Theoretical study of [ XN5 ]− (X=O, S, Se, Te) systems

A series of [XN₅]⁻ (X=O, S, Se, Te) compounds has been examined with ab initio and Density Functional Theory (DFT) methods. The five-membered nitrogen ring series of structures are global minima and may exist or be characterized due to their significant dissociation barriers (29.7–32.7 kcal mol⁻¹). Nucleus-independent chemical shifts (NICS) criteria and the presence of (4n+2) π-electrons confirmed that the five-membered nitrogen ring in their structures exhibits characteristics of aromaticity. Thus, the strong stability of the five-membered nitrogen ring structures may be attributed partially to their aromaticity.      

Natural bond orbital approach to the transmission of substituent effect through the fulvene and benzene ring systems

Electronic structure of 22 monosubstituted derivatives of benzene and exocyclically substituted fulvene with substituents: B(OH)₂, BH₂, CCH, CF₃, CH₃, CHCH₂, CHO, Cl, CMe₃, CN, COCH₃, CONH₂, COOH, F, NH₂, NMe₂, NO, NO₂, OCH₃, OH, SiH₃, SiMe₃ were studied theoretically by means of Natural Bond Orbital analysis. It is shown, that sum of π-electron population of carbon atoms of the fulvene and benzene rings, pEDA(F) and pEDA(B), respectively correlate well with Hammett substituent constants s_p⁺ \sigma_{\rm{p}}^{+} and aromaticity index NICS. The substituent effect acting on pi-electron occupation at carbon atoms of the fulvene ring is significantly stronger than in the case of benzene. Electron occupations of ring carbon atoms (except C1) in fulvene plotted against each other give linear regressions with high correlation coefficients. The same is true for ortho- and para-carbon atoms in benzene. Positive slopes of the regressions indicate similar for fulvene and benzene kind of substituent effect – mostly resonance in nature. Only the regressions of occupation at the carbon atom in meta- position of benzene against ortho- and para-positions gives negative slopes and low correlation coefficients.     

A comparative study of the aromaticity of pyrrole, furan, thiophene, and their aza-derivatives

The relative aromaticity of pyrrole, furan, thiophene, and their aza-derivatives has been examined using TRE (topological resonance energy), MRE (magnetic resonance energy), ring current (RC), and ring current diamagnetic susceptibility (χ_G) methods. The results obtained were compared with results obtained by others who used the energetic method ASE (aromatic stabilization energy), the geometric method HOMA (harmonic oscillator model of aromaticity), and the magnetic method NICS(1) (nucleus-independent chemical shift). The impact of nitrogen atoms on the aromaticity of the aza-derivatives of pyrrole, furan, and thiophene is discussed. An excellent correlation was found between the energetic (TRE, MRE) and magnetic (RC and χ_G) criteria of aromaticity for all compounds. It was expected that inclusion of a heteroatom would decrease the aromaticity relative to the cyclopentadienyl anion. Our results show that the type of the first heteroatom, which donates two electrons to the system, as well as the number of nitrogen atoms and their positions in the molecule have a strong effect on aromaticity. In general, aromaticity is enhanced when the nitrogen atom is adjacent to the first heteroatom. The magnitude of aromaticity is related closely with the uniformity of distribution of π-electrons in the molecule.     

Theoretical study on the aromaticity from d-AOs in cationic X 3 + (X = Sc,Y, La) clusters

The stable structures and aromatic characters for three cationic X₃⁺ (X = Sc, Y, and La) and three relevant neutral X₃Cl (X = Sc, Y, La) clusters are investigated at the DFT and post HF level of theory. The calculated results show that the X₃⁺ cations each has two stable structures: the regular trigon (D_3h) and the line (D_￥h {{\hbox{D}}_{\infty {\rm{h}}}} ) with the regular trigon (D_3h) being the ground state, while for three neutral X₃Cl clusters, Sc₃Cl has three stable isomers: the trigon-pyramidal (C_3v), bidentate (C_2v-1), and C_2v-2 structures, Y₃Cl and La₃Cl each has only two stable isomers: the trigon-pyramidal (C_3v) and bidentate (C_2v-1) structures. The ground states for three X₃Cl species are all the bidentate (C_2v-1) isomers. The calculations of the resonance energy (RE) and NICS show that trigonal X₃⁺ isomers exhibit higher degree of aromaticity. The detailed molecular orbital analyzes reveal that the isolated trigonal Sc₃⁺ and Y₃⁺ cations each has one delocalized π-type MO and shows single π-aromaticity, while the isolated trigonal La₃⁺ cation has one delocalized σ-type MO and shows single σ-aromaticity. The single π- or σ-aromaticity for X₃⁺ are attributed to the contributions mainly from the d AOs of the corresponding transition metal X atoms. However, when a singly negatively charged counterion Cl^- is added to Sc₃⁺, Y₃⁺, and La₃⁺ cations respectively, the aromatic type for the two Sc₃⁺, Y₃⁺ units in the corresponding neutral Sc₃Cl, Y₃Cl complexes are changed from π-aromaticity into σ-aromaticity, whereas the σ-aromaticity of the La₃⁺ units in the La₃Cl complex keeps unchanged in this process. Thus three Sc₃⁺, Y₃⁺, La₃⁺ units in the corresponding X₃Cl complexes all have only one σ-type MO and exhibit single σ-aromaticity.     

