On closed derivation formulas of the Nirmala indices from the M-polynomial of a graph

A new category of polymeric materials is dendrimers. These are monodisperse macromolecules with a high branching level. The physical and chemical characteristics of these materials are strongly influenced by their structure. Dendrimers are ideal for a wide variety of biological and industrial applications due to their distinctive behaviour. Very recently, in 2021, the Nirmala index, and the first and second inverse Nirmala indices are proposed and calculated their values for four standard dendrimers. In this present article, we propose closed derivation formulas for finding the above variations of Nirmala indices of a graph in terms of its M-polynomial. We also determine the M-polynomials and their geometrical natures for some families of dendrimers. Finally, we compute the Nirmala indices for each of the considered dendrimers using the M-polynomial approach based on the proposed closed derivation formulas and get the same numeric results as originally calculated.     

Comparative study of GQ and QG indices as potentially favorable molecular descriptors

In chemical graph theory, several degree-based topological indices are introduced and put forward in the development of quantitative structure-property relationships (QSPR)/quantitative structure-activity relationships (QSAR) studies. However, only a few of them are considered employable in the prediction of physical and chemical properties and biological activities of molecular compounds. Here, we focus our attention on some foremost characteristics of newly defined Geometric–Quadratic $$ and Quadratic–Geometric $$ indices such as prediction power, degeneracy and structure sensitivity. Based on these attributes, we discuss their comparison with other well-established degree-based topological indices with the help of statistical analysis and computational techniques on the data sets of octane, nonane and decane isomers. Some of the graphical approaches, statistical outcomes and computational tests exhibit the dominating nature of the $$ and $$ indices over other topological indices.     

On valency based topological properties of the starphene St[n,m,l] and fenestrene F[n,m]

In theoretical chemistry the quantitative parameters which are used to describe the atomic topology of graphs are termed as topological indices. Through these topological indices many physical and chemical characteristics such as melting point, entropy, energy generation and vaporisation enthalpy of chemical compounds can be predicted. The theory of graphs has a significant use in measuring the relationship of certain associated graphs with various topological indices. In this paper, we compute novel topological indices based on eV- and ve-degrees for starphene $\mathit{St}[n,m,l]$ and fenestrene $F[n,m]$. A Maple-based algorithm is proposed for the calculation of ve and eV-degree based topological indices from the graph adjacency matrix.     

Rationalizing some experimental facts on the complexation of 2-methyl naphthalenecarboxylate and hydroxypropyled cyclodextrins by molecular mechanics and molecular dynamics

Molecular mechanics (MM) and Molecular dynamics (MD) calculations were applied to study the complexation of 2-Methyl naphthalenecarboxylate (2MN) and 2-hydroxypropyl -α-, -β-, and γ-cyclodextrins (HPCDs) in the presence of water. Results showed that 1:1 complexes of 2MN with modified cyclodextrins are stable and that the non-bonded van der Waals interactions are mainly responsible for the complexation. Theoretical results are in good agreement with fluoresence results and they permit us to explain the signs and quantitative differences of ΔH ⁰ and ΔS ⁰ on the basis of the different cavity sizes and the movement of the guest inside the HPCD cavity. Results also reveal a more favorable complexation when 2MN approaches on its polar side.     

On the number of spanning trees and normalized Laplacian of linear octagonal-quadrilateral networks

The normalized Laplacian makes a great contribution on analyzing the structure properties of nonregular graphs. Let O_n be a linear octagonal-quadrilateral network. In this article, we first concern the normalized Laplacian spectrum of O_n based on the decomposition theorem for the corresponding matrices. Then we derive the closed-term formulas of the degree-Kirchhoff index and the number of spanning trees of linear octagonal-quadrilateral networks on the basis of the relations between the roots and coefficients, respectively.     

1H NMR spectroscopic study of the interaction between cyclodextrins and bicyclo[3.3.1]nonanes

The formation and structure of inclusion complexes of 2,6- and 2,9-substituted bicyclo[3.3.1]nonanes with- and-cyclodextrin (CD) has been investigated by high-resolution¹H NMR spectroscopy.- and-CD were found to form 1:1 inclusion complexes and the binding constants were estimated from titration studies. 2D ROESY experiments provided insight into the structure of the complexes.Presented in part at the 8th International Cyclodextrin Symposium, Budapest, March 30–April 2, 1996.     

