Szczepanik Research Group

D.W. Szczepanik (), M. Solà ()
Aromaticity: Modern Computational Methods and Applications (ed. I. Fernández), Chapter 8 (pp. 259−283), Elsevier, 2021.
DOI: 10.1016/B978-0-12-822723-7.00008-X.   URL    BUY 

R.F. Nalewajski (), D.W. Szczepanik, J. Mrozek
Advances in Quantum Chemistry vol. 61 (ed. J.R. Sabin, E. Brandas), Chapter 1 (pp. 1−48), Elsevier, 2011.
DOI: 10.1016/B978-0-12-386013-2.00001-2.   URL 

R. Pino-Rios, R. Baez-Grez, D.W. Szczepanik, M. Solà ().
Physical Chemistry Chemical Physics  26 (2024) accepted. DOI: 10.1039/D4CP01284D.   URL 

Anti-Kasha azulene derivatives that could carry out singlet fission (SF) have been designed. For this purpose, substituted azulenes with a donor- (OH) and/or an acceptor-group (CN) have been systematically studied. Results show that CN (OH) substituents on electrophilic (nucleophilic) carbons result in improved SF properties when compared to azulene.
 

C. Shu, D.W. Szczepanik, A. Munoz-Castro, M. Solà, Z.-M. Sun ().
Journal of the American Chemical Society  146 (2024) accepted. DOI: 10.1021/jacs.4c03024.   URL 

Inorganic fullerene clusters have attracted wide-spread attention due to their highly symmetrical geometric struc-tures and intrinsic electronic properties. However, cage-like clus-ters composed of heavy metal elements with high symmetry are rarely reported, and their synthesis is also highly challenging. In this paper, we present the synthesis of a [K2(Bi@Pd12@Bi20)]4- cluster that incorporates a {Bi20} cage with pseudo-Ih symmetry, making it the largest main group metal cluster compound composed of the bismuth element to date. Magnetic characterization and the-oretical calculations suggest that the spin state of the overall cluster is a quartet. Quantum chemical calculations reveal that the [Bi20]3- cluster has the similar electronic configuration to C606- and [Bi@Pd12@Bi20]6- cluster exhibits a unique open-shell aromatic character.
 

B. Basumatary, H. Tsuruda, D.W. Szczepanik, J. Lee, J. Ryu, S. Mori, K. Yamagata, T. Tanaka, A. Muranaka, M. Uchiyama, J. Kim (), M. Ishida (), H. Furuta ().
Angewandte Chemie International Edition  63 (2024) e202405059. DOI: 10.1002/anie.202405059.   URL 

We present herein the synthesis of novel pseudo-metalla-carbaporphyrinoid species (1M: M = Pd and Pt) achieved through the inner coordination of palladium(II) and platinum(II) with an acyclic N-confused tetrapyrrin analogue. Despite their tetrapyrrole frameworks being small, akin to well-known porphyrins, these species exhibit an unusually narrow HOMO-LUMO gap, resulting in an unprecedentedly low-energy absorption in the second near-infrared (NIR-II) region. DFT calculations revealed unique d_π-p_π-conjugated electronic structures involving the metal d_π-ligand p_π hybridized molecular orbitals of 1M. Magnetic circular dichroism (MCD) spectroscopy confirmed distinct electronic structures. Remarkably, the complexes feature an open-metal coordination site in the peripheral NN dipyrrin site, forming hetero-metal complexes (1Pd-BF2 and 1Pt-BF2) through boron difluoride complexation. The resulting hetero metalla-carbaporphyrinoid species displayed further redshifted NIR-II absorption, highly efficient photothermal conversion efficiencies (η; 62-65%), and exceptional photostability. Despite the challenges associated with the theoretical and experimental assessment of d_π-p_π-conjugated metalla-aromaticity in relatively larger (more than 18π electrons) polycyclic ring systems, these organometallic planar tetrapyrrole systems could serve as potential molecular platforms for aromaticity-relevant NIR-II dyes.
 

