Assessment of the Performance of MP2 and MP2 Variants for the Treatment of Noncovalent Interactions

Noticeable characteristics of conventional and nonconventional hydrogen bonds in the binary systems of chalcogenoaldehyde and chalcogenocarboxylic acid derivatives

Forty-eight stable structures of complexes formed between XCHZ and RCZOH (with X = H, F; R = H, F, Cl, Br, CH3, NH2; Z = O, S, Se, Te) were comprehensively investigated. It was found that the HZ-RZ complexes were more stable than the FZ-RZ ones, and their stability tendency decreased in the following order of Z: O > S > Se > Te. A predominant role of the electrostatic component was observed in XO-RO, while an outstanding contribution of the induction term was estimated in XS-RS, XSe-RSe, and XTe-RTe. A pivotal role of O compared to S, Se, and Te for improving the strength and characteristics of nonconventional Csp2 -H⋯O/S/Se/Te hydrogen bonds was proposed. The O-H⋯Z hydrogen bonds were much more stable than the nonconventional Csp2 -H⋯Z hydrogen bonds. Following complexation, the stretching frequency for Csp2 -H involving nonconventional Csp2 -H⋯Z hydrogen bonds gradually turned from the blue shift to red shift when one O of >C[double bond, length as m-dash]O in XCHO and RCOOH was substituted by S, Se, and Te, with R varying from the electron-withdrawing to electron-donating groups. A very large red-shift of the O-H⋯Z hydrogen bonds up to -535.4 cm-1 and a Csp2 -H blue-shift of the nonconventional Csp2 -H⋯O hydrogen bonds reaching 86.9 cm-1 were observed in this work. It was noted that the considerable decrease in the intramolecular electron density transfer to the σ*(Csp2 -H) orbitals significantly impacted on the blue-shift of the Csp2 -H bonds involving hydrogen bonds.

Massive Assessment of the Geometries of Atmospheric Molecular Clusters

Atmospheric molecular clusters are important for the formation of new aerosol particles in the air. However, current experimental techniques are not able to yield direct insight into the cluster geometries. This implies that to date there is limited information about how accurately the applied computational methods depict the cluster structures. Here we massively benchmark the molecular geometries of atmospheric molecular clusters. We initially assessed how well different DF-MP2 approaches reproduce the geometries of 45 dimer clusters obtained at a high DF-CCSD(T)-F12b/cc-pVDZ-F12 level of theory. Based on the results, we find that the DF-MP2/aug-cc-pVQZ level of theory best resembles the DF-CCSD(T)-F12b/cc-pVDZ-F12 reference level. We subsequently optimized 1283 acid-base cluster structures (up to tetramers) at the DF-MP2/aug-cc-pVQZ level of theory and assessed how more approximate methods reproduce the geometries. Out of the tested semiempirical methods, we find that the newly parametrized atmospheric molecular cluster extended tight binding method (AMC-xTB) is most reliable for locating the correct lowest energy configuration and yields the lowest root mean square deviation (RMSD) compared to the reference level. In addition, we find that the DFT-3c methods show similar performance as the usually employed ωB97X-D/6-31++G(d,p) level of theory at a potentially reduced computational cost. This suggests that these methods could prove to be valuable for large-scale screening of cluster structures in the future.

Aromatic Residues in Proteins: Re-Evaluating the Geometry and Energetics of π-π, Cation-π, and CH-π Interactions

Aromatic residues can participate in various biomolecular interactions, such as π-π, cation-π, and CH-π interactions, which are essential for protein structure and function. Here, we re-evaluate the geometry and energetics of these interactions using quantum mechanical (QM) calculations, focusing on pairwise interactions involving the aromatic amino acids Phe, Tyr, and Trp and the cationic amino acids Arg and Lys. Our findings reveal that π-π interactions, while energetically favorable, are less abundant in structured proteins than commonly assumed and are often overshadowed by previously underappreciated, yet prevalent, CH-π interactions. Cation-π interactions, particularly those involving Arg, show strong binding energies and a specific geometric preference toward stacked conformations, despite the global QM minimum, suggesting that a rather perpendicular T-shape conformation should be more favorable. Our results support a more nuanced understanding of protein stabilization via interactions involving aromatic residues. On the one hand, our results challenge the traditional emphasis on π-π interactions in structured proteins by showing that CH-π and cation-π interactions contribute significantly to their structure. On the other hand, π-π interactions appear to be key stabilizers in solvated regions and thus may be particularly important to the stabilization of intrinsically disordered proteins.

