Quantum chemical concept of oxidation states

Abstract The concept of the oxidation state of an atom in a chemical compound is formulated in terms of the quantum theory of many-electron systems and illustrated by calculations of oxidation numbers of calcium(I, II), phosphorus(0–V), sulfur(0–VI), fluorine(–I), oxygen(–II), and krypton(0) in CaCB 11 H 6 Cl 6 , CaCB 11 H 12 , CaC 5 H 5 , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:mi mathvariant="normal">C</m:mi> <m:mi mathvariant="normal">a</m:mi> <m:msub> <m:mrow> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi mathvariant="normal">C</m:mi> </m:mrow> <m:mrow> <m:mn mathvariant="normal">5</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi mathvariant="normal">H</m:mi> </m:mrow> <m:mrow> <m:mn mathvariant="normal">5</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn mathvariant="normal">2</m:mn> </m:mrow> </m:msub> </m:math> $\mathrm{C}\mathrm{a}{\left({\mathrm{C}}_{\mathrm{5}}{\mathrm{H}}_{\mathrm{5}}\right)}_{\mathrm{2}}$ , Ca@C 60 , P@C 60 , PF, PF 3 , PF 5 , POF 3 , P 4 O 6 , P 4 O 10 , SO, OSSO, SO 2 , SF 2 , SF 4 , SF 6 , SOF 4 , SO 2 F 2 , S 3 O 9 , and Kr@C 60 molecules. In <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mrow> <m:mi mathvariant="normal">P</m:mi> <m:msub> <m:mrow> <m:mi mathvariant="normal">O</m:mi> </m:mrow> <m:mrow> <m:mn mathvariant="normal">4</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn mathvariant="normal">3</m:mn> <m:mo>−</m:mo> </m:mrow> </m:msup> <m:mi mathvariant="normal">@</m:mi> <m:mi>a</m:mi> <m:mi>q</m:mi> <m:mi>u</m:mi> <m:mi>a</m:mi> </m:math> ${\left[\mathrm{P}{\mathrm{O}}_{\mathrm{4}}\right]}^{\mathrm{3}-}\mathrm{@}aqua$ , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mrow> <m:msub> <m:mrow> <m:mi mathvariant="normal">P</m:mi> </m:mrow> <m:mrow> <m:mn mathvariant="normal">3</m:mn> </m:mrow> </m:msub> <m:msub> <m:mrow> <m:mi mathvariant="normal">O</m:mi> </m:mrow> <m:mrow> <m:mn mathvariant="normal">9</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mn mathvariant="normal">3</m:mn> <m:mo>−</m:mo> </m:mrow> </m:msup> <m:mi mathvariant="normal">@</m:mi> <m:mi>a</m:mi> <m:mi>q</m:mi> <m:mi>u</m:mi> <m:mi>a</m:mi> </m:math> ${\left[{\mathrm{P}}_{\mathrm{3}}{\mathrm{O}}_{\mathrm{9}}\right]}^{\mathrm{3}-}\mathrm{@}aqua$ , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mrow> <m:mo stretchy="false">[</m:mo> <m:mrow> <m:mi mathvariant="normal">P</m:mi> <m:msub> <m:mrow> <m:mi mathvariant="normal">F</m:mi> </m:mrow> <m:mrow> <m:mn mathvariant="normal">6</m:mn> </m:mrow> </m:msub> </m:mrow> <m:mo stretchy="false">]</m:mo> </m:mrow> </m:mrow> <m:mrow> <m:mo>−</m:mo> </m:mrow> </m:msup> <m:mi mathvariant="normal">@</m:mi> <m:mi>a</m:mi> <m:mi>q</m:mi> <m:mi>u</m:mi> <m:mi>a</m:mi> </m:math> ${\left[\mathrm{P}{\mathrm{F}}_{\mathrm{6}}\right]}^{-}\mathrm{@}aqua$ , <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <m:msup> <m:mrow> <m:mrow>