Perspective: Found in translation: Quantum chemical tools for grasping non-covalent interactions

Rationalizing polymorphism with local correlation-based methods: a case study of pnictogen molecular crystals

A computational workflow is proposed to quantify and rationalize the relative stability of different structures of molecular crystals using cluster models and quantum chemical methods. The Hartree-Fock plus London Dispersion (HFLD) scheme is used to estimate the lattice energy of molecular crystals in various structural arrangements. The fragment-pairwise Local Energy Decomposition (fp-LED) scheme is then employed to quantify the key intermolecular interactions responsible for the relative stability of different crystal structures. The fp-LED scheme provides also in-depth chemical insights by decomposing each interaction into energy components such as dispersion, electrostatics, and exchange. Notably, this analysis requires only a single interaction energy computation per structure on a suitable cluster model. As a case study, two polymorphs of each of the following are considered: naphthyl-substituted dipnictanes (with As, Sb, and Bi as the pnictogen atom) and tris(thiophen-2-yl)bismuthane. The approach outlined offers high accuracy as well as valuable insights for developing design principles to engineer crystal structures with tailored properties, opening up new avenues in the study of molecular aggregates, potentially impacting diverse fields in materials science and beyond.

Consequences of the Pb-S Bond Formation for Lead Halide Perovskites

Lead halide perovskites are structurally not stable due to their ionic bonds. Using sulfur agents in the crystal growth improves the stability and performance of the photovoltaic and light-emitting devices. In this theoretical work, we use a small toy S-radical in place of A cation in the bulk of lead iodide perovskite, and highlight the significance of the Pb-S covalent-double-bond formation for: the charge redistribution on the neighboring bonds that also turn to be covalent, phase transformation to a stable non-perovskite structure, and superior optoelectronic properties. The chemical analysis was performed with the Quantum Theory of Atoms In Molecules (QTAIM) and Non-Covalent Interactions (NCI) index. Excitonic properties were obtained from the solution of ab initio Bethe-Salpeter equation. Presence of the spin-orbit coupling triggers an interplay between the Frenkel and charge-transfer multiexcitons, switching between the photovoltaic and laser applications. Multiexcitons obey the exciton-fission preconditions.

Improving the Efficiency of Luminescent Zn(II)-Modified N-Doped GOQD Nanomaterials in Parkinson's Disease Treatment: A Theoretical Mechanistic Framework Exploring Doping Effect

Levodopa, a widely prescribed drug in Parkinson's disease treatment, stands as the foremost prodrug of dopamine. An affordable self-testing kit is utilized to monitor levodopa content in anti-parkinson drugs in human serum. A photoluminescent trinuclear Zn(II) complex [Zn3(L)2(κ1-OAc)2(κ2-OAc)2] has been synthesized, which cleaves into mononuclear ZC in aqueous solution. ZC was found to detect L-Dopa in Tris-HCl buffer, exhibiting a moderate decrease in PL-emission. The real-life utility of the ZC probe is limited, for its lower sensitivity (LOD 35.3 μM) and separation challenges. Therefore, an interface between homogeneous and heterogeneous supports has been explored, leading to the strategic development of NGOZC, where ZC was grafted onto NGOQD (Graphene oxide quantum dots). This material enables naked- eye detection under both ambient and UV light with color change from bright cyan to green, followed by dark. The nitrogen doping effect was investigated by several comparative investigations involving the synthesis of ZC-grafted GOQD, leading to enhanced quenching performance. Steady-state and time-resolved fluorescence titration study, morphological analysis, and computational calculations have been performed to get insights into the sensing mechanism. To the best of our knowledge, this as-synthesized NGOZC (LOD 1.78 nM) represents a promising strategy and platform for applications in biosensors, especially for Parkinson's and Alzheimer's diseases.

Kohn-Sham fragment energy decomposition analysis

We introduce the concept of Kohn-Sham fragment localized molecular orbitals (KS-FLMOs), which are Kohn-Sham molecular orbitals (MOs) localized in specific fragments constituting a generic molecular system. In detail, we minimize the local electronic energies of various fragments, while maximizing the repulsion between them, resulting in the effective localization of the MOs. We use the developed KS-FLMOs to propose a novel energy decomposition analysis, which we name Kohn-Sham fragment energy decomposition analysis, which allows for rationalizing the main non-covalent interactions occurring in interacting systems both in vacuo and in solution, providing physical insights into non-covalent interactions. The method is validated against state-of-the-art energy decomposition analysis techniques and with high-level calculations.

Dispersion Control over Molecule Cohesion: Exploiting and Dissecting the Tipping Power of Aromatic Rings

ConspectusWe have learned over the past years how London dispersion forces can be effectively used to influence or even qualitatively tip the structure of aggregates and the conformation of single molecules. This happens despite the fact that single dispersion contacts are much weaker than competing polar forces. It is a classical case of strength by numbers, with the importance of London dispersion forces scaling with the system size. Knowledge about the tipping points, however difficult to attain, is necessary for a rational design of intermolecular forces. One requires a careful assessment of the competing interactions, either by sensitive spectroscopic techniques for the study of the isolated molecules and aggregates or by theoretical approaches. Of particular interest are the systems close to the tipping point, when dispersion interactions barely outweigh or approach the strength of the other interactions. Such subtle cases are important milestones for a scale-up to realistic multi-interaction situations encountered in the fields of life and materials science. In searching for examples that provide ideal competing interactions in complexes and small clusters, aromatic systems can offer a diverse set of molecules with a variation of dispersion and electrostatic forces that control the dominant and peripheral interactions. Our combined spectroscopic and theoretical investigations provide valuable insights into the balance of intermolecular forces because they typically allow us to switch the aromatic substituent on and off. High-resolution rotational spectroscopy serves as a benchmark for molecular structures, as correct calculations should be based on correct geometries. When discussing the competition with other noncovalent interactions, obvious competitors are directional hydrogen bonds. As a second counterweight to aryl interactions, we will discuss aurophilic/metallophilic interactions, which also have a strong stabilization with a small number of atoms involved. Vibrational spectroscopy is most sensitive to interactions of light atoms, and the competition of OH hydrogen bonds with dispersion forces in a molecular aggregate can be judged well by the OH stretching frequency. Experiments in the gas phase are ideal for gauging the accuracy of quantum chemical predictions free of solvent forces. A tight collaboration utilizing these three methods allows experiment vs experiment vs theory benchmarking of the overall influence of dispersion in molecular structures and energetics.

