Analysis Research Articles

Intrinsic dynamic and static natures of APn--X+--BPn σ(3c-4e) type interactions (APn = BPn = N, P, As and Sb; X = H, F, Cl, Br and I) in bicyclo[3.3.3] and bicyclo[4.4.4] systems and their behaviour, elucidated with QTAIM dual functional analysis.

The intrinsic dynamic and static natures of APn--X+--BPn (APn = BPn: N, P, As and Sb; X = H, F, Cl, Br and I) in 1a+-8c+ were elucidated with the quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA). Species 1a+-8c+ were formed by incorporating X+ between APn and BPn of APn(CH2CH2CH2)3BPn (1-4) and APn(CH2CH2CH2CH2)3BPn (5-8). The relative stabilities between the symmetric and nonsymmetric structures along with their transition states were investigated. Various natures from typical hydrogen bonds (t-HB) to classical covalent bonds were predicted for the APn-X/BPn-X interactions in APn--X+--BPn with QTAIM-DFA. The secondary interactions of H-H and X-C were also detected. The vdW to molecular complexes through charge transfer natures were predicted for them. Natural bond orbital analysis clarified that the CT terms were caused by not only n(APn)→ σ*(X-BPn) but also σ(APn-C)→σ*(X-BPn), σ(APn-C/BPn-C)→np(X+) and n(X)→ns(Pn+). The direction and magnitude of the p-character of n(APn) were the factors that determined the types of donor-acceptor interactions. Estimating the order of the interaction strengths was attempted. The σ(3c-4e) characters of APn--X+--BPn were also examined by analysing the charge distributions on APn--X+--BPn. These results would provide fundamentally important insight into designing molecules with high functionality containing X+ in symmetric and nonsymmetric structures.

Extremely stable system of 1-haloselanyl-anthraquinones: experimental and theoretical investigations.

Highly stable selanyl halides, 1-ATQSeX (X = I (1), Br (2) and Cl (3)), were prepared. The structures of 1, 2, 6 (1-ATQSeX: X = Me) and 7 (1-ATQBr) were determined. QC calculations were performed on 1-3, 4 (X = F), 5 (X = H), 6, 7 and 8 (X = SeATQ-1). The O⋯Se distances in 1-4 from the sum of the vdW radii of the atoms (Δr(Se, O1)) were less than -1 Å, in magnitude, which must be the driving force for the high stability. The O-*-Se interactions seem stronger in the order of 1 < 2 < 3 < 4. The intrinsic dynamic and static natures of O⋯Se and/or Se⋯X in 1-8 are elucidated by QTAIM dual functional analysis (QTAIM-DFA). The Se-*-I, Se-*-Br, Se-*-Cl and Se-*-F interactions in 1-4 are predicted to have the natures of covalent, TBP with CT, TBP with CT, and typical HB with covalency, respectively, whereas O-*-Ses in 1-4 are all predicted to have the nature of MC with CT. The Se-*-H, Se-*-CMe and Se-*-Se interactions in 5, 6 and 8 are all predicted to have the covalent nature, while O-*-Ses in 5, 6 and 8 are all predicted to have the nature of typical HB with no covalency. The E(2) values of 1-6 and 8 are calculated with NBO analysis, and correlate excellently with Δr(Se, O1), except for Se-*-F, for which E(2) is evaluated to be much larger. The E(2) values also correlate very well with Cii-1 for all Se-*-X in 1-4, although data from 5, 6 and 8 deviated from the correlation, where Cii is the diagonal element of the compliance (force) constant for the internal vibrations. The behaviour of the interactions is further examined based on the QTAIM-DFA parameters of θ and θp. The stabilizing effect is further confirmed by the calculations with the ν(CO) values analyzed carefully.

Dynamic and Static Nature of XH-∗-π and YX-∗-π (X = F, Cl, Br, and I; Y = X and F) in the Distorted π-System of Corannulene Elucidated with QTAIM Dual Functional Analysis.

