Theoretical Framework Group Function Theory

In the following we shall be concerned with the problem of the electronic structure of molecular systems containing N electrons and M nuclei. The validity of the usual Born-Oppenheimer, or clamped nuclei, approximation will be assumed, that is we shall investigate the distribution of electrons in the field of the fixed nuclei. In principle the approximate solution of the Schrddinger equation of all the electrons provides us with the different electronic states of the molecule, once the position of the nuclei and the number of electrons is given. Essentially this is the procedure followed in everyday routine calculations of ab initio quantum chemistry, where we do not take into account the a priori knowledge about the properties of the different fragments of the total composite system. 

Although in the following we shall mainly use the group function model for the treatment of extended systems with spatially separated fragments of functional groups, it should be mentioned that the first applications of the idea of separable electron groups were in the theoretical justification of the Tu-electron theories of quantum chemistry [70]. The most important results were summarized by the so-called a-n 

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Abstract. The group function theory described in the title paper of McWeeny is overviewed by pointing out its influence on different fields of theoretical chemistry, in particular its serving as a general framework for various forms of building blocks and local treatments of extended systems. 

Theoretical approaches to the DMS can be divided into two groups, namely the model studies and the studies based on the spin-density functional theory (DFT). The model studies mostly employ the kinetic-exchange (KE) model in the connection with a continuum approximation for the distribution of Mn atoms and other defects - that yields a disorder-free problem, although recently this model was refined to include the disorder via the supercell method in the framework of Monte Carlo simulations. ... 

From the conceptual point of view, there are two general approaches to the molecular structure problem the molecular orbital (MO) and the valence bond (VB) theories. Technical difficulties in the computational implementation of the VB approach have favoured the development and the popularization of MO theory in opposition to VB. In a recent review [3], some related issues are raised and clarified. However, there still persist some conceptual pitfalls and misinterpretations in specialized literature of MO and VB theories. In this paper, we attempt to contribute to a more profound understanding of the VB and MO methods and concepts. We briefly present the physico-chemical basis of MO and VB approaches and their intimate relationship. The VB concept of resonance is reformulated in a physically meaningful way and its point group symmetry foundations are laid. Finally it is shown that the Generalized Multistructural (GMS) wave function encompasses all variational wave functions, VB or MO based, in the same framework, providing an unified view for the theoretical quantum molecular structure problem. Throughout this paper, unless otherwise stated, we utilize the non-relativistic (spin independent) hamiltonian under the Bom-Oppenheimer adiabatic approximation. We will see that even when some of these restrictions are removed, the GMS wave function is still applicable. 

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