DOCSLIB.ORG

Applications of Topological Indices to Structure-Activity Relationship Modelling and Selection of Mineral Collectors

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Indianloumal of Chemistry Vol. 42A, June 2003, pp. 1330-1 346 Applications of topological indices to structure-activity relationship modelling and selection of mineral collectors Ramanathan Natarajan*, Palanichamy Kamalakanan & Inderjit Nirdosh Department of Chemical Engineering, Lakehead University, Thunder Bay, Ontario, Canada P7B 5EI Received 8 January 2003 Topological indices (TI) are extensively used as molecular descriptors in building Quantitative Structure-Activity Relationships (QSAR), Quantitative Structure-Property Relationships (QSPR) and Quantitative Structure-Toxicity Relationships (QSTR). We have appli ed the QSAR approach for the first time to froth flotation and :nodelled the separation efficiencies (Es) of four seri es of coll ectors namely, cupferrons, o-aminothiophenols, mercaptobenzothiozoles and ary lhydroxamic acids used for the beneficiation of uranium, lead, zinc and copper ores, respectively. Principal components extracted from topological indices are found to form linear regression equations th at can predict the separati on efficiencies of the first three classes of coll ectors. Inclusion of substituent constant or quantum mechanical parameters did not improve th e fit and th is may be due to the absence of large variation in electronic effects among the molecules in each class. A quadratic fit has been obtained instead of linear regression in the case of arylhydroxamic acids. The separation efficiencies -of the members have been predicted within experimental error (±5%) by the best regression equations in each series. From the statistical models built, it may be generalized that Es = f(TI). To extend the applications of TI in the field of mineral processing, a similarity space of 587 arylhydroxamic acids has been constructed usi ng principal components extracted from Tis. Ten compounds have been selected for synthesis and testing. The approach appears to provide an efficient scientific tool for the selection of collectors from a vi rtual database and may lead to an inexpensive and quick method for the identification of new collectors. Introduction (QSTR). These models are used in predicting toxicity of chemicals. Well established QSTR models can be QSAR modelling 1o Quantitative Structure-Activity Relationship used to predice· the toxicity of not only the known (QSAR) and Quantitative Structure-Property but also the hypothetical compounds. Relationship (QSPR) studies are mathematical QSARs/QSPRs/QSTRs have become powerful tools in contemporary chemical and medicinal research, as quantification, which are extensively used 111 pharmaceutical and agricultural chemistry for they have made it possible to predict the biological screening compounds to be tested for specific activity, specific chemical activity, toxicity and the 3 environmental fate of a chemical even before its activit/- . Regression models have been developed to correlate an experimentally determined property or synthesis. 4 5 biological activity to the molecular structure • . The descriptors used in QSAR models are empirical, Topological indices as molecular descriptors theoretical, physicochemical properties6 and quantum To develop QSAR models with good predictive mechanically calculated parameters.7 Once a ability appropriate molecular descriptors have to be correlation between structure and biological activity chosen. A molecular descriptor aims at mathematical or a physicochemical property is established, it is characterization of a molecular structure or a specific characteristic of the structure as completely as possible to predict the activity/property of any number of structurally related compounds including those that possible. Molecular Connectivity Indices (MCI) are 2 8 9 the most widely used molecular descriptors. These are yet to be synthesized and tested • • . molecular meters, MCI, are known as graph invariants The regression models where toxicity of a chemical due to their formulations from the concepts of graph replaces the biological activity are sometimes referred theory and are more commonly referred to as to as Quantitative Structure-Toxicity Relations Topological Indices (TI) as they describe the topology of a molecule. The term topological indices (TIs) is *Perrnanent address: Campion Higher Secondary School, Tiruchirappalli, Tamil Nadu, India 620 001. used hereafter to refer to MCls in this article. The 8 10 email: [email protected] large number of models developed • with TIs prove NAT ARAJAN e/ al.: APPLICATIONS OF TOPOLOGICAL INDICES 1331 that several properties can be expressed as a function CheLating agents as mineraL collectors of topological indices. TIs are fundamental in nature Chelating agents attach themselves to a mineral and easily