**1. Introduction**

Carbon is a unique element that appears in many different configurations of electronic states [1]. Materials such as graphite, graphene, carbon nanotubes, and diamond have basically the same chemical composition but a different crystal structure. This is called allotropy of carbon (see **Figure 1** [2, 3]). Carbon has six electrons occupying the 1s2 , 2s2 , and 2p2 orbitals. The 1s2 electrons are two strongly bound core electrons, while the 2s2 and 2p2 electrons are weakly bound valence electrons. The valence electrons give rise to the 2s, 2px, 2py, and 2pz orbitals in the crystal phase. These orbitals are important for the formation of covalent bonds in carbon materials. Since the energy difference between the upper 2p and lower 2s orbitals is relatively small compared to other group 4

#### **Figure 1.** *Different allotropic forms of carbon [2, 3].*

elements such as silicon (Si), the electron wave functions can easily mix with each other, which is called hybridization [4]. In spn hybridization, the (n + 1) bonds are responsible for the local structure. Thus, in sp. hybridization, a one-dimensional chain structure is formed, which is called carbyne. Carbyne [5] is a chain of carbon atoms held together by alternating double or single and triple atomic bonds. This makes it a true zero-dimensional material, unlike graphene atomic sheets that have a top and bottom, or hollow nanotubes that have an inside and outside. According to calculations by Liu et al., carbyne has twice the tensile stiffness of graphene and carbon nanotubes and nearly three times that of diamond.

An sp2 hybridization forms a two-dimensional planar structure called graphene. In sp3 hybridization, a regular three-dimensional tetrahedral structure is formed, which is known as diamond.

In graphite, in addition to the three in-plane bonds, out-of-plane π orbitals are formed with highly delocalized electrons that contribute primarily to electrical and thermal conductivity. The interaction of the free π electrons with light makes graphite appear black. In addition, the weak van der Waals interaction between the graphite sheets makes the graphite flexible and cleavable, as the graphene sheets can easily move relative to each other. A carbon nanotube can be viewed as a rolled-up graphite sheet and thus a one-dimensional structure. The bonds in the nanotubes are essentially of the sp2 type. However, the circular curvature causes quantum confinement and σ π hybridization in which the three σ bonds are slightly out of plane. In this part, we are interested in the study of diamond.

Diamond has a crystal structure consisting of a face-centered cubic lattice of which one tetrahedral site out of two is occupied by a carbon atom, as represented in **Figure 2** [6].

The elementary lattice cell of diamond has carbon atoms, and its parameter is 3.57 Å. The shortest distance between two carbon atoms, that is, the distance corresponding to the quarter of the diagonal of the mesh is 1.54 Å, which makes the crystal lattice of diamond very dense (1.76 1023 atoms cm<sup>3</sup> ) in comparison with other materials. The compactness of its structure, associated with the high energies of the carbon-carbon bonds (E(C-C) = 360 kJ mol<sup>1</sup> ), is at the origin of diamond mechanical properties, which are well known (see **Table 1**) [6].

*Ab Initio Study of the Electronic and Energy Properties of Diamond Carbon DOI: http://dx.doi.org/10.5772/intechopen.111435*

**Figure 2.** *Elementary crystal lattice cell of diamond [6].*


#### **Table 1.**

*Some physical properties of diamond compared to silicon.*

Its high hardness, estimated at 7000 kg mm<sup>2</sup> (Knoop hardness) [6], makes diamond the most resistant material. This characteristic allows it to be used in many mechanical applications such as cutting, drilling, or polishing. Its very high Young's modulus makes it advantageous for applications involving microelectromechanical system oscillators (MEMS)-type resonators [6]. In addition to its high thermal conductivity [7], which is five times greater than that of copper, diamond is used as a heat sink for electronic or optoelectronic components such as power transistors and laser diodes. More recently, it has been used for the realization of optical windows for highpower lasers or X-ray tubes; it is the combination of its optical, mechanical, and thermal properties, which is decisive [6].

Diamond is a three-dimensional crystalline material. Because of its structure, it is considered one of the most promising materials for the integrated electronic and photonic, radio, optoelectronic, and quantum device industry.

Following our publications on the electronic and magnetic structures of graphite using the Korringa-Kohn Rostoker (KKR) method [8] and on the electronic properties of the adsorption of CO and N2 molecules on graphene and on a graphite plate using

GPAW and ASE [7], we decided to set up a simulation system based on GPAW and ASE to study the electrical and energetic properties of diamond. The main results of our work are the optimization of diamond energy, as well as the calculation of the density of state and the band structure.
