DFT study of frontier orbitals and NLO properties of a phenanthroline and nitrophenol complex

Abstract

The hydrogen-bond charge transfer complex (HB-CTC) formed between the donor, 1,10-phenanthroline (Phen), and the π-acceptor, p-nitrophenol (PNP), has been thoroughly investigated through theoretical studies. The molecular structure and the HOMO–LUMO energy gap (ΔE_H–L) of this complex have been investigated by the density functional theory. This work has studied the HB-CTC complex through FTIR, ¹HNMR, ¹³CNMR, and electronic absorption spectra. A molecular electrostatic potential surface (MESP) study allowed us to explore key aspects of intermolecular interaction. Moreover, reduced density gradient analysis was conducted to visualize valuable insights into non-covalent interactions within the complex components. Quantum Theory of Atoms in Molecules was used to analyze the interaction between the 1,10-phenanthroline and p-nitrophenol. The findings from this research not only enhance our understanding of HB-CT complexes but also highlight their exciting potential for innovative applications in various fields.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-026-38340-x.

Introduction

Charge-transfer complexes (CTCs) form when multiple molecules interact, where some serve as acceptors (A) and others as donors (D)¹. The molecules assemble through resonance, facilitating charge transfer from D to A via charge transfer interactions and intermolecular hydrogen bonds^2–4.

The Mulliken theory reveals an exact linear relationship between the energy of complex formation and the square root of charge magnitude. This critical relationship underscores the strong likelihood of interactions among components in the CTC system and highlights the charge’s pivotal role in shaping these dynamics⁵. Foster has conducted comprehensive studies on this complex⁶. Recent advancements in CTC design have enhanced their catalytic properties, selective guest entrapment, and drug-receptor binding. Additionally, CTCs play significant roles in various biological systems, including DNA binding, antifungal activity, and antimicrobial functions^7–9.

Hydrogen bond-charge transfer (HB-CT) complexes are characterized by strong intermolecular interactions, with hydrogen bonds playing a vital role in stabilizing these systems^10,11. The study of these complexes is significant in various fields, including material science^12,13, organic chemistry^14,15, photochemistry^16,17, biological systems¹⁸, and biochemistry^19,20, due to their diverse applications ranging from molecular recognition to energy harvesting. A crucial aspect of understanding these systems lies in their electronic absorption spectra, which provide insights into their electronic structure and charge transfer dynamics^21,22. In HB-CT complexes, electrons transfer from the donor molecule to the acceptor, resulting in a charge-separated state. The degree of charge transfer and the environment surrounding the hydrogen bond both significantly affect the complex’s electronic properties²³.

In recent years, complexes have constituted an interesting family of molecules for nonlinear optical (NLO) materials due to their unique electronic structure²⁴. Complexes containing a ligand that readily undergoes reduction (di-thiolate) and another more prone to oxidation (di-imine) significantly absorb light in visible and ultraviolet spectra. The molecules can be tailored for prospective use as photosensitizers and photocatalysts^25–27.

Significant theoretical progress has been made to enhance the understanding of the complex structure, electronic transitions, and dynamic interactions within charge-transfer complexes²⁸. V. H. Rezvan and colleagues conducted an attractive study on a novel HB-CT complex formed through hydrogen bonding, with melanin acting as the electron donor and 1,4-dinitrobenzene as the electron acceptor. Their rigorous examination of the structure and properties of this complex, utilizing advanced spectroscopy techniques, unequivocally confirmed its stability. To enhance understanding, they used advanced computational methods to study the intermolecular interactions in the complex gas phase. Additionally, their thermodynamic analysis of the CTC formation provides crucial insights into the spontaneous formation and strong interactions among its components, insights that have significant potential for a variety of applications in chemistry. The natural bond orbital analysis provided a detailed view of electronic density distribution, charge-transfer pathways, and the underlying stabilization mechanisms within the complex, reinforcing the vital role this research could play in advancing our knowledge of charge-transfer processes²⁹. In another study, a sophisticated CTC has been successfully synthesized using melamine as the hydrogen acceptor and 4-nitrobenzoic acid as the electron donor. The intricate characteristics of this complex were thoroughly investigated using advanced techniques such as IR, NMR, and UV–vis spectroscopy. Computational analysis conducted in the gas phase offered significant insights into the structure and stability of the complex, aligning well with the experimental results. The observed negative values for free Gibbs’ energy indicate the spontaneous formation of the complex. The negative entropy value further confirms its remarkable stability, suggesting significant potential for future applications³⁰. Computational methods grounded in quantum chemistry offer valuable insights into charge-transfer interactions and hydrogen transfer between donors and acceptors³¹. Common functionals used include B3LYP, PBE0, and hybrid functionals, which balance accuracy and computational efficiency^32,33.

Khan and colleagues successfully synthesized a fascinating HB-CTC between 1,10-phenanthroline (Phen) and p-nitrophenol (PNP) in methanol at room temperature (Fig. 1). Their extensive spectrophotometric analysis revealed a robust interaction between these two compounds, where p-nitrophenol acts as an effective π-acceptor (hydrogen donor) and 1,10-phenanthroline serves as an electron donor and hydrogen acceptor. The spectroscopic results showcased new bands indicative of complex formation alongside observable changes that underscore the significance of their findings. Furthermore, the study highlighted a significant CT interaction characterized by proton migration from the acceptor to the donor, reinforced by intermolecular hydrogen bonding described as N⁺-H–O^-. Thermal analysis of the individual components and the resultant HB-CTC provided critical insights, revealing a significant weight loss at 142.2 °C due to crystallization, which coincided with a corresponding endothermic peak. This loss can be attributed to the decomposition of the HB-CTC into its constituent parts. Importantly, the researchers investigated the binding affinity of HB-CTC for calf thymus DNA, resulting in ground-breaking findings. Fluorescence spectroscopy confirmed a strong interaction between the HB-CTC and DNA, suggesting promising antibacterial and antifungal properties against various strains. This innovative work showcases the potential applications of the synthesized HB-CTC and paves the way for future research in bioactive materials³⁴. The present work investigated the CT between the 1,10-phenanthroline and p-nitrophenol through density functional theory. Charge-transfer transitions between molecules were performed using the UV–Visible spectrum of the complex and natural bond orbital (NBO) analysis³⁵. This paper investigates the electronic absorption spectra of hydrogen-bond charge-transfer complexes, emphasizing their formation, characterization, and the fundamental physical principles that govern their spectral properties. By analyzing experimental data and theoretical models, we seek to elucidate how the nature of hydrogen bonding influences CT mechanisms and, consequently, the observed spectral features. We also aim to highlight the significance of these complexes in broader chemical contexts, particularly concerning their roles in energy transfer processes and molecular recognition³⁶. Through this exploration, we hope to contribute to a deeper understanding of the fundamental processes that define the behavior of HB-CT complexes and to pave the way for future research that could harness these remarkable properties for practical applications.

Figure 1.

Schematic formation of the HB-CT complex derived from 1,10-phenanthroline and p-nitrophenol.

