Exploring the molecular spectroscopic and electronic characterization of nanocrystalline Metal-free phthalocyanine: a DFT investigation

The molecular structure optimization and harmonic vibrational frequencies of nanocrystalline metal-free phthalocyanine were investigated using the density functional theory (DFT) implemented in the Gaussian 09 program through B3LYP/6-311G basis set. Thermodynamic and non-linear optical (NLO) characteristics, total dipole moment, HOMO–LUMO energies, natural population analysis (NPA), and global chemical reactivity descriptors were examined. TD-DFT evaluations were used to interpret the electronic absorption. The experimental results and computed values match up adequately. An essential component of photovoltaic devices and the optimized HOMO–LUMO energy gap (2.16 eV) were estimated and compared with those obtained experimentally. The energy band model was used to check the probability of the transition type and estimate the values of energy gaps, which were found to be indirectly allowed. To provide a comprehensive picture for the characterization and determine the activation energy of the charge carriers, the DC electrical conductivity was also examined. It was revealed to have a value between 0.767 and 1.288 eV depending on the temperature range.


Introduction
Phthalocyanines (Pcs) are aromatic organic semiconducting materials that have attracted insignificant attention due to their important role in numerous fields of science and technology applications. They are typically known for their thermal and chemical stability (Alosabi et al. 2022a). This makes them an ideal choice for microscopic and spectroscopic investigations.
The most popular polymorphic phases of Pcs are metastable α-polymorph and the most stable β-forms (Afify et al. 2015). Phthalocyanines (Pc's) have been successfully applied in many applications such as gas sensors (El-Nahass et al. 2015b), solar cells (El-Nahass et al. 2015a;Soliman et al. 2015), and light emitting diodes (Darwish et al. 2016;Soliman et al. 2016b). One of the most common (Pc's) is Metal-free Phthalocyanine (β-H 2 Pc) which is the focus of our study. It has a chemical formula of (C 32 H 18 N 8 ).β-H 2 Pc has a range of potential applications in various fields. It can be used as a semiconducting material in organic electronic devices such as solar cells, organic light-emitting diodes (OLEDs), and organic field-effect transistors (OFETs). β-H 2 Pc has also shown high sensitivity and selectivity towards certain gases, making it a promising candidate for gas sensing applications (Yabaş et al. 2021). In addition, β-H 2 Pc can generate reactive oxygen species (ROS) upon irradiation with light, which can be used in photodynamic therapy for cancer treatment (Sen et al. 2019). β-H 2 Pc has also been studied as a catalyst for various chemical reactions and as an electrode material for electrochemical capacitors and batteries. Furthermore, it has been investigated as a contrast agent for magnetic resonance imaging (MRI) due to its paramagnetic properties.
One of the effective tools which have been used to simulate vibrational analysis of complex molecules is quantum chemical calculations. Alosabi et al. (Alosabi et al. 2022b) have studied the computational geometry of disodium phthalocyanine and estimated the theoretical bandgap between the HOMO and LUMO as 1.3 eV. They also studied the experimental structural and optical properties of thermally evaporated (Na 2 Pc) thin films. Soliman et al. (Soliman et al. 2016a) have combined the experimental and theoretical study of aluminum phthalocyanine chloride (AlPcCl) and they calculated the HOMO-LUMO energy gap equal to 2.14 eV.
Our study is driven by the desire to provide a comprehensive theoretical density functional theory (DFT) analysis for a set of newly developed, highly fabricated, nanocrystalline, β-H 2 Pc small molecules that exhibit semiconducting behavior. This is the first attempt to conduct a detailed DFT investigation of β-H 2 Pc. The findings of our study are expected to contribute significantly to the understanding of β-H 2 Pc electronic and optical properties. By utilizing DFT calculations, we aim to provide a detailed characterization of the molecular structures, electronic properties, and optical spectra of the β-H 2 Pc. By shedding light on the fundamental aspects of β-H 2 Pc, we could have significant implications in the development of new semiconducting materials with unique electronic and optical properties.
To research the optoelectronic properties of this functional organic molecule, several experimental and theoretical methods were used. Density functional theory (DFT) was used to describe the structural and spectral characteristics of β-H 2 Pc to solidify the relationship between structure and attributes. In actuality, the DFT method which includes local or non-local functionals and yields molecular force fields and vibrational wavenumbers is the instrument that is most suitable for this job. Among the numerous available DFT methods, we have selected the B3LYP method (Halim et al. 2018), which combines Becke's three-parameter hybrid exchange functional (B3) with the Lee, Yang, and Parr correlation functional (LYP) (Farag et al. 2018). B3LYP is the most widely used density functional theory (DFT) approach because it is capable of accurately predicting molecular structures and other properties . B3LYP has been shown to perform well in predicting a wide range of properties, such as molecular geometries, vibrational frequencies, and reaction energies. Additionally, B3LYP is relatively easy to use and is available in most quantum chemistry software packages (Al-Otaibi et al. 2023).
Furthermore, B3LYP is often paired with the 6-311G basis set for computational chemistry calculations due to its accuracy in predicting molecular structures and other properties. This combination, known as B3LYP/6-311G, is commonly used and has been shown to provide accurate results for various chemical systems, including organic molecules. For β-H 2 Pc, the B3LYP functional and the 6-311G basis set has been found to provide accurate geometries, vibrational frequencies, and electronic properties compared to experimental data. This is because β-H 2 Pc is a large and complex organic molecule that contains a variety of functional groups, including aromatic rings, nitrogen atoms, and sulfur atoms. The 6-311G basis set includes polarization and diffuse functions that can accurately describe the electronic structure of these functional groups. Additionally, the B3LYP functional has been found to perform well for large organic molecules and can accurately describe the electronic structure and reactivity of β-H 2 Pc (Soliman et al. 2016a).
Indeed, such computations enable the specification of the application field and provide experimentally unavailable information. The atomic charge, dipole moment, harmonic vibrational frequencies, FT-IR, equilibrium geometries, thermo-chemical parameters, energetic of the molecule, and molecular electrostatic potential maps (ESP, MEP, ED) were deeply investigated. Additionally, the effect of solvent polarity on the observed spectra of β-H 2 Pc was studied to predict some of the main physical characteristics and assign the predictable electronic transitions of our molecule using the time-dependent density functional theory (TD-DFT) . The standard statistical thermodynamic functions such as entropy S m0 , heat capacity at constant pressure C p,0 , and enthalpy changes ΔH m0 were determined for various temperature ranges from 100 to 1000 K using the theoretical harmonic frequencies. Following the creation of data processing, calculations, and the findings of cyclic voltammetry on β-H 2 Pc, the material ' s band gap was evaluated using an electrochemical method. Finally, the DC electrical conductivity was investigated at temperatures ranging from 303 to 463 K to obtain the activation energies.

