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The two new quasi-aromatic Möbius coordination compounds have been obtained and extensively characterized by experimental and computational approaches.

The first 1,4-distibinine-1,4-diide compound [(ADC)Sb]2 (5) based on an anionic dicarbene (ADC) (ADC = PhC{N(Dipp)C}2, Dipp = 2,6-iPr2C6H3) is reported as a bordeaux-red solid. Compound 5, featuring a central six-membered C4Sb2 ring with formally Sb(I) atoms may be regarded as a base-stabilized cyclic bis-stibinidene in which each of the Sb atoms bears two lone-pairs of electrons. 5 undergoes 2e-oxidation with Ph3C[B(C6F5)4] to afford [(ADC)Sb]2-[B(C6F5)4]2 (6) as a brick-red solid. Each of the Sb atoms of 6 has an unpaired electron and a lone-pair. The broken-symmetry open-shell singlet diradical solution for (6)2+ is calculated to be 2.13 kcal/mol more stable than the closed-shell singlet. The diradical character of (6)2+ according to SS-CASSCF (state-specific complete active space self-consistent field) and UHF (unrestricted Hartree-Fock) methods amounts to 39% and 36%, respectively. Treatments of 6 with (PhE)2 yield [(ADC)Sb(EPh)]2[B(C6F5)4]2 (7-E) (E = S or Se). Reaction of 5 with (cod)Mo(CO)4 affords [(ADC)Sb]2-Mo(CO)4 (8). © 2023 Wiley-VCH GmbH.

Singlet fission is a multiexciton generation process, where one singlet exciton is absorbed and two triplet excitons are produced. The potential of more efficient photovoltaic devices utilizing singlet fission materials has attracted wide interests for tuneable, stable organic chromophores with suitable excited‐state ordering. The strict energetic requirements hinder the exploration of novel organic materials, and most well‐known singlet fission materials, linear acenes, are considered to be unstable in their excited states. To solve the stability issue, excited‐state aromaticity provides a feasible research option, from which a few chromophores have been designed and studied. This review describes indolonaphthyridine (IND) derivative chromophores and discusses their ability to undergo singlet fission with superior ambient stability. Deepened theoretical analysis taking into account the excited‐state Hückel‐aromatic and diradical characters rationalizes the special properties of these chromophores. Moreover, the improved understanding of the aromatic character enables us to outline a feasible design strategy suitable for other scaffolds undergo singlet fission and excited‐state aromaticity. Hopefully, this review can light a fire on the way toward various novel singlet fission chromophores designed based on the excited‐state aromatic view.

Baird's rule has been applied to a large scope of organic molecular systems for rationalizing the aromaticity reversal in the lowest-lying triplet state. In this study, we demonstrate that Baird's rule can also be extended to all-metal systems with σ- and π-aromaticity This work was supported with funds from the China Scholarship Council (CSC) by a State Scholarship Fund (No. 201906310040, D.C.), the National Science Foundation of China (21573179, J.Z.), the Top-Notch Young Talents Program of China (J.Z.), the Ministerio de Economía y Competitividad (MINECO) of Spain (project CTQ2017-85341-P, M.S.), and the Generalitat de Catalunya (project 2017SGR39, M.S.). D.W.S. acknowledges the financial support by the European Union's Framework Programme for Research and Innovation Horizon 2020 (2014– 2020) under the Marie Skłodowska‐Curie Grant Agreement No. 797335 “MulArEffect”

Several fully pi-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel's 4n + 2 rule for each macrocyclic path, yet, their -electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with p-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic pi-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite that these molecules show substantial pi-electron delocalization they cannot be classified as true 3D-aromatics O.E.B. is grateful to the Wenner-Gren Foundations for a postdoctoral fellowship (UPD 2018-0305), and H.O., K.J., and R.A. acknowledge the Swedish Research Council for financial support (grants 2015-04538 and 2019-05618). M.S. is grateful for the financial support from the Spanish MICINN (project PID2020-113711GB-I00) and the Catalan DIUE (project 2017SGR39). D.W.S. acknowledges the financial support by the National Science Centre, Poland (2021/42/E/ST4/ 00332) and the PL-Grid Infrastructure of the Academic Computer Centre (CYFRONET). The computations were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Center (NSC), Linköping, partially funded by the Swedish Research Council through grants 2015-04538 and 2019-05618