DFT calculations

The molecular structures were drawn using GaussView 6.0 software³⁷. Quantum calculations for structure optimization were performed using the Gaussian 09 package³⁸. One of the quantum-computing techniques widely used to describe surface structures is DFT³⁹. DFT computations have been performed on energy-minimized structures of free p-nitrophenol, 1,10-phenanthroline, and the HB-CT complex, have been predicted. Geometric optimizations were performed using DFT with Becke’s three-parameter hybrid exchange method⁴⁰ for the charge-transfer complex. We utilized the Popel-B3LYP/6-311G(d,p) basis set⁴¹, which is crucial for providing accurate and reliable computational results. The hybrid functional B3LYP, originally designed to investigate vibrational absorption and circular dichroism⁴², has demonstrated remarkable computational efficiency, comprehensive applicability, and high precision. Its emergence marks a significant advancement in the field, offering an ideal balance that appeals to researchers seeking both quality and practicality in their computational studies. The B3LYP functional, combined with 6-311G (d,p) basis set, was selected to obtain optimized geometries and electronic properties for further analyses. Although it is known to have functional limitations in accurately describing long-range dispersion interactions, it provides sufficiently accurate results⁴³ for the qualitative and comparative objectives of this study. This approach enhances the dependability of our findings and strengthens the overall outcomes of the research. Vibrations are calculated with the finite difference method⁴⁴. The results from this method show that the infrared (IR) frequencies are all positive, supporting the idea that the optimized geometry corresponds to a minimum on the potential energy surface. This crucial observation underscores the validity of our results. Additionally, the bands identified in the FTIR spectra are elucidated through animated vibrational modes, offering remarkable precision and significantly deepening our understanding of their characteristics⁴⁵. The ultraviolet–visible (UV–Vis) spectra of the title compounds were obtained using the TD-DFT method⁴⁶. In this study, the chemical reactivity of the HB-CTC was analyzed by examining frontier molecular orbitals (FMOs), the HOMO–LUMO energy gap (ΔE_H–L), interaction energy, interaction enthalpy, interaction entropy, and Gibbs free energy of interaction. We utilized the powerful visualization capabilities of Multiwfn 3.8⁴⁷ and VMD software⁴⁸ to depict the three-dimensional structure of the RDG surface⁴⁹. Calculated and experimental FTIR and UV–Vis spectra were compared to validate the computational models. Furthermore, reduced density gradient (RDG), natural bond orbital (NBO), and molecular electrostatic potential (MEP) analyses were performed to elucidate intermolecular interactions. Furthermore, the quantum theory of atoms in molecules (QTAIM) was employed to evaluate the molecular systems under the influence of the field effect. For this purpose, the AIM2000 software was used⁵⁰. Frontier orbital (HOMO–LUMO), MEP, and AIM analyses were carried out using Density Functional Theory with the B3LYP functional and a 6-311G(d,p) basis set.

Results and discussion

Optimized molecular structures

DFT is employed to optimize the molecular geometry of the HB-CT complex. Accurate geometry is essential for understanding the nature of hydrogen bonds and calculating interaction energies. Figure 2 illustrates the optimized gas-phase geometries of the studied HB-CT complex, p-nitrophenol, and 1,10-phenanthroline, using distinct atomic numbering for clarity. The optimized geometries of p-nitrophenol (PNP, π-acceptor) and 1,10-phenanthroline (Phen, π-donor) are strategically aligned parallel to one another, subjected to a thorough re-optimization, and permitted to relax freely without any constraints. This approach ensures the most accurate and efficient interaction between these crucial compounds. The orientation of the two components in the HB-CT complex differs significantly from their original orientation. When donor and acceptor molecules come close together, the resulting complex [(Phen)(PNP)] can be understood as arising from the intermolecular hydrogen bonding. As illustrated in Fig. 2, the hydrogen-bonded NH bond lengths vary in strength, ranging from 1.866 to 2.605 Å. This range indicates that the intermolecular bond length of N…H–O, measuring 1.866 Å, corresponds to a strong hydrogen bond. In contrast, the intermolecular bond length of N…H-C, measuring 2.605 Å, indicates a moderate hydrogen bond or vdW interactions. There is only one type of H-bonding in [(Phen)(PNP)] complex. In this HB-CT complex, the donor molecule strategically engages the acceptor molecule through the aromatic nitrogen atom, highlighting a significant interaction. The approach of the donor molecule towards the nitrogen atom indicates that this nitrogen serves as the central point of donation. Selected bond distances of the optimized geometries of Phen, PNP, and [(Phen)(PNP)] at the B3LYP/6-311G (d, p) method in the gas phase are presented in Table 1. Following complexation, most bond lengths changed significantly, with some stretching while others stayed constant. This variability in bond length highlights the dynamic nature of molecular interactions and their impact on structural properties. This observation supports the evidence of the CT process, and similar findings have been documented in previous reports^51,52 (see Table S1).

Figur 2.

Optimized structures of (a) p-nitrophenol, (b) 1,10-phenanthroline, and (c) [(Phen)(PNP)] complex in the gas phase, along with dipole moment vectors, GaussView 6 program were used to visualize the molecular graph³⁷.

Table 1.

Selected optimized geometrical parameters (bond length, bond angle, and tortional angle) of 1,10-phenanthroline (Phen), p-nitrophenol (PNP), and [(Phen)(PNP)] complex in the gas phase.

	rO-H	rC-N	rO=N	rOC	θCOH
Phen	0.967	1.301	1.359	1.365	110.5	–	179.7
PNP	–	1.349	–	–	–	− 4.8	–
Phen in CTC	0.988	1.462	1.228	1.338	112.3	–	179.9
PNP in CTC		1.351				– 0.5	–

Several important molecular parameters were assessed at the optimized geometries of the complex and its components, yielding exact findings. Atomic charge calculations revealed that CT occurred during complex formation. The optimized structure clearly illustrates the formation of two intermolecular hydrogen bonds, underscoring the strength of interactions during complex formation⁵². Hydrogen bonds are classified based on their donor–acceptor distances. Distances below 2.5 Å are categorized as strong, indicating predominantly covalent character. Distances between 2.5 and 3 Å are considered moderate and are characterized by electrostatic interactions. Lastly, distances between 3.0 and 4.0 Å are classified as weak, reflecting purely electrostatic bonding. Additionally, the strength of hydrogen bonds depends on the bond angle X–H–Y. A bond angle close to 180° significantly increases the strength of hydrogen bonds. The hydrogen bonds N21–H37–O36 and N22–H37–O36 illustrate this concept with bond lengths of 1.866 Å and 2.605 Å, respectively (see Fig. 2). The bond angles of the hydrogen bonds are recorded at 155.7° and 129.8°. The 155.7° angle in the N…H–O bond indicates an almost linear interaction, emphasizing the presence of strong hydrogen bonds that are essential for the formation of CTC. These strong hydrogen bonds are crucial for maintaining the integrity of the interactions between the acceptor and donor molecules, effectively facilitating the spontaneous formation of the HB-CTC.