Photochemical Transformations of Peptides Containing the N-(2-Selenoethyl)glycine Moiety

The diselenide bond has attracted considerable attention due to its ability to undergo the metathesis reaction in response to visible light. In our previous study, we demonstrated visible-light-induced diselenide metathesis of selenocysteine-containing linear peptides, allowing for the convenient generation of peptide libraries. Here, we investigated the transformation of linear and cyclic peptides containing the N-(2-selenoethyl)glycine moiety. The linear peptides were highly susceptible to the metathesis reaction, whereas the cyclic systems gave only limited conversion yields of the metathesis product. In both cases, side reactions leading to the formation of mono-, di-, and polyselenides were observed upon prolonged irradiation. To confirm the radical mechanism of the reaction, the radical initiator 2,2'-azobis[2-(2-imidazolin-2-yl)propane] dihydrochloride (VA-044) was tested, and it was found to induce diselenide metathesis without photochemical activation. The data were interpreted in the light of quantum-chemical simulations based on density functional theory (DFT). The simulations were performed at the B3LYP-D3BJ/def2-TZVP level of theory using a continuum solvation model (IEF-PCM) and methanol as a solvent.

Decoding energy decomposition analysis: Machine-learned Insights on the impact of the density functional on the bonding analysis

The concept of chemical bonding is a crucial aspect of chemistry that aids in understanding the complexity and reactivity of molecules and materials. However, the interpretation of chemical bonds can be hindered by the choice of the theoretical approach and the specific method utilized. This study aims to investigate the effect of choosing different density functionals on the interpretation of bonding achieved through energy decomposition analysis (EDA). To achieve this goal, a data set was created, representing four bonding groups and various combinations of functionals and dispersion correction schemes. The calculations showed significant variation among the different functionals for the EDA terms, with the dispersion correction terms exhibiting the highest variability. More information was extracted by using machine learning in combination with dimensionality reduction on the data set. Results indicate that, despite the differences in the EDA terms obtained from different functionals, the functional has the least significant impact, suggesting minimal influence on the bonding interpretation.

Unraveling Atomic Contributions to the London Dispersion Energy: Insights into Molecular Recognition and Reactivity

We present a general framework that enables quantification with atomic resolution of the overall London dispersion energy, which can be readily integrated with currently available energy decomposition schemes. This approach can be used to determine the contribution of individual atoms and functional groups to molecular recognition, conformational preferences, molecular stability, and reactivity. Its efficacy across diverse realms of molecular chemistry and biology is demonstrated with application to molecular balances in solution, asymmetric organocatalytic transformations, and a subcomplex of the F1FO ATP synthase.

Halide Complexes of 5,6-Dicyano-2,1,3-Benzoselenadiazole with 1 : 4 Stoichiometry: Cooperativity between Chalcogen and Hydrogen Bonding

The [M4 -Hal]- (M=the title compound; Hal=Cl, Br, and I) complexes were isolated in the form of salts of [Et4 N]+ cation and characterized by XRD, NMR, UV-Vis, DFT, QTAIM, EDD, and EDA. Their stoichiometry is caused by a cooperative interplay of σ-hole-driven chalcogen (ChB) and hydrogen (HB) bondings. In the crystal, [M4 -Hal]- are connected by the π-hole-driven ChB; overall, each [Hal]- is six-coordinated. In the ChB, the electrostatic interaction dominates over orbital and dispersion interactions. In UV-Vis spectra of the M+[Hal]- solutions, ChB-typical and [Hal]- -dependent charge-transfer bands are present; they reflect orbital interactions and allow identification of the individual [Hal]- . However, the structural situation in the solutions is not entirely clear. Particularly, the UV-Vis spectra of the solutions are different from the solid-state spectra of the [Et4 N]+ [M4 -Hal]- ; very tentatively, species in the solutions are assigned [M-Hal]- . It is supposed that the formation of the [M4 -Hal]- proceeds during the crystallization of the [Et4 N]+ [M4 -Hal]- . Overall, M can be considered as a chromogenic receptor and prototype sensor of [Hal]- . The findings are also useful for crystal engineering and supramolecular chemistry.

A DFT investigation of the catalytic oxidation of benzyl alcohol using graphene oxide

CONTEXT

Metal-free heterogeneous materials have attracted great interest due to their potential to facilitate various organic transformations in line with circular economy and green chemistry principles. Among various 2D materials, graphene oxide (GO) is considered an attractive material for numerous applications in physics, chemistry, biology, material sciences, and catalysis. Furthermore, graphene-based catalysts exhibit good catalytic activity toward the selective oxidation of benzyl alcohol to benzaldehyde or benzoic acid under eco-friendly conditions. In this regard, a theoretical investigation was carried out to study both catalytic oxidation reaction pathways (i.e., benzyl alcohols to aldehyde and to benzoic acid) using GO as an eco-friendly and metal-free catalyst.

METHODS

In this study, we report a theoretical investigation at the B3LYP/6-31G level to better understand the oxidation of benzyl alcohol using GO as a metal-free catalyst. The possible bond formation was investigated using the global and local reactivity indexes derived from Fukui functions. Furthermore, we performed a non-covalent interaction (NCI) analysis to unveil the stability and the interaction nature between both reagents and GO surface. The effect of the solvent on the oxidation efficiency was also performed and the results indicate that the solvent significantly affects the decrease of reactivity by increasing the activation barriers through oxidation reactions of benzyl alcohol. Additionally, the electron localization function (ELF) analysis was performed for all intermediates showing the ionic nature of the studied epoxide structure of GO and rules out any type of covalent interaction during the oxidation reaction of benzyl alcohol. All these obtained results are in good agreement with experimental observations and reveal that the epoxide functions on the graphene surface promote an excellent catalyst turnover.