The dynamic and static nature of the XH-∗-π and YX-∗-π (X = F, Cl, Br, and I; Y = X and F) interactions in the distorted π-system of corannulene (π(C20H10)) is elucidated with a QTAIM dual functional analysis (QTAIM-DFA), where asterisks emphasize the presence of bond critical points (BCPs) on the interactions. The static and dynamic nature originates from the data of the fully optimized and perturbed structures, respectively, in QTAIM-DFA. On the convex side, H in F-H-∗-π(C20H10) and each X in Y-X-∗-π(C20H10) join to C of the central five-membered ring in π(C20H10) through a bond path (BP), while each H in X-H-∗-π(C20H10) does so to the midpoint of C=C in the central five-membered ring for X = Cl, Br, or I. On the concave side, each X in F-X-∗-π(C20H10) also joins to C of the central five-membered ring with a BP for X = H, Cl, Br, and I; however, the interactions in other adducts are more complex than those on the convex side. Both H and X in X-H-∗-π(C20H10) (X = Cl and Br) and both Fs in F-F-∗-π(C20H10) connect to the three C atoms in each central five-membered ring (with three BPs). Two, three, and five BPs were detected for the Cl-Cl, I-H, Br-Br, and I-I adducts, where some BPs do not stay on the central five-membered ring in π(C20H10). The interactions are predicted to have a vdW to CT-MC nature. The interactions on the concave side seem weaker than those on the convex side for X-H-∗-π(C20H10), whereas the inverse trend is observed for Y-X-∗-π(C20H10) as a whole. The nature of the interactions in the π(C20H10) adducts of the convex and concave sides is examined in more detail, employing the adducts with X-H and F-X placed on their molecular axis together with the π(C24H12) and π(C6H6) adducts.

Inverse Versus Normal Behavior of Interactions, Elucidated Based on the Dynamic Nature with QTAIM Dual-Functional Analysis.

In QTAIM dual-functional analysis, Hb(rc) is plotted versus Hb(rc) - Vb(rc)/2 for the interactions, where Hb(rc) and Vb(rc) are the total electron energy densities and potential energy densities, respectively, at the bond critical points (BCPs) on the interactions in question. The plots are analyzed by the polar (R, θ) coordinate representation for the data from the fully optimized structures, while those from the perturbed structures around the fully optimized structures are analyzed by (θp, κp). θp corresponds to the tangent line of the plot, and κp is the curvature; θ and θp are measured from the y-axis and y-direction, respectively. The normal and inverse behavior of interactions is proposed for the cases of θp > θ and θp < θ, respectively. The origin and the mechanism for the behavior are elucidated. Interactions with θp < θ are typically found, although seldom for [F-I-∗-F]-, [MeS-∗-TeMe]2+, [HS-∗-TeH]2+ and CF3SO2N-∗-IMe, where the asterisks emphasize the existence of BCPs in the interactions and where [Cl-Cl-∗-Cl]- and CF3SO2N-∗-BrMe were employed as the reference of θp > θ. The inverse behavior of the interactions is demonstrated to arise when Hb(rc) - Vb(rc)/2 and when the corresponding Gb(rc), the kinetic energy densities at BCPs, does not show normal behavior.

Synthesis, structures and reactions of acylsulfenyl iodides with theoretical investigations

A series of acylsulfenyl iodides (RCOSI) were synthesized by the reactions of carbothioic acid group 11-16 element derivatives with iodine or N-iodosuccinimides in moderate to good yields. The structure of the PhCOSI was nearly square planar based on the X-ray analysis, where the C[double bond, length as m-dash]O⋯I distance (3.153(5) Å) was significantly shorter than the sum of the van der Waals radii of the atoms (Σr vdW), indicating close contact within the molecule. The distances between an iodine atom and the neighbouring two iodine atoms were also less than Σr vdW, perhaps due to the energy lowering effect of the interactions. The acylsulfenyl iodides readily reacted with alkenes and alkynes to give the expected addition products in moderate to good yields at approximately 0 °C. A new synthesis of acylated sulfines, sulfenamides and sulfenochalcogenides using acylsulfenyl iodides is also described. Theoretical calculations were performed on PhCOSI with the Sapporo-TZP(+1s1p) basis sets at the MP2 level, which perfectly reproduced the observed structures. Similar calculations were performed on the reactions, exemplified by those of MeCOSI and CH2[double bond, length as m-dash]CH2, together with those of MeSI and CH2[double bond, length as m-dash]CH2. Mechanisms for both reactions were proposed, which were very similar. The proposed mechanism for the former was understood based on that of the latter. For both mechanisms, the episulfuranes and episulfonium ions played an important role. The dynamic and static nature of the bonds in the COSI group of PhCOSI and MeCOSI were elucidated based on QTAIM dual functional analysis.

Intrinsic Dynamic and Static Nature of π···π Interactions in Fused Benzene-Type Helicenes and Dimers, Elucidated with QTAIM Dual Functional Analysis.