computable using simple mathematical surface by chelate formation. The chelating tendency tools owing to their conceptual simplicity. There is a of the compounds is higher for transition metals large number of TIs in use from simple connectivity which are rendered hydrophobic in preference to indices to 3D descriptors to orthogonal descriptors. A alkali and alkaline earth metals. The valuable recent review by Pogliani II explains the trend in the minerals are normally compounds of transition and graph theoretic descriptors. inner transition metals while the gangue and clay minerals are that of silica, calcium and aluminum. This makes chelating agents to perform better than Background on froth flotation conventional collectors and has therefore attracted 12·22 Mineral processing industry is facing a tougher attention as mineral collectors in flotation research. situation due to the exhaustion of high-grade ores and Table 1 lists the types of chelating agents tested to a steady decrease in the grade of existing low-grade float different types of minerals. Chelating collectors ores. Flotation is widely used to recover minerals suffer from two main defects: (i) absence of long from low-grade ores. The low selectivity of mineral­ hydrocarbon chain in their molecules and (ii) collectors currently in use and their limitations in prohibitively high cost effectively floating non-sulphidic minerals, increase Marabini and coworkers23 and Nirdosh and the complexity of the situation. This research focuses coworkers24 had demonstrated that the first defect on using concepts of QSAR approach in developing could be overcome by new synthesis methodologies. mineral collectors that are more selective for their Once it is established that a particular chelating agent application in froth flotation. enjoys good selectivity and has promise to be used, its Pre-concentration is an inevitable step in the production in bulk would be potentially economic. economic recovery of a metal from a low-grade ore. Froth flotation is the most widely used process in this SeLection of cheLating agents beneficiation step. Though it was initially developed The molecule of a chelating collector has two parts to concentrate sulphides of base metals, it has now viz., the chelating group (hydrophilic part) and the been expanded to float oxides and oxidized minerals hydrocarbon backbone (hydrophobic part). Though and non-metallic minerals such as phosphates, the chelating group can be decided from literature and fluorites and fine coal. Organic compounds called experiments done in solvent extraction (liquid-liquid collectors are added to a slurry of a finely ground ore extraction) of metals from process and waste to impart hydrophobicity to the minerals. When air is solutions, and also from solution chemistry of metal passed through such a slurry, the hydrophobic mineral ions and their interaction with various chelating particles adhere to the air bubbles. The mineralized air agents, one has to bear in mind that the metal ion bubbles rise to the surface of the slurry. To prevent under consideration in a mineral being floated is not the mineral falling back into the slurry, a frother is present as a completely free metal ion. Rather, it is added to the dispersion. The hydrophobized mineral present on the surface of the mineral as a unionized collects in the froth as the concentrate and is entity with only some of its valencies liberated during periodically removed. In addition to collectors and . grinding. Therefore, a chelating agent, which is a frothers, other auxiliary chemicals are also added to selective extractant for afree metal ion, may not be a modify the pH or the surface properties of the mineral selective collector for the mineral of the same metal. to effect the selective separation. For example thenoyltrifluoroacetone, a good Among the various types of chemicals used, the extractant for uranium ion, was not found to function collectors play the most significant role and the as a good collector for uranium minerals?5 It is true efficiency of mineral separation and recovery depends also for tributylphosphate (TBP).25 Marabini26, 27 had on the selectivity of the collector. Petroleum laid down a guideline to choose the chelating group sulphonates and carboxylates were used as collectors based on conditional constants. Conditional constants in the early days of flotation. These collectors lack in are nothing but modified form of thermodynamic selectivity because they act by physisorption. The stability constants where concentrations of limited selectivity shown in remote cases is obtained hydroxylated metal ion and protonated-ligand are only by varying pH because the point of zero charge used instead of the concentrations of free metal ion (pzq varies from mineral to mineral. and ligand: 1332 INDIAN J CHEM,
Recommended publications
  • Intuitive Chemical Topology Concepts. / In

