Advantage of density functional

It is clear that the inclusion of correlation at appropriate levels accounts for virtually all the disagreement between theory and experiment found at the Hartree-Fock level in correlation-sensitive molecules. It remains to be seen how efficiently some of the advanced post-Hartree-Fock methods can be implemented to handle larger molecules. One of the major advantages of density functional theory is its speed relative to conventional quantum mechanical methods. If it can be extended to give somewhat better agreement with experiment, it may well be the method of choice for treating large chemical systems in the near future. 

The mathematical term functional, which is akin to function, is explained in Section 7.2.3.1. To the chemist, the main advantage of DFT is that in about the same time needed for an HF calculation one can often obtain results of about the same quality as from MP2 calculations (cf. e.g. Sections 5.5.1 and 5.5.2). Chemical applications of DFT are but one aspect of an ambitious project to recast conventional quantum mechanics, i.e. wave mechanics, in a form in which the electron density, and only the electron density, plays the key role [5]. It is noteworthy that the 1998 Nobel Prize in chemistry was awarded to John Pople (Section 5.3.3), largely for his role in developing practical wavefunction-based methods, and Walter Kohn,1 for the development of density functional methods [6]. The wave-function is the quantum mechanical analogue of the analytically intractable multibody problem (n-body problem) in astronomy [7], and indeed electron-electron interaction, electron correlation, is at the heart of the major problems encountered in... 

Alternative approaches using box and whisker plots, pie charts and different types of visualizations of density functions are discussed in Ibrekk Morgan (1987) and Morgan Henrion (1990). Each has advantages for specific tasks, but the performance of a display depends upon the information that a subject is trying to extract (central tendency or variation). 

Although mostly parent cases have been studied so far, it can be expected that because of these improvements in speed and accuracy it is likely that these methods will be increasingly used for the study of chemically important substituted cases. The current intense investigations of new functionals as well as the exploration of the limitations of density functional theory will yield an even better understanding of the advantages and disadvantages of density functional... 

With advancements in computer power and the advantage of reasonable scalability to larger systems, density functional theory has made computational chemistry widely accessible in the chemical sciences, permitting direct comparisons to be made between theory and a wide variety of experiments. Examples of the application of density functional theory for prediction, understanding, and interpretation in surface science and heterogenous catalysis include ... 

Recently, another class of calculations, density functional theory (DFT) has become quite common. This method is faster than ab initio calculations for similar levels of performance, and has the advantage that correlation effects are included, at least in part. According to this theory, the properties of a molecular system are functions of the electron density, rather than a wave function (as described by the Schrodinger equation). There is some degree of debate over whether DFT is an ab initio calculation or in a class by itself. Parenthetically, one of the recipients of the 1998 Nobel Prize for Chemistry was Walter Kohn, in recognition of his development of density functional theory. 

A major development in computational chemistry of the last decade was the emergence of density functional theory (DFT).[78-80] The main advantage of DFT is that electron correlation effects for atomic and molecular systems are considered explicitly in calculations but the computational requirements remain relatively similar to those needed by Hartree-Fock calculations. Consequently, the DFT method has attracted a lot of interest in recent years for applications to systems of increasing complexity and size. 

The early practitioners and developers of density functional theory encountered yet another problem related to the extended nature of the number density primitive— self-interaction (Dreizler and Gross 1990, op. cit ). Specialized correction procedures were developed quite successfully and are in use in all modern calculations. In our case, again, because of the extended nature of our representation of the charged particle, there is a potential problem with what amounts to self-interference which needs to be examined. The potential self-interference corrections are always finite, and generally small which is a great advantage over the situation in quantum electrodynamics. 

Latterly, increasing use has also been made of Quantum Molecular Dynamics (QMD), based on the pioneering work of Car and Parrinello (1985) (see Chapter 8). The Car-Parrinello method makes use of Density Functional Theory to calculate explicitly the energy of a system and hence the interatomic forces, which are then used to determine the atomic trajectories and related dynamic properties, in the manner of classical MD. As an ab initio technique, QMD has the advantage over classical simulation methods that it is not reliant on interatomic potentials, and should in principle lead to far more accurate results. The disadvantage is that it demands far greater computing resources, and its application has thus far been limited to relatively simple systems. 

Each of these approaches has its own advantages and disadvantages and this will become particularly clear when we discuss the implementation of density functional methods in Chapter 33. 

Pople saw the advantage in density functional theory versus the quantum chemical methods in that the former dealt with a function of three dimensions whereas to get the full wave function of the electrons, a problem in 3 dimensions had to be considered (with n being the total number of electrons). 

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