The intrinsic dynamic and static nature of the π···π interactions between the phenyl groups in proximity of helicenes 3–12 are elucidated with the quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA). The π···π interactions appear in C-∗-C, H-∗-H, and C-∗-H, with the asterisks indicating the existence of bond critical points (BCPs) on the interactions. The interactions of 3–12 are all predicted to have a p-CS/vdW nature (vdW nature of the pure closed-shell interaction), except for 2Cbay-∗-7Cbay of 10, which has a p-CS/t-HBnc nature (typical-HBs with no covalency). (See the text for definition of the numbers of C and the bay and cape areas). The natures of the interactions are similarly elucidated between the components of helicene dimers 6:6 and 7:7 with QTAIM-DFA, which have a p-CS/vdW nature. The characteristic electronic structures of helicenes are clarified through the natures predicted with QTAIM-DFA. Some bond paths (BPs) in helicenes appeared or disappeared, depending on the calculation methods. The static nature of Ccape-∗-Ccape is very similar to that of Cbay-∗-Cbay in 9–12, whereas the dynamic nature of Ccape-∗-Ccape appears to be very different from that of Cbay-∗-Cbay. The results will be a guide to design the helicene-containing materials of high functionality.

Intrinsic Dynamic and Static Nature of Halogen Bonding in Neutral Polybromine Clusters, with the Structural Feature Elucidated by QTAIM Dual-Functional Analysis and MO Calculations.

The intrinsic dynamic and static nature of noncovalent Br-∗-Br interactions in neutral polybromine clusters is elucidated for Br4–Br12, applying QTAIM dual-functional analysis (QTAIM-DFA). The asterisk (∗) emphasizes the existence of the bond critical point (BCP) on the interaction in question. Data from the fully optimized structures correspond to the static nature of the interactions. The intrinsic dynamic nature originates from those of the perturbed structures generated using the coordinates derived from the compliance constants for the interactions and the fully optimized structures. The noncovalent Br-∗-Br interactions in the L-shaped clusters of the Cs symmetry are predicted to have the typical hydrogen bond nature without covalency, although the first ones in the sequences have the vdW nature. The L-shaped clusters are stabilized by the n(Br)→σ*(Br–Br) interactions. The compliance constants for the corresponding noncovalent interactions are strongly correlated to the E(2) values based on NBO. Indeed, the MO energies seem not to contribute to stabilizing Br4 (C2h) and Br4 (D2d), but the core potentials stabilize them, relative to the case of 2Br2; this is possibly due to the reduced nuclear–electron distances, on average, for the dimers.

Linear Multiselenium Interactions in Dicationic Oligomers of 1,5-(Diselena)canes: Behavior of Semc σ(mc c-ne e) (6≤mc ≤16) Elucidated with QTAIM Dual Functional Analysis.

The intrinsic dynamic and static nature m c center‐n e electron interactions of the σ‐type σ(m cc‐n ee) were elucidated for the Se‐Se interactions in dicationic oligomers of Se(CH2CH2CH2)2Se (1 (Se, Se)) [n 2+ (Se, Se): n=1–8], especially for m c≥6, where n 2+ (Se, Se: n=1–8) are abbreviated by n 2+ (n=1–8), respectively. QTAIM dual functional analysis (QTAIM‐DFA) was applied to the interactions. Perturbed structures generated using coordinates derived from the compliance constants (Cii) were employed for QTAIM‐DFA. Each Se‐*‐Se in 1 2+ and 2 2+ has the nature of CT‐TBP (trigonal bipyramidal adduct formation through CT) and Cov‐w (weak covalent), respectively, which supply the starting points of the investigations. The asterisk emphasizes the existence of a bond critical point on the interaction. All Se‐*‐Se in 3 2+ are classified by the regular closed shell (r‐CS) interactions and characterized as CT‐MC (molecular complex formation through CT), which are denoted as r‐CS/CT‐MC, except for the central interaction, of which nature is r‐CS/CT‐TBP. Most interactions in 4 2+–8 2+ are r‐CS/t‐HBwc (typical‐HB with covalency) but some are pure‐CS/t‐HBnc (t‐HB with no covalency). The linear Se2n 2+ interactions in 2 2+–8 2+ seem close to those without any limitations, since the nature of Se‐*‐Se inside and outside of (CH2CH2CH2)2 are very similar with each other. The linear Se2n 2+ interactions in 3 2+–8 2+ are shown to be analyzed as σ(mcc‐nee: 6≤mc≤16), not by the accumulated σ(3c–4e).