To Pair or not to Pair? Machine-Learned Explicitly-Correlated Electronic Structure for NaCl in Water

The extent of ion pairing in solution is an important phenomenon to rationalize transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The relative stabilities of the paired and solvent shared states in the PMF and the barrier between them are highly sensitive to the underlying potential energy surface. However, direct application of accurate electronic structure methods is challenging, since long simulations are required. We develop wave function based machine learning potentials with the random phase approximation (RPA) and second order Møller-Plesset (MP2) perturbation theory for the prototypical system of Na and Cl ions in water. We show both methods in agreement, predicting the paired and solvent shared states to have similar energies (within 0.2 kcal/mol). We also provide the same benchmarks for different DFT functionals as well as insight into the PMF based on simple analyses of the interactions in the system.

Exploring alkali metal cation⋯hydrogen interaction in the formation half sandwich complexes with cycloalkanes: a DFT approach

Gas and solvent phase stability of half sandwich complexes between cycloalkanes viz. cyclopropane, cyclobutane, cyclopentane, cyclohexane, bicyclo[2.2.2]octane and adamantane with alkali metal cations (Li+, Na+ and K+) are analysed using density functional theory (DFT). M06-2X/6-31++G(d,p) level is primarily used for the study. The studied half sandwich complexes are stable in gas phase (stabilization energy upto 26.55 kcal mol−1). Presence of solvent phase irrespective of its dielectric, imparts negative impact on the stability of the chosen complexes. The formation of the complexes is exothermic in nature. The process of complexation is both enthalpy (ΔH) and free energy (ΔG) driven. Variation in HOMO (highest occupied molecular orbital) energy also indicates towards the chemical stability of complexes. The interaction is non-covalent with primary contribution from induction component. NBO analysis indicates that C–H bond is the donor and antibonding metal orbital is the acceptor site in the process of complexation. Stability of the complexes depends on the size of the interacting monomers.

Role of O-H⋯O/S conventional hydrogen bonds in considerable Csp2 -H blue-shift in the binary systems of acetaldehyde and thioacetaldehyde with substituted carboxylic and thiocarboxylic acids

Stable binary complexes of RCZOH⋯CH3CHZ (R = CH3, H, F; Z = O, S) are due to contributions from the O-H⋯O/S and Csp2 -H⋯O/S hydrogen bonds. The strength of Csp2 /O-H⋯O is 1.5 to 2 times greater than that of the Csp2 /O-H⋯S bond. The substitution of H(Csp2 ) of HCZOH by CH3 causes a decrease in complex stability, while the opposite trend occurs for the F atom. A very large red shift of the O-H stretching frequency in O-H⋯O/S bonds was observed. A surprising Csp2 -H blue shift up to 104.5 cm-1 was observed for the first time. It is found that the presence of O-H⋯O/S hydrogen bonds and a decisive role of intramolecular hyperconjugation interactions in the complex cause a significant blue shift of the Csp2 -H covalent bonds. A striking role of O compared to the S atom in determining the blue shift of Csp2 -H stretching vibration and stability of binary complexes is proposed. The obtained results show that the ratio of deprotonation enthalpy and proton affinity could be considered as an index for the classification of the non-conventional hydrogen bond. SAPT2+ results show that the strength of RCSOH⋯CH3CHS complexes is dominated by electrostatic and induction energies, while a larger contribution to the stability of remaining complexes is detected for the electrostatic component.

Comparative investigation of Cu(II) complexes with dithiocarbazate: Structural design, theoretical calculation, and in vitro antitumor activity

