How Different Are Aromatic π Interactions from Aliphatic π Interactions and Non-π Stacking Interactions?

The tetrel bonding role in supramolecular aggregation of lead(II) acetate and a thiosemicarbazide derivative

A new Pb^II coordination complex [PbL(OAc)], which was readily synthesized from a mixture of Pb(OAc)₂·3H₂O and 1-(pyridin-2-yl)benzylidene-4-phenylthiosemicarbazide (HL) is reported. The crystal structure analysis of [PbL(OAc)] showed that the Pb^II cation is N,N',S-chelated by the tridentate pincer-type ligand L and by the oxygen atoms of the acetate anion. In addition, the metal centre forms Pb...O and Pb...S tetrel bonds with an adjacent complex molecule, yielding a 1D zigzag polymeric chain, which is reinforced by N-H...O hydrogen bonds and π...π interactions. These chains are interlinked by C-H...py non-covalent interactions, realized between one of the acetate hydrogen atoms and the pyridine rings. According to the Hirshfeld surface analysis, the crystal packing is mainly characterized by intermolecular H...H, H...C and H...O contacts, followed by H...N, H...S, C...C, C...N, Pb...H, Pb...O and Pb...S contacts. The FTIR and ¹H NMR spectra of [PbL(OAc)] testify to the deprotonation of the parent ligand HL, while the acetate ligand exhibits an anisobidentate coordination mode as established by means of single-crystal X-ray diffraction and FTIR spectroscopy. Lastly, theoretical calculations at the PBE0-D3/def2-TZVP level of theory have been used to analyze and characterize the Pb...O and Pb...S tetrel bonds observed in the crystal of [PbL(OAc)], using a combination of QTAIM (Quantum Theory of Atoms in Molecules) and NCIPlot (Non-Covalent Interaction Plot) computational tools.

Electrostatic penetration effects stand at the heart of aromatic π interactions

The nature of the interaction in benzene-containing dimers has been analysed by means of Symmetry Adapted Perturbation Theory (SAPT). The total interaction energy and the preference for the dimers to adopt slipped structures are, apparently, consequence of the balance between repulsion and dispersion. However, our results indicate that this only holds when trends are analysed using fixed intermolecular distances. Employing the most favourable separations between rings it turns out that the changes on the total interaction energy are mostly controlled by electrostatics, while repulsion and dispersion cancel each other to a great extent. Most of the electrostatic contribution is accounted for by electrostatic penetration, so a description based on multipoles should not be employed to rationalise the interaction in benzene-containing dimers. The changes on the interaction energy in benzene-containing dimers are steered by electrostatic penetration which, though often overlooked, plays an essential role for the description of aromatic π interactions.

Dispersion Interactions between Molecules in and out of Equilibrium Geometry: Visualization and Analysis

The London dispersion interactions between systems undergoing bond breaking, twisting, or compression are not well studied due to the scarcity and the high computational cost of methods being able to describe both the dynamic correlation and the multireference character of the system. Recently developed methods based on the Generalized Valence Bond wave function, such as EERPA-GVB and SAPT(GVB) (SAPT = symmetry-adapted perturbation theory), allow one to accurately compute and analyze noncovalent interactions between multireference systems. Here, we augment this analysis by introducing a local indicator for dispersion interactions inspired by Mata and Wuttke's Dispersion Interaction Density [ J. Comput. Chem. 2017, 38, 15-23] applied on top of an EERPA-GVB computation. Using a few model systems, we show what insights into the nature and evolution of the dispersion interaction during bond breaking and twisting such an approach is able to offer. The new indicator can be used at a minimal cost additional to an EERPA-GVB computation and can be complemented by an energy decomposition employing the SAPT(GVB) method. We explain the physics behind the initial increase, followed by a decrease in the interaction of linear molecules upon bond stretching. Namely, the elongation of covalent bonds leads to the enhancement of attractive dispersion interactions. For even larger bond lengths, this effect is canceled by the increase of the repulsive exchange forces resulting in a suppression of the interaction and finally leading to repulsion between monomers.