Each distinct hydrogen bond between donor and acceptor molecules may be associated with a specific dihedral angle () that facilitates the interaction. When the relative orientation of the donor and acceptor moieties involves torsional freedom, each H-bond can correspond to a distinct angle. These angles often represent the twist between aromatic rings or planar groups and may also involve the donor-H… acceptor atom path. Our data show that the angle of the donor component in HB-CTC is larger than that of the free donor species. A larger angle suggests that the donor undergoes torsional twisting or reorientation upon participating in the HB-CTC. This change typically reflects a conformational adaptation to optimize non-covalent interactions, such as hydrogen bonding. In the free donor component, the donor may adopt a more planar or relaxed geometry. But, the HB-CTC, the increased likely reflects a twist that better aligns the donor with the acceptor, facilitating hydrogen bonding and charge transfer. In contrast, the free acceptor exhibits a larger angle than the acceptor within the HB-CTC. This larger value indicates a more twisted structure and greater conformational freedom. Upon complex formation, the angle of the acceptor decreases, reflecting a more planar and constrained geometry optimized for interaction within the HB-CTC. Figure 2 illustrates key intermolecular interactions. These geometric parameters confirm the presence of strong, directional hydrogen bonding, facilitating effective charge transfer and stabilizing the complex formation.

Thermochemistry

DFT allows the calculation of binding energies associated with the formation of HB-CT complexes. This involves evaluating the difference in electronic energy between the complex and its constituent parts⁵³. The enthalpy of formation can be computed based on the optimized energies, providing insights into the stability of the HB-CT complex. From the calculated enthalpies and estimated entropies (obtained from vibrational frequency analysis), researchers can determine the formation Gibbs free energy (ΔG), indicating the spontaneity of the complex formation. DFT can quantify vibrational modes through normal mode analyses, enabling an estimation of the entropy change, which is essential for a complete thermodynamic profile⁵⁴. In biological systems, DFT is extensively used to investigate enzyme–substrate interactions and DNA base pairing, where hydrogen bonding is crucial. Understanding the thermodynamics of these interactions helps in elucidating biological pathways⁵⁵. The DFT study of thermochemistry in HB-CT complexes serves as a powerful tool for understanding the energetics and dynamics associated with hydrogen bonding and charge transfer⁵⁶. The insights garnered from such studies have significant implications across various fields, including biochemistry, material science, and molecular electronics⁵⁷.

Table 2 shows that the key statistical thermodynamic functions, including entropy (S) and zero-point vibrational energy, are computed to provide insights into molecular behavior. The zero-point energies, internal energy, enthalpy, Gibbs free energy, and entropy of a molecular system are determined through frequency calculations⁵⁸. Specifically, the interaction enthalpy and Gibbs free energy were obtained using the following Eqs. (1, 2):

1

2

Table 2.

Calculated interaction energy(ΔEº_int), interaction enthalpy (ΔHº_int), interaction Gibbs free energy (ΔGº_int), and correction for vibrational zero-point energy (ΔZPVE) for the studied complex in the gas phase (kcal/mol).

(D)(A) complex	ΔEºint	ΔHºint	ΔZPVE	ΔGºint	-TΔS
[(Phen)(PNP)]	− 13.598	− 14.186	1.064	− 4.293	9.893

Here, ZPVE refers to the zero-point vibrational energy correction, H_thermal denotes the thermal enthalpy correction, and S represents the entropy obtained from vibrational frequency calculation⁵⁹. The BSSE correction was evaluated according to the standard expression:

3

where E_BSSEE represents the counterpoise correction obtained from monomer calculations in the presence of ghost orbitals⁶⁰. Essential thermodynamic properties have been examined for (Phen)(PNP) complex using the B3LYP/6-311G(d,p) method. According to thermodynamic principles, a spontaneous process requires the Gibbs free energy change (ΔG) to be negative. The Gibbs free energy value of − 4.293 indicates that the complex formation process is spontaneous (see Table 2).

The interaction energies of the studied system were computed using B3LYP, CAM-B3LYP, and ωB97XD functionals with the 6-311G(d,p) basis set. Both uncorrected and counterpoise-corrected energies were evaluated to assess the impact of the basis set superposition error (BSSE). The results are summarized in Table S2. The BSSE corrections are small for all methods, ranging from 0.004 to 0.005 Hartree, indicating that the chosen basis set is sufficiently large to minimize artificial stabilization due to basis set overlap. Among the functionals, ωB97XD predicts the most negative interaction energies, followed by CAM-B3LYP and B3LYP, reflecting slightly stronger predicted interactions. Overall, the minimal BSSE values demonstrate the reliability of the computed interaction energies at this level of theory.

Electronic absorption spectrum

The electronic absorption spectrum provides vital information about the energy levels of a molecule and the transitions between them⁶¹. Analyzing the electronic absorption spectra of HB-CT complexes allows researchers to glean important insights into their electronic structure, stability, and interaction dynamics⁶². UV–Vis spectroscopy provides experimental spectra that can be compared with theoretical models derived from quantum mechanical calculations⁶³. For HB-CT complexes, the absorption spectra typically exhibit distinct features corresponding to various electronic transitions, including π-π* transitions. These often occur in the donor or acceptor moieties and are linked to the chromophores’ electronic energy levels. Unique to HB-CT complexes, these transitions involve the movement of charge from the donor to the acceptor. They are typically observed at longer wavelengths compared to traditional π-π* transitions and can appear as a broad band in the spectrum. The strength and nature of the hydrogen bond influence the position and intensity of the absorption bands. Stronger hydrogen bonds typically result in red shifts and increased absorption intensities due to enhanced electron delocalization. The solvent environment can significantly alter the absorption spectrum of HB-CT complexes. Polar solvents often stabilize the charge transfer state, leading to shifts in absorption maxima. These studies not only advance the fundamental understanding of HB-CT complexes but also indicate potential applications, including organic photovoltaics, sensors, and biochemical applications⁶⁴.

Figure 3 shows the calculated UV–Vis spectra for (Phen), (PNP), and (Phen)(PNP) complex by the TD-DFT method. Table 3 presents the calculated and experimental maximum wavelengths for these compounds. Table 3 shows the CT band value for (Phen)(PNP) complex at 286 nm. The observed CT band at 286 nm in the UV–Vis spectrum is a spectroscopic signature confirming the HB–CT complex. It reflects an electronic transition arising from complex formation but does not constitute the underlying cause of the interaction (see Figure S1).

Figure 3.

Calculated UV–Vis absorption spectra of the compound obtained using different functionals (wb97xd and CAM-B3LYP), compared with the implicit solvation model of the complex in methanol.

Table 3.

Calculated and experimental maximum absorption wavelengths (λ_max, nm) of the free donor (Phen), free acceptor (PNP), and their complex (Phen)(PNP).

Compound	Experimental34	Calculated
Phen	275	300
PNP	300	320
(Phen)(PNP)	316	286

The experimental CT band appears in the range 230–316 nm, while TD-DFT calculations using the initial method (B3LYP/6-311G(d,p)) predict the corresponding transition at 286 nm. The remaining discrepancy (~ 0.41 eV) likely originates from limitations of the functional and vibronic effects in vertical excitations. Notably, inclusion of methanol as a solvent in the calculations slightly stabilizes the CT state and red-shifts the predicted wavelength, bringing the computational results closer to the experimental data. Using long-range corrected functionals, such as CAM-B3LYP or ωB97X-D, can improve the correlation with experimental observations.

