Slavko Radenković

University of Kragujevac · Department of Chemistry

This work presents a simple method for partitioning the bond-additive and atoms-pair-additive distance-based topological indices of plane graphs into the sum of contributions of inner faces. The proposed method is applied to decompose several topological indices (Wiener, hyper-Wiener, Tratch-Stankevich-Zefirov, Balaban, and Szeged indices) into the...

The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow factor to account for dynamical correlation. Two variants exist: the VB-VMC (using variational Monte Carlo) and V...

The Baird‐aromaticity of BN/CC cyclooctatetraene isosteres (azaboracyclo‐octatetraenes) in their lowest triplet states (T1) has been explored through computations of various aromaticity indices that describe the different aspects of aromaticity (magnetic, electronic, energetic and geometric). While cyclooctatetraene (COT) is aromatic in its T1 stat...

Films based on carrageenan, alginate and poloxamer 407 have been formulated with the main aim to apply prepared formulations in wound healing process. The formulated films were loaded with diclofenac, an anti-inflammatory drug, as well as diclofenac and curcumin, as multipurpose drug, in order to enhance encapsulation and achieve controlled release...

The Baird-aromaticity of BN/CC cyclooctatetraene isosteres (azaboracyclooctatetraenes) in their lowest triplet states (T1) has been explored through computations of various aromaticity indices describing the different aspects of aromaticity (magnetic, electronic, energetic and geometric). While cyclooctatetraene (COT) is aromatic in its T1 state fo...

The VB-QMC method is presented in this chapter. It consists of using in quantum Monte Carlo (QMC) approaches with a wave function expressed as a usually short expansion of classical Valence-Bond (VB) structures supplemented by a Jastrow factor to account for dynamical correlation. Two variants exist: the VB-VMC (using variational Monte Carlo) and V...

Boron clusters are polyhedral boron-containing structures that have unique features and properties. The disk-like boron clusters are among the most fascinating boron cluster forms. These clusters have a molecular orbital (MO) distribution similar to the one derived from the simple particle-on-a-disk model. In this model, the MOs come in pairs excep...

The generalized Zhang-Zhang (GZ Z) polynomial was introduced recently aiming to increase the sensitivity of the well-known Zhang-Zhang polynomial onto π-electron cyclic conjugation of 10-membered rings. Here, the recursive formulas for the calculation of the GZ Z of the benzenoid systems are derived. Then, an algorithm for calculating the GZ Z of b...

A detailed study of the geometry, aromatic character, electronic and magnetic properties for a series of positively charged N‐doped PAHs was performed. Magnetic properties of the examined molecules were analyzed by means of the magnetically induced current density calculated using the diamagnetic‐zero version of the continuous transformation of ori...

It has been shown in previous studies that the Be2B6 complex exhibits a triplet ground state with double aromaticity. In this work, the stability, electronic structure, and aromaticity of the homologous series M2B6 (M = Mg, Ca, Sr and Ba) were examined and compared to those of Be2B6. At the CCSD(T)/def2-TZVP//B3LYP/def2-TZVP level of theory, the ta...

Doping of boron clusters with Be and its heavier alkaline‐earth congener, Mg usually leads to complexes of different geometry and electronic structure. In this work we showed that both neutral BeB 8 and MgB 8 exhibit a singlet ground state umbrella‐like form. In addition, the stability, electronic structure, and aromaticity of the target molecules...

This article analyzes the nature of the chemical bond in coinage metal halides using high-level ab initio Valence Bond (VB) theory. It is shown that these bonds display a large Charge-Shift Bonding character, which is traced back to the large Pauli pressure arising from the interaction between the bond pair with the filled semicore d shell of the m...

The famous aromaticity index NICS (Nucleus Independent Chemical Shift) was introduced 25 years ago. The authors use this anniversary for a short and incomplete personal retrospect.

For all possible catacondensed Kekuléan molecules having four, five, and six hexagons, the molecular vibrational energies were calculated within the harmonic approximation at the HF, B3LYP, and M06-2X levels of theory in combination with the 6-311G(d,p) basis set. The obtained vibrational energies were found to be a linear function of the Kekulé st...