Experimental and computational evidence for stabilising parallel, offset π[C(O)N(H)NC]⋯π(phenyl) interactions in acetohydrazide derivatives

Stabilising π[C(O)N(H)NC]⋯π(phenyl) interactions are described.

Computational study on noncovalent interactions between (n, n) single-walled carbon nanotubes and simple lignin model-compounds

Composites of carbon nanotubes (CNTs) and lignin are promising and potentially cheap precursors of-to this day-expensive carbon fibers. Since the control of the CNT-lignin interface is crucial to maximize fiber performance, it is imperative to understand the fundamental noncovalent interactions between lignin and CNT. In the present study a density functional theory study is conducted to investigate the fundamental noncovalent interaction strength between metallic (n, n) single-walled CNT (SWCNT) and simple lignin model molecules. In particular, the respective adsorption energies are used to gauge the strength of interaction classes (ππ interaction, CHπ hydrogen bonding and OH-related hydrogen bonding. From the data, substituent-dependent interaction trends as well as class- and curvature-dependent interaction trends are derived. Overall, we find that most of the interaction strength trends appear to be strongly influenced by geometry: flat orientation of the test molecules relative to the (n, n) SWCNT surface and small (n, n) SWCNT curvature-that is, large diameter enhances the CHπ and ππ interactions.

AromTool: predicting aromatic stacking energy using an atomic neural network model

Aromatic stacking exists widely and plays important roles in protein-ligand interactions. Computational tools to automatically analyze the geometry and accurately calculate the energy of stacking interactions are desired for structure-based drug design. Herein, we employed a Behler-Parrinello neural network (BPNN) to build predictive models for aromatic stacking interactions and further integrated it into an open-source Python package named AromTool for benzene-containing aromatic stacking analysis. Based on extensive testing, AromTool presents desirable precision in comparison to DFT calculations and excellent efficiency for high-throughput aromatic stacking analysis of protein-ligand complexes.

Supramolecular structures of NiII and CuII with the sterically demanding Schiff base dyes driven by cooperative action of preagostic and other non-covalent interactions

This work reports on synthesis and extensive experimental and theoretical investigations on photophysical, structural and thermal properties of the NiII and CuII discrete mononuclear homoleptic complexes [Ni(L I,II)2] and [Cu(L I,II)2] fabricated from the Schiff base dyes o-HOC6H4-CH=N-cyclo-C6H11 (HL I) and o-HOC10H6-CH=N-cyclo-C6H11 (HL II), containing the sterically crowding cyclo-hexyl units. The six-membered metallocycles adopt a clearly defined envelope conformation in [Ni(L II)2], while they are much more planar in the structures of [Ni(L I)2] and [Cu(L I,II)2]. It has been demonstrated by in-depth bonding analyses based on the ETS-NOCV and Interacting Quantum Atoms energy-decomposition schemes that application of the bulky substituents, containing several C-H groups, has led to the formation of a set of classical and unintuitive intra- and inter-molecular interactions. All together they are responsible for the high stability of [Ni(L I,II)2] and [Cu(L I,II)2]. More specifically, London dispersion dominated intramolecular C-H⋯O, C-H⋯N and C-H⋯H-C hydrogen bonds are recognized and, importantly, the attractive, chiefly the Coulomb driven, preagostic (not repulsive anagostic) C-H⋯Ni/Cu interactions have been discovered despite their relatively long distances (∼2.8-3.1 Å). All the complexes are further stabilized by the extremely efficient intermolecular C-H⋯π(benzene) and C-H⋯π(chelate) interactions, where both the charge-delocalization and London dispersion constituents appear to be crucial for the crystal packing of the obtained complexes. All the complexes were found to be photoluminescent in CH2Cl2, with [Cu(L II)2] exhibiting the most pronounced emission - the time-dependent density-functional-theory computations revealed that it is mostly caused by metal-to-ligand charge-transfer transitions.

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.