    Intuitive Chemical Topology Concepts. / In

    1 Intuitive Chemical Topology Concepts Eugene V. Babaev Moscow State University, Moscow 119899, RUSSIA 1. Introduction During last two decades, chemistry underwent a strong influence from nonroutine mathematical methods. Chemical applications of graph theory [1–10], topology [11–18], and related fields of fundamental mathematics [21–27] are growing rapidly. This trend may indicate the birth of a novel interdisciplinary field, mathematical chemistry, imperceptibly flourishing on the border of chemistry and pure mathematics. The term “chemical topology” (the title of this volume) has become frequent in papers, books, and scientific conferences. Similarly, the term molecular topology (differing in its sense from molecular geometry) has become frequently used, although there may exist diverse viewpoints on the meaning of this concept. The key difference between topology and geometry is that in geometry the concepts of distances and angles are important, whereas in topology they are not. Instead, the essential topological properties are connectedness and continuity. Chemical structural formulas are good examples of topological models of molecules: the pattern of connectivity between atoms is essential, whereas the interatomic distances and angles are less important and may be neglected. A colloquial definition of topology is “rubber” geometry. Indeed, one may consider a topological object made of an ideal elastic material, so that any deformation (like stretching or distortion) retains points of this elastic object “close enough” one to another. In contrast, cutting separates previously close points, and any joining of parts makes points “closer” one to another. Such a continuous transformation of an object without cutting and joining any parts is called homeomorphism. (The term should not be confused with homomorphism.) The study of properties that are invariant to homeomorphic transformations is the fundamental goal of topology.
  • From Chemical Topology to Molecular Machines Nobel Lecture, December 8, 2016 by Jean-Pierre Sauvage University of Strasbourg, Strasbourg, France

    From Chemical Topology to Molecular Machines Nobel Lecture, December 8, 2016 by Jean-Pierre Sauvage University of Strasbourg, Strasbourg, France

    From Chemical Topology to Molecular Machines Nobel Lecture, December 8, 2016 by Jean-Pierre Sauvage University of Strasbourg, Strasbourg, France. o a large extent, the eld of “molecular machines” started aer several groups T were able to prepare reasonably easily interlocking ring compounds (named catenanes for compounds consisting of interlocking rings and rotaxanes for rings threaded by molecular laments or axes). Important families of molecular machines not belonging to the interlocking world were also designed, prepared and studied but, for most of them, their elaboration was more recent than that of catenanes or rotaxanes. Since the creation of interlocking ring molecules is so important in relation to the molecular machinery area, we will start with this aspect of our work. e second part will naturally be devoted to the dynamic properties of such systems and to the compounds for which motions can be directed in a controlled manner from the outside, i.e., molecular machines. We will restrict our discussion to a very limited number of examples which we con- sider particularly representative of the eld. CHEMICAL TOPOLOGY Generally speaking, chemical topology refers to molecules whose graph (i.e., their representation based on atoms and bonds) is non-planar [1–2]. A planar graph cannot be represented in a plane or on a sheet of paper without crossing points. In topology, the object can be distorted as much as one likes but its topo- logical properties are not modied as long as no cleavage occurs [3]. In other 111 112 The Nobel Prizes words, a circle and an ellipse are topologically identical.
  • Chem3d 17.0 User Guide Chem3d 17.0

