Russell-Saunders term symbols

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-... 

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... 

In Russell-Saunders coupling, each energy level corresponds to a particular value of L and a particular value of S and is called a term. A Russell-Saunders term symbol is assigned to each term. The main part of the symbol is a letter giving the value of L, as follows ... 

Enumerate the states in the s) 2p) configuration and assign the Russell-Saunders term symbols. 

Calculate the value of the molecular partition function of CI2 gas at 298.15 K and a pressure of 1.000 bar. Find the Russell-Saunders term symbol for the ground-state of atomic chlorine and find the degeneracy of this level. Assume that the electronic partition function can be approximated by go> the degeneracy of the ground-level. 

Find the atomic term symbols associated with an atomic occupancy Is 2s 2p Spi. Find the Russell-Saunders term symbols for the possible states of the oxygen atom with occupancy Is 2s 2p. ... 

As an example, for the lowest spin-orbit coupled state for the electronically excited lithium atom (ls 2p 3p ), L, i = 2, S,ou,i = 3/2, and J = 1/2, the term symbol is Pi/2. These are called Russell-Saunders term symbols because it is assumed that the individual orbital angular momentum are more strongly coupled than the spin-orbit coupling. If spin-orbit coupling is ignored, the J term is omitted from the term symbol. 

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.)... 

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. 

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. 

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... 

When atoms have more than one valence electron, the term schemes become more complex as a coupling between the impulse and orbital momentums of the individual electrons occurs. According to Russell and Saunders (L — S) a coupling applies, where the orbital moments of all electrons have to be coupled to a total orbital momentum, as with the spin momentum. This coupling applies for elements with Z below 20, where it is accepted that the spin-orbital interactions are much lower than the spin-spin and the orbital-orbital interactions. The fact that none of the electrons in an atom can have the same set of quantum numbers is known as the Pauli rule. The total quantum number I is obtained as L = 2,1, S = Es and J = L — S,..., I + S. The term symbol accordingly becomes ... 

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. 

Extracting Term Symbols Using Russell-Saunders Coupling... 

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. 

---