Term symbol molecular

The ground-state term symbol is always listed first. 

The symmetry of the GS term can always be determined using Hund s rules, as described in Section 4.5, where the spin multiplicity is maximized first, and then the total orbital angular momentum L is maximized. Thus, the GS term symbol for the d electron configuration is the F term. The energies of the other terms can be determined on the basis of their Racah parameters, according to Table 16.18. 

TABLE 16.17 The Racah parameters B and C/B in units of cm for selected transition metals as free ions as a function of their oxidation states. 

The energies of the terms for the d -cF electron configurations of the transition metals as free ions, assuming OB = 4.7. [Reproduced from Figgis, B. N. Hitchman, M. A. Ligand Field Theory and Its Applications, Wiley-VCH New York, 2000. This material is reproduced with permission of John Wiley Sons, Inc.] 

TABLE 16.18 The energies of the terms for each d configuration as expressed by the Racah parameters A, B, and C. 

When the electronic configuration has only filled orbitals, there is only one state 1 Tts where Tts is the totally symmetric representation. If the configuration has only one open shell (having symmetry /)) with one electron, we again have only one state 211. When there are two open shells (having symmetries 7j and TJ) each with one electron, the symmetry of the state is x /] = Cy and the overall states (including spin) are3 Ty and 1ry. 

Let us now apply this method to a specific example. Consider the ethylene molecule with D2h symmetry. As can be seen from the character table of the L 2h point group (Table 6.4.2), this group has eight symmetry species. Hence the molecular orbitals of ethylene must have the symmetry of one of these eight representations. In fact, the ground electronic configuration for ethylene is 

Some molecular orbitals of ethylene (point group Z 2h)- All are completely filled except l 2g in the ground state. The x axis points into the paper. 

So the eight pairs of electrons of this molecule occupy delocalized molecular orbitals lag to 1 3U, while the first vacant orbital is l g- Note that the names of these orbitals are simply the symmetry species of theZ)2h point group. In other words, molecular orbitals are labeled by the irreducible representations of the point group to which the molecule belongs. So for ethylene there are three filled orbitals with Ag symmetry the one with the lowest energy is called lag, the next one is 2ag, etc. Similarly, there are two orbitals with Z iu symmetry and they are called lb u and 2bi . All the molecular orbitals listed above, except the first two, are illustrated pictorially in Fig. 6.4.2. By checking the 2h character table with reference to the chosen coordinate system shown in Fig. 6.4.2, it can be readily confirmed that these orbitals do have the labeled symmetry. In passing, it is noted that the two filled molecular orbitals of ethylene not displayed in Fig. 6.4.2, lag and l iu, are simply the sum and difference, respectively, of the two carbon Is orbitals. 

in the configuration, there are a number of completely filled orbitals and one open (degenerate) shell with two (equivalent) electrons, there will be singlet as well as triplet states. To determine the spatial symmetry of these states, we make use of the formulas  

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As in the case of atoms, the molecular term symbol is written as 2S+1L, where L is the absolute value of Ml (the highest positive value). The molecular states are designated as for atoms except for the use of capital Greek letters ... 

Section treats the spatial, angular momentum, and spin symmetries of the many-electron wavefunctions that are formed as antisymmetrized products of atomic or molecular orbitals. Proper coupling of angular momenta (orbital and spin) is covered here, and atomic and molecular term symbols are treated. The need to include Configuration Interaction to achieve qualitatively correct descriptions of certain species electronic structures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of chemical reactivity is also developed. 

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. 

The main part of the molecular term symbol is a capital Greek letter that specifies the value of A ... 

The progression of sections leads the reader from the principles of quantum mechanics and several model problems which illustrate these principles and relate to chemical phenomena, through atomic and molecular orbitals, N-electron configurations, states, and term symbols, vibrational and rotational energy levels, photon-induced transitions among various levels, and eventually to computational techniques for treating chemical bonding and reactivity. 

Molecular ma.s.s is expre.s.sed in units of daltons (D) or kilodaltons (kD) in diis book alternatively, the dimension-le.ss term molecular weight,. symbolized by Mr, and defined as the ratio of die ma.ss of a molecule to 1 dalton of mass, is itsed. 

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. 

The spectroscopic term symbols for the molecular case can be obtained,... 

The dynamic state is defined by the values of certain observables associated with orbilal and spin motions of the electrons and with vibration and rotation of [lie nuclei, and also by symmetry properties of the corresponding stationary-state wave functions. Except when heavy nuclei ate present, the total electron spin angular momentum of a molecule is separately conserved with magnitude Sh. and molecular slates are classified as singlet, doublet, triplet., . according to the value of the multiplicity (25 + I). This is shown by a prefix superscript lo the term symbol, as in atoms. 

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],... 

Complex molecules may not possess any symmetry elements, or if they do, the localizations of the electrons can so distort the electron cloud that its symmetry bears little relation to the molecular symmetry. In such cases it may be best to revert to a description of states in terms of the individual orbitals. As an example, we will consider formaldehyde, although a molecule as simple as this is probably best described by the group-theoretical term symbol of the last paragraph. The last filled orbitals in H2CO can easily be shown to be. ..(jtco)2 (no)2, where no represents the nonbonding orbital on the O atom and the two electrons in it are the lone pair. The first unfilled orbitals in formaldehyde are the tt 0 and rr o antibonding orbitals. Promotion of one... 

The symmetric and antisymmetric squares have special prominence in molecular spectroscopy as they give information about some of the simplest open-shell electronic states. A closed-shell configuration has a totally symmetric space function, arising from multiplication of all occupied orbital symmetries, one per electron. The required antisymmetry of the space/spin wavefunction as a whole is satisfied by the exchange-antisymmetric spin function, which returns Fq as the term symbol. In open-shell molecules belonging to a group without... 

The superscripts denote the number of electrons in each atomic orbital. Electrons must be paired (i.e., of equal and opposite spin) in atomic orbitals containing two electrons. Paired electrons do not contribute to the atomic or molecular spin angular momentum. Hund s rule of maximum multiplicity states that in the lowest energy configuration, the electrons must be spread over as many available orbitals of equal energy as possible, in order to maximize the spin multiplicity. Since three 2p orbitals are available in which 4 electrons must be distributed, the lowest electronic state therefore has two unpaired electrons in each of two 2p orbitals. Each unpaired electron contributes to the spin angular momentum. Thus 2S + 1 = 3 for the oxygen atom, and the term symbol is 3P. 

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