1 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-H2Pc) which is the focus of our study. It has a chemical formula of (C32H18N8).β-H2Pc 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-H2Pc 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-H2Pc 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-H2Pc 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 (Na2Pc) 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-H2Pc small molecules that exhibit semiconducting behavior. This is the first attempt to conduct a detailed DFT investigation of β-H2Pc. The findings of our study are expected to contribute significantly to the understanding of β-H2Pc 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-H2Pc. By shedding light on the fundamental aspects of β-H2Pc, 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-H2Pc 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 (Roushdy et al. 2019). 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-H2Pc, 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-H2Pc 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-H2Pc (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-H2Pc 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) (Farag et al. 2019). The standard statistical thermodynamic functions such as entropy Sm0, heat capacity at constant pressure Cp,0, and enthalpy changes ΔHm0 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-H2Pc, 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.

2 Experimental details

2.1 Thin film preparation and physical characterizations

High purity Beta Metal-free Phthalocyanine (β-H2Pc) powder (C32H18N8), utilized in this study was acquired from Eastman Kodak company, USA. β-H2Pc 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-H2Pc 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-H2Pc 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-H2Pc have been performed using a Bruker Senterra dispersive Raman microscope spectrometer. Raman spectrum of β-H2Pc 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-H2Pc 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-H2Pc 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).

2.2 Computational Details

Computational calculations of H2Pc 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 H2Pc 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 (Ibrahim et al. 2021). 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 (Farag et al. 2020). Finally, calculations of the ideal-gas thermodynamic functions were carefully performed using the standalone Perl Script THERMO PL (Irikura 2002).

3 Results and discussion

3.1 Geometry optimization characterization

The ground state optimized geometry of the H2Pc 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 H2Pc electronic and optical properties. The H2Pc 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.

Fig. 1
figure 1

Molecular structure of H2Pc at B3LYP/6-311G

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Table 1 Computational optimized structural parameters of H2Pc at B3LYP/6-311G
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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 H2Pc, 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 (Sert et al. 2014). 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 H2Pc in reactions involving these bonds.

3.2 Vibrational assignments properties

3.2.1 FT–IR analysis

Our investigated compound (C32H18N8) has 58 atoms, and 168 normal vibrational modes, which are distributed as 86 A′ + 82 A′′ possessing CS 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 H2Pc, (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 H2Pc 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 H2Pc 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 H2Pc 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).

Table 2 Experimental and computational calculated vibrational wavenumbers (harmonic frequency (cm−1)), IR intensities, species and assignments of H2Pc at B3LYP/6-311G
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Fig. 2
figure 2

Experimental and calculated FT-IR spectra of H2Pc at B3LYP/6-311G

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The computed vibrations (modes 1, 2, 3, and 7) are assigned to isoindole deformation vibration at 442.17, 482.96, 616.32, and 983.03 cm−1 which are comparable to our experimental data at 431.96, 490.17, 614.25 and 1005.29 cm−1, respectively.

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 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.

Fig. 3
figure 3

Theoretical and experimental wavenumbers of H2Pc at B3LYP/6-311G

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The correlation graph is determined by the linear fitting equation, y = 1.0497 x—6.17642, and correlation values (R2 = 0.999). A good consistency was observed between the calculated and experimental wavenumbers.

3.2.2 Raman spectra analysis

Besides FT-IR analysis, the vibrational assignment properties of H2Pc were confirmed using Raman spectroscopy, which is a highly useful and accurate analytical technique. In this regard, computational Raman vibrational frequencies of H2Pc 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).

Fig. 4
figure 4

Experimental and calculated Raman spectra of H2Pc at B3LYP/6-311G

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3.3 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 H2Pc 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 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).

Table 3 Mullikan and natural atomic charges distributions of H2Pc at B3LYP/6-311G
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Fig. 5
figure 5

Mulliken and natural atomic charges distributions of H2Pc at B3LYP/6-311G

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3.4 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 (El-Mansy et al. 2017; Farag et al. 2019).

