Wave Functions and Matrix Elements of Bichromophores

As above, the active orbitals are called ([) and ( )a on one chromophore (A) and ( )j and ([), on the other chromophore (B) (Eigure 14.4). We assume that the two chro-mophores are identical, and related by symmetry operations. The ground state wave fnnction contains symmetric and antisymmetric molecular orbitals (MO) of the type ([) [)j and [)j [), . Index i and a belong to center A, and j and b to center B. We inclnde only the relevant orbitals and write the ground state wave fnnction as 

The excited state wave fnnctions are obtained by substituting by the unoccupied MOs ([)a + ([)b and ([)j - ([), with the same spin. There are eight such substitutions, but it is sufficient to do the substitution for one of the spins, a or p, and project out the correct spin function afterward. We, therefore, substitute only P spin orbitals and obtain four new functions, two (O, and O2) with transitions polarized along the intermolecular axis (x), and two (O3 and O4) polarized perpendicular to it (y) 

FIGURE 14.4 Dimer of chlorophyll (phytyl chains not shown). The shape of the dimer is due to the charges of opposite signs coming closer hy skewing the two planes. The most important attraction is between the carboxyl group at the upper left of the lower monomer and the Mg ion at the center of the upper monomer. 

The Slater determinants of Equations 14.13 through 14.16 are added and subtracted to the wave functions of Equations 14.17 through 14.20  

The wave functions and by do not interact with the functions betx and 4 jty because of the vanishing overlap between the functions centered on A and B. 

---