Dynamic and Static Nature of Br4 σ(4c-6e) and Se2Br5 σ(7c-10e) in the Selenanthrene System and Related Species Elucidated by QTAIM Dual Functional Analysis with QC Calculations.

The nature of Br4σ(4c–6e) of the BBr-∗-ABr-∗-ABr-∗-BBr form is elucidated for SeC12H8(Br)SeBr---Br-Br---BrSe(Br)C12H8Se, the selenanthrene system, and the models with QTAIM dual functional analysis (QTAIM-DFA). Asterisks (∗) are employed to emphasize the existence of bond critical points on the interactions in question. Data from the fully optimized structure correspond to the static nature of interactions. In our treatment, data from the perturbed structures, around the fully optimized structure, are employed for the analysis, in addition to those from the fully optimized one, which represent the dynamic nature of interactions. The ABr-∗-ABr and ABr-∗-BBr interactions are predicted to have the CT-TBP (trigonal bipyramidal adduct formation through charge transfer) nature and the typical hydrogen bond nature, respectively. The nature of Se2Br5σ(7c–10e) is also clarified typically, employing an anionic model of [Br-Se(C4H4Se)-Br---Br---Br-Se(C4H4Se)-Br]−, the 1,4-diselenin system, rather than (BrSeC12H8)Br---Se---Br-Br---Br-Se(C12H8Se)-Br, the selenanthrene system.

Intrinsic dynamic and static nature of each HB in the multi-HBs between nucleobase pairs and its behavior, elucidated with QTAIM dual functional analysis and QC calculations.

The intrinsic dynamic and static nature of each HB in the multi-HBs between nucleobase pairs (Nu–Nu′) is elucidated with QTAIM dual functional analysis (QTAIM-DFA). Perturbed structures generated using coordinates derived from the compliance constants (Cii) are employed for QTAIM-DFA. The method is called CIV. Two, three, or four HBs are detected for Nu–Nu′. Each HB in Nu–Nu′ is predicted to have the nature of CT-TBP (trigonal bipyramidal adduct formation through charge transfer (CT)), CT-MC (molecular complex formation through CT), or t-HBwc (typical HB with covalency), while the vdW nature is predicted for the C–H⋯X interactions, for example. Energies for the formation of the pairs (ΔE) are linearly correlated with the total values of Cii−1 in Nu–Nu′. The total Cii−1 values are obtained by summing each Cii−1 value, similarly to the case of Ohm's law for the parallel connection in the electric resistance. The total ΔE value for a nucleobase pair could be fractionalized to each HB, based on each Cii−1 value. The perturbed structures generated with CIV are very close to those generated with the partial optimization method, when the changes in the interaction distances are very small. The results provide useful insights for better understanding DNA processes, although they are highly enzymatic.

Effects from Basis Sets and Levels of Calculations on the Nature of Interactions Predicted by QTAIM Dual Functional Analysis with QTAIM Functions

AbstractInvestigations concerning the nature of interactions must be considered an issue of primary importance in the chemical sciences. The dynamic and static natures of interactions were recently proposed based on the quantum theory of atoms in molecules dual functional analysis (QTAIM‐DFA). The nature of interactions is widely investigated under various conditions, which often results in the predictions of (very) different natures. The predicted nature should be well correlated to the observed parameters, especially for experimental scientists. The effects from the basis sets and levels of calculations on the predicted parameters are carefully examined, exemplified by the interaction distances in question, the QTAIM functions for the interactions, and the QTAIM‐DFA parameters. The effects are discussed for the total (basis set + level) terms and each term. The mechanisms of the total terms are also clarified for the QTAIM‐DFA parameters. The results provide a good guideline for discussion of the nature of interactions based on the calculated parameters under various calculation conditions. The results help to establish a reliable method to elucidate the nature of interactions, such as QTAIM‐DFA.

Nature of intramolecular O-H⋯π interactions as elucidated by QTAIM dual functional analysis with QC calculations.

