Behavior of Halogen Bonds of the Y-X⋅⋅⋅π Type (X, Y=F, Cl, Br, I) in the Benzene π System, Elucidated by Using a Quantum Theory of Atoms in Molecules Dual-Functional Analysis

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.

A Theoretical Study of the Halogen Bond between Heteronuclear Halogen and Benzene

Halogen bonds play an important role in many fields, such as biological systems, drug design and crystal engineering. In this work, the structural characteristics of the halogen bond between heteronuclear halogen XD (ClF, BrCl, IBr, ICl, BrF and IF) and benzene were studied using density functional theory. The structures of the complexes between heteronuclear halogen and benzene have Cs symmetry. The interaction energies of the complexes between heteronuclear halogen XD (ClF, BrCl, IBr, ICl, BrF and IF) and benzene range from -27.80 to -37.18 kJ/mol, increasing with the increases in the polarity between the atoms of X and D, and are proportional to the angles of a between the Z axis and the covalent bond of heteronuclear halogen. The electron density (ρ) and corresponding Laplacian (∇²ρ) values indicate that the interaction of the heteronuclear halogen and benzene is a typical long-range weak interaction similar to a hydrogen bond. Independent gradient model analysis suggests that the van der Waals is the main interaction between the complexes of heteronuclear halogen and benzene. Symmetry-adapted perturbation theory analysis suggests that the electrostatic interaction is the dominant part in the complexes of C₆H₆⋯ClF, C₆H₆⋯ICl, C₆H₆⋯BrF and C₆H₆⋯IF, and the dispersion interaction is the main part in the complexes of C₆H₆⋯BrCl, C₆H₆⋯IBr.

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.

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.

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 H b(r c) versus H b(r c) - V b(r c)/2 [=(ħ 2/8m)∇2 ρ b(r c)] for the interactions at BCPs, where V b(r c) 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 (θ p, κ p), where θ p corresponds to the tangent line of each plot and κ p is the curvature. Whereas (R, θ) show the static nature, (θ p, κ p) 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.

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(C10H6 BSPh-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 H b( r c) were plotted versus H b( r c) - V b( r c)/2 for the interaction at the BCPs, where V b( r c) 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.

Behavior of the E-E' Bonds (E, E' = S and Se) in Glutathione Disulfide and Derivatives Elucidated by Quantum Chemical Calculations with the Quantum Theory of Atoms-in-Molecules Approach

The nature of the E–E’ bonds (E, E’ = S and Se) in glutathione disulfide (1) and derivatives 2–3, respectively, was elucidated by applying quantum theory of atoms-in-molecules (QTAIM) dual functional analysis (QTAIM-DFA), to clarify the basic contribution of E–E’ in the biological redox process, such as the glutathione peroxidase process. Five most stable conformers a–e were obtained, after applying the Monte-Carlo method then structural optimizations. In QTAIM-DFA, total electron energy densities H_b(r_c) are plotted versus H_b(r_c) − V_b(r_c)/2 at bond critical points (BCPs), where V_b(r_c) are potential energy densities at BCPs. Data from the fully optimized structures correspond to the static nature. Those containing perturbed structures around the fully optimized one in the plot represent the dynamic nature of interactions. The behavior of E–E’ was examined carefully. Whereas E–E’ in 1a–3e were all predicted to have the weak covalent nature of the shared shell interactions, two different types of S–S were detected in 1, depending on the conformational properties. Contributions from the intramolecular non-covalent interactions to stabilize the conformers were evaluated. An inverse relationship was observed between the stability of a conformer and the strength of E–E’ in the conformer, of which reason was discussed.

Linear Four-Chalcogen Interactions in Radical Cationic and Dicationic Dimers of 1,5-(Dichalcogena)canes: Nature of the Interactions Elucidated by QTAIM Dual Functional Analysis with QC Calculations

