Quantum chemical calculations classifications

A structural classification of 8 is difficult due to the fact that an arrangement of metal atoms as in 8 is uncommon in the whole field of molecular metal clusters. For this reason, detailed understanding of the bonding properties in 8 requires quantum chemical calculations. Theoretical analysis seems to be especially applicable to learning more about the bond between the two tetrahedra, which appears at first to be an isolated metal-metal bond between two metal atoms in the formal oxidation state zero. 

The comparison with results of high level quantum-chemical calculations proves the utility of the simple discrete models of molecular interaction for predicting the most stable topologies of water cycles and PWCs. Based on these discrete models an effective enumerating techniques was developed for hierarchical classification of proton configurations. In spite of the fact that PWCs are very complex systems with complicated interactions, the discrete models of inter-molecular interaction help us to see the wood for the trees (Fig. 3). 

The practical exploitation of the proposed criterion can be very simply demonstrated by the example of the electrocyclic transformation of butadiene to cyclobutene, for which the structure of the possible intermediates can be quite reliably estimated from the available results of quantum chemical calculations [123]. This reaction is especially convenient for the demonstration purposes since it displays both possible types of the dissection of the More O Ferrall diagrams [121] as schematically given in Figs. 9 and 10. Especially interesting is, above all, the case of forbidden disrotatory cyclization, for which the special form of the dissection allows the classification of the reaction mechanism even without the knowledge of the reaction path. As can be seen from the Fig. (9) no reaction path coimecting the reactant with the product can avoid the region of the intermediate so that the reaction has to be classified as nonconcerted. 

A classification of reactivity indices according to the particular quantum chemical method used for calculation has the advantage that it does not refer to mostly unproven assumptions on the relation between physical meaning of the index and mechanism of reactions, although a pictorial interpretation of the physical meaning... 

This book is concerned with the quantum chemical methods for the calculations of electromagnetic properties of molecules. However, in detail only so-called ab initio quantum chemical methods will be discussed in Part III. As ab initio methods one normally describes those quantmn chemical methods that start from the beginning, i.e. methods that require the evaluation of all the terms in the Schrodinger or Dirac equation and do not include other experimentally determined quantities than the nuclear charges, nuclear masses, nuclear dipole and quadrupole moments and maybe positions of the nuclei. This is in contrast to the so-called semi-empirical methods where many of the integrals over the operators in the Hamiltonian are replaced by experimentally or otherwise determined constants. However, in the case of density functional theory (DFT) methods the classification is somewhat debatable. 

The theoretical tools of quantum chemistry briefly described in the previous chapter are numerously implemented, sometimes explicitly and sometimes implicitly, in ab initio, density functional (DFT), and semi-empirical theories of quantum chemistry and in the computer program suits based upon them. It is usually believed that the difference between the methods stems from different approximations used for the one- and two-electron matrix elements of the molecular Hamiltonian eq. (1.177) employed throughout the calculation. However, this type of classification is not particularly suitable in the context of hybrid methods where attention must be drawn to the way of separating the entire molecular system (eventually - the universe itself) into parts, of which some are treated explicitly on a quantum mechanical/chemical level, while others are considered classically and the rest is not addressed at all. That general formulation allows us to cover both the traditional quantum chemistry methods based on the wave functions and the DFT-based methods, which generally claim... 

History and Concepts. A complementary approach for molecular structure calculations is available, and it is referred to as the molecular methanics or force field method it is also known as the Westheimer method. In 1946, twenty years after the impressive development of quantum theory, three papers appeared in the literature which applied classifical mechanical concepts to problems of chemical interest. Westheimer investigated the racemization of some optically active biphenyl derivatives. His work demonstrated the potential usefulness of molecular mechanics. The other two papers were attempts to tackle more complex problems. 

It should by now be clear from the preceding sections that the generally accepted view of atomic orbitals is that they are strictly non-referring in that they do not pick out any entity which may be said to physically exist in the same sense that a planetary orbit exists. This does not, however, diminish their usefulness in a multitude of computational schemes employed in quantum chemistry or their applicability to the classification of spectroscopic transitions and to a discussion of a plethora of chemical and physical phenomena. In addition, much of the success of modem quantum chemistry, including the award of the 1998 Nobel Prize for chemistry, is directly attributable to the use of calculations based on atomic and molecular orbitals. 

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