Efficient Detection of Nerve Agents through Carbon Nitride Quantum Dots: A DFT Approach

V-series nerve agents are very lethal to health and cause the inactivation of acetylcholinesterase which leads to neuromuscular paralysis and, finally, death. Therefore, rapid detection and elimination of V-series nerve agents are very important. Herein, we have carried out a theoretical investigation of carbon nitride quantum dots (C₂N) as an electrochemical sensor for the detection of V-series nerve agents, including VX, VS, VE, VG, and VM. Adsorption of V-series nerve agents on C₂N quantum dots is explored at M05-2X/6-31++G(d,p) level of theory. The level of theory chosen is quite adequate in systems describing non-bonding interactions. The adsorption behavior of nerve agents is characterized by interaction energy, non-covalent interaction (NCI), Bader's quantum theory of atoms in molecules (QTAIM), frontier molecular orbital (FMO), electron density difference (EDD), and charge transfer analysis. The computed adsorption energies of the studied complexes are in the range of -12.93 to -17.81 kcal/mol, which indicates the nerve agents are physiosorbed onto C₂N surface through non-covalent interactions. The non-covalent interactions between V-series and C₂N are confirmed through NCI and QTAIM analysis. EDD analysis is carried out to understand electron density shifting, which is further validated by natural bond orbital (NBO) analysis. FMO analysis is used to estimate the changes in energy gap of C₂N on complexation through HOMO-LUMO energies. These findings suggest that C₂N surface is highly selective toward VX, and it might be a promising candidate for the detection of V-series nerve agents.

Generalization of ETS-NOCV and ALMO-COVP Energy Decomposition Analysis to Connect Any Two Electronic States and Comparative Assessment

Energy decomposition analysis (EDA) is a useful tool for obtaining chemically meaningful insights into molecular interactions. The extended transition-state method with natural orbitals for chemical valence (ETS-NOCV) and the absolutely localized molecular orbital-based method with complementary occupied-virtual pairs (ALMO-COVP) are two successful EDA schemes. Working within ground-state generalized Kohn-Sham density functional theory (DFT), we extend these methods to perform EDA between any two electronic states that can be connected by a unitary transformation of density matrices. A direct proof that the NOCV eigenvalues are symmetric pairs is given, and we also prove that the charge and energy difference defined by ALMO are invariant under certain orbital rotations, allowing us to define COVPs. We point out that ETS is actually a 1-point quadrature to obtain the effective Fock matrix, and though it is reasonably accurate, it can be systematically further improved by adding more quadrature points. We explain why the calculated amount of transferred charge measured by ALMO-COVP is typically much smaller than that of ETS-NOCV and explain why the ALMO-COVP values should be preferred. While the two schemes are independent, ETS-NOCV and ALMO-COVP in fact give a very similar chemical picture for a variety of chemical interactions, including H-H⁺, the transition structure for the Diels-Alder reaction between ethene and butadiene, and two hydrogen-bonded complexes, H₂O···F^- and H₂O···HF.

Chalcogen Bond as a Factor Stabilizing Ligand Conformation in the Binding Pocket of Carbonic Anhydrase IX Receptor Mimic

It is postulated that the overexpression of Carbonic Anhydrase isozyme IX in some cancers contributes to the acidification of the extracellular matrix. It was proved that this promotes the growth and metastasis of the tumor. These observations have made Carbonic Anhydrase IX an attractive drug target. In the light of the findings and importance of the glycoprotein in the cancer treatment, we have employed quantum-chemical approaches to study non-covalent interactions in the binding pocket. As a ligand, the acetazolamide (AZM) molecule was chosen, being known as a potential inhibitor exhibiting anticancer properties. First-Principles Molecular Dynamics was performed to study the chalcogen and other non-covalent interactions in the AZM ligand and its complexes with amino acids forming the binding site. Based on Density Functional Theory (DFT) and post-Hartree-Fock methods, the metric and electronic structure parameters were described. The Non-Covalent Interaction (NCI) index and Atoms in Molecules (AIM) methods were applied for qualitative/quantitative analyses of the non-covalent interactions. Finally, the AZM-binding pocket interaction energy decomposition was carried out. Chalcogen bonding in the AZM molecule is an important factor stabilizing the preferred conformation. Free energy mapping via metadynamics and Path Integral molecular dynamics confirmed the significance of the chalcogen bond in structuring the conformational flexibility of the systems. The developed models are useful in the design of new inhibitors with desired pharmacological properties.

A general tight-binding based energy decomposition analysis scheme for intermolecular interactions in large molecules

In this work, a general tight-binding based energy decomposition analysis (EDA) scheme for intermolecular interactions is proposed. Different from the earlier version [Xu et al., J. Chem. Phys. 154, 194106 (2021)], the current tight-binding based density functional theory (DFTB)-EDA is capable of performing interaction analysis with all the self-consistent charge (SCC) type DFTB methods, including SCC-DFTB2/3 and GFN1/2-xTB, despite their different formulas and parameterization schemes. In DFTB-EDA, the total interaction energy is divided into frozen, polarization, and dispersion terms. The performance of DFTB-EDA with SCC-DFTB2/3 and GFN1/2-xTB for various interaction systems is discussed and assessed.