Infrared vibrational spectra analysis

Analyzing infrared (IR) vibrational spectroscopy in HB-CT complexes involves understanding how CT alters molecular vibrations, particularly in systems where hydrogen bonds facilitate charge transfer⁶⁵. Calculations based on quantum mechanics can predict vibrational spectra, thereby confirming experimental findings. This technique enhances understanding of hydrogen bonding dynamics and electron transfer by providing detailed information about couplings between different vibrational modes⁶⁶. The IR vibrational spectroscopy of HB-CT complexes offers valuable insights into the nature of hydrogen bonding and CT mechanisms. By carefully analysis spectral features, researchers can gain a deeper understanding of molecular interactions within these complexes. Theoretical IR spectral analysis of HB-CT complexes typically employs computational methods to predict vibrational frequencies and intensities based on the complex’s molecular structure. Modes associated with strong dipole changes will appear as peaks in the IR spectra⁶⁷. Each peak in the theoretical IR spectrum corresponds to a specific vibrational mode. Analyzing these peaks can provide insights into the bonding characteristics, hydrogen bonding interactions, and conformational dynamics of the complex. The strength and nature of hydrogen bonding in the complex will influence the vibrational frequencies, especially in the OH stretching region⁶⁸.

The computational IR spectra of 1,10-phenanthroline (Phen), p-nitrophenol (PNP), and their complex are exhibited in Fig. 4 and Table S3. The molecule, in which N atoms with a non-linear structure, has a maximum of 3N-6 observable vibrational modes. Phen (C₁₂H₈N₂), PNP (C₆H₅NO₃), and (Phen)(PNP) (C₁₈H₁₃N₃O₃) compounds consist of 22, 15, and 37 atoms, leading to 60, 39, and 105 normal modes, respectively. The complex has 9 inactive vibrational modes with epsilon values of 0.0. The estimated vibrational spectra show no imaginary wave numbers, providing clear evidence that the optimized geometry represents a local minimum on the potential energy surface. DFT consistently overestimates vibrational wave numbers. However, we can improve the accuracy of our results by applying suitable scale factors to correct these discrepancies⁶⁹. So, all wave numbers are multiplied by 0.967 (concerning the Computational Chemistry Comparison and Benchmark Database (CCCBDB)). A comparison of the wave numbers obtained shows that the B3LYP approach agrees with experimental observations because it includes electron correlation (see Table 4). The vibrational spectral assignments performed on the theoretically anticipated wave numbers by B3LYP/6-311G(d,p) are presented in Table 4. The differentiation of reactant molecules and the resulting complex shows a slight wavelength shift, providing strong evidence for the formation of the HB-CT complex and supporting our hypothesis. This shift in the bands is a direct result of the anticipated symmetry and charge distribution in the electronic structure following the formation of the complex. This understanding is crucial for advancing our insights into the system’s behavior. PNP acts effectively as an electron acceptor, suggesting that transferring a proton from PNP to Phen will likely produce a stable HB-CTC. The broad frequency reveals O–H stretching at 3237 cm⁻¹ in PNP, which intriguingly shifts to 3208 cm⁻¹ in the HB-CTC, highlighting the significant changes in molecular interactions. For individual PNP, the stretching frequency of the aromatic C–H bond in the HB-CTC shifts from 3154 to 3059 cm⁻¹. A new vibrational band has identified at 3094 cm⁻¹, corresponding to the stretching frequency specific to the HB-CT complex in the FT-IR spectrum. This particular frequency is notably missing in the spectra of free PNP and Phen, highlighting its significance in distinguishing the HB-CT complex. This band appears owing to the stretching vibration of a proton involved in the donor–acceptor site. The protonation of the nitrogen atom in Phen occurs through a proton transfer from the acidic hydroxyl group (-OH) on the PNP to the basic center on the nitrogen donor atom. As a result, the out-of-plane bending vibrational band of the C-H bond demonstrates a significant shift to 724 cm⁻¹ in the complex compared to 760 cm⁻¹ for Phen itself. These findings strongly support the CT process from Phen to PNP, highlighting the interactions at play. The observed proton transfer interaction in the complex is illustrated by the emergence of a new vibrational band at 3094 cm⁻¹. This distinctive band can be confidently assigned to the ν(NH‏)/(O–H–N‏) stretching, highlighting the crucial hydrogen bonding between PNP and Phen. Infrared spectral studies showed that Phen interacted with PNP through CT and hydrogen bonding. The vibrational band observed at 3094 cm⁻¹ was initially assigned to the N–H stretching vibration in the PNP–Phen complex. Although this position is lower than the typical range for free N–H stretching vibrations (3300–3500 cm⁻¹), it can be rationalized by the specific nature of the interaction between PNP and Phen. In the complex, the phenolic –OH group of PNP interacts strongly with the nitrogen atom of Phen, leading to proton transfer or the formation of a strong hydrogen bond. This results in the protonation of the nitrogen center, generating an N–H⁺ bond.

Figure 4.

Theoretical (simulated) IR spectra related to (a) PNP, (b) Phen, and (c) [(Phen)(PNP)] complex.

Table 4.

Calculated and experimentally selected vibrational modes and their assignments for (Phen)(PNP) complex.

Experimental67	Calculated	Assignments
3384	3239	ν(O–H) of PNP; ν(+NH)
3064, 2955, 2950	3115, 3096, 3088	ν(C–H); aromatic of PNP
2930, 2878, 2811, 2744, 2682, 2625	3094, 3090,3076, 3066, 3065, 3055, 3049	ν(C–H); aromatic of Phen
1650	1602, 1591, 1577, 1548, 1491	ν(C=C); aromatic of Phen
	1597, 1583	ν(C=C); aromatic of PNP
1592	1531	νas(NO2);
1494	1485	ν(C–O) + ν(C=C) of Phen
-	1480	CH-bend; phenyl
1422, 1334	1432, 1407	νas(CN)
1303, 1270	1296, 1284	ν(C–O); C–OH
1214, 1187	1324	νs(NO2)
1102, 1094	1192	νs(CN)
1042, 1009, 889, 840	1150, 1128, 1123, 1084 986 PNP
1082, 1063, of Phen	δ(CH); in-plane bend
766, 752, 730	951, 944 of PNP
971, 940, 937 of Phen	δ(CH); CH-rock
711, 688, 634, 622	875, 758, 699	δ(NH); NH def
535, 493, 465, 405	832, 753, 597, 544, 492, 400 of Phen
830, 806, 801, 677, 487, 413 of PNP	δ(CH); out-of-plan
-	622, 617, 438	Skeletal vibrations for both molecules

ν, stretching; δ, bending.

