Let
denote a molecular graph of linear
phenylene. Then the Möbius phenylenes chain
is the graph obtained from the
by identifying the opposite lateral edges in reversed way, whereas the cylinder ...phenylene chain
is the graph obtained from the
by identifying the opposite lateral edges in ordered way. In this paper, by the decomposition theorem of Laplacian polynomial and the relationship between the roots and the coefficients of the characteristic polynomial, explicit closed-form formulae of the Kirchhoff index (resp. the number of spanning trees) of
and
are obtained.
The mono/bis ratio for the Suzuki–Miyaura cross coupling of
p-dibromobiphenyl and
p-dibromo(penta-
p-phenylenes) with arylboronic acids and esters has been studied. The coupling reaction is ...demonstrated to be highly selective for monoarylation when the substrate is a
p-dibromooligoarene, while selective biarylation is obtained for
p-diiodoterphenyl. The mono/bis coupling-ratio for these compounds was highly sensitive to the nature of the halogen involved, however steric hindrance or electronic characteristics of the boronic derivative did not affect the selectivity of the reaction. The reaction yields observed were higher at room temperature and when arylboronic pinacol esters were used. These reactions also offer a useful method for the preparation of asymmetrically substituted terphenyls and hexa-
p-phenylenes, giving good yields.
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There has been a growing emphasis on the synthesis of polycyclic conjugated compounds, driven by their distinct structural characteristics that make them valuable candidates for use in cutting-edge ...technologies. In particular, acenes, a subgroup of polycyclic aromatic compounds, are sought-after synthetic targets due to their remarkable optoelectronic properties which stem from their π-conjugation and planar structure. Despite all these promising characteristics, acenes exhibit significant stability problems when their conjugation enhances. Various approaches have been developed to address this stability concern. Among these strategies, one involves the incorporation of the biphenylene unit into acene frameworks, limiting the electron delocalization through the antiaromatic four-membered ring. This review gives a brief overview of the methods used in the synthesis of biphenylenes and summarizes the recent studies on biphenylene-containing polycyclic conjugated compounds, elucidating their synthesis, and distinct optoelectronic properties.
In this manuscript, the influence of the position of the alkoxy‐substituents on the polymerization of poly(phenylenes) is investigated. For this purpose, 3‐alkoxy‐m‐phenylene is polymerized using the ...Kumada catalyst transfer condensative polymerization. Three different catalyst systems are tried, which all resulted in polymer, but with a high dispersity. Additional experiments show that the polymerization proceeds via a noncontrolled chain growth mechanism.
Metasubstituted phenylene is polymerized using the Kumada catalyst transfer condensative polymerization. The influence of the substitution on the living character is investigated. The polymerization of metasubstituted phenylene suffers from transfer reactions and the mechanism of transfer is determined.
A diradical/biradical character of organic derivatives is one of the key aspects of contemporary research focusing on the fundamental studies followed by potential applicability relying on the unique ...optical, electronic, or magnetic properties assigned to unpaired electrons. A precise involvement of two p‐phenylenes into a cyclophane‐like conjugated, diatropic system creates a flexible molecule with the two different characters of both subunits (benzene and quinone) imprinting into the structure a Kekulé delocalized system. A dynamic of both carbocyclic subunits, and their mutual interaction generates a singlet open‐shell state (J=−1.25 kcal/mol) as documented spectroscopically (NMR and EPR). The extended theoretical analysis has proved a correlation between dihedral angle and the diradicaloid character that shifts from a closed‐shell singlet to an open‐shell state, eventually showing the y0=0.86 for 78 degrees and ΔEST=−0.34 kcal/mol.
Two p‐phenylene units with dissimilar resonance character (benzene and quinone) are embedded in a macrocyclic system. Their mutual orientation, in terms of the dihedral angle between the carbocyclic units, can stabilize the diradicaloid character of the system. Detailed spectroscopic and theoretical analysis confirmed a presence of open‐shell singlet state with a low ΔEST of −0.34 kcal/mol.