Magnetically induced current densities, calculated at the M06-2X/def2-TZVP level using the diamagnetic-zero version of the continuous transformation of origin of current density (CTOCD-DZ) method, were employed to study the aromaticity in Li3B2− and Li4B2. It was found that the Li3/Li4 rings in Li3B2− and Li4B2 remarkably resemble the monocyclic Li...

Density functional calculations at three different levels of theory (B3LYP/LANL2DZp, B3LYP‐GD3/LANL2DZp, and ωB97XD/def2tzvp) were applied to different conformers of the Lehn‐type macrobicyclic polyether cryptate complex [K ⊂ [2.2.2]]+ to construct the enantiomerization pathway and to compute the energy barrier for the change in symmetry. Changes i...

The eigenvalues of the characteristic polynomial of a graph are sensitive to its symmetry-related characteristics. Within this study, we have examined three eigenvalue-based molecular descriptors. These topological molecular descriptors, among others, are gathering information on the symmetry of a molecular graph. Furthermore, they are being ordina...

Indices based on the nucleus independent chemical shift (NICS) are the most frequently used in analysis of magnetic aromaticity. The magnetically induced current density, on the other hand, is a key concept in defining magnetic aromaticity. The integrated current strength (current strength susceptibility) was found to be a very useful tool in aroma...

A multifaceted bond: High level Valence Bond calculations show that the NaBH3⁻ cluster is stabilized neither by a dative bond nor by a standard polar‐covalent bond, but rather by a unique combination of three distinct components that are accurately quantified. Abstract Bonding in the recently synthesized NaBH3⁻ cluster is investigated using the hi...

Bonding in the recently synthesized NaBH 3 – cluster is investigated using the high level Valence Bond BOVB method. Contrary to earlier conclusions, the Na–B bond is found to be neither a genuine dative bond, nor a standard polar‐covalent bond at equilibrium. It is rather revealed as a split and polarized weakly coupled electron‐pair, which allows...

There are many theoretical and experimental approaches which can be used to assess the extent of cyclic electron delocalization in polycyclic conjugated compounds. On the other hand, methodologies capable of measuring how electron delocalization in the given ring is influenced by the presence of some other ring within the same molecule have attract...

The double aromatic character of Be2B6 and Be2B7⁺ complexes in their triplet and singlet spin states was examined by means of their magnetically induced current densities, which were calculated at the B3LYP/def2-TZVP level of theory using the diamagnetic-zero variant of the continuous transformation of origin of current density (CTOCD-DZ) method. T...

The pattern of cyclic conjugation was thoroughly studied in the series of N- and P-acenaphthylene derivatives using several different aromaticity indices: the energy effect (ef), multicenter delocalization index (MCI), harmonic oscillator model of aromaticity (HOMA) index, and nucleus independent chemical shifts (NICS). The Kekulé-structure-based r...

In our recent paper the effects of molecular planarity on the local aromaticity in several series of increasingly planar fully benzenoid hydrocarbons were examined. It was found that the Clar formulas can provide correct information on the local aromaticity distribution even in non-planar fully benzenoid systems. In the present work, the influence...

Magnetically induced current densities were used to examine the aromatic character of two charged Be-B clusters, Be6B102- (1) and Be6B11- (2). The current densities were computed by means of the diamagnetic-zero variant of the continuous transformation of origin of current density (CTOCD-DZ) method. It has been shown in previous works that 1 and 2...

The extent of π-electron delocalization in the five-membered rings of 14 naphtho-annelated fluoranthenes has recently been assessed by means of several approaches, including application of the following indices: the energy effect (ef), bond resonance-energy (BRE), multi-center delocalization-energies (MCI), the index arising from the harmonic-oscil...

