Orbital ordering approach

When the Orbital Ordering Approach is Correct and When it Can Go Wrong... 

However, solving such an equation for a solid is something of a tall order because exact solutions have not yet been found for small molecules and even a small crystal could well contain of the order of lO atoms. An approximation often used for smaller molecules is that combining atomic wave functions can form the molecular wave functions. This linear combination of atomic orbitals (LCAO) approach can also be applied to solids. 

An effective Hamiltonian for a static cooperative Jahn-Teller effect acting in the space of intra-site active vibronic modes is derived on a microscopic basis, including the interaction with phonon and uniform strains. The developed approach allows for simple treatment of cooperative Jahn-Teller distortions and orbital ordering in crystals, especially with strong vibronic interaction on sites. It also allows to describe quantitatively the induced distortions of non-Jahn-Teller type. 

Whether the orbital ordering is a cooperative phenomenon in TDAE-C60 or not still remains an open question. If it is a cooperative phenomenon, one can indeed apply the approach of Asei et al. [122] with a starting Hamiltonian... 

In this article, we discuss spin, charge and orbital orders in transition metal oxides, in particular, in the rare-earth manganites which have become famous since 1993 owing to the phenomenon of colossal magnetoresistance (CMR) exhibited by them (Rao Raveau 1998). We also touch upon the issue of electronic inhomogeneities we discuss the signatures of the presence of such inhomogeneities and theoretical approaches to understand the same. 

We shall compare the potential curves obtained with the two different methods. Second order perturbation theory (CASPT2) has been used to estimate the remaining correlation effects in the FCI calculation with the smaller number of orbitals. This approach will be described in detail below. The spectroscopic constants are presented in Table 5-2. As can be seen, the two results are almost identical. The results are obviously far from experiment because of the small basis set used but that is not relevant to the present discussion. With the smaller number of orbitals we can now perform much more advanced calculations using larger basis sets and approach the experimental values. As an illustration, such a result is also given in the table. 

Abstract Keeping in mind the pedagogical goal of the presentation the first third of the review is devoted to the basic definitions and to the description of the cooperative Jahn-Teller effect. Among different approaches to the intersite electron correlation in crystals the preference is with the most fundamental and systematic Hamiltonian shift transformation method. Order parameter equations and their connection to the crystal elastic properties and to the orbital ordering are considered. An especial attention is paid to the dynamics of Jahn-Teller crystals based on the coupled electronic, vibrational, and magnetic excitations which are of big interest nowadays in orbital physics. 

Orbital Ordering Versus the Traditional Approach in the Cooperative Jahn-Teller Effect A Comparative Study... 

---