Protonated aromatic nitrogen systems are known to exhibit N–H⁺ stretching vibrations significantly red-shifted from those of neutral amines, commonly appearing in the 3100–3200 cm⁻¹ region. Moreover, extensive hydrogen bonding with the conjugate base can further lower the stretching frequency. Therefore, the band at 3094 cm⁻¹ is consistent with an N–H⁺ stretching vibration in a strongly hydrogen-bonded or protonated heteroaromatic system. This interpretation is supported by the disappearance of the free O–H stretching band of PNP and the spectral differences between the free ligand and the complex.

NMR spectroscopy

The study of NMR spectra in HB-CT complexes using DFT is an important aspect of understanding the molecular structure, dynamics, and properties of these interactions. NMR spectroscopy provides valuable information about the local environment of nuclei within a molecule, and DFT calculations can help quantitatively interpret NMR data⁷⁰. Optimized structures provide a reliable foundation for subsequent NMR calculations and facilitate a more accurate interpretation of chemical shifts. DFT calculations often involve comparing the nuclear shielding in a molecule with that of a reference compound, typically in a standard environment such as TMS for proton NMR⁷¹. DFT calculations can help clarify how these interactions affect the local electron density around the nuclei, resulting in observable changes in the NMR spectrum. For instance, the proton resonances of hydrogen-bonded protons may shift downfield due to decreased magnetic shielding from the electron-withdrawing nature of the hydrogen bond. While DFT is more efficient than some quantum mechanical methods, calculating NMR parameters for complex systems can still be computationally intensive⁷².

The NMR chemical shift calculations in this study were performed using the Gauge-Independent Atomic Orbital (GIAO) method. The GIAO formalism is one of the most reliable and widely applied quantum chemical approaches for computing nuclear magnetic shielding tensors. In the GIAO approach, the basis functions are modified by incorporating the effect of the external magnetic field directly into the wave function. This leads to gauge-origin independent results, improving both the accuracy and stability of the predicted chemical shieldings. Owing to these advantages, GIAO has become the standard method for theoretical NMR chemical shift calculations, especially when combined with DFT. Numerous studies have demonstrated that GIAO-DFT calculations yield chemical shifts in excellent agreement with experimental data for a wide range of organic, organometallic, and coordination compounds⁷³. In this study, the GIAO method was utilized at the B3LYP/6-311G (d,p) level of theory to calculate NMR chemical shifts of [(Phen)(PNP)] complex.

¹HNMR spectrum

The chemical shift values of the donor and acceptor components in the ¹HNMR spectrum of the charge transfer complex were compared with those of the free molecules⁷⁴. This is similar to the ¹HNMR spectrum of [(Phen)(PNP)] complex⁷⁵. The phenolic proton in the complex (d = 12.42 ppm⁷⁶), indicating a strong hydrogen bond with a nitrogen atom in Phen. A notable peak has emerged in the spectrum of the complex at 3.32 ppm (broad singlet, ¹H, ⁺N–H of CTC), strongly indicating the presence of the ⁺NH proton. This observation pertains to the proton transfer from PNP to Phen molecule, highlighting the significant role of the phenolic group (AOH) and one nitrogen atom from Phen. The doublets at d = 6.91 ppm and d = 8.10 ppm have been assigned to one of each of the two protons of the same type in the PNP component of the complex. In the free PNP, these protons were observed at d = 6.95 ppm and d = 8.25 ppm, respectively⁷⁷. The observed displacement shifts for chemical shifts highlight a significant increment in electron density within the complex’s PNP section. This increase is predominantly due to the (N⁺H) charge transfer interaction between Phen and PNP molecules. The triplet and singlet peaks at d = 7.75 ppm and d = 7.99 ppm demonstrate only a minor change in chemical shift. These peaks correspond to one of the two protons in the complex. Furthermore, the complex spectrum reveals two doublets at d = 8.477 ppm and d = 9.09 ppm, suggesting each peak is allocated to the two protons.

Figure 5 illustrates the ¹HNMR spectrum of the complex settled in the presence of DMSO-d6. The primary purpose of the ¹HNMR spectrum is to indicate the presence of the CT interactions in the HB-CT complex and emphasize the resulting proton transfer interactions within this complex. ¹HNMR of the resulting complex displays thirteen distinct peaks with a broad signal of the -OH group at (12.42, s, H) (see Table 5. This high-field shift in the proton signal of PNP reinforces the conclusion that a HB-CT complex is formed, highlighting the interaction between PNP and Phen.

Figure 5.

Calculated ¹HNMR spectrum of [(Phen)(PNP)] complex in DMSO-d6 solvent.

Table 5.

Calculated and experimental chemical shifts (in ppm) of [(Phen)(PNP)] complex in the ¹HNMR spectrum.

	Types of H atoms	δ (ppm)
	Experimental67	Calculated
H17	–	9.19
H15	–	7.65
H19	–	7.73
H18	7.75	7.93
H14	8.48	7.97
H31	6.91	8.03
H30	8.10	8.28
H32	–	7.21
H29	–	6.94
H20	–	9.26
H37	10.77	12.42
H11	7.99	8.37
H16	9.09	8.29

¹³CNMR spectrum

We obtained the ¹³CNMR spectrum in DMSO-d6 solvent to confirm the formation of HB-CTC and the hydrogen bonding interactions between Phen and PNP. The spectrum of Fig. 6 indicates distinct peaks for the carbons of PNP and Phen, providing clear evidence of the formation of the HB-CTC. The increase of electron density in Phen resulting from the CT from PNP led to a displacement shift in the carbon atoms of Phen, indicating movement toward lower chemical shift values. In pure Phen, the carbon atoms of C2 and C10, C12 and C1, CH13 and CH5 are chemically equivalent and exhibit identical chemical shifts. However, in the [(Phen)(PNP)] complex, these carbons become inequivalent; for instance, δ(C2) = 139.16 and δ(C10) = 140.43. This difference is significant for the formation of the [(Phen)(PNP)] complex (see Table 6).

Figure 6.

Calculated ¹³CNMR spectrum of [(Phen)(PNP)] complex in DMSO-d6 solvent.

Table 6.

Calculated chemical shifts (in ppm) of [(Phen)(PNP)] complex in the ¹³CNMR spectrum.

Types of C atoms	Chemical shifts (ppm)
C28	171.62
CH5	154.33
CH13	152.61
C2	139.16
C10	140.43
C25	145.68
C4	150.03
C7	150.21
C27	116.68
C23	118.30
C12	126.41
C1	126.77
C26	129.21
C24	129.95
C9	130.15
C6	131.59
C3	132.61
C8	132.86

