Nomenclature and chemical formulae for bridged dinuclear chromium complexes
$\require{unicode}$The rules for formulating and naming coordination compounds are presented in Chapter IR-9 of the current version of Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005 (Red Book). An abridged version is included in the IUPAC Technical Report Brief guide to the nomenclature of inorganic chemistry. Pure Appl. Chem. 2015, 87(9–10), 1039–1049 as well as in the corresponding four-sided lift-out document, which is available as supplementary material.

The line formula for a simple coordination entity is constructed within square brackets. The symbol for the central atom is placed first and is then followed by the symbols or abbreviations for the ligands (in alphabetical order according to the way they are presented in the formula).


  IR-9.2.3.1 Sequence of symbols within the coordination formula
  
  (i) The central atom symbol(s) is (are) listed first.
  
  (ii) The ligand symbols (line formulae, abbreviations or acronyms) are then listed in alphabetical order (…). Thus, $\ce{CH3CN}$, $\ce{MeCN}$ and $\ce{NCMe}$ would be ordered under C, M and N respectively, and $\ce{CO}$ precedes $\ce{Cl}$ because single letter symbols precede two letter symbols. The placement of the ligand in the list does not depend on the charge of the ligand.
  
  (iii) More information is conveyed by formulae that show ligands with the donor atom nearest the central atom; this procedure is recommended wherever possible, even for coordinated water.


Note that according to the recommendations in Item (iii), where possible, the coordinating (ligating) atom should be placed nearer the central atom in order to provide more information about the structure of the complex. Therefore, the line formula of the hexaaquachromium(3+) complex ion should be written as $\ce{[Cr(OH2)6]^3+}$ rather than $\ce{[Cr(H2O)6]^3+}$.

For the same reason, if possible, bridging ligands should be placed between the central atom symbols. Bridging ligands are those bound to more than one central atom. They are differentiated in names by the addition of the prefix ‘μ’.


  IR-9.2.5.2 Bridging ligands
  
  Bridging ligands, as far as they can be specified, are indicated by the Greek letter μ appearing before the ligand symbol or name and separated from it by a hyphen; (…)  
  
  (…) In formulae, bridging ligands are placed after terminal ligands of the same kind. (…)
  
  The bridging index $n$, the number of coordination centres connected by a bridging ligand, is placed as a right subscript. The bridging index $2$ is not normally indicated. (…)


Polynuclear complexes may be named differently according to whether only stoichiometry is to be specified or partial or complete structural information is to be included.


  IR-9.2.3 Formulae of coordination compounds
  
  (…) Different applications may require flexibility in the writing of formulae. Thus, on occasion it may be desirable to violate the (…) guidelines in order to provide more information about the structure of the compound that the formula represents. In particular, this is the case for dinuclear compounds where a great deal of structural information can be provided by relaxing the ordering principles outlined in Section IR-9.2.3.1. (…)


​


  IR-9.2.5.1 General
  
  (…)
  
  As a general principle, as much structural information as possible should be presented when writing the formula or name of a polynuclear complex. However, polynuclear complexes may have structures so large and extended as to make a rational structure-based nomenclature impractical. Furthermore, their structures may be undefined or not suitably elucidated. In such cases, the principal function of the name or formula is to convey the stoichiometric proportions of the various moieties present.
  
  (…)
  
  Note, however, that the rules for formula writing may be relaxed in various ways in order better to display particular features of the structures in question. (…)




As a first approximation, the systematic line formula for the complex ion shown in Picture 1 is $\ce{[(H2O)3Cr($\unicode[Times]{x3BC}$-OH)2($\unicode[Times]{x3BC}$-SO4)Cr(OH2)3]^2+}$. Note: pay attention to the Greek letter; it is to be written upright.

However, since this complex ion is symmetric, its formula may be further simplified.


  IR-9.2.5.4 Symmetrical dinuclear entities
  
  For symmetrical dinuclear entities, the name may be simplified by employing multiplicative
  prefixes.
  
  (…)


The resulting formula is: $\ce{[\{Cr(OH2)3\}2($\unicode[Times]{x3BC}$-OH)2($\unicode[Times]{x3BC}$-SO4)]^2+}$. The corresponding name is di-μ-hydroxido-μ-sulfato-bis(triaquachromium)(2+).



The corresponding formula for the complex ion shown in Picture 2 is $\ce{[\{Cr(OH2)2(SO4)\}2($\unicode[Times]{x3BC}$-OH)2($\unicode[Times]{x3BC}$-SO4)]^2-}$. The corresponding name is 
di-μ-hydroxido-μ-sulfato-bis(diaquasulfatochromate)(2−).

Furthermore, if necessary, you can indicate the connectivity of the sulfato ligand using the kappa convention (sulfato-2κ​O).