In this work, the nature of the bonding interaction between Au(III) ion and aromatic nitrogen-containing heterocycles (N-heterocycles) in a series of Au(III) complexes was studied by means of the natural bond orbital (NBO), atoms in molecule (AIM), charge decomposition analysis (CDA) and energy decomposition analysis (EDA) methods at the B3LYP/cc-p...

The McClelland formula, based on the upper bound \(\sqrt{2mn}\), is capable of reproducing over 99.5% of the total \(\pi \)-electron energy (\(E_\pi \)) of a conjugated hydrocarbon, whose molecules possess n carbon atoms and m carbon–carbon bonds. Its weak point is that it predicts equal \(E_\pi \)-values for all isomers. We now show how this failu...

Gold(III) complexes with 1,7- and 4,7-phenanthroline ligands, [AuCl3(1,7-phen-κN7)] (1) and [AuCl3(4,7-phen-κN4)] (2) were synthesized and structurally characterized by spectroscopic (NMR, IR and UV–vis) and single-crystal X-ray diffraction techniques. In these complexes, 1,7- and 4,7-phenanthrolines are monodentatedly coordinated to the Au(III) io...

The Clar aromatic sextet theory can provide the qualitative description on the dominant modes of cyclic π-electron conjugation in benzenoid molecules, and on the relative stability among a series of isomeric benzenoid systems. In a series of non-planar fully benzenoid hydrocarbons, the predictions of the Clar theory were tested by means of several...

In a recent paper (Radenkovic et al. Chem Phys Lett 625:69–72, 2015), a new method for quantifying the strain energy in benzenoid molecules, resulting from the repulsion between the bay H-atoms was elaborated. In this work, we present a modified procedure, capable of estimating the strain energy in a single-step calculation. Strain energies were ob...

The nature of the single bond in the three isoelectronic coinage metal dimers Cu2, Ag2 and Au2 is investigated by means of the ab initio Breathing Orbital Valence Bond (BOVB) method, which allows one to calculate the respective contributions of the covalent and ionic structures to the total wave function, as well as the resonance energy arising fro...

In 2004 Randić and Balaban employed Kekulé structures to assess the π-electron content (EC) of rings in benzenoid hydrocarbons. In this paper we showed how ab initio valence bond (VB) calculations based on the set of Kekulé structures of a given polycyclic conjugated molecule can be used to obtain more accurate π-electron contents of rings (VB-EC)...

The quantitative structure-activity relationship (QSAR) models for predicting antioxidative capacity of 21 structurally similar natural and synthetic phenolic antioxidants was considered. The one-, two- and three-descriptor QSAR models were developed. For this purpose the literature data on the vitamin C equivalent antioxidative capacity (VCEAC) va...

Dinuclear gold(III) complexes {[AuCl3]2(μ-4,4’-bipy)} (1) and {[AuCl3]2(μ-bpe)} (2) with bridging aromatic nitrogen-containing heterocyclic ligands, 4,4’-bipyridine (4,4’-bipy) and 1,2-bis(4-pyridyl)ethane (bpe), were synthesized and characterized by NMR (1H and 13C), UV-vis and IR spectroscopic techniques. The crystal structure of 1 was determined...

Various Kekulé–structure–based models, aimed at describing π-electron conjugation in polycyclic aromatic compounds are briefly described. Our main concern are benzenoid hydrocarbons, π-electron systems in which the Kekulé–structure–based approaches are expected to yield the best results. Although there are numerous examples in which reasonings base...

A relation is obtained between the total π-electron energy Eπ and the HOMO energy EHOMO, valid within the HMO approximation. This seems to be the very first relation between Eπ and EHOMO ever established. It enables a much more accurate assessment of Eπ of alternant conjugated hydrocarbons than that based on McClelland's formula and on other (n, m)...

Benzenoid molecules possessing bays, but no coves and fjords, are traditionally considered as "strain-free". Yet, repulsion between the two bay H-atoms affects the length of the near-lying carbon-carbon bonds as well as the corresponding bond angles. A method is developed to estimate the energy of this strain. In the case of chrysene and triphenyle...

