SEMI-EMPIRICAL INVESTIGATION OF ELECTRONIC, VIBRATIONAL AND THERMODYNAMIC PROPERTIES OF PERYLENE MOLECULE (C 20 H 12 )

This work investigates computationally the spectroscopic and thermodynamics properties of the perylene molecule (C 20 H 12 ) in the gas phase by utilizing a semi-empirical method [Hyper Chem8.0 and WinMopac7.0] programs, via (MNDO-PM3). This method is providing more simplicity and quick performance. The electronic properties such as total energy, dissociation energy, molecular orbital, ionization potentials, electronic affinity, and energy gap were calculated. However, vibration analysis and UV-visible spectra have been calculated. Moreover, the thermodynamic properties at the standard temperature such as heat of formation, entropy, enthalpy, heat capacity, and Gibbs free energy were calculated.


INTRODUCTION
In the last few years, there has been an important effort in the preparation of new organic semiconductors for their application in electronics and optoelectronic devices.Specifically, the development of novel organic semiconductors with effective charge transport capability is an attractive topic in the field of organic electronics for many applications such as organic thin-film transistors (OTFT) and organic light-emitting diodes (OLED) [1][2][3][4].Current and future applications of organic semiconductors range from commercially available OLED displays [5], and infrared applications [6][7], over potentially printable organic [8] and hybrid organic/inorganic solar cells [9], to printable electronic circuits based on organic field-effect transistors (OFET) [10].While OLED displays outperform their inorganic counterparts in terms of energy efficiency [11].Compared to inorganic materials, the use of organic semiconductors are attractive because these materials offer many advantages, for example, low cost and the ability to form thin films, which enable the fabrication of large-area and flexible devices.Organic semiconductors include both small molecules and polymers, small molecules have advantages such as easier synthetic procedures, purification methods, and characterization in view of their small size and well-defined structure [12].In addition, their optical and electronic properties can be easily tuned by means of molecular design.Nature has conserved an infinite variety of organic chemicals, and these materials have much better ranges for ease of making, shaping, and adjusting the properties of materials compared to inorganic chemicals [13].π-π stacking of organic chemicals reveals good conductivity of charge carriers [13][14].Regarding the optical performance, the nano/sub-micron organic structures showed a quantum yield close to that of photoluminescence [15].Subsequently, organic single crystals with excellent optical and electrical properties are critical for the development of organic optoelectronics [16].
Perylene is a brown solid that is a multi-cyclic aromatic hydrocarbon with the chemical formula C20H12.It exhibits blue fluorescence and is utilized as a pure or substituted blue-emitting dopant material in OLEDs.Perylene is also utilized as an organic photoconductor and has been used as technical dyes for many years attributed to its high temperature, photo, and chemical constancy [17].Besides that, in the last years, such compounds gained large widespread because of their use in optical devices [18][19].These π conjugated dyes show high photosensitivity and high electron mobility [20][21].As well as photo physical properties, particularly the sensitivity of their fluorescence lifetime to the PH, render them very useful as probes for live-cell fluorescence lifetime imaging [22].Perylene dyes are a representative framework of electron transport (n-type) organic semiconductors.The energy of their electron transport level is the electron affinity (EA), which is an important parameter in selecting the electron transport materials for device application and the material's electronaccepting ability [23].
The research employed semi-empirical programs that had fast computational cycles.One of these semi-empirical methods is the MNDO-PM3 approach, which calculates the experimentally measured practical values.This program has adopted one of the molecular modeling methods (HyperChem8.0),and by means of the molecules are drawn in a preliminary way, while fixing the nature of the bonds between two atoms of the molecule.Additionally, the spatial geometry of the molecule is calculated to the nearest energy -stable geometric shape by conducting the process of reducing energy to the optimum limit (Geometry optimization).The potential energy curve is drawn by changing the length of the bond between the two atoms and keeping the total energy at each change as low as possible.Quasiexperimental methodologies are based on the electronic Schrödinger equation gained after detach the nuclear and electronic motion, (Born-Oppenheimer approximation) Here r and R indicate the coordinates of the electrons and the nucleus respectively [24].This study's aim is to investigate Perylene's (C 20 H 12 ) vibration spectrum and electronic structure in the IR region and electronic transition in the UV-visible region, using semi-empirical calculations (MNDO-PM3).It has a planar structure with D 2h point symmetry.The research purpose to calculate the lower energy of the stabilized state of the molecule way potential energy curves.One important characteristics that have been studied are for the thermodynamic principles which is concerned with the energy transformation of the substance in the empty space that the substance occupies (system) and the subsequent shift in its energy level the internal energy is a type of potential energy in the system which plays a role in many concepts, including heat capacity its unit cal.mol -1 .deg - [25], All materials have an enthalpy that depends on pressure, temperature, and internal energy, with the exception of gases, which behave ideally or almost ideally [26].The distinctive characteristic that relates to the stability of the compound is either the heat of formation or the enthalpy of formation; if it is positive, the compound is unstable, and if it is negative the compound is stable.Entropy (S), which it is a measure of the resulting randomness of a compound due to the change in temperature degrees, is another function [27].Additionally, free Gibbs energies were calculated using the [HyperChem8.0and WinMopac7.0]software.