Understanding the structural changes taking place during the assembly of single atoms leading to the formation of atomic clusters and bulk materials remains challenging. The isolation and theoretical characterization of medium-sized clusters can shed light on the processes that occur during the transition to a solid-state structure. In this work, we synthesize and isolate a continuous 24-atom cluster Ge244−, which is characterized by X-ray diffraction analysis and Energy-dispersive X-ray spectroscopy, showing an elongated structural characteristic. Theoretical analysis reveals that electron delocalization plays a vital role in the formation and stabilization of the prolate cluster. In contrast with carbon atoms, 4 s orbitals of Ge-atoms do not easily hybridize with 4p orbitals and s-type lone-pairs can be localized with high occupancy. Thus, there are not enough electrons to form a stable symmetrical fullerene-like structure such as C24 fullerene. Three aromatic units with two [Ge9] and one [Ge6] species, connected by classical 2c-2e Ge-Ge σ-bonds, are aligned together forming three independent shielding cones and eventually causing a collapse of the global symmetry of the Ge244− cluster.

Very recently, Liddle and coworkers extended the range of aromaticity to a record seventh row of the periodic table by successful isolation of the crystalline actinide cluster 3 containing at its heart the σ-aromatic tri-thorium ring. In this study we prove that the authors have misinterpreted the experimental Raman spectrum of 3, which eventually led to the wrong conclusions about the role of the σ-aromatic tri-thorium bonding in the synthesized cluster. We demonstrate that the thorium-thorium bond in 3 is not very different from the already known extremely weak actinide-actinide bonds, and the marginal σ-aromatic stabilization in the Th3 ring makes it hardly distinguishable from ordinary non-aromatic rings. Also, we show that the multicenter charge-shift bonding in the Th3Cl6 cage is a vital factor that determines the uniqueness and remarkable thermodynamic stability of 3. By clarifying the misleading conclusions of the original Nature paper and drawing special attention to the essential stabilizing role of actinide-halogen charge-shift bonding, this study may have broader implications for understanding the chemistry of actinides and future attempts to design and synthesize new stable actinide complexes.

The exact energies of the lowest singlet and triplet excited states in organic chromophores are crucial to their performance in optoelectronic devices. The possibility of utilizing singlet fission to enhance the performance of photovoltaic devices has resulted in a wide demand for tuneable, stable organic chromophores with wide S1–T1 energy gaps (>1 eV). Cibalackrot-type compounds were recently considered to have favorably positioned excited state energies for singlet fission, and they were found to have a degree of aromaticity in the lowest triplet excited state (T1). This work reports on a revised and deepened theoretical analysis taking into account the excited state Hückel-aromatic (instead of Baird-aromatic) as well as diradical characters, with the aim to design new organic chromophores based on this scaffold in a rational way starting from qualitative theory. We demonstrate that the substituent strategy can effectively adjust the spin distribution on the chromophore and thereby manipulate the excited state energy levels. Additionally, the improved understanding of the aromatic characters enables us to demonstrate a feasible design strategy to vary the excited state energy levels by tuning the number and nature of Hückel-aromatic units in the excited state. Finally, our study elucidates the complications and pitfalls of the excited state aromaticity and antiaromaticity concepts, highlighting that quantitative results from quantum chemical calculations of various aromaticity indices must be linked with qualitative theoretical analysis of the character of the excited states., Cibalackrot-type compounds are Hückel instead of Baird aromatic in their first triplet states (T1). By choice of substituents and additional benzannelation we adjust the T1 energies, providing a new strategy for singlet fission chromophore design.

We present the synthesis and structural and computational characterization of a heteroleptic dinuclear discrete complex [Cd2(μ1,3-NCS)2(NCS)2(LI)2]·4MeOH (1·4MeOH), where LI is the product of hydrolysis of one of the 2-PyC(Ph) groups of the parent ligand 1,2-diphenyl-1,2-bis((phenyl(pyridin-2-yl)methylene)hydrazono)ethane (L), fabricated from a mixture of Cd(NO3)2·4H2O and NH4NCS in methanol. An analogous procedure but in EtOH and iPrOH yielded crystals of the heteroleptic dinuclear discrete complex [Cd2(μ1,3-NCS)2(NCS)2(L)2] (2) and the polymeric complex of the composition [Cd3(NCS)6(L)]n (3). The bulky helical ligand L in the constituting CdII based synthons has been found to exhibit a quasi-aromatic Mobius features as revealed by the electron density of delocalized bonds method as well as the extended transition state coupled with natural orbitals for chemical valence calculations. It means that a transition metal induces π-electron delocalization solely in the ligand’s part; however, the d orbitals of...

