Bholanath Mandal
@buruniv.ac.in
Professor of Chemistry, Department of Chemistry
The University of Burdwan
EDUCATION
M. Sc., PhD
RESEARCH, TEACHING, or OTHER INTERESTS
Chemistry, Physical and Theoretical Chemistry, Materials Chemistry, Mathematical Physics
Scopus Publications
Scholar Citations
Scholar h-index
Scholar i10-index
Scopus Publications
Soukat Ghosh, Uday Maji, Swapnadeep Mondal, and Bholanath Mandal
Walter de Gruyter GmbH
Abstract Atom-bond-connectivity (ABC) indices are obtained in analytical forms for graphene sheets, zigzag single walled carbon nanotubes (SWCNTs), and single walled carbon nanotori in terms of number of rings (r) that measures the length and the number of hexagons in between two rings (h) that dictates the width of the concerned systems. The procedures followed for ABC index have been used to obtain the expressions of augmented Zagreb and Randić indices for such systems. Logarithm of ABC indices of zigzag SWCNTs are found to correlate linearly well with the bond dissociation energies per C–C bond and the Young’s moduli of said SWCNTs with fixed number of rings (r) but varying number of hexagons (h) in between two successive rings. The plot of logarithm of ABC index versus Young’s modulus of such SWCNTs in varying both r and h simultaneously is not a straight line but fits well with the sigmoidal (Boltzmann) curve. Wiener index, one of the important distance based index, has recently been found to have similar correlations with the concerned properties of such systems. Similar plots would appear for the said properties of the zigzag SWCNTs with other degree-based indices like augmented Zagreb and Randić indices, as have been indicated from their respective expressions obtained.
Madhusree Nag and Bholanath Mandal
Informa UK Limited
Tapanendu Ghosh and Bholanath Mandal
Elsevier BV
Bholanath Mandal and Douglas J. Klein
Springer Science and Business Media LLC
Sukanya Mondal and Bholanath Mandal
Elsevier BV
Sukanya Mondal and Bholanath Mandal
Wiley
Douglas J. Klein and Bholanath Mandal
Croatian Chemical Society
: Structural possibilities are considered for what arguably is the most general class of connected “pure-polyhex” π -networks (of carbon atoms). These are viewed as hexagonal-network coverings ( i.e. , a tiling by hexagons) of a connected locally Euclidean surface S possibly with holes which can be simple cycles of sizes other than 6 . The surface S can curve around to connect to itself in different ways, e.g ., with handles of different sorts. This then includes ordinary benzenoids, coronoids, carbon nanotubes, bucky-tori, carbon nano-cones, carbon nano-belts, certain fullerenes & fulleroids, various benzenoid polymers, a great diversity of defected (disclinational or dislocational) graphene flakes, and many other novel pure- polyhexes. A topological classification is made, and several combinatorial conditions on chemical sub -structure counts are identified. These counts include that of “combinatorial curvature”, such as is related to curvature stresses, as also relate to the Gaussian curvatures of the embedding surface.
Swapnadeep Mondal and Bholanath Mandal
Informa UK Limited
ABSTRACT Algorithm for obtaining characteristic polynomial (CP) coefficients of an alternant edge-weighted cycle is used to arrive at the algorithm for that of the cycloparaphenylene (CPP) graphs in matrix product form. The algorithm gives a recursive relation in expressing the sum of the CP coefficients of a CPP in terms of that of its two immediately preceding analogues which ultimately ends up with the use of transfer matrix in an analytical form. The sum of CP coefficients, being combinatorial in nature, is found to be used as a topological index showing much similarity with Hosoya index (sum all matching polynomial coefficients), cardinality and number of Kekulé valence structures of CPP graphs compared to the Wiener index which is the distance sum of all pairs of vertices in the graph. The sum of CP coefficients has been found to model the physical properties like strain energy and diameter of CPPs that are verified by the respective excellent correlations. GRAPHICAL ABSTRACT
Tapanendu Ghosh, Swapnadeep Mondal, Sukanya Mondal, and Bholanath Mandal
Walter de Gruyter GmbH
Abstract Hückel molecular orbital (HMO) quantities, viz., electron densities, charge densities, bond orders, free valences, total π-electron energies and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO–LUMO) or band gaps of {X,Y}-cyclacene graphs under next-nearest-neighbour (nnn) approximations are expressed in analytical forms within a certain range of nnn approximation parameter (m). The critical values of m for {X,Y}-cyclacenes with varying X (=C, N, B) and Y (=C, N, B) are calculated. For {X,X}-cyclacenes with a π-electron on each atom, all HMO quantities except total π-electron energies for a given value of m are found to be independent of X. The cyclic dimer (CD) is constructed in obtaining the eigenvalues corresponding to the singular points of the density of states (DOS) of such {X,Y}-cyclacene. Although the HOMO–LUMO gap of the CD differs from that of the cyclacene with a large number of repeating units (i.e. n ⟶ ∞) but becomes the same for m = 0. The analytical expressions can be used for facile computer programming in obtaining the HMO quantities. Such nnn interaction approximations actually release, to some extent, the strain that results in due to the geometrical structures of such cyclacenes, which is evident from the plots of strain energy per segment vs. contribution of such interactions on the total π-electron energy, where the slopes decrease with an increase in m. The vertical absorption energy difference for singlet-triplet states bears excellent linear correlation with the HOMO–LUMO gaps for a certain m value (m = 0.3) in the case of an even n, but for an odd n, such energy difference remains invariant.