σ-Holes, π-holes and electrostatically-driven interactions

A positive π-hole is a region of positive electrostatic potential that is perpendicular to a portion of a molecular framework. It is the counterpart of a σ-hole, which is along the extension of a covalent bond to an atom. Both σ-holes and π-holes become more positive (a) in going from the lighter to the heavier atoms in a given Group of the periodic table, and (b) as the remainder of the molecule is more electron-withdrawing. Positive σ- and π-holes can interact in a highly directional manner with negative sites, e.g., the lone pairs of Lewis bases. In this work, the complexes of 13 π-hole-containing molecules with the nitrogen lone pairs of HCN and NH₃ have been characterized computationally using the MP2, M06-2X and B3PW91 procedures. While the electrostatic interaction is a major driving force in π-hole bonding, a gradation is found from weakly noncovalent to considerably stronger with possible indications of some degree of coordinate covalency.     

Theoretical description of hydrogen bonding in oxalic acid dimer and trimer based on the combined extended-transition-state energy decomposition analysis and natural orbitals for chemical valence (ETS-NOCV)

In the present study we have analyzed hydrogen bonding in dimer and trimer of oxalic acid, based on a recently proposed charge and energy decomposition scheme (ETS-NOCV). In the case of a dimer, two conformations, α and β, were considered. The deformation density contributions originating from NOCV’s revealed that the formation of hydrogen bonding is associated with the electronic charge deformation in both the σ—(Δρ_σ) and π-networks (Δρ_π). It was demonstrated that σ-donation is realized by electron transfer from the lone pair of oxygen on one monomer into the empty r_{H - O}^* \rho_{H - O}^* orbital of the second oxalic acid fragment. In addition, a covalent contribution is observed by the density transfer from hydrogen of H-O group in one oxalic acid monomer to the oxygen atom of the second fragment. The resonance assisted component (Δρ_π), is based on the transfer of electron density from the π—orbital localized on the oxygen of OH on one oxalic acid monomer to the oxygen atom of the other fragment. ETS-NOCV allowed to conclude that the σ(O---HO) component is roughly eight times as important as π (RAHB) contribution in terms of energetic estimation. The electrostatic factor (ΔE_elstat) is equally as important as orbital interaction term (ΔE_orb). Finally, comparing β-dimer of oxalic acid with trimer we found practically no difference concerning each of the O---HO bonds, neither qualitative nor quantitative.     

Aromaticity and kinetic stability of fullerene C36 isomers and their molecular ions

The aromatic character of fullerene C₃₆ isomers was examined by the Hess-Schaad resonance energy (HSRE), topological resonance energy (TRE) and the percentage topological resonance energy (%TRE) models. According to the nucleus-independent chemical shift (NICS) at the cage center, C₃₆ fullerene isomers must be highly aromatic with negative values. However, they are predicted to be antiaromatic with negative HSREs and negative TREs. The TRE method revealed that they all are aromatized by acquiring two or more electrons. NICSs at the cage center and the 2(N + 1)² rule cannot be used as an indicator of the aromatic stabilization for C₃₆ isomers and their molecular ions. We utilized the bond resonance energy (BRE) model to estimate the kinetic stability of C₃₆ isomers and their molecular ions. C₃₆ isomers are only stabilized kinetically in penta- and hexavalent molecular anions. All the results indicate that aromaticity and kinetic stability are closely related to the cyclic motion of π electrons.     