P. Pakulski (), M. Magott, S. Chorazy, M. Sarewicz ,M. Srebro-Hooper, D. Tabor, L. Lapok. D.W. Szczepanik, S. Demir, D. Pinkowicz ()
Chem  10 (2024) 1−27. DOI: 10.1016/J.CHEMPR.2023.12.024.   URL 

Manufacturing green devices down to subnanometers requires innovative multifunctional molecules. Specifically, several input and output capabilities at the molecular level allow such entities to be used as nanosensors, nanoswitches, and nanovalves. Contriving multifunctional molecules is synthetically and conceptually challenging yet highly coveted, as the desired single-molecule devices may be simultaneously operated by light, electric fields, and/or magnetic fields and be responsive to small signaling molecules. Here, the isolation and study of a redox-active variant of the archetypical pseudo-[6]oxocarbon, named tripak, are reported. Tripak can hold up to six electrons, and five of the six valence forms were confirmed by crystallography. Notably, the properties of tripak vary dramatically as a function of oxidation state, allowing access to an unprecedented wide range of functionalities, unique for simple molecular frameworks. The molecule paves the way for Swiss-knife-like single-molecule devices.
 

H. Saeidian (), S.M.M. Asadabad, D.W. Szczepanik, N.J.M. Al-Juaifari, Z. Mirjafary, A.H. Abdulzahra
International Journal of Quantum Chemistry  (2024) e27271. DOI: 10.1002/qua.27271.   URL 

Due to the insufficient interaction of the phosphorus lone pair with the butadiene moiety, the aromaticity of the phosphole ring is lower than that of its counterpart's pyrrole, furan, and thiophene. Considering the high importance of phosphole core in organic chemistry, increasing its stability through reinforcement its aromaticity can be very valuable. In the present work, the aromaticity of the phosphole on the anomeric carbon in both the axial and equatorial conformers of the unsaturated six-membered heterocycles, using structural, electronic, energetic, and magnetic indices were investigated by the DFT-B3LYP/6-311++G(d,p) computational method. Electron pumping through anomeric and then Schleyer hyperconjugative interaction increase the aromaticity of the phosphole ring in axial conformer of compounds 1-11. Based on various types of aromaticity indices, the results showed that the phosphole ring in the axial position has far higher aromaticity than the equatorial position. The phosphole ring containing cyano groups shows an efficient anomeric effect and, as a result, higher aromaticity. Excellent correlations were observed between aromaticity indices with different backgrounds.
 

D.W. Szczepanik ()
RSC Advances  13 (2023) 34224−34229. DOI: 10.1039/D3RA06603G.   URL 

Actinides have been known to form extremely weak homonuclear bonds with their d-type orbitals, and one should therefore expect the superposition of cyclic resonance forms containing such bonds to bring rather marginal aromatic stabilization to the system, if any. It is for this very reason that the discovery of the cyclically delocalized Th₃ σ-bonding in the crystalline cluster isolated by Liddle and co-workers has sparked such vigorous discussion on the actual role of molecular aromaticity on the periphery of the periodic table. It has recently been argued that the tri-thorium ring at the heart of the cluster features considerable aromatic stabilization energy comparable to the heterocyclic π-aromatic rings such as thiophene. However, previous investigations involved highly ionized model clusters like Th₃Cl₆⁴⁺ or Th₃¹⁰⁺ in which aromatic stabilization associated with the cyclic delocalization of charge is dramatically exaggerated. In this work we investigate the model tri-thorium clusters at different geometries and ionization states to show that cyclic delocalization of electrons in the isolated crystalline cluster may be associated with rather marginal σ-aromatic stabilization energy thus strongly suggesting its non-aromatic character.
 

K. Nakanishi, L.I. Lugo-Fuentes, J. Manabe, S. Kikkawa, S. Yamazoe, K. Komaguchi, S. Kume, D.W. Szczepanik, M. Solà, J.O.C. Jimenez-Halla, S. Nishihara, K. Kubo, Y. Yamamoto, M. Nakamoto, T. Mizuta, R. Shang ()
Chemistry - A European Journal  29 (2023) e202302303. DOI: 10.1002/CHEM.202302303.   URL 