The isolated‐pentagon rule (IPR) is a determining structural feature accounting for hollow fullerene stabilization and properties related to Cn (n ≥ 60) cages. The recent characterization of an unprecedented non‐IPR hydrofullerene, C2v‐C66H4, bearing two heptagons with adjacent fused‐pentagons motif, largely dismiss this feature. Herein, employing DFT calculations, we explore the 13C‐NMR pattern and aromatic behavior of C2v‐C66H4. Our results show the presence of three π‐aromatic circuits at the bottom boat section of C66H4 indicating the unique features of this hydrofullerene in comparison to pristine C60. In addition, under specific orientations of the external field, certain π‐aromatic circuits are enabled, resulting in a more aromatic fullerene than C60, but lower in comparison to the spherical aromatic C606‐ fulleride. Noteworthy, under a field‐aligned along with the saturated carbon atoms, non‐aromatic characteristics are exposed. This reveals that spherical‐like cages can involve a complex magnetic response that heavily depends on the orientation of the applied field A.M.-C. acknowledges to FONDECYT/ANID 1180683 grant. This work was also supported with funds from the China Scholarship Council (CSC) by a State Scholarship Fund (No. 201906310040, D.C.), the National Science Foundation of China (21873079, J.Z.), the Top-Notch Young Talents Program of China (J.Z.), the Ministerio de Economía y Competitividad (MINECO) of Spain (project CTQ2017-85341-P, M.S.), and the Generalitat de Catalunya (project 2017SGR39, M.S.). D.W.S. acknowledges the financial support by the European Union's Framework Programme for Research and Innovation Horizon 2020 (2014– 2020) under the Marie Skłodowska‐Curie Grant Agreement No. 797335 “MulArEffect”

In this work, we report solvent-induced complexation properties of a new N2S2 tetradentate bis-thiosemicarbazone ligand (H2LI), prepared by the condensation of 4-phenylthiosemicarbazide with bis-aldehyde, namely 2,2’-(ethane-1,2-diylbis(oxy)dibenzaldehyde, towards nickel(II). Using ethanol as a reaction medium allowed the isolation of a discrete mononuclear homoleptic complex [NiLI ] (1), for which its crystal structure contains three independent molecules, namely 1-I, 1-II, and 1-III, in the asymmetric unit. The doubly deprotonated ligand LI in the structure of 1 is coordinated in a cis-manner through the azomethine nitrogen atoms and the thiocarbonyl sulfur atoms. The coordination geometry around metal centers in all the three crystallographically independent molecules of 1 is best described as the seesaw structure. Interestingly, using methanol as a reaction medium in the same synthesis allowed for the isolation of a discrete mononuclear homoleptic complex [Ni(LII)2 ] (2), where LII is a monodeprotonated ligand 2-(2-(2-(2-(dimethoxymethyl)phenoxy)ethoxy)benzylidene)-N-phenylhydrazine-1-carbothioamide (HLII). The ligand LII was formed in situ from the reaction of LI with methanol upon coordination to the metal center under synthetic conditions. In the structure of 2, two ligands LII are coordinated in a trans-manner through the azomethine nitrogen atom and the thiocarbonyl sulfur atom, also yielding a seesaw coordination geometry around the metal center. The charge and energy decomposition scheme ETS-NOCV allows for the conclusion that both structures are stabilized by a bunch of London dispersion-driven intermolecular interactions, including predominantly N–H···S and N–H···O hydrogen bonds in 1 and 2, respectively; they are further augmented by less typical C–H···X (where X = S, N, O, π), CH···HC, π···π stacking and the most striking, attractive long-range intermolecular C–H···Ni preagostic interactions. The latter are found to be determined by both stabilizing Coulomb forces and an exchange-correlation contribution as revealed by the IQA energy decomposition scheme. Interestingly, the analogous long-range C–H···S interactions are characterized by a repulsive Coulomb contribution and the prevailing attractive exchange-correlation constituent. The electron density of the delocalized bonds (EDDB) method shows that the nickel(II) atom shares only ~0.8|e| due to the σ-conjugation with the adjacent in-plane atoms, demonstrating a very weak σ-metalloaromatic character. © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This paper has been supported by the RUDN University Strategic Academic Leadership Program (Fedor I. Zubkov, synthesis of the ligands). DFT calculations were partially performed using the PL-Grid Infrastructure and resources provided by the ACC Cyfronet AGH (Cracow, Poland). M. P. Mitoraj acknowledges the financial support of the Polish National Science Center within the Sonata Bis Project 2017/26/E/ST4/00104.

