Static and dynamical correlation

In the preceding discussion of the electronic structure of the hydrogen molecule, we have seen how the superposition of determinants may serve several purposes. Let us now summarize our reasons for going beyond the single-configuration representation of the electronic wave function. 

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A great deal more could be said about models - to understand behavior like strong correlation, Coulomb blockade, and actual line shapes, it is necessary to use a number of empirical parameters, and a quite sophisticated form of density functional theory that deals with both static and dynamic correlation at a high level. Often this can be done only within a very simple representation of the electrons - something like the Hubbard model [51-53], which is very common in this situation. 

In summary, it can be said that multireference Cl methods provide a balanced description of static and dynamic correlation effects. This comes at the cost of a considerably increased computational demand compared to single-reference methods. Nevertheless, a multireference approach is inevitable for systems with a genuine multiconfigurational character such as symmetric transition metal compounds. 

S(q, co). As stated earlier, such a slow tail in F(q, t) can significantly increase the friction. In calculating the friction, the effect of the inhomogeneity on the static and dynamic correlations is to be considered only for intermediate and long wavenumbers. The small wavevector limit probes the collective dynamics of the solvent, and hence it is the average friction which contributes in this region. It is fair to assume that qa 1 separates small from intermediate wavenumber regime. 

BOVB - A valence bond method incorporating static and dynamic correlation effects... 

DFT-like approximation techniques might provide a Fock-like Agff operator that can incorporate static and dynamic correlation effects of excited states in a mean-field sense. 

A unified framework for treating static and dynamical correlation is the concept of a restricted active space (RAS) [4]. As for CAS wave functions, the orbitals of RAS wave functions are divided into three classes - inactive, active and secondary orbitals. In addition, there is a further subdivision of the active orbitals into three categories - the RASl, RAS2 and RAS3 orbitals. In the construction of the RAS wave function, a lower limit is placed on the allowed number of... 

The energy that cannot be accounted for within the HF procedure is then defined as the correlation energy. It consists of two components, namely static and dynamic correlation. Dynamic correlation energy is associated with the fact that within HF, electrons are not kept sufficiently apart in other words it relates to the interaction between electrons in the system. Static correlation is associated with the use of a single determinant. The underestimation of the static correlations arises from the fact that there may be several almost degenerate frontier orbitals for which the assignment of occupancy cannot be unambiguously done within HF. 

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. 

ZaccareUi E., Eoffi G., Dawson K.A., Buldyrev S.V., Sciortino F, and Tartaglia P. 2003. Static and dynamical correlation functions behaviour in attractive colloidal systems from theory and simulation. J. Phys. Condes. Matter 15 S367-S374. 

The errors associated with variational CCD are significantly larger in the double zeta basis (Fig. 2) than in die minimal basis (Fig. 1). This single trial wave function can do a near quantitatively accurate job of approximating the valence space (static) correlation (which is all that is present in the STO-3G basis), but is less successful in reproducing both static and dynamic correlation in the larger DZ basis. 

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