Accurate, Precise, and Efficient Theoretical Methods To Calculate Anion−π Interaction Energies in Model Structures

Small-Basis Set Density-Functional Theory Methods Corrected with Atom-Centered Potentials

Density functional theory (DFT) is currently the most popular method for modeling noncovalent interactions and thermochemistry. The accurate calculation of noncovalent interaction energies, reaction energies, and barrier heights requires choosing an appropriate functional and, typically, a relatively large basis set. Deficiencies of the density-functional approximation and the use of a limited basis set are the leading sources of error in the calculation of noncovalent and thermochemical properties in molecular systems. In this article, we present three new DFT methods based on the BLYP, M06-2X, and CAM-B3LYP functionals in combination with the 6-31G* basis set and corrected with atom-centered potentials (ACPs). ACPs are one-electron potentials that have the same form as effective-core potentials, except they do not replace any electrons. The ACPs developed in this work are used to generate energy corrections to the underlying DFT/basis-set method such that the errors in predicted chemical properties are minimized while maintaining the low computational cost of the parent methods. ACPs were developed for the elements H, B, C, N, O, F, Si, P, S, and Cl. The ACP parameters were determined using an extensive training set of 118655 data points, mostly of complete basis set coupled-cluster level quality. The target molecular properties for the ACP-corrected methods include noncovalent interaction energies, molecular conformational energies, reaction energies, barrier heights, and bond separation energies. The ACPs were tested first on the training set and then on a validation set of 42567 additional data points. We show that the ACP-corrected methods can predict the target molecular properties with accuracy close to complete basis set wavefunction theory methods, but at a computational cost of double-ζ DFT methods. This makes the new BLYP/6-31G*-ACP, M06-2X/6-31G*-ACP, and CAM-B3LYP/6-31G*-ACP methods uniquely suited to the calculation of noncovalent, thermochemical, and kinetic properties in large molecular systems.

Fast and Accurate Quantum Mechanical Modeling of Large Molecular Systems Using Small Basis Set Hartree-Fock Methods Corrected with Atom-Centered Potentials

There has been significant interest in developing fast and accurate quantum mechanical methods for modeling large molecular systems. In this work, by utilizing a machine learning regression technique, we have developed new low-cost quantum mechanical approaches to model large molecular systems. The developed approaches rely on using one-electron Gaussian-type functions called atom-centered potentials (ACPs) to correct for the basis set incompleteness and the lack of correlation effects in the underlying minimal or small basis set Hartree-Fock (HF) methods. In particular, ACPs are proposed for ten elements common in organic and bioorganic chemistry (H, B, C, N, O, F, Si, P, S, and Cl) and four different base methods: two minimal basis sets (MINIs and MINIX) plus a double-ζ basis set (6-31G*) in combination with dispersion-corrected HF (HF-D3/MINIs, HF-D3/MINIX, HF-D3/6-31G*) and the HF-3c method. The new ACPs are trained on a very large set (73 832 data points) of noncovalent properties (interaction and conformational energies) and validated additionally on a set of 32 048 data points. All reference data are of complete basis set coupled-cluster quality, mostly CCSD(T)/CBS. The proposed ACP-corrected methods are shown to give errors in the tenths of a kcal/mol range for noncovalent interaction energies and up to 2 kcal/mol for molecular conformational energies. More importantly, the average errors are similar in the training and validation sets, confirming the robustness and applicability of these methods outside the boundaries of the training set. In addition, the performance of the new ACP-corrected methods is similar to complete basis set density functional theory (DFT) but at a cost that is orders of magnitude lower, and the proposed ACPs can be used in any computational chemistry program that supports effective-core potentials without modification. It is also shown that ACPs improve the description of covalent and noncovalent bond geometries of the underlying methods and that the improvement brought about by the application of the ACPs is directly related to the number of atoms to which they are applied, allowing the treatment of systems containing some atoms for which ACPs are not available. Overall, the ACP-corrected methods proposed in this work constitute an alternative accurate, economical, and reliable quantum mechanical approach to describe the geometries, interaction energies, and conformational energies of systems with hundreds to thousands of atoms.

