Generalized Multistructural Method Theoretical Foundations and Applications

Generalized Multistructural Method Theoretical Foundations and Applications 

Instituto de Qui mica, Departamento de Fisico-Quimica, Universidade Federal do Rio de Janeiro. 21949-900, Rio de Janeiro-RJ, Brasil 

The Generalized Multistructural Wave Function (GMS) [1,2] is presented as a general variational many-electron method, which encompasses all the variational MO and VB based methods available in the literature. Its mathematical and physico-chemical foundations are settled. It is shown that the GMS wave function can help bringing physico-chemical significance to the classical valence-bond (VB) concept of resonance between chemical structures. The final wave functions are compact, easily interpretable, and numerically accurate. 

Ab initio calculations of electronic wave functions are well established as useful and powerful theoretical tools to investigate physical and chemical processes at the molecular level. Many computational packages are available to perform such calculations, and a variety of mathematical methods exist to approximate the solutions of the electronic hamiltonian. Each method is based (or should be) on a well defined physical model, specified by a certain partition of the electronic hamiltonian, in such a way as to include a subset of all the interactions present in the exact one. It is expected that this subset contains the most important effects to describe consistently the situation of interest. The identification of which physical interactions to include is a major step in developing and applying quantum chemical theory to the study of real problems. 

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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