Hydrogen Intrinsic State

The Kier-Hall electronegativity is used to define the HE-state index HS [19]  

in each molecule, there are two sets of E-state values one for all nonhydrogen atoms and the second for the hydrogen atoms. The HS values are zero for atoms without hydrogens. 

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Another approach [Kier and Hall, 1999] is to apply the -state definition to each vertex of the molecular graph where the hydrogens of polar groups (-OH, -NH, -COOH, etc.) are explicitly considered as independent vertices. In this case, the intrinsic state of polar hydrogens will be ... 

The final graph theoretical index popularised by Kier and Hall that we shall consider is the electrotopological state index [Hall et al. 1991], Unlike the molecular connectivity and shape indices this is determined for each atom (including the hydrogen atoms, if so desired). This index depends upon the intrinsic state of an atom, which for an atom i (in the first row of the periodic table) is given by ... 

A spinning electron also has a spin quantum number that is expressed as 1/2 in units of ti. However, that quantum number does not arise from the solution of a differential equation in Schrodinger s solution of the hydrogen atom problem. It arises because, like other fundamental particles, the electron has an intrinsic spin that is half integer in units of ti, the quantum of angular momentum. As a result, four quantum numbers are required to completely specify the state of the electron in an atom. The Pauli Exclusion Principle states that no two electrons in the same atom can have identical sets of four quantum numbers. We will illustrate this principle later. 

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