Thin film preparation and physical characterizations
High purity Beta Metal-free Phthalocyanine (β-H 2 Pc) powder (C 32 H 18 N 8 ), utilized in this study was acquired from Eastman Kodak company, USA. β-H 2 Pc thin films were prepared using a high vacuum coating unit (Edwards Co., E306-A, England) through the technique of thermal evaporation. The films were deposited onto cleaned quartz substrates for optical measurements at room temperature and the pressure inside the working chamber is about 10 -4 Pa. the evaporation boat of molybdenum charged by β-H 2 Pc powder was slowly heated to sublime the used powder to perform the thin films. A maintained rate of deposition at about 2.5 Å/s using a quartz crystal thickness monitor (FTM6, Edwards Co., England) attached to the coating unit. The thickness of the film was observed by that thickness monitor.
FTIR spectrum of β-H 2 Pc was recorded in the region 400-4000 cm −1 on a Bruker (Alpha II) spectrophotometer equipped with a Platinum diamond ATR module, with a spectral resolution of 2 cm −1 , at room temperature. Raman micro-spectroscopic analyses of β-H 2 Pc have been performed using a Bruker Senterra dispersive Raman microscope spectrometer. Raman spectrum of β-H 2 Pc was recorded in the region 40-4450 cm −1 with a spectral resolution of 0.5 cm −1 , at room temperature. The spectral dependence of the absorption of the prepared samples was investigated in various solvents using a spectrophotometer, JASCO 550.
Optical characterizations of the as-deposited β-H 2 Pc films were carried out using a computer-aided double-beam spectrophotometer (V670 UV-VIS-NIR, JASCO Co., Japan) at normal incidence of light in the spectral range 190-2500 nm at the room temperature. A blank quartz substrate was used as a reference for the transmission scan, which was the same substrate used for the film deposition. However, the reflection scan was performed at an incident angle of 5º with a reference Al-mirror.
To establish ohmic contacts with the as-deposited β-H2Pc thin film on a glass substrate, high-purity gold (Au) electrodes were evaporated from a helix tungsten wire. These electrodes were used for both electrical conductivity measurements and electrochemical characterizations.
Electrochemical measurements involving cyclic voltammetry (CV) were performed by a three-electrode system using (Biologic analyzer model SP300, Germany) with attached galvanostat/potentiostat/EIS modules. The three-electrode cell configuration utilized the above-fabricated gold (Au) electrode as the working electrode, an ultra-pure carbon rod as the counter electrode, and a silver/silver chloride (Ag/AgCl) electrode as the reference electrode. All tests were conducted at room temperature (23 °C) in ambient conditions with aqueous (5 ml N, N-Dimethylformamide (DMF) dissolved in 15 ml of water) as an aqueous solution electrolyte. For the CV measurements, (6 cycles) were implemented with the potential limits between -2 V and 2 V and a scan rate of 50 mV/s. The dark DC electrical conductivity of the β-H 2 Pc thin films was measured using 2 point-probe technique in a closed furnace under air conditions to prevent a sudden drop in the heater temperature. A high impedance programmable electrometer Keithley model 6512, USA, was used to obtain the resistance of the thin film in the temperature range 303-473 K with an accuracy of ± 0.5%. The temperature was measured using cromel alumel thermocouple connected to a hand-held digital multimeter (DT9208A).

