Design Pollution Gas Sensor Using Graphene Ribbon: Density Function Theory (DFT)

Density Function theory (DFT) calculation used to employed ground and excitation states for graphene ribbons, types of adsorption, energy gap, maximum wave length and optical band gap. Adsorption energy showed that CO 2 gas molecule have chemical adsorption in distance 1 and 1.5 Angstrom, distance 2 and 2.5 Angstrom appear physical adsorption, adsorption energy decreased when distance between surface and gas molecule increasing. Resulting from chemical adsorption energy gap change with distance 1 and 1.5 Angstrom because attract gas molecule with surface. Excitation energy for nano system in sample 1 and 4 shifted to low wavelength (blue shift) change from 1018 nm to 993 nm and 718 nm on series. Other sample have red shift and energy gap becoming open. Result showed that graphene ribbon sense carbon dioxide gas (CO 2 ).


1-Introduction
Graphene as a two dimensional material (2D) sp 2 hybrids for carbon atoms arranged like honeycomb lattice, graphene have exceptional characteristic such as superior surface to volume fraction, outstanding transport properties and few electrical noise [1]. Graphene a mono atomic layer of graphite considered to be an excellent sensor material [2]. Ability of adsorption and fraction surface to volume of graphene make it an ideal gas sensing material, different atmospheric gases adsorbed on graphene has been investigated simulation and applications [3]. Graphene sensing applications are inspired by perfect flat structure which make all atom on surface exposed to the environment [4]. Electronic characteristic of pure graphene upon adsorption of different gas molecule on its surface is remembered as one of the essential subjects for improvements of graphene basis sensor [5]. Charge transfer between graphene sheet and the gas molecule relates to the direction of gas molecule with respect to graphene ribbon [6].

2-Simulation details
Optimization structure, electronic state, adsorption energy and transition energy calculations are computed using density function theory (DFT). Ground state calculation provide geometrical structure, molecular orbitals and adsorption energy.
Excitation state computed by time depending-density function theory (TD-DFT).
basis set using in present study is 6-31G and hybrid function B3LYP. Firstly, computed most geometrical structure between gas molecule and surface of graphene ribbon, change the distance between gas molecule ad surface of ribbon. Also determination type of adsorption between gas molecule and ribbon if it physical or chemical adsorption, finally computed ultra violetvisible spectra (UV-Visible).

3-Theoretical Background
The Schrödinger equation, which was proposed by Erwin Schrödinger in 1925, is central to the development of the theory of quantum mechanics. Any problem in the electronic structure of matter is covered by Schrödinger equation [7]: Where Ψ is the wave function, it expresses the mathematical form of the de Broglie wave associated with the particle, Ĥ is the Hamiltonian operator, and E is the total energy of the system. Where: m e and M A are the electron and nuclear mass, respectively,∇ i 2 is the laplacian operator of i electrons, which in Cartesian coordinates has the form: The potential energy operators are represented as: ̂e e = ∑ e 2 r ij i< (8) Where = |⃑ ⃑ − ⃑ ⃑ | and is the charge of nuclei A, r Ai is the distance between nucleus and electron, r ij is the distance between i electron and j electron and R AB is the distance between A nucleus and B nucleus [10].
The first major step in simplifying the general molecular problem in quantum mechanics is the Born-Oppenheimer approximation. This approximation is based on the fact that the nuclear masses are much greater than those of the electrons.
Therefore, nuclei move much more slowly and they are nearly fixed compared with the electrons motion [11].

4-Result and discussion
We used equation (1) for calculation adsorption energy E ad for system [12]: (E ribbon ) total energy for graphene ribbon before interaction, (E gas ) total energy for gas molecule and (E isolated ribbon + E gas ) total energy for graphene ribbon and gas molecule during adsorption in electron volt unit (eV).

1-Relaxation Structure and Adsorption Energy
We calculated most relaxation between gas molecule in this case CO 2 gas, the most distance equal (3.64) Å with adsorption energy (3.003) eV, this value represents physical adsorption because distance between CO2 gas molecule and surface of graphene ribbon is greater than covalent bond between carbon-carbon bond is equal (1.4600) Ang. Value calculated is modification in physical adsorption in study [12], that computed adsorption energy for most relaxation is -0.148 eV. After that study effect of distance on adsorption energies between gas molecule and ribbon the distance equal (1, 1.5, 2 and 2.5) ang., table 1 explain the adsorption energy for CO 2 as function of distance. From the table (1) we conclude that gas molecule in distance 1 and 1.5 have higher adsorption energy, the C-C length bond equal 1.43 (aromatic) for present study that agreement with [9], nearest gas molecule to graphene surface resulting high adsorption energy high interaction between gas and nano system. In distance 1 Å result show that high adsorption energy because the gas molecule is became close to graphene surface also oxygen atoms attract with carbon atom related to graphene ribbon. attract oxygen atom increasing adsorption energy and chemical interaction become very high. in this case chemical adsorption. For distance 1.5 Å, the gas molecule distance reached approximately from C-C bond and the adsorption energy become (-29.1021) eV. This result show that gas molecule adsorption chemically.
For distance 2 and 2.5 became grater from C-C covalent bonding and the energy decreased rabidly with increase distance between gas molecule and graphene ribbon surface. in other hand high adsorption distance low adsorption energy. Increasing in adsorption distance change case of interaction energy from high to low chemical adsorption. Graphene nano ribbon sense CO 2 gas molecule chemically [12].

3-Optical proprieties
We used TD-DFT calculation to obtain UV-Visible properties improving basis set 6-31G hybrid function B3LYP, firstly for isolated system and change the distance between gas molecule and graphene ribbon. Finally calculated maximum wave length (λ max ) and optical band gap, also shifting for UV-Visible spectrum.
We can calculate optical band gap from equation 3 as fallow [14]: For Isolated graphene ribbon maximum wave length (λ max ) is equal 1018 nm with optical band gap 1.22 eV, absorbance wave length in infrared near from visible light.
Distance 1 Å. Wave length shifted towered red region of electromagnetic radiation with 993 nm and optical band gap energy 1.24 eV [13]. that concluded have same behavior with study in [14].

4-Conclusions
 Result of geometrical. Electronic and optical proprieties of graphene material was agreement with experimental result.
 Chemical bond formed when gas molecule near the surface of graphene ribbon.
 Calculation of adsorption energy show that CO 2 gas molecule intract chemically with graphene nano ribbon.
 Increasing in adsorption distance the chemical interaction decreased.