Electron correlation, model description

It should be noted that CASSCF methods inherently tend to give an unbalanced description, since all the electron correlation recovered is in die active space, but none in the inactive space, or between the active and inactive electrons. This is not a problem if all the valence electrons are included in the active space, but this is only possible for small systems. If only part of die valence electrons are included in the active space, the CASSCF methods tend to overestimate the importance of biradical structures. Consider for example acetylene where the hydrogens have been bent 60° away from hnearity (this may be considered a model for ort/zo-benzyne). The in-plane jt-orbital now acquires significant biradical character. The true structure may be described as a hnear combination of the three configurations shown in Figure 4.11. 

It is important to realize that whenever qualitative or frontier molecular orbital theory is invoked, the description is within the orbital (Hartree-Fock or Density Functional) model for the electronic wave function. In other words, rationalizing a trend in computational results by qualitative MO theory is only valid if the effect is present at the HF or DFT level. If the majority of the variation is due to electron correlation, an explanation in terms of interacting orbitals is not appropriate. 

On the other hand in the exciton description occasionnally adopted by some authors to interpret the main absorption peak in the polydiacetylenes one finds x " negative and its values two orders of magnitude lower than expression 6 since electron correlation (28) is essential in the exciton model, the calculation of even the simplest optical properties becomes prohibitively complicated and the physical insight is obscured. 

The CCS, CC2, CCSD, CC3 hierarchy has been designed specially for the calculation of frequency-dependent properties. In this hierarchy, a systematic improvement in the description of the dynamic electron correlation is obtained at each level. For example, comparing CCS, CC2, CCSD, CC3 with FCI singlet and triplet excitation energies showed that the errors decreased by about a factor 3 at each level in the coupled cluster hierarchy [18]. The CC3 error was as small as 0.016 eV and the accuracy of the CC3 excitation energies was comparable to the one of the CCSDT model [18]. 

In section 2, we provide a description of the methods employed in the present study the generation of Gaussian-type basis sets, the independent particle model and the treatment of electron correlation effects, and, the computational details. Results are presented and discussed in section 3. Section 4 contains our conclusions. 

The failures of Hartree-Fock models can be traced to an incomplete description of electron correlation or, simply stated, the way in which the motion of one electron affects the motions of all the other electrons. Two fundamentally different approaches for improvement of Hartree-Fock models have emerged. 

It might be expected that methods that provide inadequate treatment of electron correlation, specifically Hartree-Fock models, would perform better here than they would in their description of reactions in which total bond count is not conserved. However, bonding changes associated with hydrogenation are great and Hartree-Fock models might still prove unacceptable. 

It is clear that proper description of the energetics of homolytic bond dissociation requires models that account for electron correlation. Are correlated models also needed for accurate descriptions of relative homolytic bond dissociation energies where the relevant reactions are expressed as isodesmic processes A single example suggests that they may not be. Table 6-15 compares calculated and measured CH bond dissociation energies in hydrocarbons, R-H, relative to the CH bond energy in methane as a standard ... 

If experimental data is used to parameterize a semi-empirical model, then the model should not be extended beyond the level at which it has been parameterized. For example, experimental bond energies, excitation energies, and ionization energies may be used to determine molecular orbital energies which, in turn, are summed to compute total energies. In such a parameterization it would be incorrect to subsequently use these mos to form a wavefunction, as in Sections 3 and 6, that goes beyond the simple product of orbitals description. To do so would be inconsistent because the more sophisticated wavefunction would duplicate what using the experimental data (which already contains mother nature s electronic correlations) to determine the parameters had accomplished. 

The difficulties are mainly caused by two problems (1) the fact that even a qualitatively correct description of excited states often requires multiconfigurational wave functions and (2) that dynamic electron correlation effects in excited states are often significantly greater than in the electronic ground states of molecules, and may also vary greatly between different excited states. For explanations of the concepts invoked in this section, see Section 3.2.3 of Chapter 22 in this volume. Therefore, an accurate modeling of electronic spectra requires methods that account for both effects simultaneously. 

The combination of the cluster model approach and modem powerful quantum chemistry techniques can provide useful information about the electronic structure of local phenomena in metal oxides. The theoretical description of the electronic states involved in local optical transitions and magnetic phenomena, for example, in these oxides needs very accurate computational schemes, because of the generally very large differential electron correlation effects. Recently, two very promising methods have become available, that allow to study optical and magnetic phenomena with a high degree of precision. The first one, the Differ-... 

We found that these more sophisticated spin-coupled calculations, which used larger basis sets with polarization functions on all of the atoms and which allowed the a orbitals to relax, produced a picture of bonding in the 7t-electron system of benzene which is practically identical to that described earlier. As before, we found six equivalent spin-coupled orbitals which are transformed into one another by successive C6 rotations. The overlaps between the orbitals, ordered cpa to cp6 around the ring, are reported in Table 1. In this case, the electron correlation effects incorporated in the spin-coupled model provide an energy improvement over the SCF description of 170 kJ mol - with a further lowering of 20 kJ mol -1 on including spin-coupled ionic structures. 

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