Computational Details
Computational calculations of H 2 Pc were carried out using the Gaussian 09W software package program (Frisch et al. 2009b) at the density functional theory DFT/B3LYP utilizing the 6-311G basis set level (Elkanzi et al. 2020) on Core I5/2.40 GHz personal computer. All the calculations were visualized using Gauss View 5.0.9 molecular visualization program Package (Frisch et al. 2009a). First, the input geometry of H 2 Pc was fully optimized in the ground state without imposing any external constraint on the potential energy surfaces for C, N, and H atoms. Second, the resultant optimized geometry was used as input for vibrational frequency calculations to characterize all stationary points as minima. Many physical parameters, including thermochemistry, HOMO/LUMO Band gap, overall dipole moment (TDM), nuclear repulsion energy, electron affinity (A), ionization energy (I), electronic chemical potential (μ), global hardness (η), global electrophilicity index (ψ) and softness (ζ) have been computed. In addition, the nonlinear optical (NLO) properties such as total static dipole moment (μ), mean polarizability (α), anisotropy of the polarizability (∆α), and mean first order hyperpolarizability (β) were studied.
Natural bond orbital (NBO) calculations were carried out using the program NBO 3.1 (Glendening et al. 1996) implemented in the Gaussian 09W program package. Additionally, the density of state spectra (DOS) was obtained using GaussSum 3.0 program (O'Boyle et al. 2008). The time-dependent density functional theory (TD-DFT) was utilized to compute the excited state energies and the electronic absorption spectra in various solvents using a new hybrid exchange-correlation functional by the Coulomb-attenuating system CAM-B3LYP . The traditional B3LYP functional has been found to have some limitations when it comes to modeling excited state properties of molecules. To overcome these limitations, a new hybrid exchange-correlation functional, called CAM-B3LYP, was developed. CAM-B3LYP includes a Coulomb-attenuating method that better accounts for the long-range effects of electron-electron interactions in excited states . Finally, calculations of the ideal-gas thermodynamic functions were carefully performed using the standalone Perl Script THERMO PL (Irikura 2002).

Geometry optimization characterization
The ground state optimized geometry of the H 2 Pc molecule using DFT at B3LYP/6-311G basis set is depicted in Fig. 1, along with the atomic numbering. The optimized geometrical parameters such as bond lengths, bond angles, and dihedral angles are presented in     Table 1. The most stable geometry of the studied compound is approximately planar structures as indicated by the dihedral angles (where the dihedral angle is nearly equal to 0.00° or 180°). The optimized bond lengths can provide insights into H 2 Pc electronic and optical properties. The H 2 Pc molecule has a planar structure with alternating double and single bonds in the six-member ring, which makes it a conjugated system. Conjugation can lead to a decrease in the molecule's energy, making it more stable. Additionally, conjugation can result in interesting optical and electronic properties such as color, fluorescence, and electrical conductivity.
The bond lengths of the C-C and C-N bonds in a molecule can provide important insights into its chemical properties and reactivity. In the case of H 2 Pc, the six-member ring displays a similarity to the benzene molecule in terms of the C-C bond lengths. The C-C bond length in benzene has been reported to be approximately 1.396 Å (Dereli et al. 2011), and our calculations using the B3LYP/6-311G method yielded optimized bond lengths falling within the range of 1.39-1.41 Å for the C-C bonds in the benzene ring.
In the pyrrole ring, the C-C and C-N bond lengths have been previously observed as 1.366-1.483 Å and 1.356-1.394 Å, respectively . Our calculations using the B3LYP/6-311G method yielded slightly longer C-C bond lengths, ranging from 1.45-1.47 Å. Similarly, the C-N bond lengths were calculated to be slightly longer, ranging from 1.381-1.387 Å. These differences could potentially impact the chemical behavior of H 2 Pc in reactions involving these bonds.

