Wavefunction embedded-cluster

The last ingredient of the AIMP/SM method is (iv) an iterative procedure which leads to the minimisation of Ej fecmecryaai [Eq. (41)] with respect to the wavefunction of the embedded cluster, the positions of the cluster nuclei, and the positions of the cores and shells defining the environment, which in turn gives the positions of the ions of the environment and their electric dipole polarisation. The details of this procedure are described in Refs. [17] and [52]. 

In this Section, we will show the results of sfss CGWB-AIMP embedded cluster calculations on the structure and spectroscopy of several actinide ions in chloride hosts. Altogether, they are aimed at showing the potentialities of present days wavefunction-based ab initio methods of Quantum Chemistry in materials made of heavy element ions in solids, with several open-shell electrons and a very large number of excited states of interest. 

The methods of choice must be adequate for manifolds of electronic states that are localized around a lanthanide ion in a solid host. The combination of a solid environment, a heavy element, and 4/, 5d, and other open-shells, demands the consideration of the effects of the solid host, the use of relativistic Hamiltonians up to spin-orbit coupling, the correct treatment of static and dynamic correlation, and handling large manifolds of quasi-degenerate excited states. We decided to use embedded-cluster wavefunction theory-based (EC-WFT) methods, with a two-component relativistic Hamiltonian to be used in two-steps, a multi-configurational variational treatment of static correlation, and a multireference second-order perturbation theory treatment of dynamic correlation. 

Since the pioneering cluster calculation on the KNiFs solid of Shulman and Sugano [6] there has been a wide variety of proposals of procedures to handle relatively localized electronic states of a solid with a molecule-like Hamiltonian that includes the relevant solid host effects, depending on the type of solids and on methodological flavors (Green s functions, wavefunctions, density functional, etc.). A recent summary of practical methods can be found in Huang and Carter [7]. Here we describe our choice of embedded-cluster method, particularly useful in ionic materials. 

The Multireference Space. The calculations of the embedded-cluster wavefunctions have a first step where multiconfigurational self-consistent field wavefunctions and energies are calculated using complete and/or restricted active spaces (CASSCF [32-34] and/or RASSCF [35,36]). The lanthanide 4/, 5d, and 6s shells must be included in the active space for the calculation of the 4/, 4f 5d, and manifolds, N being the num-... 

The main drawback of the chister-m-chister methods is that the embedding operators are derived from a wavefunction that does not reflect the proper periodicity of the crystal a two-dimensionally infinite wavefiinction/density with a proper band structure would be preferable. Indeed, Rosch and co-workers pointed out recently a series of problems with such chister-m-chister embedding approaches. These include the lack of marked improvement of the results over finite clusters of the same size, problems with the orbital space partitioning such that charge conservation is violated, spurious mixing of virtual orbitals into the density matrix [170], the inlierent delocalized nature of metallic orbitals [171], etc. 

In summary, full wavefunction methods are the most accurate ab initio methods, if electronic correlation is accounted for properly and the basis set for expansion of the electronic wavefunction is sufficiently complete — this might be difficult to judge by a non-expert. Furthermore, if a cluster model is used, it needs to be of sufficient size or be properly embedded for conclusions to be representative of an extended M/C interface. 

Another type of the embedding scheme focuses only on the long-range electrostatic effect of the environment on the wavefunction of the cluster. This can be considered as a special case of the additive scheme (Es = + E °ling ). The electrostatic potential of... 

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