    Chem3d 17.0 User Guide Chem3d 17.0

    Chem3D 17.0 User Guide Chem3D 17.0 Table of Contents Recent Additions viii Chapter 1: About Chem3D 1 Additional computational engines 1 Serial numbers and technical support 3 About Chem3D Tutorials 3 Chapter 2: Chem3D Basics 5 Getting around 5 User interface preferences 9 Background settings 10 Sample files 10 Saving to Dropbox 10 Chapter 3: Basic Model Building 12 Default settings 12 Selecting a display mode 12 Using bond tools 13 Using the ChemDraw panel 15 Using other 2D drawing packages 15 Building from text 16 Adding fragments 18 Selecting atoms and bonds 18 Atom charges 21 Object position 23 Substructures 24 Refining models 27 Copying and printing 29 Finding structures online 32 Chapter 4: Displaying Models 35 © Copyright 1998-2017 PerkinElmer Informatics Inc., All rights reserved. ii Chem3D 17.0 Display modes 35 Atom and bond size 37 Displaying dot surfaces 38 Serial numbers 38 Displaying atoms 39 Atom symbols 40 Rotating models 41 Atom and bond properties 44 Showing hydrogen bonds 45 Hydrogens and lone pairs 46 Translating models 47 Scaling models 47 Aligning models 47 Applying color 49 Model Explorer 52 Measuring molecules 59 Comparing models by overlay 62 Molecular surfaces 63 Using stereo pairs 72 Stereo enhancement 72 Setting view focus 73 Chapter 5: Building Advanced Models 74 Dummy bonds and dummy atoms 74 Substructures 75 Bonding by proximity 78 Setting measurements 78 Atom and building types 81 Stereochemistry 85 © Copyright 1998-2017 PerkinElmer Informatics Inc., All rights reserved. iii Chem3D 17.0 Building with Cartesian
  • Cheminformatics for Genome-Scale Metabolic Reconstructions

    Cheminformatics for Genome-Scale Metabolic Reconstructions

    CHEMINFORMATICS FOR GENOME-SCALE METABOLIC RECONSTRUCTIONS John W. May European Molecular Biology Laboratory European Bioinformatics Institute University of Cambridge Homerton College A thesis submitted for the degree of Doctor of Philosophy June 2014 Declaration This thesis is the result of my own work and includes nothing which is the outcome of work done in collaboration except where specifically indicated in the text. This dissertation is not substantially the same as any I have submitted for a degree, diploma or other qualification at any other university, and no part has already been, or is currently being submitted for any degree, diploma or other qualification. This dissertation does not exceed the specified length limit of 60,000 words as defined by the Biology Degree Committee. This dissertation has been typeset using LATEX in 11 pt Palatino, one and half spaced, according to the specifications defined by the Board of Graduate Studies and the Biology Degree Committee. June 2014 John W. May to Róisín Acknowledgements This work was carried out in the Cheminformatics and Metabolism Group at the European Bioinformatics Institute (EMBL-EBI). The project was fund- ed by Unilever, the Biotechnology and Biological Sciences Research Coun- cil [BB/I532153/1], and the European Molecular Biology Laboratory. I would like to thank my supervisor, Christoph Steinbeck for his guidance and providing intellectual freedom. I am also thankful to each member of my thesis advisory committee: Gordon James, Julio Saez-Rodriguez, Kiran Patil, and Gos Micklem who gave their time, advice, and guidance. I am thankful to all members of the Cheminformatics and Metabolism Group.
  • Topological Analysis of Electron Density

    Topological Analysis of Electron Density

    Jyväskylä Summer School on Charge Density August 2007 Topological Analysis of Electron Density Louis J Farrugia Jyväskylä Summer School on Charge Density August 2007 What is topological analysis ? A method of obtaining chemically significant information from th e electron density ρ (rho ) ρ is a quantum -mechanical observable , and may also be obtained from experiment “It seems to me that experimental study of the scattered radiati on, in particular from light atoms, should get more attention, since in this way it should be possible to determine the arrangement of the electrons in the atoms.” P. Debye, Ann. Phys. (1915) 48 , 809. Jyväskylä Summer School on Charge Density August 2007 Why analyse the charge density ? The traditional way of approaching the theoretical basis of chem istry is though the wavefunction and the molecular orbitals obtained through (approximate) solutions to the Schr ödinger wave equation HHΨΨ == EE ΨΨ The Hohenberg -Kohn theorem confirmed that the density, ρ(r), is the fundamental property that characterises the ground state of a sy stem - once ρ(r) is known, the energy of the system is uniquely defined, and from there a diverse range of molecular properties can, in princ iple, be deduced. Thus a knowledge of ρ(r) opens the door to understanding of all the key challenges of chemistry. ρ is a quantum -mechanical observable. 9 P. Hohenberg, W. Kohn Phys. Rev. 1964 , 136 , B864. Jyväskylä Summer School on Charge Density August 2007 Can we ever observe orbitals ? Simply not ever possible - see E. Scerri (2000) J. Chem. Ed. 77 , 1492 . However ?? - see J.
  • Chemical Graph Transformation with Stereo-Information