The present work reports the synthesis and investigation by semi-empirical Density Functional Theory (DFT), physical chemistry, and spectroscopic methods of two dithiocarbazates, 2-acetylpyridine-S-p-bromobenzyl-dithiocarbazate (HL¹) and 2-acetylpyridine-S-p-nitrobenzyl-dithiocarbazate (HL²) and their Cu(II) complexes, [Cu(L¹)Cl] (1), [Cu(L¹)Br] (2), [Cu(L²)Cl] (3) and [Cu(L²)Br] (4). Single crystal X-ray analyzes showed distorted square planar geometry to the metal centers, which tridentate ligands coordinated by the NNS system and an additional halogen (Cl^- or Br^-) to complete the coordination sphere. Mass spectrometry data indicated the presence of [Cu(L¹)(DMF)]⁺ and [Cu(L²)(DMF)]⁺, due to the exchanging of chloride/bromide ions and characteristic fragmentations of the compounds. The DFT composite method B97-3c was employed to optimize the geometries of ligands and complexes and IR spectra were calculated revealing good agreement with experimental data. Hydrogen bonds and π⋅⋅⋅π stacking interactions upon the molecular packing were investigated by Hirshfeld surface and fingerprint plots with the main interactions attributed to the H⋅⋅⋅H contacts. The biological activity of the dithiocarbazates and their Cu(II) complexes were evaluated in vitro against the human glioma U251 cells. Results revealed that the free dithiocarbazates present great in vitro antitumor activity that is increased after the complexation with copper. The measurement of cytotoxicity of the compounds showed biological activity in a low range of concentration, which indicates high efficiency as potential drugs.

Influence of cation-π interactions to the structural stability of phycocyanin proteins: A computational study

The influences of cation-π interactions in phycocyanin proteins and their environmental preferences were analyzed. The number of interactions formed by arginine showed to be higher than those formed by the lysine in the cationic group, while histidine is comparatively higher than phenylalanine and N-terminal residue in the π group. Arg-Tyr and Arg-Phe interacting pairs are predominant among the various pairs analyzed. Cation-π interactions are distance-dependent and can be realized above a wider area above the π ring. We analyzed the energy contribution resulting from cation-π interactions using ab initio calculations. The energy contribution resulting from the most frequent cation-π interactions was in the lower range of strong hydrogen bonds. The results showed that, while most of their interaction energies lay ranged from - 2 to - 8 kcal/mol, those energies could be up to -12- 12 kcal/mol. Stabilization centers for these proteins showed that all residues found in cation-π interactions are important in locating one or more of such centers. In the cation-π interacting residues, 54% of the amino acid residues involved in these interactions might be conserved in phycocyanins. From this study, we infer that cation-π forming residues play an important role in the stability of the multiply commercially used phycocyanin proteins and could help structural biologists and medicinal chemists to design better and safer drugs.

Formation of sandwich and multidecker complexes between O2 and alkali/alkaline earth metals: A DFT study

Abstract: Feasibility of formation of sandwich and multidecker complexes between O2 molecules and alkali/alkaline earth metal has been analyzed in the light of density functional theory (DFT). High value of...

Investigations on the role of cation-π interactions in active centers of superoxide dismutase

In this study, we have analysed the influence of cation-? interactions on stability and properties of superoxide dismutase (SOD) active centres. The number of interactions formed by arginine is higher than lysine in the cationic group, while histidine is comparatively higher in the ? group. The energy contribution resulting from most frequent cation-? interactions was in the lower range of strong hydrogen bonds. The cation-? interactions involving transition metal ions as cation have energy more negative than -418.4 kJ mol-1. Stabilization centres for these proteins showed that all residues involved in cation-? interactions were important in locating one or more of such centres. The majority of the residues involved in cation-p interactions were evolutionarily conserved and might have a significant contribution towards the stability of SOD proteins. The results presented in this work can be very useful for understanding the contribution of cation-? interactions to the stability of SOD active canters.

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

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

Local energy decomposition analysis and molecular properties of encapsulated methane in fullerene (CH4@C60)