New porous three-dimensional metal-organic frameworks are synthesized that contain infinite chains of Srn and Ban rectangles. Their structures are elucidated by means of spectroscopic techniques such as nuclear magnetic resonance and Fourier transform infrared, and the respective crystal structures are determined. The electronic structure of basic...

Porous 3D metal-organic frameworks containing infinite chains of Srn and Ban rectangles have been synthesized and their structures determined. The bonding and reactivity have been analyzed. On page 1501 (DOI:10.1002/qua.24970), Subhajit Mandal et al. have found from simulations that a neon atom can fit selectively into a pore inside the crystal str...

All Kekulé-structure-based theories predict that the central five-membered ring in fluoranthene and naphtho-annelated fluoranthenes is nonaromatic. In the present work, a detailed study of the local aromaticity in a series of naphtho-annelated fluoranthene derivatives was performed by means of the following aromaticity indices: the energy effect (e...

Benzenoid molecules possessing bays are traditionally considered as “strain–free”. Yet, repulsion between the two bay H-atoms affects the length of the near-lying carbon–carbon bonds. A method is developed to estimate the energy of this strain. In the case of phenanthrene its value was found to be about 7 kJ/mol.

The effect of benzo and benzocyclobutadieno annelation on the current density induced in a series of biphenylene derivatives is examined at the B3LYP/cc-pVDZ level of theory, by using the CTOCD-DZ method. Angular benzo annelation increases, whereas linear benzo annelation decreases the intensity of paratropic (antiaromatic) current density along th...

The effect of benzo-annelation on the local aromaticity of the central ring of acridine (1), 9H-carbazole (2), dibenzofuran (3) and dibenzothiophene (4) was analyzed by means of the energy effects (ef), pairwise energy effects (pef), multicentre delocalization index (MCI), electron density at ring critical points ( ), harmonic oscillator model of a...

According to the Pauling bond orders, the lengths of the rung carbon-carbon bonds along the central hexagonal chain in chevron-type benzenoid molecules are monotonically changed. The calculated bond lengths obtained at the B3LYP/6-311G(d,p) level of theory show that this regularity holds only for the first few members of the chevron homologous seri...

The relation between Pauling and Coulson bond orders in benzenoid hydrocarbons is examined. The carbon-carbon bonds of benzenoid hydrocarbons have to be classified into three classes, depending on the number of attached hydrogen atoms. Within each class the correlation between the bond orders is linear. The results can be used to rationalize the re...

A structure-descriptor EE, recently proposed by Estrada, is examined. If λ1, λ2,...,λn are the eigenvalues of the molecular graph, then EE = Σi=1n eλi. In the case of benzenoid hydrocarbons with n carbon atoms and m carbon-carbon bonds, EE is found to be accurately approximated by means of the formula a1 n cosh (√2m/n) + a2, where a 1 ≈ 1.098 and a...

Within series of isomeric benzenoid hydrocarbons there is a very good linear correlation between the topological resonance energy (T RE) and the total π-electron energy (E π). Furthermore, the slope of the T RE vs. E π regression line is almost independent of the benzenoid isomers considered, and (for all sets of isomers) is nearly equal to 0.5. Th...

A detailed electronic structure study of singlet and triplet states of a series of biradicaloid pleiadene-like molecules was performed using the DFT and complete active space methods. It was shown that the singlet–triplet gaps obtained with the B3LYP, B2PLYP, and CASSCF methods are not a monotone function of the number of annelated benzene rings. A...

The aromatic stabilization of closed-shell charged polybenzenoid hydrocarbons (PBHs) has been scrutinized by means of energetic and magnetic aromaticity criteria and by direct measures of electron delocalization. Thus, topological resonance energies and their circuit contributions, ring current maps and multicenter delocalization indices have been...

The Clar aromatic sextet theory predicts that the intensity of cyclic conjugation in chevron-type benzenoid hydrocarbons monotonically decreases along the central chain. This regularity has been tested by means of several independent theoretical methods (by the energy effects of the respective six-membered rings, as well as by their HOMA, NICS, and...