Synthetic strategies to access high-valent iridium complexes usually require use of π donating ligands bearing electronegative atoms (e. g. amide or oxide) or σ donating electropositive atoms (e. g. boryl or hydride). Besides the η⁵-(methyl)cyclopentadienyl derivatives, high-valent η¹ carbon-ligated iridium complexes are challenging to synthesize. To meet this challenge, this work reports the oxidation behavior of an all-carbon-ligated anionic bis(CCC-pincer) Ir^III complex. Being both σ and π donating, the diaryl dipyrido-annulated N-heterocyclic carbene (dpa-NHC) Ir^III complex allowed a stepwise 4e^- oxidation sequence. The first 2e^- oxidation led to an oxidative coupling of two adjacent aryl groups, resulting in formation of a cationic chiral Ir^III complex bearing a CCCC-tetradentate ligand. A further 2e^- oxidation allowed isolation of a high-valent tricationic complex with a triplet ground state. These results close a synthetic gap for carbon-ligated iridium complexes and demonstrate the electronic tuning potential of organic π ligands for unusual electronic properties.
 

H. Steffenfauseweh, D. Rottschäfer, Y.V. Vishnevskiy, B. Neumann, H.G. Stammler, D.W. Szczepanik, R.S. Ghadwal ()
Angewandte Chemie International Edition  62 (2023) e202216003. DOI: 10.1002/anie.202216003.   URL 

The first 1,4-distibabenzene-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^-1 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 36 % and 39 %, 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]₂Mo(CO)₄ (8).
 

W. Zeng, D.W. Szczepanik, H. Bronstein ()
Journal of Physical Organic Chemistry  36 (2023) e4441. DOI: 10.1002/POC.4441.   URL 

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.
 

D.W. Szczepanik ()
Angewandte Chemie International Edition 61 (2022) e202204337. DOI: 10.1002/anie.202204337.   URL     URL  
Angewandte Chemie 61 (2022) e202204337. DOI: 10.1002/anie.202204337.   URL 

O.E. Bakouri, D.W. Szczepanik, K. Jorner, R. Ayub, P.O. Norrby, P. Bultinck, M. Solà (), H. Ottosson ()
Journal of the American Chemical Society 144 (2022) 8560−8575. DOI: 10.1021/jacs.1c13478.   URL     URL  

Several fully π-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 ?-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic ?-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 the fact that these molecules show substantial ?-electron delocalization, they cannot be classified as true 3D-aromatics.
 

H.L. Xu, N.V. Tkachenko, D.W. Szczepanik, I.A. Popov, A. Munoz-Castro, A.I. Boldyrev (), Z.M. Sun ()
Nature Communications  13 (2022) 2149. DOI: 10.1038/s41467-022-29626-5.   URL     URL  

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 Ge₂₄^4-, 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, 4s 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 Ge₂₄^4- cluster.
 

G. Mahmoudi (), V. Alizadeh, A. Castineiras, F.A. Afkhami, B.B. M.P. Mitoraj (), D.W.Szczepanik, I. Konyaeva, K. Robeyns, D.A. Safin ()
CrystEngComm  24 (2022) 2836−2844. DOI: 10.1039/d2ce00046f.   URL 

W. Zeng, O. El Bakouri, D.W. Szczepanik (), H. Bronstein (), H. Ottosson ()
Chemical Science  12 (2021) 6159−6171. DOI: 10.1039/D1SC00382H.   URL     URL  

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 (>1eV). 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.
 

G. Mahmoudi (), M. Babashkina, W. Maniukiewicz (), F.A. Afkhami, B.B. Nunna, F.I. Zubkov, A.L. Ptaszek, D.W. Szczepanik, M.P. Mitoraj (), D.A. Safin ()
International Journal of Molecular Sciences  22 (2021) 5337. DOI: 10.3390/ijms22105337    URL 

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 has allowed to isolate a discrete mononuclear homoleptic complex [NiLI] (1), which 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 co-ordination 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 has allowed to isolate 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 coordi-nation 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 to conclude, 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, ?), CH•••HC, ?•••? 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 exchange-correlation contribution as revealed by the IQA energy decomposition scheme. Interestingly, the analogous long-range C–H•••S interactions are characterized by repulsive Coulomb contribution and the prevailing attractive ex-change-correlation constituent. The electron density of delocalized bonds (EDDB) method shows, that the nickel(II) atom shares only ~0.8|e| due to the π-conjugation with the adjacent in-plane atoms, what demonstrate very weak ?-metalloaromatic character.
 