Methane has been successfully encapsulated within cages of C₆₀ fullerene, which is an appropriate model system to study confinement effects. Its chemistry and physics are also relevant for theoretical model descriptions. Here we provide insights into intermolecular interactions and predicted spectroscopic responses of the CH₄@C₆₀ complex and compared them with results from other methods and with data from the literature. Local energy decomposition analysis (LED) within the domain-based local pair natural orbital coupled cluster singles, doubles, and perturbative triples (DLPNO-CCSD(T)) framework was used, and an efficient protocol for studies of endohedral complexes of fullerenes is proposed. This approach allowed us to assess energies in relation to electronic and geometric preparation, electrostatics, exchange, and London dispersion for the CH₄@C₆₀ endohedral complex. The calculated stabilization energy of CH₄ inside the C₆₀ fullerene was -13.5 kcal mol^-1 and its magnitude was significantly larger than the latent heat of evaporation of CH₄. Evaluation of vibrational frequencies and polarizabilities of the CH₄@C₆₀ complex revealed that the infrared (IR) and Raman bands of the endohedral CH₄ were essentially "silent" due to the dielectric screening effect of C₆₀, which acted as a molecular Faraday cage. Absorption spectra in the UV-vis domain and ionization potentials of C₆₀ and CH₄@C₆₀ were predicted. They were almost identical. The calculated ¹H/¹³C NMR shifts and spin-spin coupling constants were in very good agreement with experimental data. In addition, reference DLPNO-CCSD(T) interaction energies for complexes with noble gases (Ng@C₆₀; Ng = He, Ne, Ar, Kr) were calculated. The values were compared with those derived from supramolecular MP2/SCS-MP2 calculations and estimates with London-type formulas by Pyykkö and coworkers [Phys. Chem. Chem. Phys., 2010, 12, 6187-6203], and with values derived from DFT-based symmetry-adapted perturbation theory (DFT-SAPT) by Hesselmann & Korona [Phys. Chem. Chem. Phys., 2011, 13, 732-743]. Selected points at the potential energy surface of the endohedral He₂@C₆₀ trimer were considered. In contrast to previous theoretical attempts with the DFT/MP2/SCS-MP2/DFT-SAPT methods, our calculations at the DLPNO-CCSD(T) level of theory predicted the He₂@C₆₀ trimer to be thermodynamically stable, which is in agreement with experimental observations.

Exploring the Limits of Second- and Third-Order Møller-Plesset Perturbation Theories for Noncovalent Interactions: Revisiting MP2.5 and Assessing the Importance of Regularization and Reference Orbitals

This work systematically assesses the influence of reference orbitals, regularization, and scaling on the performance of second- and third-order Møller-Plesset perturbation theory wave function methods for noncovalent interactions (NCIs). Testing on 19 data sets (A24, DS14, HB15, HSG, S22, X40, HW30, NC15, S66, AlkBind12, CO2Nitrogen16, HB49, Ionic43, TA13, XB18, Bauza30, CT20, XB51, and Orel26rad) covers a wide range of different NCIs including hydrogen bonding, dispersion, and halogen bonding. Inclusion of potential energy surfaces from different hydrogen bonds and dispersion-bound complexes gauges accuracy for nonequilibrium geometries. Fifteen methods are tested. In notation where nonstandard choices of orbitals are denoted as methods:orbitals, these are MP2, κ-MP2, SCS-MP2, OOMP2, κ-OOMP2, MP3, MP2.5, MP3:OOMP2, MP2.5:OOMP2, MP3:κ-OOMP2, MP2.5:κ-OOMP2, κ-MP3:κ-OOMP2, κ-MP2.5:κ-OOMP2, MP3:ωB97X-V, and MP2.5:ωB97X-V. Furthermore, we compare these methods to the ωB97M-V and B3LYP-D3 density functionals, as well as CCSD. We find that the κ-regularization (κ = 1.45 au was used throughout) improves the energetics in almost all data sets for both MP2 (in 17 out of 19 data sets) and OOMP2 (16 out of 19). The improvement is significant (e.g., the root-mean-square deviation (RMSD) for the S66 data set is 0.29 kcal/mol for κ-OOMP2 versus 0.67 kcal/mol for MP2) and for interactions between stable closed-shell molecules, not strongly dependent on the reference orbitals. Scaled MP3 (with a factor of 0.5) using κ-OOMP2 reference orbitals (MP2.5:κ-OOMP2) provides significantly more accurate results for NCIs across all data sets with noniterative O(N⁶) scaling (S66 data set RMSD: 0.10 kcal/mol). Across the entire data set of 356 points, the improvement over standard MP2.5 is approximately a factor of 2: RMSD for MP3:κ-OOMP2 is 0.25 vs 0.50 kcal/mol for MP2.5. The use of high-quality density functional reference orbitals (ωB97X-V) also significantly improves the results of MP2.5 for NCI over a Hartree-Fock orbital reference. All our assessments and conclusions are based on the use of the medium-sized aug-cc-pVTZ basis to yield results that are directly compared against complete basis set limit reference values.