Spectroscopic study and antioxidant properties of the inclusion complexes of rosmarinic acid with natural and derivative cyclodextrins

Measurement of total antioxidant activity/capacity of polyphenols in various solvent media necessitates the use of cyclodextrins to solubilize lipophilic antioxidants of poor aqueous solubility. The inclusion complexes of the slightly water soluble antioxidant, rosmarinic acid (RA), with α-cyclodextrin (α-CD), β-cyclodextrin (β-CD), 2-hydroxypropyl-β-cyclodextrin (HP-β-CD), 2-hydroxyethyl-β-cyclodextrin (HE-β-CD), and methyl-β-cyclodextrin (M-β-CD) were investigated for the first time. The effect of cyclodextrins (CDs) on the spectral features of RA was measured in aqueous medium using UV-vis and steady-state fluorescence techniques by varying the concentrations of CDs. The molar stoichiometry of RA-CD inclusion complexes was verified as 1:1, and the formation constants of the complexes were determined from Benesi-Hildebrand equation using fluorescence spectroscopic data. Among the CDs, maximum inclusion ability was measured in the case of M-β-CD followed by HP-β-CD, HE-β-CD, β-CD and α-CD. Solid inclusion complexes were prepared by freeze drying, and their functional groups were analyzed by IR spectroscopy. Antioxidant capacity of CD-complexed rosmarinic acid was measured to be higher than that of the lone hydroxycinnamic acid by the CUPric Reducing Antioxidant Capacity (CUPRAC) method. The mechanism of the TAC increase was interpreted as the stabilization of the 1-e oxidized o-catechol moiety of RA by enhanced intramolecular H-bonding in a hydrophobic environment provided by CDs, mostly by M-β-CD.     

Representations and descriptors unifying the study of molecular and bulk systems

Establishing a unified framework for describing the structures of molecular and periodic systems is a long-standing challenge in physics, chemistry, and material science. With the rise of machine learning methods in these fields, there is a growing need for such a method. This perspective aims to discuss the development and use of three promising approaches—topological, atom-density, and symmetry-based—for the prediction and rationalization of physical, chemical, and mechanical properties of atomistic systems across different scales and compositions.     

基于DFT和分子连接性指数方法研究醇类化合物的水溶解度和分配系数

将DFT方法计算得到的量化参数和分子连接性指数联合应用到60个醇类化合物的溶解度和辛醇/水分配系数的QSPR研究中,分别通过逐步回归得到具有显著统计意义的4个参数和5个参数的QSPR方程.以此4个参数和5个参数分别作为输入参数,采用BPNN,RBFNN方法建立了QSPR预测模型,使用Latin-partition交叉验证方法评价模型的预测能力.BPNN,RBFNN模型对溶解度预测的相关系数分别为0.993和0.994,而对辛醇/水分配系数预测的相关系数分别0.990和0.997,结果令人满意.     

Isomorphous substitution of Mn(II), Ni(II) and Zn(II) in AlPO-31 molecular sieves and study of their catalytic performance

Isomorphously substituted molecular sieves, MAPO-31, NAPO-31 and ZAPO-31, were prepared under mild hydrothermal conditions from gels containing sources of aluminium, phosphorus, appropriate metal and dipropylamine (DPA), presumably acting as a structure-directing template. They were characterized by XRD, FTIR, TGA, inductively coupled plasma (ICP), ESR, Brunauer, Emmett, Teller (BET) and diffusion reflectance spectroscopy (DRS) techniques. In the XRD, the peak at 2θ = 16.7° of the metal substituted AlPO-31 is more intense than that of pure AlPO-31 suggesting preferential occupation of the plane corresponding to it as compared to other planes. The O-H stretch in the IR spectra of the metal-substituted molecular sieves is blue-shifted with respect to the parent AlPO-31 molecular sieves possibly due to metal substitution. Theg values obtained from the ESR spectra of MAPO-31 and NAPO-31 also substantiate framework substitution. Ethylation of toluene was carried out between 300 and 450°C over the above catalysts as a model test reaction. The high toluene conversion over metal-substituted molecular sieves proves the isomorphic substitution of metal ions in the AlPO-31 framework.     

Multinuclear magnetic resonance study of the structure and tautomerism of azide and iminophosphorane derivatives of chloropyridazines

Some azido‐ and iminophosphorane derivatives of 3,6‐dichloro‐ and 3,4,5,6‐tetrachloropyridazine were synthesized and studied by means of NMR measurements. Based on multinuclear data (chemical shifts, coupling constants) for compounds containing the azide group, no potentially possible tetrazole–azide equilibrium can be observed, even under acidic conditions. An unusual substitution of a chlorine atom (in position 4) of tetrachloropyridazine in the reaction with hydrazine was demonstrated by NMR measurements of two newly synthesized compounds containing azido‐ and iminophosphorane groups. Using multinuclear magnetic resonance data, the sites of ethylation and protonation of azido‐ and iminophosphorane derivatives of chloropyridazines were established. In the case of the tetrazolopyridazines, ethylation occurs at the N1′ and N2′ atoms, whereas for monocyclic compounds it takes place at the N1 and/or N2 atoms of the pyridazine ring. Preferred sites of protonation are the N1′ atom of the tetrazole ring and the N1 atom of the pyridazine ring. Moreover, the structures of potassium salts of 6‐(3‐cyano‐1‐triazeno)tetrazolo[1,5‐b] pyridazine and its amido derivative were established using NMR data, especially ¹⁵N NMR chemical shifts. Copyright © 2002 John Wiley & Sons, Ltd.     