D. Chen, D.W. Szczepanik, J. Zhu, A. Muñoz-Castro (), M. Solà ()
Chemistry - A European Journal  27 (2021) 802−808. DOI: 10.1002/CHEM.202004322.   URL 

The isolated-pentagon rule (IPR) is a determining structural feature accounting for hollow fullerene stabilization and properties related to C_n (n ≥ 60) cages. The recent characterization of an unprecedented non-IPR hydrofullerene, C_2v-C₆₆H₄, bearing two heptagons with adjacent fused-pentagons motif, largely dismiss this feature. Herein, employing DFT calculations, we explore its ¹³C-NMR pattern and aromatic behavior. Our results unravel the unique features of C₆₆H₄ in comparison to pristine C₆₀, where three π-aromatic circuits are found at the bottom section of this fullerene derivative. 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 C₆₀^6- 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.
 

D. Chen, D.W. Szczepanik, J. Zhu (), M. Solà ()
Chemical Communications  56 (2020) 12522−12525. DOI: 10.1039/D0CC05586G.   URL     CHEMISTRY WORLD - News  

The 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 the Baird's rule can be also extended to all-metal systems with σ- and π-aromaticity.
 

D. Chen, D.W. Szczepanik, J. Zhu (), M. Solà ()
Chemistry - A European Journal  26 (2020) 12964−12971. DOI: 10.1002/chem.202001830.   URL 

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.
 

D.S. Shapenova, A.N. Zvezda, A.A Shiryaev, M. Bolte, M. Kukulka, D.W. Szczepanik, J. Hooper, M.G. Babashkina, G. Mahmoudi, M.P. Mitoraj (), D.A. Safin ()
Chemistry - A European Journal  26 (2020) 12987−12995. DOI: 10.1002/chem.202001551.   URL 

We report extensive experimental and theoretical investigations on the nature of resonance assisted hydrogen bonding phenomenon (RAHB) and its influence on photophysical and thermochromic properties of the newly designed dyes differing in donor-acceptor properties: ethyl N-salicylideneglycinate ( 1 ), ethyl N-(5-methoxysalicylidene)glycinate ( 2 ), ethyl N-(5-bromosalicylidene)glycinate ( 3 ) and ethyl N-(5-nitrosalicylidene)glycinate ( 4 ). 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, based on the ETS-NOCV and EDDB methods, that RAHB is based on electrons pumping or sucking through both the π- and σ-channels, what accordingly exerts chemical bonding changes at both the phenyl ring and predominantly a distant O-H···N area.
 

M.P. Mitoraj (), F. Sagan, D.W. Szczepanik, J. Lange, A. Ptaszek, D.M.E. Niekerk, I. Cukrowski ()
ChemPhysChem  21 (2020) 494−502. DOI: 10.1002/cphc.202000066.   URL 

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" vs "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 dominating intra-molecular CH···HC interactions.
 

G. Pareras, D.W. Szczepanik, M. Duran, M. Solà (), S. Simon ()
Journal of Organic Chemistry  84 (2019) 15538−15548. DOI: 10.1021/acs.joc.9b02526.   URL 

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 o-hydroxyaldehyde substituents. Calculations with the CAM-B3LYP/6-311++G(d,p)+GD3B method show that for long acenes or phenacenes, once the substituent effect loses importance because quasi-rings are pull apart far from each other, the different topologies rule the HB distances. This fact can be explained in most cases using an extended Clar's aromatic π-sextet model. In some kinked systems, however, the justification from the Clar model has to be complemented by taking into account the repulsion between hydrogen atoms. Triphenylene-like compounds with different number of benzene rings have been studied finding out a very good relationship between aromaticity of the ipso- and quasi-rings with the RAHB distances. This result confirms the importance of the communication of the π-systems of the ipso- and quasi-rings.
 

D.W. Szczepanik (), M. Solà ()
ChemistryOpen  8 (2019) 219−227. DOI: 10.1002/open.201900014.   URL 

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.
 