New Type of Aromatic π-Systems for Anion Recognition: Strong Anion-π and C-H⋅⋅⋅Anion Interactions Between Halides and Aromatic Ligands in Half-Sandwich Compounds

Half-sandwich compounds of benzene, cyclopentadienyl, pentamethylcyclopentadienyl, and indenyl were studied as a new type of aromatic π-systems for interactions with halide anions. Although uncoordinated benzene forms only C-H⋅⋅⋅anion interactions, and hexafluorobenzene forms only anion-π interactions, aromatic ligands in half-sandwich compounds can form both types of interactions, because their entire electrostatic potential surface is positive. These aromatic ligands can form stronger anion-π interactions than organic aromatic molecules, as a consequence of more pronounced dispersion and induction energy components. Moreover, C-H⋅⋅⋅anion interactions of aromatic ligands are stronger than anion-π interactions, and significantly stronger than C-H⋅⋅⋅anion interactions of benzene. Our study shows that transition-metal coordination can make aromatic moieties suitable for strong interactions with anions, and gives insight into the design of new anion receptors.

An accurate single descriptor for ion-π interactions

Non-covalent interactions between ions and π systems play an important role in molecular recognition, catalysis and biology. To guide the screen and design for artificial hosts, catalysts and drug delivery, understanding the physical nature of ion-π complexes via descriptors is indispensable. However, even with multiple descriptors that contain the leading term of electrostatic and polarized interactions, the quantitative description for the binding energies (BEs) of ion-π complexes is still lacking because of the intrinsic shortcomings of the commonly used descriptors. Here, we have shown that the impartment of orbital details into the electrostatic energy (coined as OEE) makes an excellent single descriptor for BEs of not only spherical, but also multiply-shaped, ion-π systems, highlighting the importance of an accurate description of the electrostatic interactions. Our results have further demonstrated that OEEs from a low-level method could be calibrated to BEs from a high-level method, offering a powerful practical strategy for an accurate prediction of a set of ion-π interactions.

Toward a less costly but accurate calculation of the CCSD(T)/CBS noncovalent interaction energy

The popular method of calculating the noncovalent interaction energies at the coupled-cluster single-, double-, and perturbative triple-excitations [CCSD(T)] theory level in the complete basis set (CBS) limit was to add a CCSD(T) correction term to the CBS second-order Møller-Plesset perturbation theory (MP2). The CCSD(T) correction term is the difference between the CCSD(T) and MP2 interaction energies evaluated in a medium basis set. However, the CCSD(T) calculations with the medium basis sets are still very expensive for systems with more than 30 atoms. Comparatively, the domain-based local pair natural orbital coupled-cluster method [DLPNO-CCSD(T)] can be applied to large systems with over 1,000 atoms. Considering both the computational accuracy and efficiency, in this work, we propose a new scheme to calculate the CCSD(T)/CBS interaction energies. In this scheme, the MP2/CBS term keeps intact and the CCSD(T) correction term is replaced by a DLPNO-CCSD(T) correction term which is the difference between the DLPNO-CCSD(T) and DLPNO-MP2 interaction energies evaluated in a medium basis set. The interaction energies of the noncovalent systems in the S22, HSG, HBC6, NBC10, and S66 databases were recalculated employing this new scheme. The consistent and tight settings of the truncation parameters for DLPNO-CCSD(T) and DLPNO-MP2 in this noncanonical CCSD(T)/CBS calculations lead to the maximum absolute deviation and root-mean-square deviation from the canonical CCSD(T)/CBS interaction energies of less than or equal to 0.28 kcal/mol and 0.09 kcal/mol, respectively. The high accuracy and low cost of this new computational scheme make it an excellent candidate for the study of large noncovalent systems.

Construction of a Range-Separated Dual-Hybrid Direct Random Phase Approximation

Blending the good performance of the global hybrid PBE0 functional at short-range and the dual-hybrid dRPA75 functional at long range, we propose a new range-separated direct random phase approximation (dRPA75rs), which considerably improves on the accuracy of the calculated reaction energies and barrier heights compared to the parent approaches and provides a good description of noncovalent interactions without any dispersion correction. We also combine the new scheme with spin-component scaling (SCS-dRPA75rs), which enables the accurate calculation of energy differences for processes involving electron pair breaking, such as atomization. The new method scaling as the fourth power of the system size shows a balanced performance on a broad test set involving radicals, transition metal atoms, and heavy atoms, which makes it competitive with the best double-hybrid functionals based on the second-order perturbation theory. According to the results for the homogeneous electron gas, our dRPA75rs method expectedly gives errors for metallic systems similar to the dRPA approach with an additional error cancellation in the case of partial spin polarization.

