Author: Anupa Bhattacharya

Density functional theory is one of the most popular quantum mechanical energy

minimization process used in physics, chemistry and materials science to investigate the

electronic structure of many-body systems. The name "density functional theory" comes from the use of functionals, i.e, function of functions, which in this case is spatially dependent

electron density.

For one-electron systems like the hydrogen atom, it is very easy to solve the Schrödinger

equation exactly, and calculate the possible energy states of the system by obtaining the

energy eigenvalue. The Schrödinger equation is represented as:

where H is the Hamiltonian operated on the wave-function (psi), and E is the energy eigenvalue.

However, the difficulty of the calculation increases with the dimension of the problem.

Therefore, it is very difficult to solve this equation for many-electron systems like polyatomic

molecules. DFT is nothing but a computational technique for achieving an approximate

solution to the Schrödinger equation for many-body systems [1]. The wave function of a N

electronic system is a function of 3N number of variables (coordinates of all the N atoms),

whereas taking electron density functional reduces the number of variables to 3 (x,y,z),

making the calculation easier. Also, it has been established by the Hohenburg-Kohn theorem

[2] that the electron density of any system determines all the ground state properties of that

system. By focusing on the electron density, it is possible to derive an effective one-electron

type Schrödinger equation for a many-electron system and get all possible energy states of

that system by solving it. Presently one of the most successful and promising approach

towards investigating the electronic structure, the applicability of DFT ranges from atoms,

molecules and solids to nuclei, quantum and classical fluids. It predicts a great variety of

molecular properties, structures, atomization energies, reaction pathways, etc.

It is an extraordinary tool in the in silico screening and design of active pharmaceutical

ingredients. A small work was done by me for my Master’s dissertation, which involved the in

silico screening of Non Steroidal Anti Inflammatory drugs using DFT and molecular

docking. Among the various properties that can be predicted from DFT, we had mainly

focused on the energy difference of the Highest Occupied Molecular Orbital (HOMO) and

Lowest Unoccupied Molecular Orbital (LUMO) of a molecule. It has been studied that the

inhibitory activity of a molecule is generally affected by its total energy, entropy, polarity and

electron transition probability. The electron transition probability is further dependent on the

HOMO-LUMO energy gap of a molecule. This energy gap, also gives us an idea about the

stability of a molecule, which follows a reverse order with electron transition probability.

Lower the HOMO-LUMO energy gap of a molecule, the more active and less stable is it, and

vice-versa. [3]. The DFT calculations were performed using DMOL 3 code [4, 5], under

Generalized Gradient Approximation (GGA) [6]. The density functional BLYP [7, 8] was

used along with the Double Numeric Plus polarization (DNP) basis set. The optimization was

carried out without any structural constraint and HOMO-LUMO energy gap was computed in

electron volts (eV).

Molecular docking is another popular aspect in structural molecular biology and computer-assisted drug design. It is used to predict the preferred orientation of one molecule to another when they are bound to form a stable complex [9], thus also giving an idea of binding affinity of one molecule to the other. Due to the ability of this technique to predict the binding conformation of a small molecule to its appropriate target (essentially macromolecules like proteins), molecular docking is found to have an extensive use in structure-based drug design.

Molecular docking mainly approaches towards achieving optimized conformations for both

the protein and ligand, and the relative orientation of the protein and ligand, so that the free

energy of the overall system is minimized. The ligand and the protein adjust their

conformation to achieve a “best-fit” conformationally as well as energetically [10]. The

mechanics of docking broadly involves two steps:

1. Search algorithms: Theoretically, a search space consists of all possible

conformations and orientations of the ligand bound to the protein. In actual practice, it

is not possible to explore the search space minutely, as molecules are dynamic and

exist as an ensemble of various conformational states. Therefore most docking

programs employ easier conformational search strategies. Among these, the most

widely used is the “genetic algorithm” which is used for evolving low energy

conformations, where the score of each bound conformation acts as the fitness

function to select molecules for the next iteration.

2. Scoring function: Among the potential protein-ligand conformations generated by a

docking program, some are rejected outright due to clashes. But the rest are evaluated

using a scoring function, representing a favorable binding interaction and ranking the

conformations relative to each other. The scoring function is generally represented as

a cumulative free energy for binding taking into account all other contributions

including solvent effects, conformational changes, etc.[11]. A lower (negative)

binding energy indicates a stable system and more likely binding interaction.

[Protein-ligand docking. http://biochemlabsolutions.com/Docking/screen.jpg.]

## References

[1] Belaidi. S., Mellaoui. M., (2011), “Electronic Structure and Physical-Chemistry Property

Relationship for Oxazole Derivatives by Ab-Initio and DFT Methods”, Organic Chemistry

International, 2011, 7 pages.

[2] P. Hohenberg. P., Kohn. W., (1964),“Inhomogeneous Electron Gas”, Physical

Review, 136, B864.

[3] Ghosh. D.C. , Jana. J., (1999), “A study of correlation of the order of chemical reactivity

of a sequence of binary compounds of nitrogen and oxygen in terms of frontier orbital

theory”, Current Science, 76, 570-573.

[4] Bhattacharya. A. et al, (2010), “Crystal structure and electronic properties of two

nimesulide derivatives: A combined X-ray powder diffraction and quantum mechanical

study”, Chemical Physics Letters, 493, 151-157.

[5] Delley. B., (1998), “An all‐electron numerical method for solving the local density

functional for polyatomic molecules”, The Journal of Chemical Physics, 92, 508 (1990).

[6] Perdew. J.P. et al, (1996), “Generalized Gradient Approximation Made Simple”, Physical

Review Letters, 77 ,3865.

[7] Becke. A.D., (1988), “Density-functional exchange-energy approximation with correct

asymptotic behaviour”, Physical Review A, 38, 3098.

[8] Lee. A. C. et al, (1988), “Development of the Colle-Salvetti correlation-energy formula

into a functional of the electron density”, Physical Review B, 37, 785-789.

[9] Lengauer. T., Rarey. M., (1996), “Computational methods for biomolecular docking",

Current Opinion in Structural Biology, 6,402–406.

[10] Wei. B.Q et al, (2004). “Testing a flexible receptor docking algorithm in a model

binding site”, Journal of Molecular Biology”, 337, 1161–1182.

[11] Murcko. M.A., (1995). “Computational Methods to Predict Binding Free Energy in

Ligand Receptor Complexes”,Journal of Medicinal Chemistry. 38, 4953–4967.

## About the Author

Anupa Bhattacharya is a 26 year old from West Bengal, India. She has completed her Master's in Applied Chemistry and has previously worked for two years as a high school chemistry teacher. She likes to describe herself as an avid reader, dreamer and science enthusiast, specifically in interdisciplinary research. Apart from that she is also highly interested in literature and performing arts.

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