Fast Quantum Approach for Evaluating the Energy of Non-Covalent Interactions in Molecular Crystals: The Case Study of Intermolecular H-Bonds in Crystalline Peroxosolvates

Energy/enthalpy of intermolecular hydrogen bonds (H-bonds) in crystals have been calculated in many papers. Most of the theoretical works used non-periodic models. Their applicability for describing intermolecular H-bonds in solids is not obvious since the crystal environment can strongly change H-bond geometry and energy in comparison with non-periodic models. Periodic DFT computations provide a reasonable description of a number of relevant properties of molecular crystals. However, these methods are quite cumbersome and time-consuming compared to non-periodic calculations. Here, we present a fast quantum approach for estimating the energy/enthalpy of intermolecular H-bonds in crystals. It has been tested on a family of crystalline peroxosolvates in which the H∙∙∙O bond set fills evenly (i.e., without significant gaps) the range of H∙∙∙O distances from ~1.5 to ~2.1 Å typical for strong, moderate, and weak H-bonds. Four of these two-component crystals (peroxosolvates of macrocyclic ethers and creatine) were obtained and structurally characterized for the first time. A critical comparison of the approaches for estimating the energy of intermolecular H-bonds in organic crystals is carried out, and various sources of errors are clarified.

Visible Light-Induced Regio- and Enantiodifferentiating [2 + 2] Photocycloaddition of 1,4-Naphthoquinones Mediated by Oppositely Coordinating 1,3,2-Oxazaborolidine Chiral Lewis Acid

A range of asymmetric photochemical transformations using visible light have recently become considerably attractive. Among the various approaches, chiral Lewis acid association to enones for [2 + 2] and ortho photocycloadditions and oxadi-π-methane rearrangements have shown to be very promising. Naturally, chiral Lewis acid coordination protects one of the prochiral faces of the C═C double bond, which enables an effective enantiodifferentiation in the following bond-forming process(es). Here, we studied regio- and enantiodifferentiating [2 + 2] photocycloaddition reactions of naphthoquinone derivatives mediated by chiral oxazaborolidines. A stereochemical control was quite challenging for the 2-ene-1,4-dione substrate, as a double coordination of Lewis acid essentially cancels out the face selectivity, and a mono-coordination to each carbonyl group leads to an opposite stereochemical outcome. Furthermore, a stepwise coordination in the ground state of Lewis acid in a 1:1 fashion was practically inaccessible. We found that the excited-state decomplexation is a key to accomplish high regio- and enantioselectivities in the photocycloaddition of an ene-dione.

Coordination of Ethylamine on Small Silver Clusters: Structural and Topological (ELF, QTAIM) Analyses

Amine ligands are expected to drive the organization of metallic centers as well as the chemical reactivity of silver clusters early growing during the very first steps of the synthesis of silver nanoparticles via an organometallic route. Density functional theory (DFT) computational studies have been performed to characterize the structure, the atomic charge distribution, and the planar two-dimensional (2D)/three-dimensional (3D) relative stability of small-size silver clusters (Ag_n, 2 ≤ n ≤ 7), with or without an ethylamine (EA) ligand coordinated to the Ag clusters. The transition from 2D to 3D structures is shifted from n = 7 to 6 in the presence of one EA coordinating ligand, and it is explained from the analysis of the Ag-N and Ag-Ag bond energies. For fully EA saturated silver clusters (Ag_n-EA_n), the effect on the 2D/3D transition is even more pronounced with a shift between n = 4 and 5. Subsequent electron localization function (ELF) and quantum theory of atoms in molecules (QTAIM) topological analyses allow for the fine characterization of the dative Ag-N and metallic Ag-Ag bonds, both in nature and in strength. Electron transfer from ethylamine to the coordinated silver atoms induces an increase of the polarization of the metallic core.

Strength and Nature of Host-Guest Interactions in Metal-Organic Frameworks from a Quantum-Chemical Perspective

Metal-organic frameworks (MOFs) offer a convenient means for capturing, transporting, and releasing small molecules. Their rational design requires an in-depth understanding of the underlying non-covalent host-guest interactions, and the ability to easily and rapidly pre-screen candidate architectures in silico. In this work, we devised a recipe for computing the strength and analysing the nature of the host-guest interactions in MOFs. By assessing a range of density functional theory methods across periodic and finite supramolecular cluster scale we find that appropriately constructed clusters readily reproduce the key interactions occurring in periodic models at a fraction of the computational cost. Host-guest interaction energies can be reliably computed with dispersion-corrected density functional theory methods; however, decoding their precise nature demands insights from energy decomposition schemes and quantum-chemical tools for bonding analysis such as the quantum theory of atoms in molecules, the non-covalent interactions index or the density overlap regions indicator.

Computational investigation of a covalent triazine framework (CTF-0) as an efficient electrochemical sensor

In the current study, a covalent triazine framework (CTF-0) was evaluated as an electrochemical sensor against industrial pollutants i.e., O₃, NO, SO₂, SO₃, and CO₂. The deep understanding of analytes@CTF-0 complexation was acquired by interaction energy, NCI, QTAIM, SAPT0, EDD, NBO and FMO analyses. The outcome of interaction energy analyses clearly indicates that all the analytes are physiosorbed onto the CTF-0 surface. NCI and QTAIM analysis were employed to understand the nature of the non-covalent interactions. Furthermore, SAPT0 analysis revealed that dispersion has the highest contribution towards total SAPT0 energy. In NBO analysis, the highest charge transfer is obtained in the case of SO₃@CTF-0 (−0.167 e⁻) whereas the lowest charge transfer is observed in CO₂@CTF-0. The results of NBO charge transfer are also verified through EDD analysis. FMO analysis revealed that the highest reduction in the HOMO–LUMO energy gap is observed in the case of O₃ (5.03 eV) adsorption onto the CTF-0 surface, which indicates the sensitivity of CTF-0 for O₃ analytes. We strongly believe that these results might be productive for experimentalists to tailor a highly sensitive electrochemical sensor using covalent triazine-based frameworks (CTFs).

In the current study, a covalent triazine framework (CTF-0) was evaluated as an electrochemical sensor against industrial pollutants i.e., O₃, NO, SO₂, SO₃, and CO₂.