The dynamic and static nature of extended hypervalent interactions of the ^BE···^AE···^AE···^BE type are elucidated for four center-seven electron interactions (4c-7e) in the radical cationic dimers (1·⁺) and 4c-6e in the dicationic dimers (1²⁺) of 1,5-(dichalcogena)canes (2: ^AE(CH₂CH₂CH₂)₂^BE: ^AE, ^BE = S, Se, Te, and O). The quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA) is applied for the analysis. Total electron energy densities H_b(r_c) are plotted versus H_b(r_c) - V_b(r_c)/2 [= (ℏ²/8m)∇²ρ_b(r_c)] at bond critical points (BCPs) of the interactions, where V_b(r_c) values show potential energy densities at BCPs. Data from the fully optimized structures correspond to the static nature of the interactions. Those from the perturbed structures around the fully optimized ones are also plotted, in addition to those of the fully optimized ones, which represent the dynamic nature of interactions. The ^BE···^AE-^AE···^BE interactions in 1²⁺ are stronger than the corresponding ones in 1·⁺, respectively. On the one hand, for 1²⁺ with ^AE, ^BE = S, Se, and Te, ^AE···^AE are all classified by the shared shell interactions and predicted to have the weak covalent nature, except for those in 1a²⁺ (^AE = ^BE = S) and 1d²⁺ (^AE = ^BE = Se), which have the nature of regular closed shell (r-CS)/trigonal bipyramidal adduct formation through charge transfer (CT-TBP). On the other hand, ^AE···^BE are predicted to have the nature of r-CS/molecular complex formation through charge transfer for 1a²⁺, 1b²⁺ (^AE = Se; ^BE = S), and 1d²⁺ or r-CS/CT-TBP for 1c²⁺ (^AE = Te; ^BE = S), 1e²⁺ (^AE = Te; ^BE = Se), and 1f²⁺ (^AE = ^BE = Te). The ^BE···^AE-^AE···^BE interactions in 1·⁺ and 1²⁺ are well-analyzed by applying QTAIM-DFA.

Nature ofE2X2σ(4c–6e) of theX---E—E---Xtype at naphthalene 1,8-positions and model, elucidated by X-ray crystallographic analysis and QC calculations with the QTAIM approach

The nature ofE2X2σ(4c–6e) of theX-*-E-*-E-*-Xtype is elucidated for 1-(8-XC10H6)E–E(C10H6X-8′)-1′ [(1)E,X= S, Cl; (2) S, Br; (3) Se, Cl; (4) Se, Br] after structural determination of (1), (3) and (4), together with modelA[MeX---E(H)—E(H)---XMe (E= S and Se;X= Cl and Br)]. The quantum theory of atoms-in-molecules dual functional analysis (QTAIM-DFA) is applied. The total electron energy densitiesHb(rc) are plottedversus Hb(rc) –Vb(rc)/2 for the interactions at the bond critical points (BCPs; *), whereVb(rc) show the potential energy densities at the BCPs. 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 were analysed using the polar coordinate (R, θ) representation of the data of the fully optimized structures. Data containing the perturbed structures were analysed by (θp, κp), where θpcorresponds to the tangent line of the plot and κpis the curvature. Whereas (R, θ) shows the static nature, (θp, κp) represents the dynamic nature of interactions.E-*-Eare all classified as shared shell (S) interactions for (1)–(4) and as weak covalent (Cov-w) in nature (S/Cov-w). The nature ofpureCS (closed shell)/typical-HB (hydrogen bond) with no covalency is predicted forE-*-Xin (1) and (3),regularCS/typical-HB nature with covalency is predicted for (4), and an intermediate nature is predicted for (2). The NBO energies evaluated forE-*-Xin (1)–(4) are substantially larger than those in modelAdue the shortened length at the naphthalene 1,8-positions. The nature ofE2X2of σ(4c–6e) is well elucidatedviaQTAIM-DFA.

Behavior of interactions between hydrogen chalcogenides and an anthracene π-system elucidated by QTAIM dual functional analysis with QC calculations

The nature of the interactions between chalcogenides and the anthracene p-system, EH₂-*-p(C₁₄H₁₀), is predicted to be close to that of EH₂-*-p(C₁₀H₈), although the partial structures around the central rings can be found in EH₂-*-p(C₆H₆).

Nature of S2Se2 σ(4c–6e) at naphthalene 1,8-positions and models, elucidated by QTAIM dual functional analysis

The nature of ^BE–*–^AE–*–^AE–*–^BE σ(4c–6e) is primarily elucidated at naphthalene 1,8-positions: while the weak covalent nature is predicted for all ^AE–*–^AE, the HB nature with covalency or the CT-MC (MC formation through CT) nature is for ^AE–*–^BE.