Joint QTAIM and Hirshfeld study of the sigma and pi charge distribution and electron delocalization in carbonyl compounds: a comparative study with the resonance model

Atomic charges and delocalization indexes (DIs) for a series of carbonyl compounds comprising dimethyl ketone, acetaldehyde, acetic acid, methyl acetate, acetamide, methyl vinyl ketone, divinyl ketone, and benzoic acid were studied using two different atomic partitionings: the QTAIM and the Hirshfeld (stockholder) scheme. The resonance model, traditionally employed to explain the reactivity of these compounds, is not in line with the total atomic charges and DIs calculated by both methodologies. However, the resonance model is supported to some extent by the pi charges and pi DIs calculated by both schemes, but the calculated values indicate that the pi population delocalizes only to a small degree. Although the absolute values of QTAIM and stockholder atomic charges are significantly different, the pi charges and the values of the DIs show similar trends for all the atoms and molecules of this study; this is especially the case for the pi DIs. A study of the electron density on the level of a single MO performed for CO, H2CO, F2CO, and H2CS reveals that the differences in the atomic sigma charges computed with both partitionings can be traced back to their different treatment of interatomic regions.     

Topological analysis of the electron delocalization range

The electron delocalization range function EDR( ) (Janesko et al., J. Chem. Phys. 2014, 141, 144104) quantifies the extent to which an electron at point in a calculated wavefunction delocalizes over distance d. This work shows how topological analysis distills chemically useful information out of the EDR. Local maxima (attractors) in the EDR occur in regions such as atomic cores, covalent bonds, and lone pairs where the wavefunction is dominated by a single orbital lobe. The EDR characterizes each attractor in terms of a delocalization length D and a normalization , which are qualitatively consistent with the size of the orbital lobe and the number of lobes in the orbital. Attractors identify the progressively more delocalized atomic shells in heavy atoms, the interplay of delocalization and strong (nondynamical) correlation in stretched and dissociating covalent bonds, the locations of valence and weakly bound electrons in anionic water clusters, and the chemistry of different reactive sites on metal clusters. Application to ammonia dissociation over silicon illustrates how this density‐matrix‐based analysis can give insight into realistic systems. © 2016 Wiley Periodicals, Inc.     

Electron delocalization in linearly pi-conjugated systems: a concept for quantitative analysis

Donor- and/or acceptor-substituted pi-conjugated systems represent an important class of compounds in organic chemistry. However, up to now, a general method to quantitatively address the efficiency of a conjugated path is still missing. In this work, a novel computational approach based on deletion energies and on second-order orbital interaction energies in a natural bond orbital (NBO) scheme is employed to quantitatively assess ("measure") delocalization energies. Moreover, the purpose of this work is to assess the efficiency of distinct pi-conjugated paths, that is, geminal, cis, and trans, as well as to predict the impact of substituents on a given backbone. This study is focused on various mono-, di-, tri-, and tetrasubstituted tetraethynylethenes (TEEs). These model systems are suitable for our analysis, because they offer distinct conjugation paths within the same molecule, and can also be substituted in multiple ways. Differences between conjugation paths, the effect of neighbor paths, and the impact of donor and acceptor substituents on the various paths are discussed.     

On the chemical bonding features in palladium containing compounds: A combined QTAIM/DFT topological analysis

Topological analyses of the electron density on N-benzoyl-L-pheylalanine and its palladium(II) complexes are carried out using the quantum theory of atoms in molecules (QTAIM) at the M06/6-31G(d) theoretical level. The topological parameters derived from the Bader theory are also analyzed; these are characteristics of Pd bond critical points and ring critical points. The calculated structural parameters are the highest occupied molecular orbital energy (E _HOMO), the lowest unoccupied molecular orbital energy (E _LUMO), the hardness (η), the softness (S), the absolute electronegativity (χ), the electrophilicity index (ω), and the fractions of electrons transferred (ΔN) from ethylenediamine, 2,2′-bipyridine and 1,10-phenanthroline complexes to N-benzoyl-L-pheylalanine. The numerous correlations and dependences between the energy terms of the symmetry adapted perturbation theory approach, geometrical, topological, and energy parameters are detected and described.     

