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E. R. Tuttle in 1967 proposed a suitable method to determine the spectral terms for equivalent electrons in an atom in LS coupling condition. You may download the paper here, or E. R. Tuttle; Terms Obtained from Configurations of Equivalent Electrons. Am. J. Phys. 1 January 1967; 35 (1): 26–29.

I am having the difficulty to understand it properly. You can read the method described in pictures below or just download the article from the above link. enter image description here enter image description here

So in the above mentioned method I don’t understand step (b) properly in II. METHOD section. As a consequence, I don’t understand why $L = 0$ or $S $ state is not considered after the term ${}^{4}P$ in the example in table I for $ nd^3 $ case.

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why $L = 0$ or $S $ state is not considered after the term ${}^{4}P$ in the example in table I for $ nd^3 $ case ?

The answer is the two $M_L=0$ entries after $M_L=1$ entries belong to the last two spectral terms. We could have a $ L = 0 $ state if we had three $M_L =0$ entries instead of two.

Same for other terms. Check the picture below. enter image description here

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