Electronic triplet states

The expressions for the rotational energy levels (i.e., also involving the end-over-end rotations, not considered in the previous works) of linear triatomic molecules in doublet and triplet II electronic states that take into account a spin orbit interaction and a vibronic coupling were derived in two milestone studies by Hougen [72,32]. In them, the isomorfic Hamiltonian was inboduced, which has later been widely used in treating linear molecules (see, e.g., [55]). 

Figure 9.18 shows a typical energy level diagram of a dye molecule including the lowest electronic states Sq, and S2 in the singlet manifold and and T2 in the triplet manifold. Associated with each of these states are vibrational and rotational sub-levels broadened to such an extent in the liquid that they form a continuum. As a result the absorption spectrum, such as that in Figure 9.17, is typical of a liquid phase spectrum showing almost no structure within the band system. 

Fig. 4. Chemistry of poly(vinyl cinnamate) negative-acting resist. Initial light absorption by the photosensitizer is followed by energy transfer to produce a pendant cinnamate group in a triplet electronic state. This combines with a second cinnamate on another polymer chain, forming a polymer—polymer...

Fig. 1. Schematic energy-level diagram for a dye molecule. Electronic states Sq = ground singlet state = first excited singlet state S2 = second excited singlet state Tj = first excited triplet state T2 = second excited triplet state EVS = excited vibrational states. Transitions A = absorption excited states ...

In the lowest optieally excited state of the molecule, we have one eleetron (ti ) and one hole (/i ), each with spin 1/2 which couple through the Coulomb interaetion and can either form a singlet 5 state (5 = 0), or a triplet T state (S = 1). Since the electric dipole matrix element for optical transitions — ep A)/(me) does not depend on spin, there is a strong spin seleetion rule (AS = 0) for optical electric dipole transitions. This strong spin seleetion rule arises from the very weak spin-orbit interaction for carbon. Thus, to turn on electric dipole transitions, appropriate odd-parity vibrational modes must be admixed with the initial and (or) final electronic states, so that the w eak absorption below 2.5 eV involves optical transitions between appropriate vibronic levels. These vibronic levels are energetically favored by virtue... 

To calculate AG = Gts - Greactant, we need and AS AHf is directly the difference in elecfi onic energy between the TS and the reactant. Except for complicated reactions involving several electronic states of different degeneracy (e.g. singlet molecules reacting via a triplet T, A5 g, is zero. 

Both CSs and CSs were also successfully generated by the fragmentation of ionized 4,5-dioxo-2-thioxo-l,3-dithione (65) and 2-thioxo-l,3-dithiole (66) (90JA3750). Tire three sulfur atoms in the anion and cation radicals were chemically equivalent, suggesting that they take the D h (or C2u) form (67 or 68). On the other hand, under similar conditions, 3-thioxo-1,2-dithiole (69) yielded two isomeric cation radicals the (or 2 ) form and the carbon disulfide 5-sulfide form (70). Ab initio calculations on three electronic states of CS3 at the 6-31G -l-ZPVE level indicated that the C21, form (68) was more stable than the carbon disulfide 5-sulfide form (70) in the neutral (both singlet and triplet states) and the anion radical states, but 68 was less stable than 70 in the radical cation state. 

Postulate (i) follows from the fact that when two radicals, produced by whatever means, encounter each other, the interaction of the electron spin of one radical with that on the other radical can give rise to two mutually exclusive spin states, triplet and singlet. Random combination of the two possible electron spin states for the two electrons yields the three components of the triplet state, represented as T+i, To, and T i, and the singlet state, S. Throughout this article, S is assumed to be the singlet state of lowest energy. 

Reactions occurring on two (or more) electronic states can lead to the same product asymptote. These pathways may occur if more than one electronic state correlates adiabatically to the same asymptote (e.g., single or triplet coupling of two approaching species), or if nonadiabatic transition(s) move population from one state to another. Here, I make the distinction that products of the same structural formula do not represent the same exit channel if they are produced in different electronic states. For example, in the reaction... 

Figure 7. Potential energy diagram of CH2O. After excitation to specific rovibrational levels of Si, internal conversion leads to highly excited molecules in the ground electronic state So, whereas intersystem crossing populates the lowest triplet state Ti.

In metal complexes of FTF5 and DPA, both single two-electron and double one-electron redox couples were observed. [(FTF5)Zn2] is diamagnetic, whereas the EPR spectmm of [(DPA)Zn2] was interpreted as that of a triplet that was complicated by aggregation. Why the ground electronic state of [(DPA)Zn2] is a triplet remains to be established a triplet porphyrin diradical was thought to be unique in porphyrin chemistry [LeMest et al., 1992]. 

Studies have shown that carbene reactivity toward a wide variety of substrates is dramatically affected by the nature and multiplicity of the electronic state. - Similarly, the structure, electronic state, thermochemical stability, and reaction kinetics of both singlet and triplet carbenes can be significantly affected by the R-substituents. If R provides steric hindrance, the carbene center can be shielded to slow down inter-molecular reactions (kinetic stabilization). Additionally, bulky and/or geometrically... 

Interestingly, it was possible to probe the spin-forbidden component of the tunneling reaction with internal and external heavy atom effects. Such effects are well known to enhance the rates of intersystem crossing of electronically excited triplets to ground singlet states, where the presence of heavier nuclei increases spin-orbit coupling. Relative rates for the low-temperature rearrangements of 12 to 13 were... 

These results clearly showed that biradical 83 was not formed from ground state triplet nitrene 82, either classically or via tunneling. The anthors specnlated that the biradical might have been prodnced from a higher energy electronically excited nitrene than was available from irradiation of 82. Alternatively, it is possible that the biradical might have formed directly from excited azide. 

The nitrogen analogs of carbenes are called nitrenes. As with carbenes, both singlet and triplet electronic states are possible. 

Scheme 1 Electronic states involved in the absorbtion bands in the region of the first singlet—triplet intersection for octahedral, tetragonal and trigonal complexes of nickel(II).336 Solid arrows denote spin-allowed absorbtion transitions, dotted arrows connect pairs of interacting levels. (reprinted with permission from ref. 336 1998, American Chemical Society).

Figure 5.11. Geometry of formaldehyde in its (a) ground, (b) first excited singlet, and (c) first excited triplet electronic states.

With the exception of the a-naphtho position, bridging to aromatic sites is very unfavorable in the barrelene-semibullvalene rearrangements. If we exclude anthraceno-vinyl bridging, there is insufficient energy available (43 kcal/mole) for vinyl-vinyl bridging (58 kcal/mole) in the lowest anthrabarrelene triplet state. Consequently, it is not surprising that the 7 state is unreactive. In contrast, (76 kcal/mole) and T2 (74 kcal/mole) are not subject to this limitation. Evidence in favor of one or the other of these two possible electronic states is not available. 

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