How accurate is the density functional theory combined with symmetry-adapted perturbation theory approach for CH–π and π–π interactions? A comparison to supermolecular calculations for the acetylene–benzene dimer

Benchmarking Swaths of Intermolecular Interaction Components with Symmetry-Adapted Perturbation Theory

A benchmark database for interaction energy components of various noncovalent interactions (NCIs) along their dissociation curve is one of the essential needs in theoretical chemistry, especially for the development of force fields and machine-learning methods. We utilize DFT-SAPT or SAPT(DFT) as one of the most accurate methods to generate an extensive stock of the energy components, including dispersion energies extrapolated to the complete basis set limit (CBS). Precise analyses of the created data, and benchmarking the total interaction energies against the best available CCSD(T)/CBS values, reveal different aspects of the methodology and the nature of NCIs. For example, error cancellation effects between the S2 approximation and nonexact xc-potentials occur, and large charge transfer energies in some systems, including heavy atoms, can explain the lower accuracy of DFT-SAPT. This method is perfect for neutral complexes containing light nonmetals, while other systems with heavier atoms should be treated carefully. In the last part, a representative data set for all NCIs is extracted from the original data.

On the Potentiality of X-T-X3 Compounds (T = C, Si, and Ge, and X = F, Cl, and Br) as Tetrel- and Halogen-Bond Donors

The versatility of the X-T-X3 compounds (where T = C, Si, and Ge, and X = F, Cl, and Br) to participate in tetrel- and halogen-bonding interactions was settled out, at the MP2/aug-cc-pVTZ level of theory, within a series of configurations for (X-T-X3)2 homodimers. The electrostatic potential computations ensured the remarkable ability of the investigated X-T-X3 monomers to participate in σ-hole halogen and tetrel interactions. The energetic findings significantly unveil the favorability of the tetrel···tetrel directional configuration with considerable negative binding energies over tetrel···halogen, type III halogen···halogen, and type II halogen···halogen analogs. Quantum theory of atoms in molecules and noncovalent interaction analyses were accomplished to disclose the nature of the tetrel- and halogen-bonding interactions within designed configurations, giving good correlations between the total electron densities and binding energies. Further insight into the binding energy physical meanings was invoked through using symmetry-adapted perturbation theory-based energy decomposition analysis, featuring the dispersion term as the most prominent force beyond the examined interactions. The theoretical results were supported by versatile crystal structures which were characterized by the same type of interactions. Presumably, the obtained findings would be considered as a solid underpinning for future supramolecular chemistry, materials science, and crystal engineering studies, as well as a fundamental linchpin for a better understanding of the biological activities of chemicals.

Highly efficient synthesis of non-planar macrocycles possessing intriguing self-assembling behaviors and ethene/ethyne capture properties

It has been a challenging topic and perpetual task to design and synthesize covalent macrocycles with characteristic self-assembling behaviors and excellent host-guest properties in supramolecular chemistry. Herein, we present a family of macrocyclic diphenylamine[n]arenes (DPA[n]s, n = 3-7) consisting of methyldiphenylamine units through a facile one-pot synthesis strategy. Unlike many other reported macrocyclic arenes, the resultant non-planar DPA[n]s feature intrinsic π-π stacking interactions, interesting self-assembling behaviors and ethene/ethyne capture properties. Specifically, strong multiple intermolecular edge-to-face aromatic interactions in DPA[3] have been systematically investigated both in solid and solution states. The intriguing findings on the intermolecular edge-to-face stacking interaction mode in the macrocycle would further highlight the importance of noncovalent π-π interaction in supramolecular self-assembly. This study will also shed light on the macrocyclic and supramolecular chemistry and, we expect, will provide a direction for design and synthesis of covalent macrocycles in this area.

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.

Theoretical study of the complexes of dichlorobenzene isomers with argon. II. SAPT analysis of the intermolecular interaction