M.P. Mitoraj (), F. Afkhami, G. Mahmoudi (), A. Khandar, A. Gurbanov, F. Zubkov, R. Waterman, M. Babashkina, D.W. Szczepanik, H. Jena, D.A. Safin ()
RSC Advances  9 (2019) 23764−23773. DOI: 10.1039/c9ra05276c.    URL 
RSC Advances  9 (2019) 26547−26547. DOI: 10.1039/c9ra90062d.    URL   (Correction)

In this contribution we report for the first time fabrication, isolation, structural and theoretical characterization of the quasi-aromatic Mobius complexes XXXXX (1-3) constructed from 1,2-diphenyl-1,2-bis((phenyl(pyridin-2-yl)methylene)hydrazono)ethane (LI)) or benzilbis(acetylpyridin-2-yl)methylidenehydrazone (LII), respectively, and ZnCl2 mixed with NH4NCS or NaN3. Structures 1–3 are dictated by both the bulkiness of the organic ligand and the nature of the inorganic counter ion. As evidenced from single crystal X-ray diffraction data species 1 has a neutral discrete heteroleptic mononuclear structure, whereas, complexes 2 and 3 exhibit a salt-like structure. Each structure contains a ZnII atom chelated by one tetradentate twisted ligand LI creating the unusual Mobius type topology. Theoretical investigations based on the EDDB method allowed us to determine that it constitutes the quasi-aromatic Mobius motif where a metal only induces the p-delocalization solely within the ligand part: 2.44|e| in 3, 3.14|e| in 2 and 3.44|e| in 1. It is found, that the degree of quasi-aromatic p-delocalization in the case of zinc species is significantly weaker (by 50%) than the corresponding estimations for cadmium systems – it is associated with the Zn–N bonds being more polar than the related Cd–N connections. The ETS-NOCV showed, that the monomers in 1 are bonded primarily through London dispersion forces, whereas long-range electrostatic stabilization is crucial in 2 and 3. A number of non-covalent interactions are additionally identified in the lattices of 1–3.
 

M.P. Mitoraj (), M.G. Babashkina, K. Robeyns, F. Sagan, D.W. Szczepanik, Y. Garcia, D.A. Safin ()
Organometallics  38 (2019) 1973−1981. DOI: 10.1021/acs.organomet.9b00062.   URL 

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 electrostatic in nature due to significant metal-hydrogen distances (2.3−3.0 Å). Contrary to the current state of knowledge, it is shown herein by quantum chemical computations based on the case study of new square-planar Ni(II) isomers based on N−thiophosphorylated thiourea, that despite significant metal-hydrogen anagostic distances, the covalent-type charge delocalization contribution [Ni(dz2)→σ*(C−H) and σ(C−H)→Ni(dz2)] exists and it covers, together with the London dispersion energy, up to 40% of the overall anagostic stabilization. This charge delocalization component is found to amplify the metalloaromaticity phenomenon although lack of any stabilizing charge transfer is expected at such long metal-hydrogen distances (> 3 Å). Remarkably, for the relatively short regime (<3 Å) of anagostic distances, the electrostatic Coulomb forces are destabilizing, which leads to the repulsive anagostic interactions, whereas, surprisingly an increase of anagostic distance above 3 Å makes anagostic interactions stabilizing mostly due to attractive Coulomb forces. It shows unprecedented agostic (attractive) ↔ anagostic (repulsive) transitions in ubiquitous d8 square-planar Ni(II) complexes containing elongated metal-hydrogen distances.
 

M.P. Mitoraj (), G. Mahmoudi (), F. Afkhami, A. Castineiras, G. Giester, I. Konyaeva, A.A. Khandar, F. Qu (), A. Gupta (), F. Sagan, D.W. Szczepanik, D.A. Safin ()
Crystal Growth Design  19 (2019), 1649−1659. DOI: 10.1021/acs.cgd.8b01569.   URL 

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 Cd(II) based synthons has been found to exhibit a quasi-aromatic Möbius 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 Cd(II) do not overlap with the π-system of L. It is further found that the donor/acceptor character of the substituents attached to L can tune the Möbius quasi-aromaticity. Finally, formation of the crystals is driven not only by the typical ionic/dative Cd−N bonds, but also by a number of noncovalent interactions starting from classic hydrogen bonds (N−H···N, N−H···O) going through π···π, C−H···π, to end up with nonintuitive and recently topical Lp···Lp interactions (Lp - lone pair): e.g., C···C, N···N, N···S, S···S as well as London dispersion dominated homopolar dihydrogen interactions C−H···H−C.
 