    Chemical Graph Transformation with Stereo-Information

    Chemical Graph Transformation with Stereo-Information Jakob L. Andersen Christoph Flamm Daniel Merkle Peter F. Stadler SFI WORKING PAPER: 2017-04-012 SFI Working Papers contain accounts of scienti5ic work of the author(s) and do not necessarily represent the views of the Santa Fe Institute. We accept papers intended for publication in peer-reviewed journals or proceedings volumes, but not papers that have already appeared in print. Except for papers by our external faculty, papers must be based on work done at SFI, inspired by an invited visit to or collaboration at SFI, or funded by an SFI grant. ©NOTICE: This working paper is included by permission of the contributing author(s) as a means to ensure timely distribution of the scholarly and technical work on a non-commercial basis. Copyright and all rights therein are maintained by the author(s). It is understood that all persons copying this information will adhere to the terms and constraints invoked by each author's copyright. These works may be reposted only with the explicit permission of the copyright holder. www.santafe.edu SANTA FE INSTITUTE Chemical Graph Transformation with Stereo-Information Jakob L. Andersen1;9 (B), Christoph Flamm2;8, Daniel Merkle1 (B), and Peter F. Stadler2−7 1 Department of Mathematics and Computer Science, University of Southern Denmark, Odense M DK-5230, Denmark {jlandersen,daniel}@imada.sdu.dk 2 Institute for Theoretical Chemistry, University of Vienna, Wien A-1090, Austria [email protected] 3 Bioinformatics Group, Department of Computer Science,and
  • Mathematical Chemistry! Is It? and If So, What Is It?

    Mathematical Chemistry! Is It? and If So, What Is It?

    Mathematical Chemistry! Is It? And if so, What Is It? Douglas J. Klein Abstract: Mathematical chemistry entailing the development of novel mathe- matics for chemical applications is argued to exist, and to manifest an extreme- ly diverse range of applications. Yet further it is argued to have a substantial history of well over a century, though the field has perhaps only attained a de- gree of recognition with a formal widely accepted naming in the last few dec- ades. The evidence here for the broad range and long history is by way of nu- merous briefly noted example sub-areas. That mathematical chemistry was on- ly recently formally recognized is seemingly the result of its having been somewhat disguised for a period of time – sometimes because it was viewed as just an unnamed part of physical chemistry, and sometimes because the rather frequent applications in other chemical areas were not always viewed as math- ematical (often involving somewhat ‘non-numerical’ mathematics). Mathemat- ical chemistry’s relation to and distinction from computational chemistry & theoretical chemistry is further briefly addressed. Keywords : mathematical chemistry, physical chemistry, computational chemistry, theoretical chemistry. 1. Introduction Chemistry is a rich and complex science, exhibiting a diversity of reproduci- ble and precisely describable predictions. Many predictions are quantitative numerical predictions and also many are of a qualitative (non-numerical) nature, though both are susceptible to sophisticated mathematical formaliza- tion. As such, it should naturally be anticipated that there is a ‘mathematical chemistry’, rather likely with multiple roots and with multiple aims. Mathe- matical chemistry should focus on mathematically novel ideas and concepts adapted or developed for use in chemistry (this view being much in parallel with that for other similarly named mathematical fields, in physics, or in biology, or in sociology, etc.
  • Six Questions on Topology in Theoretical Chemistry