FT-IR analysis
Our investigated compound (C 32 H 18 N 8 ) has 58 atoms, and 168 normal vibrational modes, which are distributed as 86 A′ + 82 A′′ possessing C S point group symmetry. A' modes represent stretching and in-plane vibrations, while the out-of-plane vibrations are represented by A" modes. However, only 16 active modes of vibrations for H 2 Pc, (10 A′ + 6 A′′) were considered to be fitted and compared with our experimental results. Vibrational spectral assignments were performed on the recorded FT-IR spectrum, based on the computationally predicted wavenumbers by B3LYP/6-311G. All calculated modes were numbered from the lowest to the highest frequency within each fundamental wavenumber. The computed vibrational wavenumbers for H 2 Pc at B3LYP/6-311G basis set were scaled with a scaling factor of 0.96 (El-Mansy 2017) corresponding to the theory level used in our calculations. In this perspective, the experimental and computational calculated vibrational wavenumbers, IR intensities, species, and the corresponding assignments of H 2 Pc were collected in Table 2. This data is comparable with the theoretical studies of aluminum phthalocyanine chloride (Soliman et al. 2016a) and disodium phthalocyanine (Alosabi et al. 2022b). In addition, the results of experimental and calculated FT-IR spectra for H 2 Pc at B3LYP/6-311G basis set are displayed in Fig. 2. The absence of the characteristic peak at 713 cm −1 of the α-form and the presence of the absorption peak at 734 cm −1 instead confirms the formation of the β-form (Farid et al. 2007).
The spectral range 675-900 cm −1 is most likely to contain the C-H out-of-plane bending vibrations (Rajesh et al. 2015). The computed vibrations (modes 4, 5, and 6) are assigned Page 11 of 40 662 to C-H out of plan bending vibrations 714.23, 726.31, and 890.18 cm −1 respectively, and appeared as small peaks at 682.86, 735.32, and 871.86 cm −1 , respectively. However, the C-H in-plane bending vibration can be observed in the region 1025-1280 cm −1 (Ibrahim et al. 2012). The computed vibrations (modes 8, 9, and 10) are assigned to C-H in-plane bending vibration at 1100.36, 1156.37, and 1174.61 cm −1 and appear as sharp peaks at 1112.67, 1156.89, and 1190.50 cm −1 , respectively. In aromatic compounds, the ring C = C stretching vibrations generally appear in the spectral range of 1480-1630 cm −1 (Soliman et al. 2013). Therefore, the computed vibrations (modes 11 and 13) were assigned to C = C stretching vibration at 1326.10 and 1515.97 cm −1 and experimentally observed at 1326.66 and 1499.18 cm −1 wavenumbers, respectively. Similarly, C = N stretching vibrations typically appear in the spectral range 1550-1600 cm −1 (El-Mansy et al. 2013). The computed vibrations (modes 12 and 14) are assigned to C = N stretching vibration at 1440.24 and 1591.22 cm −1 which are comparable to the experimental peaks at 1437.06 and 1616.09 cm −1 , respectively.
Moreover, the aromatic C-H stretching vibrations are expected to appear in the spectral range of 3000-3100 cm −1 (El-Mansy and Ismail 2015). The computed vibration (mode 15) was assigned to aromatic C-H symmetric stretching vibration at 3041.52 cm −1 and the experimental peak at 2924.51 cm −1 .
In contrast, a broad medium band was observed at 3441 cm −1 in our experimental FT-IR spectra as shown in Fig. 2, which was assigned to O-H bond stretching vibration. It is well known that free O-H stretching vibration may generally occur in the region of 3700-3500 cm −1 , but in bonded form, a broad and intense band appears in the region of 3550-3200 cm −1 (Sheela et al. 2015). However, neither the investigated molecular structure nor the theoretical calculations support this group. The presence of the hydroxyl group O-H may indicate that our investigated material absorbed water from its surrounding atmosphere. The medium peaks observed at 3400-3300 cm −1 in our calculated FT-IR spectra are due to the N-H stretching.
A comparison of the vibrational frequencies calculated at B3LYP/6-311G with experimental values (see Table 2) revealed that the 6-311G basis set gives reasonable deviations from the experimental values. Any disagreement noted between calculated and experimental vibrational frequencies may be because the calculations were performed on a single molecule in the gaseous state, contrary to the experimental values recorded in the presence of intermolecular interactions (Alosabi et al. 2022b). To evaluate the consistency between both data, the correlation between the calculated and experimental wavenumbers was computed and demonstrated in Fig. 3.
The correlation graph is determined by the linear fitting equation, y = 1.0497 x-6.17642, and correlation values (R 2 = 0.999). A good consistency was observed between the calculated and experimental wavenumbers.

Raman spectra analysis
Besides FT-IR analysis, the vibrational assignment properties of H 2 Pc were confirmed using Raman spectroscopy, which is a highly useful and accurate analytical technique. In this regard, computational Raman vibrational frequencies of H 2 Pc were calculated using the B3LYP/6-311G basis set. The results for the experimental and calculated data were compared and the plot is shown in Fig. 4. It is evident that most of the vibrational modes were observed in the range of 1700-400 cm −1 . This observation strongly supports the findings obtained from FT-IR analysis. Notably, the peaks that appear above 3000 cm −1 for the calculated data were found to be due to C-H stretching which is also comparable to other theoretical studies of metal phthalocyanine (Soliman et al. 2016a).

