Orbitally degenerate ground state

Orbitally Degenerate Ground States. For all orbitally degenerate ground states the g values are calculated to be markedly anisotropic and to deviate substantially from 2. Thus, writing the effective orbital reduction factor as k (equivalent to k of Section 4), the g values are found (101) to be as follows for the systems shown -... 

The final application of LFMM concerns a subtle yet unexpectedly significant Jahn-Teller effect. The classic examples of Jahn-Teller distortions are associated with d9and high-spin d4 systems with orbitally degenerate ground states of E symmetry... 

In this section we have described the calculation of u (1) and 1) with TDDFT perturbed by a magnetic field. These quantities, in combination with u/0) and (0) obtained from an unperturbed TDDFT calculation, can be used with Eqs. (11, 17, 30, or 32) as appropriate to evaluate, respectively, Bj, Aj, Cj 1, or C/° 2 and thus an MCD spectrum using Eq. (33). We have explicitly avoided orbitally degenerate ground states and therefore cannot yet calculate classical C terms. This problem will be discussed in Section II.C.4 but before doing so, we will describe the calculation of MCD intensity from the imaginary part of the Verdet constant where the MCD intensity itself is calculated rather than parameters associated with the various MCD terms. 

In the context of orbitally degenerate ground states the alternative reference was termed a transformed reference via an intermediate configuration (TRIC) and the overall method was called TRIC-KS TDDFT or TRICKS-TDDFT (88). 

As noted in Section II.C.4, the calculation of C term parameters for molecules with orbitally degenerate ground states requires a rather different approach to the process applied for the other types of parameter. The iron complexes described in the last few paragraphs provided a useful opportunity to test this methodology. The calculated MCD spectra for [Fe(CN)6]3- and the two related complexes where a CN ligand is substituted by SCN-and N3 will be discussed here (89,127). 

Nickel(II) in tetrahedral symmetry has an orbitally degenerate ground state and the magnetic moments of tetrahedral complexes are expected to be substantially higher than those of six-coordinate complexes because of the larger orbital contribution. The magnetic moments are usually found to be in the range 3.3-4.0 BM at room temperature and tend to zero at very low temperatures. 

Tetrahedral and trigonal bipyramidal complexes have orbitally degenerate ground states while octahedral and square pyramidal complexes possess orbitally non-degenerate ground... 

Since the ground state of tetrahedral complexes is orbitally degenerate (37i), it can be expected that the shifts observed in NMR spectra of pseudotetrahedral complexes are due to both contact and pseudocontact contributions. Kurland and McGarvey436 have derived the equations for calculating contact and pseudocontact terms in complexes with nearly orbitally degenerate ground states. Calculations of NMR shifts in pseudotetrahedral complexes are reported in ref. 437. Selected examples of pseudotetrahedral complexes whose NMR spectra have been studied are reported in Table 28 and ref. 455. 

Many inorganic ions are not readily detected because they have orbitally degenerate ground states. Spin relaxation in these states is so rapid that the EPR spectrum cannot be observed at typical temperatures where electrochemical experiments are carried out. Temperatures of 4 K or lower are required to observe these ions. Table 29.1 lists transition metal ions that occur in nondegenerate ground states due to crystal field splittings and as such are amenable to observation. 

Case 5 Elongated tetragonal bipyramid, small Aax A, orbitally degenerate ground state needs a solution of the 12 x 12 secular equation (which is partly factored) to... 

It should be noted that several aromatic hydrocarbon ions with an unpaired electron and threefold or higher axis of symmetry, such as CgHg and CgHg are known to have orbitally degenerate ground states. Linear radicals with orbital moments, such as NO, OH, SH, NCO,... 

In the second part of this review, we have focused on systems which can be treated equally well by AI theory as Werner type complexes, but for which classical LFT breaks down or at least needs to be extended. These are systems with orbitally degenerate ground states such as tetrahedral CuCl42 (d9,2T2) and NICI42 (dx, 3Tj). 

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