Electronically-coupled tungsten-tungsten quadruple bonds: comparisons of electron delocalization in 3,6-dioxypyridazine and oxalate-bridged compounds

The preparation of the 3,6-dioxypyridazine-bridged tungsten complex, [W(2)(O(2)C(t)Bu)(3)](2)(mu-H(2)C(4)N(2)O(2)), I, is described, along with its single-electron oxidized cation, I(+), formed in the reaction between I and Ag(+)PF(6)(-). Compound I has been structurally characterized as a PPh(3) adduct, and I(+)PF(6)(-) as a THF solvate, by single-crystal X-ray studies. The geometric parameters of these compounds compare well with those calculated for the model compounds [W(2)(O(2)CH)(3)](2)(mu-H(2)C(4)N(2)O(2)) and [W(2)(O(2)CH)(3)](2)(micro-H(2)C(4)N(2)O(2))(+) by density functional theory employing the Gaussian 98 and 03 suite of programs. The calculations indicate that the two W(2) centers are strongly coupled by M(2) delta-to-bridge pi-bonding, and further coupled by direct M(2)...M(2) bonding. Compound I is purple and shows an intense absorption in the visible region due to a metal-to-bridge charge transfer and, with excitation within this absorption, compound I exhibits pronounced resonance Raman bands associated with symmetric vibrations of the bridge and the M(4) unit. The cyclic voltammogram of I in THF, the EPR spectrum of I(+)PF(6) in 2-MeTHF and the electronic absorption spectrum of I(+)PF(6)(-) in THF are consistent with electron delocalization over both W(2) units. These new data are compared with previous data for the molybdenum analogue, related oxalate-bridged compounds and closely related cyclic polyamidato-bridged Mo(4)-containing compounds. It is proposed that, while the electronic coupling occurs principally by an electron-hopping mechanism for oxalate-bridged compounds, hole-hopping contributes significantly in the cases of the amidate bridges and that this is more important for M = Mo than for M = W. Furthermore, for Class III fully delocalized mixed-valence compounds, the magnitude of K(c), determined from electrochemical methods, is not necessarily a measure of the extent of electron delocalization.     

Characterization of pericyclic reactions using multicenter electron delocalization analysis.

This work investigates the applicability of multicenter delocalization analysis to the characterization of pericyclic reactions. The results indicate that multicenter delocalization indices are a powerful tool for studying concerted processes, allowing the characterization of aromatic transition states with a significant increase in the electron delocalization. Moreover, an advantage over magnetic-based indices is that multicenter delocalization indices are not influenced by local electron currents but by the electron delocalization along the multiple (n) centers, and provide, in a quantitative sense, more reliable results. A thorough comparison with magnetic-based indices is carried out for the trimerization reaction of acetylene. Tracking the values of multicenter delocalization indices along the reaction path allows investigation of the nature of concerted mechanisms. Six-center electron delocalization displays a maximum at the transition state of the Diels-Alder reaction, whereas a similar maximum of four-center electron delocalization is slightly displaced to butadiene for the ring opening of cyclobutene. The profile of multicenter electron delocalization indices along the reaction path of [2+2] cycloaddition of ketene to ethene shows the presence of the two independent mechanisms that agree with the two HOMO/LUMO orbital interactions previously proposed to dominate this reaction.     

Through versus cross electron delocalization in polytriacetylene oligomers: a computational analysis.

