MO Models for the Description of Light Absorption

The determination of state energies and transition moments requires the knowledge of the wave functions o( ) and f(g) of the ground state 0 and the excited (final) state f. In general, the exact wave functions are not known, but nowadays approximate semiempirical or even ab initio LCAO-MO-SCF-CI wave functions are fairly easily available for most molecules. 

These wave functions are obtained starting with atomic orbitals (AOs) from which molecular orbitals (MOs) are formed as linear combinations by application of the self-consistent field (SCF) method  

Multiplying each MO with one of the spin functions a and p yields the spin orbitals % j) = and V /O ) = Here, the space 

The configurational functions of all three components of the triplet state are listed on the three lines of Equation (1.17). From top to bottom, they correspond to the occupation of the MOs 0, and 0, with two electrons with an a spin, with one electron each with a and jS spin, and with two electrons with a p spin. The z component of the total spin is equal to M5 = 1,0, and — 1, respectively. The three triplet functions are degenerate (i.e., have the same energy) in the absence of external fields and ignoring relativistic effects (i.e., with a spin-free Hamiltonian). For our purposes, it is therefore sufficient to consider only one of the components, e.g., the one corresponding to Ms = 0. 

Finally, states of given multiplicity M = IS + 1, e.g., singlet (S = 0) and triplet (5=1) states, may be described by a linear combination of configurational functions of appropriate multiplicity and symmetry  

Here can be either the ground configuration t o or any of the singly or multiply excited configurational functions d ,, etc. The coefficients C  

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