Quantum chemistry aspects of the solvent effects on the ene reaction of 1‐Phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene

A density functional theory study was used to investigate the quantum aspects of the solvent effects on the kinetic and mechanism of the ene reaction of 1‐phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene. Using the B3LYP/6–311++ G(d,p) level of the theory, reaction rates have been calculated in the various solvents and good agreement with the experimental data has been obtained. Natural bond orbital analysis has been applied to calculate the stabilization energy of N18? H19 bond during the reaction. Topological analysis of quantum theory of atom in molecule (QTAIM) studies for the electron charge density in the bond critical point (BCP) of N18? H19 bond of the transition states (TSs) in different solvents shows a linear correlation with the interaction energy. It is also seen form the QTAIM analysis that increase in the electron density in the BCP of N18? H19, raises the corresponding vibrational frequency. Average calculated ratio of 0.37 for kinetic energy density to local potential energy density at the BCPs as functions of N18? H19 bond length in different media confirmed covalent nature of this bond. Using the concepts of the global electrophilicity index, chemical hardness and electronic chemical potentials, some correlations with the rate constants and interaction energy have been established. Mechanism and kinetic studies on 1‐phenyl‐1,3,4‐triazolin‐2,5‐dione and 2‐methyl‐2‐butene ene reaction suggests that the reaction rate will boost with interaction energy enhancement. Interaction energy of the TS depends on the solvent nature and is directly related to electron density of the bonds involved in the reaction proceeding, global electrophilicity index and electronic chemical potential. However, the chemical hardness relationship is reversed. Finally, an interesting and direct correlation between the imaginary vibrational frequency of the N18? H19 critical bond and its electron density at the TS has been obtained. © 2014 Wiley Periodicals, Inc.     

Electron density based characterization of π bonds in planar molecules

A new method has been developed to detect and analyze molecular π systems. The concept of bonding critical point is generalized to electronic π systems, and it is shown how a π bond can be characterized via the corresponding bond critical point (BCP) in planar molecules. In this context, charge density and its Laplacian at the BCP(π) of a strongly delocalized π system can be distinguished from that of a localized one. The presented formalism is applied to three types of nanoconductors as conjugated polyenes, which revealed the alternative pattern of the double bonds. Also, several cyclic conjugated molecules are considered to explore their π electronic structure and aromaticity.     

Aromatic pathways in mono- and bisphosphorous singly Möbius twisted [28] and [30]hexaphyrins

Magnetically induced current densities and strengths of currents passing through selected bonds have been calculated for monophosphorous [28]hexaphyrin ((PO)[28]hp) and for bisphosphorous [30]hexaphyrin ((PO)(2)[30]hp) at the density functional theory level using our gauge-including magnetically induced current (GIMIC) approach. The current-density calculations yield quantitative information about electron-delocalization pathways and aromatic properties of singly M?bius twisted hexaphyrins. The calculations confirm that (PO)[28]hp sustains a strong diatropic ring current (susceptibility) of 15 nA T(-1) and can be considered aromatic, whereas (PO)(2)[30]hp is antiaromatic as it sustains a paratropic ring current of -10 nA T(-1). Numerical integration of the current density passing through selected bonds shows that the current is generally split at the pyrroles into an outer and an inner pathway. For the pyrrole with the NH moiety pointing outwards, the diatropic ring current of (PO)[28]hp takes the outer route across the NH unit, whereas for (PO)(2)[30]hp, the paratropic ring current passes through the inner C(β)=C(β) double bond. The main diatropic ring current of (PO)[28]hp generally prefers the outer routes at the pyrroles, whereas the paratropic ring current of (PO)(2)[30]hp prefers the inner ones. In some cases, the ring current is rather equally split along the two pathways at the pyrroles. The calculated ring-current pathways do not agree with those deduced from measured (1)H NMR chemical shifts.     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

Strength and nature of hydrogen bonding interactions in mono- and di-hydrated formamide complexes