COMPUTATION METHODS
Semi-empirical calculation investigations were carried out using MNDO-PM3 in order to understand the geometrical optimization and electron structures of perylene in the neutral and singlet states.Computation the electronic properties like the ionization energy of electronic states, and energy gap (Eg), geometric optimization of Perylene in the gas phase by the semi-empirical way, and calculated the highest occupied molecular orbital in electron (HOMO) and lowest unoccupied molecular orbital in electron (LUMO).In addition, computation of the IR spectrum in the ground state, ionization potential (IP) and electronic affinity (EA) by using the following equations [28], Also, the electronegativity (χ) has been computed by using the equation [29],   While the hardness (η) is defined [29],   Whereas the softness (S) and electrophilic (W) is defined by equations [30], Several thermodynamic properties of the perylene molecule have been investigated using computer programs (WinMopac 7.0).These properties determine the most important conditions for conducting reactions as well as the effect of temperatures on a molecule within the three phases and for a variety of temperatures that include melting, boiling, and standard degrees, as well as comparing the results with experimental values taken from the literature.

RESULTS AND DISCUSSION
Molecular Structure The geometric shape of the perylene molecule (C20H12) was drawn through a program HyperChem8.0 that relies on calculating the internal coordinate (r, θ, φ) and on the geometric form at the equilibrium case of the perylene as in Figure 1.
After getting the matrix and inserting it into the program WinMopac 7.0, some important properties of the perylene molecule were determined, such as the final heat of formation, the total energy at the stability posture, the binding energy, the electronic energy, the core-core interaction, the zero-point energy, the ionization potential, and the electronic affinity, as shown in Table 1.The Un-Harmonic Potential Energy Calculation (Perylene) Studying the potential curve, which represents the correlation between the total energy of the molecule and the interatomic distance of the active bonds in the perylene molecule, permitted to determine the lowest energy value of the curve, which represents the equilibrium point (the bottom of the curve).At the distance of (re=1.1A), it has a value of (-3961.55)kcal/mol for (C10-H21) and (-3962.5510)kcal/mol for (C17-H28).
The potential curve depicted the force between the atoms (C10-H21) and (C17-H28) for perylene, and these forces illustrate the total of the forces of repulsion and attraction.When the distance between the atoms is reduced, the force of attraction from the other nucleus begins to effect each electron.At the same time, electrons and nuclei begin to repel each other [31].When the atoms are separated from each other by increasing the distance, the gravitational force will present that the total energy decreases due to the decrease in the potential energy and the electronic-nucleus attraction, thus; increasing the energy reduction until it reaches the lowest total energy value.The dissociation energy of the molecule is calculated from the difference between its lowest energy value and its value when r is infinity.Furthermore, when the distance between two atoms is infinite, the potential energy becomes zero [31], and the value of dissociation energy is as follows: (C10-H21) (De = 182.44kcal/mol.)as shown in Figure 2, and (C17-H28) (De = 209.08kcal/mol.)illustrated in Figure 3.