The interaction of argon with dichlorobenzene isomers (DCB-Ar) has been analyzed with the help of the symmetry-adapted perturbation theory based on the density functional description of monomer properties (DFT-SAPT). The global potential energy surface (PES) of these complexes determined from the DFT-SAPT interaction energy (E_int) values has been compared to the CCSD(T) (coupled cluster method including single and double excitations with perturbative triple excitations) PES reported in the companion Paper I [J. Makarewicz and L. Shirkov, J. Chem. Phys. 150, 074301 (2019)]. The equilibrium structures and the binding energies found using DFT-SAPT and CCSD(T) methods combined with adequate basis sets are in good agreement. Besides DCB-Ar, we confirmed that DFT-SAPT gives accurate values of these quantities for other complexes containing an aromatic molecule and Ar. However, DFT-SAPT PES of DCB-Ar is flatter than the corresponding CCSD(T) one. As a result, the intermolecular vibrational energies are systematically underestimated. The analytical form of the important interrelations between SAPT components of E_int, established previously by us [J. Makarewicz and L. Shirkov, J. Chem. Phys. 144, 204115 (2016)], has been approved for the DCB-Ar complexes. Simplified SAPT models based on these relations have been employed to explain physical reasons for differences in the structures and the binding energies of DCB-Ar isomers. It is shown that the equilibrium distance of Ar to DCB plane and the binding energy are determined mainly by dispersion energy. The shift of Ar toward Cl is caused by both exchange and dispersion terms.

Understanding non-covalent interactions in larger molecular complexes from first principles

Non-covalent interactions pervade all matter and play a fundamental role in layered materials, biological systems, and large molecular complexes. Despite this, our accumulated understanding of non-covalent interactions to date has been mainly developed in the tens-of-atoms molecular regime. This falls considerably short of the scales at which we would like to understand energy trends, structural properties, and temperature dependencies in materials where non-covalent interactions have an appreciable role. However, as more reference information is obtained beyond moderately sized molecular systems, our understanding is improving and we stand to gain pertinent insights by tackling more complex systems, such as supramolecular complexes, molecular crystals, and other soft materials. In addition, accurate reference information is needed to provide the drive for extending the predictive power of more efficient workhorse methods, such as density functional approximations that also approximate van der Waals dispersion interactions. In this perspective, we discuss the first-principles approaches that have been used to obtain reference interaction energies for beyond modestly sized molecular complexes. The methods include quantum Monte Carlo, symmetry-adapted perturbation theory, non-canonical coupled cluster theory, and approaches based on the random-phase approximation. By considering the approximations that underpin each method, the most accurate theoretical references for supramolecular complexes and molecular crystals to date are ascertained. With these, we also assess a handful of widely used exchange-correlation functionals in density functional theory. The discussion culminates in a framework for putting into perspective the accuracy of high-level wavefunction-based methods and identifying future challenges.

Theory and practice of modeling van der Waals interactions in electronic-structure calculations

The accurate description of long-range electron correlation, most prominently including van der Waals (vdW) dispersion interactions, represents a particularly challenging task in the modeling of molecules and materials. vdW forces arise from the interaction of quantum-mechanical fluctuations in the electronic charge density. Within (semi-)local density functional approximations or Hartree-Fock theory such interactions are neglected altogether. Non-covalent vdW interactions, however, are ubiquitous in nature and play a key role for the understanding and accurate description of the stability, dynamics, structure, and response properties in a plethora of systems. During the last decade, many promising methods have been developed for modeling vdW interactions in electronic-structure calculations. These methods include vdW-inclusive Density Functional Theory and correlated post-Hartree-Fock approaches. Here, we focus on the methods within the framework of Density Functional Theory, including non-local van der Waals density functionals, interatomic dispersion models within many-body and pairwise formulation, and random phase approximation-based approaches. This review aims to guide the reader through the theoretical foundations of these methods in a tutorial-style manner and, in particular, highlight practical aspects such as the applicability and the advantages and shortcomings of current vdW-inclusive approaches. In addition, we give an overview of complementary experimental approaches, and discuss tools for the qualitative understanding of non-covalent interactions as well as energy decomposition techniques. Besides representing a reference for the current state-of-the-art, this work is thus also designed as a concise and detailed introduction to vdW-inclusive electronic structure calculations for a general and broad audience.

Physisorption of H2 on Fullerenes and the Solvation of C60 by Hydrogen Clusters at Finite Temperature: A Theoretical Assessment

The interaction between hydrogen and carbonaceous nanostructures is of fundamental interest in various areas of physical chemistry. In this contribution we have revisited the physisorption of hydrogen molecules and H₂ clusters on fullerenes, following a first-principles approach in which the interaction is quantitatively evaluated for the C₂₀ system using high-level electronic structure methods. Relative to coupled cluster data at the level of single, double, and perturbative triple excitations taken as a benchmark, the results for rotationally averaged physisorbed H₂ show a good performance of MP2 variants and symmetry-adapted perturbation theory, but significant deviations and basis set convergence issues are found for dispersion-corrected density functional theory. These electronic structure data are fitted to produce effective coarse-grained potentials for use in larger systems such as C₆₀-H₂. Using path-integral molecular dynamics, the potentials are also applied to parahydrogen clusters solvated around fullerenes, across the regime where the first solvation shell becomes complete and as a function of increasing temperature. For C₆₀ our findings indicate a sensible dependence of the critical solvation size on the underlying potential. As the temperature is increased, a competition is found between the surface and radial expansions of the solvation shell, with one molecule popping away at intermediate temperatures but getting reinserted at even higher temperatures.