In this work, mono- and di-hydrated complexes of the formamide were studied. The calculations were performed at the MP2/6-311++G(d,p) level of approximation. The atoms in molecules theory (AIM), based on the topological properties of the electronic density distribution, was used to characterize the different types of bonds. The analysis of the hydrogen bonds (H-bonds) in the most stable mono- and di-hydrated formamide complexes shows a mutual reinforcement of the interactions, and some of these complexes can be considered as "bifunctional hydrogen bonding hydration complexes". In addition, we analyzed how the strength and the nature of the interactions, in mono-hydrated complexes, are modified by the presence of a second water molecule in di-hydrated formamide complexes. Structural changes, cooperativity, and electron density redistributions demonstrate that the H-bonds are stronger in the di-hydrated complexes than in the corresponding mono-hydrated complexes, wherein the σ- and π-electron delocalization were found. To explain the nature of such interactions, we carried out the atoms in molecules theory in conjunction with reduced variational space self-consistent field (RVS) decomposition analysis. On the basis of the local Virial theorem, the characteristics of the local electron energy density components at the bond critical points (BCPs) (the 1/4? (2)ρ(b) component of electron energy density and the kinetic energy density) were analyzed. These parameters were used in conjunction with the electron density and the Laplacian of the electron density to analyze the characteristics of the interactions. The analysis of the interaction energy components for the systems considered indicates that the strengthening of the hydrogen bonds is manifested by an increased contribution of the electrostatic energy component represented by the kinetic energy density at the BCP.     

Comparative analysis of blue‐shifted hydrogen bond versus conventional hydrogen bond in methyl radical complexes

Methyl radical complexes H₃C…HCN and H₃C…HNC have been investigated at the UMP2(full)/aug‐cc‐pVTZ level to elucidate the nature of hydrogen bonds. To better understand the intermolecular H‐bond interactions, topological analysis of electron density at bond critical points (BCP) is executed using Bader's atoms‐in‐molecules (AIM) theory. Natural bond orbital (NBO) analysis has also been performed to study the orbital interactions and change of hybridization. Theoretical calculations show that there is no essential difference between the blue‐shift H‐bond and the conventional one. In H₃C…HNC complex, rehybridization is responsible for shortening of the N? H bond. The hyperconjugative interaction between the single electron of the methyl radical and N? H antibonding orbital is up to 7.0 kcal/mol, exceeding 3.0 kcal/mol, the upper limit of hyperconjugative n(Y)→σ*(X–H) interaction to form the blue‐shifted H‐bond according to Alabugin's theory. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Density functional theory study on the possibility of Si‐, Ge‐, and Sn‐doped carbon nanotubes as efficient support materials for platinum

PBEPBE‐D3 calculations were performed to investigate how platinum (Pt) interacts with the internal and external surfaces of single‐walled pristine, Si‐, Ge‐, and Sn‐doped (6,6) carbon nanotubes (CNTs). Our calculations showed that atomic Pt demonstrates stronger binding strength on the external surfaces than the internal surface adsorption for the same type of nanotube. In cases of external surface adsorptions, Si‐, Ge‐, and Sn‐doped CNTs show comparable binding energies for Pt, at least 1.40 eV larger than pristine CNT. This enhancement can be rationalized by the strong covalent interactions between Pt and X? C (X = Si, Ge, and Sn) pairs based on structural and projected density of states analysis. In terms of internal surface adsorptions, Ge and Sn doping could significantly enhance the binding of Pt. Pt atom shows much more delocalized and bonding states inside Ge‐ and Sn‐doped CNTs, indicating multiple‐site interaction pattern when atomic Pt is confined inside the nanotubes. However, the internal surface of Si‐doped CNT presents limited enhancement in Pt adsorption with respect to that of pristine CNT because of their similar binding geometries. © 2016 Wiley Periodicals, Inc.     

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.     

Magnetic euripi in corannulene

Ab initio current densities induced by an external magnetic field have been computed for corannulene dianion, dication, and tetraanion. The pi-ring currents are found to be large with respect to benzene and to undergo remarkable changes in response to variations in the oxidation state. According to the results obtained here, the three corannulene ions plus the neutral species constitute a very special set that spans all of the possible patterns of rim and hub circulations: diatropic/hub-paratropic/rim (the dianion), paratropic/hub-paratropic/rim (the dication, assuming conformationally averaged current density), diatropic/hub-diatropic/rim (the tetraanion), and paratropic/hub-diatropic/rim (the neutral, as already reported by other authors). Orbital contributions and their breakdown into explicit contributions from virtual excitations have been analyzed. It is shown that the dianion and dication are both (2p) systems characterized by a single highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) rotationally allowed transition. For the dianion, this transition is responsible not only for the outer paratropic circulation but also for the inner diatropic circulation, a behavior that requires an extension of the few electron model based on orbital contributions to be fully rationalized. For the dication, the HOMO-LUMO transition provides a paratropic circulation localized on one indene subunit. However, because of the fast exchange of conformers, it is sensible to calculate an averaged current density field, which is characterized by con-rotating paratropic inner and outer ring currents. For the tetraanion, the calculated current pattern is in agreement with a previous indication, while the orbital analysis reveals that the HOMO and the HOMO - 1 contribute to both inner and outer circulations. Despite the small 6-31G** basis set employed to calculate current densities and magnetic properties, a satisfactory agreement between computed and available experimental (1)H and (13)C chemical shifts is found, providing a firm basis for the above conclusions. Remarkably, the "diamagnetic" corannulene dianion observed in NMR at low temperature is predicted to be a paramagnetic closed-shell species.     