Herein, we report a systematic theoretical investigation of the molecular and electronic properties of unsubstituted polytriacetylene (PTA) and iso-polytriacetylene (iso-PTA) oligomers, which are characterized by through and cross pi-conjugation pathways, respectively. The goal of the study is to compare through versus cross conjugation on the basis of the computed molecular geometries of the neutral, anionic, and cationic species, the electron affinities, ionization potentials, excitation energies, and nonlinear optical properties for oligomers up to the nonamer. Differences in the effective conjugation length are directly related to electron delocalization in cross- and through-conjugated pathways. As in the through-conjugated oligomers, that is, the PTAs, the frontier orbitals of the iso-PTA oligomers are delocalized along the entire carbon backbone, suggesting that pi-delocalization can extend through cross-linked carbon atoms. However, in contrast to the PTA oligomers, the bond lengths remain strictly constant and the reduction of the energy gap beyond the trimer is completely due to the correlation contribution. On the other hand, in the anions and cations, the bond lengths do change significantly with increasing chain length. Therefore, oxidation or reduction of the iso-PTA oligomer appears to switch on delocalization through cross-linked carbon atoms. Obviously, the effective conjugation length is specific and depends on the observable considered.     

trans versus geminal electron delocalization in tetra- and diethynylethenes: a new method of analysis

trans-Diethynylethene [(E)-hex-3-ene-1,5-diyne (1 a)], geminal-diethynylethene [3-ethynyl-but-3-ene-1-yne (1 b)], and tetraethynylethene [3,4-diethynyl-hex-3-ene-1,5-diyne (2)] are flexible molecular building blocks for pi-conjugated polymers with interesting electronic and photonic properties. The type of functionalization, the length of the polymer chain, and the choice of pi-conjugation pattern, play a crucial role in determining the properties of these compounds. To rationalize the impact of the different delocalization pathways in the various types of isomers (trans or geminal) on the molecular and electronic structure, a detailed theoretical investigation is presented. We develop a method based on the natural bond orbital (NBO) analysis of Weinhold, which allows one to correlate electron delocalization with molecular and electronic structure observables. The method reveals that the difference between trans (or through) and geminal (or cross) conjugation is not only due to the vertical pi conjugation, but also to the in-plane sigma hyperconjugation. The method is used to correlate the changes in molecular and electronic observables, such as the bond lengths or the absorption frequencies, with the electronic structure of the compounds under investigation. Moreover, this method allows us to predict how a certain substituent will affect the molecular structure and the electronic properties of a given backbone.     

A sodium atom in a large water cluster: electron delocalization and infrared spectra

Ab initio molecular dynamics simulations modeling low-energy collisions of a sodium atom with a cluster with more than 30 water molecules are presented. We follow the dynamics of the atom-cluster interaction and the delocalization of the valence electron of sodium together with the changes in the electron binding energy. This electron tends to be shared by the nascent sodium cation and the water cluster. IR spectra of the sodium-water cluster are both computationally and experimentally obtained, with a good agreement between the two approaches.     

An open library of relativistic core electron density function for the QTAIM analysis with pseudopotentials

Based on two‐component relativistic atomic calculations, a free electron density function (EDF) library has been developed for nearly all the known ECPs of the elements Li (Z = 3) up to Ubn (Z = 120), which can be interfaced into modern quantum chemistry programs to save the .wfx wavefunction file. The applicability of this EDF library is demonstrated by the analyses of the quantum theory of atoms in molecules (QTAIM) and other real space functions on HeCuF, , OgF₄, and TlCl₃(DMSO)₂. When a large‐core ECP is used, it shows that the corrections by EDF may significantly improve the properties of some density‐derived real space functions, but they are invalid for the wavefunction‐depending real space functions. To classify different chemical bonds and especially some nonclassical interactions, a list of universal criteria has also been proposed. © 2018 Wiley Periodicals, Inc.     

Aromaticity in heterocyclic analogues of benzene: comprehensive analysis of structural aspects, electron delocalization and magnetic characteristics

The degree of aromaticity of six-membered monoheterocycles with IV-VI group heteroatoms (C(6)H(5)X, where X = SiH, GeH, N, P, As, O(+), S(+), Se(+)) was analyzed using the results of ab initio calculations at the MP2/cc-pvtz level. Values of common aromaticity indices including those based on electronic delocalization properties, structural-dynamic features and magnetic properties all indicate high aromaticity of all considered heterocycles. A decrease in aromaticity is observed with increasing atomic number of the heteroatom, except in the case of the pyrylium cation. However, not all types of indices or even different indices within the same type correlate well among each other. Ring currents have been obtained at the HF/cc-pvdz level using the ipsocentric formulation. Ring current maps indicate that in the case of cationic heterocycles the ring current persists in all molecules under consideration. The different conclusions reached depending on the type of index used are a manifestation of the fact that when not dealing with hydrocarbons, aromaticity is ill-defined. One should always express explicitly which property of the molecules is considered to establish a degree of "aromaticity".     