Symmetry-adapted perturbation theory potential for the adenine dimer

A new ab initio intermolecular interaction potential for the adenine dimer has been developed.

Multi-spectroscopic and theoretical analyses on the diphenyl ether–tert-butyl alcohol complex in the electronic ground and electronically excited state

Multi-spectroscopic and theoretical investigations on the isolated diphenyl ether–tert-butyl alcohol complex – an ideal benchmark system for theory with strongly competing OH–O and OH–π binding motifs.

Character of intermolecular interaction in pyridine-argon complex: Ab initio potential energy surface, internal dynamics, and interrelations between SAPT energy components

The pyridine-Ar (PAr) van der Waals (vdW) complex is studied using a high level ab initio method. Its structure, binding energy, and intermolecular vibrational states are determined from the analytical potential energy surface constructed from interaction energy (IE) values computed at the coupled cluster level of theory with single, double, and perturbatively included triple excitations with the augmented correlation consistent polarized valence double-ζ (aug-cc-pVDZ) basis set complemented by midbond functions. The structure of the complex at its global minimum with Ar at a distance of 3.509 Å from the pyridine plane and shifted by 0.218 Å from the center of mass towards nitrogen agrees well with the corresponding equilibrium structure derived previously from the rotational spectrum of PAr. The PAr binding energy De of 392 cm(-1) is close to that of 387 cm(-1) calculated earlier at the same ab initio level for the prototypical benzene-Ar (BAr) complex. However, under an extension of the basis set, De for PAr becomes slightly lower than De for BAr. The ab initio vdW vibrational energy levels allow us to estimate the reliability of the methods for the determination of the vdW fundamentals from the rotational spectra. To disclose the character of the intermolecular interaction in PAr, the symmetry-adapted perturbation theory (SAPT) is employed for the analysis of different physical contributions to IE. It is found that SAPT components of IE can be approximately expressed in the binding region by only two of them: the exchange repulsion and dispersion energy. The total induction effect is negligible. The interrelations between various SAPT components found for PAr are fulfilled for a few other complexes involving aromatic molecules and Ar or Ne, which indicates that they are valid for all rare gas (Rg) atoms and aromatics.

The van der Waals interactions in rare-gas dimers: the role of interparticle interactions

We investigate the potential energy curves of rare-gas dimers with various ranges and strengths of interparticle interactions (nuclear–electron, electron–electron, and nuclear–nuclear interactions).

First principles potential for the cytosine dimer

A new first principles potential for the cytosine dimer.

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).

Thermo- and mechanical-grinding-triggered color and luminescence switches of the diimine-platinum(II) complex with 4-bromo-2,2'-bipyridine

The square-planar diimine-platinum(II) complex, Pt(4-Brbpy)(C≡CC6H5)2 (1) (4-Brbpy = 4-bromo-2,2'-bipyridine), was prepared and characterized. Solid-state 1 exhibits reversible thermo- and mechanical-grinding-triggered color and luminescence changes. When crystalline 1·2(CH2Cl2) or 1·2(CHCl3) are heated or ground, the original bright yellow-green emission centered at 525 (549, sh) nm changed to 637 and 690 nm, corresponding to thermo- and mechanochromic response shifts of approximately 88-112 nm and 141-165 nm, respectively. Meanwhile the crystalline state changes into an amorphous phase in both processes. Once the amorphous sample absorbs organic vapors, it can be reverted to the original crystalline state, along with red luminescence turning back to yellow-green emission. The reversibility of thermo- and mechanical-grinding-triggered chromic luminescence properties has been dynamically monitored by emission spectra and X-ray diffraction patterns. The dramatic thermo- and mechanical-grinding-triggered emission red shifts are most likely due to the conversion of the (3)MLCT/(3)LLCT emission state into the (3)MMLCT triplet state.

