Origin of the Surprising Enhancement of Electrostatic Energies by Electron-Donating Substituents in Substituted Sandwich Benzene Dimers

Quantum Mechanics Characterization of Non-Covalent Interaction in Nucleotide Fragments

Accurate calculation of non-covalent interaction energies in nucleotides is crucial for understanding the driving forces governing nucleic acid structure and function, as well as developing advanced molecular mechanics forcefields or machine learning potentials tailored to nucleic acids. Here, we dissect the nucleotides' structure into three main constituents: nucleobases (A, G, C, T, and U), sugar moieties (ribose and deoxyribose), and phosphate group. The interactions among these fragments and between fragments and water were analyzed. Different quantum mechanical methods were compared for their accuracy in capturing the interaction energy. The non-covalent interaction energy was decomposed into electrostatics, exchange-repulsion, dispersion, and induction using two ab initio methods: Symmetry-Adapted Perturbation Theory (SAPT) and Absolutely Localized Molecular Orbitals (ALMO). These calculations provide a benchmark for different QM methods, in addition to providing a valuable understanding of the roles of various intermolecular forces in hydrogen bonding and aromatic stacking. With SAPT, a higher theory level and/or larger basis set did not necessarily give more accuracy. It is hard to know which combination would be best for a given system. In contrast, ALMO EDA2 did not show dependence on theory level or basis set; additionally, it is faster.

Mechanism and Enantioselectivity in QUINOX-Catalyzed Asymmetric Allylations of Aromatic Aldehydes: Solvent and Substituent Effects

Computational investigations were conducted on the QUINOX-catalyzed asymmetric allylation of aromatic aldehydes with allyltrichlorosilanes. Our calculations provide evidence that the catalytic allylation can follow distinct mechanisms, depending on the solvent employed. In toluene and CH2Cl2, the QUINOX-catalyzed allylation predominantly follows an associative pathway, while in CH3CN, a dissociative pathway becomes more favorable. Noncovalent interactions, such as π-stacking effects for the associative mechanism and CH/π interactions for the dissociative mechanism, play a pivotal role in enantiostereodifferentiation in the asymmetric QUINOX-catalyzed reactions of benzaldehyde. Furthermore, the study unveils how different aldehyde substituents exert differing influences on the catalytic allylation reaction. Specifically, the QUINOX-catalyzed allylation of 4-(trifloromethyl)benzaldehyde displays a strong preference for the associative pathway, yielding excellent results in both yield and enantioselectivity. Conversely, 4-methoxybenzaldehyde tends to favor a dissociative mechanism with reduced yields and enantioselectivity. The mechanistic basis for these remarkable substituent effects on the catalytic allylation reaction was also elucidated. In summary, this research enhances our understanding of the QUINOX-catalyzed asymmetric allylation, shedding light on the role of solvents and substituents in the reaction mechanism and enantioselectivity.

Direct Through-Space Substituent-π Interactions in Noncovalent Arene-Fullerene Assemblies

The arene-arene interactions between electron-rich and deficient aromatics have been less understood. Herein, we focus on a [60]fullerene π-surface as an electron-deficient aromatics. Using a 1H signal of H2O@C60 as a magnetic probe, the presence of benzene-fullerene interactions was confirmed. To investigate substituent effects on the noncovalent arene-fullerene interactions, NMR titration experiments were carried out using an open-[60]fullerene and a series of substituted benzenes, i. e., PhX (X=NO2, CN, Cl, OMe, H, CH3, and NH2), demonstrating a 1 : 2 stoichiometry with a positive correlation between stabilization energies upon the first association (ΔG1) and Hammet constants (σm). The destabilization of the self-assembled structure for X=OMe with a σ-withdrawing nature clearly showed direct through-space substituent-π interactions describable by the Wheeler-Houk model while the second association was suggested to be considerably perturbed by the secondary effects.

Effect of electronegative atoms on π - π stacking and hydrogen bonding behavior in simple aromatic molecules - An Ab initio MD study

Ab initio molecular dynamics studies have been performed on fluorobenzene, phenol, and aniline, which have the three most electronegative atoms, fluorine, oxygen, and nitrogen, respectively. Radial distribution functions show strong hydrogen bonding in the phenolic -OH group, whereas it is less prominent in the -NH2 group of aniline. Fluorobenzene does not show strong hydrogen bonds as no solvation shell is found between the fluorine atom and different aromatic hydrogens of the molecule. Spatial distribution functions show that the nitrogen atom of aniline interacts with the aromatic plane, the oxygen atom of phenol is concentrated near the -OH group and fluorobenzene's fluorine atom interacts with the para hydrogen. Liquid phase dimer structures of these systems reveal that perpendicular orientation (Y-shaped) is preferred over parallel ones. Almost half of the total dimer population tends to prefer 90∘±30° angle. H-bond analyses show that fluorobenzene has the longest mean H-bond lifetime for the H-bond between the aromatic hydrogens and the fluorine atoms, whereas the aniline has the least. The mean lifetime between aromatic hydrogens and electronegative atoms increases steadily from aniline to fluorobenzene. Phenolic -OH and amino -NH2 groups show considerably longer mean H-bond lifetime than the aromatic hydrogens. Gas-phase binding energies obtained from quantum chemical calculations show that aniline and phenol dimers have higher binding energy values than the fluorobenzene dimer. Only the phenol dimer shows a perpendicular structure as a stable one, while aniline and fluorobenzene prefer the parallel orientation.