Somnath Karmakar and Bholanath Mandal
Informa UK Limited
ABSTRACT Eigensolutions of {X( = C,B,N),Y( = C,B,N)}-cyclacene graphs with next nearest neighbor (nnn) interactions have been obtained in analytical forms by adapting n-fold rotational symmetry followed by two-fold rotational symmetry (or a plane of symmetry). Expressions of eigensolution indicate the subspectral relationship among such cyclacenes with an even number of hexagonal rings e.g., eigenvalues of {X,Y}-di-cyclacene are found in the eigenspectra of all such even cyclacenes. Total π-electron energies and highest occupied molecular orbital and lowest unoccupied molecular orbital (HOMO–LUMO) gaps are calculated using the analytical expressions obtained and are found to vary negligibly with the variation of nnn interactions in such cyclacenes. Total π-electron energy is found to increase due to increase in restriction intensity of nnn interactions, whereas the HOMO–LUMO gap of polyacenecs having the even number of hexagonal rings and with one electron at each site (atom) decreases with increase in the restriction intensity since such systems contain degenerate half-filled HOMO (bonding or nonbonding) that are much more vulnerable for perturbations imposed through nnn interactions.
Tapanendu Ghosh, Sukanya Mondal, Swapnadeep Mondal, and Bholanath Mandal
Elsevier BV
Sukanya Mondal and Bholanath Mandal
Walter de Gruyter GmbH
AbstractThe effects of sodium dodecyl sulfate (SDS), cetyltrimethylammonium bromide (CTAB) and Brij 35 on the oscillations of the cerium-catalyzed Belousov-Zhabotinsky (B-Z) reaction with ninhydrin as the organic substrate at 30 °C were described by following the change in absorbance of the reaction mixtures at 357 nm. The behavior of the oscillatory parameters was determined: (i) the induction period (IP) increases first and then decreases with increasing the concentration of all used surfactants (ii) the number of oscillations decreases with the SDS concentration, while for Brij 35 and CTAB it remains nearly constant, and (iii) the mean amplitude of the oscillations decreases with increasing concentration of CTAB and SDS, while it varies irregularly with that of Brij 35. The ability of micelles to selectively shield ions and molecules may explain their effect on the oscillation parameters of the studied B-Z system.
Tapanendu Ghosh, Sukanya Mondal, and Bholanath Mandal
Informa UK Limited
ABSTRACT A general approach to determine the matching polynomial (MP) of a graph with two parts connected by an edge is presented in matrix product that is ultimately used in deducing recursion formulas for obtaining the MP coefficients of linear and cylindrical poly(p-phenylene) (PPP) graphs. The Hosoya indices of linear and cylindrical PPPs are derived in terms of that of the two immediately preceding graphs as well as in analytical forms with the use of transfer matrices. Ambient condition density and bulk modulus of linear PPPs with 2–6 phenyl rings have been found to correlate well with the logarithm of their Hosoya indices. Excellent correlations of diameters with the logarithm of Hosoya indices and strain energies with the inverse of the logarithm of Hosoya indices for cylindrical PPPr with r (= 6–16, 18, 20) phenyl rings are obtained. The linear relation between the logarithm of Hosoya indices and diameter and the inverse relation between diameter and strain energy corroborate the fact.
Sukanya Mondal and Bholanath Mandal
The Chemical Society of Japan
First order or pseudo-first order reactions involving reversible linear chain and cyclic reaction networks are considered here for obtaining the respective characteristic polynomials (CPs) in analytical forms as well as the recursion relations among the CP coefficients. The zeros of the CP concerned are the decay constants that are useful in expressing the concentrations of the chemical species involved in the chemical reaction network at any instant of time. Illustrations are given for obtaining the CP coefficients of a few such graphs and some consequences thereof are presented. Facile computer programming can be made with these recursion relations for generating such polynomials.
