Relative Atomic Moments as Squared Principal Eigenvector Coefficients

A proof is presented that the limit of each relative atomic moment (RAM) in tight-binding approximation is equal to the respective squared atomic coefficient in the principal eigenvector. It is also proved that this limit is reached when each higher RAM is obtained from the preceding one by multiplying by the squared largest eigenvalue. Relationships are obtained between the RAM limit and Ruckers' limit of the relative walk counts. Higher molecular branching and cyclicity as well as higher symmetry are shown to favor the convergence. The necessary and sufficient conditions are formulated for a RAM to reach its limit as early as in the second moment. Relationships between different RAMs are obtained for several classes of molecules