Kinetics, thermodynamics, equilibrium, surface modelling, and atomic absorption analysis of selective Cu(ii) removal from aqueous solutions and rivers water using silica-2-(pyridin-2-ylmethoxy)ethan-1-ol hybrid material

The removal of heavy metals is attracting considerable attention due to their undesirable effects on the environment. In this investigation, a new adsorbent based on silica functionalized with pyridin-2-ylmethanol (SiPy) was successfully synthesized to yield to a hybrid material. FTIR, SEM, TGA, and specific surface area analysis were used to characterize the structure and morphology of the SiPy hybrid material. Various heavy metal ions such as Cu(ii), Zn(ii), Cd(ii), and Pb(ii) were selected to examine the adsorption efficiency of the newly prepared adsorbent, optimized at varying solution pH, contact time, concentration, and temperature. The adsorbent SiPy displayed good adsorption capacity of 90.25, 75.38, 55.23, and 35.12 mg g⁻¹ for Cu(ii), Zn(ii), Cd(ii), and Pb(ii), respectively, at 25 min and pH = 6. The adsorption behaviors of metal ions onto the SiPy adsorbent fitted well with the pseudo-second-order kinetic mode and the isotherm was better described by the Langmuir isotherm. The thermodynamic studies disclose spontaneous and endothermic adsorption process. Furthermore, the SiPy adsorbent retained good selectivity and regeneration properties after five adsorption–desorption cycles of Cu(ii). A computational investigation of the adsorption mechanism indicates that the N-pyridine, O-hydroxyl, and ether O-atoms play a predominant role during the capture of Cu(ii), Zn(ii), Cd(ii), and Pb(ii). This study proposes the SiPy adsorbent as an attractive material for the selective removal of Cu(ii) from real river water and real industrial wastewater.

The removal of heavy metals is attracting considerable attention due to their undesirable effects on the environment.

XEDA, a fast and multipurpose energy decomposition analysis program

A fast and multipurpose energy decomposition analysis (EDA) program, called XEDA, is introduced for quantitative analysis of intermolecular interactions. This program contains a series of variational EDA methods, including LMO-EDA, GKS-EDA and their extensions, to analyze non-covalent interactions and strong chemical bonds in various environments. XEDA is highly efficient with a similar computational scaling of single point energy calculations. Its efficiency and universality are validated by a series of test examples including van der Waals interactions, hydrogen bonds, radical-radical interactions and strong covalent bonds.

A Comprehensive Picture of the Structures, Energies, and Bonding in the Alanine Dimers

High level quantum mechanical computations and extensive stochastic searches of the potential energy surfaces of the Alanine dimers uncover rich and complex structural and interaction landscapes. A total of 416 strongly bound (up 13.4 kcal mol^-1 binding energies at the DLPNO-CCSD(T)/6-311++G(d,p) level corrected by the basis set superposition error and by the zero point vibrational energies over B3LYP-D3 geometries), close energy equilibrium structures were located, bonded via 32 specific types of intermolecular contacts including Y⋅⋅⋅H-X primary and Y⋅⋅⋅H-C secondary hydrogen bonds, H⋅⋅⋅H dihydrogen contacts, and non conventional anti-electrostatic Y δ - ⋯ X δ - interactions. The putative global minimum is triply degenerate, corresponding to the structure of the common dimer of a carboxylic acid. All quantum descriptors of chemical bonding point to a multitude of weak individual interactions within each dimer, whose cumulative effect results in large binding energies and in an attractive fluxional wall of non-covalent interactions in the interstitial region between the monomers.

Unveiling the complex pattern of intermolecular interactions responsible for the stability of the DNA duplex

Herein, we provide new insights into the intermolecular interactions responsible for the intrinsic stability of the duplex structure of a large portion of human B-DNA by using advanced quantum mechanical methods. Our results indicate that (i) the effect of non-neighboring bases on the inter-strand interaction is negligibly small, (ii) London dispersion effects are essential for the stability of the duplex structure, (iii) the largest contribution to the stability of the duplex structure is the Watson-Crick base pairing - consistent with previous computational investigations, (iv) the effect of stacking between adjacent bases is relatively small but still essential for the duplex structure stability and (v) there are no cooperativity effects between intra-strand stacking and inter-strand base pairing interactions. These results are consistent with atomic force microscope measurements and provide the first theoretical validation of nearest neighbor approaches for predicting thermodynamic data of arbitrary DNA sequences.

CLIFF: A component-based, machine-learned, intermolecular force field

Computation of intermolecular interactions is a challenge in drug discovery because accurate ab initio techniques are too computationally expensive to be routinely applied to drug-protein models. Classical force fields are more computationally feasible, and force fields designed to match symmetry adapted perturbation theory (SAPT) interaction energies can remain accurate in this context. Unfortunately, the application of such force fields is complicated by the laborious parameterization required for computations on new molecules. Here, we introduce the component-based machine-learned intermolecular force field (CLIFF), which combines accurate, physics-based equations for intermolecular interaction energies with machine-learning models to enable automatic parameterization. The CLIFF uses functional forms corresponding to electrostatic, exchange-repulsion, induction/polarization, and London dispersion components in SAPT. Molecule-independent parameters are fit with respect to SAPT2+(3)δMP2/aug-cc-pVTZ, and molecule-dependent atomic parameters (atomic widths, atomic multipoles, and Hirshfeld ratios) are obtained from machine learning models developed for C, N, O, H, S, F, Cl, and Br. The CLIFF achieves mean absolute errors (MAEs) no worse than 0.70 kcal mol^-1 in both total and component energies across a diverse dimer test set. For the side chain-side chain interaction database derived from protein fragments, the CLIFF produces total interaction energies with an MAE of 0.27 kcal mol^-1 with respect to reference data, outperforming similar and even more expensive methods. In applications to a set of model drug-protein interactions, the CLIFF is able to accurately rank-order ligand binding strengths and achieves less than 10% error with respect to SAPT reference values for most complexes.