Dong Ye, Yujun Yang, Bholanath Mandal, and Douglas J. Klein
Elsevier BV
Tapanendu Ghosh, Sukanya Mondal, Somnath Karmakar, and Bholanath Mandal
Informa UK Limited
ABSTRACT Three classes of reciprocal graphs, viz. monocycle (GCn), linear chain (GLn) and star (GKn) with reciprocal pairs of eigenvalues (λ, 1/λ), are well known. Reciprocal graphs of monocycle (GCn) and linear chain (GLn) are obtained by putting a pendant vertex to each vertex of simple monocycle (Cn) and simple linear chain (Ln), respectively. A star graph of such kind is obtained by attaching a pendant vertex to the central vertex and to each of the (n − 1) peripheral vertices of the star graph (K1, (n−1)). An n-fold rotational axis of symmetry for GCn and (n − 1)-fold rotational axis of symmetry for GKn have been exploited for obtaining their respective condensed graphs. The condensed graph for GLn has been generated from that of GCn incorporating proper boundary conditions. Condensed graphs are lower dimensional graphs and are capable of keeping all eigeninformation in condensed form. Thus the eigensolutions (i.e. the eigenvalues and the eigenvectors) in analytical forms for such graphs are obtained by solving 2 × 2 or 4 × 4 determinants that in turn result in the charge densities and bond orders of the corresponding molecules in analytical forms. Some mathematical properties of the eigenvalues of such graphs have also been explored.
Somnath Karmakar, Sukanya Mondal, and Bholanath Mandal
Informa UK Limited
A graph of {X, Y}-cyclopolyacene with n of hexagonal rings has been presented that contains four orbits, of which orbits 1 and 4 are occupied by the X-type of vertex and orbits 2 and 4 are occupied by the Y-type, or vice versa. Eigensolutions for such a graph have been derived in analytical form through the use of rotational symmetry followed by a plane of symmetry. Varying X ( = C, N, B, …) and Y ( = C, N, B, …) several types of cyclopolyacene graph may be obtained. Eigenvalue-expressions for such systems containing C, N and B have been shown in analytical form and their total π-electron energies with 2–6 hexagonal rings have been calculated with the help of the expressions developed.
Piyali Ghosh, Somnath Karmakar, and Bholanath Mandal
Informa UK Limited
Recurrence relation for the cardinalities of linear and cylindrical poly(p-phenylene) (PPP) compounds has been developed that requires the cardinalities of two of their immediate lower homologues. Such recurrence relation reduces into analytical expressions for the cardinalities under transfer matrix formalism. Ambient condition density and bulk modulus of linear PPPs are found to bear excellent linear correlation with the inverse of logarithm of their cardinalities. Topological bond orders obtained from the cardinalities of such PPPs have been found to have good linear correlations with the respective Hückel bond orders.
Piyali Ghosh, Douglas J. Klein, and Bholanath Mandal
Informa UK Limited
Analytical eigenspectra for the graphs of linear chains and cycles with alternant edge weights has been derived with the use of two independent methods, namely, the characteristic polynomial and the graph squaring. In the former method the rotational symmetry and the trigonometric identity have been exploited. These methods along with the expressions of eigenspectra so obtained have been found to be very useful in expressing analytical eigensolutions of some important as well as novel benzenoids, for example, linear p-methylene poly(p-phenylene), cylindrical poly(p-phenylene), zigzag edge graphene, carbon nanotube and carbon nanotori. Some of these eigensolutions have been analysed in exploring some consequences thereof.
Somnath Karmakar and Bholanath Mandal
American Chemical Society (ACS)
Graph theoretical solutions for kinetic rate equations of some reaction networks involving linear chains and cycles have been derived; condensation polymerization and long chain of radioactive decay come under the purview of the former whereas the interconversion of the species in cycles under the later. The reactions for the linear chains considered here proceed monotonically to the steady states with time whereas the cycle with all irreversible steps has been found to have either periodic or monotonic time evaluation of concentrations depending on the values of rate constants of the involved paths. In case of a cyclic reaction having all reversible paths, the condition for the microscopic reversibility has been derived on the basis of the assumption that the decay constants obtained for this case are all real.
Piyali Ghosh and Bholanath Mandal
Informa UK Limited
Formulas for the characteristic polynomial (CP) coefficients of three classes of (n + p)-vertex graphs, i.e. linear chains, cycles and stars where p pendant vertices are attached to n base vertices in one-to-one correspondence (p = 0, 1, 2, …, n), have been developed. Such pendant graphs become reciprocal graphs for linear chains and cycles if p = n. The n-vertex star graphs follow the same rule as paths and cycles, they become reciprocal on adding a pendant vertex to each of n vertices. The formulas so developed have been expressed in matrix product and in analytical forms for the three classes of graphs that require only the values of n and p for calculation of the respective CP coefficients. Such formulas have the general applicability for a large variety of molecular graphs with varying n and p and have been shown to be reduced to the corresponding formulas for reciprocal graphs that are the special cases of the graphs discussed here.
Somnath Karmakar and Bholanath Mandal
American Chemical Society (ACS)
A graph theoretical procedure for solving multistep coupled kinetic rate equations and thereby obtaining the concentrations of the species involved in the reaction has been developed. The method so developed has been illustrated with some well-known reaction schemes.
Piyali Ghosh, Somnath Karmakar, and Bholanath Mandal
Elsevier BV