D.W. Szczepanik ()
International Journal of Quantum Chemistry  118 (2018) e25696. DOI: 10.1002/qua.25696.   URL 

In this work, we introduce an approximate method for the multicenter index calculation that is very simple in implementation and has the same computational cost as the pseudo-π approach. In contrast to the latter, however, the newly proposed method does not require additional single-point calculations and is capable of quantifying multicenter electron sharing in aromatic rings containing heteroatoms and transition metals.
 

D.W. Szczepanik (), M. Solà, T.M. Krygowski, H. Szatylowicz, M. Andrzejak, B. Pawelek, J. Dominikowska, M. Kukulka, K. Dyduch
Physical Chemistry Chemical Physics  20 (2018) 13430−13436. DOI: 10.1039/c8cp01108g.   URL 

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 p-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.
 

G. Mahmoudi (), F. Afkhami, A. Castineiras, I. Garcia-Santos, A. Gurbanov, F.I. Zubkov, M.P. Mitoraj (), M. Kukulka, F. Sagan, D.W. Szczepanik, D.A. Safin ()
Inorganic Chemistry  57 (2018) 4395−4408. DOI: 10.1021/acs.inorgchem.8b00064.   URL 

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 Möbius 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.
 

D.W. Szczepanik (), M. Andrzejak, J. Dominikowska, B. Pawełek, T.M. Krygowski, H. Szatylowicz, M. Solà
Physical Chemistry Chemical Physics  19 (2017) 28970−28981. DOI: 10.1039/c7cp06114e.   URL 

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.
 

D.W. Szczepanik (), M. Solà, M. Andrzejak, B. Pawełek, J. Dominikowska, M. Kukułka, K. Dyduch, T.M. Krygowski, H. Szatylowicz
Journal of Computational Chemistry  38 (2017) 1640−1654. DOI: 10.1002/jcc.24805.   URL 

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.
 

D.W. Szczepanik (), E.J. Zak, J. Mrozek
Computational and Theoretical Chemistry  1115 (2017) 80−87. DOI: 10.1016/j.comptc.2017.05.041.   URL 

The orbital communication theory (OCT) by Nalewajski is derived step by step from first principles of quantum mechanics. It is shown that the entropy representation within the molecular orbital theory arises as a natural consequence of the probabilistic interpretation of quantum superposition. The algebra of selected types of molecular information channels is reinvestigated within the framework of the theory of Markov chains and several representative models of molecular communication systems in atomic-orbital resolution are discussed. The presented results show that the Shannon entropy alone, i.e. with no insight into its components - mutual information and conditional entropy, does not allow one to correctly identify the source of uncertainty connected with the electron probability distribution, which in some cases leads to wrong conclusions about the electron delocalization effects in a molecule.
 

D.W. Szczepanik ()
Computational and Theoretical Chemistry  1100 (2017), 13−17. DOI: 10.1016/j.comptc.2016.12.003.   URL 

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.
 

D.W. Szczepanik ()
Computational and Theoretical Chemistry  1080 (2016) 33−37. DOI: 10.1016/j.comptc.2016.02.003.   URL 

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.
 

M. Andrzejak (), D.W. Szczepanik, Ł. Orzeł
Physical Chemistry Chemical Physics  17 (2015) 5328−5337. DOI: 10.1039/c4cp03327b.   URL 

Theoretical methods that were previously used to give a good quantitative description of the 31Bu 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.
 

D.W. Szczepanik (), M. Andrzejak, K. Dyduch, E.J. Zak, M. Makowski, G. Mazur, J. Mrozek,
Physical Chemistry Chemical Physics  16 (2014) 20514−20523. DOI: 10.1039/c4cp02932a.   URL 

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") interaction 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.
 

D.W. Szczepanik (), E.J. Zak, K. Dyduch, J. Mrozek
Chemical Physics Letters  593 (2014) 154−159. DOI: 10.1016/j.cplett.2014.01.006.   URL 

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.
 

D.W. Szczepanik (), J. Mrozek
Computational and Theoretical Chemistry  1026 (2013) 72−77. DOI: 10.1016/j.comptc.2013.10.015.   URL 

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.
 