Local aromaticity in polycyclic aromatic hydrocarbons: electron delocalization versus magnetic indices

The local aromaticity of benzenoid rings is examined by means of the Polansky index (P) and generalized population analysis (GPA). The results are found to agree very well with recently published circuit-condensed ring currents and magnetic-energetic aromaticity indices, but no correlation is found with nucleus independent chemical shifts (NICS). This is usually seen as a manifestation of the more general multidimensional nature of aromaticity. This paper examines the sources for the observed correlations, showing that some indices give conflicting results because they inherently reflect different phenomena.     

Flow injection analysis: A complementary or alternative concept to biosensors

In practical applications biosensors are often forced to operate under less than optimal conditions. Because of their construction, and the physical processes and chemical reactions involved in their operation, compromise conditions are frequently required to synchronize all events taking place. In this communication it is shown Flow Injection Analysis offers itself as a complementary facility to augment the performance of biosensors, and in many cases as an attractive alternative. Based on the argument that instead of striving to force different reactions to work under compromise conditions, it is much better to separate them, optimize them individually and let them interact with each other in harmony, selected flow-injection applications are discussed. Initially, comments are made on operating sensors in the FIA mode, while the following sections deal with selected examples of enzymatic assays, aimed either at measuring substrate concentrations, including the use of enzyme amplification schemes, or determining enzyme activities.     

A concept of an electron transfer stopped-flow method

A new concept of an electron transfer stopped-flow (ETSF) method is proposed. In the ETSF method, unstable cation radicals are formed via the electron transfer reactions with stable cation radicals whose oxidation potential is positive to that of unstable ones. Thus, by combining the electron transfer reactions with the stopped-flow operation, absorption spectroscopic measurements for short-lived cation radical become possible with a reduced dead time from the point of the generation of cation radicals to the point of the optical measurement, in particular, with a help of a rapid-scan spectrophotometer. By mixing an acetonitrile (AN) solution of tris(p-bromophenyl)amine cation radical (TBPA^⋅+) with an AN solution of methyldiphenylamine (MDPA) or diphenylamine (HDPA), the kinetic analyses could be carried out successfully for the dimerization reactions of MDPA^⋅+ and HDPA^⋅+ as well as the observations of their absorption spectra. It was found that fast reactions whose second order rate constants are around 10⁷ M⁻¹s⁻¹ can be analyzed using the ETSF method.     

Analysis of electron delocalization in aromatic systems: individual molecular orbital contributions to para-delocalization indexes (PDI)

Our research group has recently defined two new aromaticity indexes based on the analysis of electron delocalization in aromatic species using the quantum theory of atoms-in-molecules. One of these indexes is the para-delocalization index (PDI) that measures the electronic delocalization between para-related carbon atoms in six-membered rings. In this paper, we show that this index can be partitioned into individual molecular orbital contributions. We have applied this PDI decomposition to several polycyclic aromatic hydrocarbons showing that this partitioning provides new insight into the origin of aromaticity.     

A viable way to tailor carbon nanomaterials by irradiation-induced transformations

Since the discovery of carbon nanotubes (CNT), transmission electron microscopy (TEM) has been the most important tool in their investigation. It is possible to use electron irradiation in a TEM to construct a single-walled carbon nanotube (SWCNT) from an amorphous carbon film. Here we show that such a synthesis method creates a large number of carbon ad-atoms, which after some critical amount of radiation act to restore the system by reconstructing the carbon film. The behavior of the ad-atoms can be controlled by adjusting the current density in the microscope, suggesting that carbon nanomaterials can be tailored by electron irradiation.     

