Mulliken labels

Muetterties, E. L., 223, 241 Mflller, K. A., 285 Mulliken-Jaffd electronegativities, 183-186, 258 Mulliken labels, 61 Multiplicity. 26-27 Myoglobin... 

For the function 4.2, therefore, its transformation or symmetry properties in the C2 point group are described by the characters in the top row of Table 4.1. For the C v point group there are only four different types of allowed wavefunctions or irreducible representations. Tliey are given the Mulliken labels a, 02, b, and ftj. The wavefunction of equation 4.2 therefore belongs to theai irreducible representa-... 

Here, the indices i and k, which label the spin-orbital having variables r are grouped together, and j and 1, which label spin-orbitals referring to the r variables appear together. The above permutational symmetries, when expressed in terms of the Mulliken integral list read ... 

The starting points for many conventions in spectroscopy are the paper by R. S. Mulliken in the Journal of Chemical Physics (23, 1997, 1955) and the books of G. Herzberg. Apart from straightforward recommendations of symbols for physical quantities, which are generally adhered to, there are rather more contentious recommendations. These include the labelling of cartesian axes in discussions of molecular symmetry and the numbering of vibrations in a polyatomic molecule, which are often, but not always, used. In such cases it is important that any author make it clear what convention is being used. 

The subscript labels a, b,... (i, j,...) correspond to unoccupied (occupied) bands. The Mulliken notation has been chosen to define the two-electron integrals between crystalline orbitals. Two recent studies demonstrate the nice converging behaviour of the different direct lattice sums involved in the evaluation of these two-electron integrals between crystalline orbitals [30]. According to Blount s procedure [31], the z-dipole matrix elements are defined by the following integration which is only non zero for k=k ... 

If necessary, numerical subscripts are added to the labels to distinguish the non-equivalent irreducible representations which are not distinguished by the foregoing rules. Except for the fact that the totally symmetric representation (one-dimensional unit matrices) is numbered and listed first, the numbering is arbitrary and the reader is referred to Appendix I or Mulliken s report for the internationally accepted conventions. 

We have introduced certain labels in (9.36) for the three nonequivalent irreducible representations of 63v. The conventions (formulated by Mulliken) for such labels are the following ... 

An s orbital, because it b spherical, will always be symmetric (i.e, it will remain unchanged) with respect to all operations of a point group. Thus it will always belong to a representation for which all characters are equal to I (a "totally symmetric" representation), although this is not explicitly indicated in character tables. The totally symmetric representation for a point group always appears first in its character table and has an A designation (A i. Aa,Ale> etc.). When these or any other Mulliken symbols are used to label orhitals or other one-electron functions, the convention is to use the lower case a1( a, etc. 

The nature of the interaction between alkenes and halogens (complex 26 of Scheme 10) preceding the reactions of addition of the halogens to the C=C double bond is labelled according to Mulliken s classification71 as a CT complex. The nature of the carbonium... 

The IRs are labeled using both Bethe and Mulliken notation. 

Because there is no unique principal axis in D2, the Mulliken conventions are not used in naming the representations of D2. These two groups are isomorphous and the character systems of the four IRs are identical, but corresponding representations are labeled differently, which tends to obscure rather than emphasize the isomorphism. Note that C2x and ox are corresponding elements, and so are C2y and totally symmetric representation in D2). In C2V, the Mulliken designations B and B2 are arbitrary because there are two equivalent improper binary axes normal to z. 

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