Effect of hydrophilicity-imparting substituents on exciton delocalization in squaraine dye aggregates covalently templated to DNA Holliday junctions

Molecular aggregates exhibit emergent properties, including the collective sharing of electronic excitation energy known as exciton delocalization, that can be leveraged in applications such as quantum computing, optical information processing, and light harvesting. In a previous study, we found unexpectedly large excitonic interactions (quantified by the excitonic hopping parameter Jm,n) in DNA-templated aggregates of squaraine (SQ) dyes with hydrophilic-imparting sulfo and butylsulfo substituents. Here, we characterize DNA Holliday junction (DNA-HJ) templated aggregates of an expanded set of SQs and evaluate their optical properties in the context of structural heterogeneity. Specifically, we characterized the orientation of and Jm,n between dyes in dimer aggregates of non-chlorinated and chlorinated SQs. Three new chlorinated SQs that feature a varying number of butylsulfo substituents were synthesized and attached to a DNA-HJ via a covalent linker to form adjacent and transverse dimers. Various characteristics of the dye, including its hydrophilicity (in terms of log Po/w) and surface area, and of the substituents, including their local bulkiness and electron withdrawing capacity, were quantified computationally. The orientation of and Jm,n between the dyes were estimated using a model based on Kühn-Renger-May theory to fit the absorption and circular dichroism spectra. The results suggested that adjacent dimer aggregates of all the non-chlorinated and of the most hydrophilic chlorinated SQ dyes exhibit heterogeneity; that is, they form a mixture of dimers subpopulations. A key finding of this work is that dyes with a higher hydrophilicity (lower log Po/w) formed dimers with smaller Jm,n and large center-to-center dye distance (Rm,n). Also, the results revealed that the position of the dye in the DNA-HJ template, that is, adjacent or transverse, impacted Jm,n. Lastly, we found that Jm,n between symmetrically substituted dyes was reduced by increasing the local bulkiness of the substituent. This work provides insights into how to maintain strong excitonic coupling and identifies challenges associated with heterogeneity, which will help to improve control of these dye aggregates and move forward their potential application as quantum information systems.

Energy landscape of perylenediimide chromophoric aggregates

Understanding the self-assembly of conjugated organic materials at the molecular level is crucial in their potential applications as active components in electronic and optoelectronic devices. The type of aggregation significantly influences the intriguing electronic and optical characteristics differing from their constituent molecules. Perylenediimides (PDIs), electron-deficient molecules exhibiting remarkable n-type semiconducting properties, are among the most explored organic fluorescent materials due to their high fluorescence efficiency, photostability, and optoelectronic properties. PDI derivatives are reported to form well-tailored supramolecular architectures: cofacial with minor slip (H-aggregates), staggered with major slip (J-aggregates), magic angle stacking (M-aggregates), rotated (X-aggregates), rotated orthogonal ((+)-aggregates), etc. H*-aggregates are defined here as an ideal case of H-aggregate with an eclipsed configuration. Although numerous reports regarding the formation and optical properties of various PDI aggregates are known, the key driving force within the PDI units guiding the self-assembly to form distinct aggregate systems remains elusive. To unravel the molecular-level mechanisms behind the self-assembly of PDI units by probing the intermolecular interactions, symmetry-adapted perturbation theory-based energy decomposition, potential energy surface scans, and non-covalent interaction index analyses were employed on PDI dimer models. Quantum theory of atoms in molecules and frontier molecular orbital analyses were implemented on the dimer models to comprehend the effect of heteroatoms and orbital interactions in stabilising the X-aggregates over the other PDI aggregate systems. Competition between the attractive and repulsive non-covalent interactions dictates a stability order of X > H > J > M > (+) > H* for the PDI aggregate system, while in the parent perylene system, the stability order was found to be X > (+) > H > M > J > H*.