Calculation the Vibrational Frequencies of the Perylene Molecule
After drawing the potential energy curve of the molecule at the equilibrium position, the modes of vibration frequencies of the molecule were calculated from this point, which was 90 modes according to (3N-9) and by using (HyperChem 8.0 and WinMopac 7.0) expressed in wavenumber and unit cm -1 .The results showed that the calculated values were close to practical and theoretical values in the literature, as shown in Table 2.We conclude from the above table that the vibration between the atoms (C-H) at the wavenumber (796.71cm-1) [32] is close to the results of the measured literature, both experimentally and theoretically, and is equal to 794 cm-1, which is also consistent with previous studies (793 cm-1) [33].To describe the vibration modes of the perylene molecule HyperChem8.0 a program was used, as the molecule is drawn and the special main axes are determined for being a nonlinear molecule.According to the rule (3N-6), we get 90 basic vibrational frequencies, and these modes were described through the program by clarifying the directions of vibration of the atoms with arrows with an indication of the intensity, and the symmetry of each mode, as shown in Figure 4.

The Eigenvalues of the Orbitals of the Perylene Molecule
The energy levels of the perylene molecule were plotted using HyperChem8.0 software after the stable shape of the molecule was obtained, and the energy values for the highest occupied molecular orbital were equal to EHO-MO = -1.277eV and the lowest unoccupied molecular orbital, ELUMO = -7.984eV, and the symmetry of each orbit is shown in Figure 5. 46 was the number of orbitals occupied by the electrons, and 46 orbitals were unoccupied by the electrons.through which the energy gap between the two levels can be calculated (Eg = ELUMO-EHOMO) and is equal to 6.707 eV.

Electronic Properties of Perylene
After calculated the values of HOMO and LUMO for perylene molecules (C20H12), also calculated electronic properties (EA.IP) and calculated the global chemical indices such as (S, W, χ, η) by used semi-empirical way (MNDO-PM3) and was (IP=7.984eV),(EA=1.277eV),(χ=4.6309eV),(η=3.3535eV),(S=1.6767eV) and (W=3.197eV).By using equations 2, 3, 4, and 5 respectively.Additional to previous study we can also calculate the parameter for total charge density and electrostatic potential, illustrated in (2D contours) as shown in Figure 6.As we noticed from Figure 6b, the electronic charge density was centralized around the carbon atoms in the perylene molecule, in which the carbon atom is more negativity than the hydrogen atom.Figure 6a illustrates the electrostatic potential, which shows the plot of a contour map in 2D.

UV-Vis Spectroscopy of Perylene
The electronic transition was computed using the semi-empirical electronic spectrum from the configuration interaction (CI) method using the HyperChem8.0 program after obtaining the best balanced and stable geometric shape of the perylene molecule.Figure 7 depicts the absorption spectra, which exhibit two different bands (Q-band and B-band).The Q-band was found to be 412.3nm, which is due to the π-π* transition from the highest occupied molecular orbital (HOMO) to the lowest unoccupied molecular orbital (LUMO); this value agreed with previous studies, which found the Q-band to be 435 nm [34].The B-band was identified to be 239.6 nm due to the transition from π levels to LUMO.Table 3 shows the absorbance range calculated between 180 and 650 nm.Thermodynamic Properties of Perylene Molecule One of the important properties that have been studied is the thermal properties of the perylene molecule, which deter-mine the most important conditions on the basis of which chemical reactions take place.After getting the energetically stationary shape of the molecule and obtaining the final matrix containing the charges of the atoms that make up the molecule through the WinMopac7.0program, The MNDO-PM3 method has been used to obtain thermal functions during the three phases of the molecule, and for a number of temperatures that involve melting, boiling, and standard degrees, the dimensions between these atoms (r), the best position of these atoms (Opt.), the values of the angles (θº) and the angles of the diagonal (o) are shown in Table 4.