Mulliken atomic charges analyses
The atomic charges can affect many properties of the molecular system, such as electronic structure, dipole moment, acidity-basicity behavior, molecular polarizability, and electrostatic potential surfaces. Atomic charges analysis by Mulliken (Şahin et al. 2015) is one of the most widely used population analyses to partition an electron density or a wave function into bond orders and charges on the nuclei. The mulliken atomic charge can explain the impact of atomic displacement on the electronic structure. It also can describe the charge transfer in chemical reactions and the processes of electronegativity equalization (El-Mansy 2017; Sheela et al. 2015).
In this perspective, Mulliken population analyses were conducted to describe the bonding and electronic features of the H 2 Pc compound. Mulliken charge distributions were computed along with the natural atomic charge distributions at B3LYP by using a 6-311G basis set. The Mullikan and natural atomic charges distributions were then presented in Table 3 and Fig. 5. The analysis showed that most of the carbon atoms exhibited negative charges, while the carbon atoms attached directly to the negatively charged nitrogen atoms, C(41), C(42), C(43), C(44), C(45), C(46), C(47), and C(48) had positive charges due to a charge transfer from carbon atoms to nitrogen atoms. All of the hydrogen atoms display a net positive charge connected to the carbon in the benzene ring due to their accepting

Raman Intensity
Cal. Raman capacity (Fayed et al. 2020). Also, most of the negative charges were found to be on the nitrogen atoms because of their giving capacity and electron-withdrawing nature. The stability of the metal-free phthalocyanine is due to the intramolecular charge transfer (Soliman et al. 2016a).

Molecular electrostatic potential surface analysis
Furthermore, electrostatic potential mapping can be visualized in a 3D plot over the whole constant electron density surface, which is known as the molecular electrostatic potential (MEP). This physicochemical analysis gives a clear picture of the molecular structure, size, and inner electrostatic potential values. The MEP presents the partial charges and relative polarity of the investigated molecule by providing a visual relative polarity mapping of the molecule (El-Mansy 2017). A color scale is used to indicate the positive and negative charged electrostatic potential in the molecule. The negative extreme, which indicates the minimum electrostatic potential or the greatest repulsion (electrophilic attack), is represented by the red color (Sheela et al. 2015). On the other hand, the blue color is used as a positive extreme which indicates the maximum electrostatic potential or the strongest attraction (nucleophilic attack) (Fayed et al. 2020). In between, there are orange, yellow, and green colors while the potential order increases, respectively Farag et al. 2019). The molecular electrostatic potential (MEP), electrostatic potential (ESP), and electron density (ED) for H 2 Pc at the level of B3LYP/6-311G theory with optimized geometry are shown in Fig. 6. It is seen that the negative ESP is localized more over the nitrogen atoms, and the positive ESP is localized on the rest of the title molecule. While the ED plot for H 2 Pc displays a uniform distribution. As exhibited in the MEP map of H 2 Pc, the electrophilic attack sites appear at the largest negative potential regions, which are localized on the nitrogen atoms shown in red color. Whereas the nucleophilic attack parts appear at the greatest positive potential regions that are localized over all the hydrogen atoms indicated by the blue color. In contrast, the carbon atoms that are linked to each other are shown as orange and yellow color indicating intermediate potential that represents the slightly electron-rich region (Roushdy et al. 2021). Table 4 presents the natural charge, natural population, natural population of the total electrons on the subshells, and natural electronic configuration of active sites for H 2 Pc at the B3LYP/6-311G. The more positively charged atom is, the more likely to take electrons. The atoms with the highest negative charge centers were N49, N50, N51, N52, N53, N54, N57, and N58 atoms. These negatively charged atoms tend to attract electrons from the surrounding regions of the H 2 Pc molecule. Moreover, the natural population analysis revealed that 266 electrons in H 2 Pc are coordinated to subshells as a total Lewis and a total non-Lewis structure, as shown in Table 5.

Natural bond orbital (NBO) characteristics
NBO (natural bond orbital) analysis was carried out to study inter-and intramolecular bonding and interactions, including bonds, as well as charge transfer from an electron donor to an acceptor (Roushdy et al. 2021). The stabilization energy E (2) (energy of hyper conjugative interaction) related to the i → j delocalization was evaluated using the secondorder Fock matrix for each acceptor NBO (j) and donor NBO (i), according to the following formula: Here, q i is the occupancy donor orbital, E i and E j are diagonal elements (orbital energies) and F(i, j) is the NBO Fock matrix element with off-diagonal members ). The higher the stabilization energy E (2) for these transitions, the more intensive the interaction between electron acceptors and electron donors is, and the larger the extent of conjugation of the whole system (Sheela et al. 2015).