Many of the commonly used aromaticity descriptors suffer from serious issues such as the arbitrariness of choice of a reference system and parameterization, ring-size extensivity problems, limited applicability, computational inefficiency, as well as methodological shortcomings and interpretative mistiness. Thus, introducing new aromaticity measures makes sense nowadays only if their performance provides an advantage over the already existing descriptors or they offer similar quality but at a significantly lower computational cost. In this chapter, the recently proposed electron density of delocalized bonds method will be described, which may fulfill these conditions by a wide margin providing a uniform approach not only to quantify but also to visualize electrons delocalized through the system of all (global) or selected (local) conjugated bonds in a wide range of aromatic species regardless of their size and topology.

The isolated-pentagon rule (IPR) is a determining structural feature that accounts for hollow fullerene stabilization and properties related to C

Species with adaptive aromaticity are aromatic in the ground and lowest‐lying triplet excited states and they have normally intermediate singlet‐triplet gaps. Few examples of compounds with adaptive aromaticity are known to date, including 16‐valence‐electron (16e) metallapentalenes. A sweeping search could be conducted to discover new members of this group, but efficient designs with an explicit strategy would facilitate the quest for new members of this elusive family. Density functional theory calculations and aromaticity evaluations have been performed to reveal the nature of triplet‐state aromaticity in 16e metallapentalenes. Our results show that coordination of strong σ‐ or π‐donor ligands helps achieving adaptive aromaticity of 16e metallapentalenes by means of a spin delocalization mechanism. These results have important implications for understanding the unusual properties of the organometallic adaptive aromatics, leading the way to efficient design of new compounds with tunable singlet‐triplet gaps This work was supported with funds from the China Scholarship Council (CSC) by a State Scholarship Fund (No. 201906310040, D.C.), the National Science Foundation of China (21573179, J.Z.), the Top-Notch Young Talents Program of China (J.Z.), the Ministerio de Economía y Competitividad (MINECO) of Spain (project CTQ2017-85341-P), and the Generalitat de Catalunya (project 2017SGR39). D.W.S. acknowledges the financial support by the European Union's Framework Programme for Research and Innovation Horizon 2020 (2014–2020) under the Marie Skłodowska‐Curie Grant Agreement No. 797335 “MulArEffect

It is shown herein that intuitive and text-book steric-clash based interpretation of the higher energy "in-in" xylene isomer (as arising solely from the repulsive CH⋅⋅⋅HC contact) with respect to the corresponding global-minimum "out-out" configuration (where the clashing C-H bonds are tilted out) is misleading. It is demonstrated that the two hydrogen atoms engaged in the CH⋅⋅⋅HC contact in "in-in" are involved in attractive interaction so they cannot explain the lower stability of this isomer. We have proven, based on the arsenal of modern bonding descriptors (EDDB, HOMA, NICS, FALDI, ETS-NOCV, DAFH, FAMSEC, IQA), that in order to understand the relative stability of "in-in" versus "out-out" xylenes isomers one must consider the changes in the electronic structure encompassing the entire molecules as arising from the cooperative action of hyperconjugation, aromaticity and unintuitive London dispersion plus charge delocalization based intra-molecular CH⋅⋅⋅HC interactions.

Extensive experimental and theoretical investigations are reported on the nature of resonance-assisted hydrogen bonding phenomenon (RAHB) and its influence on photophysical properties of the newly designed dyes differing in donor-acceptor properties, namely ethyl N-salicylideneglycinate (1), ethyl N-(5-methoxysalicylidene)glycinate (2), ethyl N-(5-bromosalicylidene)glycinate (3) and ethyl N-(5-nitrosalicylidene)glycinate (4). All compounds are thermochromic in the solid state and they contain a typical intramolecular O-H⋅⋅⋅N hydrogen bond formed between the hydroxyl hydrogen atom and the imine nitrogen atom, yielding the enol form in the solid state. It is unveiled, that the magnitude of RAHB effect fine tunes the strength of the O-H⋅⋅⋅N bonding and accordingly the relative populations of the enol, cis-keto and trans-keto forms leading to variation of the photophysical properties of 1-4. It is determined, that the electron-withdrawing NO2 in 4 amplifies the most RAHB effect causing the breaking of the O-H⋅⋅⋅N hydrogen bond and accordingly formation of the dominant cis-keto isomer in both the solid state and EtOH. To this end, the UV/Vis spectra of 1-3 in EtOH revealed the exclusive presence of the enol form, while the prevalent contribution of the cis-keto form was found for 4. Furthermore, only compound 4 is emissive in the solid state in ambient condition due to dual emission arising from the cis-keto* and trans-keto* forms, while 2 was found to be highly emissive in EtOH. It is revealed qualitatively and quantitatively, based on the ETS-NOCV charge and energy decomposition scheme and the EDDB population-based method, that RAHB is strongly a non-local phenomenon based on electrons pumping or sucking through both the π- and σ-channels, which accordingly exerts chemical bonding changes at both the phenyl ring and predominantly a distant O-H⋅⋅⋅N area.

