Self-consistent field theory accuracy

The accurate calculation of these molecular properties requires the use of ab initio methods, which have increased enormously in accuracy and efficiency in the last three decades. Ab initio methods have developed in two directions first, the level of approximation has become increasingly sophisticated and, hence, accurate. The earliest ab initio calculations used the Hartree-Fock/self-consistent field (HF/SCF) methodology, which is the simplest to implement. Subsequently, such methods as Mpller-Plesset perturbation theory, multi-configuration self-consistent field theory (MCSCF) and coupled-cluster (CC) theory have been developed and implemented. Relatively recently, density functional theory (DFT) has become the method of choice since it yields an accuracy much greater than that of HF/SCF while requiring relatively little additional computational effort. 

The substitution of Eqs. (17) into (15) makes the semi-axes of the equilibrium conformational ellipsoid identical and equal to the undeformed Flory coil radius x° = R, . Let us underline two important circumstances. First, SARW statistics leads to the same result, that is, to Eq. (2), that Flory method, which takes into account the effect (repulsion) of the volume interaction between monomer links in the self-consistent field theory. However, as it was explained by De Gennes [6], accuracy of Eq. (2) in Flory method is provided by excellent cancellation of two mistakes top-heavy value of repulsion energy as a result of neglecting of correlations and also top-heavy value of elastic energy, written for ideal polymer chain, that is in Gaussian statistics. Additionally, one must note, that Eq. (2) is only a special case of Eq. (15), which represents conformation of polymer chain in the form of ellipsoid with semi-axes x° 4- allowing to consider this conformation as deformed state of Flory coil. 

It is evident that the approach described so far to derive the electronic structure of lanthanide ions, based on perturbation theory, requires a large number of parameters to be determined. While state-of-the-art ab initio calculation procedures, based on complete active space self consistent field (CASSCF) approach, are reaching an extremely high degree of accuracy [34-37], the CF approach remains widely used, especially in spectroscopic studies. However, for low point symmetry, such as those commonly observed in molecular complexes, the number of CF... 

A question of philosophy arises concerning the molecular properties to be predicted by semiempirical treatments. On the one hand, the molecular orbital NDO methods were designed to mimic minimum basis set ab initio self-consistent field (SCF) property calculations parameters were chosen accordingly. Although internally consistent, this procedure is limited in accuracy by the minimum basis ab initio SCF results themselves. An alternative approach is to fit, and predia, measured physical properties. This is not internally consistent because experimental values cannot, in principle, be obtained from self-consistent field molecular orbital theory, regardless of basis set, because of the lack of elearon correlation. Furthermore, experimental values of properties obtained at room temperature cannot be equated to those calculated for 0° K. Nonetheless, the relatively high level of accuracy that can be achieved makes such an approach useful, and that is why it has been pursued by Dewar and co-workers in their series of M(odified)NDO methods. 

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