Physical nature of silane⋯carbene dimers revealed by state-of-the-art ab initio calculations.

Using the SAPT2 + 3(CCD)δMP2 method in complete basis set (CBS) limit, it is shown that the interactions in the recently studied silane⋯carbene dimers are mainly dispersive in nature. Consequently, slow convergence of dispersion energy also forces slow convergence of the interaction energy. Therefore, obtaining very accurate values requires extrapolation of the correlation part to the CBS limit. The most accurate values obtained at the CCSD(T)/CBS level of theory show that the studied silane⋯carbene dimers are rather weakly bound, with interaction energies ranging from about -1.9 to -1.3 kcal/mol. Comparing to CCSD(T)/CBS, it will be shown that SCS-MP2 and MP2C methods clearly underestimate and methods based on SAPT2+ and having some third-order corrections, as well as the MP2 method, overestimate values of interaction energies. Popular SAPT(DFT) method performs better than SCS-MP2 and MP2C; nevertheless, underestimation is still considerable. The underestimation is slightly quenched if third-order dispersion energy and its exchange counterpart is added to the SAPT(DFT). The closest value of CCSD(T)/CBS has been given by the SAPT2 + (3)(CCD)δMP2 method in quadruple-ζ basis set. © 2019 Wiley Periodicals, Inc.

Substituent effects in the so-called cationπ interaction of benzene and its boron-nitrogen doped analogues: overlooked role of σ-skeleton.

Despite massive efforts to pinpoint the substituent effects in the so-called cationπ systems, no consensus has been yet reached on how substituents exercise their effects in the interaction of the aromatic molecule with the metal ion. The π-polarization (the Hunter model) and the direct local effect (the Wheeler-Houk model) are two lines of thought applied to this problem, but the justification of both approaches is based on insufficiently proven assumptions and approximations. In order to shed more light on this issue we propose a new approach which enables us to gauge directly the energetic trends resulting from the interaction of the ring with the cation. In our method we add one more partitioning level to the interacting quantum atoms (IQA) scheme and decompose the IQA interaction energies into contributions resulting from σ and π electron densities of the aromatic ring. The new approach, which is named partitioned-IQA, abbreviated as p-IQA, has been applied to complexes of derivatives of benzene or azaborine interacting with a sodium cation. The p-IQA approach reveals that in these systems both σ and π electronic moieties are polarized. Interestingly, for the majority of cases the σ-polarization outweighs the π one, contrary to the Hunter model. However, the Wheeler-Houk model is not precise, either, since the σ-polarization shows some degree of non-locality. In addition, the substituents are found to have a negligible influence on the ring orbital-overlapping capability, i.e. the covalency. Therefore, the substituent effect in the cationπ interaction is a nonlocal classical effect, indicating that neither Hunter model nor Wheeler-Houk model is able to fully describe all the aspects of the substituent effects. The p-IQA conclusions for the considered systems have been compared with the results from the functional-group SAPT (F-SAPT) method. We believe that the presented partitioning in the IQA framework will provide a deeper insight into the substituent effects in the cationπ interactions, which is beyond the σ-π atomic charge population separation.

Interaction of Non-polarizable Cations with Azaborine Isomers and Their Mono-Substituted Derivatives: Position, Induction, and Non-Classical Effects Matter.

Progress in BN/CC isosterism has opened an overwhelming urge to find prospective applications of this class of materials. Herein, the interaction of three BN isosteres of benzene, i. e. 1,2-, 1,3-, 1,4-azaborines and their mono-substituted derivatives with Na+ and Mg2+ cations has been surveyed in light of symmetry-adapted perturbation theory (SAPT) and interacting quantum atoms method (IQA). We have found that the orientation of the cations towards azaborines depends considerably on boron and nitrogen dispersion pattern. However, this tendency cannot be justified by electrostatics alone, without taking into account the induction as the major stabilizing factor, and Pauli repulsion, which effectively shapes the potential energy surface. Due to the significant role of induction, molecular electrostatic potentials (MEPs) can predict the interaction strength and anisotropy only if they are obtained from densities perturbed by the effective field of the cations. Through-bond and through-space effects of the substituents strongly depend on their position in the ring, where the through-bond effects are dominated by the inductive contribution. The importance of the induction energy even at short distances, and of the non-classical IQA component signify the multi-center covalency character of azaborine-cation interactions. Therefore, a pure classical view on the interaction between the cation and compounds standing on the organic/inorganic border is to a large extent misleading.

Revealing the physical nature and the strength of charge-inverted hydrogen bonds by SAPT(DFT), MP2, SCS-MP2, MP2C, and CCSD(T) methods.