The fact that intramolecular resonance-assisted hydrogen bonds (RAHBs) are stronger than conventional ones is attributed to the partial delocalization of the π-electrons within the hydrogen bond (HB) motif, the so-called quasi-ring. If an aromatic ring is involved in the formation of the RAHB, previous studies have shown that there is an interplay between aromaticity and HB strength. Moreover, in 1,3-dihydroxyaryl-2-aldehydes, some of us found that the position of the quasi-ring formed by the substituents interacting through RAHB influences the strength of the H bonding, the HBs being stronger when a kinked-like structure is generated by formation of the quasi-ring. In this work, we explore this concept further by considering a set of acenes and phenacenes of different sizes with two

In this work the relationship between the formal number of π-electrons, d-orbital conjugation topology, π-electron delocalization and aromaticity in d-block metallacycles is investigated in the context of recent findings concerning the correlation of π-HOMO topology and the magnetic aromaticity indices in these species. It is demonstrated that for π-electron rich d-metallacycles the direct link between aromaticity, the number of π-electrons and the frontier π-orbital topology does not strictly hold and for such systems it is very difficult to unambiguously associate their aromaticity with the '4n+2' (Hückel) and '4n' (Möbius) rules. It is also shown that the recently proposed electron density of delocalized bonds (EDDB) method can successfully be used not only to quantify and visualize aromaticity in such difficult cases, but also - in contrast to magnetic aromaticity descriptors - to provide a great deal of information on the real role of d-orbitals in metallacycles without the ambiguity of bookkeeping of electrons in the π-subsystem of the molecular ring. Interestingly, some of the metallacycles studied cannot be classified exclusively as Hückel or Möbius because they have a hybrid Hückel-Möbius or even quasi-aromatic nature Thisresearch was supported by the European Union’s FrameworkProgramme for Research and Innovation Horizon 2020 (2014–2020) under the Marie Skłodowska-Curie Grant Agreement No. 797335 “MulArEffect” and INFRAIA-2016-1 Grant Agreement No.730897 “HPC-Europa3” (Contract No: HPC17158J2). It was alsopartially supported by the National Science Centre, Poland underthe Sonata IX Grant No. 2015/17/D/ST4/00558, as well as Facultyof Chemistry at Jagiellonian University in Krakow and Institute ofComputational Chemistry and Catalysis at University of Girona.We also acknowledge the financial support from the SpanishMINECO (project CTQ2017-85341-P), the Catalan DIUE(2017SGR39, XRQTC, and ICREA Academia 2014 Award to M.S.),and the FEDER fund (UNGI10-4E-801)

Anagostic C–H···M (M = a metal center) intramolecular interactions, one of the most fundamental and elusive forces in organometallic chemistry, are intuitively considered as repulsive and purely el...

In this work we extend the concept of migrating Clar's sextets to explain local aromaticity trends in linear acenes predicted by theoretical calculations and experimental data. To assess the link between resonance and reactivity and to rationalize the constant-height AFM image of pentacene we used the electron density of delocalized bonds and other functions of the one-electron density from conceptual density functional theory. The presented results provide evidence for migration of Clar's π-sextets and larger circuits in these systems, and clearly show that the link between the theoretical concept of aromaticity and the real electronic structure entails the separation of intra- and inter-ring resonance effects, which in the case of [n]acenes (n = 3, 4, 5) comes down to solving a system of simple linear equations.

We report the design as well as structural and spectroscopic characterizations of two new coordination compounds obtained from Cd(NO3)2·4H2O and polydentate ligands, benzilbis(pyridin-2-yl)methylidenehydrazone (LI) and benzilbis(acetylpyridin-2-yl)methylidenehydrazone (LII), in a mixture with two equivalents of NH4NCS in MeOH, namely [Cd(SCN)(NCS)(LI)(MeOH)] (1) and [Cd(NCS)2(LII)(MeOH)] (2). Both LI and LII are bound via two pyridyl-imine units yielding a tetradentate coordination mode giving rise to the 12 π electron chelate ring. It has been determined for the first time (qualitatively and quantitatively), using the EDDB electron population-based method, the HOMA index, and the ETS-NOCV charge and energy decomposition scheme, that the chelate ring containing CdII can be classified as a quasi-aromatic Mobius motif. Notably, using the methyl-containing ligand LII controls the exclusive presence of the NCS- connected with the CdII atom (structure 2), while applying LI allows us to simultaneously coordinate NCS- and SCN- ligands (structure 1). Both systems are stabilized mostly by hydrogen bonding, C-H···π interactions, aromatic π···π stacking, and dihydrogen C-H···H-C bonds. The optical properties have been investigated by diffused reflectance spectroscopy as well as molecular and periodic DFT/TD-DFT calculations. The DFT-based ETS-NOCV analysis as well as periodic calculations led us to conclude that the monomers which constitute the obtained chelates are extremely strongly bonded to each other, and the calculated interaction energies are found to be in the regime of strong covalent connections. Intramolecular van der Waals dispersion forces, due to the large size of LI and LII, appeared to significantly stabilize these systems as well as amplify the aromaticity phenomenon.