Perimeter Effects on Ring Currents in Polycyclic Aromatic Hydrocarbons: Circumcoronene and Two Hexabenzocoronenes

Current‐density maps are calculated at an ab initio level for the three symmetrical polycyclic aromatic hydrocarbons, circumcoronene [ 1 (D_6h)], hexabenzo[bc,ef,hi,kl,no,qr]coronene [ 2 a (D_6h) and 2 b (D_3d)], and hexabenzo[a,d,g,j,m,p]coronene [ 3 a (D_6h), 3 b (D₆) and 3 c (D_3d)], all of which can be formally derived by annelation of benzene rings to a coronene core. Whilst 1 is planar, 2 has a non‐planar minimum that is effectively isoenergetic with its planar form, and 3 has a well defined non‐planar structure. The shape of the molecular boundary rather than the planarity of the molecule plays the critical rôle in the character of the predicted currents. Formal deletion of outer hexagons from circumcoronene ( 1 ) in two different ways produces either hexabenzocoronene 2 with a prediction of disjoint local benzenoid diatropic currents linked by a global perimeter, or 3 with a giant diatropic perimeter current enclosing a weak paramagnetic circulation on the central hexagon. The current density map of 1 is effectively a superposition of those of 2 and 3 . Its strong diatropic perimeter current subsumes the six weaker diatropic benzenoid circulations evident in 2 , and bifurcates in the six outer benzenoid rings that form the corners of the giant hexagon; its benzene “hub” sustains a diatropic current, as would be expected from the partial cancellation of the strong diatropic hub current of 2 by the weaker paratropic hub current of 3 . The relationship between the three molecules is rationalised by considering orbital contributions to their current density maps.     

FALDI‐based decomposition of an atomic interaction line leads to 3D representation of the multicenter nature of interactions

Atomic interaction lines (AILs) and the QTAIM's molecular graphs provide a predominantly two‐center viewpoint of interatomic interactions. While such a bicentric interpretation is sufficient for most covalent bonds, it fails to adequately describe both formal multicenter bonds as well as many non‐covalent interactions with some multicenter character. We present an extension to our Fragment, Atomic, Localized, Delocalized and Interatomic (FALDI) electron density (ED) decomposition scheme, with which we can measure how any atom‐pair's delocalized density concentrates, depletes or reduces the electron density in the vicinity of a bond critical point. We apply our method on five classical bonds/interactions, ranging from formal either two‐ or three‐center bonds, a non‐covalent interaction (an intramolecular hydrogen bond) to organometallic bonds with partial multicenter character. By use of 3D representation of specific atom‐pairs contributions to the delocalized density we (i) fully recover previous notion of multicenter bonding in diborane and predominant bicentric character of a single covalent C C bond, (ii) reveal a multicenter character of an intramolecular H‐bond and (iii) illustrate, relative to a Schrock carbene, a larger degree of multicenter M C interaction in a Fischer carbene (due to a presence of a heteroatom), whilst revealing the holistic nature of AILs from multicenter ED decomposition. © 2018 Wiley Periodicals, Inc.     

The possible covalent nature of N-H...O hydrogen bonds in formamide dimer and related systems: an ab initio study

The N-H...O hydrogen bonds are analyzed for formamide dimer and its simple fluorine derivatives representing a wide spectrum of more or less covalent interactions. The calculations were performed at the MP2/6-311++G(d,p) level of approximation. To explain the nature of such interactions, the Bader theory was also applied, and the characteristics of the bond critical points (BCPs) were analyzed: the electron density at BCP and its Laplacian, the electron energy density at BCP and its components, the potential electron energy density, and the kinetic electron energy density. These parameters are used to justify the statement that some of the interactions analyzed are partly covalent in nature. An analysis of the interaction energy components for the systems considered indicates that the covalent character of the hydrogen bond is manifested by a markedly increased contribution of the delocalization term relative to the electrostatic interaction energy. Moreover, the ratio of stabilizing the delocalization/electrostatic contributions grows linearly with the decreasing lengths of the hydrogen bond.     