The Energetic Origins of Pi-Pi Contacts in Proteins

Accurate potential energy models of proteins must describe the many different types of noncovalent interactions that contribute to a protein's stability and structure. Pi-pi contacts are ubiquitous structural motifs in all proteins, occurring between aromatic and nonaromatic residues and play a nontrivial role in protein folding and in the formation of biomolecular condensates. Guided by a geometric criterion for isolating pi-pi contacts from classical molecular dynamics simulations of proteins, we use quantum mechanical energy decomposition analysis to determine the molecular interactions that stabilize different pi-pi contact motifs. We find that neutral pi-pi interactions in proteins are dominated by Pauli repulsion and London dispersion rather than repulsive quadrupole electrostatics, which is central to the textbook Hunter-Sanders model. This results in a notable lack of variability in the interaction profiles of neutral pi-pi contacts even with extreme changes in the dielectric medium, explaining the prevalence of pi-stacked arrangements in and between proteins. We also find interactions involving pi-containing anions and cations to be extremely malleable, interacting like neutral pi-pi contacts in polar media and like typical ion-pi interactions in nonpolar environments. Like-charged pairs such as arginine-arginine contacts are particularly sensitive to the polarity of their immediate surroundings and exhibit canonical pi-pi stacking behavior only if the interaction is mediated by environmental effects, such as aqueous solvation.

Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory

Intramolecular symmetry-adapted perturbation theory (ISAPT) is a method to compute and decompose the noncovalent interaction energy between two molecular fragments A and B covalently connected via a linker C. However, the existing ISAPT algorithm displays several issues for many fragmentation patterns (that is, specific assignments of atoms to the A/B/C subsystems), including an artificially repulsive electrostatic energy (even when the fragments are hydrogen-bonded) and very large and mutually cancelling induction and exchange-induction terms. We attribute those issues to the presence of artificial dipole moments at the interfragment boundary, as the atoms of A and B directly connected to C are missing electrons on one of their hybrid orbitals. Therefore, we propose several new partitioning algorithms which reassign one electron, on a singly occupied link hybrid orbital, from C to each of A/B. Once the contributions from these link orbitals are added to fragment density matrices, the computation of ISAPT electrostatic, induction, and dispersion energies proceeds exactly as normal, and the exchange energy expressions need only minor modifications. Among the link partitioning algorithms introduced, the so-called ISAPT(SIAO1) approach (in which the link orbital is obtained by a projection onto the intrinsic atomic orbitals (IAOs) of a given fragment followed by orthogonalization to this fragment's occupied space) leads to reasonable values of all ISAPT corrections for all fragmentation patterns, and exhibits a fast and systematic basis set convergence. This improvement is made possible by a significant reduction in magnitude (even though not a complete elimination) of the unphysical dipole moments at the interfragment boundaries. We demonstrate the utility of the improved ISAPT partitioning by examining intramolecular interactions in several pentanediol isomers, examples of linear and branched alkanes, and the open and closed conformations of a family of N-arylimide molecular torsion balances.

π-Stacking Isomerism in Polycyclic Aromatic Hydrocarbons: The 2-Naphthalenethiol Dimer

π-Stacking is a common descriptor for face-to-face attractive forces between aromatic hydrocarbons. However, the physical origin of this interaction remains debatable. Here we examined π-stacking in a model homodimer formed by two thiol-substituted naphthalene rings. Two isomers of the 2-naphthalenethiol dimer were discovered using rotational spectroscopy, sharing a parallel-displaced crossed orientation and absence of thiol-thiol hydrogen bonds. One of the isomers presents C₂ symmetry, structurally analogous to the global minimum of the naphthalene dimer. The experimental data were rationalized with molecular orbital calculations, revealing a shallow potential energy surface. Noncovalent interactions are dominated by dispersion forces according to SAPT energy decomposition. In addition, the reduced electronic density shows a diffuse and extended region of inter-ring interactions, compatible with the description of π-stacking as a competition between dispersion and Pauli repulsion forces.

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

Hybrid or "extended" symmetry-adapted perturbation theory (XSAPT) replaces traditional SAPT's treatment of dispersion with better performing alternatives while at the same time extending two-body (dimer) SAPT to a many-body treatment of polarization using a self-consistent charge embedding procedure. The present work presents a systematic study of how XSAPT interaction energies and energy components converge with respect to the choice of Gaussian basis set. Errors can be reduced in a systematic way using correlation-consistent basis sets, with aug-cc-pVTZ results converged within <0.1 kcal/mol. Similar (if slightly less systematic) behavior is obtained using Karlsruhe basis sets at much lower cost, and we introduce new versions with limited augmentation that are even more efficient. Pople-style basis sets, which are more efficient still, often afford good results if a large number of polarization functions are included. The dispersion models used in XSAPT afford much faster basis-set convergence as compared to the perturbative description of dispersion in conventional SAPT, meaning that "compromise" basis sets (such as jun-cc-pVDZ) are no longer required and benchmark-quality results can be obtained using triple-ζ basis sets. The use of diffuse functions proves to be essential, especially for the description of hydrogen bonds. The "δ(Hartree-Fock)" correction for high-order induction can be performed in double-ζ basis sets without significant loss of accuracy, leading to a mixed-basis approach that offers 4× speedup over the existing (cubic scaling) XSAPT approach.