Theoretical methods that were previously used to give a good quantitative description of the 3(1)Bu state of trans-2,2'-bithiophene are applied to characterize the lowest triplet states of three bridged cis-2,2'-bithiophenes: 3,3'-cyclopentadithiophene (CPDT), 3,3'-dithienylpyrrole (DTP), and 3,3'-dithienylthiophene (DTT). By obtaining highly accurate reproductions of the phosphorescence spectra of all three compounds, we rationalize the observed vibronic activity, further explore the performance of the applied theoretical methods, and address the quality of the reported experimental spectra. Over the course of this study we have, first, characterized the changes in the electronic structures between the ground state and the lowest triplet state and, second, expressed the related geometrical differences in terms of the Huang-Rhys factors. The Huang-Rhys factors have then been used to generate theoretical emission spectra with vibronic resolution. The applied procedure has yielded quantitative reproductions of the previously reported experimental phosphorescence spectra of DTT and DTP. The experimental spectrum of CPDT, on the other hand, turned out to be considerably narrower and intensity-deficient in its low energy region when compared with the theoretical results. Our experimental reinvestigation of the CPDT phosphorescence has given a refined spectrum that is significantly wider than the previously reported one, and is in nearly quantitative agreement with the theoretical prediction. This enabled us to attribute the observed discrepancy to an experimental artifact associated with the sensitivity characteristics of the commonly used photomultipliers.

In this article, we address the role of the long-range exchange corrections in description of the cyclic delocalization of electrons in aromatic systems at the density functional theory level. A test set of diversified monocyclic and polycyclic aromatics is used in benchmark calculations involving various exchange-correlation functionals. A special emphasis is given to the problem of local aromaticity in acenes, which has been a subject of long-standing debate in the literature. The presented results indicate that the noncorrected exchange-correlation functionals significantly overestimate cyclic delocalization of electrons in heteroaromatics and aromatic systems with fused rings, which in the case of acenes leads to conflicting local aromaticity predictions from different criteria The research was supported in part by the Foundation for Polish Science (FNP START 2015, stipend 103.2015, DS), National Science Centre, Poland (NCN SONATA, grant 2015/17/D/ST4/ 00558, DS) as well as the PL-Grid Infrastructure of the Academic Computer Centre CYFRONET, with the calculations performed on cluster platforms Zeus and Prometheus. MS thanks for the support of the Ministerio de Economía y Competitividad of Spain (Project CTQ2014-54306-P), Generalitat de Catalunya (project number 2014SGR931, Xarxa de Referència en Química Teòrica i Computacional, and ICREA Academia prize), and European Fund for Regional Development (FEDER grant UNGI10-4E-801)

A new development of the Electron Density of Delocalized Bonds formalism (EDDB) is proposed that provides marked improvement in the description of electron delocalization in aromatic rings. Special attention is paid to charged aromatic hydrocarbons of different size, for which the total population of electrons delocalized between adjacent bonds from the original formulation of the EDDB method significantly overestimates the multicenter π -electron sharing effects. The revised bond-orbital projecting scheme gives rise to systematic improvement of the results of the EDDB analysis, which now supports findings by other researchers.

