Transition-dipole vector-coupling

The fact that three peroxide-to-copper charge-transfer transitions are observed in oxyhemocyanin and oxytyrosinase led us to consider the spectral effects of bridging peroxide between two Cu(II) ions. A transition-dipole vector-coupling (TDVC) model was developed that predicts that each charge-transfer state in a Cu-peroxide monomer... 

Fig. 35. Diagrammatic explanation of the transition dipole vector coupling treatment for two possible peroxide bridging geometries, /<-dioxo and ft-monooxo, and comparison to oxyhemocyanin (see text for explanation)...

Figure 8.2 Orientation of transition moments of cyanine fluorophores terminally attached to double-stranded DNA. (A) The orientation parameter K2. The transition dipole vectors for the coupled donor and acceptor fluorophore are indicated by the arrows, labeled D and A. Vector A is generated by the in-plane translation of vector A to share its origin with vector D. The definition of K2, given in Eq. (8.5), is based upon the angles shown. (B) If the fluorophores he in parallel planes, the orientation parameter simplifies to K2 — cos2 T and varies between 0 and 1. The schematic shows the limiting cases, where the transition moments are parallel (k2 = 1) and crossed (K2 — 0). If the transition moments are colinear, K2 = 4.

Each rotational state is coupled to all other states through the potential matrix V defined in (3.22). Initial conditions Xj(I 0) are obtained by expanding — in analogy to (3.26) — the ground-state wavefunction multiplied by the transition dipole function in terms of the Yjo- The total of all one-dimensional wavepackets Xj (R t) forms an R- and i-dependent vector x whose propagation in space and time follows as described before for the two-dimensional wavepacket, with the exception that multiplication by the potential is replaced by a matrix multiplication Vx-The close-coupling equations become computationally more convenient if one makes an additional transformation to the so-called discrete variable representation (Bacic and Light 1986). The autocorrelation function is simply calculated from... 

Figure 3.7. Dispersion of the 2D monolayer polariton real part (left) and imaginary part (right) of the excitonic energy renormalization RK(

IR absorptions involve elastic or Rayleigh45 or constant-energy scattering of light in more detail, the electric field vector E of the input light must couple with the transition electric dipole moment fi,f as E fi,f. If E Lp,if, then no IR transition is seen. Allowed IR transitions require that the transition moment vector fii be nonzero—i.e., that is, that the static electric dipole moment fi of the molecule change during the IR absorption. 

Fig. 4 Geometry of chlorophyll interactions for dipolar approximation, (a) Porphyrin ring of a chlorophyll molecule. The transition dipole moment for the Qy state is approximately along a vector connecting the and N/) atoms, (b) Inter-chlorophyll coupling between two chlorophylls in the dipolar approximation is determined by their transition dipole moments d/ and the vector r,j connecting their central Mg atoms, see Eq. (3).

The relative intensities of a group of spectral lines which arise in electric dipole transitions between one L-S fine structure multiplet and another may be calculated from equation (5.26). The angular factors in this expression depend on the quantum numbers (S,L,J) and (S, L, J ) of the levels involved and may be calculated by vector coupling techniques. Unfortunately the formulae so derived are themselves rather complicated and the reader is referred to standard works on atomic spectroscopy, for instance Condon and Shortley (1967), where tabulations of the relative intensities may be found. 

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