Decoding Chemical Bonds: Assessment of the Basis Set Effect on Overlap Electron Density Descriptors and Topological Properties in Comparison to QTAIM

Quantum chemical bonding descriptors based on the total and overlap density can provide valuable information about chemical interactions in different systems. However, these descriptors can be sensitive to the basis set used. To address this, different numerical treatments of electron density have been proposed to reduce the basis set dependency. In this work, we introduce overlap properties (OPs) obtained through numerical treatment of the electron density and present the topology of overlap density (TOP) for the first time. We compare the basis set dependency of numerical OP and TOP descriptors with their quantum theory of atoms in molecules (QTAIM) counterparts, considering the total electron density. Three single (C-C, C-O, and C-F) bonds in ethane, methanol, and fluoromethane and two double (C═C and C═O) bonds in ethene and formaldehyde were analyzed. Diatomic molecules Li-X with X = F, Cl, and Br were also analyzed. Eight parameters, including QTAIM descriptors and OP/TOP descriptors, are used to assess the basis dependency at the ωB97X-D level of theory using 28 basis sets from three classes: Pople, Ahlrichs, and Dunning. The study revealed that the topological overlap electron density properties exhibit comparatively lesser dependence on the basis set compared to their total electron density counterparts. Remarkably, these properties retain their chemical significance even with reduced basis set dependency. Similarly, numerical OP descriptors show less basis set dependency than their QTAIM counterparts. The excess of polarization functions increases charge concentration in the interatomic region and influences both QTAIM and OP descriptors. The basis sets Def2TZVP, 6-31++G(d,p), 6-311++G(d,p), cc-pVDZ, cc-pVTZ, and cc-pVQZ demonstrate reduced variability for the tested bond classes in this study, with particular emphasis on the triple-ζ quality Ahlrichs' basis set. We recommend against using basis sets with numerous polarization functions, such as augmented Dunning's and Ahlrichs' quadruple-ζ.

The Ultrashort Spike-Ring Interaction in Substituted Iron Maiden Molecules

The in forms of molecular iron maidens are known for their unique ultrashort interaction between the apical hydrogen atom or its small substituent and the surface of the benzene ring. It is generally believed that this forced ultrashort X⋯π contact is associated with high steric hindrance, which is responsible for specific properties of iron maiden molecules. The main aim of this article is to investigate the influence of significant charge enrichment or depletion of the benzene ring on the characteristics of the ultrashort C-X⋯π contact in iron maiden molecules. For this purpose, three strongly electron-donating (-NH2) or strongly electron-withdrawing (-CN) groups were inserted into the benzene ring of in-[34,10][7]metacyclophane and its halogenated (X = F, Cl, Br) derivatives. It is shown that, despite such extremely electron-donating or electron-accepting properties, the considered iron maiden molecules surprisingly reveal quite high resistance to changes in electronic properties.

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

Energetic and Geometric Characteristics of Substituents, Part 3: The Case of NO2 and NH2 Groups in Their Mono-Substituted Derivatives of Six-Membered Heterocycles

Substituted heterocyclic arenes play important roles in biochemistry, catalysis, and in the design of functional materials. Exemplary six-membered heteroaromatic molecules, that differ from benzene by inclusion of one heteroatom, are pyridine, phosphorine, arsabenzene, and borabenzene. This theoretical study concerns the influence of the heteroatom present in these molecules on the properties of substituents of two types: electron-donating (ED) NH2 group and electron-accepting (EA) NO2 group, attached at the 2-, 3-, or 4-position. The effect is evaluated by the energy of interaction (Erel) between the substituent and the substituted system and electronic properties of the substituents described by the charge of the substituent active region (cSAR) index. In addition, several geometric descriptors of the substituent and heteroaromatic ring, as well as changes in the aromaticity, are considered. The latter are assessed using the Electron Density of Delocalized Bonds (EDDBs) property of delocalized π electrons. The obtained results show that the electronegativity (EN) of the heteroatom has a profound effect on the EA/ED properties of the substituents. This effect is also reflected in the geometry of studied molecules. The Erel parameter indicates that the relative stability of the molecules is highly related to the electronic interactions between the substituent and the heteroarene. This especially applies to the enhancement or weakening of π-resonance due to the EN of the heteroatom. Additionally, in the 2-heteroarene derivatives, specific through-space ortho interactions contribute to the heteroatom effects.

