Notations Mulliken notation

It is also common to represent these same two-electron integrals in a notation referred to as Mulliken notation in which ... 

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 ... 

In this equation, the Mulliken notation for the repulsion integrals is used, that is ... 

Linear molecules belong to either 6 or the character tables are given in Section 9.12. The operation Ca(z) is a rotation by an angle a about the CM axis. In addition to the Mulliken notation, the spectroscopic symbols 2,n,A,... are also given. As we saw in Section 1.19, apart from spin degeneracy, 2 electronic levels are nondegenerate (A), whereas... 

The IRs are labeled using both Bethe and Mulliken notation. 

In the groups C4v, D3h, and D3d which E1, M1, and E2 transitions are allowed from a T i ground state In each of the three groups, identify the ground state in Mulliken notation. For the El transitions, state any polarization restrictions on the radiation. 

Table 3.17 Mulliken notation for Tj and Tj for the dihedral family of groups. Tj is the character of the space spanned hy (x iy)J...

Configuration Mulliken Notation Group Theoretical Label... 

Fig. 3.5/ and 6d manifolds in an octahedral field and their correlation with free ion one-electron levels. Note that the crystal field lowers the energy of the 6d levels (relative to 5J) prior to splitting. Bethe notation is used for the Kramers s doublets and Mulliken notation for the spin-free Hamiltonian states, as usual. 

If we abbreviate the diagonal matrix elements of the one-electron part of the Hamiltonian with respect to as Hkk and use the Mulliken notation for two-electron integrals, we get the following expectation values Eavsq for Papsg, Ejf for and Eo for the single Slater determinant. In all cases we limit ourselves to a closed-shell state and we assume the coefficients to be real. 

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