Frontier molecular orbitals (FMOs) analysis

The nature of the HOMO and LUMO (FMOs), as well as the energy gap between them, is fundamental in understanding molecular chemical reactivity and kinetic stability^78,79. By examining these key features, one can gain invaluable insights into how a molecule behaves. Figure 7 presents 3D plots of FMOs, effectively showcasing the significant gap between HOMO and LUMO orbitals. These HOMO and LUMO plots show the CT within a molecule⁸⁰. The positive phase is indicated by red, while the negative phase is represented by green. It was striking to observe that the HOMO and LUMO were extensively placed across the entire molecule, highlighting the unique electronic properties it possesses. The charge delocalization, kinetic stability, and chemical reactivity of the complex can be effectively elucidated by analyzing its orbitals and corresponding energy levels. A detailed HOMO–LUMO analysis of (Phen)(PNP) complex reveals that HOMO is localized on PNP, whereas LUMO is placed on Phen. This clear separation between the HOMO and LUMO indicates that the electronic transition represented by the HOMO–LUMO energy gap (ΔE_(H–L)) corresponds to an interfragmentary CT process rather than a delocalized or intramolecular excitation within a unified electronic system. Therefore, while the computed ΔE _(H–L) still provides a qualitative measure of the energetic feasibility of CT between fragments, it cannot be interpreted as a direct measure of the intrinsic electronic excitation energy of the entire complex. In other words, ΔE _(H–L) in this case represents the energy cost of electron transfer from the donor to the acceptor moiety, rather than a pure intramolecular transition. The energy gap between the HOMO and LUMO levels is 3.89 eV, a value calculated using the B3LYP/6-311G(d,p) method. This significant finding underscores the potential implications for electronic properties and behaviors in our research. Additionally, the HB-CT complex exhibits a high dipole moment of 11.63 Debye, attributed to electronic and nuclear contributions, indicating significant stability. The large value of the dipole moment acts as a driving force behind the formation of (Phen)(PNP) complex.

Figure 7.

HOMO and LUMO plots for [(Phen)(PNP)] complex (The surfaces were generated from the Gaussian output at the optimization level of theory and visualized by GaussView 6 software)³⁷.

Table 7 presents calculated dipole moment (μ, Debye) and frontier molecular orbital energies (in eV) for 1,10-phenanthroline, p-nitrophenol, and their HB-CTC in the gas phase. An energy gap of 3.89 eV between the HOMO and LUMO in [(Phen)(PNP)] tells us the complex is relatively stable electronically, with limited low-energy charge transfer absorption, primarily absorbing UV light. In applications such as dyes or optoelectronic materials, a smaller gap generally favors visible light absorption, so this complex would be more UV-active.

Table 7.

Calculated dipole moment (μ, Debye), energy gap (ΔE_(H–L), eV), and frontier molecular orbital energies (in eV) for 1,10-phenanthroline, p-nitrophenol, and [(Phen)(PNP)] complex in the gas phase.

Compound	µ	EHOMO	ELUMO	ΔE(H–L)
Phen	3.19	− 6.49	− 1.67	4.81
PNP	5.62	− 7.09	− 2.44	4.64
[(Phen)(PNP)]	11.63	− 6.22	− 2.34	3.89

Polarizability and hyperpolarizability

Anticipating the non-linear optical (NLO) properties of molecules using quantum chemistry aids in understanding how electron density is bonded and delocalized. This process involves transitioning from occupied Lewis-type natural bond orbitals (NBOs), which act as electron donors, to appropriately unoccupied non-Lewis-type orbitals. These concepts are essential in designing materials used in modern information technology, signal processing, and integrated photonics⁸¹. Organic compounds are a focal point in research due to their remarkable NLO susceptibilities, primarily driven by the movement of π-electron clouds from donor to acceptor sites. Their rapid NLO response times, outstanding laser damage thresholds, and remarkably poor dielectric constants further enhance their appeal. Organic molecules typically exhibit low thermal stability and can rapidly adopt random orientations, which may impede their effectiveness in various applications. Despite these concerns, the potential benefits of organic molecules in NLO applications warrant further exploration and development⁸². Polarizability plays a significant role in HB-CT complexes by influencing the strength and nature of molecule interactions. It contributes to the stabilization of the HB-CT complex by enhancing dispersion and induction interactions; however, this effect is distinct from the electrostatic component of the hydrogen bond. When a molecule can easily distort its electron cloud, it can better interact with the proton of the hydrogen bond donor. In HB-CT complexes, the ability of molecules to polarize can facilitate the movement of charge from donor to acceptor. Increased polarizability typically leads to more stable complexes due to stronger electrostatic interactions⁸³.

In spectroscopic studies, such as UV–Vis or IR spectroscopy, polarizability affects transition dipole moments, thus influencing absorption characteristics⁸⁴. The calculated average polarizability (α_ave) of Phen, PNP, and [(Phen)(PNP)] complex is detailed in Table 8. According to the data in this table, the value of α_ave for the HB-CT complex is 35.25 × 10^–24 esu. This value is more than the components of (Phen)(PNP) complex, which means better CT between Phen and PNP and more stability of the formed complex.

Table 8.

Calculated average polarizability (α_ave) and first-order hyperpolarizability (β_total) for urea, (Phen)(PNP) complex, Phen, and PNP.

Compound	αave (in a.u.)	αave (in esu)	βtotal (in a.u.)	βtotal (in esu)
(Phen)	145.97	21.63 × 10–24	74.67	0.65 × 10–30
(PNP)	82.08	12.16 × 10–24	831.60	7.19 × 10–30
[(Phen)(PNP)]	237.89	35.25 × 10–24	1376.10	11.89 × 10–30
				0.60 × 10–30
Urea	28.00	4.15 × 10–24	69.95	0.1947 × 10–30 84

The first-order hyperpolarizability (β_total) of Phen, PNP, and (Phen)(PNP) complex is comprehensively detailed in Table 8, highlighting their significance in understanding the compound’s properties. The tensor components of the static first hyperpolarizability have been measured precisely through the identical method. By leveraging these computed tensor components, we can effectively determine β_total for Phen, PNP, and (Phen)(PNP) complex. The β tensor is derived by incorporating Kleiman symmetry equations, coupled with the squared norm of the Cartesian expression, ensuring a robust and comprehensive calculation⁸⁵. The expressions utilized for the calculations are outlined below, emphasizing their critical importance in achieving accurate and reliable results⁸⁶.

4

The calculated β_total value for (Phen)(PNP) complex is 11.89 × 10^–30 esu. In contrast, the determined value for urea (a standard NLO material) using the B3LYP/6-311G(d,p) method is only 0.60 × 10^–30 esu. Remarkably, β_total of the complex is 20 times higher than that of urea. This significant difference suggests that the title complex holds a promising candidate for developing NLO materials.

Natural bond orbital (NBO) analysis

The NBO analysis is a powerful method for investigating all potential interactions between ‘filled’ (donor) Lewis-type NBOs and ‘empty’ (acceptor) non-Lewis NBOs. We can accurately assess their energetic significance by employing second-order perturbation theory, supplying valuable insights into molecular behavior⁸⁷. Interactions that result in the loss of occupancy from the localized NBOs of the idealized Lewis structure into the unoccupied non-Lewis orbitals are termed delocalization corrections to the zeroth-order natural Lewis structure⁸⁸. Unlike a standard Lewis structure, which does not account for antibonding orbitals, their presence highlights important deviations. Recognizing these deviations enhances our comprehension of molecular bonding and stability. Anti-bonding localized orbitals, often known as non-Lewis NBOs, play a crucial role in molecular interactions⁸⁹. When their occupancy deviates from the ideal value of 2.0, it leads to noticeable variations from the expected Lewis structure. We employed a donor–acceptor interaction approach, providing valuable insights into the complexities of molecular behavior. The stabilization process hinges critically on the interactions between LUMO and HOMO orbitals. This calculation is performed through Eq. 5, highlighting the sophistication of molecular behavior.