The molecular electrostatic potential (MEP), electrostatic potential (ESP), and electron density (ED) for H2Pc 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 H2Pc displays a uniform distribution. As exhibited in the MEP map of H2Pc, 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).

Fig. 6
figure 6

Molecular surfaces including molecular electrostatic potential (MEP), electron density (ED) and electrostatic potential (ESP) of H2Pc at B3LYP/6-311G

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3.5 Natural charges and natural population analysis

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 H2Pc 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 H2Pc molecule. Moreover, the natural population analysis revealed that 266 electrons in H2Pc are coordinated to subshells as a total Lewis and a total non-Lewis structure, as shown in Table 5.

Table 4 Natural charge, natural population analysis of H2Pc at B3LYP/6− 311G
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Table 5 Total charge analysis of H2Pc at B3LYP/6-311G
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3.6 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 second-order Fock matrix for each acceptor NBO (j) and donor NBO (i), according to the following formula:

$${E}^{(2)}=\Delta {E}_{ij}={q}_{i}\frac{{F(i, j)}^{2}}{{E}_{j}-{E}_{i}}$$
(1)

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 (Sert et al. 2014). 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).

The stabilization of donor–acceptor interaction corresponds to electron density delocalization between unoccupied (Rydberg or anti-bond) non-Lewis NBO orbital and occupied (lone pair or bond) Lewis NBO orbitals. The second-order perturbation theory analysis of the Fock matrix in the NBO basis of a molecule shows strong intramolecular hyper conjugative interactions and stability of the molecule. According to the stabilization energy, the seven highest probable transitions in this molecule can be ordered in descending order as follows: π*(C5-C6) → π*(C3-C4), π*(C22-C23) → π*(C24-C25), π*(C5-C6) → π*(C1-C2), π*(C22-C23) → π*(C21-C26), the lone pair (C11) → π*(C48-N51), π*(C41-N52) → π*(C42-N57), and π*(C46-N50) → π*(C45-N58). Table 6 shows the second-order perturbation theory analysis of the Fock matrix in the NBO basis as the bonds type, acceptors NBO, donors NBO, the occupancy of electrons, stabilization energy E(2), the Energy difference between donor and acceptor i and j NBO orbitals, and the Fock matrix element between i and j NBO orbitals. The reported data illustrated the stability of H2Pc.

Table 6 Second order perturbation theory of Fock matrix for the optimized structure H2Pc of the selected interactions in the NBO analysis at B3LYP/6-311G
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3.7 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 H2Pc. 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 (CV), thermal energy, dipole moment, nuclear repulsion energy, spin, number of alpha (spin↑), beta (spin↓) electrons and finally HOMO–LUMO energy gap at room temperature.

Table 7 The optimized calculations of total energies, zero-point vibrational energies, rotational constants, entropies, specific heat, thermal energy, nuclear repulsion energy, spin, number of alpha (spin↑), beta (spin↓) electrons, total dipole moment, HOMO–LUMO energy gap, Ionization energy, Electron affinity, Global hardness, Chemical potential, Electronegativity, Global electrophilicity index, and Softness of H2Pc at B3LYP/6-311G
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The calculated total energy, zero-point vibrational energy, rotational constants, and entropy for H2Pc 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 H2Pc 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 H2Pc molecule was calculated to be 0.0014 Debye. This value indicates that H2Pc 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, 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 H2Pc. The HOMOs of H2Pc 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 H2Pc compound is a highly recommended material to be used in organic 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 H2Pc is comparable with another metal phthalocyanine.

Fig. 7
figure 7

HOMO–LUMO energy gap of H2Pc at B3LYP/6-311G

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The electronic density of the state spectra (DOS) for H2Pc 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.