Tetrel Bonding and Other Non-Covalent Interactions Assisted Supramolecular Aggregation in a New Pb(II) Complex of an Isonicotinohydrazide

A new supramolecular Pb(II) complex [PbL(NO₂)]_n was synthesized from Pb(NO₃)₂, N’-(1-(pyridin-2-yl)ethylidene)isonicotinohydrazide (HL) and NaNO₂. [PbL(NO₂)]_n is constructed from discrete [PbL(NO₂)] units with an almost ideal N₂O₃ square pyramidal coordination environment around Pb(II). The ligand L⁻ is coordinated through the 2-pyridyl N-atom, one aza N-atom, and the carbonyl O-atom. The nitrite ligand binds in a κ²-O,O coordination mode through both O-atoms. The Pb(II) center exhibits a hemidirected coordination geometry with a pronounced coordination gap, which allows a close approach of two additional N-atoms arising from the N=C(O) N-atom of an adjacent molecule and from the 4-pyridyl N-atom from the another adjacent molecule, yielding a N₄O₃ coordination, constructed from two Pb–N and three Pb–O covalent bonds, and two Pb⋯N tetrel bonds. Dimeric units in the structure of [PbL(NO₂)]_n are formed by the Pb⋯N=C(O) tetrel bonds and intermolecular electrostatically enforced π⁺⋯π⁻ stacking interactions between the 2- and 4-pyridyl rings and further stabilized by C–H⋯π intermolecular interactions, formed by one of the methyl H-atoms and the 4-pyridyl ring. These dimers are embedded in a 2D network representing a simplified uninodal 3-connected fes (Shubnikov plane net) topology defined by the point symbol (4∙8²). The Hirshfeld surface analysis of [PbL(NO₂)] revealed that the intermolecular H⋯X (X = H, C, N, O) contacts occupy an overwhelming majority of the molecular surface of the [PbL(NO₂)] coordination unit. Furthermore, the structure is characterized by intermolecular C⋯C and C⋯N interactions, corresponding to the intermolecular π⋯π stacking interactions. Notably, intermolecular Pb⋯N and, most interestingly, Pb⋯H interactions are remarkable contributors to the molecular surface of [PbL(NO₂)]. While the former contacts are due to the Pb⋯N tetrel bonds, the latter contacts are mainly due to the interaction with the methyl H-atoms in the π⋯π stacked [PbL(NO₂)] molecules. Molecular electrostatic potential (MEP) surface calculations showed marked electrostatic contributions to both the Pb⋯N tetrel bonds and the dimer forming π⁺⋯π⁻ stacking interactions. Quantum theory of atoms in molecules (QTAIM) analyses underlined the tetrel bonding character of the Pb⋯N interactions. The manifold non-covalent interactions found in this supramolecular assembly are the result of the proper combination of the polyfunctional multidentate pyridine-hydrazide ligand and the small nitrito auxiliary ligand.

Stacking interactions of resonance-assisted hydrogen-bridged rings and C6-aromatic rings

Stacking interactions between six-membered resonance-assisted hydrogen-bridged (RAHB) rings and C6-aromatic rings were systematically studied by analyzing crystal structures in the Cambridge Structural Database (CSD). The interaction energies were calculated by quantum-chemical methods. Although the interactions are stronger than benzene/benzene stacking interactions (-2.7 kcal mol-1), the strongest calculated RAHB/benzene stacking interaction (-3.7 kcal mol-1) is significantly weaker than the strongest calculated RAHB/RAHB stacking interaction (-4.7 kcal mol-1), but for a particular composition of RAHB rings, RAHB/benzene stacking interactions can be weaker or stronger than the corresponding RAHB/RAHB stacking interactions. They are also weaker than the strongest calculated stacking interaction between five-membered saturated hydrogen-bridged rings and benzene (-4.4 kcal mol-1) and between two five-membered saturated hydrogen-bridged rings (-4.9 kcal mol-1). SAPT energy decomposition analyses show that the strongest attractive term in RAHB/benzene stacking interactions is dispersion, however, it is mostly canceled by a repulsive exchange term; hence the geometries of the most stable structures are determined by an electrostatic term.