5

where ε_j^(NL) represents the non-Lewis NBO energy, ε_i^(L) denotes the Lewis NBO energy, and F_ij signifies the off-diagonal NBO Fock matrix element⁹⁰. As a result, a higher probability of transferring electrons to acceptor orbitals increases stabilization energy. Our comprehensive NBO analysis of the complex system and its components shows significant insights. These findings are summarized in Table 9 and are also referenced in Table S4.

Table 9.

NBO atomic charges of Phen, PNP in pure forms, and (Phen)(PNP) complex at the B3LYP/6-311G (d, p) level of theory.

NBO atomic charges [in the electronic charge units]
PNP (pure)		PNP in [CTC]		Δδ	Phen (pure)		Phen in [CTC]		Δδ
O14	− 0.348	O36	− 0.69	− 0.342	N21	− 0.186	N21	− 0.454	− 0.168
H15	0.263	H37	0.515	0.252	C5	0.066	C5	0.091	0.025
C6	0.181	C28	0.379	0.198	H17	0.107	H17	0.19	0.083
C1	− 0.099	C23	− 0.257	− 0.158	C1	− 0.170	C1	− 0.229	− 0.059
H7	0.119	H29	0.216	0.097	H15	0.099	H15	0.213	0.114
C7	− 0.041	C24	− 0.168	− 0.127	C2	0.040	C2	− 0.139	− 0.179
H8	0.138	H30	0.233	0.095	H16	0.092	H16	0.208	0.116
C3	0.100	C25	0.019	− 0.081	C3	− 0.069	C3	− 0.084	− 0.015
N11	0.171	N33	0.513	0.342	C6	− 0.054	C6	− 0.167	− 0.113
O12	− 0.275	O34	− 0.404	− 0.129	H14	0.088	H14	0.208	0.12
O13	− 0.277	O35	− 0.407	− 0.13	C9	− 0.055	C9	− 0.173	− 0.118
C4	− 0.044	C26	− 0.167	− 0.123	H18	0.088	H18	0.208	0.12
H9	0.138	H31	0.232	0.094	C8	− 0.073	C8	− 0.083	− 0.01
C5	− 0.129	C27	− 0.281	− 0.152	C10	0.042	C10	− 0.132	− 0.174
H10	0.104	H33	0.221	0.117	H11	0.092	H11	0.209	0.117
					C12	− 0.171	C12	− 0.231	− 0.06
				–	H19	0.099	H19	0.215	0.116
–	–	–	–	–	C13	0.067	C13	0.0971	0.0301
					H20	0.108	H20	0.194	0.086
					N22	− 0.289	N22	− 0.49	− 0.201
					C7	0.091	C7	0.204	0.113
					C4	0.087	C4	0.191	0.104
Sum			− 0.046					0.046

The oxygen atoms within the nitro functional group (− NO₂) on the HB-CTC have a notably greater negative partial charge than those in PNP. This observation holds, even though after the formation of the complex, the arrangement of the molecules leads to a reduction in the negative charge of the N11 atom, resulting in a more positive character for that atom. The NBO charge sum analysis reveals that, within the complex, Phen and PNP exhibit total atomic charges of + 0.046 e⁻ and –0.046 e⁻, respectively. This indicates that Phen donates electron density while PNP acts as the electron acceptor. Such charge redistribution suggests effective orbital overlap and strong donor–acceptor interactions, contributing to the overall stability of the complex. Therefore, based on the NBO charge data, the CTC formed between Phen and PNP is stable, with Phen serving as the electron donor and PNP as the electron acceptor. These findings are consistent with expected CT behavior and support the presence of a directional and stabilizing interaction. A larger NBO charge sum for the donor in the CTC reflects a loss of electron density compared to its free form, consistent with electron donation through CT interactions or hydrogen bonding. Conversely, a smaller NBO charge sum for the acceptor in the CTC compared to the free acceptor indicates a gain in electron density. In the complex, the acceptor gains a more negative charge as it takes up electrons. This pattern confirms the typical behavior of donor–acceptor complexes, where electrons flow from donor to acceptor, and the NBO charge analysis effectively captures this redistribution.

Analysis of molecular electrostatic surface potential (MESP)

The molecular electrostatic potential surface (MESP) is an invaluable visual tool for comprehensively comprehending the relative polarity of different compounds⁹¹. Figure 8 shows the electrostatic potential map, providing a detailed view of the three-dimensional charge distributions within the molecule. Understanding charge distributions is essential as they offer valuable insights into molecular interactions. One purpose of determining the electrostatic potential is to recognize a molecule’s reactive site, significantly improving our ability to predict its chemical behavior and reactivity^92,93. The electrostatic potential map reveals semi-spherical blue shapes emerging from the edges, representing the presence of hydrogen atoms. MEP at a specific point r in the space, surrounding a molecule (in atomic units), can be articulated as follows⁹⁴:

6

Figure 8.

MEP surfaces of (a) p-nitrophenol, (b) 1,10-phenanthroline, and (c) [(Phen)(PNP)] complex at an iso-density surface of 0.002 a.u

In Eq. 6, demonstrates the charge on nucleus A, located at position . The function ρ(r ´) signifies the electronic density of the molecule. The first term represents the potential arising from the contribution of the nuclei, while the second term reflects the potential associated with the electrons. The function V(r) displays the complete electrostatic effect at point r, resulting from the electrons and nuclei within the molecule⁹⁵.

Figure 8 illustrates the MESP-mapped surface of Phen, PNP, and [(Phen)(PNP)] complex, along with its projections in both the molecular and the perpendicular planes. These images present the electrostatic potential model of the compounds, calculated at an iso-density surface of 0.002 a.u⁹⁶. Figure 9 illustrates the electrostatic potential contour map for both positive and negative potentials, a potent tool for understanding molecular interactions. In the MESP map, regions with negative electrostatic potentials are vividly represented in red, with deeper shades indicating stronger potential energy. Positive potentials are exhibited in blue, while green zones signify regions where potentials hover near zero. This figure effectively illustrates the chemically active sites and highlights the comparative reactivity of various atoms. The electrostatic potential shapes at these sites correspond closely to the polar groups, highlighting their importance in chemical interactions. Oxygen atoms with lone pairs create localized areas of negative electrostatic potential, while the bonded nitrogen in the ring generates a corresponding positive potential in the surrounding regions. Notably, a pronounced local positive electrostatic potential (represented in blue) is on the hydrogen atoms involved in both Phen and PNP bonds. Green regions represent the areas of the molecule where electrostatic potentials are effectively minimized. This zone of negligible potential encompasses the π system of the aromatic rings, making the adjacent plane of hydrogen atoms significantly more electrophilic.

Figure 9.

MEP mapped onto the van der Waals surface with a color scale ranging from negative (red) to positive (blue) for (a) p-nitrophenol, (b) 1,10-phenanthroline, and (c) [(Phen)(PNP)] complex, GaussView 6 program were used to visualize the molecular graph³⁷.

