Mixed-symmetry states values

Even at high n s one needs to follow the system for many orbital periods if one is to mimic the experimental results. The difficulty is compounded if one measures the time in units of periods of the core motion. This suggests that the time evolution be characterized using the stationary states of the Hamiltonian rather than propagating the initial state. We have done so, but our experience is that in the presence of DC fields of experimental magnitude (which means that Stark manifolds of adjacent n values overlap), and certainly so in the presence of other ions that break the cylindrical symmetry and hence mix the m/ values, the size of the basis required for convergence is near the limit of current computers. In our experience, truncating the quan-... 

The condition -M + q + M = 0 determines which non-diagonal matrix elements will occur in the energy matrix for a given symmetry (the -values are constrained by symmetry). The non-diagonal matrix elements are responsible for the fact that M will not remain a good quantum number for a lanthanide ion in a crystal field. The wave function of a crystal-field level will be a sum of states M + mq m is an integer). To classify the M states which can be mixed by the crystal-field Hamiltonian, the crystal quantum number jx has been introduced by Hellwege (1949) ... 

We hope that by now the reader has it finnly in mind that the way molecular symmetry is defined and used is based on energy invariance and not on considerations of the geometry of molecular equilibrium structures. Synnnetry defined in this way leads to the idea of consenntion. For example, the total angular momentum of an isolated molecule m field-free space is a conserved quantity (like the total energy) since there are no tenns in the Hamiltonian that can mix states having different values of F. This point is discussed fiirther in section Al.4.3.1 and section Al.4.3.2. 

The major contribution to the components of the D tensor as well as the deviations of the g values from 2.0023 arises from the mixing of ligand field states by SOC other contributions to D result from direct spin-spin coupling, which mixes states of the same spin S. The D tensor and the g matrix both carry chemical information as they are related to the strength and symmetry of the LF, which is competing and counteracting to the effects of SOC. Details on the chemical interpretation of the parameters by quantum chemical means is found in Chap. 5. 

Conventional EPR techniques have been successfully used to measure the D and E values of matrix-isolated carbenes in the ground triplet state because the steady-state concentration of triplet species is sufficiently high in the system. The technique cannot be used, however, for excited species having triplet hfetimes of the order of 10-100 ns, since their steady-state concentration is too low. The D parameters are estimated from the external magnetic field effect on the T—T fluorescence decay in a hydrocarbon matrix at low temperamre. The method is based on the effect of the Zeeman mixing on the radiative and nonradiative decay rates of the T -Tq transition in the presence of a weak field. The D values are estimated by fitting the decay curve with that calculated for different D values. The D T ) values estimated for nonplanar DPC (ci symmetry) is 0.20... 

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