Cluster Hamiltonian

Hmi is the i-th cluster hamiltonian referred to its space fixed frame with axes parallel to the laboratory frame. Kcmi is the i-th cluster kinetic energy operator with total mass Mj. The existence of electronic wave functions for each system is taken for granted as their spectra can be determined in isolation. 

Perturbation Theory Energies from the Coupled Cluster Hamiltonian... 

The strategy adopted in the work of Wolverton (1999, 2000) follows in the tradition of the models introduced in chap. 6. In particular, a cluster Hamiltonian which includes the energy cost of elastic distortions is fitted on the basis of a series of first-principles calculations. The set of structures used to effect this fit include special quasirandom structures, a clever idea introduced in a way that allows periodic structures to mimic their random counterparts, supercells including Cu layers and a variety of short period superlattices. The resulting effective... 

Summarising, the valence-only spin-orbit CGWB-AIMP embedded cluster Hamiltonian, which results from choosing the CGWB-AIMP for the isolated cluster, reads ... 

This is the Hamiltonian used in the calculations presented in Section 3. Simple changes in it, which are explicit in 2.1.2, would lead to a DKH-AIMP embedded cluster Hamiltonian. Embedding AIMPs have been obtained for a number of halide and oxide crystals [37]. AIMP embedded cluster calculations can readily be performed with the MOLCAS code [15]. 

Calculated spectroscopic constants of the Sf and 6d manifolds of Cs2ZrCl6 (PaCl6) corresponding to the CGWB-AIMP spin-orbit embedded cluster Hamiltonian. Available experimental data are shown in parentheses. ... 

The isolated cluster Hamiltonian can be either the non-relativistic many-electron Hamiltonian or a suitable relativistic choice, both in their all-electron versions or in any effective core potential version. We will discuss later. The embedding potential acting on the cluster electrons reads ... 

Our choices of relativistic isolated cluster Hamiltonian allow us to write the embedded-cluster Hamiltonian of equation 9.1 as a sum of spin-free and spin-orbit coupling Hamiltonians,... 

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