The intrinsic dynamic and static nature of intramolecular OH–*–π interactions is elucidated using a QTAIM dual functional analysis (QTAIM-DFA) after clarifying the structural features. Asterisks (*) are employed to emphasize the presence of bond critical points (BCPs) on the bond paths (BPs), which correspond to the interactions in question. Data from the fully optimized structures correspond to the static nature of the interactions. In our treatment, data from the perturbed structures, which are based around the fully optimized structure, are employed for the analysis in addition to those from the fully optimized structure, which represent the dynamic nature of the interaction. Seven intramolecular OH–*–C(π) interactions were detected in six-membered rings, with six BPs and BCPs for each, among the 72 conformers of the species examined here (1–15). The interactions are predicted to have a vdW or t-HBnc (typical hydrogen bonds with no covalency) nature, which appeared in the pure closed shell region. They appear to be stronger than the corresponding intermolecular interactions. Nine BPs with BCPs were also detected for the intramolecular O–*–X interactions (X = C(π) and H(π), joined to C(π)) in the 5–7-membered rings. The E(2) values of the interactions, as obtained by NBO, are discussed in relation to the stabilities of the conformers and the BPs with BCPs.

Behavior of I4 σ(4c–6e) in tellurolane system and related species, elucidated by QTAIM dual functional analysis with QC calculations

AbstractThe nature of the AI‐*‐AI and AI‐*‐BI interactions in BI‐*‐AI‐*‐AI‐*‐BI of I4 σ(4c–6e) in the tellurolane system, C4H8(I)Te–I···I–I···I–Te(I)C4H8 (1), and the models is elucidated with QTAIM dual functional analysis (QTAIM‐DFA). Asterisks (*) are employed to emphasize the existence of bond critical points (BCPs) on the interactions in question. Data from the fully optimized structures correspond to the static nature. Data from the perturbed structures around the fully optimized ones with the fully optimized structures represent the dynamic nature of interactions in QTAIM‐DFA. The AI‐*‐AI and AI‐*‐BI interactions in the optimized structure of 1 (Ci)calcd are predicted to have the Cov‐w (weak covalent) nature appeared in the shared shell region and the t‐HBwc (typical hydrogen bonds with covalency) nature appeared in the regular closed shell (r‐CS) region, respectively. However, both AI‐*‐AI and AI‐*‐BI interactions in the observed structure in crystals (1 (Ci)obsd) appear in the r‐CS region. The isolated structure of only one molecule in vacuum for 1 (Ci)calcd vs that surrounded by the same molecules for 1 (Ci)obsd arises the different results. The nature of AI‐*‐AI and AI‐*‐BI in BI‐*‐AI‐*‐AI‐*‐BI of I4 σ(4c–6e) for the models is similarly analyzed.

Behavior of Multi-HBs in Acetic Acid Dimer and Related Species: QTAIM Dual Functional Analysis Employing Perturbed Structures Generated Using Coordinates from Compliance Force Constants

Abstract The dynamic and static nature of each hydrogen bond (HB) in acetic acid dimer (1), acetamide dimer (2a), thio- and seleno-derivatives of 2a (2b and 2c, respectively), and acetic acid–acetamide mixed dimer (3) was elucidated with QTAIM dual functional analysis (QTAIM-DFA). Such multi-HBs will form in 1–3, in close proximity in space, and interact mutually and strongly with each other. Perturbed structures generated using coordinates derived from the compliance force constants (Cij: the method being called CIV) are employed in QTAIM-DFA, for the establishment of the methodology to elucidate the nature of each HB in the multi-HBs. The dynamic nature of interactions with CIV is described as the “intrinsic dynamic nature of interactions”, since the coordinates corresponding to Cij are invariant to the choice of the coordinate system. Each HB in the multi-HBs of 1–3 are predicted to have the nature of CT-MC (molecular complex formation through charge transfer) appear at the regular closed shell region, which are stronger than each HB of the isomers of 1–3. The methodology to elucidate the nature of multi-HBs is well established, which employs the perturbed structures generated with CIV for QTAIM-DFA.

Intrinsic Dynamic Nature of Neutral Hydrogen Bonds Elucidated with QTAIM Dual Functional Analysis: Role of the Compliance Force Constants and QTAIM-DFA Parameters in Stability.

Invited for this month's cover picture is Professor Satoko Hayashi's group from the Faculty of Systems Engineering at Wakayama University (Japan). The cover picture shows Japanese lanterns for the Bon festival dance dangling on two ropes, and several molecular graphs with contour maps for hydrogen bonds (HBs) emerging from the lanterns. The curves of the ropes may correspond to the ΔE (energy of formation) and C ij (compliance constant) values for HBs, for which the product will be constant. Read the full text of their Full Paper at https://doi.org/10.1002/open.201800051.

