Correlation diagrams limitations

Figure 3-17. A partial correlation diagram for d showing weak- (left) and strong-field (right) limits for spin-triplet terms.

Fig. 14. Energy level and correlation diagram of the C2H5 photodissociation system in C8 and C v symmetry. Upper limits of the adiabatic energies of the A2A (3s) and B2A (Sp) states are based on absorption spectra. The crossing of the 2B2 and 2Ai states in Civ symmetry becomes an avoided intersection in Cs. The Biu state of C2H4 is reduced to B2 in C2v when the 2 axis is chosen to be perpendicular to the C2H4 plane. (From Amaral et al.39)...

With this definition, due to Child and Halonen (1984), local-mode molecules are near to the = 0 limit, normal mode molecules have —> 1. The correlation diagram for the spectrum is shown in Figure 4.3, for the multiplet P = va + vb = 4. It has become customary to denote the local basis not by the quantum numbers va, vh, but by the combinations... 

Figure 4.3 Correlation diagram between the local- and normal-mode limits as a function of the parameter E,. Note how the degeneracies typical of the local-mode limit are split and as % —> 1 become the almost harmonic spacings characteristic of the normalmode limit.

Fig. 6. Orbital correlation diagram for the DHP-cis-stilbene conrotatory path. R is the C(4a) — C(4b) separation. The dotted line indicates the ground state occupancy limit. The molecular orbitals were computed by the Extended Hiickel method )...

If we imagine the nuclei to be forced together to = 0, the wave function Is A + Iss will approach, as a limit, a charge distribution around the united atom that has neither radial nor angular nodal planes. This limiting charge distribution has the same symmetry as the Is orbital on the united atom, Helium. On the other hand, the combination Isa Iss has a nodal plane perpendicular to the molecular axis at all intemuclear separations. Hence its limit in the united atom has the symmetry properties of a 2p orbital. A simple correlation diagram for this case is ... 

Fig. 2. Correlation diagram of the doublet states between weak (left) and strong (right) spin-orbit coupling. In the strong coupling limit the splitting pattern is determined by the pseudo-./ quantum number...

Figure 8.15. Correlation diagram between levels of a rigid rotor K = 0 (water dimer with Cs symmetry in the nontunneling limit), a rotor with internal rotation of the acceptor molecule around the C2 axis (permutation-inversion group G ), and group G16. The arrangement of levels is given in accordance with the hypothesis by Coudert et al. [1987], The arrows show the allowed dipole transitions observed in the (H20)2 spectrum. The pure rotational transitions E + (7 = 0) - E (J = 1) and E (7 = 1) <- E + (/ = 2) have frequencies 12 321 and 24 641 MHz, respectively. The frequencies of rotationtunneling transitions in the lower triplets AI (7 = 1) <- A,+ (7 = 2) and A," (7 = 3) <- A,+ (7 = 4) are equal to 4863 and 29 416 MHz. The transitions B2(7 = 0)<- B2(7 = l) and BJ(7 = 2) <- B2 (7 = 3) with frequencies 7355 and 17123 MHz occur in the higher multiplets.

Correlation diagram A diagram which shows the relative energies of orbitals, configurations, valence bond structures, or states of reactants and products of a reaction, as a function of the molecular geometry, or another suitable parameter. An example involves the interpolation between the energies obtained for the united atoms and the values for the separated atoms limits. 

Similarly, irreducible representations may be obtained for the strong-field limit configurations (in our example, t2g, hg g and Cg ). The irreducible representations for the two limiting situations must match each irreducible representation for the free ion must match, or correlate with, a representation for the strong-field limit. This is shown in the correlation diagram for in Figure 11-3. 

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