Density functional theory history

Slater s Xa method is now regarded as so much history, but it gave an important stepping stone towards modem density functional theory. In Chapter 12, I discussed the free-electron model of the conduction electrons in a solid. The electrons were assumed to occupy a volume of space that we identified with the dimensions of the metal under smdy, and the electrons were taken to be non-interacting. 

Density Functional Theory and the Local Density Approximation Even in light of the insights afforded by the Born-Oppenheimer approximation, our problem remains hopelessly complex. The true wave function of the system may be written as i/f(ri, T2, T3,. .., Vf ), where we must bear in mind, N can be a number of Avogadrian proportions. Furthermore, if we attempt the separation of variables ansatz, what is found is that the equation for the i electron depends in a nonlinear way upon the single particle wave functions of all of the other electrons. Though there is a colorful history of attempts to cope with these difficulties, we skip forth to the major conceptual breakthrough that made possible a systematic approach to these problems. 

The role of quantum theory in chemistry has a history of almost 100 years, and the advances have been important. Nowadays, it is possible to do quantitative predictions with chemical accuracy for middle-size molecules, and some type of calculations, especially density functional-based methodologies, are routinely done in many chemical laboratories. One very important aspect on the influence of quantum theory in chemistry is the one of understanding. There are many chemical concepts which can be understood only through the laws of quantum mechanics. This chapter is about conceptual understanding and is not about the other very important issue of computing with chemical accuracy. 

Simultaneously studies will be continued to understand the physical basis of DF theory better, in particular to understand which are the essential ingredients that make DFT work and whether it is possible to arrive at any desired accuracy. If one is very optimistic one will hope that a hierarchy of density functionals will be found, such that it is also possible to go to the next higher level, if the lower one was not good enough. At present one is very far from this situation. The history of DFT is rich in examples of improvements based on formal arguments which rather deteriorated the agreement with experiment. 

The shape function had a role in theoretical chemistry and physics long before it was named by Parr and Bartolotti. For example, in x-ray measurements of the electron density, what one actually measures is the shape function—the relative abundance of electrons at different locations in the molecule. Determining the actual electron density requires calibration to a standard with known electron density. On the theoretical side, the shape function appears early in the history of Thomas-Fermi theory. For example, the Majorana-Fermi-Amaldi approximation to the exchange potential is just [3,4]... 

The ultimate purpose of these types of tests is to evaluate two similar (in results) but different occurrences. These are runaway chemical reactions and exothermic chemical decompositions. The first may actually just be a desired reaction out of control while the second is an undesired reaction out of control. Among the purposes which analytical tests serve are the determination of the "onset" of exothermic (endothermic) decomposition. While frequently a specific temperature is cited for such "onsets," one must remember that this temperature is highly dependent on instrument sensitivity, degree of adiabaticity and time-temperature history. It should be stated that tests results are accurate only for the exact conditions under which they were run. Physical factors such as density and geometry can also influence test data. In theory, reaction rates are not a step function but are continuous. 

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