Hydroxyl group as a substituent with varying electronic properties: Effect of strength of H-bonding on charge density changes in Ph–OH…F<Superscript>−</Superscript> complexes

Due to gradual and controlled changes of interatomic distances between heavy atoms in OH…F⁻ of C₆H₅OH…F⁻ systems it was possible to study the electronic structure evolution. Computation at B3LYP/6-311+G(d,p) level of theory was performed for this purpose. Changes in charges at atoms and characteristics at bond critical points (BCPs) of the H-bond region and also in distant parts of the systems were investigated by means of natural bond orbitals (NBO) and atoms in molecules (AIM) analyses. It is shown that at the border line between partially covalent and non-covalent H-bonding (Espinosa et al. in J Chem Phys 117:5529, 2002; Grabowski et al. in J Phys Chem B 110:6444, 2006) with the H…F interatomic distance ∼1.8 Ǻ the hydrogen atom has the most positive charge. In addition, the change in the atomic charge values in the interacting region affects the phenyl ring properties. The decrease of the sum of atomic charges as well as of the aromaticity was noticed when the OH….F distance is shortened.     

A MP2 and DFT study of the aromatic character of polyphosphaphospholes. Is the pyramidality the only factor to take into consideration?

A comprehensive MP2/6-311 + G(d,p) and B3LYP/6-311 + G(d,p) study of the aromatic character of phospholes, P _n (CH)_4-n PH with n = 0-4 was conducted. For this purpose, the structures for these compounds were optimized at both theoretical levels and different magnetic properties (magnetic susceptibility anisotropy, χ_anis, and the nucleus-independent chemical shifts, NICS) were evaluated. For comparison, these magnetic properties were also calculated in the optimized structures with planarity constraints. We have also applied the ACID (anisotropy of the current-induced density) method in this analysis. The main conclusions are the aromatic character of these compounds, the relationship between aromaticity and planarity and the importance of other factors in this aromaticity.     

An urn model study of variability within a compartment

Formulas are derived for the mean and variance of the number of radioactive atoms present in a compartment (or urn). Initally,n ₁ radioactive atoms andb stable atoms are placed in the urn; and subsequently,r stable atoms are added and an equal number,r, of a random mixture of stable and radioactive atoms is removed per unit time. The expected number of radioactive atoms,E(t), present at timet is, as expected,n ₁ e^−λt where λ=(r/Δt)/(b+r+n ₁). The relative variance, σ²(t)/n ₁ ² , vanishes to zero forr=1, atoms per unit time and for a large number ofn ₁ radioactive atoms; but for a large number of bothr andn ₁ atoms the relative variance is ∼e ^−λt , equal to the fractional retention, fort>1/λ. Thus in studies where radionuclides are injected into animals and a single compartment represents the data, if a large variance is observed it might be due to the fact that large numbers of atoms are transferred out in unit time. When a small variance is observed, this is probably due to the fact that few atoms are transferred in smaller units of time (such that λ is the same in both cases). Research sponsored by the Energy Research and Development Administration under contract with Union Carbide Corporation.     

Ab initio and DFT study of the aromaticity of some Fulvalenes derived from Methylidenecyclopropabenzene

Methylidencyclopropabenzene (MCPB) 1 and Fulvalenes 2–4 are molecules of special interest due to the relation between structure and aromaticity. The aim of this work was to analyze this relation and to quantify the aromaticity in 1–4 using different methods. Magnetic properties are directly related with aromaticity; here we studied the magnetic susceptibility and the anisotropy of the magnetic susceptibility. Nucleus indepedent chemical shift (NICS) and the anisotropy of the induced current density (ACID) were also employed. Tools of very different nature, geometric indexes HOMA and Bird, were determinated too for 1–4. All of these measures were found to be in agreement. Figure Both spatial NICS and ACID plot allow to show the aromaticity/antiaromaticity of a ring     

Structures and aromaticity of X2Y 2 − (X = C, Si, Ge and Y = N, P, As) anions

The equilibrium geometries, total energies, and vibrational frequencies of anions X₂Y₂ ⁻ (X = C, Si, Ge and Y = N, P, As) are theoretically investigated with density functional theory (DFT) method. Our calculation shows that for C₂N₂ ⁻ species, the D _2h isomer is the most stable four-membered structure, and for other species the C _2v isomer in which two X atoms are contrapuntal is the most stable structure at the B3LYP/6-311 +G_* level. Wiberg bond index (WBI) and negative nucleus-independent chemical shift (NICS) value indicate the existence of delocalization in stable X₂Y₂ ⁻ structures. A detailed molecular orbital (MO) analysis further reveals that stable isomers of these species have strongly aromatic character, which strengthens the structural stability and makes them closely connected with the concept of aromaticity.     