Thermo-dynamical and other physical properties
In this section, DFT at B3LYP/ 6-311G basis set was used to compute various thermochemical and physical parameters to gain more insights into the properties of the investigated compound H 2 Pc. Table 7 summarizes many calculated parameters such as total energy, zero-point vibrational energy (ZPVE), rotational constants, entropy (S), molar specific heat at constant volume (C V ), thermal energy, dipole moment, nuclear repulsion energy, spin, number of alpha (spin↑), beta (spin↓) electrons and finally HOMO-LUMO energy gap at room temperature.
The calculated total energy, zero-point vibrational energy, rotational constants, and entropy for H 2 Pc are comparable with the data obtained for aluminum phthalocyanine chloride (Soliman et al. 2016a) at the same basis set B3LYP/6-311G which supports our results.
It is notable that in a paired orbital, the alpha electron (spin↑) has + 1/2 spin, while the beta electron (spin↓) has − 1/2 spin. Therefore, the total spin (S) is zero. The spin multiplicity in this case, X = (2S + 1), is equal to one (singlet). However, The total spin (S) of the unpaired electron is + 1/2, and therefore the spin multiplicity of molecules with one half-filled orbital, singly occupied molecular orbital (SOMO), is equal to two (doublet) (El-Nahass et al. 2011a). A singlet spin multiplicity was observed for the ground state H 2 Pc molecule because it has no unpaired orbital, and the number of alpha electrons (spin↑) is equal to the beta (spin↓) electrons (see Table 7). The total dipole moment is one of the remarkable physical quantities which shows the capability of the studied molecule to interact with the surrounding molecules (Soliman et al. 2012). The determination of a precise dipole moment is very significant as the magnitude of the dipole moment is directly related to the stability of the structure. The dipole moment is lower for the higher structural stability (Çirak et al. 2014). The resultant dipole-moment for H 2 Pc molecule was calculated to be 0.0014 Debye. This value indicates that H 2 Pc has low reactivity to interact with the neighboring molecules and high structural stability. This behavior was due to high symmetry and unremarkable electron carry through metal-free phthalocyanine (El-Mansy et al. 2021).
Frontier molecular orbitals (FMOs) are the most important orbitals in a molecule (highest occupied molecular orbitals, HOMOs, and lowest unoccupied molecular orbitals,  (2)   LUMOs). The intramolecular charge transfer (ICT) interaction between the molecule and its surroundings is explained with the help of the frontier orbital gap (Al-Muntaser et al. 2020). The electronic transition from the ground state to the first excited state due to the absorption of energy is typically described by the excitation of an electron from HOMO (acts as the ability to give an electron) to LUMO (acts as the ability to gain an electron) as an electron acceptor. The HOMO and LUMO molecular orbitals energy gap helps to characterize the kinetic stability and chemical reactivity of the molecule (El-Mansy and Yahia 2014). The smaller the energy gap between the HOMO and LUMO, the easier the electron transport charge between the energy orbitals (Kalaichelvan et al. 2012). This is also more polarizable, has high chemical reactivity, low kinetic stability, and is characterized as a soft molecule (El-Nahass et al. 2011a, 2011b. Figure 7 shows a three-dimensional (3D) plot of the estimated HOMO-LUMO molecular orbitals at the B3LYP/6-311G basis set of H 2 Pc. The HOMOs of H 2 Pc are π orbitals, while the LUMOs are π* orbitals. Red and green colors are used to denote the positive (sharpest repulsion) and negative (strongest attraction) phases of the HOMO and LUMO, respectively. The energy gap between HOMO and LUMO was found to be 2.1595 eV, indicating that the H 2 Pc compound is a highly recommended material to be used in organic Fig. 7 HOMO-LUMO energy gap of H 2 Pc at B3LYP/6-311G solar cells. The calculated energy difference between LUMO and HOMO for AlPcCl is 2.1422 eV (Soliman et al. 2016a) and 2.17 eV for MgPc (Thiruppathiraja et al. 2020). Therefore, the computed HOMO / LUMO gap of H 2 Pc is comparable with another metal phthalocyanine.
The electronic density of the state spectra (DOS) for H 2 Pc is displayed in Fig. 8. The DOS spectra were created by convoluting the molecular orbital information with the Gaussian cures of unit height. DOS spectra denote the number of states per energy interval for occupied and virtual energy levels.
According to Koopman's theorem, HOMO and LUMO energies are directly related to the ionization potential (I) and the electron affinity (A), respectively. The ionization energy (I) is defined as the minimum required energy to remove an electron (to infinity) from the atom or molecule in the gaseous state. On the other hand, electron affinity (A) is the energy released when an electron is added to a neutral atom or molecule to form a negative ion in the gaseous state. These values were calculated for H 2 Pc using relations (Parida et al. 2021): They are found to be 5.3852 and 3.2257 eV respectively. It is worth noting that the electron affinity for H 2 Pc was found to be positive. The calculated ionization potential and electron affinity values for H 2 Pc are comparable to those of MgPc, which are 4.92 eV and 2.75 eV, respectively (Thiruppathiraja et al. 2020).
(2) Quantum chemical parameters such as electronic chemical potential (μ) and electronegativity (χ) can provide information about the potential energy released or absorbed during a chemical reaction. The chemical potential (μ) and electronegativity (χ) are given, respectively, by equations (Rajesh et al. 2015): The prediction of whether the material change happens voluntarily or not is one of the chemical potential (μ) applications. The chemical potential of the H 2 Pc molecule was found to be negative, indicating that it can be created readily from the elements due to its smaller tendency to change into the elements it is created from. This molecule has high stability and does not decompose.
Furthermore, the global hardness (η), which is resistance to the deformation of the electron cloud or polarization of chemical systems produced due to small, faced disturbance during the chemical reaction and is well associated with the reactivity and stability of the chemical system), is given by (El-Mansy et al. 2021): A hard molecule has a large HOMO-LUMO gap, while a soft molecule has a small HOMO-LUMO gap. The stability of a molecule can correlate with hardness. A smaller gap improves quantum mixing, which strengthens chemical reactivity. The computed chemical hardness for H 2 Pc was found 1.07975 eV, which is similar to the estimated value for MgPc as 1.09 eV (Thiruppathiraja et al. 2020).
Moreover, the global electrophilicity index (ψ) is a measure of the ability of the molecular to give electrons. It classifies within an unparalleled absolute scale as the electron acceptors' tendency to gain further electronic charge from the surrounding. The active positions of electrophiles can also be known from this index, and therefore characterize the intramolecular selectivity in the systems. For electrophilicity, Parr suggested (ψ) index in the system containing the charge transfer is directly related to the energy difference for the change in electronic charge, and is given by the following equation (El-Mansy 2017): The larger the value of (μ) and the smaller the value of (η), the better the electrophile is. In a chemical reaction involving two molecules, the nucleophile has a lower value of (ψ) while the electrophile has a higher value of (ψ). Further, softness ( ) which is the multiplicative inverse of global hardness) is given by ): Finally, the maximum number of electrons transferred in a chemical reaction (which is the ratio between electronegativity and global hardness) is given by (Fayed et al. 2020): (4) = −(I + A)∕2