The physical nature of charge-inverted hydrogen bonds in H3 XH ⋯YH3 (X = Si, Ge; Y = Al, Ga) dimer systems is studied by means of the SAPT(DFT)-based decomposition of interaction energies and supermolecular interaction energies based on MP2, SCS-MP2, MP2C, and CCSD(T) methods utilizing dimer-centered aug-cc-pCVnZ (n = D, T, Q) basis sets as well as an extrapolation to the complete basis set limit. It is revealed that charge-inverted hydrogen bonds are inductive in nature, although dispersion is also important. Computed interaction energies form the following relation: EintSAPT

Attractive PHHP interactions revealed by state-of-the-art ab initio calculations.

We report in this work a combined structural and state-of-the-art computational study of homopolar P-HH-P intermolecular contacts. Database surveys have shown the abundance of such surprisingly unexplored contacts, which are usually accompanied by other weak interactions in the solid state. By means of a detailed theoretical study utilizing SAPT(DFT), MP2, SCS-MP2, MP2C and CCSD(T) methods and both aug-cc-pVXZ and aug-cc-pCVXZ (X = D, T, Q, 5) basis sets as well as extrapolation to the CBS limit, we have shown that P-HH-P contacts are indeed attractive and considerably strong. SAPT(DFT) calculations have revealed the dispersive nature of the P-HH-P interaction with only minor contribution of the inductive term, whereas the first-order electrostatic term is clearly overbalanced by the first-order exchange energy. In general the computed interaction energies follow the trend: E ≈ E < E < E. Our results have also shown that the aug-cc-pVDZ (or aug-cc-pCVDZ) basis set is not yet well balanced and that the second-order dispersion energy term is the slowest converging among all SAPT(DFT) energy components. Compared to aug-cc-pVXZ basis sets, their core-correlation counterparts have a modest influence on all supermolecular interaction energies and a negligible influence on both the SAPT(DFT) interaction energy and its components.

Interaction of Boron-Nitrogen Doped Benzene Isomers with Water.

The interaction of 1,2-dihydro-1,2-, 1,3-dihydro-1,3- and 1,4-dihydro-1,4-azaborine isomers with one and two water molecules has been studied using a variety of supermolecular (Møller-Plesset = MP, and coupled cluster = CC) as well as perturbational (symmetry-adapted perturbation theory = SAPT) electron-correlation methods in the complete basis-set limit. It has been found that the water molecule binds to azaborine isomers through O-H···π, π-H···O, and dihydrogen bonding linkages. The SAPT interaction energy decomposition shows that these complexes are mostly stabilized by dispersion followed closely by induction contributions. Pauli repulsion hinders water molecule to be polarized by azaborine in the O-H···π type of complexes. According to the interacting-quantum-atoms analysis, the structures with a primary binding of the O-H···π type benefit from an additional stabilization factor resulting from the interaction of the oxygen and the second hydrogen atom of water, i.e., the one which does not point toward the ring, while the interaction of hydrogens from water with azaborines plays a destabilizing role for the π-H···O type. The same method states that the intermolecular bindings between azaborines and the water molecule have a multicenter character with a small bond polarization, and they are classified as closed-shell (noncovalent) by quantum theory of atoms-in-molecules analysis at bond critical points. The complexes of azaborines with two water molecules tend to arrange in a circular fashion with a recognizable water dimer attached to the azaborine molecule. A comparison with the CCSD(T) benchmarks shows that the nonadditive contribution to the interaction energy of the trimers is negative and with a good accuracy can be accounted for by the MP2 method. A good agreement between Hartree-Fock (HF) and MP2 nonadditive energy, as well as the decomposition of HF nonadditive interaction energies divulge the importance of nonadditive induction energy in the trimers. The interaction energies for the azaborine with one water calculated with the SAPT(DFT), MP2, SCS-MP2, and MP2C methods are in satisfactory agreement with each other. Finally, it has been found that the population analysis from the electron localization function offers the most comprehensive explanation of the orientational preferences of the water molecule in the complex.

Interplay between tetrel and triel bonds in RC6H4CN⋯MF3CN⋯BX3 complexes: A combined symmetry-adapted perturbation theory, Møller-Plesset, and quantum theory of atoms-in-molecules study.

