Chemical bonding theories, effective state independence

A fundamental aspect of semi-empirical chemical bonding theories is their requirement that the model operators be state independent [56]. This property is, of course, not required of effective operators if only the numerical values are desired for the matrix elements of operators. Indeed, some semi-empirical theories, used in other areas of physics, do not impose the requirement of state independence. For instance, LS-dependent parameters are employed in describing the hyperfine coupling of two-electron atoms [31]. However, whenever effective operators themselves are the quantities of interest, as when studying semi-empirical theories of chemical bonding, state independence of effective operators becomes a necessity. This paper thus examines conditions leading to the generation of state-independent effective operators. 

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