Inclusion complexation of diclofenac with natural and modified cyclodextrins explored through phase solubility, 1H-NMR and molecular modeling studies

Guest–host interactions were examined for neutral diclofenac (Diclo) and Diclofenac sodium (Diclo sodium) with each of the cyclodextrin (CD) derivatives: α-CD, β-CD, γ-CD and 2-hydroxypropyl-β-cyclodextrin (HP-β-CD), all in 0.05 M aqueous phosphate buffer solution adjusted to 0.2 M ionic strength with NaCl at 20 °C, and with β-CD at different pHs and temperatures. The pH solubility profiles were measured to obtain the acid–base ionization constants (pK _as) for Diclo in the presence and absence of β-CD. Phase solubility diagrams (PSDs) were also measured and analyzed through rigorous procedures to obtain estimates of the complex formation constants for Diclo/CD and Diclo sodium/CD complexation in aqueous solutions. The results indicate that both Diclo and Diclo sodium form soluble 1:1 complexes with α-, β-, and HP-β-CD. In contrast, Diclo forms soluble 1:1 Diclo/γ-CD complexes, while Diclo sodium forms 1:1 and 2:1 Diclo/γ-CD, but the 1:1 complex saturates at 5.8 mM γ-CD with a solubility product constant (pK _sp = 5.5). Therefore, though overall complex stabilities were found to follow the decreasing order: γ-CD > HP-β-CD > β-CD > α-CD, some complex precipitation problems may be faced with aqueous formulations of Diclo sodium with γ-CD, where the overall concentration of the latter exceeds 5.8 mM γ-CD. Both ¹H-NMR spectroscopic and molecular mechanical modeling (MM⁺) studies of Diclo/β-CD indicate the possible formation of soluble isomeric 1:1 complexes in water.     

The study of the relationship between the new topological index A(m) and the gas chromatographic retention indices of hydrocarbons by artificial neural networks

The newly developed topological indices A_m1-A_m3 and the molecular connectivity indices ^mX were applied to multivariate analysis in structure-property correlation studies. The topological indices calculated from the chemical structures of some hydrocarbons were used to represent the molecular structures. The prediction of the retention indices of the hydrocarbons on three different kinds of stationary phase in gas chromatography can be achieved applying artificial neural networks and multiple linear regression models. The results from the artificial neural networks approach were compared with those of multiple linear regression models. It is shown that the predictive ability of artificial neural networks is superior to that of multiple linear regression method under the experimental conditions in this paper. Both the topological indices ²X and A_m1 can improve the predicted results of the retention indices of the hydrocarbons on the stationary phase studied.     

Inclusion complex formation of anthracycline antibiotics with cyclodextrins; a proton nuclear magnetic resonance and molecular modelling study

The inclusion complexation of the anthracyline antibiotics doxorubicin and daunorubicin with cyclodextrins has been studied by proton NMR and molecular modelling. The anthracyclines were found to complex with -cyclodextriny-cyclodextrin, whereby the aglyconic part of the molecule is included in the cyclodextrin cavity. Job ratio plots based on NMR data indicate that the complex has a stoichiometry of 1 : 1. Complex constant values of 345 M^–1 and 323 M^–1 (at pH 3) were found for doxorubicin and daunorubicin, respectively.     

Comparative analysis of nucleotide translocation through protein nanopores using steered molecular dynamics and an adaptive biasing force

The translocation of nucleotide molecules across biological and synthetic nanopores has attracted attention as a next generation technique for sequencing DNA. Computer simulations have the ability to provide atomistic‐level insight into important states and processes, delivering a means to develop a fundamental understanding of the translocation event, for example, by extracting the free energy of the process. Even with current supercomputing facilities, the simulation of many‐atom systems in fine detail is limited to shorter timescales than the real events they attempt to recreate. This imposes the need for enhanced simulation techniques that expand the scope of investigation in a given timeframe. There are numerous free energy calculation and translocation methodologies available, and it is by no means clear which method is best applied to a particular problem. This article explores the use of two popular free energy calculation methodologies in a nucleotide‐nanopore translocation system, using the α‐hemolysin nanopore. The first uses constant velocity‐steered molecular dynamics (cv‐SMD) in conjunction with Jarzynski's equality. The second applies an adaptive biasing force (ABF), which has not previously been applied to the nucleotide‐nanpore system. The purpose of this study is to provide a comprehensive comparison of these methodologies, allowing for a detailed comparative assessment of the scientific merits, the computational cost, and the statistical quality of the data obtained from each technique. We find that the ABF method produces results that are closer to experimental measurements than those from cv‐SMD, whereas the net errors are smaller for the same computational cost. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.