Conceptual understanding, physical methods

In this section, we will analyze an elementary problem in quantum mechanics, the square barrier. The purpose is twofold. First, such an analysis can provide physical insight into the process, to gain a conceptual understanding. Second, analytically soluble models are indispensable for assessing the accuracy of approximate methods, such as the MBA. 

Two other approaches have been taken in order to model the active site and its environment. The first has been to use somewhat less accurate quantum-chemical methods to obtain a more qualitative understanding of the key surface states, reaction pathways and mechanism. The key parameters can then be refined by the use of high level theory and/or experiments on model systems which are much smaller. The main benefit of theory then has been the design of a physically justifiable microscopic description of the catalytic system, with a qualitatively correct conceptual understanding. 

In this review, we have discussed the Feshbach-Lowdin PT as a tool for studying multidimensional quantum dynamics of (molecular) systems. The central element in this approach is the emergence of overlapping resonances through the application of the PT on the Hilbert space of the system under study, and the possibility that such resonances ultimately interfere. The TOR, which is the result of this approach, provides a fruitful method to understand and conceptually link diverse physical phenomena and processes. We have tried to demonstrate this by discussing various examples, as FIT and ORIT, the suppression of spontaneous decay in atoms and molecules, and the CC of IC in pyrazine and / -carotene, as well as of IVR in the OCS molecule. 

In this section, I provide a simplified physical picture of pulse NMW spectroscopy, including a simple conceptual model to help you understand multidimensional NMR. Then I briefly discuss the problems of assigning resonances and determining distance restraints for molecules as large and complex as proteins, and the methods for deriving a structure from this information. Finally, I discuss the contents of coordinate files from NMR structure determination and provide some hints on judging the quality of models. 

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. 

Two conflicting needs appear when working in the field of quantum chemistry. On one hand, the extreme need for high precision calculations, which certainly implies the need for better and more complex wavefunctions needed for the design of new materials with specific characteristics. On the other hand, the need for conceptual interpretations, which will allow for the development of physical and chemical intuition. The development of this intuition is certainly difficult if the wavefunctions are too complex. Since this review is oriented toward the uses of precise first principles methods complementing molecular dynamics simulations, we are focusing on how the development of precise methods helps to improve our understanding and... 

Quantum mechanics provides the conceptual framework for understanding chemistry. The ab initio methods of nonrelativistic quantum mechanics aim at the solution of the time-independent Schrodinger equation, employing well-defined approximations that can be improved systematically on a convergent path to the exact solution. They do not use experimental data, except for the fundamental physical constants. 

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