Advantages of Density Functional Theory

This new perspective has enriched the theory of electronic structure and chemical reactivity by both rationalizing and quantifying basic, classical ideas and rules of chemistry, e.g., the electronegativity/chemical potential equalization of Sanderson [104] or the hard-soft acids and bases (HSAB) principle of Pearson [95,105], bringing about a deeper understanding of the nature of chemical bonds and variety of reactivity preferences [3-5,11,117]. 

In DFT the frontier electron theory has also been given a more rigorous foundation in terms of the new reactivity index for open molecular systems, called the electronic FF [3-5,84,92,118-122], the CS measuring a response in the local electron density per unit displacement in the system global number of electrons N  

As we have indicated above, it can be also interpreted, by the Maxwell relation, as the response in the system global chemical potential to a unit local displacement in the external potential. 

The electronic ground-state energy /i TV, v for a given average number of electrons N and the external potential v of the BO approximation is also the functional of the grand-canonical ensemble density [123]  

The corresponding second partials of the system electronic energy, P = 92 /9X9X = 9Y/9X = y(X), group the system conjugate principal BO charge sensitivities. These canonical derivatives include  

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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. 

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. 

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). 

A currently popular alternative to the ah initio method is density functional theory, in which the energy is expressed in terms of the electron density rather than the wave-function itself. The advantage of this approach is that it is less demanding computationally, requires less computer time, and in some cases—particularly for d-metal complexes—gives better agreement with experimental values than other procedures. 

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