In this study the recently developed electron density of delocalized bonds (EDDB) is used to define a new measure of aromaticity in molecular rings. The relationships between bond-length alternation, electron delocalization and diatropicity of the induced ring current are investigated for a test set of representative molecular rings by means of correlation and principal component analyses involving the most popular aromaticity descriptors based on structural, electronic, and magnetic criteria. Additionally, a qualitative comparison is made between EDDB and the magnetically induced ring-current density maps from the ipsocentric approach for a series of linear acenes. Special emphasis is given to the comparative study of the description of cyclic delocalization of electrons in a wide range of organic aromatics in terms of the kekulean multicenter index KMCI and the newly proposed EDDBk index The research was supported in part by the Faculty of Chemistry at Jagiellonian University (grant K/DSC/001469, DS), Foundation for Polish Science (FNP START 2015, stipend 103.2015, DS), National Science Centre, Poland (NCN SONATA, grant 2015/17/ D/ST4/00558, DS) as well as the PL-Grid Infrastructure of the Academic Computer Centre CYFRONET with the calculations performed on the cluster platform ‘‘Prometheus’’. MS thanks for the support of the Ministerio de Economa y Competitividad of Spain (Project CTQ2014-54306-P), Generalitat de Catalunya (project number 2014SGR931, Xarxa de Refere`ncia en Qumica Teo`rica i Computacional, and ICREA Academia prize), and European Fund for Regional Development (FEDER grant UNGI10-4E-801)

Correction for ‘Structural versatility of the quasi-aromatic Möbius type zinc(ii)-pseudohalide complexes – experimental and theoretical investigations’ by Mariusz P. Mitoraj et al., RSC Adv., 2019, 9, 23764–23773.

The formalism of the through-space and through-bridge communications proposed by Nalewajski within the framework of the Orbital Communication Theory is used to evaluate the correlation effect between electron populations of two chemical bonds. Proposed in this paper purely-probabilistic formalism defines the correlation between two chemical bonds as determined by the difference between appropriately normalized fourth-order joint probabilities corresponding to direct (through-space) and indirect (through-bridge) communication within a four-state time-homogeneous Markov chain. Alternative bond-correlation coefficient introduced earlier by Yamasaki and Goddard is based on the concept of the hierarchy of statistical covariance operators. The proposed correlation coefficient requires computing only the second-order probability terms when working within the condensed-atomic resolution and thus they are far less computationally expensive making them suitable for correlation analysis of chemical interactions between large molecular fragments.

Several alternative procedures of orthogonalization involving the metric of the linear vector space formed by columns of the matrix of LCAO MO coefficients are briefly discussed and exemplified using electron population analyzes and orbital-atom assignment descriptors. The newly proposed procedures put emphasis on the resemblance constraints between the relevant non-orthogonal and pre-orthogonalized LCAO MO column matrices representing the subspace of occupied molecular orbitals in the final orthogonalization step. Since only the subspaces of occupied MOs completely determines the electronic structure of chemical species they give rise to definitely more adequate and chemically meaningful orthogonal atomic orbitals than the original Lowdin’s atomic orbitals.

The original method of electron density partitioning is introduced that allows one to probe electron localization and delocalization within one theoretical paradigm. The newly proposed method makes use of the age-old concept of bond-order orbitals as well as the recently developed bond-orbital projection formalism to decompose the one-electron density into density layers representing electrons localized on atoms (inner shells, lone pairs), shared between atoms (chemical bonds) and delocalized between adjacent bonds (multi-center bonding). The details of the current implementation are briefly discussed and several illustrative examples are provided.

A novel method for investigating the multicenter bonding patterns in molecular systems by means of the so-called Electron Density of Delocalized Bonds (EDDB) is introduced and discussed. The EDDB method combines the concept of Jug’s bond-order orbitals and the indirect (‘‘through-bridge’’) inter- action formalism and opens up new opportunities for studying the interplay between different atomic interactions as well as their impact on both local and global resonance stabilization in systems of conjugated bonds. Using several illustrative examples we demonstrate that the EDDB approach allows for a reliable quantitative description of diverse multicenter delocalization phenomena (with special regard to evaluation of the aromatic stabilization in molecular systems) within the framework of a consistent theoretical paradigm.

A new index of electron delocalization in atomic rings is introduced and briefly discussed. The newly proposed delocalization descriptor is defined as an atom averaged measure of the effectiveness of forming linear combinations from two-center bond-order orbitals for a given sequence of bonded atomic triplets, and corresponds directly to electron population analysis; it allows one to get very compact and intuitive description of π -conjugation effects without additional parametrization and calibration to the reference molecular systems. The numerical results of illustrative calculations for several typical aromatic and homoaromatic compounds seem to validate the presented methodology and definitions.

A simple method of evaluating a semilocal (regional) nucleophilicity is introduced. The concept involves use of the natural orbitals for atomic populations to identify the most “reactive population” of electrons on particular atom in molecule. The results of test calculations considering the regioselectivity problem in electrophilic aromatic substitution to the benzene derivatives are presented and briefly discussed.

