Schrodinger equation conventional quantum chemistry

The most serious reservation expressed about relativistic formulations of quantum chemistry in [2] is to know to what question they are supposed to be the answer, in the circumstances in which we And ourselves . This article is intended to demonstrate that one may formulate a valid theory of quantum chemistry without invoking the Schrodinger equation, and that the conventional quantum chemistry that we would And in, say, [3, 4] may be obtained as a limiting case of our formulation. We prefer to keep the relativistic structure of the Dirac theory intact at all times, which means that our formulation does not contain relativistic corrections . This is quite deliberate, and a feature which we will turn into a computational advantage. 

Relativistic quantum chemistry is currently an active area of research (see, for example, the review volume edited by Wilson [102]), although most of the work is beyond the scope of this course. Much of the effort is based on Dirac s relativistic formulation of the Schrodinger equation this results in wave functions that have four components rather than the single component we conventionally think of. As a consequence the mathematical and computational complications are substantial. Nevertheless, it is very useful to have programs for Dirac-Fock (the relativistic analogue of Hartree-Fock) calculations available, as they can provide calibration comparisons for more approximate treatments. We have developed such a program and used it for this purpose [103]. 

The quantum mechanical methods described in this book are all molecular orbital (MO) methods, or oriented toward the molecular orbital approach ab initio and semiempirical methods use the MO method, and density functional methods are oriented toward the MO approach. There is another approach to applying the Schrodinger equation to chemistry, namely the valence bond method. Basically the MO method allows atomic orbitals to interact to create the molecular orbitals of a molecule, and does not focus on individual bonds as shown in conventional structural formulas. The VB method, on the other hand, takes the molecule, mathematically, as a sum (linear combination) of structures each of which corresponds to a structural formula with a certain pairing of electrons [16]. The MO method explains in a relatively simple way phenomena that can be understood only with difficulty using the VB method, like the triplet nature of dioxygen or the fact that benzene is aromatic but cyclobutadiene is not [17]. With the application of computers to quantum chemistry the MO method almost eclipsed the VB approach, but the latter has in recent years made a limited comeback [18],... 

The FC method is completely different from the conventional quanmm chemistry. In the state-of-the-art quantum chemistry, one first defines Harfree-Fock orbitals based on the initially chosen basis set and then expands many-electron correlated wave functions by means of the Hartree-Fock orbitals. In this approach, any theory lies between the Hartree-Fock and the full Cl and so, tiie full Cl is a goal of this type of the theory. However, the full Cl cannof be tiie exacf solution of the Schrodinger equation because of the incompleteness of the basis set first introduced. When we use numerical Hartree-Fock that is free from the basis set, the full Cl becomes infinite expansion that cannot be handled in principle. 

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