Front Cover: Intrinsic Dynamic Nature of Neutral Hydrogen Bonds Elucidated with QTAIM Dual Functional Analysis: Role of the Compliance Force Constants and QTAIM‐DFA Parameters in Stability (ChemistryOpen 8/2018)

Front Cover: Intrinsic Dynamic Nature of Neutral Hydrogen Bonds Elucidated with QTAIM Dual Functional Analysis: Role of the Compliance Force Constants and QTAIM‐DFA Parameters in Stability (ChemistryOpen 8/2018)

Intrinsic Dynamic Nature of Neutral Hydrogen Bonds Elucidated with QTAIM Dual Functional Analysis: Role of the Compliance Force Constants and QTAIM-DFA Parameters in Stability.

The dynamic and static nature of various neutral hydrogen bonds (nHBs) is elucidated with quantum theory of atoms‐in‐molecules dual functional analysis (QTAIM‐DFA). The perturbed structures generated by using the coordinates derived from the compliance force constants (Cij) of internal vibrations are employed for QTAIM‐DFA. The method is called CIV. The dynamic nature of CIV is described as the “intrinsic dynamic nature”, as the coordinates are invariant to the choice of the coordinate system. nHBs are, for example, predicted to be van der Waals (H2Se−✶−HSeH; ✶=bond critical point), t‐HBnc (typical‐HBs with no covalency: HI−✶−HI), t‐HBwc (t‐HBs with covalency: H2C=O−✶−HI), CT‐MC [molecular complex formation through charge transfer (CT): H2C=O−✶−HF], and CT‐TBP (trigonal bipyramidal adduct formation through CT: H3N−✶−HI) in nature. The results with CIV were the same as those with POM in the calculation errors, for which the perturbed structures were generated by partial optimization, and the interaction distances in question were fixed suitably in POM. The highly excellent applicability of CIV for QTAIM‐DFA was demonstrated for the various nHBs, as well as for the standard interactions previously reported. The stability of the HBs, evaluated by ΔE, is well correlated with Cij (ΔE×Cij=constant value of −165.64), and the QTAIM parameters, although a few deviations were detected.

Perturbed structures generated using coordinates derived from compliance constants in internal vibrations for QTAIM dual functional analysis: Intrinsic dynamic nature of interactions

AbstractPerturbed structures for QTAIM dual functional analysis (QTAIM‐DFA) are proposed to generate using the coordinates corresponding to the compliance force constants in internal vibrations (CIV). In QTAIM‐DFA, total electron energy densities Hb(rc) are plotted versus Hb(rc) – Vb(rc)/2 at bond critical points (BCPs) of interactions in question, where Vb(rc) are potential energy densities at BCPs. Each plot of an interaction based on the data from both perturbed structures and fully optimized one takes the form (θp, κp), where θp corresponds to the tangent line of the plot and κp is the curvature. The θp values evaluated with CIV are equal to those obtained by partial optimizations with the interaction distance in question being fixed suitably, within the calculation errors. Very high applicability of CIV is demonstrated to generate the perturbed structures for QTAIM‐DFA. Dynamic nature of interactions based on (θp, κp) with CIV is called “intrinsic dynamic nature of interactions.”

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.

Behaviour of the XH-*-π and YX-*-π interactions (X, Y = F, Cl, Br and I) in the coronene π-system, as elucidated by QTAIM dual functional analysis with QC calculations.

The dynamic and static nature of XH-*-π and YX-*-π in the coronene π-system (π(C24H12)) is elucidated by QTAIM dual functional analysis, where * emphasizes the presence of bond critical points (BCPs) in the interactions. The nature of the interactions is elucidated by analysing the plots of the total electron energy densities Hb(rc) versus Hb(rc) − Vb(rc)/2 [=(ħ2/8m)∇2ρb(rc)] for the interactions at BCPs, where Vb(rc) are the potential energy densities at the BCPs. The data for the perturbed structures around the fully optimized structures are employed for the plots in addition to those of the fully optimized structures. The plots are analysed using the polar coordinate of (R, θ) for the data of the fully optimized structures, while those containing the perturbed structures are analysed using (θp, κp), where θp corresponds to the tangent line of each plot and κp is the curvature. Whereas (R, θ) show the static nature, (θp, κp) represent the dynamic nature of the interactions. All interactions in X–H-*-π(C24H12) (X = F, Cl, Br and I) and Y–X-*-π(C24H12) (Y–X = F–F, Cl–Cl, Br–Br, I–I, F–Cl, F–Br and F–I) are classified by pure CS (closed shell) interactions and are characterized as having the vdW nature, except for X–H = F–H and Y–X = F–Cl, F–Br and F–I, which show the typical-HB nature without covalency. The structural features of the complexes are also discussed.