Semilocal

Mueller, C. R., J. Chem. Phys. 19, 1498, Scmilocalized orbitals. II. A comparison of atomic, molecular and semilocalized orbital methods for diatomic hydrogenfluoride. ... 

Itoh, T., and Yoshizumi, H., J. Phys. Soc. Japan 10. 201, "Application of the alternant orbital method to benzene." Construction of a determinant using the semilocalized MO and selection of the singlet component of it. 

Morita, A., and Takahashi, K., Progr. Theoret. Phys. [Kyoto) 19, 257, Theory of cohesive energy of LiH crystal—the method of semilocalized crystalline orbitals."... 

Since the CH bond orbitals are relatively distant, their interaction is very weak and the six crCH semilocalized orbitals are very close in energy. On the other hand the bond orbitals interact strongly so that the energies of the six semilocalized orbitals are spread out, with the lower ones falling well below the group of crCH orbitals. 

We nowr go one step further and allow for the mixing of semilocalized orbitals with the semilocalized orbitals of appropriate symmetry. This mixing occurs just like that of the [Pg.24]

The electronic interactions between the MMe3 substituents and the sulphur rm orbital were analysed121 on the basis of the semilocalized orbitals approximation in two series of the structures S(MMe3)2 and MeSMMe3 (M = C, Si, Ge, Sn, Pb). 

The approach that we take to the question of how local and semilocal density functionals work for systems with large density gradients was pioneered by Gunnarsson, Jonson, and Lundqvist [41,42]. Define u = r — r, the separation of two points in the system. Then the spherically-averaged hole is... 

Note added in proof Since this article was written, a method for improving the energy of semilocal functionals, using the ideas of Section 3.1, has appeared [83], and further examples of abnormal systems have been identified [84]. 

Burke K, Perdew JP, Ernzerhof M, Why semilocal functionals work Accuracy of the on-top hole density, in preparation for J Chem Phys... 

In the lineage of the methodology developed above, the ADA and the WDA are nonlocal extensions of the EDA formulation. In this sense, the TF model discussed in Section II. 1 is the EDA counterpart for the OF-KEDF. however, the vW model discussed in Section III. 1 is somewhat different, because the ansatz in Eq. (39) departs from the EDA ansatz in Eq. (23). For later convenience, we name the strategy in Section III. 1 the Semilocal-Density Approximation (SEDA). In the following, through a detailed analysis of the exchange energy density functional (XEDF) and the OF-KEDF, we shall see the classical WDA is actually closely related to the SEDA. 

As all numerical results indicate that the WDA is heading into the right direction, incorporating the correct LR behavior - becomes the next logical step. The ADA immediately comes into mind, but proper modifications have to be made. The Semilocal Average-Density Approximation (SADA) constitutes the first step towards this goal. 

The concerted bimolecular /3-elimination reaction of substituted alkanes (X-Ca H2-Cp H2-...) has been studied using the semilocalized quantum chemical approach.3... 

Valence Bond Wave Functions with Semilocalized AOs... 

Here, a and b are purely localized AOs, while Coulson—Fischer orbitals energy minimization, are generally not very delocalized (e < 1), and as such they can be viewed as distorted orbitals that remain atomic-like in nature. However, minor as this may look, the slight delocalization renders the Coulson—Fischer wave function equivalent to the VB-full wave function (Eq. 3.4a) with the three classical structures. A straightforward expansion of the Coulson—Fischer wave function leads to the linear combination of the classical structures in Equation 3.6. 

Note that if instead of using purely localized AOs for a and b, we use semilocalized Coulson-Fischer orbitals, Equation 3.37 will no more be the... 

This equivalence clearly projects that the MO—VB rivalry, discussed in Chapter 1, is unfortunate and senseless. Both VB and MO theories are not so diametrically different that they exclude each other, but rather two representations of reality, which are mathematically equivalent. The best approach is to use these two representations jointly and benefit from their complementary insight. In fact, from the above discussion of how to write a VB wave function, it is apparent that there is a spectrum of orbital representations that stretches between the fully local VB representations through semilocalized CF orbitals, to the use of delocalized fragment orbitals VB (FO—VB), and all... 

VALENCE BOND METHODS BASED ON SEMILOCALIZED ORBITALS 239... 

All the VB methods that deal with semilocalized orbitals use a generalization of the Coulson—Fischer idea (12), whereby a bond is described as a singlet coupling between two electrons in nonorthogonal orbitals that possess small delocalization tails resulting from the variational orbital optimization. Albeit formally covalent, this description implicitly involves some optimal contributions of ionic terms, as a decomposition of the wave function in terms of pure AO determinants would show (see Eqs. 3.5 and 3.6). For a polyatomic... 

CF orbitals Coulson-Fisher-type orbitals. These are semilocalized AOs, also called overlap enhanced orbitals (OEOs) which are localized on a given center, but have small delocalization tails on other centers. Special cases of CF AOs are BDOs (see above). 

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