Theoretical study of hydrogenation of the doubly aromatic B 7 − cluster

We have studied the influence of hydrogenation on the relative stability of the low-lying isomers of the anionic B₇⁻ cluster, computationally. It is known that the pure-boron B₇⁻ cluster has a doubly (σ- and π-) aromatic C_6v (³A₁) quasi-planar wheel-type triplet global minimum (structure 1), a low-lying σ-aromatic and π-antiaromatic quasi-planar singlet C_2v (¹A₁) isomer 2 (0.7 kcal mol⁻¹ above the global minimum), and a planar doubly (σ- and π-) antiaromatic C_2v (¹A₁) isomer 3 (7.8 kcal mol⁻¹ above the global minimum). However, upon hydrogenation, an inversion in the stability of the species occurs. The planar B₇H₂⁻ (C_2v, ¹A₁) isomer 4, originated from the addition of two hydrogen atoms to the doubly antiaromatic B₇⁻ isomer 3, becomes the global minimum structure. The second most stable B₇H₂⁻ isomer 5, originated from the quasi-planar triplet wheel isomer 1 of B₇⁻, was found to be 27 kcal mol⁻¹ higher in energy. The inversion in stability occurs due to the loss of the doubly aromatic character in the wheel-type global minimum isomer (C_6v, ³A₁) of B₇⁻ upon H₂−addition. In contrast, the planar isomer of B₇⁻ (C_2v, ¹A₁) gains aromatic character upon addition of two hydrogen atoms, which makes it more stable. Figure The B₇H₂-global minimum structure and its σ-aromatic and π-antiaromatic MOs Dedicated to Professor Dr. Paul von Ragué Schleyer on the occasion of his 75th birthday.     

Expansion of the σ-hole concept

The term “σ-hole” originally referred to the electron-deficient outer lobe of a half-filled p (or nearly p) orbital involved in forming a covalent bond. If the electron deficiency is sufficient, there can result a region of positive electrostatic potential which can interact attractively (noncovalently) with negative sites on other molecules (σ-hole bonding). The interaction is highly directional, along the extension of the covalent bond giving rise to the σ-hole. σ-Hole bonding has been observed, experimentally and computationally, for many covalently-bonded atoms of Groups V–VII. The positive character of the σ-hole increases in going from the lighter to the heavier (more polarizable) atoms within a Group, and as the remainder of the molecule becomes more electron-withdrawing. In this paper, we show computationally that significantly positive σ-holes, and subsequent noncovalent interactions, can also occur for atoms of Group IV. This observation, together with analogous ones for the molecules (H₃C)₂SO, (H₃C)₂SO₂ and Cl₃PO, demonstrates a need to expand the interpretation of the origins of σ-holes: (1) While the bonding orbital does require considerable p character, in view of the well-established highly directional nature of σ-hole bonding, a sizeable s contribution is not precluded. (2) It is possible for the bonding orbital to be doubly-occupied and forming a coordinate covalent bond. Figure Two views of the calculated electrostatic potential on the 0.001 au molecular surface of SiCl₄. Color ranges, in kcal/mole, are: purple, negative; blue, between 0 and 8; green, between 8 and 11; yellow, between 11 and 18; red, more positive than 18. The top view shows three of the four chlorines. In the center is the σ-hole due to the fourth Cl−Si bond, its most positive portion (red) being on the extension of that bond. In the bottom view are visible two of the σ-holes on the silicon. In both views can be seen the σ-holes on the chlorines, on the extensions of the Si−Cl bonds; their most positive portions are green     

Theoretical studies on nitrogen rich energetic azoles

Different nitro azole isomers based on five membered heterocyclics were designed and investigated using computational techniques in order to find out the comprehensive relationships between structure and performances of these high nitrogen compounds. Electronic structure of the molecules have been calculated using density functional theory (DFT) and the heat of formation has been calculated using the isodesmic reaction approach at B3LYP/6-31G* level. All designed compounds show high positive heat of formation due to the high nitrogen content and energetic nitro groups. The crystal densities of these energetic azoles have been predicted with different force fields. All the energetic azoles show densities higher than 1.87 g/cm³. Detonation properties of energetic azoles are evaluated by using Kamlet-Jacobs equation based on the calculated densities and heat of formations. It is found that energetic azoles show detonation velocity about 9.0 km/s, and detonation pressure of 40GPa. Stability of the designed compounds has been predicted by evaluating the bond dissociation energy of the weakest C-NO₂ bond. The aromaticity using nucleus independent chemical shift (NICS) is also explored to predict the stability via delocalization of the π-electrons. Charge on the nitro group is used to assess the impact sensitivity in the present study. Overall, the study implies that all energetic azoles are found to be stable and expected to be the novel candidates of high energy density materials (HEDMs).     