The Bifurcated σ-Hole···σ-Hole Stacking Interactions

The bifurcated σ-hole···σ-hole stacking interactions between organosulfur molecules, which are key components of organic optical and electronic materials, were investigated by using a combined method of the Cambridge Structural Database search and quantum chemical calculation. Due to the geometric constraints, the binding energy of one bifurcated σ-hole···σ-hole stacking interaction is in general smaller than the sum of the binding energies of two free monofurcated σ-hole···σ-hole stacking interactions. The bifurcated σ-hole···σ-hole stacking interactions are still of the dispersion-dominated noncovalent interactions. However, in contrast to the linear monofurcated σ-hole···σ-hole stacking interaction, the contribution of the electrostatic energy to the total attractive interaction energy increases significantly and the dispersion component of the total attractive interaction energy decreases significantly for the bifurcated σ-hole···σ-hole stacking interaction. Another important finding of this study is that the low-cost spin-component scaled zeroth-order symmetry-adapted perturbation theory performs perfectly in the study of the bifurcated σ-hole···σ-hole stacking interactions. This work will provide valuable information for the design and synthesis of novel organic optical and electronic materials.

Three types of noncovalent interactions studied between pyrazine and XF

Three types noncovalent interactions (type I, II and III) between pyrazine (C₄H₄N₂) and XF (X = F, Cl, Br, and I) have been discovered at the MP2/aug-cc-pVTZ level. TypeI is σ-hole interaction between the positive site on the halogen X of XF and the negative site on one of the pyrazine nitrogens. Type II is counterintuitive σ-hole interaction driven by polarization between the positive site on the halogen X of XF and a portion of the pyrazine ring. Type III is an interaction between the lateral regions of the halogen X of XF and the position of the pyrazine ring. Through comparing the calculated interaction energy, we can know that the type II and type III interactions are weaker than the corresponding type I interactions, and type III interactions are weaker than the corresponding type II interactions in C₄H₄N₂-XF complexes. SAPT analysis shows that the electrostatic energy are the major source of the attraction for the type I (σ-hole) interactions while the type III interactions are mainly dispersion energy. For the type II (counterintuitive σ-hole) interactions in C₄H₄N₂-XF (X = F and Cl) complexes, electrostatic energy are the major source of the attraction, while in C₄H₄N₂-XF (X = Br and I) complexes, the electrostatic term, induction and dispersion play equally important role in the total attractive interaction. NBO analysis, AIM theory, and conceptual DFT are also being utilized.

NENCI-2021. I. A large benchmark database of non-equilibrium non-covalent interactions emphasizing close intermolecular contacts

In this work, we present NENCI-2021, a benchmark database of ∼8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation-π and anion-π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion-π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (E_int) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The E_int values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from -38.5 to +186.8 kcal/mol, with a mean (median) E_int value of -1.06 kcal/mol (-2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent-these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation-π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the E_int values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive E_int values, and maximum errors of ±0.2-0.3 kcal/mol (i.e., ∼±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials.

Substituent effects on the regium-π stacking interactions between Au6 cluster and substituted benzene

The regium-π stacking interactions in the Au₆···PhX (X = H, CH₃, OH, OCH₃, NH₂, F, Cl, Br, CN, NO₂) complexes are studied using quantum chemical methods. The present study focuses on the different effects of electron-donating and electron-withdrawing substituent. The structure and binding strength of the complexes are examined. The interactions between Au₆ cluster and various substituted benzene become strengthened relative to the Au₆···benzene complex. The interaction region indicator analysis was performed, and the interaction region and interaction between the substituent and Au₆ cluster are discussed. It is found that the substituent effects on the regium-π stacking interactions between Au₆ cluster and substituted benzene are different from π···π interactions of benzene dimer. Energy decomposition analysis was carried out to study the nature of regium-π stacking interactions, and the substituent effects are mainly reflected on the electrostatic interaction and dispersion.

Influence of a Substituted Methyl on the Photoresponsive Third-Order Nonlinear-Optical Properties Based on Azobenzene Metal Complexes

For studying the effect of a substituted group on the photoresponsive third-order nonlinear-optical (NLO) properties, photosensitive azobenzene derivative H₂L1 was first selected to construct metal complexes {[Zn₂(L1)₂(H₂O)₃]·2DMA)}_n (1) and {[Cd(L1)(4,4'-bpy)H₂O]·H₂O}_n (2). Then H₂L2 with a substituted methyl on the azobenzene ring was used to construct complexes {[Zn(L2)(4,4'-bpy)(H₂O)]}_n (3) and {[Cd(L2)(4,4'-bpy)(H₂O)]}_n (4). When the azobenzene moiety of the complexes is trans, the NLO behaviors of the complexes are the same. However, after the azobenzene moiety is excited by ultraviolet (UV) light to change from trans to cis, the substituted methyl increases the repulsion between two azobenzene rings in 3 and 4, thereby affecting their NLO behaviors. Therefore, the nonlinearity of the two types of complexes is different after UV irradiation. Density functional theory calculations support this result. The substituted methyl has a significant influence on the nonlinear absorption behaviors of 3 and 4. This work not only reports the examples of photoresponsive NLO materials based on metal complexes but also provides a new idea to deeply explore NLO properties.