Intermolecular ternary complexes composed of: (1) the centrally placed trifluoroacetonitrile or its higher analogs with central carbon exchanged by silicon or germanium (M = C, Si, Ge), (2) the benzonitrile molecule or its para derivatives on one side, and (3) the boron trifluoride of trichloride molecule (X = F, Cl) on the opposite side as well as the corresponding intermolecular tetrel- and triel-bonded binary complexes, were investigated by symmetry-adapted perturbation theory (SAPT) and the supermolecular Møller-Plesset method (MP2) at the complete basis set limit for optimized geometries. A character of interactions was studied by quantum theory of atoms-in-molecules (QTAIM). A comparison of interaction energies and QTAIM bond descriptors for dimers and trimers reveals that tetrel and triel bonds increase in their strength if present together in the trimer. For the triel-bonded complex, this growth leads to a change of the bond character from closed-shell to partly covalent for Si or Ge tetrel atoms, so the resulting bonding scheme corresponds to a preliminary stage of the SN2 reaction. Limitations of the Lewis theory of acids and bases were shown by its failure in predicting the stability order of the triel complexes. The necessity of including interaction energy terms beyond the electrostatic component for an elucidation of the nature of σ- and π-holes was presented by a SAPT energy decomposition and by a study of differences in monomer electrostatic potentials obtained either from isolated monomer densities, or from densities resulting from a perturbation with the effective field of another monomer.

Structure and Energetics of Complexes of B12N12 with Hydrogen Halides-SAPT(DFT) and MP2 Study.

Molecular complexes of a fullerene analogue B12N12 with hydrogen halides (HCl, HBr, and HI) were studied with symmetry-adapted perturbation theory with density-functional theory applied for a description of monomers (SAPT(DFT)), Møller-Plesset theory to the second order (MP2), and its spin-component-scaled variant (SCS-MP2) in a limit of a complete basis set. For each halide five symmetry-distinct minimum structures of the complex have been found on the potential energy hypersurface, with interaction energies ranging from -6 to -18 kJ/mol. The natural bond orbital and the atom-in-molecules analysis of noncovalent bonds resulted in a division of these configurations into three categories: hydrogen-bonded, halogen-bonded, and those of a mixed type, involving simultaneously a hydrogen bonding and a π-hole bonding between halogen and boron atoms. A comparison of various approaches for the calculation of interaction energies shows that the SCS-MP2 supermolecular method gives results which are in a close agreement with SAPT(DFT), while the MP2 interaction energies are systematically more negative than the SAPT values. The ability of the B12N12 nanocage to bind hydrogen halides through several active sites on its surface puts under question the selectivity of the binding necessary in crystal engineering, especially for the hydrogen bromide and hydrogen iodide cases, which show small differences in stabilization energies for their minimum structures. The directionality of noncovalent bonds is explained on grounds of the anisotropy of some SAPT components, like electrostatics and induction, as well as by the σ-hole and π-hole models.

Using Noncovalent Interactions to Test the Precision of Projector-Augmented Wave Data Sets.

The projector-augmented wave (PAW) method is one of the approaches that are widely used to approximately treat core electrons and thus to speed up plane-wave basis set electronic structure calculations. However, PAW involves approximations, and it is thus important to understand how they affect the results. Tests of the precision of PAW data sets often use the properties of isolated atoms or atomic solids. While this is sufficient to identify problematic PAW data sets, little information has been gained to understand the origins of the errors and suggest ways to correct them. Here, we show that the interaction energies of molecular dimers are very useful not only to identify problematic PAW data sets but also to uncover the origin of the errors. Using dimers from the S22 and S66 test sets and other dimers, we find that the error in the interaction energy is composed of a short-range component with an exponential decay and a long-range electrostatic part caused by an error in the total charge density. We propose and evaluate a simple improvable scheme to correct the long-range error and find that even in its simple and readily usable form, it is able to reduce the interaction energy errors to less than half on average for hydrogen-bonded dimers.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage.

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH4···(H2O)20, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

Random Phase Approximation Applied to Many-Body Noncovalent Systems.

The random phase approximation (RPA) has received considerable interest in the field of modeling systems where noncovalent interactions are important. Its advantages over widely used density functional theory (DFT) approximations are the exact treatment of exchange and the description of long-range correlation. In this work, we address two open questions related to RPA. First, we demonstrate how accurately RPA describes nonadditive interactions encountered in many-body expansion of a binding energy. We consider three-body nonadditive energies in molecular and atomic clusters. Second, we address how the accuracy of RPA depends on input provided by different DFT models, without resorting to self-consistent RPA procedure, which is currently impractical for calculations employing periodic boundary conditions. We find that RPA based on the SCAN0 and PBE0 models, that is, hybrid DFT, achieves an overall accuracy between CCSD and MP3 on a data set of molecular trimers from Rezác et al. ( J. Chem. Theory. Comput. 2015 , 11 , 3065 ). Finally, many-body expansion for molecular clusters and solids often leads to a large number of small contributions that need to be calculated with high precision. We therefore present a cubic-scaling (or self-consistent field (SCF)-like) implementation of RPA in atomic basis set, which is designed for calculations with high numerical precision.