    Six Questions on Topology in Theoretical Chemistry

    Six Questions on Topology in Theoretical Chemistry Paul L. Ayersa, Russell J. Boydb, Patrick Bultinckc, Michel Ca↵areld, Ramon Carbó-Dorcae, Mauro Causáf, Jerzy Cioslowskig, Julia Contreras-Garciah, David L. Cooperi, Philip Coppensj, Carlo Gattik, Simon Grabowskyl, Paolo Lazzerettim, Piero Macchin, Ángel Martín Pendáso, Paul L. A. Popelierp,q, Klaus Ruedenbergr, Henry Rzepas, h t u v h, w Andreas Savin , Alexander Sax , W. H. Eugen Schwarz , Shant Shahbazian , Bernard Silvi ⇤, Miquel Solà , Vladimir Tsirelsonx aDepartment of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, L8S 4M1, Hamilton, Ontario, Canada bDepartment of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4R2 cDepartment of Inorganic and Physical Chemistry, Ghent University, Krijgslaan 281 (S3), B9000 Ghent, Belgium dLaboratoire de Chimie et Physique Quantiques, CNRS-IRSAMC Université de Toulouse, France eInstitute of Computational Chemistry, University of Girona, Campus de Montilivi, 17071 Girona, Spain fDipartimento di Chimica Paolo Corradini, Universitá degli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy gInstitute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland hSorbonne Universités, UPMC, Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, case courrier 137, 4 place Jussieu, F-75005 Paris, France iDepartment of Chemistry, University of Liverpool, Liverpool L69 7ZD, United Kingdom jChemistry Department, University at Bu↵alo, SUNY, Bu↵alo, New York 14260-3000, United States kCNR-ISTM Istituto di Scienze e Tecnologie Molecolari, via Golgi 19, 20133 Milano, Italy lSchool of Chemistry and Biochemistry, Chemistry M310, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia mDipartimento di Scienze Chimiche e Geologiche, Universitá degli Studi di Modena, via G.
  • Chemical Graph Theory and the Sherlock Holmes Principle

    Chemical Graph Theory and the Sherlock Holmes Principle

    Chemical Graph Theory and the Sherlock Holmes Principle Alexandru T. Balaban Dedicated to Professor Lemont B. Kier for his 80 th anniversary Abstract : The development of chemical applications of graph theory is re- viewed from a personal perspective. Graph-theoretical methods for finding all graphs fulfilling certain mathematical conditions followed by eliminating chemically impossible solutions are equivalent to the ‘Sherlock Holmes prin- ciple’. For molecular graphs, this is illustrated by monocyclic aromatic systems and by valence isomers of annulenes. Using dualist graphs for benzenoids and diamond hydrocarbons it was possible to develop simple encoding systems that allowed convenient enumerations of isomers. Starting with the invention of reaction graphs in 1966 that included the Petersen graph which is also the 5- cage (the smallest graph with girth 5) two gaps were filled by discovering the first 10-cage and the unique 11-cage, showing how chemical clues can lead to interesting mathematical developments. Graphs of a third type are represented by synthon graphs that are helping chemical synthesis. Connections between chemical structure and molecular properties allow the design of biologically active substances on the basis of quantitative structure-activity relationships (QSARs). Some of the simplest tools for QSAR are topological indices and they are briefly discussed. Keywords : mathematical chemistry, molecular graphs, reaction graphs, synthon graphs, topological indices, QSAR . 1. Introduction This article presents a personal account of the author’s research activity cen- tered on chemical applications of graph theory including an overview of the interactions between chemistry and discrete mathematics. A few previous retrospective essays have been published earlier (Balaban 1993a, 1995, 2000b, 2005, 2011a, 2012a,b).
  • The Bond-Valence Substituent Index for Predicting the Boiling Temperatures of Aliphatic Hydrocarbons

    The Bond-Valence Substituent Index for Predicting the Boiling Temperatures of Aliphatic Hydrocarbons

