3 and 4, respectively, analogous to the nomenclature for naming atomic orbitals.) We deduce from Hund's first rule that the ground state term is one of the two triplets, and from Hund's second rule that this term is 3F (with ) rather than 3P (with ). There is no 3G term since its state would require two electrons each with , in violation of the Pauli principle. (Here and are the components of the total orbital angular momentum L and total spin S along the z-axis chosen as the direction of an external magnetic field.) Rule 3 This rule considers the energy shifts due to spin–orbit coupling. In the case where the spin–orbit coupling is weak compared to the residual electrostatic interaction, and are still good quantum numbers and the splitting is given by: The value of changes from plus to minus for shells greater than half full. This term gives the dependence of the ground state energy on the magnitude of . Examples The lowest energy term of Si consists of three levels, . With only two of six possible electrons in the shell, it is less than half-full and thus is the ground state. For sulfur (S) the lowest energy term is again with spin–orbit levels , but now there are four of six possible electrons in the shell so the ground state is . If the shell is half-filled then , and hence there is only one value of (equal to ), which is the lowest energy state. For example, in phosphorus the lowest energy state has for three unpaired electrons in three 3p orbitals. Therefore, and the ground state is . Excited states Hund's rules work best for the determination of the ground state of an atom or molecule. They are also fairly reliable (with occasional failures) for the determination of the lowest state of a given excited electronic configuration. Thus, in the helium atom, Hund's first rule correctly predicts that the 1s2s triplet state (3S) is lower than the 1s2s singlet (1S). Similarly for organic molecules, the same rule predicts that the first triplet state (denoted by T1 in photochemistry) is lower than the first excited singlet state (S1), which is generally correct. However Hund's rules should not be used to order states other than the lowest for a given configuration. For example, the titanium atom ground state configuration is ...3d2 for which a naïve