The configuration-interaction model

In the Cl method, the wave function is constructed as a linear combination of determinants or CSFs 

As described in Section 4.2, this condition is equivalent to a set of eigenvalue equations for the energy and the expansion coefficients 

In Cl theory, only the configuration expansion is variationally optimized - the orbitals are generated separately in a preceding Hartree-Fock or MCSCF calculation and are held fixed during the optimization of the configuration expansion. In contrast, the MCSCF wave function of Section 5.5 

The FCI wave function is often dominated by a single reference configuration, usually the Hartree-Fock state. It is then convenient to think of the FCI wave function as generated from this reference configuration by the application of a linear combination of spin-orbital excitation operators 

we may charaeterize the determinants in the FCI expansion as single (S), double (D), triple (T), quadruple (Q), quintuple (5), sextuple (6) and higher excitations relative to the Hartree-Fock state. 

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Spin-correlated crystal field 276 4.5. The configuration interaction model ... 

The configuration-interaction model simulated by ATOME was utilized by Parent et al. (1994) to prove the reality of copper pairs in CuZr2(P04)3 they carried out a calculation on the Cu -Cu system and reproduced in a quite satisfactory way all the data of the luminescence spectra, i.e. band positions and transition intensities. 

One of the major ingredient for the understanding of alloy phase stability is the configurational energy. Models have been proposed to represent the configurational energies in terms of effective multisite interactions, in particular effective pair interactions (EPls). 

As usual, the Hartree-Fock model can be corrected with perturbation theory (e.g., the Mpller-Plesset [MP] method29) and/or variational techniques (e.g., the configuration-interaction [Cl] method30) to account for electron-correlation effects. The electron density p(r) = N f P 2 d3 2... d3r can generally be expressed as... 

This chapter reviews models based on quantum mechanics starting from the Schrodinger equation. Hartree-Fock models are addressed first, followed by models which account for electron correlation, with focus on density functional models, configuration interaction models and Moller-Plesset models. All-electron basis sets and pseudopotentials for use with Hartree-Fock and correlated models are described. Semi-empirical models are introduced next, followed by a discussion of models for solvation. 

Conceptually, the most straightforward approach is the so-called full configuration interaction model. Here, the wavefunction is written as a sum, the leading term of which, Fo, is the Hartree-Fock wavefunction, and remaining terms, Fs, are wavefunctions derived from the Hartree-Fock wavefunction by electron promotions. 

Correlated Models. Models which take implicit or explicit account of the Correlation of electron motions. Moller-Plesset Models, Configuration Interaction Models and Density Functional Models... 

Size Consistent. Methods for which the total error in the calculated energy is more or less proportional to the (molecular) size. Hartree-Fock and Moller-Plesset models are size consistent, while Density Functional Models, (limited) Configuration Interaction Models and Semi-Empirical Models are not size consistent. 

Variational. Methods for which the calculated energy represents an upper bound to the exact (experimental) energy. Hartree-Fock and Configuration Interaction Models are variational while Moller-Plesset Models, Density Functional Models and Semi-Empirical Models are not variational. 

This mixing of configurations is commonly termed configuration interaction. Since application of the configuration mixing model is non-mathematical, the cumbersome mathematical description of various wave-functions in... 

In view of the remarkably swift development of the chemistry of sulfur heterocycles, an extension of quantum-chemical calculations to various additional physical properties as well as a more systematic approach in both experimental and theoretical studies can be expected in the near future. Even though it is not possible to put forward responsibly an optimum unique set of HMO empirical parameters, Model B (8S = 1, 3C(a) = 0.1, pcs = 0.7) may perhaps be recommended for the beginning of a systematic treatment. As for other parameters, the set given by Streitwieser4 can be recommended the value 0.5 has proved suitable for p8S. It is quite obvious, however, that such studies should develop simultaneously with application of more sophisticated methods, above all the configuration interaction method.42... 

Following Refs. [61, 62], a two-band (valence and conduction band) configuration interaction model is introduced, using a basis of monoexcited configurations on the polymer chain. These correspond to electron-hole states n) = nen h) = ne)c <8> n h)v localized at sites n and n of the chain. Here,... 

The conceptual simplicity of the configuration interaction (Cl) approaches has attracted the interest of researchers working in the field of solvation methods [2,16,17] to introduce electron correlation effects. However, despite this apparent simplicity, the application of the Cl scheme to solvation models raises some delicate issues, not present for isolated molecules. 

In the following we want to focus on some problems which arise if ab initio methods are used to calculate isotropic hfcc s. We will mostly concentrate on approaches where the Configuration Interaction (Cl) method is used in various versions. To illustrate the performance of other theoretical methods such as M0ller-Plesset perturbation theory (MP), Coupled Cluster methods (CC) or quadratic Cl (QCISD), the results obtained with those approaches will be compared for a few model systems. Because an understanding of the influences... 

The energies of the unperturbed (sub)states have been defined above. Ha is the configuration interaction Hamiltonian, which describes essentially the electron-electron interaction [128]. The off-diagonal terms are taken as the perturbation. The aim of this discussion is, at least for this simple model, to present the structure of the corresponding perturbational formulas. For example, it will be shown that different energy denominators occur, which are connected to the different states involved. In this model, we neglect any diagonal contributions to the model Hamilton operator and treat the matrix elements as real for simplicity. 

This configuration interaction model will have an important bearing on the intensities of the bands at 16 and 20 kK. In derivatives which lie to the left of Fig. 10, the 16 kK band will be mostly charge transfer, but as we move towards the right-hand side of the diagram, this band will acquire an increasing proportion of n - n character. Since we suppose... 

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