Term symbol

Seetion treats the spatial, angular momentum, and spin symmetries of the many-eleetron wavefunetions that are formed as anti symmetrized produets of atomie or moleeular orbitals. Proper eoupling of angular momenta (orbital and spin) is eovered here, and atomie and moleeular term symbols are treated. The need to inelude Configuration Interaetion to aehieve qualitatively eorreet deseriptions of eertain speeies eleetronie struetures is treated here. The role of the resultant Configuration Correlation Diagrams in the Woodward-Hoffmann theory of ehemieal reaetivity is also developed. 

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. 

Section 3 Electronic Configurations, Term Symbols, and States... 

A2, and 1 Ai term symbols are Pauli forbidden. Onee again, the methods needed to identify whieh term symbols arise in the equivalent-eleetron ease are treated later. 

One needs to learn how to tell whieh term symbols will be Pauli exeluded, and to learn how to write the spin-orbit produet wavefunetions eorresponding to eaeh term symbol and to evaluate the eorresponding term symbols energies. 

Given the box entries, one ean identify those term symbols that arise by applying the following proeedure over and over until all entries have been aeeounted for ... 

Knowing an S, L eombination, one knows the first term symbol that arises from this eonfiguration. In the p2 example, this is P. 

After identifying as many sueh states as possible by inspeetion, one uses L+ and S+ to generate states that belong to the same term symbols as those already identified but whieh have higher or lower Ml and/or Ms values. 

If, after applying the above proeess, there are term symbols for whieh states have not yet been formed, one may have to eonstruet sueh states by forming linear eombinations that are orthogonal to all those states that have thus far been found. 

The term symbol is handled in like fashion. Beginning with the Ml = 2 state IpiapiPI, one applies L. to generate the Ml = 1 state ... 

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... 

Finally, for linear molecules in Z states, the wavefunctions can be labeled by one additional quantum number that relates to their symmetry under reflection of all electrons through a ay plane passing through the molecule s Coo axis. If F is even, a + sign is appended as a superscript to the term symbol if F is odd, a - sign is added. 

A. Term Symbols for Non-Degenerate Point Group Symmetries... 

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... 

For the given orbital oeeupations (eonfigurations) of the following systems, determine all possible states (all possible allowed eombinations of spin and spaee states). There is no need to form the determinental wavefunetions simply label eaeh state with its proper term symbol. One method eommonly used is Harry Grays "box method" found in Eleetrons and Chemical Bonding. 

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

Denoting J as a term symbol subseript one ean identify all the levels and subsequent (2J + 1) states ... 

The term symbols are G, P, D, P, and S. The L and S angular momenta ean be veetor eoupled to produee further splitting into levels ... 

As illustrated in this ehapter a p2 eonfiguration (two equivalent p eleetrons) gives rise to the term symbols 2p, iD, and S. Coupling an additional eleetron (3d to this p2... 

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