Hexagonal and quadrilateral structures are very common in the molecular structure of organic chemistry, especially in polycyclic aromatic compounds. Let L
n
be a generalized phenylene with t hexagons ...and t quadrangles, where
Zhu and Liu (2018) determined the normalized Laplacian spectrum and then gave the explicit formulas of the multiplicative degree-Kirchhoff index and the number of spanning trees of L
n
, respectively. In this article, we completely determine the Laplacian spectrum and Kirchhoff index of L
n
. Moreover, we show that the Kirchhoff index of L
n
is nearly one half of its Wiener index.
Singly and doubly 1,2‐phenylene‐inserted NiII porphyrin arch‐tape dimers 3 and 9 were synthesized from the corresponding β‐to‐β 1,2‐phenylene‐bridged NiII porphyrin dimers 5 and 11 via Ni0‐mediated ...reductive cyclization and DDQ/Sc(OTf)3‐promoted oxidative cyclization as key steps, respectively. Owing to the fused eight‐membered ring(s), 3 showed a more contorted structure than those of previously reported arch‐tape dimers 2 a and 2 b possessing a fused seven‐membered ring. Furthermore, 9 displayed much larger molecular contortion. As the molecular contortion increases, the Q band of the absorption spectrum becomes more red‐shifted and the electrochemcial HOMO–LUMO gap becomes smaller, reaching at 1294 nm and 0.77 eV in 9, respectively. The effect of molecular contortion on the electronic properties was studied by means of DFT calculations.
Arch‐shaped NiII porphyrin tapes with single and double 1,2‐phenylene insertions were prepared. These porphyrin arch‐tapes display highly contorted structures owing to the presence of the embedded eight‐membered ring(s). The more contorted doubly inserted dimer exhibits the lowest energy Q‐band at 1294 nm and a remarkably small electrochemical HOMO–LUMO gap of 0.77 eV.
Sterically highly crowded and twisted thienylene‐phenylenes are synthesized and structurally characterized. Single‐crystal X‐ray structure analyses and theoretical studies give evidence of ...through‐space delocalization of π‐electrons of peripheral (hetero)aromatic rings in toroidal and catenated topology.
Sterically highly crowded and twisted thienylene‐phenylenes are synthesized and structurally characterized. Single‐crystal X‐ray structure analyses and theoretical studies give evidence of through‐space delocalization of π‐electrons of peripheral (hetero)aromatic rings in toroidal and 4catenated topology (light blue rings).
Molecular topological indices are numerical descriptor of molecular structure obtained via molecular graph G. The forgotten topological index F(G) is a vertex degree based topological index and it ...can be expressed with
where d(u) denotes the degree of u. The forgotten co-index Co-F(G) is defined as the sum of squares of a graph's vertex degrees which is not adjacent. In this study, the F(G) and Co-F(G) index of HAC
5
C
7
, HAC
5
C
6
C
7
, linear n-phenylenes and cyclic phenylenes nanostructures are computed for possible works in the properties of molecules such as structure-property relationship. In addition, polynomials of the forgotten index and co-index are found for these nanostructures.
Let L
n
be the linear
phenylene. Then let
be the molecular graph obtained from L
n
by connecting each pair of non-adjacent vertices on each 4-cycle of L
n
by an edge. In this paper, according to the ...decomposition theorem of Laplacian polynomial, we study the Laplacian spectra of L
n
and
respectively. By applying the relationship between the roots and coefficients of the characteristic polynomial of L
n
(resp.
), explicit closed formulae of Kirchhoff index and the number of spanning trees of L
n
and
are, respectively, derived in terms of the corresponding Laplacian spectrum. Furthermore, it is surprising to find that the Kirchhoff index of L
n
is approximately to one half of its Wiener index, whereas the Kirchhoff index of
is approximately to
of its Wiener index.
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