    KIMIKA Volume 31, Number 1, pp. 38-55 (2020) © 2020 Kapisanang Kimika ng Pilipinas All rights reserved. Printed in the Philippines. ISSN 0115-2130 (Print); 2508-0911 (Online) https://doi.org/10.26534/kimika.v31i1.38-55 The Bond-Valence Substituent Index for Predicting the Boiling Temperatures of Aliphatic Hydrocarbons Florentino C. Sumera*, Stephani Jacutin, Jan Michael Aficial and Aileen Filipino Institute of Chemistry, University of the Philippines, Diliman, Quezon City, Philippines *Author to whom correspondence should be addressed; email: [email protected] ABSTRACT A simple molecular descriptor based on molecular structure for predicting the boiling temperature (BT) of alkanes was developed in this paper. This topological index was used to correlate the boiling temperature of aliphatic hydrocarbons with their bond-valence substituent structure instead of by atom-to-atom branching framework. The predictive power of the bond-valence substituent index (BVSI) was evaluated by comparing it with the popular predictor in literature, the Randic index and the more recently proposed index, the Fi of Manso et al. (2012). The model developed through a second order regression of the plot of the alkane’s boiling temperature versus the BVSI index proved successful in its predictive power such that the method was also applied to a combination of aliphatic hydrocarbons, the alkanes, alkenes, alkynes and cycloalkanes. This topological index provided higher correlation with small deviations compared to the topological index used for comparison. A further study of the BVSI index can be explored for other organic compounds with different functional groups and other physical properties besides their boiling temperatures in the future.
  • Spin Density Topology

    Spin Density Topology

    molecules Article Spin Density Topology Giovanna Bruno 1 , Giovanni Macetti 2 , Leonardo Lo Presti 1 and Carlo Gatti 3,4,* 1 Dipartimento di Chimica, Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy; [email protected] (G.B.); [email protected] (L.L.P.) 2 Laboratoire de Physique et Chimie Théoriques (LPCT), Université de Lorraine & CNRS, 1 Boulevard Arago, F–57078 Metz, France; [email protected] 3 CNR–SCITEC, Istituto di Scienze e Tecnologie Chimiche sezione di via Golgi, c/o Università degli Studi di Milano, via Golgi 19, 20133 Milano, Italy 4 Istituto Lombardo, Accademia di Scienze e Lettere, via Brera 28, 20100 Milano, Italy * Correspondence: [email protected] Academic Editor: Ángel Martín Pendás Received: 30 June 2020; Accepted: 1 August 2020; Published: 2 August 2020 Abstract: Despite its role in spin density functional theory and it being the basic observable for describing and understanding magnetic phenomena, few studies have appeared on the electron spin density subtleties thus far. A systematic full topological analysis of this function is lacking, seemingly in contrast to the blossoming in the last 20 years of many studies on the topological features of other scalar fields of chemical interest. We aim to fill this gap by unveiling the kind of information hidden in the spin density distribution that only its topology can disclose. The significance of the spin density critical points, the 18 different ways in which they can be realized and the peculiar topological constraints on their number and kind, arising from the presence of positive and negative spin density regions, is addressed.
  • Chemical Graph Theory-Facts and Fiction

    Chemical Graph Theory-Facts and Fiction

    Indian Journal of Chemistry Vol. 42A, June 2003, pp. 1207- 1218 Review Chemical graph theory-Facts and fiction Milan Randic National Institute of Chemistry, Hajdrihova 19, Ljubljana. Slovenia Received 31 January 2003 Graph Theory (GT) and its applications in chemistry, the so-call ed Chemical Graph Theory (CGT), appear to be two of the most misunderstood areas of theoretical chemi stry. We outline briefly possible causes for mi sunderstanding and suggest remedies, incl uding a test on the knowledge of GT and CGT. Introduction "primitive." The Conjugated Circuits method Graph Theory (GT) is a not so young branch of enumerates circuits within individual Kekule valence discrete mathematics. It is generally accepted that it structures of polycyclic conjugated hydrocarbons started with Leonhard Euler's paper I on the seven circuits in which there is a regular alternation of CC l9 bridges of Konigsberg published in 1736. It has single and CC double bonds . The outcomes of such received due attention after the first book on Graph enumeration are analytical expressions for molecular 20 Theori, which appeared two hundred years later, was resonance energy (RE). Schaad and Hess have published in 1936. Since then GT became one of the shown that the method of Conjugated Circuits is fastest expanding branched of mathematics, the closely related to Herndon's Resonance Theory21, a importance of which has been particularly recognized variant of VB calculations based solely on the set of in its role with development of the algorithms for Kekule valence structures of a molecule, that has been 22 computer applications of GT3. Graph theory has been in fact considered some time ago by Simpson , but 4 accepted and appreciated in physics as well as in was mostly (undeservingly) overlooked.