**5. Challenges for DFT**

In principle, DFT is exact; however its effectiveness depends on the development as well as advancement in exchange-correlation (Exc) functionals which may be achieved by optimizing against larger data-sets and using improved functional arrangements that are more flexible and contain more elements. Smoothness has also been prioritized in recent enhancements, which helps to alleviate problems like grid-size convergence and self-consistent field iterations. In this section, we will go through some of DFT's challenges that may differ from those that appears to be "solved" to those that are still being explored. There are numerous more that are less well-known, and yet crucial to DFT's future growth as well as use.

#### **5.1 Strong correlation**

DFT's inadequacy for strongly correlated systems utilizing typical approximations has been acknowledged since its inception, and this can be investigated as well as linked to standard approximation localization or delocalization inaccuracies when integer or half-integer electron quantities are found in distinct locations [49]. In quantum computational physics and chemistry, the Kohn-Sham gap among two states becomes too narrow, and the wave function of a many-body system is very nearly equal to mixing of two slater determinants, which is referred to as static correlation. The failure of approximations under these situations cause the challenges, not the KS scheme itself, as demonstrated by the two-site Hubbard model, in which the precise KS system is simple to design, even when one deal with strongly correlated systems [50]. This problem can be addressed by breaking the symmetry of evenly spaced atomic chains into multiple solutions, and one of which will have the least amount of energy [51]. This is such a significant issue; hence, a great deal of research has been done on it, particularly by Weitao Yang's group [52], but also by Scuseria [53] and Becke [54].

## **5.2 Development of uniformly better and simple functionals**

One of the biggest problems for DFT is to preserve some aspect of simplicity as its foundations. When DFT functionals get as complicated as full configuration interaction, one of the theory's most significant properties, namely simplicity, is lost, which is particularly true in terms of computational environment. This simplicity, however, must not be at the expense of accuracy, nor should it become an exclusively empirical approach. The precise representation of binding energies and geometries of simple molecules was one of DFT's first major hurdles in chemistry. Becke, Perdew, Langreth, and Parr presented the density's first derivative in the form of generalized gradient approximation in the 1980s, which was the first step towards chemists being able to correctly use DFT. In the early 1990s, Becke described the proportion of Hartree-Fock exact exchange (HF) which is included in the functionals, and as a result of this effort, B3LYP [55], the utmost extensively utilized of all the functionals, was developed, and has demonstrated outstanding performance in variety of systems. Despite the introduction of new concepts into more current functionals of varying complication, it remains the prevalent, and DFT will likely benefit from developing functionals that improves on B3LYP [56].

#### **5.3 Dispersion and reaction barriers**

To provide a comprehensive chemistry explanation, it is indispensable to go beyond explaining a molecule in equilibrium geometry to similarly explain weakly interacting atoms or molecules, and chemical reaction transition states. It's challenging to describe reaction barriers with LDA or GGA functional since they consistently underestimate the difficulty of transitioning from one condition to another. Formerly the functionals may be utilized to represent potential energy surfaces, and this systematic imperfection must be corrected. Transition states, covalent bonding, and van der Waals attraction are all challenging to represent precisely and effectively, though efforts are to be made to address these problems. This is especially true when DFT becomes more widely applied to biologically important regions, where all of these interactions might occur at the same time [57].

#### **5.4 Static correlation and delocalization errors**

The enactment of DFT, as evidenced by significant errors for one-electron systems, is another important issue. In DFT, a single electron system has no exceptional role; in fact, one electron can interrelate with itself, as the self-interaction error has long proved. Of course, there is no self-interaction in the accurate

*Fundamentals of Density Functional Theory: Recent Developments, Challenges and Future… DOI: http://dx.doi.org/10.5772/intechopen.99019*

**Figure 3.** *Potential application areas of DFT [61].*

functional; the exchange energy precisely cancels the coulomb energy of single electron. In increasingly complicated systems, they can be linked to systematic flaws like static correlation and delocalization error, and despite most recent advancements, even the simplest systems can contain mistakes in most recent functionals [58]. Hence, these basic systems should not be overlooked since they hold the vital knowledge of functionals that can lead to advancements [57].

### **6. New horizons**

The applications of warm dense matter vary from modeling planetary interiors to inertial confinement fusion [59], which is a completely new field for DFT, and has been exploded in the last decade, with considerable temperatures on the electronic scale of roughly 10<sup>5</sup> K but not to the point that the Thomas- Fermi hypothesis or classical performance takes precedence. This domain is so "new" that temperature-dependent exchange-correlation energy of a uniform gas, which is the input to thermal LDA, is just now being computed with remarkable precision [60]. **Figure 3** summarizes some of the potential application areas of DFT.