D.W. Szczepanik (), J. Mrozek
Journal of Chemistry  2013 (2013) 684134 (1−6). DOI: 10.1155/2013/684134.   URL 

Within the framework of the Frontier Molecular Orbital theory the effect of substituent groups is sometimes evaluated by means of the electron population analysis of the highest occupied molecular orbital (HOMO). In this paper we propose a "reverse scenario" of evaluating a semilocal (regional) nucleophilicity of ring members in aromatic species, in which we focus on the electron population of particular atom first and then we consider the highest expectation values of the Fock operator within the representation of atomic natural orbitals (ANO). Interesingly, contrariwise to the commonly used atomic indices of nucleophilicity by Franke and Fukui, the resulting "energies" calculated for each atom in the ring enable one to succesfully identify and assess the ring activation/deactivation effect of electron donating and electron withdrawing groups in the electrophilic aromatic substitution.
 

D.W. Szczepanik (), J. Mrozek
Journal of Mathematical Chemistry  51 (2013) 2687−2698. DOI: 10.1007/s10910-013-0230-z.   URL 

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.
 

D.W. Szczepanik (), J. Mrozek
Computational and Theoretical Chemistry  1023 (2013) 83−87. DOI: 10.1016/j.comptc.2013.09.008.   URL 

The criterion of maximum separation of non−degenerated eigenvalues in the one-electronc reduced 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. The proposed definition involves factorization of natural−orbital contributions to the ground−state bond-covalency index and is essential for the Markov's stationarity condition of the one-electron reduced density matrix 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 selected small but informative molecules.
 

D.W. Szczepanik (), J. Mrozek
Journal of Mathematical Chemistry  51 (2013) 1619−1633. DOI: 10.1007/s10910-013-0169-0.   URL 

A simple method of analysing and localization of canonical molecular orbitals for particular chemical bond using the MO−resolved bond−order decomposition 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.
 

D.W. Szczepanik (), J. Mrozek
Journal of Mathematical Chemistry  51 (2013) 1388−1396. DOI: 10.1007/s10910-013-0153-8.   URL 

Stationarity of electron probability distribution within the resolution of atomic orbitals is considered involving some concepts from Orbital Communication Theory and the theory of Markov Processes. A new method of evaluating electron conditional probabilities based on natural orbitals is proposed and briefly discussed.
 

D.W. Szczepanik (), J. Mrozek
Computational and Theoretical Chemistry  1008 (2013) 15−19. DOI: 10.1016/j.comptc.2012.12.013.   URL 

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 Löwdin's atomic orbitals.
 

D.W. Szczepanik (), J. Mrozek
Computational and Theoretical Chemistry  996 (2012) 103−109. DOI: 10.1016/j.comptc.2012.07.021.   URL 

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 the Mulliken and Löwdin population analyses.
 

D.W. Szczepanik (), J. Mrozek
Chemical Physics Letters  521 (2012) 157−160. DOI: 10.1016/j.cplett.2011.11.047.   URL 

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 Löwdin 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.
 

R.F. Nalewajski (), D.W. Szczepanik, J. Mrozek
Journal of Mathematical Chemistry  50 (2012) 1437−1457. DOI: 10.1007/s10910-012-9982-0.   URL 

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 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, containing the polarization function, the use of only 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 to its semi-augmented form, which facilitates the near minimum basis set interpretation of bond descriptors and extraction of communications involving the polarization functions. 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.
 

D.W. Szczepanik (), J. Mrozek
Journal of Theoretical and Computational Chemistry  10 (2011) 471−482. DOI: 10.1142/s021963361100658x.   URL 

A new bond multiplicity measure based on the Evarestov-Veriazov equation and the conditional probability matrix concept 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.
 

D.W. Szczepanik (), J. Mrozek
Journal of Mathematical Chemistry  49 (2011) 562−575. DOI: 10.1007/s10910-010-9763-6.   URL 

Communication Theory of Chemical Bond (CTCB) in atomic orbital resolution is used to define entropic bond orders of diatomic molecular fragments. Partial communication channels for separated information flows from atomic centers and two alternative output-reducion schemes with their entropic descriptors are proposed. Also two types of information that can be transmitted through communication system are identified: information about molecular electron occupations and information about bonding shares of atomic orbitals. The former is used to evaluate an average number of electrons engaged in bond forming process while the latter provides information about electron localization in chemical bond. Calculated entropic bond orders and their IT-covalency and IT-ionicity components are in good agreement with both chemical intuition and MO theory predictions.
 