Fig. 8
figure 8

Density of state (DOS) spectrum of H2Pc at B3LYP/6-311G

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3.8 Global reactivity parameters calculations

The global reactivity indices for the H2Pc molecule were evaluated at B3LYP/ 6-311G basis set, including ionization potential (I), electron affinity (A), chemical potential (μ), electronegativity (χ), hardness (η), electrophilicity index (ψ), softness (ζ) and the maximum number of electrons transferred in a chemical reaction (∆Nmax) (Devi et al. 2022; Rijal et al. 2023; Roushdy et al. 2021). These values are tabulated in Table 7.

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 H2Pc using relations (Parida et al. 2021):

$$I=-{E}_{HOMO}$$
(2)
$$A=-{E}_{LUMO}$$
(3)

They are found to be 5.3852 and 3.2257 eV respectively. It is worth noting that the electron affinity for H2Pc was found to be positive. The calculated ionization potential and electron affinity values for H2Pc are comparable to those of MgPc, which are 4.92 eV and 2.75 eV, respectively (Thiruppathiraja et al. 2020).

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):

$$\mu =-\left(I+A\right)/2$$
(4)
$$\chi =\left(I+A\right)/2$$
(5)

The prediction of whether the material change happens voluntarily or not is one of the chemical potential (μ) applications. The chemical potential of the H2Pc 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):

$$\eta =(I-A)/2$$
(6)

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 H2Pc 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):

$$\psi ={\mu }^{2}/2\eta ={\chi }^{2}/2\eta$$
(7)

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 (\(\zeta\)) which is the multiplicative inverse of global hardness) is given by (El-Mansy et al. 2017):

$$\zeta =1/\eta$$
(8)

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):

$$\Delta {N}_{max}=-\mu /\eta =\chi /\eta$$
(9)

3.9 Nonlinear optical (NLO) analysis

To study the relations between non-linear optical properties (NLO) and molecular structures, the polarizabilities and first-order hyperpolarizabilities of H2Pc were estimated using the B3LYP method and the 6-311G basis set, based on finite field approach calculations. The dipole moment, polarizability and hyperpolarizability components (µx, µy, µz, αxx, αxy, αyy, αxz, αyz, αzz and βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz, βyzz, βzzz) were obtained by a frequency job output file from Gaussian 09W and are presented in Table 8. The complete formulas for evaluating the magnitude of the total static dipole moment (µtot), the average value of the polarizability (αtot), the anisotropy of polarizability (Δα), and the mean first-order hyperpolarizability (βtot) are as follows (Akhtari et al. 2014; El-Mansy et al. 2021):

Table 8 Total static dipole moment (μtot), mean polarizability (αtot), anisotropy of the polarizability (∆α), and mean first- order hyperpolarizability (βtot), of H2Pc at B3LYP/6-311G. Also, Non-linear optical parameters, third-order nonlinear optical susceptibility (\({\chi }^{(3)}\)) and the nonlinear refractive index (n2) of the as-deposited β-H2Pc thin film
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$${\mu }_{tot}=\sqrt{{\mu }_{x}^{2}+{\mu }_{y}^{2}+{\mu }_{z}^{2}}$$
(10)
$${\alpha }_{tot}=\frac{{\alpha }_{xx}+{\alpha }_{yy}+{\alpha }_{zz}}{3}$$
(11)
$$\Delta \alpha =\sqrt{\frac{{\left({\alpha }_{xx}-{\alpha }_{yy}\right)}^{2}+{\left({\alpha }_{yy}-{\alpha }_{zz}\right)}^{2}+{\left({\alpha }_{zz}-{\alpha }_{xx}\right)}^{2}+6{\alpha }_{xy}^{2}+6{\alpha }_{yz}^{2}+6{\alpha }_{xz}^{2}}{2}}$$
(12)
$${\beta }_{tot}=\sqrt{{\left({\beta }_{xxx}+{\beta }_{xyy}+{\beta }_{xzz}\right)}^{2}+{\left({\beta }_{yyy}+{\beta }_{yzz}+{\beta }_{yxx}\right)}^{2}+{\left({\beta }_{zzz}+{\beta }_{zxx}+{\beta }_{zyy}\right)}^{2}}$$
(13)

