Term symbols diatomic

For linear molecules or ions the symbols are usually those derived from the term symbols for the electronic states of diatomic and other linear molecules. A capital Greek letter E, n, A, O,... is used, corresponding to k — 0,1,2,3,..., where A. is the quantum number for rotation about the molecular axis. For E species a superscript + or - is added to indicate the symmetry with respect to a plane that contains the molecular axis. 

We will see in due course that there are important correlation rules between atomic term symbols and molecular electronic states, rules that are important in understanding both the formation and dissociation of diatomic molecules. Elementary accounts of the theory of atomic structure are to be found in books by Softley [3] and Richards and Scott [4], Among the more comprehensive descriptions of the quantum mechanical aspects, that by Pauling and Wilson [5] remains as good as any whilst group theoretical aspects are described by Judd [6],... 

Figure 2.2 presents a schematic diagram of the possible vibrational modes for diatomic, linear triatomic, and bent triatomic molecules. The vibrational term symbol provides an ordered list of quantum numbers... 

In general, term symbols indicate both spin angular momentum (S for atoms, X for diatomic molecules) and orbital angular momentum (L for atoms, A for diatomic molecules). The term symbol is written 2S+1L for atoms and 2S+1A for molecules. We will not concern ourselves here... 

Polyatomic molecules have different term symbols, but again the spin multiplicity is given by the left-hand superscript. For example, the ground state of the ozone molecule is denoted by the term 1 Ai. Note that these terms should not be confused with the excited states of diatomic molecules, which can also contain A, B, etc. in their term symbols. 

In the case of diatomic molecules, we find that the Schrodinger equation requires that the component of the angular momentum along the molecular axis be quantized. The quantum number. A, describing this component is the basis for the term symbols for diatomic molecules. The quantum number A may have the values, A = 0, 1, 2,. For diatomic molecules, we use a Greek letter code for A. 

The E states, A = 0, are described as either E" or E depending on the behavior of the wave function upon reflection in the plane containing the internuclear axis. The E" wave function is invariant under this operation, while the E wave function changes sign on reflection in this plane. To the term symbols for homonuclear diatomic molecules, we... 

Table 13.2 lists D, Re, and Ve= Vg/c for the ground electronic states of some homonuclear diatomic molecules, where is the harmonic vibrational frequency (13.27). The table also lists the bond order, which is one-half the difference between the number of bonding and antibonding electrons. As the bond order increases, Dg and Vg tend to increase and Rg. decreases. (The high Vg of H2 is due to its small reduced mass /A.) The term symbols in this table are explained in the next section. 

For homonuclear diatomic molecules, a g or m right subscript is added to the term symbol to show the parity of the electronic states belonging to the term. Terms arising from an electron configuration that has an odd number of electrons in molecular orbitals of odd parity are odd (u) all other terms are even (g). This is the same rule as for atoms. 

M.L. Campbell (1996) Journal of Chemical Education, vol. 73, p. 749 - A systematic method for determining molecular term symbols for diatomic molecules is an extremely good sunnnary of a related topic not covered in this book. 

D. The El selection rules in Eq. 2.78 indicate that there are no El-allowed transitions connecting any two of these levels with different L if the spin-orbit coupling is small. This is an example of a general rule that no El transitions connect two term symbols arising from the same electron configuration (in this case, p ). El-allowed transitions can, however, occur between states from different electron configurations, say s p p. This proves to be a useful principle that carries over to the electronic spectroscopy of diatomic and polyatomic molecules. 

The question of which diatomic term symbols may be obtained by adiabatically bringing together atoms A and B, initially in electronic states with angular momentum quantum numbers (/a, Sa) and Sb), can be answered without recourse to electronic structure calculations. Since the electronic (orbital plus spin) degeneracies on the respective atoms are (2/a + 1)(2sa + 1) and (2/b + 1X2% + 1), a total of (2/a + 1)(2sa + 1)(2/b + 1)(2sb + 1) diatomic states must correlate with the separated-atom states. According to one of the... 

Evaluating the possible term symbols for diatomics with partially filled MOs is slightly more involved. A valence electron with 2 = 0 and s = j. Since... 

For a heteronuclear diatomic molecule, determine the electronic term symbols that correlate with -I- atoms. 

For a homonuclear diatomic molecule, what term symbols A can arise (a) from an equivalent configuration and (b) from a nonequivalent (e.g., TT TTg) configuration ... 

TABLE 7.1 Term symbols and term energies of selected diatomic molecules. The term energy is Tg, in eV (and relative to the ground state. 

As for atoms, term symbols can be defined for diatomic molecules. The term symbols for diatomic molecules are determined similarly to the K quantum number... 

The excited electron in the a antibonding orbital is in a molecular orbital that has 2u symmetry, and the electron still in the tt orbital has Ilg symmetry. The direct product of these two symmetries is simply Hg. (Verify this.) The a and tt electrons can have either the same direction spin or different direction spin (rather, the z components of their spin), so multiplicities of 3 or 1 are possible. Therefore, the term symbols for this excited-state electron configuration are and II states are doubly degenerate. In this case, there are two possible, degenerate tt molecular orbitals for the unexcited electron. Complete term symbols would have values for ft included. For the triplet state, H can be 2,1, or 0. For the singlet state, Q, can only be 1. Unlike atomic term symbols, it is relatively uncommon to see the fi values listed explicitly in the term symbols of diatomic molecules. One would see Ilu to represent all three individual states, rather than Ilu 2> Ilu i, and Ilu o-... 

Why do heteronuclear diatomic molecules not use the labels g and u on their term symbols ... 

Of the five parts of trans d can always be considered symmetric as far as the Pauli principle is concerned (no matter which type of particle—a fermion or a boson—the nucleus is). The electronic wavefunction eiect almost always symmetric. For homonuclear diatomic molecules, there is usually a + superscript on the term symbol of the ground electronic state that implies symmetric behavior however, some diatomic molecules—O2 is the noteworthy one—have a superscript minus (—) in their term symbol, indicating that the groimd electronic state is actually antisymmetric Ignoring these rare exceptions (but see the end-of-chapter exercises), ultimately the and the partition functions combine to determine the overall symmetry of Q for the molecule. 

As with atoms, term symbols are used to designate values of angular momentum quantum numbers for homonuclear diatomic molecules. The scheme is slightly different from the Russell-Saunders scheme that is used for atoms, since L is not a good quantum number. The operator does commute with the electronic Hamiltonian and an energy eigenfunction can be an eigenfunction of Lj ... 

Argue that the same term symbol occurs for a homonuclear diatomic molecule if the 3Tu2, —1 and jru2, - -1 orbitals are considered instead of the 7tu2px and ita2py orbitals. 

Give the term symbol for the ground-state electron configuration of each of the second-row homonuclear diatomic molecules (Li2 through F2). 

Excited states of diatomic neon exist, although the ground state has bond order zero. Give the electron configuration and term symbol for two different excited states that might exist. 

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