Dependence of the substituent energy on the level of theory

Most often, the substituent effects are described using rather troublesome Hammett constants. Quite recently, it has been proposed to use the so-called substituent energy, which is based on total energies of the X-substituted polycyclic aromatic hydrocarbon and phenyl. This article concerns the influence of the applied level of theory (i.e., both the basis set and the method) on the determined values of the substituent energies. For this purpose, the energies of the NH₂ and NO₂ groups in 16 unique positions of naphthalene, anthracene, tetracene, phenanthrene, and pyrene were calculated using 10 different basis sets and 23 various exchange-correlation functionals representing the entire Jacob's Ladder, from local, through gradient- and meta-gradient-corrected, to hybrid and double-hybrid ones. Additionally, using even larger 6-311++G(2df,2p) basis set, the energies of NH₂ , NO₂ , CN, and Cl were also computed. Both the basis set and the method used have little effect on the substituent energy if the substituent is in the benzene-like position. On the contrary, the effect of the level of theory is pronounced especially in the case of the most spatially crowded 4-substituted phenanthrene. Substituent energies have been shown to be very useful theoretical parameters describing the proximity effect in the substituted derivatives of polycyclic aromatic hydrocarbons.

Theoretical Study of N-Heterocyclic-Carbene-ZnX2 (X = H, Me, Et) Complexes

This article discusses the properties of as many as 30 carbene–ZnX2 (X = H, Me, Et) complexes featuring a zinc bond C⋯Zn. The group of carbenes is represented by imidazol-2-ylidene and its nine derivatives (labeled as IR), in which both hydrogen atoms of N-H bonds have been substituted by R groups with various spatial hindrances, from the smallest Me, iPr, tBu through Ph, Tol, and Xyl to the bulkiest Mes, Dipp, and Ad. The main goal is to study the relationship between type and size of R and X and both the strength of C⋯Zn and the torsional angle of the ZnX2 plane with respect to the plane of the imidazol-2-ylidene ring. Despite the considerable diversity of R and X, the range of dC⋯Zn is quite narrow: 2.12–2.20 Å. On the contrary, D0 is characterized by a fairly wide range of 18.5–27.4 kcal/mol. For the smallest carbenes, the ZnX2 molecule is either in the plane of the carbene or is only slightly twisted with respect to it. The twist angle becomes larger and more varied with the bulkier R. However, the value of this angle is not easy to predict because it results not only from the presence of steric effects but also from the possible presence of various interatomic interactions, such as dihydrogen bonds, tetrel bonds, agostic bonds, and hydrogen bonds. It has been shown that at least some of these interactions may have a non-negligible influence on the structure of the IR–ZnX2 complex. This fact should be taken into account in addition to the commonly discussed R⋯X steric repulsion.

Solvent Effect on the Stability and Reverse Substituent Effect in Nitropurine Tautomers

The solvent effect on the stability and electron-accepting properties (EA) of the nitro group attached to the C2, C6, or C8 position of nitropurine NH tautomers is investigated. For this purpose, the density functional theory (DFT) and the polarizable continuum model (PCM) of solvation in a wide range of solvents (1 < ε < 109) are used. We show that the EA properties of the NO2 group, described by the charge of the substituent active region (cSAR) model, are linearly dependent on the reciprocal of the solvent dielectric constant; in all cases, solvation enhances the EA properties of this group. Furthermore, the sensitivity of EA properties of the nitro group to the solvent effect depends on the proximity effects. It has been shown that the proximity of two endocyclic N atoms (two repulsive interactions) results in higher sensitivity than the asymmetric proximity of the endocyclic N atom and NH group (one repulsive and one attractive interaction). To explain this phenomenon, the geometry of the nitro group in coplanar form and after forcing its rotation around the CN bond is discussed. Relative stabilities of nitropurine tautomers in different solvents are also presented. Differences in the stabilities and solvation energies are explained by aromaticity, electronic structure, and intramolecular interactions of the nitropurine tautomers.

The Structures of ZnCl2-Ethanol Mixtures, a Spectroscopic and Quantum Chemical Calculation Study

We report in this article the structural properties, spectral behavior and heterogeneity of ZnCl₂-ethanol (EtOH) mixtures in a wide-composition range (1:3 to 1:14 in molar ratios), using ATR-FTIR spectroscopy and quantum chemical calculations. To improve the resolution of the initial IR spectra, excess spectroscopy and two-dimensional correlation spectroscopy were employed. The transformation process was suggested to be from EtOH trimer and EtOH tetramer to EtOH monomer, EtOH dimer and ZnCl₂-3EtOH complex upon mixing. The theoretical findings showed that increasing the content of EtOH was accompanied with the flow of negative charge to ZnCl₂. This led to reinforcement of the Zn←O coordination bonds, increase of the ionic character of Zn‒Cl bond and weakening and even dissociation of the Zn‒Cl bond. It was found that in some of the ZnCl₂-EtOH complexes optimized at the gas phase or under the solvent effect, there existed hydroxyls with a very special interactive array in the form of Cl‒Zn⁺←O‒H^…Cl^-, which incredibly red-shifted to wavenumbers <3000 cm^-1. This in-depth study shows the physical insights of the respective electrolyte alcoholic solutions, particularly the solvation process of the salt, help to rationalize the reported experimental results, and may shed light on understanding the properties of the deep eutectic solvents formed from ZnCl₂ and an alcohol.