The computed (µtot), (αtot), (Δα), and (βtot) values of the H2Pc molecule, are presented in Table 8. The calculated values have been converted into electrostatic units (esu) (α; 1 a.u. = 0.1482 × 10−24 esu, β; 1 a.u. = 8.6393 × 10−33 esu). The calculated total static dipole moment value is 0.0014 Debye. The calculated average value of the polarizability is found to be equal to 30.9493 × 10−24 esu. The calculated anisotropy of polarizability is equal to 46.4782 × 10−24 esu. The magnitude of the first order hyperpolarizability determines the NLO response of the molecule. The calculated mean first order hyperpolarizability of H2Pc is equal to 4.9820 × 10−30 esu, which is 13 times magnitude of urea (βurea = 0.3728 × 10−30 esu). This result reveals the nonlinearity of H2Pc molecule and its potential for NLO technology and optoelectronic device applications. Furthermore, the non-linear experimental optical parameters of the as-deposited β-H2Pc thin film, such as the third-order nonlinear optical susceptibility (\({\chi }^{(3)}\)) and the nonlinear refractive index (n2), were determined and listed at Table 8 at different photon energies.

3.10 Thermodynamical property analysis

The standard statistical thermodynamic functions, such as entropy\({S}_{m}^{0}\), heat capacity at constant pressure\({C}_{p, m}^{0}\), and enthalpy changes \(\Delta {H}_{m}^{0}\), were determined for various temperature ranges (100 to 1000 K) using the theoretical harmonic frequencies for H2Pc 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.

Table 9 Thermodynamic parameters of H2Pc at different temperature at B3LYP/6-311G
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Quadratic polynomial formulas were used to fit the correlation equations between the thermodynamic functions \({S}_{m}^{0}\), \({C}_{p, m}^{0}\), \(\Delta {H}_{m}^{0}\) and temperatures. The fitting factors (R2) for these thermodynamic properties are all within 0.999. The correlation relationships can be used to predict the values of heat capacity at constant pressure, entropy, and enthalpy changes at any other temperature approximately. The correlation graphics of thermodynamical parameters are displayed in Fig. 9. All these thermodynamic parameters provide the required data for potential research on H2Pc. The corresponding fitting equations of the H2Pc compound are as follows:

Fig. 9
figure 9

Thermodynamic properties of H2Pc at different temperature at B3LYP/6-311G

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$$\Delta {H}_{m}^{0}=-24.10001+0.18238T+5.44767\times {10}^{-4}{T}^{2} \left({R}^{2}=0.9994\right)$$
(14)
$${C}_{p, m}^{0}=-53.8347+2.0992T-9.23098\times {10}^{-4}{T}^{2} \left({R}^{2}=0.9991\right)$$
(15)
$${S}_{m}^{0}=237.90758+1.80742T+-3.06238\times {10}^{-4}{T}^{2} \left({R}^{2}=0.9998\right)$$
(16)

The calculated thermodynamic characteristics of H2Pc at different temperatures have the same behavior as those of the LMO compound (Sheela et al. 2015).

3.11 Electronic absorption spectra

The influence of the polar and non-polar solvents on the electronic absorption spectra of H2Pc 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 H2Pc is red-shifted by 3–9 nm under the influence of solvent types. The excited configurations considered in compound H2Pc can be assigned to the electron excitation of the four highest occupied molecular orbitals φ130−1φ133 and the lowest three vacant molecular orbitals φ134−1φ136.

