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Consider an atom with (Equation presented) active or accessible orbitals and (Equation presented) is the maximum occupation number of the active subshell (Equation presented). Let (Equation presented) be the number of ECs with a total number of (Equation presented) electrons in all active orbitals. In fact, (Equation presented) is the partition function for partitioning the integer (Equation presented) into (Equation presented) integers. In number theory, the generating function of (Equation presented) is given by -k Ckxk= (1-x)-N Πj=1N (1-xgj+1). Then the total number of ECs with (Equation presented) to (Equation presented) is given by (Equation presented)
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Consider an atom with (Equation presented) active or accessible orbitals and (Equation presented) is the maximum occupation number of the active subshell (Equation presented). Let (Equation presented) be the number of ECs with a total number of (Equation presented) electrons in all active orbitals. In fact, (Equation presented) is the partition function for partitioning the integer (Equation presented) into (Equation presented) integers. In number theory, the generating function of (Equation presented) is given by -k Ckxk= (1-x)-N Πj=1N (1-xgj+1). Then the total number of ECs with (Equation presented) to (Equation presented) is given by (Equation presented).
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