The relative roles of electrostatics and dispersion in the stabilization of halogen bonds

In this work we highlight recent work aimed at the characterization of halogen bonds. Here we discuss the origins of the σ-hole, the modulation of halogen bond strength by changing of neighboring chemical groups (i.e. halogen bond tuning), the performance of various computational methods in treating halogen bonds, and the strength and character of the halogen bond, the dihalogen bond, and two hydrogen bonds in bromomethanol dimers (which serve as model complexes) are compared. Symmetry adapted perturbation theory analysis of halogen bonding complexes indicates that halogen bonds strongly depend on both dispersion and electrostatics. The electrostatic interaction that occurs between the halogen σ-hole and the electronegative halogen bond donor is responsible for the high degree of directionality exhibited by halogen bonds. Because these noncovalent interactions have a strong dispersion component, it is important that the computational method used to treat a halogen bonding system be chosen very carefully, with correlated methods (such as CCSD(T)) being optimal. It is also noted here that most forcefield-based molecular mechanics methods do not describe the halogen σ-hole, and thus are not suitable for treating systems with halogen bonds. Recent attempts to improve the molecular mechanics description of halogen bonds are also discussed.

QM/MM investigations of organic chemistry oriented questions

About 35 years after its first suggestion, QM/MM became the standard theoretical approach to investigate enzymatic structures and processes. The success is due to the ability of QM/MM to provide an accurate atomistic picture of enzymes and related processes. This picture can even be turned into a movie if nuclei-dynamics is taken into account to describe enzymatic processes. In the field of organic chemistry, QM/MM methods are used to a much lesser extent although almost all relevant processes happen in condensed matter or are influenced by complicated interactions between substrate and catalyst. There is less importance for theoretical organic chemistry since the influence of nonpolar solvents is rather weak and the effect of polar solvents can often be accurately described by continuum approaches. Catalytic processes (homogeneous and heterogeneous) can often be reduced to truncated model systems, which are so small that pure quantum-mechanical approaches can be employed. However, since QM/MM becomes more and more efficient due to the success in software and hardware developments, it is more and more used in theoretical organic chemistry to study effects which result from the molecular nature of the environment. It is shown by many examples discussed in this review that the influence can be tremendous, even for nonpolar reactions. The importance of environmental effects in theoretical spectroscopy was already known. Due to its benefits, QM/MM can be expected to experience ongoing growth for the next decade.In the present chapter we give an overview of QM/MM developments and their importance in theoretical organic chemistry, and review applications which give impressions of the possibilities and the importance of the relevant effects. Since there is already a bunch of excellent reviews dealing with QM/MM, we will discuss fundamental ingredients and developments of QM/MM very briefly with a focus on very recent progress. For the applications we follow a similar strategy.

Benzene⋯acetylene: a structural investigation of the prototypical CH⋯π interaction

The benzene⋯acetylene dimer is a symmetric top with μ = 0.438(11) D and H⋯π = 2.4921(1) Å.

Nature of noncovalent interactions in catenane supramolecular complexes: calibrating the MM3 force field with ab initio, DFT, and SAPT methods

The design and assembly of mechanically interlocked molecules, such as catenanes and rotaxanes, are dictated by various types of noncovalent interactions. In particular, [C-H···O] hydrogen-bonding and π-π stacking interactions in these supramolecular complexes have been identified as important noncovalent interactions. With this in mind, we examined the [3]catenane 2·4PF6 using molecular mechanics (MM3), ab initio methods (HF, MP2), several versions of density functional theory (DFT) (B3LYP, M0X), and the dispersion-corrected method DFT-D3. Symmetry adapted perturbation theory (DFT-SAPT) provides the highest level of theory considered, and we use the DFT-SAPT results both to calibrate the other electronic structure methods, and the empirical potential MM3 force field that is often used to describe larger catenane and rotaxane structures where [C-H···O] hydrogen-bonding and π-π stacking interactions play a role. Our results indicate that the MM3 calculated complexation energies agree qualitatively with the energetic ordering from DFT-SAPT calculations with an aug-cc-pVTZ basis, both for structures dominated by [C-H···O] hydrogen-bonding and π-π stacking interactions. When the DFT-SAPT energies are decomposed into components, we find that electrostatic interactions dominate the [C-H···O] hydrogen-bonding interactions, while dispersion makes a significant contribution to π-π stacking. Another important conclusion is that DFT-D3 based on M06 or M06-2X provides interaction energies that are in near-quantitative agreement with DFT-SAPT. DFT results without the D3 correction have important differences compared to DFT-SAPT, while HF and even MP2 results are in poor agreement with DFT-SAPT.