Doublets, state

In the remainder of this section, we focus on the two lowest doublet states of Li3. Figures 3 and 4 show relaxed triangular plots [68] of the lower and upper sheets of the 03 DMBE III [69,70] potential energy surface using hyper-spherical coordinates. Each plot corresponds to a stereographic projection of the... 

Calculated s ) jfor the Vibrational Levels of the First-Excited Electronic Doublet State of Lig... 

Figure 10. Level spaeitig distributions P s/ s)) for the cone states of the first-excited electronic doublet state of Li3 with consideration of GP effects [12] (a) Ai symmetry (b) A2 symmetry (c) E symmetry (d) full spectrum. Also shown by the solid lines are the corresponding fits to a Poisson distribution.

The above treatment of a three-eleetron ease shows how to generate quartet (spin states are named in terms of their spin degeneraeies 2S+1) and doublet states for a eonfiguration of the form... 

Is2s3s. Not all three-eleetron eonfigurations have both quartet and doublet states for example, the Is 2s eonfiguration only supports one doublet state. The methods used above to generate S = 3/2 and... 

It only remains to eonstmet the doublet states whieh are orthogonal to these quartet states. Reeall that the orthogonal eombinations for systems having three equal eomponents (for... 

With all semi-empirical methods, HyperChem can also perform pseudo-RHF calculations for open-shell systems. For a doublet state, all electrons except one are paired. The electron is formally divided into two half electrons with paired spins. Each half elec-... 

A — P transition, shown in Figure 7.10(b), has six components. As with doublet states the multiplet splitting decreases rapidly with L so the resulting six lines in the spectrum appear, at medium resolution, as a triplet. For this reason the fine structure is often called a compound triplet. 

The ground and first excited doublet states of 10 are both U, Flund s case (a) states (see Section 122). They both have two components, Tli/2 and Il2/2, which are inverted, the 1 3/2 component being the lower in energy. Therefore, the ground state is II2/2, with the... 

This specfmm is dominated by ftmdamenfals, combinations and overtones of fofally symmefric vibrations. The intensify disfribufions among fhese bands are determined by fhe Franck-Condon factors (vibrational overlap integrals) between the state of the molecule and the ground state, Dq, of the ion. (The ground state of the ion has one unpaired electron spin and is, therefore, a doublet state, D, and the lowest doublet state is labelled Dq.) The... 

Fig. 2. Steps in advanced oxidation process (AOPs) involving o2one, hydrogen peroxide, and uv light of 254 nm. ( D) represents the doublet state ( ) represents quantum yield, and the other numbers associated with the reaction arrows are rate constants in units of (Af-s). Dashed arrows indicate...

Figure 3.4 Illustrating an RHF singlet, and ROHF and UHF doublet states...

If a charge exchange process, A + + B- A -f- B +, occurs when the distance between the two particles is large, we expect that no transfer of translational energy takes place in the reaction and that the same selection rules govern the ionization as in spectroscopic transitions. This means that if the molecule B is in a singlet state before the ionization, the ion B + will be formed in a doublet state after ionization of one electron without rearrangements of any other electrons, at least for small molecules. 

S is the spin quantum number. The expected magnetic moments for a sextet and a doublet state are 5.91 and 1.73 respectively, measured in Bohr magnetons. The values calculated from the observed paramagnetic susceptibilities of the crystals are 5.88 for (NH aFeFg and 2.0 for... 

Correlated or geminate radical pairs are produced in unimolecular decomposition processes (e.g. peroxide decomposition) or bimolecular reactions of reactive precursors (e.g., carbene abstraction reactions). Radical pairs formed by the random encounter of freely diffusing radicals are referred to as uncorrelated or encounter (P) pairs. Once formed, the radical pairs can either collapse, to give combination or disproportionation products, or diffuse apart into free radicals (doublet states). The free radicals escaping may then either form new radical pairs with other radicals or react with some diamagnetic scavenger... 

Radicals escaping from a radical pair become uncorrelated as approaches zero. In the free (doublet) state they are detectable by e.s.r. spectroscopy. However, just as polarization of nuclear spins can occur in the radical pair, so polarization of electron spins can be produced. Provided that electron spin-lattice relaxation and free radical scavenging processes do not make the lifetime of the polarized radicals too short. 

Even the photoelectron spectroscopy of closed-shell molecules is valuable for the physical chemistry of radicals because a difference between the nth and the first adiabatic ionization potentials determines the excitation energy in a radical cation for a transition from the ground doublet state to the (n — 1) excited doublet state. 

As seen in the previous section, one characteristic of the triplet state is its paramagnetism. This alone would of course not suffice as a definition of the triplet since there are many odd-electron species that also exhibit paramagnetism but do not exist as triplets. Thus we might state that a triplet is a paramagnetic even-electron species. This still does not constitute a limiting definition since compounds containing even numbers of electrons may exhibit two, three, or even five distinct electronic levels. For example, when in a biradical the radical centers are separated by several carbon atoms as below, no interaction between the electron spins occurs and the radicals appear as two doublet states ... 

However, if the molecular configuration is such as to bring the radical centers into close contact (say, to within some critical distance D), interaction will begin and the two doublet states will collapse since the spins of the two electrons are no longer independent of each other. Quantum mechanics tells us that under these conditions the total number of states is dependent upon the sum of the spin quantum numbers for the two electrons ... 

Ceulemans, A. The Doublet States in Chromium (III) Complexes. A Shell-Theoretic View. 171, 27-68(1994). 

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