The homologous series of benzenoid hydrocarbons, whose first members are perylene (P 1), bisanthrene (P 2), and tetrabenzo[bc,ef,kl,no]coronene (P 3), are usually considered as consisting of to two polyacene fragments, joined by essentially single carbon–carbon bonds, forming “empty” rings, devoid of any cyclic conjugation. In higher members of thi...

Induced current densities, calculated at the coupled HF level of theory, using the CTOCD-DZ method, are studied in the homologous series of benzenoid hydrocarbons whose first members are perylene, bisanthrene, and tetrabenzo[bc,ef,kl,no]coronene. In the first three members of this series, current density is in good agreement with the predictions of...

A new polydentate fac-trioxo molybdenum complex, [MoO(3)L](3-) {LH(3) = nitrilotriacetic acid}, has been synthesized by the reaction of lithium molybdate with iminodiacetic acid. The trinegative complex anion coordinates the alkali metal cations, K(+), Rb(+) or Cs(+). The potassium, rubidium and cesium complexes, [Li{K(H(2)O)(2)}MoO(3)L](n) (1), [L...

In this paper, a detailed study of the local aromaticity in a series of cyclopenta-fused linear polyacenes (acenaphthylene derivatives) was performed using several different criteria of aromaticity. Namely, the energy effect (ef), bond resonance energy (BRE), harmonic oscillator model of aromaticity (HOMA) index, multi centre delocalization indices...

A detailed analysis of the local aromaticity in tetraoxa[8]circulene and its benzo-annelated derivates was performed by means of the energy effect (ef), multicenter delocalization indices (MCI), harmonic oscillator model of aromaticity (HOMA) index, nucleus independent chemical shifts (NICS), and ring current maps. According to the indices employed...

In this Letter a detailed electronic structure study of singlet and triplet states of a series of azulene-like molecules was performed using several DFT and complete active space (CAS) methods. According to the results obtained at the B3LYP level of theory using the unrestricted symmetry-broken method, the singlet–triplet splitting for the members...

A critical re-examination confirms that the atom-bond connectivity index (ABC) is well reproducing the heats of formation of alkanes (ΔH° f). Moreover, the simple empirical formula ΔH° f = - (a+b·ABC), with a = 65.98, b = 20.37, reproduces the heats of formation with an accuracy comparable to that of high-level ab initio and DFT (MP2, B3LYP) quantu...

The diradical character of zethrenes was investigated using a symmetry-broken UB3LYP/6-311G(d,p) method. The number of hexagons in the investigated molecules ranges from 6 to 12. It was found that all zethrenes are singlet diradicals, whose diradical character increases with the increasing size of the molecules. A singlet diradical structure provid...

An electronic structure study of singlet and triplet states of two series of polyacenequinododimethides was performed using the B3LYP method. It was found that the ground state of all examined polyacenequinododimethides is a singlet with significant diradical character. The diradical character of the compounds under investigation was estimated usin...

In the recent work by Khatua et al. (Khatua, S.; Roy, D. R.; Bultinck, P.; Bhattacharjee, M.; Chattaraj, P. K. Phys. Chem. Chem. Phys.2008, 10, 2461-2474) the synthesis and structure of a fac-trioxo molybdenum metalloligand and its sodium complex containing 1D hexagonal chains of sodium ions was reported. In the same paper, the aromaticity of hexag...

Several measures of aromaticity including energetic, magnetic, and electron density criteria are employed to show how aromatic stabilization can explain the stability sequence of hydroporphyrins, ranging from porphin to octahydroporphin, and their preferred hydrogenation paths. The methods employed involve topological resonance energies and their c...

If λ i , i = 1, 2,. .. , n, are the eigenvalues of the graph G, then the Estrada index EE of G is the sum of the terms e λi. This graph invariant appeared for the first time in year 2000, in a paper by Ernesto Estrada, dealing with the folding of protein molecules. Since then a remarkable variety of other chemical and non-chemical applications of E...