From Intermolecular Interaction Energies and Observable Shifts to Component Contributions and Back Again: A Tale of Variational Energy Decomposition Analysis

Quantum chemistry in the form of density functional theory (DFT) calculations is a powerful numerical experiment for predicting intermolecular interaction energies. However, no chemical insight is gained in this way beyond predictions of observables. Energy decomposition analysis (EDA) can quantitatively bridge this gap by providing values for the chemical drivers of the interactions, such as permanent electrostatics, Pauli repulsion, dispersion, and charge transfer. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. This review describes the second-generation version of the absolutely localized molecular orbital EDA (ALMO-EDA-II). The effects of different physical contributions on changes in observables such as structure and vibrational frequencies upon complex formation are characterized via the adiabatic EDA. Example applications include red- versus blue-shifting hydrogen bonds; the bonding and frequency shifts of CO, N₂, and BF bound to a [Ru(II)(NH₃)₅]^{2 +} moiety; and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. Additionally, the use of ALMO-EDA-II to benchmark and guide the development of advanced force fields for molecular simulation is illustrated with the recent, very promising, MB-UCB potential.

Switchable supramolecular ensemble for anion binding with ditopic hydrogen-bonded macrocycles

A novel supramolecular strategy has been proposed by using a ditopic H-bonded amide macrocycle that is capable of controlling the binding process in response to external stimulus due to its assembly-and-disassembly-induced anion binding.

Consistent inclusion of continuum solvation in energy decomposition analysis: theory and application to molecular CO2 reduction catalysts

To facilitate computational investigation of intermolecular interactions in the solution phase, we report the development of ALMO-EDA(solv), a scheme that allows the application of continuum solvent models within the framework of energy decomposition analysis (EDA) based on absolutely localized molecular orbitals (ALMOs). In this scheme, all the quantum mechanical states involved in the variational EDA procedure are computed with the presence of solvent environment so that solvation effects are incorporated in the evaluation of all its energy components. After validation on several model complexes, we employ ALMO-EDA(solv) to investigate substituent effects on two classes of complexes that are related to molecular CO2 reduction catalysis. For [FeTPP(CO2-κC)]2- (TPP = tetraphenylporphyrin), we reveal that two ortho substituents which yield most favorable CO2 binding, -N(CH3)3 + (TMA) and -OH, stabilize the complex via through-structure and through-space mechanisms, respectively. The coulombic interaction between the positively charged TMA group and activated CO2 is found to be largely attenuated by the polar solvent. Furthermore, we also provide computational support for the design strategy of utilizing bulky, flexible ligands to stabilize activated CO2 via long-range Coulomb interactions, which creates biomimetic solvent-inaccessible "pockets" in that electrostatics is unscreened. For the reactant and product complexes associated with the electron transfer from the p-terphenyl radical anion to CO2, we demonstrate that the double terminal substitution of p-terphenyl by electron-withdrawing groups considerably strengthens the binding in the product state while moderately weakens that in the reactant state, which are both dominated by the substituent tuning of the electrostatics component. These applications illustrate that this new extension of ALMO-EDA provides a valuable means to unravel the nature of intermolecular interactions and quantify their impacts on chemical reactivity in solution.

Effects of structural variations on π-dimer formation: long-distance multicenter bonding of cation-radicals of tetrathiafulvalene analogues

The multicenter (pancake) bonding between cation-radicals of tetramethyltetraselenafulvalene, TMTSF⁺˙, tetramethyltetrathiafulvalene, TMTTF⁺˙, and bis(ethylenedithio)-tetrathiafulvalene, ET⁺,˙ was compared to that of tetrathiafulvalene, TTF⁺˙. To minimize counter-ion effects, the cation-radical salts with weakly coordinating anions (WCA), tetrakis(3,5-trifluoromethylphenyl)borate, dodecamethylcarborane and hexabromocarborane were prepared. Solid-state (X-ray and EPR) measurements revealed diamagnetic π-dimers in the TMTSF and ET salts and the separate monomers in the TTF salts with all WCAs, while TMTTF existed as a dimer in one and a monomer in two salts. The variable-temperature UV-Vis studies of these salts in solution showed that the thermodynamics of formation of the π-bonded dimers of TMTTF⁺˙ was close to that of TTF⁺˙, while TMTSF⁺˙ and ET⁺˙ showed a higher propensity for π-dimerization. These data indicated that the replacement of sulfur with heavier selenium or insertion of ethylenedithia-substituents into the TTF core increases the π-dimers' stability. Yet, computational analysis indicated that the weakly covalent component of π-bonding decreases in the order TTF > TMTTF > TMTSF > ET. The higher stability of the π-dimers of TMTSF⁺˙ and ET⁺˙ cation-radicals was related to a decrease of the electrostatic repulsion between cationic counter-parts and an increase of dispersion components in these associations.

N-Heterocyclic Carbene Organocatalysis: With or Without Carbenes?

In this work the mechanism of the aldehyde umpolung reactions, catalyzed by azolium cations in the presence of bases, was studied through computational methods. Next to the mechanism established by Breslow in the 1950s that takes effect through the formation of a free carbene, we have suggested that these processes can follow a concerted asynchronous path, in which the azolium cation directly reacts with the substrate, avoiding the formation of the carbene intermediate. We hereby show that substituting the azolium cation, and varying the base or the substrate do not affect the preference for the concerted reaction mechanism. The concerted path was found to exhibit low barriers also for the reactions of thiamine with model substrates, showing that this path might have biological relevance. The dominance of the concerted mechanism can be explained through the specific structure of the key transition state, avoiding the liberation of the highly reactive, and thus unstable carbene lone pair, whereas activating the substrate through hydrogen-bonding interactions. Polar and hydrogen-bonding solvents, as well as the presence of the counterions of the azolium salts facilitate the reaction through carbenes, bringing the barriers of the two reaction mechanisms closer, in many cases making the concerted path less favorable. Thus, our data show that by choosing the exact components in a reaction, the mechanism can be switched to occur with or without carbenes.