Approximate bandwidths for π and σ energy states in poly (dA.dT)

Using energy levels of the π and σ orbitals for adenine and thymine obtained by the CNDO method, the widths of those levels for poly (dA · dT) are calculated approximately. The results indicate that the bands are very narrow and that the exciton theory provides the best approximation for these biopolymers. This investigation was supported in part by NIH Fellowship (1F03 CA 5296-01) from the National Cancer Institute. Operated by the Union Carbide Corporation for the U.S. Atomic Energy Commission.     

XH/<Emphasis Type="Italic">π</Emphasis> interactions with the <Emphasis Type="Italic">π</Emphasis> system of porphyrin ring in porphyrin-containing proteins

Searching structures of porphyrin-containing proteins from the Protein Data Bank revealed that the π system of every porphyrin ring is involved in XH/π interactions, with most of the porphyrins having several interactions. Both five-membered pyrrole rings and six-membered chelate rings are involved in XH/π interactions; the number of interactions with five-membered rings is larger than the number of interactions with six-membered rings. We found interactions with C–H and N–H groups as hydrogen-atom donors; however, the number of CH/π interactions is much larger than the number of NH/π interactions. The amino acids involved in the interactions show a high conservation score. Our results that every porphyrin is involved in XH/π interactions and that amino acids involved in these interactions are highly conserved demonstrate that XH/π interactions play an important role in porphyrin–protein stability. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Theoretical study of crown ethers with incorporated azobenzene moiety

A series of crown ethers containing the azobenzene moiety incorporated into crowns of various sizes [Cr(O₆)_, Cr(O₇) and Cr(O₈)] and their corresponding alkali metal cation (Li⁺, Na⁺, K⁺, Rb⁺) complexes have been studied theoretically. The density functional theory (DFT) method was employed to elucidate the stereochemical structural natures and thermodynamic properties of all of the target molecules at the B3LYP/6-31 G(d) and LANL2DZ level for the cation Rb⁺. The fully optimized geometries had real frequencies, thus indicating their minimum-energy status. In addition, the bond lengths between the metal cation and oxygen atoms, atomic torsion angles and thermodynamic energies for complexes were studied. Natural bond orbital (NBO) analysis was used to explore the origin of the internal forces and the intermolecular interactions for the metal complexes. The calculated results show that the most significant interaction is that between the lone pair electrons of electron-donating oxygens in the cis-forms of azobenzene crown ethers (cis-ACEs) and the LP* (1-center valence antibond lone pair) orbitals of the alkali-metal cations (Li⁺, Na⁺, K⁺ and Rb⁺). The electronic spectra for the cis-ACEs [cis-Cr(O₆), cis-Cr(O₇) and cis-Cr(O₈)] are obtained by the time-dependent density functional theory (TDDFT) at the B3LYP/6-31 G(d) level. The spectra of the cis-isomers show broad π → π* (S₀ → S₂) absorption bands at 310–340 nm but weaker n → π* (S₀ → S₁) bands at 480–490 nm. The calculated results are in good agreement with the experimental results.     

Ab initio and DFT conformational study on N-nitrosodiethylamine, (C2H5)2N-N=O

Ab initio (MP2) and DFT (B3LYP) calculations, using the cc-pVTZ and aug-cc-pVTZ basis sets, have been performed to characterize some stationary points on the ground state potential energy surface of the title molecules. Several properties as, for instance, relative energies, the barriers for NO rotation around the NN bond, NBO charges on O and amino N atoms, as well as the dipole moments, have been calculated and analyzed in the light of the structures found. Both computational levels here employed yield three minima, in which the C₂NNO frame is ‘planar’ or ‘quasi-planar’. Important correlations between NBO charges and geometric parameters, as well as between some structural features and dipole moments are also discussed. A total of 17 structures have been found for the (C₂H₅)₂N-N=O molecule. Two ranges of values have been obtained for the dipole moment, with the largest values occurring for the structures in which the nitrogen lone pair is parallel to the NO group π system. For instance, these two ranges are from ~4.1 to 4.5 D, and from ~1.6 to 2.1 D, at the MP2/cc-pVTZ level. These ranges are consistent with a larger and a smaller contribution of a dipolar resonance structure, respectively. As the method or basis set changes the values of the dipole moments change by at most ~0.23 D.