Heat of Formation
The heat of formation was computed for the perylene molecule in its energy-stable form and for various temperatures ranging from 100 to 300 °K (Table 5), as it included both the boiling and melting points as well as the standard temperature.Figure 8 shows that the heat of formation is temperature dependent and increases as temperature increases.The heat of formation at the standard temperature of 298 °K is 82 kcal.mol - , which is close to the result measured in the literature, which was 72.17 kcal.mol - [35].
Table 5.The values of the heat of formation for the perylene molecule and their corresponding temperature  Entropy Among the thermal properties that were calculated is the entropy for different temperatures to describe the randomness of the compound during the three phases, and the entropy value at the standard degree was 298K by (116) Cal.mol -1 .K -1 , which is close to the measured value from previous studies (112.14)Cal.mol -1 .K -1 [35].The randomness of the molecule begins to increase with increasing temperature as shown in Figure 9 and Table 6.Table 6. the values of the entropy for the perylene molecule and their corresponding temperature

Heat Capacity
The heat capacity of the perylene is a function of temperature and is directly proportional to it, as the increase in temperature increases the number of particles in the upper vibration energy level, and the heat capacity increases with constant pressure.At a temperature of 298 K and a pressure of 1 atmosphere, the heat capacity was 57.2 Cal•mol -1 K -1 , which is close to the practical value of 49.13 Cal•mol -1 K -1 [35].The heat capacity was also calculated for different values of temperature (100-300 °K) as shown in Figure 10 and Table 7. Enthalpy The enthalpy function was determined for a variety of temperatures (Table 8) and represents the sum of the system's internal and external energy.and its value at standard temperature was 8740 Cal•mol -1 , which is near to the sources determined by other methods, which were equal to 9080 Cal•mol -1 , as shown in Figure 11.We observe that the enthalpy increases with rising temperature, demonstrating that the enthalpy is temperature dependent.Gibbs Free Energy After the change in entropy and enthalpy was calculated for the temperature range of 100-300 °K (Table 9) of the perylene molecule, the free energy of Gibbs was calculated in order to determine whether the reaction occurs spontaneously or not, using the equation (ΔG=ΔE-TΔS) and for the same temperatures.and it was at the standard temperature of -2600.7 Cal•mol -1 , and the relation between Gibb's energy and temperature was drawn as in Figure 12.And the relationship was inverse between the two values; as the temperature increased, the free energy of Gibbs gradually decreased.

Figure 1 .
Figure 1.shows the molecular structure of the perylene molecule that was drawn in the program HyperChe8.0.

Figure 4 .
Figure 4. the basic vibrational modes of the perylene molecule were drawn using the HyperChem8.0 program, explaining the intensity, frequency and symmetry.

Figure 5 .Figure 6 .
Figure 5. shows the values of the energy levels of the perylene molecule, showing the highest occupied molecular orbital (EHOMO) and the lowest unoccupied orbital (ELUMO), and the symmetry of each orbital calculated through the program HyperChem8.0

Figure 9 .
Figure 9.The relationship between the entropy of the Perylene molecule and temperature

Figure 9 .
Figure 9.The relationship between the entropy of the Perylene molecule and temperature

Table 1 .
show the result of some important properties of the perylene molecule was calculated, by using (HyperChem8.0and WinMopac7.0)

Table 2 .
vibrational frequencies of perylene calculated by using (HyperChem8.0and WinMopac7.0)programs and Comparison with practical values and other works.

Table 3 .
show the electron transition of perylene

Table 4 .
The final matrix of the perylene molecule is obtained from the WinMopac7.0,showing the interior coordinates (r, θº, φº) in the balance condition.

Table 7 .
Shows the values between the heat capacity and temperature of perylene molecule

Table 8 .
Shows the values between the enthalpy and temperature of perylene molecule Figure 11.The relationship between the enthalpy and Perylene temperature

Table 9 .
the Gibbs free energy values of perylene molecule and the corresponding temperature Figure 12.Show the relation between the Gibbs free energy and temperature of perylene molecule