Towards a quantitative bond valence description of coordination spheres – the concepts of valence entropy and valence diversity coordination numbers

Two novel definitions of chemical coordination numbers – valence entropy coordination number ⁿVECN and valence diversity coordination number ⁿVDCN – are proposed. Their originality stems from the fact that they are the first definitions based solely on bond valences. The expressions for them are derived from their definitions and their properties are studied. The unexpected close relationship of ⁿVECN to Shannon entropy and ⁿVDCN to diversity are revealed and the names of the new coordination numbers are taken therefrom. Finally, as an example, a study of arsenic(III) lone electron pair stereoactivity with respect to As^III coordination number is carried out to demonstrate the usefulness and advantages of the new definitions as well as to compare them with the existing ones.