Fig. 10
figure 10

Theoretical electronic absorption spectra of H2Pc in different solvents at the CAM/B3LYP/6-311G

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Fig. 11
figure 11

Experimental electronic absorption spectra of β-H2Pc in different solvents

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Table 10 Theoretical and experimental wavelengths at high absorption (λmax) at several solvents of H2Pc at CAM-B3LYP/6-311G
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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 H2Pc at CAM-B3LYP/6-311G by TD method.

Fig. 12
figure 12

The charge density maps of the occupied states levels of H2Pc at B3LYP/6-311G

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Fig. 13
figure 13

The charge density maps of the un-occupied states levels of H2Pc at B3LYP/6-311G

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Table 11 Computed excitation energies (eV), electronic transition configurations, and oscillator strengths (ƒ) of H2Pc at CAM-B3LYP/6-311G
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3.12 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 (Eg) 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):

$$\alpha h\nu = A {\left(h\nu -{E}_{g}\right)}^{m}$$
(17)

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 Eg.

Figure 14 shows \({\left(\alpha h\nu \right)}^{1/2}\) vs. \(h\nu\) for β-H2Pc thin film of thickness 1583 nm. This figure gives the best straight fit indicating an indirect allowed band gap. The interception with the \(h\nu\) axis at \({\left(\alpha h\nu \right)}^{1/2}=0\) 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.

Fig. 14
figure 14

The (αhv)1/2 versus photon energy of β-H2Pc thin film

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3.13 Cyclic voltammetry (CV) characterizations

Cyclic voltammetry measurements were conducted to directly estimate the (LUMO) and (HOMO) energy levels of β-H2Pc, depending on the reduction and oxidation onset potentials, and to obtain the band gap energy (Farag et al. 2021). The HOMO and LUMO energy levels were determined corresponding to the following subsequent relations (El-Nahass et al. 2011a, 2011b; Soliman et al. 2016b):

$${E}_{HOMO}=-({E}_{ox}+4.71) eV$$
(18)
$${E}_{LUMO}=-({E}_{red}+4.71) eV$$
(19)
$$Energy gap=({E}_{HOMO}-{E}_{LUMO}) eV$$
(20)

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-H2Pc 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-H2Pc 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 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.

Fig. 15
figure 15

Cyclic voltammogram of β-H2Pc thin film recorded in DMF

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Table 12 The main parameters deduced from cyclic voltammetry of β-H2Pc thin film
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3.14 DC electrical analysis

The temperature dependence of electrical conductivity (σdc) for β-H2Pc films with a thickness of 1583 nm, measured in two-point probe configurations, displayed in Fig. 16. The plot of lnσdc against 1000/T can be expressed by the Arrhenius relation (Farag et al. 2012):

$$\sigma ={\sigma }_{^\circ }\mathrm{exp}\left(\frac{-\Delta {E}_{a} }{{k}_{B}T}\right)$$
(21)

where \({\sigma }_{^\circ }\) is the pre-exponential factor including the mobility of the charge carrier and the density of states, \({k}_{B}\) is the Boltzmann constant, \(\Delta {E}_{a}\) 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 \(\Delta {E}_{1}\) and \({E}_{2}\). This behavior is common for many perovskites, semiconductors, and oxides.

Fig. 16
figure 16

The temperature dependence of electrical conductivity σdc for β-H2Pc thin film

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The activation energy values have been deduced from a linear adjustment at the data points. In the low-temperature region, the activation energy \({E}_{1}=0.767 eV\). In the high-temperature region, the activation energy \(\Delta {E}_{2}=1.288 eV.\) The activation energy \(\Delta {E}_{1}\) is most likely related to the extrinsic generation process. Nerveless, the activation energy \(\Delta {E}_{2}\) 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 \({E}_{g}=2\Delta {E}_{2}\), matching the results estimated from the optical absorption spectrum characteristics in this work.

4 Conclusion

The molecular structure and optical properties of nanocrystalline metal-free phthalocyanine (H2Pc) films were investigated using computational and experimental investigations. H2Pc 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 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 H2Pc 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.