A Scalable Graph Neural Network Method for Developing an Accurate Force Field of Large Flexible Organic Molecules

An accurate force field is the key to the success of all molecular mechanics simulations on organic polymers and biomolecules. Accurate correlated wave function (CW) methods scale poorly with system size, so this poses a great challenge to the development of an extendible ab initio force field for large flexible organic molecules at the CW level of accuracy. In this work, we combine the physics-driven nonbonding potential with a data-driven subgraph neural network bonding model (named sGNN). Tests on polyethylene glycol, polyethene, and their block polymers show that our strategy is highly accurate and robust for molecules of different sizes and chemical compositions. Therefore, one can develop a parameter library of small molecular fragments (with sizes easily accessible to CW methods) and assemble them to predict the energy of large polymers, thus opening a new path to next-generation organic force fields.

Noncovalent Interactions from Models for the Møller-Plesset Adiabatic Connection

Given the omnipresence of noncovalent interactions (NCIs), their accurate simulations are of crucial importance across various scientific disciplines. Here we construct accurate models for the description of NCIs by an interpolation along the Møller-Plesset adiabatic connection (MP AC). Our interpolation approximates the correlation energy, by recovering MP2 at small coupling strengths and the correct large-coupling strength expansion of the MP AC, recently shown to be a functional of the Hartree-Fock density. Our models are size consistent for fragments with nondegenerate ground states, have the same cost as double hybrids, and require no dispersion corrections to capture NCIs accurately. These interpolations greatly reduce large MP2 errors for typical π-stacking complexes (e.g., benzene-pyridine dimers) and for the L7 data set. They are also competitive with state-of-the-art dispersion enhanced functionals and can even significantly outperform them for a variety of data sets, such as CT7 and L7.

Data-efficient machine learning for molecular crystal structure prediction

The combination of modern machine learning (ML) approaches with high-quality data from quantum mechanical (QM) calculations can yield models with an unrivalled accuracy/cost ratio. However, such methods are ultimately limited by the computational effort required to produce the reference data. In particular, reference calculations for periodic systems with many atoms can become prohibitively expensive for higher levels of theory. This trade-off is critical in the context of organic crystal structure prediction (CSP). Here, a data-efficient ML approach would be highly desirable, since screening a huge space of possible polymorphs in a narrow energy range requires the assessment of a large number of trial structures with high accuracy. In this contribution, we present tailored Δ-ML models that allow screening a wide range of crystal candidates while adequately describing the subtle interplay between intermolecular interactions such as H-bonding and many-body dispersion effects. This is achieved by enhancing a physics-based description of long-range interactions at the density functional tight binding (DFTB) level-for which an efficient implementation is available-with a short-range ML model trained on high-quality first-principles reference data. The presented workflow is broadly applicable to different molecular materials, without the need for a single periodic calculation at the reference level of theory. We show that this even allows the use of wavefunction methods in CSP.

The phenoxyl group-modulated interplay of cation-π and σ-type interactions in the alkali metal series

The interaction potential energy surfaces (IPESs) of four alkaline metal cations (Na+, K+, Rb+ and Cs+) complexed with phenol and catechol were explored by accurate ab initio calculations to investigate the interplay of different noncovalent interactions and their behavior along the alkali metal series and upon -OH substitution. Selected one-dimensional interaction energy curves revealed two different minimum energy configurations for all phenol- and catechol-metal complexes, characterized either by cation-π or σ-type interactions. For each investigated complex several two-dimensional IPES maps were also computed, exploiting the computational advantages of the MP2mod approach. The size of the alkali cation was found to play a similar role in modulating both kinds of complexes, as the interaction strength always decreases along the metal series, from Na+ to Cs+. Conversely, the number of hydroxyl substituents markedly affected cation-π complexes vs. σ-type ones. As a most relevant finding, in catechol-metal complexes the strength of cation-π interactions is around half that of the σ-type ones. It is argued that the combined effect of cation dimensions and hydroxyl substitution in catechol-Na+ complexes makes σ-type configurations remarkably more stable and easily accessible than cation-π ones. Besides shedding new light on the origin of biological phenomena connected with underwater adhesion, the quantum mechanical interaction energy database provided herein may offer a useful reference for tuning accurate force fields, suitable for molecular dynamics simulations, where environmental effects might be also taken into account.