Sigma-hole carbon-bonding interactions in carbon-carbon double bonds: an unnoticed contact

In this manuscript, we combine high-level ab initio calculations on some small complexes and a CSD survey to analyze the existence of unprecedented noncovalent carbon bonds in X₂C[double bond, length as m-dash]CH₂Y systems (Y = electron-rich atom or group). The methylene group is usually seen as a weak hydrogen bond donor when interacting with an electron-rich atom. However, we demonstrate that when the electron-rich atom is located equidistant from the two H atoms and along the C[double bond, length as m-dash]C bond a σ-hole noncovalent carbon-bonding interaction is established, instead of a bifurcated hydrogen bond, as derived from Atoms-in-Molecules (AIM) and Natural bond orbital (NBO) analyses. The physical nature of the interaction has been analyzed using the Symmetry Adapted Perturbation Theory (SAPT) method. The results indicate that electrostatics is very important followed by either the induction or dispersion terms in anionic and neutral complexes, respectively. In addition the CSD analysis reveals the existence of such interactions, giving reliability to our calculations, which are much more numerous for neutral than for anionic Y systems.

The nature of intermolecular interactions in pyridinium–anion–β-hexachlorocyclohexane molecular crystals

The nature of intermolecular interactions in different molecular crystal configurations formed by pyridinium cations, chloride or bromide anions as well as β-hexachlorocyclohexane (β-HCH) molecules has been investigated using high level ab initio quantum chemistry methods.

Anion Complexes with Tetrazine-Based Ligands: Formation of Strong Anion-π Interactions in Solution and in the Solid State

Ligands L1 and L2, consisting of a tetrazine ring decorated with two morpholine pendants of different lengths, show peculiar anion-binding behaviors. In several cases, even the neutral ligands, in addition to their protonated HL(+) and H2L(2+) (L = L1 and L2) forms, bind anions such as F(-), NO3(-), PF6(-), ClO4(-), and SO4(2-) to form stable complexes in water. The crystal structures of H2L1(PF6)2·2H2O, H2L1(ClO4)2·2H2O, H2L2(NO3)2, H2L2(PF6)2·H2O, and H2L2(ClO4)2·H2O show that anion-π interactions are pivotal for the formation of these complexes, although other weak forces may contribute to their stability. Complex stability constants were determined by means of potentiometric titration in aqueous solution at 298.1 K, while dissection of the free-energy change of association (ΔG°) into its enthalpic (ΔH°) and entropic (TΔS°) components was accomplished by means of isothermal titration calorimetry measurements. Stability constants are poorly regulated by anion-ligand charge-charge attraction. Thermodynamic data show that the formation of complexes with neutral ligands, which are principally stabilized by anion-π interactions, is enthalpically favorable (-ΔG°, 11.1-17.5 kJ/mol; ΔH°, -2.3 to -0.5 kJ/mol; TΔS°, 9.0-17.0 kJ/mol), while for charged ligands, enthalpy changes are mostly unfavorable. Complexation reactions are invariably promoted by large and favorable entropic contributions. The importance of desolvation phenomena manifested by such thermodynamic data was confirmed by the hydrodynamic results obtained by means of diffusion NMR spectroscopy. In the case of L2, complexation equilibria were also studied in a 80:20 (v/v) water/ethanol mixture. In this mixed solvent of lower dielectric constant than water, the stability of anion complexes decreases, relative to water. Solvation effects, mostly involving the ligand, are thought to be responsible for this peculiar behavior.

Is Aerogen-π Interaction Capable of Initiating the Noncovalent Chemistry of Group 18?

The interactions between atoms of noble gases and π systems are generally considered as van der Waals interaction, which have not attracted attention yet. Herein, we present high-level ab initio calculations to show the unexpected noncovalent interaction between a covalently bonded noble gas atom and a delocalized aromatic π electron using XeO3⋅benzene as the prototype. The CCSD(T)/CBS reference data show its strength amounting to -10.2 kcal mol(-1), comparable to a typical H-bond or an anion-π interaction. The energy decomposition analysis reveals that the aerogen-π interaction is favored by the electrostatic interaction (27.7%), the induction (13.4%), and the dispersion (21.6%). This interaction may prompt us to consider the noncovalent chemistry of aerogen derivatives in the near future.