QTAIM as a research programme: a reply to Shahbazian

In this paper I briefly reply to Shant Shahbazian’s comments on my paper “Austere quantum mechanics as a reductive basis for chemistry” and argue that quantum theory of atoms in molecules can be characterised as a research programme in the theories of chemistry. I also explore the areas in which Shahbazian and me agree and disagree.     

A nuclear isotope effect for interfacial electron transfer: excited-state electron injection from Ru ammine compounds to nanocrystalline TiO2

The coordination compounds Ru(deeb)(NH3)4(PF6)2 and Ru(deeb)(NH2(CH2)2NH2)4(PF6)2, where deeb is 4,4'-(CO2CH2CH3)2-2,2'-bipyridine, were synthesized and attached to optically transparent nanocrystalline (anatase) TiO2 films. The compounds were found to be nonemissive in fluid acetonitrile and when attached to TiO2 with excited-state lifetimes <10 ns. Infrared measurements showed the expected isotopic substitution of the deuterated compounds on TiO2 thin films. A small 10-15 mV shift in the RuIII/II reduction potentials was measured upon deuteration. Metal-to-ligand charge-transfer (MLCT) excitation resulted in interfacial electron transfer into the TiO2 semiconductor with quantum yields that were dependent on the excitation wavelength and deuteration of the ammine ligands. The quantum yields were optimized with blue light excitation (417 nm) and deuterium substitution. In contrast, the kinetic rate constants for charge recombination were insensitive to deuteration and the excitation wavelength. Control experiments with Ru(deeb)(bpy)2(PF6)2 indicated that deuteration of the TiO2 surface alone does not affect the injection or recombination processes. A model is proposed wherein electron injection occurs in competition with vibrational relaxation and/or intersystem crossing of the excited states. Exchange of hydrogen by deuterium slows vibrational relaxation and/or intersystem crossing, resulting in higher injection yields.     

An efficient method for computing the QTAIM topology of a scalar field: The electron density case

An efficient method for computing the quantum theory of atoms in molecules (QTAIM) topology of the electron density (or other scalar field) is presented. A modified Newton–Raphson algorithm was implemented for finding the critical points (CP) of the electron density. Bond paths were constructed with the second‐order Runge–Kutta method. Vectorization of the present algorithm makes it to scale linearly with the system size. The parallel efficiency decreases with the number of processors (from 70% to 50%) with an average of 54%. The accuracy and performance of the method are demonstrated by computing the QTAIM topology of the electron density of a series of representative molecules. Our results show that our algorithm might allow to apply QTAIM analysis to large systems (carbon nanotubes, polymers, fullerenes) considered unreachable until now. © 2012 Wiley Periodicals, Inc.     

Valence-shell charge concentrations and electron delocalization in alkyllithium complexes: negative hyperconjugation and agostic bonding

In this paper we present the results of density functional theory (DFT) calculations on the ethyl ligand and some related organic moieties; we then proceed to consider a range of alkyllithium complexes studied by DFT calculations and high-resolution X-ray and neutron diffraction. Topological analysis of the charge density is used to follow changes in the electronic structure of the organic fragment. The charge concentrations (CCs) in the valence shell at the alpha and beta atoms reveal faithfully the delocalization of the lone pair at the Calpha atom or of the Li-C bonding electrons. Negative hyperconjugation is thus shown to arise from delocalization of the lone pair or the Li-C bonding electrons over the alkyl fragment, with depletion of the metal-directed charge concentration at Calpha, and characteristic ellipticity profiles for the bonds involved in hyperconjugative delocalization. In the case of so-called lithium agostic complexes, we show that close Li.H contacts are a consequence of this delocalization and further secondary interactions, with Li.H-C agostic interactions, playing only a minor role. The ellipticity profiles and the magnitude of the CCs at Calpha provide a quantitative measure of the extent of delocalization, and show excellent agreement between experiment and theory.