Semiclassical Dispersion Corrections Efficiently Improve Multiconfigurational Theory with Short-Range Density-Functional Dynamic Correlation

Multiconfigurational wave functions are known to describe the electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamic correlation originating from the many configurations involving excitations out of the restricted orbital space, the active space, must be considered. Standard procedures involve approximations that eventually limit the ultimate accuracy achievable (most prominently, multireference perturbation theory). At the same time, the computational cost increases dramatically due to the necessity to obtain higher-order reduced density matrices. It is this disproportion that leads us here to propose an MC-srDFT-D hybrid approach of semiclassical dispersion (D) corrections to cover long-range dynamic correlation in a multiconfigurational (MC) wave function theory, which includes short-range (sr) dynamic correlation by density functional theory (DFT) without double counting. We demonstrate that the reliability of this approach is very good (at negligible cost), especially when considering that standard second-order multireference perturbation theory usually overestimates dispersion interactions.

Weak Interactions Get Strong: Synergy between Tetrel and Alkaline-Earth Bonds

Weak and strong noncovalent interactions such as tetrel bonds and alkaline-earth bonds, respectively, cooperate and get reinforced when acting together in ternary complexes of general formula RN··· SiH₃F···MY, where MY is a Be or Mg derivative and RN is a N-containing Lewis base with different hybridization patterns. Cooperativity has been studied in the optimized MP2/aug'-cc-pVTZ ternary complexes by looking at changes on geometries, binding energies, ²⁹Si NMR chemical shifts, and topological features according to the atoms in molecules theoretical framework. Our study shows that cooperativity in terms of energy is in general significant: more than 40 kJ/mol, and up to 83.6 kJ/mol in the most favorable case. The weakest the isolated interaction, the strongest the reinforcement in the ternary complex; in this sense, the tetrel bond is shortened enormously, between 0.3 and 0.6 Å. This dramatic reinforcement of the tetrel bond is also nicely reflected in the positive variations of the ²⁹Si chemical shifts in all the ternary complexes. At the same time the ternary complexes are characterized by the presence of totally planar silyl group, due to the pentacoordination of the Si atom. Both the hybridization of the N base and the geometry imposed by the alkaline-earth ligands have a strong influence on the binding energies, as they modify the donor ability of N and the Lewis acid character of the alkaline-earth metal.

Third-Order Møller-Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics, and Intermolecular Interactions

We develop and test methods that include second- and third-order perturbation theory (MP3) using orbitals obtained from regularized orbital-optimized second-order perturbation theory, κ-OOMP2, denoted as MP3:κ-OOMP2. Testing MP3:κ-OOMP2 shows RMS errors that are 1.7-5 times smaller than those of MP3 across 7 data sets. To do still better, empirical training of the scaling factors for the second- and third-order correlation energies and the regularization parameter on one of those data sets led to an unregularized scaled (c₂ = 1.0; c₃ = 0.8) denoted as MP2.8:κ-OOMP2. MP2.8:κ-OOMP2 yields significant additional improvement over MP3:κ-OOMP2 in 4 of 6 test data sets on thermochemistry, kinetics, and noncovalent interactions. Remarkably, these two methods outperform coupled cluster with singles and doubles in 5 of the 7 data sets considered, at greatly reduced cost (no O(N6) iterations).

Can the solvent enhance the rate of chemical reactions through C-H/π interactions? insights from theory

The current computational study with density functional theory (DFT) shows that the rate of chemical reactions can be influenced through non-covalent C-H/π interactions between substrates and the solvent. It is shown that intramolecular carbon-carbon interaction and CO2 activation by a low valent silicon complex are both favourably affected by the explicit presence of the solvent toluene, due to C-H/π interactions between toluene and the silicon complex. Furthermore, ab initio molecular dynamics (AIMD) simulations demonstrate that even if the C-H/π interacting solvent molecule is displaced from the complex, another would quickly take its place, thus maintaining the interaction. Hence, the current work shows how non-covalent interactions between solvent and substrate can enhance the rate of the reaction and expands our understanding of the role and influence of the solvent in effecting important chemical transformations.

The 1-Naphthol Dimer and Its Surprising Preference for π-π Stacking over Hydrogen Bonding

Using chirped-pulse Fourier transform microwave spectroscopy, we have experimentally identified the most abundant dimer of an alcohol analogue of naphthalene, 1-naphthol. The 1-naphthol dimer features a V-shaped, partially overlapping π-π stacked structure with no canonical hydrogen bonds between the subunits. This structural assignment is in contradiction to an earlier study of the 1-naphthol dimer using UV-IR dip double resonance spectroscopy in the O-H stretch region, which assigns a π-stacked but also canonically hydrogen-bonded structure. We use an improved theoretical analysis to resolve this discrepancy and show that the new, V-shaped structure is also consistent with the previously measured UV-IR data. These new computational and spectroscopic results shed light on the complicated nature of evaluating energetics and structures for larger, dispersion-bound systems.