The relative position of π-π interacting rings notably changes the nature of the substituent effect

The substituent effect in monosubstituted benzene dimers mostly follows changes on electrostatics mainly controlled by the direct interaction of the substituent and the other phenyl ring, whereas the contribution from the interacting rings is smaller. As the substituent is located further away the two contributions become of similar magnitude, so the global result is a combination of both effects. These trends are confirmed in larger systems containing a contact between phenyl rings; at closer distances the interaction of the substituent and the other ring clearly dominates over changes associated with the substituted ring, but as the substituent is located further away its contribution decreases and the contribution from the ring becomes more relevant. Care should be taken in larger systems because the observed energy change can also be affected by interactions with other regions of the molecule not directly involved in the π-π interaction.

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.

Recurrent π–π stacking motifs in three new 4,5-dihydropyrazolyl–thiazole–coumarin hybrids: X-ray characterization, Hirshfeld surface analysis and DFT calculations

Two different π–π stacking modes are described, studied and characterized in the crystal structures of 4,5-dihydropyrazolyl–thiazole–coumarin hybrids, including a partial aliphatic ring.

A new spodium bond driven coordination polymer constructed from mercury(ii) azide and 1,2-bis(pyridin-2-ylmethylene)hydrazine

In this manuscript, the synthesis and X-ray characterization of a new spodium bond driven coordination polymer constructed from mercury(ii) azide and 1,2-bis(pyridin-2-ylmethylene)hydrazine are reported.

Adsorption of acetylene on a rutile TiO2(110) surface: a low temperature STM study

Structure evolution of acetylene on the TiO₂(110) surface.

Fine-tuning the effect of π-π interactions on the stability of the NTB phase

The synthesis and liquid-crystalline properties are reported for novel bent-shaped dimers in which a naphthyl group has been incorporated into the mesogenic cores. In addition to the nematic and twist-bend nematic phase, a new liquid-crystalline phase was observed. The combined experimental and computational study demonstrated how the interplay between the molecular geometry and π-π interactions affects the thermal stability of the twist-bend nematic and nematic phases. Correlation between mesomorphic properties and molecular geometry revealed that a greater conformational diversity leads to a broader distribution of bend-angles and destabilization of the NTB phase. Qualitative correlation between the thermal behaviour and electronic structure of the molecules of a similar geometry suggested that the transition temperatures of both nematic phases depend on the relative contribution of dispersion and electrostatic energies which determines the strength of the π-π interactions. These results provide an insight into how subtle changes in chemical structure can be exploited to tune the intermolecular interactions and influence the thermal stability of the liquid crystalline phase.

On the Nature of σ-σ, σ-π, and π-π Stacking in Extended Systems

Stacking interactions have been evaluated, employing computational methods, in dimers formed by analogous aliphatic and aromatic species of increasing size. Changes in stability as the systems become larger are mostly controlled by the balance of increasing repulsion and dispersion contributions, while electrostatics plays a secondary but relevant role. The interaction energy increases as the size of the system grows, but it does much faster in π-π dimers than in σ-π complexes and more remarkably than in σ-σ dimers. The main factor behind the larger stability of aromatic dimers compared to complexes containing aliphatic molecules is related to changes in the properties of the aromatic systems due to electron delocalization leading to larger dispersion contributions. Besides, an extra stabilization in π-π complexes is due to the softening of the repulsive wall in aromatic species that allows the molecules to come closer.

On the formation of sandwich and multidecker complexes via π⋯π interaction: a DFT study

Sandwich and multidecker complexes via organic π–inorganic π interaction.