Study of Beryllium, Magnesium, and Spodium Bonds to Carbenes and Carbodiphosphoranes

The aim of this article is to present results of theoretical study on the properties of C⋯M bonds, where C is either a carbene or carbodiphosphorane carbon atom and M is an acidic center of MX2 (M = Be, Mg, Zn). Due to the rarity of theoretical data regarding the C⋯Zn bond (i.e., the zinc bond), the main focus is placed on comparing the characteristics of this interaction with C⋯Be (beryllium bond) and C⋯Mg (magnesium bond). For this purpose, theoretical studies (ωB97X-D/6-311++G(2df,2p)) have been performed for a large group of dimers formed by MX2 (X = H, F, Cl, Br, Me) and either a carbene ((NH2)2C, imidazol-2-ylidene, imidazolidin-2-ylidene, tetrahydropyrymid-2-ylidene, cyclopropenylidene) or carbodiphosphorane ((PH3)2C, (NH3)2C) molecule. The investigated dimers are characterized by a very strong charge transfer effect from either the carbene or carbodiphosphorane molecule to the MX2 one. This may even be over six times as strong as in the water dimer. According to the QTAIM and NCI method, the zinc bond is not very different than the beryllium bond, with both featuring a significant covalent contribution. However, the zinc bond should be definitely stronger if delocalization index is considered.

On differences in substituent effects in substituted ethene and acetylene derivatives and their boranyl analogs

This article is the first attempt to present different influence of substituent effects on double and triple bonds and, conversely, to present the impact of these bonds on the electronic structure of substituents. For this purpose, quantum-mechanical calculations were made for X-substituted derivatives of ethene and acetylene with 27 diverse substituents representing a wide spectrum of electronic properties, from strongly electron-accepting to strongly electron-donating ones. In addition to these systems, their boranyl derivatives are also investigated. It turns out that the Hammett substituent constants do not correctly describe changes in the CC bond length in any of the considered family of systems. However, the relationships with the CB bond length are significantly better. It is shown that the triple bond in acetylene derivatives is much more resistant to external perturbations than the double bond in the analogs containing an ethene unit. As a consequence, in acetylene derivatives, the substituent effects on CC bond length are about half of the substituent effects in ethene derivatives. We suggest that the observed lack of a clear linear correlation between the length of the CC triple bond in acetylene derivatives and the value of electron density on this bond is due to the disturbing additional interaction between the structure of the X substituent in the xy plane and the π bond being in the same plane in the acetylene unit—on the contrary, this interaction is not possible in ethene analogs.

Non-linear optical properties of polystyrene and polyvinyl alcohol composites with 4-methoxy-1-naphthol

The analysis of the NLO properties of 4-methoxy-1-naphthol (4M1N) reveals that this molecule has the value of polarizability tensor, α, more than 340% greater than that obtained, at the same level of theory, for urea molecule. This improvement grows to 500% when the second-order hyperpolarizability is considered. Calculations performed within LR-PCM-B3LYP/6-311+G(3d,2p) model proved that embedding of 4M1N in the polymer matrix significantly improved these results suggesting applications of 4M1N as the cheap and effective NLO material. The molecule was also studied, both theoretically and experimentally, to determine its full vibrational characterisation and structural description. Calculations were performed with HF, MP2, SVWN and B3LYP methods, in two, varying in size, basis sets, to find optimized structures, conformational isomers and UV–VIS, IR and Raman spectra. The accordance of simulated oscillation and absorption spectra with experimental ones is very good; IR values are slightly red-shifted. NBO charge distribution analysis was made to generate frontier orbitals and find most reactive parts of the molecule.

Changes in Electron Structure of the Triple Bond in Substituted Acetylene and Diacetylene Derivatives

The substituent effect is usually considered by means of various Hammett-like substituent constants and is most often related to aromatic systems. Unlike this, we present results of our research on the influence of 27 substituents spanning a wide range of electronic properties, from strongly electron-withdrawing to strongly electron-donating, on the electron structure of X-substituted acetylenes and diacetylenes - thus the systems which until now have practically not been subject of any deeper studies. It is shown that the interaction through triple bond(s) is associated with a significant advantage of resonance effects and that the substituent effect transmitted by the C≡C-C≡C unit is about half of that transmitted by the C≡C unit alone. Substituent X mainly affects the closest carbon atom by means of proximity effect, hence changes of charge on this atom do not follow any substituent constants. The effect on further carbon atoms is much smaller. The presence of the C≡C-C≡C unit withdraws more charge from X than a triple bond alone, and hinders communication between X and the terminal H atom. Comparison of substituent effects to those present in X-substituted benzene derivatives shows that the electronic properties of the terminal hydrogen atom in acetylenes and diacetylenes are most similar to the electronic properties of ortho and para hydrogen atoms in X-substituted benzene derivatives.