First-principles theoretical designing of planar non-fullerene small molecular acceptors for organic solar cells: manipulation of noncovalent interactions

Non-fullerene small molecular acceptors (NFSMAs) exhibit promising photovoltaic performance; however, their electron mobilities are still relatively lower than those of fullerene derivatives. The construction of a highly planar conjugated system is an important strategy to achieve high charge mobility. In chemical parlance, it is tedious and costly to synthesize planar compounds by restricting the rotation at a specific bond. Recently, nonbonding intramolecular interactions, also termed "conformational locks," have been considered as an alternative way to achieve planar geometry. The successful implementation of this approach for designing polymers has been extensively reported. Recently, several examples of NFSMAs containing conformational locks have been presented in the literature. This situation encourages us to perform a detailed theoretical investigation in designing planar small molecular acceptors. Various nonbonding interactions were studied using accurate computational methods, and molecules with multiple nonbonding interactions showed high planarity. Planar acceptors showed red-shifted absorption with high oscillator strengths. In addition, backbone planarity plays a very important role in tuning the charge transport properties and decreasing reorganization energy. Our results could provide important information to guide the further design of promising NFSMA materials.

Quantum Chemical View on the Growth Mechanisms of Odd-Sized Nitrogen Cluster Anions

The stable structures of odd-numbered anionic nitrogen clusters, N_{2 n+3}^-, have been theoretically investigated in the size range n = 1-9 using a variety of quantum chemistry methods that include perturbation theory, coupled cluster, and density-functional theory with different exchange-correlation functionals. We generally find that the clusters are composed of an azide chromophore N₃^- surrounded by essentially neutral nitrogen molecules. The growth initially proceeds by placing the neutral molecules parallel to the azide anion, completing a first shell at N₁₃^-, above which the extra molecules arrange on the side but with a significantly lower binding energy. Comparison with the cyclic N₅^- anionic core shows that the latter is unfavorable, the spectral signatures of both N₅^- and N₂N₃^- being provided in both the infrared and ultraviolet ranges. The trend of these clusters to be highly stable as (N₂) _nN₃^- agrees with recent mass spectrometry experiments under the cryogenic environment of helium droplets. The issues associated with the successful development of a nonreactive force field for such clusters are also highlighted.

Density Functional Study on the Adsorption of 5-Membered N-Heterocycles on B/N/BN-Doped Graphene: Coronene as a Model System

Adsorption of seven 5-membered N-heterocycles on B/N/BN-doped graphene (with coronene as a model system) has been studied using density functional theory (DFT). The geometry of the complexes validated the involvement of both π···π stacking and N-H···π interaction in the adsorption process. The stability of the complexes is measured in terms of stabilization energy, and the results suggested that the complexes are stable enough (stabilization energies are in the range of 7.61-14.77 kcal mol^-1). Studies confirmed the stability of complexes in the solvent phase too irrespective of the dielectric of the solvent. Dispersive force is the major mode of interaction in stabilizing the complexes. Natural bond orbital analysis indicated a small contribution from electrostatic and covalent interactions. Thermochemical analysis revealed that the complexation is exothermic in nature and favorable at a lower temperature. Adsorption of N-heterocycles exerts a nominal impact on the electronic properties of the undoped/doped graphene. The study presents a simple approach to introduce an arbitrary functionality to undoped/doped graphene by preserving its electronic properties.

The S66 Non-Covalent Interactions Benchmark Reconsidered Using Explicitly Correlated Methods Near the Basis Set Limit

The S66 benchmark for non-covalent interactions has been re-evaluated using explicitly correlated methods with basis sets near the one-particle basis set limit. It is found that post-MP2 ‘high-level corrections’ are treated adequately well using a combination of CCSD(F12*) with (aug-)cc-pVTZ-F12 basis sets on the one hand, and (T) extrapolated from conventional CCSD(T)/heavy-aug-cc-pV{D,T}Z on the other hand. Implications for earlier benchmarks on the larger S66×8 problem set in particular, and for accurate calculations on non-covalent interactions in general, are discussed. At a slight cost in accuracy, (T) can be considerably accelerated by using sano-V{D,T}Z+ basis sets, whereas half-counterpoise CCSD(F12*)(T)/cc-pVDZ-F12 offers the best compromise between accuracy and computational cost.