Reinterpreting π-stacking

The nature of π-π interactions has long been debated. The term "π-stacking" is considered by some to be a misnomer, in part because overlapping π-electron densities are thought to incur steric repulsion, and the physical origins of the widely-encountered "slip-stacked" motif have variously been attributed to either sterics or electrostatics, in competition with dispersion. Here, we use quantum-mechanical energy decomposition analysis to investigate π-π interactions in supramolecular complexes of polycyclic aromatic hydrocarbons, ranging in size up to realistic models of graphene, and for comparison we perform the same analysis on stacked complexes of polycyclic saturated hydrocarbons, which are cyclohexane-based analogues of graphane. Our results help to explain the short-range structure of liquid hydrocarbons that is inferred from neutron scattering, trends in melting-point data, the interlayer separation of graphene sheets, and finally band gaps and observation of molecular plasmons in graphene nanoribbons. Analysis of intermolecular forces demonstrates that aromatic π-π interactions constitute a unique and fundamentally quantum-mechanical form of non-bonded interaction. Not only do stacked π-π architectures enhance dispersion, but quadrupolar electrostatic interactions that may be repulsive at long range are rendered attractive at the intermolecular distances that characterize π-stacking, as a result of charge penetration effects. The planar geometries of aromatic sp² carbon networks lead to attractive interactions that are "served up on a molecular pizza peel", and adoption of slip-stacked geometries minimizes steric (rather than electrostatic) repulsion. The slip-stacked motif therefore emerges not as a defect induced by electrostatic repulsion but rather as a natural outcome of a conformational landscape that is dominated by van der Waals interactions (dispersion plus Pauli repulsion), and is therefore fundamentally quantum-mechanical in its origins. This reinterpretation of the forces responsible for π-stacking has important implications for the manner in which non-bonded interactions are modeled using classical force fields, and for rationalizing the prevalence of the slip-stacked π-π motif in protein crystal structures.

Physical Mechanisms Governing Substituent Effects on Arene-Arene Interactions in a Protein Milieu

Arene-arene interactions play important roles in protein-ligand complex formation. Here, we investigate the characteristics of arene-arene interactions between small organic molecules and aromatic amino acids in protein interiors. The study is based on X-ray crystallographic data and quantum mechanical calculations using the enzyme acetylcholinesterase and selected inhibitory ligands as a model system. It is shown that the arene substituents of the inhibitors dictate the strength of the interaction and the geometry of the resulting complexes. Importantly, the calculated interaction energies correlate well with the measured inhibitor potency. Non-hydrogen substituents strengthened all interaction types in the protein milieu, in keeping with results for benzene dimer model systems. The interaction energies were dispersion-dominated, but substituents that induced local dipole moments increased the electrostatic contribution and thus yielded more strongly bound complexes. These findings provide fundamental insights into the physical mechanisms governing arene-arene interactions in the protein milieu and thus into molecular recognition between proteins and small molecules.

Electrostatics does not dictate the slip-stacked arrangement of aromatic π-π interactions

Benzene dimer has long been an archetype for π-stacking. According to the Hunter–Sanders model, quadrupolar electrostatics favors an edge-to-face CH⋯π geometry but competes with London dispersion that favors cofacial π-stacking, with a compromise “slip-stacked” structure emerging as the minimum-energy geometry. This model is based on classical electrostatics, however, and neglects charge penetration. A fully quantum-mechanical analysis, presented here, demonstrates that electrostatics actually exerts very little influence on the conformational landscape of (C₆H₆)₂. Electrostatics also cannot explain the slip-stacked arrangement of C₆H₆⋯C₆F₆, where the sign of the quadrupolar interaction is reversed. Instead, the slip-stacked geometry emerges in both systems due to competition between dispersion and Pauli repulsion, with electrostatics as an ambivalent spectator. This revised interpretation helps to rationalize the persistence of offset π-stacking in larger polycyclic aromatic hydrocarbons and across the highly varied electrostatic environments that characterize π–π interactions in proteins.

According to the Hunter–Sanders model, geometries in π–π systems arise from competition between quadrupolar electrostatics (favoring an edge-to-face geometry) and London dispersion (favoring stacking), but this model misrepresents the molecular physics.

