Computational determination of the Electronic and Nonlinear Optical properties of the molecules 2-(4-aminophenyl) Quinoline, 4-(4-aminophenyl) Quinoline, Anthracene, Anthraquinone and Phenanthrene

Highlights

• Dipole moment, average polarizability and hyperpolarizability are determined.

• Electric susceptibility, refractive index and dielectric constant are determined.

• RHF, B3PW91 and B3LYP methods were used employing 6-31+G** basis set.

• Results reveal nonlinear optical, optoelectronics and photonics applications.

• LUMO-HOMO energy gaps show optoelectronics and nonlinear optical applications.

Abstract

The Electronic and Nonlinear Optical properties of the donor-acceptor molecules 2-(4-aminophenyl) Quinoline, 4-(4-aminophenyl) Quinoline, Anthraquinone; and the molecules Anthracene and Phenanthrene have been determined and some of these properties compared with literature values. The theoretical calculations were performed at the RHF level of theory and with two different hybrid density functional theories (DFT) (B3LYP and B3PW91), using the 6-31+G** basis set. The results show that these molecular systems have large average polarizability, anisotropy and first molecular hyperpolarizabilities. The small values of ε, and LUMO-HOMO energy band gap (E_gap) and the high values χ, η,<α>, and (β_mol) show that the molecules have very good electronic, nonlinear optical, optoelectronic and photonic applications. Furthermore, the (E_gap) of Phenanthrene shows that Phenanthrene is a good promising organic superconductor material.

Introduction

The quest for suitable materials to be used in opto-electronics and photonics devices has been of great importance in Physics, Chemistry and Materials science. Due to the fact that photons can carry information faster, more efficiently and over larger distances than electrons, systems that use light as carrier of information are of great interest to information and communication technologies. Materials which exhibit high nonlinear optical (NLO) responses have been potential candidates for such devices, because of their high processing speed, transmission and data storage [1], [2], [3], [4], [5], [6], [7]. The NLO effects, second and third order effects provide means for the conversion of optical frequency, optical switching, and operations of optical memory [8], [9], [10], [11]. The majority of the early NLO materials were based on inorganic crystals but in the last three decades the focus has shifted toward organic compounds due to their promising potential applications in optical signal processing [9], [12]. In particular, Organic conjugated molecules and polymers have been used as special elements in solid state devices because of their high second and third order responses [13], [14]. These conjugated molecules and polymers have emerged as a dominant class of photonic materials because they show large and utra-fast NLO responses associated with their delocalized pi-electrons. Furthermore, organic materials offered some advantages compared with their inorganic counterparts such as thermal and chemical stability, the high values of electronic susceptibility fast response times and much greater versatility in molecular design or engineering [15], [16], [17]. Organic molecules have π-molecular orbitals, from which electrons can become delocalized, giving rise to metallic conductivity due to orbital overlap between adjacent molecules. An increase of transition temperature with increasing number of benzene rings suggests that organic hydrocarbons with long chains of benzene rings are potential superconductors with high transition temperature [18]. NLO processes occur when a medium is subjected to an intense electric field E, which polarizes the medium. For many materials, the induced polarization P, is found to be proportional to the electric field E.

$\overrightarrow{P}={\epsilon }_0{\chi }_e\overrightarrow{E}$ χ is the electric susceptibility of the material. For the response to a strong electric field, the susceptibility at a particular frequency is often expanded in a power series as,

$$\chi ={\chi }^{(1)}+{\chi }^{(2)}+{\chi }^{(3)}+{\chi }^{(4)}+\mathrm{.........}.$$

Many nonlinear Phenomena, such as Kerr self focusing or self-phase modulation [14] can be well understood by restricting the series to lowest-order nonlinear term ${\chi }^{(3)}$ of the expansion. ${\chi }^{(1)}$ refers to the linear response and ${\chi }^{(3)}$ is the macroscopic susceptibility of interest, as centrosymmetric systems have vanishing ${\chi }^{(2)}$ and ${\chi }^{(4)}$due to symmetry [19]. If the molecule or material lacks a center of symmetry, it is the second NLO effects that are of interest. Equally, a dipole moment can be induced through the electric polarizability α under the influence of an external electric field E. The corresponding polarizability tensor α is defined by $\overrightarrow{\mu }=\alpha \overrightarrow{E}$ which is sufficient for weak fields. For very strong fields, in the dipolar approximation, the corresponding polarizability tensor α due an external field is usually written as; $\overrightarrow{\mu }=\alpha \overrightarrow{E}+\beta {\left|\overrightarrow{E}\right|}^2+\gamma {\left|\overrightarrow{E}\right|}^3$which is the basis of NLO effect [20]. Here $\beta$is a third rank tensor known as the hyperpolarizability and $\gamma$ known as the second hyperpolarizability. $\beta$and $\gamma$ constitute the nonlinear responses of the molecule. The corresponding macroscopic quantity to the molecular second order hyperpolarizability, $\gamma$ (microscopic quantity) is the macroscopic susceptibility,${\chi }^{(3)}$ [21], [22]. The first molecular hyperpolarizability ${\beta }_{molec}$, can be calculated from the Gaussian output by using the equation: [23], [24].${\beta }_{mole}={\left[{({\beta }_{xxx}+{\beta }_{xyy}+{\beta }_{xzz})}^2+{({\beta }_{yyy}+{\beta }_{yxx}+{\beta }_{yzz})}^2+{({\beta }_{zzz}^2+{\beta }_{zxx}+{\beta }_{zyy})}^2\right]}^{\frac{1}{2}}$

The mean (isotropic) polarizability <$\alpha$> is obtained from: [23], [24].

$<\alpha >=\frac{1}{3}\left(〈{\alpha }_{xx}〉+〈{\alpha }_{yy}〉+〈{\alpha }_{zz}〉\right)$ and anisotropy $\Delta \alpha$ from: $\Delta \alpha =\frac{1}{2}{\left[\begin{array}{c}{\left(〈{\alpha }_{xx}〉-〈{\alpha }_{yy}〉\right)}^2+{\left(〈{\alpha }_{yy}〉-〈{\alpha }_{zz}〉\right)}^2+{\left(〈{\alpha }_{zz}〉-〈{\alpha }_{xx}〉\right)}^2\hfill \\ +6\left({〈{\alpha }_{xy}〉}^2+{〈{\alpha }_{yz}〉}^2+{〈{\alpha }_{zx}〉}^2\right)\hfill \end{array}\right]}^{\frac{1}{2}}$.