Thermodynamical property analysis
The standard statistical thermodynamic functions, such as entropyS 0 m , heat capacity at constant pressureC 0 p,m , and enthalpy changes ΔH 0 m , were determined for various temperature ranges (100 to 1000 K) using the theoretical harmonic frequencies for H 2 Pc compound using DFT at B3LYP/6-311G level. These results are recorded in Table 9. It is well known that these thermodynamic parameters increase with increasing temperatures because the molecular vibrational intensities increase with increasing temperatures, as the molecular vibrational intensities also increase.
Quadratic polynomial formulas were used to fit the correlation equations between the thermodynamic functions S 0  The calculated thermodynamic characteristics of H 2 Pc at different temperatures have the same behavior as those of the LMO compound (Sheela et al. 2015).

Electronic absorption spectra
The influence of the polar and non-polar solvents on the electronic absorption spectra of H 2 Pc are displayed in Figs. 10 and 11 for both TD-DFT calculated and experimental results, respectively. Table 10 demonstrates the theoretical and experimental first detected (n-π*) transition observed at wavelengths with maximum absorption at several polar and non-polar solvents. When the polarity of the solvent is increased, a red shift and an increase in the absorption wavelength occur. This results in the excited state becoming more stabilized, while the intensity gets reduced. The inconsistency between the experimentally observed and theoretically computed transitions is acceptable. The spectrum in all solvents consists of three bands. The absorption bands in the visible region are typical transitions of (n-π*) and (π-π*) shifts. The maximum absorption band of H 2 Pc is red-shifted by 3-9 nm under the influence of solvent types. The excited configurations considered in compound H 2 Pc can be assigned to the electron excitation of the four highest occupied molecular orbitals φ 130 −1 φ 133 and the lowest three vacant molecular orbitals φ 134 −1 φ 136 . Fig. 12 The charge density maps of the occupied states levels of H 2 Pc at B3LYP/6-311G The charge density maps of the occupied and vacant MO's considered in the transitions are displayed in Figs. 12 and 13, respectively. Table 11 illustrates the theoretical and experimental excitation energies, electronic transition configurations, and oscillator strengths for the optical transitions of the absorption bands in the UV-vis. regions (involving HOMOs) of H 2 Pc at CAM-B3LYP/6-311G by TD method.

Optical band gap determinations
Here, the measured data of transmittance, T(λ), and reflectance, R(λ), obtained from the spectrophotometer were corrected to eliminate the effect of the quartz substrate using the relations given in Ref. (Dongol et al. 2012;Shehata et al. 2018). The corrected absolute values of transmittance, reflectance, and film thickness (1583 nm) were used to estimate the absorption coefficient α. The estimation of α was carried out using the equation given in Ref. (Afify et al. 2015;Al-Muntaser et al. 2022).
The energy band gap (E g ) was obtained by analyzing the variation of the absorption coefficient α with the photon energy hν in the high absorption region for the inter-band transition as follows (Al-Muntaser et al. 2019;Darwish et al. 2016): Fig. 13 The charge density maps of the un-occupied states levels of H 2 Pc at B3LYP/6-311G where A is a constant (independent of the photon energy) and m is an exponent parameter that depends on the type of electronic transition. It is well known that, m = 2 for indirect allowed transition, m = 1/2 for direct allowed transition, m = 3 for forbidden indirect transition, and m = 3/2 for forbidden direct transition. The relation between (αhν) m versus hν was plotted to extract the value of the energy gap E g . Figure 14 shows ( h ) 1∕2 vs. h for β-H 2 Pc thin film of thickness 1583 nm. This figure gives the best straight fit indicating an indirect allowed band gap. The interception with the h axis at ( h ) 1∕2 = 0 gives the corresponding indirect energy band gap. Two linear portions were presented in the curve. The first portion can be referred to the onset absorption of 1.49 eV due to the formation of a bound electron-hole pair, or Frenkel exciton. However, the second portion could be attributed to the fundamental energy gap between HOMO and LUMO of 2.42 eV. The estimated value of the optical band gap was reliable with the theoretical value calculated by B3LYP/6-311G.

