Triplet state, orthogonal

An alternative scheme (Scheme 7) proposed by Lenoble and Becker [56] will be developed and shown in the next section when we discuss the nonpolar solvent case. However, for an immediate comparison, in Scheme 7 the triplet state that was oxygen quenched is assigned to a nonplanar transient historically named X, which has an orthogonal spiropyran type of conformation, as opposed to the proposed triplet merocyanine of Corner and Chibisov. 

The 5(7 function is best described as a nonbonding orbital located principally on the C atom. In Table 16.8 the 27t orbital is the virtual orbital from the ground state RHF treatment. The primed orbitals on H are the same as we have used before, but those on CO are based upon an ROHF n jt calculation of the first triplet state. The raw 5a, 5a, lit, and lit taken directly from the calculations will not work, however. Their overlaps are much too large for an S matrix of any size (> 2 or 3) to be considered nonsingular by standard 16-place accuracy calculations. Therefore, for each high-overlap pair the sum and difference were formed. These are orthogonal, and do not cause any problems. 

The state R in Equation 6.4 strictly keeps the HL wave function of the product P, and is hence a quasi/spectroscopic state that has a finite overlap with R. If one orthogonalizes the pair of states R and R, by, for example, a Graham—Schmidt procedure (see Exercise 6.3), the excited state becomes a pure spectroscopic state in which the A—Y is in a triplet state and is coupled to X to yield a doublet state. In such an event, one could simply use, instead of Equation 6.5, the spectroscopic gap Gs in Equation 6.6 that is simply the singlet—triplet energy gap of the A—Y bond ... 

Here, x, y, and z are the three orthogonal ZF levels of the lowest triplet state. Since the reaction is much slower than the other photochemical processes, these rate equation can be solved under a pseud-steady-state approximation. The rate constant for this photoreaction at certain light level, k(I), is found to be... 

The problem of two valence electrons that are singlet-coupled is richer than the problem of two electrons triplet-coupled because the two orbitals need not be orthogonal, i.e. for the triplet state the one-electron eigenvalue problem (Eq. (6)) returns two orthonormal orbitals. Consider the singlet ground state of the hydrogen molecule. In the approximate two-determinantal wavefunction of Heitler and London (1927),... 

In spite of the fact that the method of calculation is somewhat different, the HTH model is very close to the Anderson one. This model may be seen as the reduction of the homo-(poly)nuclear Anderson model to the homo-(bi)nuclear case (A = B). The HTH model also focuses on the two-singly occupied magnetic orbitals in the triplet state [Pg.242]

The orthogonality of the magnetic orbitals in [CuVO] explains why the triplet state is the lowest but does not provide any information on the magnitude of the phenomenon. Equation (28) suggests a topological approach of this problem. 

---