Canonical orbital contributions to the magnetic fields induced by global and local diatropic and paratropic ring currents

The induced magnetic field (IMF) of naphthalene, biphenyl, biphenylene, benzocyclobutadiene, and pentalene is dissected to contributions from the total π system, canonical π‐molecular orbitals (CMO), and HOMO→π* excitations, to evaluate and interpret relative global and local diatropicity and paratropicity. Maps of the IMF of the total π system reveal its relative strength and topology that corresponds to global and local diatropic and paratropic ring currents. The total π magnetic response is determined by this of canonical HOMOs and particularly by paratropic contributions of rotational excitations from HOMOs to unoccupied π * orbitals. Low energy excitations and similar nodal structure of HOMO and π * induce strong paratropic fields that dominate on antiaromatic rings. High energy excitations and different nodal structures lead to weak paratropic contributions of canonical HOMOs, which are overwhelmed by diatropic response of lower energy canonical orbitals in aromatic rings. CMO‐IMF analysis is found in agreement with ring current analysis. © 2017 Wiley Periodicals, Inc.     

Experimental and Theoretical Charge Density Study on Di‐2‐pyrazylamine (Hdpza) Molecule in Crystal

Electron density distribution of Di‐2‐pyrazylamine ( Hdpza ) is studied both by single‐crystal X‐ray diffraction method at 100K and theoretical calculation. Structural determination reveals that Hdpza molecules crystalize in a syn‐anti conformation with an intramolecular C? H?N hydrogen bond between two pyrazine rings and then gather together via two intermolecular N? H?N and C? H?N hydrogen interaction and π? π stacking interaction between pyrazine rings. Charge density analysis is made in terms of deformation density (Δπ), Laplacian distribution and topological analysis of total electron density based on multipole model and theoretical calculation. The agreement between experiment and theory is good. The topological properties at bond critical points of C? C and C? N bonds reveal a covalent bond character, and those of intermolecular interactions, such as hydrogen bonds and π? π stacking interactions, reveal a closed‐shell interaction. The potential energy curve of Hdpza molecule shows that the syn‐anti conformation is the most stable one (global minima) than the other two of syn‐syn and anti‐anti conformations.     

Silaboration of [1.1.1]Propellane: A Storable Feedstock for Bicyclo[1.1.1]pentane Derivatives

The silaboration of [1.1.1]propellane enables direct introduction of B and Si functional groups onto the bicyclo[1.1.1]pentane (BCP) scaffold in high yield under mild, additive‐free conditions. The silaborated BCP can be obtained on a gram‐scale in a single step without the need for column‐chromatographic purification, and is storable and easy to handle, providing a versatile synthetic intermediate for BCP derivatives. We also describe various conversions of the C?B/C?Si bonds on the BCP scaffold, including development of a modified Suzuki–Miyaura cross‐coupling reaction at the highly sterically hindered bridgehead sp³ carbon center of the BCP skeleton using a combination of highly activated BCP boronic esters, copper(I) oxide, and a PdCl₂(dppf) catalyst system.     

Continua of interactions between pairs of atoms in molecular crystals

The electron density distributions in crystals of five previously studied DMAN complexes and five Schiff bases (two new ones) have been analysed in terms of various properties of bond critical points (BCPs) found in the pair-wise interactions in their lattices. We analysed the continua of interactions including covalent/ionic bonds as well as hydrogen bonds and all other types of weak interactions for all pairs of interacting atoms. The charge density at BCPs and local kinetic and potential energy densities vary exponentially with internuclear distance (or other measures of separation). The parameters of the dependences appear to be characteristics of particular pairs of atom types. The Laplacian and the total (sum of kinetic and potential) energy density at BCPs show similar behaviour with the dependence being of the Morse type. The components lambda1, lambda2, lambda3 of the Laplacian at BCPs vary systematically with internuclear distance according to the type of atom pair. For lambda1 and lambda2 the distribution is of the exponential type, whereas lambda3 does not seem to follow any simple functional form, consistent with previous theoretical findings. Analytical nonlinear dependences of Laplacian on charge density have been found. They agree reasonably well with those obtained by least square fit of the Laplacian to charge density data. There are four distinct regions of the [symbol: see text]2rho(BCP)/rho(BCP) space, generated by E(BCP) = 0 and G(BCP)/rho(BCP) = 1 conditions. Two regions clearly correspond to the shared-shell and closed-shell interactions and the other two to some intermediate situation.     

Magnetic properties and induced current density in acetylene

Coupled Hartree–Fock perturbation theory, within the framework of an accurate calculation, has been employed to visualize the electronic current density vector field induced by an external uniform magnetic field in the acetylene molecule. The current regime in a plane containing the molecular axis is rather different from those usually accounted for, evidencing the presence of a toroidal vortex in the C? H bond. The maps are useful in rationalizing the experimentally observed proton and carbon NMR chemical shifts.