Efficient and Environmentally Friendly Adsorbent Based on β-Ketoenol-Pyrazole-Thiophene for Heavy-Metal Ion Removal from Aquatic Medium: A Combined Experimental and Theoretical Study

A new sustainable and environmentally friendly adsorbent based on a β-ketoenol-pyrazole-thiophene receptor grafted onto a silica surface was developed and applied to the removal of heavy-metal ions (Pb(II), Cu(II), Zn(II), and Cd(II)) from aquatic medium. The new material SiNPz-Th was well characterized and confirms the success of covalent binding of the receptor on the silica surface. The effect of environmental parameters on adsorption including pH, contact time, temperature, and the initial concentration were investigated. The maximum adsorption capacities of SiNPz-Th for Pb(II), Cu(II), Zn(II), and Cd(II) ions were 102.20, 76.42, 68.95, and 32.68 mg/g, respectively, at 30 min and pH = 6. The adsorption isotherms, kinetics, and thermodynamic process were investigated and showed efficiency and selectivity toward Pb(II) and good regeneration performance. Density functional theory, noncovalent-interaction, and quantum theory of atoms in molecules calculations were used to study and to gain a deeper understanding of both the adsorption mechanism and selectivity of metal ions onto the adsorbent. Accordingly, metal ions such as Pb(II), Cu(II), and Zn(II) were bidentate coordinated with the adsorbent by nitrogen and oxygen atoms of the Schiff base C=N and hydroxyl group -OH, respectively, to form stable complexes. Whereas Cd(II) was coordinated in a monodentate fashion with oxygen atom of the hydroxyl group. Furthermore, the affinity of SiNPz-Th toward the metal ions was decreased in the order of Pb(II) > Cu(II) > Zn(II) > Cd(II), in good agreement with the experimental results. All these results highlight that SiNPz-Th has good potential to be an advanced adsorbent for the removal of lead ions from real water.

Diversity and uniformity in anion-π complexes of thiocyanate with aromatic, olefinic and quinoidal π-acceptors

Despite the progress in the study of anion-π interactions, there are still inconsistencies in the use of this term and the experimental data about factors affecting the strength of such bonding are limited. To shed light on these issues, we explored supramolecular associations between NCS^- anions and a series of aromatic, olefinic or quinoidal π-acceptors. Combined experimental and computational studies revealed that all these complexes were formed by an attraction of the anion to the face of the π-system, and the arrangements of thiocyanate followed the areas of the most positive potentials on the surfaces of the π-acceptors. The stabilities of the complexes increased with the π-acceptor strength (reflected by their reduction potentials), and were essentially independent of the magnitudes of the maximum electrostatic potentials on their surfaces. The complexes showed intense absorption bands in the UV-Vis range, and the energies of these bands were correlated with the difference of the redox potentials of the anions and π-acceptors. Such features, as well as results of atoms-in-molecules and non-covalent index analyses suggested that besides electrostatics, molecular orbital interactions play a substantial role in the formation of these complexes. The unified trends in variations of the characteristics of the complexes between thiocyanate and a variety of π-acceptors point to their common nature. To embrace diversity and uniformity of the anion-π associates, we suggest (following the halogen bond's definition) that anion-π bonding occurs when there is evidence of a net attraction between the anions and the face of the electrophilic π-system.

Probing radical-molecule interactions with a second generation energy decomposition analysis of DFT calculations using absolutely localized molecular orbitals

Intermolecular interactions between radicals and closed-shell molecules are ubiquitous in chemical processes, ranging from the benchtop to the atmosphere and extraterrestrial space. While energy decomposition analysis (EDA) schemes for closed-shell molecules can be generalized for studying radical-molecule interactions, they face challenges arising from the unique characteristics of the electronic structure of open-shell species. In this work, we introduce additional steps that are necessary for the proper treatment of radical-molecule interactions to our previously developed unrestricted Absolutely Localized Molecular Orbital (uALMO)-EDA based on density functional theory calculations. A "polarize-then-depolarize" (PtD) scheme is used to remove arbitrariness in the definition of the frozen wavefunction, rendering the ALMO-EDA results independent of the orientation of the unpaired electron obtained from isolated fragment calculations. The contribution of radical rehybridization to polarization energies is evaluated. It is also valuable to monitor the wavefunction stability of each intermediate state, as well as their associated spin density profiles, to ensure the EDA results correspond to a desired electronic state. These radical extensions are incorporated into the "vertical" and "adiabatic" variants of uALMO-EDA for studies of energy changes and property shifts upon complexation. The EDA is validated on two model complexes, H₂O˙F and FH˙OH. It is then applied to several chemically interesting radical-molecule complexes, including the sandwiched and T-shaped benzene dimer radical cation, complexes of pyridine with benzene and naphthalene radical cations, binary and ternary complexes of the hydroxyl radical with water (˙OH(H₂O) and ˙OH(H₂O)₂), and the pre-reactive complexes and transition states in the ˙OH + HCHO and ˙OH + CH₃CHO reactions. These examples suggest that this second generation uALMO-EDA is a useful tool for furthering one's understanding of both energetic and property changes associated with radical-molecule interactions.

Surprisingly broad applicability of the cc-pVnZ-F12 basis set for ground and excited states

Excellent convergence properties for the (aug-)cc-pVnZ-F12 basis set family, purpose-made for explicitly correlated calculations, are demonstrated with conventional wave function methods and Kohn-Sham density functional theory for various ground and excited-state calculations. Among the ground-state properties studied are dipole moments, covalent bond lengths, and interaction and reaction energies. For excited states, we looked at vertical excitation energies, UV absorption, and excited-state absorption spectra. Convergence is compared against the basis sets cc-pVnZ, def2-nVD, aug-pcseg-n, and nZaPa-NR. It is established that the cc-pVnZ-F12 family consistently yields results of n + 1 quality and better. Especially, the cc-pVDZ-F12 basis set is found to be a basis set of good cost vs performance trade-off.