What Is Special about Aromatic-Aromatic Interactions? Significant Attraction at Large Horizontal Displacement

High-level ab initio calculations show that the most stable stacking for benzene-cyclohexane is 17% stronger than that for benzene-benzene. However, as these systems are displaced horizontally the benzene-benzene attraction retains its strength. At a displacement of 5.0 Å, the benzene-benzene attraction is still ∼70% of its maximum strength, while benzene-cyclohexane attraction has fallen to ∼40% of its maximum strength. Alternatively, the radius of attraction (>2.0 kcal/mol) for benzene-benzene is 250% larger than that for benzene-cyclohexane. Thus, at relatively large distances aromatic rings can recognize each other, a phenomenon that helps explain their importance in protein folding and supramolecular structures.

Revisiting the Potential Energy Surface of the Stacked Cytosine Dimer: FNO-CCSD(T) Interaction Energies, SAPT Decompositions, and Benchmarking

Nucleobase stacking interactions are crucial for the stability of nucleic acids. This study investigates base stacking energies of the cytosine homodimer in different configurations, including intermolecular separation plots, detailed twist dependence, and displaced structures. Highly accurate ab initio quantum chemical single point energies using an energy function based on MP2 complete basis set extrapolation ([6 → 7]ZaPa-NR) and a CCSD(T)/cc-pVTZ-F12 high-level correction are presented as new reference data, providing the most accurate stacking energies of nucleobase dimers currently available. Accurate SAPT2+(3)δMP2 energy decomposition is used to obtain detailed insights into the nature of base stacking interactions at varying vertical distances and twist values. The ab initio symmetry adapted perturbation theory (SAPT) energy decomposition suggests that the base stacking originates from an intricate interplay between dispersion attraction, short-range exchange-repulsion, and Coulomb interaction. The interpretation of the SAPT data is a complex issue as key energy terms vary substantially in the region of optimal (low energy) base stacking geometries. Thus, attempts to highlight one leading stabilizing SAPT base stacking term may be misleading and the outcome strongly depends on the used geometries within the range of geometries sampled in nucleic acids upon thermal fluctuations. Modern dispersion-corrected density functional theory (among them DSD-BLYP-D3, ωB97M-V, and ωB97M-D3BJ) is benchmarked and often reaches up to spectroscopic accuracy (below 1 kJ/mol). The classical AMBER force field is benchmarked with multiple different sets of point-charges (e.g. HF, DFT, and MP2-based) and is found to produce reasonable agreement with the benchmark data.

AMOEBA+ Classical Potential for Modeling Molecular Interactions

Classical potentials based on isotropic and additive atomic charges have been widely used to model molecules in computers for the past few decades. The crude approximations in the underlying physics are hindering both their accuracy and transferability across chemical and physical environments. Here we present a new classical potential, AMOEBA+, to capture essential intermolecular forces, including permanent electrostatics, repulsion, dispersion, many-body polarization, short-range charge penetration, and charge transfer, by extending the polarizable multipole-based AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) model. For a set of common organic molecules, we show that AMOEBA+ with general parameters can reproduce both quantum mechanical interactions and energy decompositions according to Symmetry-Adapted Perturbation Theory (SAPT). Additionally, a new water model based on the AMOEBA+ framework captures various liquid-phase properties in molecular dynamics simulations while remaining consistent with SAPT energy decompositions, utilizing both ab initio data and experimental liquid properties. Our results demonstrate that it is possible to improve the physical basis of classical force fields to advance their accuracy and general applicability.

Understanding the interplay between π–π and cation–π interactions in [janusene–Ag]+ host–guest systems: a computational approach

Guiding the development of new systems with increased cation–π interaction capability.

Quantification of noncovalent interactions – promises and problems

Quantification of noncovalent interactions is the key for the understanding of binding mechanisms, of biological systems, for the design of drugs, their delivery and for the design of receptors for separations, sensors, actuators, or smart materials.

Exploration of relative π-electron localization in naphthalene aromatic rings by C–H⋯π interactions: experimental evidence, computational criteria, and database analysis

In C–H⋯π interaction, the relative π-electron localization in aromatic ring led to the change of contact position from centre to edges of the ring (C–H⋯π_e) which was confirmed by experimental evidences, computational criteria, and database analysis.

Stacking Principles on π- and Lamellar Stacking for Organic Semiconductors Evaluated by Energy Decomposition Analysis

Two stacking manners, that is, π- and lamellar stacking, are generally found for organic semiconductors, in which the π-stacking occurs between conjugated groups and the lamellar stacking refers to the separation of the conjugated and aliphatic moieties. The stacking principles are yet not well-defined. In this work, extended transition state-natural orbitals for chemical valence (ETS-NOCV), an energy decomposition analysis, is utilized to examine the π- and lamellar stacking for a series of naphthalenetetracarboxylic diimide (R-NDI) crystals. The crucial role of dispersion is validated. The perception that π-stacking is merely determined by the conjugated moiety is challenged. The stacking principles are associated with the closest packing model. Nanoscopic phase separation of conjugated and aliphatic moieties and the formation of lamellar and herringbone motifs in the R-NDIs can thus be clarified. Moreover, the interactions between NDI and the alkyl chain are investigated, revealing that the interactions can be significant, being contradictory to the conventional point of view. Along with R-NDIs, additional organic crystals consisting of various conjugated functionalities and substituents are also investigated by ETS-NOCV. The sampling scope is up to 108 conjugated molecules. The dominant role of dispersion force irrespective of the variation in the conjugated moieties and substituents is further confirmed. It is envisaged that the established principles are applicable to other organic semiconductors. The perspective toward the π- and lamellar stacking might be modified, paving the way for ultimate morphological control.

