Russel-Saunders state

Due to the intermediate coupling the sign of the crystal field matrix element 6 is reversed compared to the pure Russell-Saunders state. Thus for 8-fold cubic coordination a F7 ground state was found. From EPR measurements on Pu3"1" diluted in fluorite host lattices, a magnetic moment at T=0 K can be calculated, ranging from li ff = 1.333 (in Ce02) to y ff = 0.942 (in SrCl2) (24,... 

Of the Russell-Saunders states arising from a given electron configuration those with the largest value of S lie lowest, those with the next largest... 

Russell-Saunders States of Atoms Allowed by the Pauli Exclusion Principle... 

By adding the values of 2J + 1 for the ten Russell-Saunders states listed above we see that there are in fact 36 states based upon the configuration 2p3p and that application of a magnetic field gives rise to 36 energy levels. 

In Table IV-2 are listed the allowed Russell-Saunders states for equivalent s p, dy and some cases of / electrons. 

A spectroscopic or Russell-Saunders state is designated rL, where r is the electron spin multiplicity and L is the total atomic orbital angular momentum... 

In the picture of spin-orbit perturbed Russell-Saunders states, the dipole transition moment of a spin-forbidden radiative transition is thus a sum of spin-allowed dipole transitions weighted by spin-orbit coupling coefficients (e.g., the expansion coefficients in Eq. [218]). The fact that the transition dipole moment of a spin-forbidden radiative transition is a weighted sum of spin-allowed dipole transition moments is exactly what experimentalists mean when they speak of intensity borrowing. The contribution of perturbing states to the oscillator strength can be positive or negative. In other words, per-turbers can not only lend intensity to a spin-forbidden transition, they can also take it away. 

There are a number of different approaches to the description of molecular electronic states. In this section we describe molecular orbital theory, which has been by far the most significant and popular approach to both the qualitative and quantitative description of molecular electronic structure. In subsequent sections we will describe the theory of the correlation of molecular states to the Russell Saunders states of the separated atoms we will also discuss what is known as the united atom approach to the description of molecular electronic states, an approach which is confined to diatomic molecules. 

If the interactions between different Russell-Saunders states are not large, the spin-orbit coupling operator may be written... 

The Russell-Saunders states that arise from interelectronic interactions in a free ion with an electronic configuration d are F, D, P, G, and S, with the F being the ground state as dictated by Hund s first and second rules. An approximate calculation in which the F state is outlined here. 

The energies of the various Russell-Saunders states of an atom or ion are not the same, and Hund s first and second rules can be used to decide which is the ground state ... 

The reader can verify that these correspond to the sum of the degeneracies of the Russell-Saunders states generated by diagonalizing the 8x8 7 .v-block for the lithium ground state and the 70x70 block for the carbon ground state, as shown in Table 1. 

In his theoretical treatment, Nugent (5(5) has pointed out that the relativistic spin-orbit coupling would not contribute considerably towards the tetrad effect, and he based his explanation of the tetrad theory on Russell-Saunders states for the lantha-... 

Splitting of Russell-Saunders States in Octahedral and Tetrahedral Electrostatic Fields... 

Similar energy level diagrams may be drawn for dn systems in tetrahedral crystal fields. There is an interesting relationship between these and the ones for certain systems in octahedral fields. We have already seen that the splitting pattern for the d orbitals in a tetrahedral field is just the inverse of that for the d orbitals in an octahedral field. A similar inverse relationship exists between the energy level diagrams of dn systems in tetrahedral and octahedral fields. The components into which each Russell-Saunders state is split are reversed in their energy order in the tetrahedral compared to the octahedral... 

Fig. 20-18. Partial energy-level diagram for the Mn" ion, showing only the 6.S state and the quartet states. The separations of the Russell-Saunders states at A = 0 are those appropriate for the [Mn(H20)6]2+ ion (not the actual free Mn2+ ion) and the vertical line is at the A value (8600 cm-1) for this species.

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