Topological Analysis of Ag-Ag and Ag-N Interactions in Silver Amidinate Precursor Complexes of Silver Nanoparticles

A series of silver amidinate complexes has been studied both experimentally and theoretically, in order to investigate the role of the precursor complex in the control of the synthesis of silver nanoparticles via an organometallic route. The replacement of the methyl substituent of the central carbon atom of the amidinate anion by a n-butyl group allows for the crystallization of the tetranuclear silver amidinate complex 3 instead of a mixture of di- and trinuclear silver amidinate complexes 1 and 2, as obtained with a methyl substituent. The relative stabilities and dissociation schemes of various isomeric arrangements of silver atoms in 3 are investigated at the computational DFT level of calculation, depending on the substituents of the amidinate ligand. The tetranuclear silver amidinate complex 4, exhibiting a diamondlike arrangement of the four silver atoms, is also considered. Ag-N bonds and argentophilic Ag-Ag interactions are finely characterized using ELF and QTAIM topological analyses and compared over the series of the related di-, tri-, and tetranuclear silver amidinate complexes 1-4. In contrast to the Ag-N dative bonds very similar over the series, argentophilic Ag-Ag interactions of various strengths and covalence degree are characterized for complexes 1-4. This gives insight into the role of the amidinate substituents on the nuclearity and intramolecular chemical bonding of the silver amidinate precursors, required for the synthesis of dedicated AgNPs with chemically well defined surfaces.

Modified Density Functional Dispersion Correction for Inorganic Layered MFX Compounds (M = Ca, Sr, Ba, Pb and X = Cl, Br, I)

MFX (M = Ca, Ba, Sr, Pb and X = Cl, Br, I) compounds have received considerable attention due to their technological application as X-ray detectors, pressure sensors, and optical data storage materials, when doped with rare-earth ions. MFX compounds belong to the class of layered materials with a tetragonal Matlockite crystal structure, characterized by weakly stacked double-halide layers along the crystallographic c-axis. These layers predominantly determine phase transitions, elastic, and mechanical properties. However, the correct description of the lattice parameter c is a challenge for most standard DFT functionals, which tend to overestimate the lattice parameter c. Because of the weak interactions between the halide layers, dispersion-corrected functionals seem to be a better choice. We investigated 11 different inorganic layered MFX compounds for which experimental data are available, with standard and dispersion-corrected functionals to assess their performance in reproducing the lattice parameter c, structural, and vibrational properties of the MFX compounds. Our results revealed that these functionals do not describe the weak interactions between the halide layers in a balanced way. Therefore, we modified Grimme's popular DFT-D2 dispersion correction scheme in two different ways by (i) replacing the dispersion coefficients and van der Waals radii with those of noble gas atoms or (ii) increasing the van der Waals radii of the MFX atoms up to 40%. Comparison with the available experimental data revealed that the latter approach applied to the PBE (Perdew-Burke-Ernzerhof)-D2 functional with 30% increased van der Waals radii, which we coined PBE-D2* (S_rvdw 1.30) is best suited to fine-tune the description of the weak interlayer interactions in MFX compounds, thus significantly improving the description of their structural, vibrational, and mechanical properties. Work is in progress applying this new, computationally inexpensive scheme to other inorganic layered compounds and periodic systems with weakly stacked layers.

Interplay of π-stacking and inter-stacking interactions in two-component crystals of neutral closed-shell aromatic compounds: periodic DFT study

This paper bridges the gap between high-level ab initio computations of gas-phase models of 1 : 1 arene–arene complexes and calculations of the two-component (binary) organic crystals using atom–atom potentials. The studied crystals consist of electron-rich and electron-deficient compounds, which form infinite stacks (columns) of heterodimers. The sublimation enthalpy of crystals has been evaluated by DFT periodic calculations, while intermolecular interactions have been characterized by Bader analysis of the periodic electronic density. The consideration of aromatic compounds without a dipole moment makes it possible to reveal the contribution of quadrupole–quadrupole interactions to the π-stacking energy. These interactions are significant for heterodimers formed by arenes with more than 2 rings, with absolute values of the traceless quadrupole moment (Q_zz) larger than 10 D Å. The further aggregation of neighboring stacks is due to the C–H⋯F interactions in arene/perfluoroarene crystals. In crystals consisting of arene and an electron-deficient compound such as pyromellitic dianhydride, aggregation occurs due to the C–H⋯O interactions. The C–H⋯F and C–H⋯O inter-stacking interactions make the main contribution to the sublimation enthalpy, which exceeds 150 kJ mol⁻¹ for the two-component crystals formed by arenes with more than 2 rings.

The interplay of π-stacking and inter-stacking interactions in two-component organic crystals without conventional hydrogen bonds.

Electron density learning of non-covalent systems

Chemists continuously harvest the power of non-covalent interactions to control phenomena in both the micro- and macroscopic worlds. From the quantum chemical perspective, the strategies essentially rely upon an in-depth understanding of the physical origin of these interactions, the quantification of their magnitude and their visualization in real-space. The total electron density ρ( r ) represents the simplest yet most comprehensive piece of information available for fully characterizing bonding patterns and non-covalent interactions. The charge density of a molecule can be computed by solving the Schrödinger equation, but this approach becomes rapidly demanding if the electron density has to be evaluated for thousands of different molecules or very large chemical systems, such as peptides and proteins. Here we present a transferable and scalable machine-learning model capable of predicting the total electron density directly from the atomic coordinates. The regression model is used to access qualitative and quantitative insights beyond the underlying ρ( r ) in a diverse ensemble of sidechain-sidechain dimers extracted from the BioFragment database (BFDb). The transferability of the model to more complex chemical systems is demonstrated by predicting and analyzing the electron density of a collection of 8 polypeptides.