Russell Saunders symbols

The most stable atomic energy levels of the carbon atom are shown in Figure 4-4. The three lowest levels, with Russell-Saunders symbols P, lDt and lS, correspond to the configuration 2s72pt. This configura-... 

In tier (1) of the diagram (for the electronic structure of iron(III)), only the total energy of the five metal valence electrons in the potential of the nucleus is considered. Electron-electron repulsion in tier (2) yields the free-ion terms (Russel-Saunders terms) that are usually labeled by term ° symbols (The numbers given in brackets at the energy states indicate the spin- and orbital-multiplicities of these states.)... 

It has been pointed out above that two electrons in the Is orbital must have their spins opposed, and hence give rise to the singlet state So, with no spin or orbital angular momentum, and hence with no magnetic moment. Similarly it is found that a completed subshell of electrons, such as six electrons occupying the three 2p orbitals, must have S — 0 and L = 0, corresponding to the Russell-Saunders term symbol lS0 such a completed subshell has spherical symmetry and zero magnetic moment. The application of the Pauli exclusion prin-... 

We are now in position to derive the electronic states arising from a given electronic configuration. These states have many names spectroscopic terms (or states), term symbols, and Russell-Saunders terms, in honor of spectroscopists H. N. Russell and F. A. Saunders. Hence, the scheme we use to derive these states is called Russell-Saunders coupling. It is also simply referred to as L-S coupling. 

With light elements (e.g. first-row and second-row transition metals), to which principal consideration is given in this book, the Russell-Saunders (or IS) coupling scheme suffices. Every microstate is designated with a term symbol of the general form where 25 -I- 1 is the spin multiplicity (5 = 5,), L is the total orbital angular momentum... 

The electronic configurations of the lanthanides are described by using the Russell-Saunders coupling scheme. Values of the quantum numbers S and L corresponding to the lowest energy are derived in the conventional manner. These are then expressed for each ion in the form of a ground term with the symbolism that S, P, D, F,. .. correspond to L = 0, 1,... 

The term symbol does not account for the true complexity found in most atoms. This arises from the interaction between the spin and the orbital momentum (spin-orbit coupling) that is ignored in Russell-Saunders coupling. A new quantum number, J, is needed. It is given by ... 

A term scheme is a representation of an energy level in an isolated many-electron atom, derived via the Russell-Saunders coupling scheme. In general, a term scheme is written as a collection of many-electron quantum numbers S and L. The value of S is not used directly but is replaced by the spin multiplicity, 2S +1. Similarly, the total angular momentum quantum number, L, is replaced by a letter symbol similar to that used for the single-electron quantum number 1. The term scheme is written States with a multiplicity of 1 are called singlet states, states with a multiplicity of 2 are called doublet states, those with a multiplicity of three are called triplets, those with a multiplicity 4 are called quartets and so on. Hence, S is called singlet S, and is called triplet P. 

For atoms with more than one valence electron, coupling of the spin- and orbital angular momentum must be considered (Russel—Saunders- or I—S-coupling). The orbital momenta of all electrons have to be coupled to the total orbital momentum, as have the spin momenta. The total quantum number L is obtained by replacing L = 1,1, S = Is, and J = L - S.I + S. The term symbol thus becomes ... 

Atomic states characterized by S and L are often called free-ion terms (sometimes Russell-Saunders terms) because they describe individual atoms or ions, free of ligands. Their labels are often called term symbols. Term symbols are composed of a letter relating to the value of L and a left superscript for the spin multiplicity. For example, the term symbol corresponds to a state in which L = 2 and the spin multiplicity (25 + 1) is 3 marks a state in which L = 3 and 25 -I- 1 = 5. 

Extracting Term Symbols Using Russell-Saunders Coupling... 

Electronic-state configurations are described by the standard quantum numbers or principal quantum number n, angular momentum quantum number L, spin quantum number S and total angular momentum quantum number J. In the so-called Russel-Saunders approximation of electron coupling, electronic states are commonly described symbolically by n For... 

TERM SYMBOLS FOR LINEAR MOLECULES Electronic states of a linear molecule may be classified conveniently in terms of angular momentum and spin, analogous to the Russell-Saunders term-symbol scheme for atoms. The unique molecular axis in linear molecules is labeled the axis. The combining atomic orbitals in any given molecular orbital have the same mi value. Thus an mi quantum number is assigned to each different type of MO, as indicated in Table 2-3. The term designations are of the form... 

Tlie discussion of atomic structure does not start with the Schrodinger equation, but with the Bohr theory. I believe most students appreciate the opportunity of learning the development of atomic theory in this century and can make the transition from orbits to orbitals without much difficulty. The student can also calculate several important physical quantities from the simple Bohr theory. At the end of the first chapter, there is a discussion of atomic-term symbols in the Russell-Saunders LSMiMs approximation. 

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