R.F. Nalewajski (), D.W. Szczepanik, J. Mrozek
Advances in Quantum Chemistry vol. 61 (ed. J.R. Sabin, E. Brandas), Chapter 1 (pp. 1−48), Elsevier, 2011.   URL 

Information-theoretic (IT) probe of molecular electronic structure, within the orbital-communication theory (OCT) of the chemical bond, uses the standard entropy/information descriptors of the Shannon theory of communication to characterize the scattering of electron probabilities and their information content throughout the system network of chemical bonds generated by the occupied molecular orbitals (MOs). Thus, the molecule is treated as information network, which propagates the "signals" of the electron allocation to constituent atomic orbitals (AOs) or general basis functions between the channel AO "inputs" and "outputs". These orbital "communications" are determined by the two-orbital conditional probabilities of the output AO events given the input AO events. It is argued, using the quantum-mechanical superposition principle, that these conditional probabilities are proportional to the squares of corresponding elements of the first-order density matrix of the AO charges and bond orders (CBO) in the standard self-consistent field (SCF) theory using linear combinations of AO (LCAO) to represent MO. Therefore, the probability of the interorbital connections in the molecular communication system is directly related to the Wiberg-type quadratic indices of the chemical bond multiplicity. Such probability propagation in molecules exhibits the communication "noise" due to electron delocalization via the system chemical bonds, which effectively lowers the information content in the output signal distribution, compared with that contained in probabilities determining its input signal, molecular or promolecular. The orbital information systems are used to generate the entropic measures of the chemical bond multiplicity and their covalent/ionic composition. The average conditional-entropy (communication noise, electron delocalization) and mutual-information (information capacity, electron localization) descriptors of these molecular channels generate the IT covalent and IT ionic bond components, respectively. A qualitative discussion of the mutually decoupled, localized bonds in hydrides indicates the need for the flexible-input generalization of the previous fixed-input approach, in order to achieve a better agreement among the OCT predictions and the accepted chemical estimates and quantum-mechanical bond orders. In this extension, the input probability distribution for the specified AO event is determined by the molecular conditional probabilities, given the occurrence of this event. These modified input probabilities reflect the participation of the selected AO in all chemical bonds (AO communications) and are capable of the continuous description of its decoupling limit, when this orbital does not form effective combinations with the remaining basis functions. The occupational aspect of the AO decoupling has been shown to be properly represented only when the separate communication systems for each occupied MO are used, and their occupation-weighted entropy/information contributions are classified as bonding (positive) or antibonding (negative) using the extraneous information about the signs of the corresponding contributions to the CBO matrix. This information is lost in the purely probabilistic model since the channel communications are determined by the squares of such matrix elements. The performance of this MO-resolved approach is then compared with that of the previous, overall (fixed-input) formulation of OCT for illustrative π-electron systems, in the Hückel approximation. A qualitative description of chemical bonds in octahedral complexes is also given. The bond differentiation trends in OCT have been shown to agree with both the chemical intuition and the quantum-mechanical description. The numerical Restricted Hartree-Fock (RHF) applications to diatomic bonds in representative molecular systems are reported and discussed. The probability weighted scheme for diatomic molecular fragments is shown to provide an excellent agreement with both the Wiberg bond orders and the intuitive chemical bond multiplicities.
 

P. Wieczorkiewicz, H. Sundström, M. Dratwinski, W. Sitkowska, M. Andrzejak, D.W. Szczepanik (), in preparation.  

P. Wieczorkiewicz, M. Andrzejak, M. Solà, D.W. Szczepanik (), in preparation.  

S. Escayola, J. Labella, D.W. Szczepanik, A. Poater, T. Torres (), M. M. Solà (), E. Matito (), in preparation.  

F. Ebeler, M.K. Sharma, Y.V. Vishnevskiy, ..., D.W. Szczepanik, R.S. Ghadwal (), submitted.

X. Lv, F. Chen, S. Tu, D.W. Szczepanik, S. Xue (), under revision.

D.W. Szczepanik (), O.E. Bakouri (), under review.

D.W. Szczepanik (), M. Solà (), under revision.