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.

Noncovalent Interactions in the Catechol Dimer

Noncovalent interactions play a significant role in a wide variety of biological processes and bio-inspired species. It is, therefore, important to have at hand suitable computational methods for their investigation. In this paper, we report on the contribution of dispersion and hydrogen bonds in both stacked and T-shaped catechol dimers, with the aim of delineating the respective role of these classes of interactions in determining the most stable structure. By using second-order Møller⁻Plesset (MP2) calculations with a small basis set, specifically optimized for these species, we have explored a number of significant sections of the interaction potential energy surface and found the most stable structures for the dimer, in good agreement with the highly accurate, but computationally more expensive coupled cluster single and double excitation and the perturbative triples (CCSD(T))/CBS) method.

Molecular dynamics simulations of fluid cyclopropane with MP2/CBS-fitted intermolecular interaction potentials

Modeling fluid cycloalkanes with molecular dynamics simulations has proven to be a very challenging task partly because of lacking a reliable force field based on quantum chemistry calculations. In this paper, we construct an ab initio force field for fluid cyclopropane using the second-order Møller-Plesset perturbation theory. We consider 15 conformers of the cyclopropane dimer for the orientation sampling. Single-point energies at important geometries are calibrated by the coupled cluster with single, double, and perturbative triple excitation method. Dunning's correlation consistent basis sets (up to aug-cc-pVTZ) are used in extrapolating the interaction energies at the complete basis set limit. The force field parameters in a 9-site Lennard-Jones model are regressed by the calculated interaction energies without using empirical data. With this ab initio force field, we perform molecular dynamics simulations of fluid cyclopropane and calculate both the structural and dynamical properties. We compare the simulation results with those using an empirical force field and obtain a quantitative agreement for the detailed atom-wise radial distribution functions. The experimentally observed gross radial distribution function (extracted from the neutron scattering measurements) is well reproduced in our simulation. Moreover, the calculated self-diffusion coefficients and shear viscosities are in good agreement with the experimental data over a wide range of thermodynamic conditions. To the best of our knowledge, this is the first ab initio force field which is capable of competing with empirical force fields for simulating fluid cyclopropane.

Noncovalent Interactions in Specific Recognition Motifs of Protein-DNA Complexes

In view of the importance of protein-DNA interactions in biological processes, we extracted from the Protein Data Bank several one-to-one complexes of amino acids with nucleotides that matched certain geometric and energetic specificity criteria and investigated them using quantum chemistry methods. The CCSD(T)/CBS interaction energies were used as a benchmark to compare the performance of the MP2.5, MP2-F12, DFT-D3, and PM6-D3H4 methods. All methods yielded good agreement with the reference values, with declining accuracy from MP2.5 to PM6-D3H4. Regardless of the site of interaction, the minima found after full optimization in implicit solvent with high dielectric constant were close to the structures experimentally detected in protein-DNA complexes. According to DFT-SAPT analysis, the nature of noncovalent interactions strongly depends on the type of amino acid. The negatively charged sugar-phosphate backbone of DNA heavily influences the strength of interactions and must be included in the computational model, especially in the case of interactions with charged amino acids.

CCSD(T)/CBS fragment-based calculations of lattice energy of molecular crystals

A comparative study of the lattice energy calculations for a data set of 25 molecular crystals is performed using an additive scheme based on the individual energies of up to four-body interactions calculated using the coupled clusters with iterative treatment of single and double excitations and perturbative triples correction (CCSD(T)) with an estimated complete basis set (CBS) description. The CCSD(T)/CBS values on lattice energies are used to estimate sublimation enthalpies which are compared with critically assessed and thermodynamically consistent experimental values. The average absolute percentage deviation of calculated sublimation enthalpies from experimental values amounts to 13% (corresponding to 4.8 kJ mol(-1) on absolute scale) with unbiased distribution of positive to negative deviations. As pair interaction energies present a dominant contribution to the lattice energy and CCSD(T)/CBS calculations still remain computationally costly, benchmark calculations of pair interaction energies defined by crystal parameters involving 17 levels of theory, including recently developed methods with local and explicit treatment of electronic correlation, such as LCC and LCC-F12, are also presented. Locally and explicitly correlated methods are found to be computationally effective and reliable methods enabling the application of fragment-based methods for larger systems.

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.