Reduced density gradient (RDG) analysis

The RDG analysis offers a visual representation of intra- and inter-non-covalent interactions (NCI) regions. This invaluable tool is grounded in the foundational work of Johnson⁹⁷. The Reduced Density Gradient (RDG) values were computed using the Multiwfn program⁴⁷, setting the stage for insightful analysis. We then generated 2D gradient subsurface plots of RDG against the electron density ρ(r), incorporating the sign of the second Hessian eigenvalue ρ(λ₂). This advanced visualization, produced with Multiwfn version 3.8⁹⁸, provides deeper insight into the data. Finally, the powerful capabilities of VMD version 1.9.4⁹⁹ were used to vividly illustrate the isosurface gradient derived from the Multiwfn output, providing a clear representation of our findings. By examining the sign of ρ(λ₂), we can discern the strength of these diverse interactions. The nature of interactions is determined by the sign of ρ(λ₂): it is repulsive for sign ρ(λ₂) > 0, attractive for sign ρ(λ₂) < 0, and weak for Van der Waals when sign ρ(λ₂) approaches zero. The value of λ₂ varies within the range of -0.05 a.u. to 0.05 a.u., and the colors of the surfaces are based on a scale of blue, green, and red, which correspond to the values of λ₂. Blue indicates strong intermolecular forces, while red signifies the repulsive steric interactions between atoms. The green spikes show weak noncovalent interactions, including dipole–dipole and London dispersion forces^100,101.

The blue color flakes observed between Phen (specifically the hydrogen atom of the hydroxyl group, –OH) and PNP (associated with the nitrogen atom) are illustrated in Fig. 10. This observation suggests the presence of strong non-covalent interactions and hydrogen bonds, as indicated by λ₂(r) < 0 for the iso-surface of RDG < 0.5. A spike is observed in the region where λ₂(r) < 0, specifically in the low-density area (between -0.04 a.u. and -0.035 a.u.). The low gradient in this region indicates a strong and stable interaction between Phen and PNP. These findings are consistent with the results from the previous sections. Furthermore, the green spikes ranging from 0 a.u. to -0.01 a.u. in the RDG scatter graphs of [(Phen)(PNP)] complex signify weaker dispersion forces. Additionally, the flaky region between 0.00 a.u. and 0.01 a.u. in the RDG plot confirms the presence of O–H…π interactions, represented by red and green colors, which occur between hydrogen atoms of Phen and π-electrons of PNP. Lastly, red color spikes in the region where sign ρ(λ₂) > 0 indicate the repulsion forces between the carbon atoms of the aromatic rings in the molecules.

Figure 10.

The gradient iso-surfaces and scatter graphs of [(Phen)(PNP)] complex based on 1,10-phenanthroline and p-nitrophenol. The Multiwfn 3.8⁹⁸ and VMD 1.9.4⁹⁹ programs were used to visualize the 3D-NCI map and RDG plot.

Topological analysis

AIM (Atoms in Molecules) analysis was employed to determine the locations and properties of the electron density within molecules^102–104. According to AIM theory, critical points in electron density are categorised into four types: atomic (ACP), bond (BCP), ring (RCP), and cage (CCP). The identification and characterization of intermolecular interactions are primarily influenced by the electron density and its Laplacian. This study presents a topological analysis of the electron density for the complex formed between Phen and the π-acceptor PNP, to elucidate both intermolecular and intramolecular interactions. The electron density value, , and the sign of its Laplacian, , at the bond critical point (BCP), provide insight into the nature of the bonding between atoms. A negative combined with a high value is indicative of shared-shell interactions, characteristic of covalent bonding (see Fig. 11).

Figure 11.

Molecular graph of the crystal packing of [(Phen)(PNP)] complex, AIM 2000 program were used to visualize the molecular graph¹⁰⁵.

According to the data reported in Table 10, for all three cases of the Phen _C–H···PNP_N interaction, the small value of , the positive value of , along with a ratio close to 1 indicates that this type of interaction is ionic in nature. In contrast, for the interaction between the H atom (from—OH) of Phen molecule and the N atom of the π-acceptor PNP, a small value of , a positive that is lower than that observed for the Phen_C–H– PNP_N interaction, and a G(r)/|V(r)| ratio greater than 1 is observed, all of which confirm the presence of a hydrogen bond between H and N.

Table 10.

Calculated AIM parameters of critical points (CPs) of [(Phen)(PNP)] complex.

Properties	Phen C–H– PNPN	Phen O–H– PNPN
	6.19E−03	3.58E−02
	1.86E−02	9.64E−02
	2.61E−02	3.94E−03
	− 7.07E−04	1.95E−03
	− 4.65E−03	− 2.41E−02
	2.80E−02	3.23E−03
G(r)/|V(r)|	9.30E−01	1.22

*Units for reported values are: ρ(r)\e/bohr³, ∇2ρ(r)\ e/bohr⁵, G(r), V(r), L(r), and K(r): Hartree/bohr³.

Conclusion

The successful synthesis of the HB-CT complex between 1,10-phenanthroline and p-nitrophenol has significant implications and was thoroughly investigated using advanced computational methods. Using MESP topology analysis, we highlighted the complex’s promising chemical reactivity. Notably, Natural Bond Orbital (NBO) analysis confirmed the essential charge transfer between the active sites, demonstrating the intricate interactions at play. Reduced Density Gradient (RDG) analysis was utilized, providing a clear visualization of the non-covalent interactions that enrich the stability and efficacy of the complex. Frontier molecular orbital analysis revealed a significant charge transfer, and the calculated NLO parameters demonstrated promising nonlinear optical properties. These findings suggest this complex has potential applications in optoelectronic and photonic technologies.

The electronic absorption spectra of hydrogen bond-charge transfer complexes reveal critical information about the electronic transitions and interactions within these fascinating molecular systems. By studying these spectra, we gain valuable insights into the fundamental principles governing molecular interactions and the potential applications of HB-CT complexes in various scientific and technological domains. Continued research in this area may lead to innovative strategies for harnessing the unique properties of these complexes in practical applications.

Polarizability is crucial for understanding the properties and effectiveness of hydrogen bond-charge transfer complexes. It directly influences their stability, interaction strength, and dynamic behavior. As such, polarizability is a critical element across diverse fields, including molecular chemistry, biochemistry, and materials science. Understanding this property is essential for advancing research and technological applications in these areas.

Supplementary Information

Below is the link to the electronic supplementary material.

Author contributions

“Vahideh Hadigheh Rezvan . Conceptualization, Methodology, Formal Analysis, Writing – Original Draft Preparation and Samaneh Barani Pour . Data Curation, Investigation, Visualization, Writing – Review & Editing. Mitra Dabbagh Hosseini Pour. Supervision, Project Administration, Validation, Writing – Review & Editing. Jaber Jahanbin Sardroodi. Software, Resources, Formal Analysis, Writing – Review & Editing. All authors have read and approved the final version of the manuscript.”

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

Data availability

Data is provided within the manuscript or supplementary information files.

Competing interests

The authors declare no competing interests.