Singlet 5 term

Some of the corresponding combinations of singlet terms and of intercombinations between singlet and triplet terms of Pb III have been found by the writer. A more comprehensive account of the spectra of mercurylike atoms will be given at a later date. 

As it is known, the minima of the HS and LS terms lie on the right and on the left positions relative to the cross-section point of the pure electronic quintet and singlet terms of the d-shell in Fe(II) complexes. Systematic error may be due to some shift of that point from its true position. We obtained a negative value of the mean error which is an indication that the cross-section point is shifted towards shorter bond lengths. Thus, moving... 

Another study (12) concerns the nominally tetrahedral complex, bis(/V-isopropylsalicylidene)nickel(II) shown in Fig. 14. The principal crystal susceptibilities over the temperature range 20-300°K have been fitted, as shown in Fig. 14, within the complete spin-triplet basis 3F + 3P (further calculations demonstrated the unimportance of including spin-singlet terms in the model) using the parameter set B f k, e (0), eCT(N), e n(N), e i(N), e,m(0), e i(0). 

Tetrahedral Ni11 complexes are well established. There is a band in the near IR which arises from 3A2 -3Tl (e 20) which is usually simple, and another, often more complex, in the visible at —15000 cm-1 (e ss 100) which is assigned to 37j(i>)<-37 1.38>67 The lowest-energy band, 3T2 -3TX, is rarely observed. The value of —410 cm-1 for Dq in NiCl42- is typical, as is the value of B/B0 — 0.75. The transitions to singlet terms may be quite strong, e == 1. 

Let us now consider the second mechanism, namely, the appearance of the electronic contribution gj due to the interaction with the paramagnetic electronic states. In particular, the singlet terms 1II and of one parity (either u u or g - g) interact because of the non-zero matrix elements of the electron-rotation operator [—l/(2/iro)](J+L- + J L+), where // is the reduced mass, ro is the internuclear distance (in atomic units) and the cyclic components of the vectors are defined in the same way as in [267] = Lx iLy, = Jx iJy connecting the x and y... 

Figure 1.20. Electronic singlet term system for I- and 2-phenylnaphthalene calculated for ground and excited-state geometries. The weakly allowed character of transitions between the ground state and the L state is indicated by broken arrows (by permission from Gustav et al., 1980).

In the simplest adiabatic case with an orbital singlet term, potential energy of the crystal lattice is parabolic with one minimum point. At low temperatures, vibrations of the lattice are localized at the bottom of this well, and as a rule, the so-called harmonic approximation applies. This corresponds to the so-called polaron effect and brings us to the concept of electrons coated with phonons. 

The energy levels for the calcium atom are shown in Fig. 24.10. These levels comprise two groups, singlets and triplets. Since the selection rule, AS = 0, permits no change in multiplicity, transitions between a singlet term and a triplet term are forbidden. Consequently, the emission spectrum exhibits two independent series of lines. One series results from transitions between singlet terms and the other from transitions between triplet terms. 

We shall now apply Eq. (112) to compute the reduced matrix element within the Ti term, the latter arsising from the electronic configuration t e. A single electron in an e-orbital can produce only term, namely, E. The four electrons comprising t may be shown to give rise to Ai, E, iTa and Ti. The E cannot combine with any of the singlet terms to form the quartet term reduced matrix element has the form... 

In the case of the singlet term. = 1, because J = L. Thus, the difference between the energy levels is iXgB and is independent of the symbol. This is visualized in Figure 11. According to the selection rule Amy = 0, 1, three... 

Figure 11 The splitting of the singlet term in a magnetic field and the allowed transitions...

On passage from the alkali metals to the alkaline earths the number of electrons in the optical system may reasonably be supposed to increase from one to two. With two electrons, 8 may have the values J = 0, or = 1. With 8 = 0 there is only one value of L- -8 for a given value of L. This means singlet terms (whatever value L itself may actually have). With N = 1, the values of the resultant of L and 8 can be L, or i—1, that is to say there is a triplet... 

To reduce this microstate table into its component free-ion terms, note that each of the terms described in the examples and in Exercise 11.2 consists of a rectangular array of microstates. To reduce the microstate table into its terms, all that is necessary is to find the rectangular arrays. This process is illustrated in Table 11.4. For each term, the spin multiplicity is the same as the number of columns of microstates a singlet term (such as D) has a single column, a doublet term has two columns, a triplet term (such as P) has three columns, and so forth. 

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