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Toward a Comprehensive Definition of Oxidation State (IUPAC Technical Report)

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Toward a Comprehensive Definition of Oxidation State (IUPAC Technical Report) DOI 10.1515/pac-2013-0505 Pure Appl. Chem. 2014; 86(6): 1017–1081 IUPAC Technical Report Pavel Karen*, Patrick McArdle and Josef Takats Toward a comprehensive definition of oxidation state (IUPAC Technical Report) Abstract: A generic definition of oxidation state (OS) is formulated: “The OS of a bonded atom equals its charge after ionic approximation”. In the ionic approximation, the atom that contributes more to the bonding molecular orbital (MO) becomes negative. This sign can also be estimated by comparing Allen electronega- tivities of the two bonded atoms, but this simplification carries an exception when the more electronegative atom is bonded as a Lewis acid. Two principal algorithms are outlined for OS determination of an atom in a compound; one based on composition, the other on topology. Both provide the same generic OS because both the ionic approximation and structural formula obey rules of stable electron configurations. A sufficiently simple empirical formula yields OS via the algorithm of direct ionic approximation (DIA) by these rules. The topological algorithm works on a Lewis formula (for a molecule) or a bond graph (for an extended solid) and has two variants. One assigns bonding electrons to more electronegative bond partners, the other sums an atom’s formal charge with bond orders (or bond valences) of sign defined by the ionic approximation of each particular bond at the atom. A glossary of terms and auxiliary rules needed for determination of OS are pro- vided, illustrated with examples, and the origins of ambiguous OS values are pointed out. An electrochemical OS is suggested with a nominal value equal to the average OS for atoms of the same element in a moiety that is charged or otherwise electrochemically relevant. Keywords: bond order; bond valence; chemistry; electronegativity; iconicity; ionic approximation; IUPAC Inorganic Chemistry Division; Lewis acids; Lewis bases; oxidation state; quantum chemistry. *Corresponding author: Pavel Karen, Department of Chemistry, University of Oslo, P.O.B. 1033 Blindern, 0315 Oslo, Norway, e-mail: [email protected] Patrick McArdle: School of Chemistry, NUI Galway, Galway, Ireland Josef Takats: Department of Chemistry, University of Alberta, Edmonton, Alberta, Canada T6G 2G2 Article note: Sponsoring body: IUPAC Inorganic Chemistry Division: see more details on p. 1063. CONTENT 1. PREAMBLE ��������������������������������������������������������������������������������������������������������������������������������� 1020 2. INTRODUCTION ��������������������������������������������������������������������������������������������������������������������������1021 3. EXPERIMENTAL ��������������������������������������������������������������������������������������������������������������������������1021 4. NOTATION OF OS ������������������������������������������������������������������������������������������������������������������������1022 5. THE GENERIC DEFINITION OF OS ..................................................................................................... 1022 5.1 Ionic approximation .................................................................................................................... 1023 5.1.1 Determination .................................................................................................................. 1023 5.1.2 Estimate using electronegativities .................................................................................... 1023 5.2 Bond order ...................................................................................................................................1024 5.2.1 A chemist’s formula approach ..........................................................................................1024 5.2.2 Bond-valence approach ....................................................................................................1024 6. BONDLESS APPROACH TO OS ���������������������������������������������������������������������������������������������������� 1025 6.1 The rule of noble-gas configuration ............................................................................................. 1025 6.2 OS algorithm of direct ionic approximation (DIA) ........................................................................ 1025 © 2014 IUPAC & De Gruyter 1018 P. Karen et al.: Definition of oxidation state 7. BOND APPROACH TO OS ������������������������������������������������������������������������������������������������������������ 1025 7.1 OS algorithm of moving bonds..................................................................................................... 1025 7.2 Structural representations used in this Report ............................................................................1026 7.2.1 Lewis formula of a molecule .............................................................................................1026 7.2.2 Bond graph of an extended solid ......................................................................................1026 7.2.3 Notations for solid-state connectivity ...............................................................................1026 7.3 Stable electron-configuration rules used in this Report ............................................................... 1027 7.3.1 The 8−N rule ..................................................................................................................... 1027 7.3.2 The (8+)N rule .................................................................................................................. 1027 7.3.3 The 18-electron rule .......................................................................................................... 1027 7.3.4 The Hückel (aromaticity) rule ........................................................................................... 1027 7.3.5 The 12−N (s2) rule .............................................................................................................. 1027 7.4 Some structure-predicting rules ...................................................................................................1028 7.4.1 The generalized 8−N rule ..................................................................................................1028 7.4.2 The Wade–Mingos rules ...................................................................................................1028 7.5 Electron-counting variables .........................................................................................................1028 7.5.1 Formal charge and electroneutrality principle .................................................................1028 7.5.2 Bond order sum (BOS) and ionized bond order sum (iBOS) .............................................. 1029 7.5.3 Relation between OS and iBOS in a Lewis formula ........................................................... 1029 7.5.4 When OS equals iBOS ....................................................................................................... 1029 7.6 OS algorithm of summing bond orders (bond valences) ..............................................................1030 8. SIMPLE EXAMPLES OF OS ���������������������������������������������������������������������������������������������������������� 1030 8.1 OS from a Lewis formula ..............................................................................................................1030 8.2 OS from a bond graph .................................................................................................................. 1031 8.3 Further OS examples for molecules and solids ............................................................................ 1033 9. OS IN SPECIES WITH HOMONUCLEAR BONDS ........................................................................... 1036 9.1 Chains of atoms of the same element ...........................................................................................1036 9.1.1 Polysulfanes .....................................................................................................................1036 9.1.2 Triiodide anion .................................................................................................................1036 9.1.3 Azide anion ...................................................................................................................... 1037 9.1.4 Dinitrogen monoxide ........................................................................................................1038 9.1.5 Pentanitrogen cation (1+) ..................................................................................................1038 9.1.6 Thiosulfate .......................................................................................................................1039 9.2 Boranes ........................................................................................................................................1039 2− 9.2.1 The closo-borane B6H6 anion ..........................................................................................1039 9.2.2 The nido borane B6H10...................................................................................................... 1040 9.3 Carboranes.................................................................................................................................. 1040 9.4 Metallaboranes ............................................................................................................................ 1041 9.5 Other main-group clusters ...........................................................................................................1042
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