Read between the Molecules: Computational Insights into Organic Semiconductors

The performance and key electronic properties of molecular organic semiconductors are dictated by the interplay between the chemistry of the molecular core and the intermolecular factors of which manipulation has inspired both experimentalists and theorists. This Perspective presents major computational challenges and modern methodological strategies to advance the field. The discussion ranges from insights and design principles at the quantum chemical level, in-depth atomistic modeling based on multiscale protocols, morphological prediction and characterization as well as energy-property maps involving data-driven analysis. A personal overview of the past achievements and future direction is also provided.

Tipping the Balance between S-π and O-π Interactions

A comprehensive experimental survey consisting of 36 molecular balances was conducted to compare 18 pairs of S-π versus O-π interactions over a wide range of structural, geometric, and solvent parameters. A strong linear correlation was observed between the folding energies of the sulfur and oxygen balances across the entire library of balance pairs. The more stable interaction systematically switched from the O-π to S-π interaction. Computational studies of bimolecular PhSCH₃-arene and PhOCH₃-arene complexes were able to replicate the experimental trends in the molecular balances. The change in preference for the O-π to S-π interaction was due to the interplay of stabilizing (dispersion and solvophobic) and destabilizing (exchange-repulsion) terms arising from the differences in size and polarizability of the oxygen and sulfur atoms.

Organic 2D Optoelectronic Crystals: Charge Transport, Emerging Functions, and Their Design Perspective

2D organic semiconductor crystals are emerging as a fascinating platform with regard to their applications in organic field-effect transistors (OFETs), attributed to their enhanced charge transport efficiency and their new optoelectronic functions, based on their unique morphological features. Advances in material processing techniques have not only enabled easy fabrication of few-monolayered 2D nanostructures but also facilitated exploration of the interesting properties induced by characteristic 2D morphologies. However, to date, only a limited number of representative organic semiconductors have been utilized in organic 2D optoelectronics. Therefore, in order to further spur this research, an intuitive crystal engineering principle for realizing organic 2D crystals is required. In this regard, here, not only the important implications of applying 2D structures to OFET devices are discussed but also a crystal engineering protocol is provided that first predicts molecular arrangements depending on the molecular factors, which is followed by realizing 2D supramolecular synthon networks for different molecular packing motifs. It is expected that 2D organic semiconductor crystals developed by this approach will pave a promising way toward next-generation organic 2D optoelectronics.

Analogues of P and Z as Efficient Artificially Expanded Genetic Information System

To artificially expand the genetic information system and to realize artificial life, it is necessary to discover new functional DNA bases that can form stable duplex DNA and participate in error-free replication. It is recently proposed that the 2-amino-imidazo[1,2- a]-1,3,5-triazin-4(8 H)one (P) and 6-amino-5-nitro-2(1 H)-pyridone (Z) would form a base pair complex, which is more stable than that of the normal G-C base pair and would produce an unperturbed duplex DNA. Here, by using quantum chemical calculations in aqueous medium, it is shown that the P and Z molecules can be modified with the help of electron-withdrawing and -donating substituents mainly found in B-DNA to generate new bases that can produce even more stable base pairs. Among the various bases studied, P3, P4, Z3, and Z5 are found to produce base pairs, which are about 2-15 kcal/mol more stable than the P-Z base pair. It is further shown that these base pairs can be stacked onto the G-C and A-T base pairs to produce stable dimers. The consecutive stacking of these base pairs is found to yield even more stable dimers. The influence of charge penetration effects and backbone atoms in stabilizing these dimers are also discussed. It is thus proposed that the P3, P4, Z3, and Z5 would form promiscuous artificial genetic information system and can be used for different biological applications. However, the evaluations of the dynamical effects of these bases in DNA-containing several nucleotides and the efficacy of DNA polymerases to replicate these bases would provide more insights.