A Computational Scheme To Evaluate Hamaker Constants of Molecules with Practical Size and Anisotropy

We propose a computational scheme to evaluate Hamaker constants, A, of molecules with practical sizes and anisotropies. Upon the increasing feasibility of diffusion Monte Carlo (DMC) methods to evaluate binding curves for such molecules to extract the constants, we discussed how to treat the averaging over anisotropy and how to correct the bias due to the nonadditivity. We have developed a computational procedure for dealing with the anisotropy and reducing statistical errors and biases in DMC evaluations, based on possible validations on predicted A. We applied the scheme to cyclohexasilane molecule, Si₆H₁₂, used in "printed electronics" fabrications, getting A ≈ 105 ± 2 zJ, being in plausible range supported even by other possible extrapolations. The scheme provided here would open a way to use handy ab initio evaluations to predict wettabilities as in the form of materials informatics over broader molecules.

Using Density Functional Theory To Study Neutral and Ionized Stacked Thymine Dimers

Stacking interactions in thymine dimers are studied with density functional theory. According to our calculations, six dimers of comparable stability can be prepared at low temperature, but dimerization is impossible at room temperature due to the large entropy contribution that accompanies it. Analysis of vibrational anharmonic coupling terms shows that each of the dimers exhibits distinct vibrational dynamics. Properties of electron density in the intermolecular region are used to analyze neutral stacked species and their ionized forms. Bond paths and critical points in the intermolecular region are identified, but a simple relationship between binding energy and total electron density in the intermolecular critical points could not be found due to an uneven electron distribution in the binding region. The reduced density gradient was confirmed to be a useful tool for analysis of weak stacking interactions. Those interactions also affect vertical and adiabatic ionization energies, which are computed to be slightly lower for the dimers compared to the monomer.

Analysis of the interactions of sulfur-containing amino acids in membrane proteins

The interactions of Met and Cys with other amino acid side chains have received little attention, in contrast to aromatic-aromatic, aromatic-aliphatic or/and aliphatic-aliphatic interactions. Precisely, these are the only amino acids that contain a sulfur atom, which is highly polarizable and, thus, likely to participate in strong Van der Waals interactions. Analysis of the interactions present in membrane protein crystal structures, together with the characterization of their strength in small-molecule model systems at the ab-initio level, predicts that Met-Met interactions are stronger than Met-Cys ≈ Met-Phe ≈ Cys-Phe interactions, stronger than Phe-Phe ≈ Phe-Leu interactions, stronger than the Met-Leu interaction, and stronger than Leu-Leu ≈ Cys-Leu interactions. These results show that sulfur-containing amino acids form stronger interactions than aromatic or aliphatic amino acids. Thus, these amino acids may provide additional driving forces for maintaining the 3D structure of membrane proteins and may provide functional specificity.

Self-Assembled Dehydro[24]annulene Monolayers at the Liquid/Solid Interface: Toward On-Surface Synthesis of Tubular π-Conjugated Nanowires

We have studied the self-assembly behavior of dehydro[24]annulene (D24A) derivatives 1, 2a-2d, and 3a-3c at the liquid/solid interface using scanning tunneling microscopy (STM). Both the relative placement and the nature of the four D24A substituents strongly influence the self-assembly pattern. Overall, the eight D24A derivatives examined in this study display seven types of 2D packing patterns. The D24A derivatives 1, 2a, and 3a have either two or four stearate groups and adopt face-on configurations of their macrocyclic cores with respect to the highly oriented pyrolytic graphite (HOPG) surface. Their 2D packing pattern is determined by the interchain spacings and number of stearate substituents. The D24A derivatives 2b-2d and 3b-3c bear hydrogen-bonding carbamate groups to further strengthen intermolecular interactions. Face-on patterns were also observed for most of these compounds, while an unstable edge-on self-assembly was observed in the case of 2b at room temperature. Stable edge-on self-assemblies of D24A derivatives were sought for this work as an important stepping stone to achieving the on-surface topochemical polymerization of these carbon-rich macrocycles into tubular π-conjugated nanowires. The overall factors determining the 2D packing patterns of D24As at the liquid/solid interface are discussed on the basis of theoretical simulations, providing useful guidelines for controlling the self-assembly pattern of future D24A macrocycles.

