Term symbols atoms

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. 

When this overall sign is positive, the funetion P is termed "even" and its term symbol is appended with an "e" superseript (e.g., the 2p level of the O atom, whieh has Is22s22p4 oeeupaney is labeled 2pe) if the sign is negative P is ealled "odd" and the term symbol is so amended (e.g., the 2p level of Is22si2pi B+ ion is labeled 2po). 

For homonuclear molecules (e.g., O2, N2, etc.) the inversion operator i (where inversion of all electrons now takes place through the center of mass of the nuclei rather than through an individual nucleus as in the atomic case) is also a valid symmetry, so wavefunctions F may also be labeled as even or odd. The former functions are referred to as gerade (g) and the latter as ungerade (u) (derived from the German words for even and odd). The g or u character of a term symbol is straightforward to determine. Again one... 

To illustrate this point, consider how the state of Carbon would be expected to interact with an approaching Ne atom. This term symbol s wavefunction = 3"k2 [ IpoapoPI - Ip-iapipl... 

Determine all term symbols that arise from the Is22s22p23dl configuration of the excited N atom. 

The first excited state of the molecule, c N , is built from normal atoms, and has the term symbol 2n. It lies 1.78 v. e. above the normal state. 

In a manner similar to that by which the atomic states were designated as s, p, d, or /, the letters S, P, D, and F correspond to the values of 0, 1, 2, and 3, respectively, for the angular momentum vector, L. After the values of the vectors L, S, and / have been determined, the overall angular momentum is described by a symbol known as a term symbol or spectroscopic state. This symbol is constructed as Ps+1)Lj where the appropriate letter is used for the L value as listed earlier, and the quantity (2S + 1) is known as the multiplicity. For one unpaired electron, (2S + 1) = 2, and a multiplicity of 2 gives rise to a doublet. For two unpaired electrons, the multiplicity is 3, and the state is called a triplet state. 

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 ... 

In an atomic term symbol the value of L = 1,2,..., etc. is coded according to spectroscopic notation as 5, P, D,F,G,... etc. (alphabetically for L > 3). Likewise, each atomic state can be characterized by a total electronic spin quantum number S,... 

The numerical value of the quantity 25 + 1 (total multiplicity) is used as a left superscript with the corresponding term code to define the total atomic term symbol, e.g. for L = 2 and 5 = 1, the term symbol is ZD. Closed subshells make no contribution to L and 5 and may be ignored. 

The term symbol summarizes the properties of any state and also permits a concise representation of spectral transitions. It consists of an upper case letter (S, P, D. ..) to represent the net orbital angular momentum (L) and a number written as a superscript on the upper left to indicate spin multiplicity (i. e. the number of possible orientations of total spin of the atom). L is zero for Fe " (no angular momentum) and 2 for Fe ". The spin multiplicity is defined as (2S -i- 1) S = 5/2 and 2 for Fe " and Fe ", respectively. The ground state term symbol for Fe " is, therefore, 85 2 and for Fe " it is 04. The subscript on the right is the value J. 

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. 

For multielectron atoms, the term symbol for an energy state is represented as... 

A.12-1 for a brief review of atomic-spectroscopic notation). In a given term-symbol, T will be S, P, D, F, or G etc. depending on whether the total electronic orbital angular-momentum quantum number L is 0, 1,... 

A. 12-1. Spectroscopic states end term symbols for meny-electron atoms or ions... 

As the electronic energy of an atom or ion will depend on the quantum numbers L, 5, and J, we designate the various energy states which may arise from a given electronic configuration by what is known as a spectro-scopic term symbol ... 

Atomic States, Term Symbols, and Hand s Rule... 

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