Steric "attraction": not by dispersion alone

Non-covalent interactions between neutral, sterically hindered organic molecules generally involve a strong stabilizing contribution from dispersion forces that in many systems turns the 'steric repulsion' into a 'steric attraction'. In addition to London dispersion, such systems benefit from electrostatic stabilization, which arises from a short-range effect of charge penetration and gets bigger with increasing steric bulk. In the present work, we quantify this contribution for a diverse set of molecular cores, ranging from unsubstituted benzene and cyclohexane to their derivatives carrying tert-butyl, phenyl, cyclohexyl and adamantyl substituents. While the importance of electrostatic interactions in the dimers of sp2-rich (e.g., π-conjugated) cores is well appreciated, less polarizable assemblies of sp3-rich systems with multiple short-range CH···HC contacts between the bulky cyclohexyl and adamantyl moieties are also significantly influenced by electrostatics. Charge penetration is drastically larger in absolute terms for the sp2-rich cores, but still has a non-negligible effect on the sp3-rich dimers, investigated herein, both in terms of their energetics and equilibrium interaction distances. These results emphasize the importance of this electrostatic effect, which has so far been less recognized in aliphatic systems compared to London dispersion, and are therefore likely to have implications for the development of force fields and methods for crystal structure prediction.

Substituent effect of the stacking interaction between carbon monoxide and benzene

Noncovalent interactions (NCIs) between carbon monoxide and substituted benzene were investigated at the M06-2X/6-311++G(d,p) level. rThe results of interaction energy analysis indicated different effects for the electron-donating (-NH₂, -OH, -CH₃) and electron-withdrawing (-F, -CN, -NO₂) groups on the CO⋯PhX complex. Atoms in molecules analysis confirmed the NCIs between CO and PhX. NCI analysis revealed that these interactions belong to van der Waals interactions. The electron density shift of the complexes was investigated with electron density difference analysis. Ternary CO⋯PhX⋯Bz complexes were designed to study the interplay between CO⋯π and π⋯π stacking interactions.

Influence of hydrogen bonds on edge-to-face interactions between pyridine molecules

Edge-to-face interactions between two pyridine molecules and the influence of simultaneous hydrogen bonding of one or both of the pyridines to water on those interactions were studied by analyzing data from ab initio calculations. The results show that the edge-to-face interactions of pyridine dimers that are hydrogen bonded to water are generally stronger than those of non-H-bonded pyridine dimers, especially when the donor pyridine forms a hydrogen bond. The binding energy of the most stable edge-to-face interacting H-bonded pyridine dimer is -5.05 kcal/mol, while that for the most stable edge-to-face interacting non-H-bonded pyridine dimer is -3.64 kcal/mol. The interaction energy data obtained in this study cannot be explained solely by the differences in electrostatic potential between pyridine and the pyridine-water dimer. However, the calculated cooperative effect can be predicted using electrostatic potential maps.

Aerogen bonds formed between AeOF2 (Ae = Kr, Xe) and diazines: comparisons between σ-hole and π-hole complexes

The interaction between KrOF₂ or XeOF₂ and the 1,2, 1,3, and 1,4 diazines is characterized chiefly by a Kr/XeN aerogen bond, as deduced from ab initio calculations. The most stable dimers take advantage of the σ-hole on the aerogen atom, wherein the two molecules lie in the same plane. The interaction is quite strong, as much as 18 kcal mol^-1. A second class of dimer geometry utilizes the π-hole above the aerogen atom in an approximate perpendicular arrangement of the two monomers; these structures are not as strongly bound: 6-8 kcal mol^-1. Both sorts of dimers contain auxiliary CHF H-bonds which contribute to their stability, but even with their removal, the aerogen bond energy remains as high as 14 kcal mol^-1. The nature and strength of each specific interaction is confirmed and quantified by AIM, NCI, NBO, and electron density shift patterns. There is not a great deal of sensitivity to the identity of either the aerogen atom or the position of the two N atoms in the diazine.

Stacked homodimers of substituted contorted hexabenzocoronenes and their complexes with C60 fullerene

Computations show that the tendency of contorted hexabenzocoronene (c-HBC) to form either homodimers or complexes with C₆₀ can be tuned by changing the curvature of the c-HBC via the addition of substituents.

Implications of Charge Penetration for Heteroatom-Containing Organic Semiconductors

The noncovalent interactions of neutral π-conjugated cores, pertinent to organic semiconductor materials, are intimately related to their charge transport properties and involve a subtle interplay of dispersion, Pauli repulsion, and electrostatic contributions. Realizing structural arrangements that are both energetically preferred and sufficiently conductive is a challenge. We tackle this problem by means of charge penetration contribution to the interaction energy, boosted in systems containing large heteroatoms (e.g., sulfur, selenium, phosphorus, silicon, and arsenic). We find that in both the model and "realistic" dimers of such heteroatom-containing cores dispersion is balanced out by the exchange and interaction energy is instead governed by substantial charge penetration. These systems also feature stronger electronic couplings compared to the dispersion-driven dimers of oligoacenes and/or the herringbone assemblies. Thus, charge penetration, enhanced in the π-conjugated cores comprising larger heteroatoms, arises as an attractive strategy toward potentially more stable and efficient organic electronic materials.