Interactions of Molecules with cis and trans Double Bonds: A Theoretical Study of cis- and trans-2-Butene

Noncovalent interactions of cis- and trans-2-butene, as the smallest model systems of molecules with cis and trans double bonds, were studied to find potential differences in interactions of these molecules. The study was performed using quantum chemical methods including very accurate CCSD(T)/CBS method. We studied parallel and displaced parallel interactions in 2-butene dimers, in butane dimers, and between 2-butene and saturated butane. The results show the trend that interactions of 2-butene with butane are the strongest, followed by interactions in butane dimers, whereas the interaction in 2-butene dimers are the weakest. The strongest calculated interaction energy is between trans-2-butene and butane, with a CCSD(T)/CBS energy of -2.80 kcal mol(-1) . Interactions in cis-2-butene dimers are stronger than interactions in trans-2-butene dimers. Interestingly, some of the interactions involving 2-butene are as strong as interactions in a benzene dimer. These insights into interactions of cis- and trans-2-butene can improve understanding of the properties and processes that involve molecules with cis and trans double bonds, such as fatty acids and polymers.

On the energetics of P–P bond dissociation of sterically strained tetraamino-diphosphanes

Thermochemical data for the homolytic P–P bond fission in tetraaminodiphosphanes (R₂N)₂P–P(NR₂)₂ were determined experimentally and computationally. The results confirm that radical formation is favoured by entropic and structural relaxation effects, and disfavoured by dispersion forces. Unlike aminophosphenium cations, the radicals display no strong preference for a planar (R₂N)₂P unit.

Aliphatic–aromatic stacking interactions in cyclohexane–benzene are stronger than aromatic–aromatic interaction in the benzene dimer

Stacking interactions between cyclohexane and benzene were studied in crystal structures from the Cambridge Structural Database and by ab initio calculations.

Exploiting Dispersion-Driven Aggregators as a Route to New One-Dimensional Organic Nanowires

The efficiency of charge carrier mobility in organic semiconductors is heavily dependent upon the long-range organization (i.e., morphology) and the local relative arrangement of the transporting molecules. Here, we exploit London dispersion forces as a design principle to construct compact one-dimensional (1-D) assemblies of quaterthiophene cores. We demonstrate that the substitution of quaterthiophene with dispersion-driven aggregators (e.g., [7]ladderanes, hydrogenated pyrenes, etc.) leads to the formation of highly stable and tightly packed 1-D supramolecular assemblies with electronic compactness superior to that of quaterthiophene crystals. Tunability and even tighter stacking arrangements can be achieved by inserting molecular linkers between the quaterthiophene fragments and the dispersion-driven components. The proposed 1-D nanowires represent an original route toward the rational design of efficient organic semiconductors.

Density functional theory based study of molecular interactions, recognition, engineering, and quantum transport in π molecular systems

CONSPECTUS: In chemical and biological systems, various interactions that govern the chemical and physical properties of molecules, assembling phenomena, and electronic transport properties compete and control the microscopic structure of materials. The well-controlled manipulation of each component can allow researchers to design receptors or sensors, new molecular architectures, structures with novel morphology, and functional molecules or devices. In this Account, we describe the structures and electronic and spintronic properties of π-molecular systems that are important for controlling the architecture of a variety of carbon-based systems. Although DFT is an important tool for describing molecular interactions, the inability of DFT to accurately represent dispersion interactions has made it difficult to properly describe π-interactions. However, the recently developed dispersion corrections for DFT have allowed us to include these dispersion interactions cost-effectively. We have investigated noncovalent interactions of various π-systems including aromatic-π, aliphatic-π, and non-π systems based on dispersion-corrected DFT (DFT-D). In addition, we have addressed the validity of DFT-D compared with the complete basis set (CBS) limit values of coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)] and Møller-Plesset second order perturbation theory (MP2). The DFT-D methods are still unable to predict the correct ordering in binding energies within the benzene dimer and the cyclohexane dimer. Nevertheless, the overall DFT-D predicted binding energies are in reasonable agreement with the CCSD(T) results. In most cases, results using the B97-D3 method closely reproduce the CCSD(T) results with the optimized energy-fitting parameters. On the other hand, vdW-DF2 and PBE0-TS methods estimate the dispersion energies from the calculated electron density. In these approximations, the interaction energies around the equilibrium point are reasonably close to the CCSD(T) results but sometimes slightly deviate from them because interaction energies were not particularly optimized with parameters. Nevertheless, because the electron cloud deforms when neighboring atoms/ions induce an electric field, both vdW-DF2 and PBE0-TS seem to properly reproduce the resulting change of dispersion interaction. Thus, improvements are needed in both vdW-DF2 and PBE0-TS to better describe the interaction energies, while the B97-D3 method could benefit from the incorporation of polarization-driven energy changes that show highly anisotropic behavior. Although the current DFT-D methods need further improvement, DFT-D is very useful for computer-aided molecular design. We have used these newly developed DFT-D methods to calculate the interactions between graphene and DNA nucleobases. Using DFT-D, we describe the design of molecular receptors of π-systems, graphene based electronic devices, metalloporphyrin half-metal based spintronic devices as graphene nanoribbon (GNR) analogs, and graphene based molecular electronic devices for DNA sequencing. DFT-D has also helped us understand quantum phenomena in materials and devices of π-systems including graphene.

