Embedded Cluster Approach

The intrinsic local nature of the interaction between two localized spin moments suggests the possibility to study the magnetic interactions in solids with a cluster model. In this approach, a small yet relevant piece is cut from the crystal and treated like a molecule. These bare clusters are only a reasonable choice in the case of molecular crystals, but otherwise nearly always too cmde a representation. Therefore it is necessary to account for the effect of the rest of the crystal especially when dealing with ionic or covalent lattices. Here, we will shortly review a few representative examples of the different approaches for improving the bare cluster model that find their basis in the theory of electron separability of McWeeny, the subsystem formulation of DFT of Cartona or the incremental scheme of Fulde and Stoll. 

Electrostatic embedding In the case of ionic compounds, the largest contribution to the potential exerted by the rest of the crystal on the (central region of the) cluster is due to long-range electrostatic interactions. These are accurately represented by the point charge approximation, that is, the Madelung potential  

Density-based embeddings This approach starts with a calculation on the whole system to construct an approximate yet accurate representation of the total density Plot by performing a periodic DFT calculation. Then, a guess density of the cluster is constructed from a calculation on the isolated unit or using some simple embedding scheme as described above. The total density is now divided in two parts ptot = Pi+ P2 and the one-electron embedding potential is constructed from the functional derivative of interaction energy with respect to the cluster density pi. 

WF in DFT approach is especially interesting for the application to systems with unpaired electrons because the multideterminental nature of the wave function can be rigorously treated while the embedding can be generated with DFT. 

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Ravenek W and Geurts EMM 1986 Hartree-Fock-Slater-LCAO implementation of the moderately large-embedded-cluster approach to chemisorption. Calculations for hydrogen on lithium (100) J. Chem. Phys. 84 1613-23... 

The description of defects is frequently achieved with the embedded cluster approach, where a small cluster, which includes the defect, is embedded in the surrounding bulk. This model is usefully applied when the bulk can be described with simpler methods than the embedded cluster. Embedding of a cluster can be done both with and without use of periodic boundary conditions. Therefore, the embedded cluster model can be seen merely as a modification of the first two models. 

The embedded cluster approach is based on schemes that smoothly link the quantum-mechanical solution of the cluster to the perfect crystal. Different methods have been developed based on either Green function " or group-function (localized crystalHne orbitals) " techniques. 

Pisani C, Bierkenheuer U Embedded-cluster approach to the study of catalytic reactions in zeolite cavities. Int J Quantum Cham 1995, 29 221-234. 

In the embedded cluster approach, a rigorous QM method is used to model the local... 

We have employed an embedded cluster approach in which a QM cluster was embedded into a finite nano-cluster representation of the polarisable host lattice via the shell model. Relaxation of both electronic and ionic subsystems of the host lattice is performed self-consistently with the charge density of the QM cluster calculated using the B3LYP density functional. The self-consistent scheme of calculations has been described in more details elsewhere [82,83], The QM cluster used in these studies is shown in Fig, 4,5a, All anions and all fully coordinated cations have been treated as all electron atoms using the standard 6-3IG basis set. Cations at the border of the QM cluster have been treated using Hay and Wadt effective core pseudopotentials [84] and one contracted s-function. 

The embedded cluster approach was utilized for the calculations to include the environmental effect, as it is computationally less expensive. Within the embedded cluster method, the magnitude of reorganization energies for both the charge carriers are further reduced in comparison to individual molecules due to the presence of intermolecular interactions X iectron = O.llSeV and = 0.04eV. 

Jacob, T., Geschke, D., Fritzsche, S., Sepp, W.-D., Fricke, B., Anton, J., Varga, S. Adsorption on surfaces simulated by an embedded cluster approach within the relativistic density functional theory. Surf. Sci. 486, 194—202 (2001)... 

Goumans TPM et al (2008) Hydrogenation of CO on a silica surface an embedded cluster approach. J Chem Phys 128 6... 

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