**2. Computational quantum methods for polymer solar cells**

Computational quantum chemistry may play an essential role in the development of OPV research and technology. In addition, the results of these computations can be used as a low-cost guide for developing and improving solar materials. Overall, the field's research can be divided into quantum science and charge transfer dynamics, new structures and creative concepts, and materials development for various applications. Understanding the functioning mechanism of polymer solar cells is the primary focus of the study. The main point of contention is how the bonded electron–hole pair breaks. The "hot exciton effect" is the most frequently recognized answer to this subject. When an electron is absorbed by one semiconductor material from another, it brings energy differences, causing the electron to

### *Applications of Current Density Functional Theory (DFT) Methods in Polymer Solar Cells DOI: http://dx.doi.org/10.5772/intechopen.100136*

get heated and acquire velocity, allowing it to escape from the confined exciton state. Even though this idea has recently gained widespread acceptance, numerous investigations have cast doubt on its validity [21].

These methods are now being used to predict component excited-state properties in light-harvesting systems. Nonetheless, this is a difficult task. Furthermore, large systems pose a significant challenge to conventional quantum chemistry techniques for excited states. Thus, calculations and theoretical models are beneficial when used in conjunction with CT experiments. Optical absorption investigations can measure exciton binding energies. Electrochemistry can be used to assess OPV components' oxidation and reduction potentials, as well as their HOMO–LUMO gaps [22]. The charge transfer and recombination kinetics can be studied using femtosecond transient absorption and time-resolved emission measurements [22]. These studies rely on well-established electron and energy transmission [23, 24] and their thermodynamic and kinetic consequences [25].

In polymer solar cells, computational quantum theories such as density functional theory (DFT) are used. TD-DFT is the essential instrument in the quantum mechanical simulation of quantum chemistry for computing excited-state characteristics and charge-transfer (CT) excitations in large systems [26]. TD-DFT can extract excitation energies, frequency-dependent response qualities, and photoabsorption spectra from molecules and materials. There are several hurdles to implementing TD-DFT computations on photovoltaic systems. Assumptions in these applications can cause catastrophic modeling errors. Many hypotheses and refinements to this basic technique have been proposed [27].

Density Functional Theory (DFT) investigates the electronic structure (principally the ground state) of many-body systems, such as atoms, molecules, and condensed phases. A many-electron system's properties can be determined using functionals, i.e. function of another function. Inorganic photovoltaic properties such as bandgap, optical absorption, intra-molecular and inter-molecular charge transfer, exciton binding energy, charge transfer integral, reorganization energy and rate of charge transfer and recombination in donor-acceptor complexes can be calculated or developed using DFT based computational methods. In practice, the effects of organic photovoltaic media on these qualities should be considered. Although the impact of the medium varies depending on the transitions involved, polarization continuum solvation models may commonly be used to account for solvation at a low computational cost [28].

The Schrödinger equation, which explains the behavior of electrons in a system, is reformulated in density functional theory (DFT) so that approximate solutions are tractable for functional materials. Hohenberg and Kohn [29] proposed the idea in 1964, claiming that all ground-state features may be expressed as an operative of the charge density that must be reduced in energy. However, rather than tackling the Schrödinger Equation [30] head-on, these theorems showed that an initial guess of the charge density might be improved iteratively.

Hohenberg, Kohn, and Sham created such a theory in density functional theory (DFT) [31], leading to two of the top ten most preferred articles of all time6 and for which Kohn received the Nobel Prize in Chemistry in 1999. The Schrödinger equation's ground-state solutions are restated in DFT to find energy as a charge density function.

The exchange-correlation functional chosen determines the precision of the DFT calculation. Although theorists may frequently improve computation accuracy by employing more intricate functionals (at a higher processing cost), there are some highly coupled electron systems that most functionals fail. Other disadvantages of traditional DFT include the small system size, the difficulty of modeling weak (van der Waals) interactions, dynamics over long periods, and non-ground state

characteristics (finite temperatures or excited conditions). Larger systems can be tackled with the linear scaling approach [32], finite-temperature effects can be addressed with lattice dynamics [33] and cluster expansion [34], electronic excitations can be modeled with time-dependent DFT [35], the GW method [36], and the Bethe–Saltpeter [37], and several approaches can be used to overcome these limitations. In his assessment, Carter [38] gives a quick outline of some of these options. A DFT calculation requires the coordinates and orientations of the atoms in the material within a repeating lattice, the exchange-correlation functional, parameters and algorithms for numerical and iterative convergence, and, optionally, a method for more efficiently treating the system's core electrons (for example, through the use of pseudopotentials). DFT generates the electronic charge density, total energy, magnetic configuration, and electronic band structure.