C-H···π interactions and the nature of the donor carbon atom

The influence of multiple substituents (F, CH3, NO2, CN, Cl, OH and NH2) on the C-H···π interaction in benzene-ethylene complex was investigated using the estimated CCSD(T) method and complete basis set limit. The results were compared with our earlier reported complexes of benzene-acetylene and benzene-methane, thus completing the sp, sp(2) and sp(3) series of C-H donors. The stabilization energy values for multiple fluoro-substituted benzene-ethylene complexes are found to be very close to those of the multiple fluoro-substituted benzene-methane complexes. Expectedly, the stabilization energies for the multiple methyl-substituted benzene-ethylene complexes lie between those of the multiple methyl-substituted benzene-methane and benzene-acetylene complexes. Energy decomposition analysis using the DFT-SAPT method predicts the dispersion energy to be dominant, similar to the benzene-methane complexes. For the symmetrically disubstituted complexes (-OH, -Cl, -NH2, -CN and -NO2), additional C-H···X interaction was observed, possibly due to the angular orientation of the ethylene molecule. Multidimensional correlation analysis between the electrostatic, dispersion and exchange-repulsion with the C-H···π interaction distance (r), Hammett constant (σ) and the molar refractivity (MR) revealed strong correlation between dispersion energy and the C-H···π interaction distance (r) as well as molar refractivity (MR).

Understanding the fundamental role of π/π, σ/σ, and σ/π dispersion interactions in shaping carbon-based materials

Noncovalent interactions involving aromatic rings, such as π-stacking and CH/π interactions, are central to many areas of modern chemistry. However, recent studies proved that aromaticity is not required for stacking interactions, since similar interaction energies were computed for several aromatic and aliphatic dimers. Herein, the nature and origin of π/π, σ/σ, and σ/π dispersion interactions has been investigated by using dispersion-corrected density functional theory, energy decomposition analysis, and the recently developed noncovalent interaction (NCI) method. Our analysis shows that π/π and σ/σ stacking interactions are equally important for the benzene and cyclohexane dimers, explaining why both compounds have similar boiling points. Also, similar dispersion forces are found in the benzene⋅⋅⋅methane and cyclohexane⋅⋅⋅methane complexes. However, for systems larger than naphthalene, there are enhanced stacking interactions in the aromatic dimers adopting a parallel-displaced configuration compared to the analogous saturated systems. Although dispersion plays a decisive role in stabilizing all the complexes, the origin of the π/π, σ/σ, and σ/π interactions is different. The NCI method reveals that the dispersion interactions between the hydrogen atoms are responsible for the surprisingly strong aliphatic interactions. Moreover, whereas σ/σ and σ/π interactions are local, the π/π stacking are inherently delocalized, which give rise to a non-additive effect. These new types of dispersion interactions between saturated groups can be exploited in the rational design of novel carbon materials.