The criterion of maximum separation of non-degenerated eigenvalues in a density matrix spectrum is utilized to generalize the definition of the standard Wiberg-type bond covalency index on the case of multi-determinant state functions. This novel approach involves factorization of natural-orbital contributions to the ground-state bond-covalency and is essential for the stationarity condition of the electron population analysis within representation of atomic orbitals. The ground-state projecting technique is introduced to facilitate evaluation of bond orders in excited-state molecular systems. The performance of the presented methodology is tested on three small but educational and diversified molecules.

The criterion of maximum overlap with the canonical free-atom orbitals is used to construct a minimal set of molecule-intrinsic orthogonal atomic orbitals that resemble the most their promolecular origins. Partial atomic charges derived from population analysis within representation of such molecule-adopted atomic orbitals are examined on example of first-row hydrides and compared with charges from other methods. The maximum overlap criterion is also utilized to approximate the exact free-atom orbitals obtained from ab initio calculations in any arbitrary basis set and the influence of the resulting fitted canonical atomic orbitals on properties of molecule- adopted atomic orbitals is briefly discussed.

A simple method of analysing and localization of canonical molecular orbitals for particular chemical bond using the MO-resolved bond-order decompo- sition scheme is presented. An alternative definition of classical bond order orbitals is provided and links to communication theory of the chemical bond are outlined and briefly discussed. The introduced procedure of decomposition of quadratic bond orders allows one to analyse two- as well as three- center chemical bonds within the framework of the same theory.

The criterion of maximum overlap with the Huzinaga’s MINI basis functions as well as the “physical” orthogonalization concept are used to rationalize the standard atomic charges calculated within representation of extended basis sets and to compare charge distributions calculated using different basis sets. The generalization of “physical” orthogonalization approach on natural orbitals is introduced and briefly discussed. Numerical results fully validate the presented methodology identifying the newly proposed atomic charges as an interesting alternative to classical Mulliken’s and Lowdin’s population analyses.

An alternative procedure of orthogonalization involving a metric matrix of the linear vector space formed by the columns of LCAO matrix is introduced. It is proved that this procedure is fully equivalent the original Lowdin’s scheme. Also, a few modifications involving a two-step orthogonalization scheme are outlined and briefly discussed. Numerical results of test calculations of atomic charges for several representative molecules seem to fully validate the newly proposed methodology.

Information channels from SCF MO calculations using different basis sets and their entropic bond descriptors are compared within the orbital communication theory. In this information-theoretic (IT) treatment of communications between basis functions the overall covalency and ionicity bond components reflect the average communication noise and information flow, respectively, in the resolution level specified by the adopted set of basis functions. The basis-set dependence of the orbital conditional probabilities and their entropic descriptors of the information covalency/ionicity content is explored. Compared to the minimum set \({{\bf \chi}}\) of the occupied atomic orbitals of the separated constituent atoms, the extended basis sets of Gaussian orbitals and/or their formal contractions generally give rise to a higher IT-covalency and lower IT-ionicity descriptors of the system chemical bonds. In the augmented set case, \({{\bf \chi}^{aug.} = ({\bf \chi},{\bf \psi})}\) , containing the polarization function complement \({{\bf \psi}}\) of \({{\bf \chi}}\) , the use of only \({{\bf \chi} \rightarrow {\bf \chi}}\) communications is advocated in a semi-quantitative chemical interpretation of the IT bond indices. The maximum-overlap criterion is used to transform the general (orthonormal) extended basis \({{\bf \xi}}\) to its semi-augmented form \({\widetilde{\bf \chi}^{aug.} = \widetilde{\bf \xi}=(\widetilde{\bf \chi}, \widetilde{\bf \psi}),}\) in which \({\widetilde {\bf \chi} \approx {\bf \chi}}\) and \({\widetilde {\bf \psi} \approx{\bf \psi}}\), which facilitates the near minimum basis set interpretation of bond descriptors and extraction of communications involving the polarization functions \({{\widetilde {\mathbf \psi}}}\) . A similar transformation using the minimum information distance criterion can be also envisaged. The effect of the atomic reduction of the molecular channels, which misses the effect of the “internal” communications (bonds) on constituent atoms, is also examined. As intuitively expected, the IT descriptors of such reduced channels are found to be less sensitive to the basis set enlargement.

A new bond multiplicity measure based on the Wiberg-type bond covalency index and the atomic charge from population analysis is presented. Heuristically derived formulas allow one to evaluate the character of the chemical bond, especially its ionicity degree. Numerical results at RHF/ROHF theory level demonstrate that full multiplicities of typical chemical bonds are close to formal orders and their basis set dependence is inconsiderable, especially for highly polarized chemical bonds.