Cyclic voltammetry (CV) characterizations
Cyclic voltammetry measurements were conducted to directly estimate the (LUMO) and (HOMO) energy levels of β-H 2 Pc, depending on the reduction and oxidation onset potentials, and to obtain the band gap energy . The HOMO and LUMO energy levels were determined corresponding to the following subsequent relations (El-Nahass et al. 2011a, 2011bSoliman et al. 2016b): where E ox and E red are the onset of weak oxidation (anodic) and strong reduction (cathodic) potential peaks versus Ag/AgCl, respectively. The cyclic voltammogram of the as deposited β-H 2 Pc thin film is shown in Fig. 15. The potentials were internally calibrated using Ag/AgCl redox couple, which has an oxidation potential of − 4.71 eV versus vacuum. The values of the onset oxidation and reduction potential, the calculated values of the HOMO and LUMO energy levels, and the estimated energy band gap of the deposited β-H 2 Pc thin film, obtained from the cyclic voltammetry (CV) data, are tabulated in Table 12. The obtained energy band gap estimated from (CV) was quite close to that extrapolated from absorption onset (optical energy band gap) which equals 1.49 eV. A good consistency was   . 16 The temperature dependence of electrical conductivity σ dc for β-H 2 Pc thin film observed between the value of the energy band gap obtained from the previous calculations and the cyclic voltammetry. This indicates the reliability of the electrochemical evaluation of LUMO and HOMO energy levels.

DC electrical analysis
The temperature dependence of electrical conductivity (σ dc ) for β-H 2 Pc films with a thickness of 1583 nm, measured in two-point probe configurations, displayed in Fig. 16. The plot of lnσ dc against 1000/T can be expressed by the Arrhenius relation (Farag et al. 2012): where • is the pre-exponential factor including the mobility of the charge carrier and the density of states, k B is the Boltzmann constant, ΔE a is the thermal activation energy of the free charge carriers, and T is the temperature in Kelvin. Two regions with different negative slopes are viewed on a straight line. Therefore, two different conduction mechanism regions are observed indicating two activation energies ΔE 1 and E 2 . This behavior is common for many perovskites, semiconductors, and oxides. The activation energy values have been deduced from a linear adjustment at the data points. In the low-temperature region, the activation energy E 1 = 0.767eV . In the hightemperature region, the activation energy ΔE 2 = 1.288eV. The activation energy ΔE 1 is most likely related to the extrinsic generation process. Nerveless, the activation energy ΔE 2 is related to intrinsic conduction. The extrinsic behavior in phthalocyanine could be due to the presence of oxygen in the ambient, which establishes an energy level above the valence band, acting as an acceptor level. The change in the slope and hence the activation energy is explained as a change from extrinsic to intrinsic conduction (Haggag et al. 2011). In the intrinsic region the value of the thermal energy gap E g = 2ΔE 2 , matching the results estimated from the optical absorption spectrum characteristics in this work.

Conclusion
The molecular structure and optical properties of nanocrystalline metal-free phthalocyanine (H 2 Pc) films were investigated using computational and experimental investigations. H 2 Pc films were effectively deposited using the traditional thermal evaporation method. The optimal geometric structure, vibrational bands, and energy gap were calculated using the DFT function B3LYP and the 6-311G basis set. The most stable geometry at the B3LYB/6-311G level of the studied compound was found to be planar. According to our computed results, metal-free phthalocyanine is strongly suggested to be a promising structure for numerous applications in optoelectronic devices due to its smaller HOMO-LUMO energy gap of 2.16 eV. Two different optical transitions were recognized as permitted indirect transition correlated to the onset and onset gaps, with values of 1.49 and 2.42 eV, respectively. The experimental and the calculated FT-IR spectra results confirmed that the powder is the β-form. The calculated vibrational frequencies were compared to the experimental values, and it was observed that B3LYP using the 6-311G basis set produced a reasonable deviation from the experimental values. However, this difference may be explained by the fact that our calculated calculations were conducted (21) = • exp −ΔE a k B T on a single gaseous molecule, as opposed to the experimental values, which were recorded on numerous molecules with intermolecular interactions. The 3D maps of the well-defined molecular electrostatic potentials were evaluated and discussed. The standard statistical thermodynamic functions increased with increasing temperatures. The TD-DFT analysis for the absorption spectra in different polarity solvents spectra has been studied with detected (π-π*) and (n-π*) transition bands. The natural population analysis revealed a distribution of 266 electrons. The HOMO-LUMO energy gap was also determined using cyclic voltammetry, and it was found to be 1.49 eV. The DC conductivity of H 2 Pc films was examined, and the estimated values of the two activation energies are 0.767 and 1.288 eV in the low and high-temperature regions, respectively. Availability of data and materials All of the material is owned by the authors and/or no permissions are required.

Conflict of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Ethical approval This declaration is "not applicable".
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