Cyclic conjugation in benzo-annelated triphenylenes was studied by means of the energy effect (ef) and the π-electron content (EC) of the six-membered rings. A regularity that was earlier discovered in the case of acenaphthylene and fluoranthene congeners is now shown to hold also for benzo-annelated triphenylenes: Benzenoid rings that are annelate...

The cyclic conjugation in benzo-annelated coronenes is studied by means of the energy effect (ef) and pi-electron content (EC) of the six-membered rings. Some peculiarities of the pi-electron structure of benzo-coronenes, inferred by the Clar aromatic sextet theory, could be tested and verified. A regularity that earlier was discovered in the case...

Local aromaticity in rings of conjugated hydrocarbons can be measured in a variety of ways. In the present paper, we concentrate on two of these, namely, EC, i.e., the pi-electron content or pi-electron partition, and ef, the energy effect of cycles. For the central ring in five bipartite conjugated hydrocarbons (anthracene, triphenylene, perylene,...

Abstract Previous analysis of cyclic conjugation in benzo-annelated perylenes has revealed that annelation of a benzene ring in the angular position increases the extent of cyclic conjugation in the central ring whereas annelation of a benzene ring in the linear position reduces it. We now present a general method for assessing the effect of a ring...

In a recent work, a method was developed for assessing the influence ief(G, Z0|Z1) of a ring Z1 on the energy effect of another ring Z0 in a polycyclic conjugated molecule G. Herein, a report is given of detailed numerical investigations of ief(G, Z0|Z1) aimed at the elucidation of the influence of various six-membered rings on the intensity of cyc...

DFT calculations have been used to corroborate two regularities resulting from the analysis of cyclic conjugation in benzo-annelated perylenes reported earlier, viz., (a) the annelation of a benzene ring in angular position increases the extent of cyclic conjugation in the central ring, and, (b) the annelation of a benzene ring in linear position d...

AbstractAccording to the recently discovered phenylcyclopentadienyl (PCP) rule, the intensity of cyclic conjugation in the five-membered ring of acenaphthylene and fluoranthene-type polycyclic conjugated hydrocarbons increases with the number of PCP fragments present in the molecule. We now tested this rule by DFT calculations at the B3LYP/6-31G(d)...

The formation of dicyclopenta[de,mn]anthracene (P1) and its isomerization into dicyclopenta[jk,mn]phenanthrene (P3) was investigated using density functional theory. It was shown that P1 is formed from 1,4-diethynilanthracene, but due to its instability, it undergoes further transformation. This transformation involves rearrangements of some hydrog...

Recent studies of the π-electron properties of acenaphthylene, fluoranthene, and their congeners showed that the presence of phenyl–cyclopentadienyl (PCP) fragments amplifies the intensity of cyclic conjugation in the five-membered ring of the respective molecules. We now show that there exists a reasonably good correlation between two quantum mech...

Fluoranthenes form a class of polycyclic conjugated molecules, structurally very similar to benzenoid systems. They consist of two benzenoid units joined through a five-membered ring. The basic features of the structure dependence of the total π-electron energy of fluoranthenes have been established. The focus of the studies is on the joinder energ...

Two mechanisms for the isomerization of cyclopenta[fg]aceanthrylene to acefluoranthene were revealed. The first pathway occurs via a cyclobutyl intermediate, whereas the second pathway involves a transition state that contains an sp 3-hybridized carbon atom. Both patterns show that the Stone-Wales rearrangement requires extremely high activation en...

The commonly accepted opinion that the thermodynamic stability of isomeric benzenoid hydrocarbons (assessed by their total π-electron energy and various resonance energies) increases with increasing number of Kekulé structures is shown to be violated in numerous cases. The smallest examples of such anomalous behavior are two hexacyclic pericondense...

Fluoranthenes form a class of polycyclic conjugated molecules, structurally very similar to benzenoid systems. They consist of two benzenoid units joined through a five-membered ring. The basic features of the structure dependence of the total 7C-electron energy of fluoranthenes have been established. The focus of the studies is on the joinder ener...