DFT and QTAIM analysis of fluorenol and fluorenone in molecular nanoelectronics

Abstract

This study investigates the electronic properties of Fluorenone (A) and Fluorenol (B) for potential applications in molecular nanoelectronics. Using Density Functional Theory (DFT), Quantum Theory of Atoms in Molecules (QTAIM), and Landauer transport theory, we analyze the impact of electric fields on their conductivity and structural stability. Fluorenone, characterized by its conjugated carbonyl group, demonstrates electron-withdrawing capabilities, whereas Fluorenol, with its hydroxyl group, exhibits tunable electronic properties through hydrogen bonding. Computational modeling at the CAM-B3LYP/6-311 + G level reveals that Fluorenol consistently exhibits a smaller HOMO–LUMO gap than Fluorenone, suggesting superior charge transport efficiency. Density of States (DOS) and UV–Vis spectrum confirm these trends. Additionally, under varying electric field intensities, both molecules exhibit structural stability with minor length variations, supporting their suitability for nanoelectronic applications. The I–V characteristics show that Fluorenol-based systems (Au-B-Au) demonstrate higher conductivity than Fluorenone-based systems (Au-A-Au), attributed to enhanced charge delocalization. Furthermore, Joule and Peltier’s heating analysis confirms lower heat dissipation in Fluorenol, making it an ideal candidate for thermally stable nanoelectronic devices, including medical implants. Electron Localization Function (ELF) and Localized Orbital Locator (LOL) analyses further validate Fluorenol’s superior charge transport properties. These findings highlight Fluorenol as a promising material for molecular wires and next-generation nanoelectronic applications.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-025-06924-8.

Introduction

Single-molecule nanoelectronics is vital for designing nanoelectronic devices as it allows for precise control of electrical properties at the molecular level, leading to enhanced performance and miniaturization. This approach enables developing next-generation electronic devices with high sensitivity and efficiency^1–3. Important parts used in molecular nanoelectronic systems include molecular transistors, diodes, molecular switches, molecular memories, and molecular nanowires^4,5. In the meantime, molecular nanowires play a vital role in high-performance and low-power applications by acting as the essential conduit for electron transfer, enabling efficient connection and miniaturization in nanoelectronic circuits^6,7. Nanowires can be classified into metal, semiconductor, oxide, and organic types based on the composition of materials⁸. Among the types of nanowires, organic nanowires have received attention⁹. Designing and synthesizing organic nanowires are essential in advancing modern technology, particularly bioelectronics, flexible electronics, and medical devices^10,11. Unlike their inorganic counterparts, organic nanowires offer unique advantages, including flexibility, lightweight, and biocompatibility, making them well-suited for implantable medical electronic devices such as medical implants. In addition, organic materials offer a tunable molecular structure that enables them to be used for specific applications¹². As the demand for miniaturized, flexible, and sustainable devices grows, organic nanowires stand at the forefront of nanoelectronics and biomedical engineering innovations. Designing nanowires using computational methods before their synthesis is essential for predicting their properties and optimizing performance, reducing experimental trial and error. So far, various nanowires have been designed using computational methods, which have become the basis for synthesizing new and high-performance nanowires. For example, Ying-Qin Zhao and colleagues designed boron-nitride nanowires and studied the relationship between conductivity and chain length; K. Senthil Kannan and his team explored CuS nanowires’ electronic transport properties and V-I characteristics. Syed Abdul Moiz and colleagues designed poly-3,4-ethylenedioxythiophene nanowires for hybrid solar cells^13–15.

Therefore, designing and optimizing the properties of nanowires before synthesis using computational methods has been proposed as a reliable and efficient approach in the development of molecular nanoelectronic devices^16,17. One of the key advantages of computational design is the ability to fine-tune the electronic properties of nanowires, such as conductivity, by manipulating the molecular structures. For example, tuning the energy gap (HLG) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) directly affects the conductivity of a molecule¹⁸. By computationally modeling these factors, researchers can design nanowires with properties tailored to specific applications, making them a powerful tool in advancing nanoelectronics and related fields. Despite extensive research in molecular nanoelectronics, there is no comprehensive study on the electronic properties of Fluorenol and Fluorenone for their potential use in nanoelectronic systems. Fluorenol and Fluorenone possess several properties that make them promising candidates for use in molecular nanoelectronic systems¹⁹. Both molecules exhibit strong structural stability, crucial for maintaining performance under varying conditions in electronic devices. With its conjugated carbonyl group, Fluorenone offers enhanced electron-withdrawing capability, potentially leading to favorable electron transport properties²⁰. Conversely, Fluorenol has a hydroxyl group that can engage in hydrogen bonding and modify the electronic environment, allowing for tunable electronic characteristics²¹. Additionally, their planar molecular structure facilitates efficient π-π stacking interactions, which can improve charge transport in nanoelectronic applications²². These features and the ability to adjust their electronic properties through molecular modifications make Fluorenol and Fluorenone attractive for further exploration in nanoelectronic systems^23,24.

Therefore, in this study, we present, for the first time, a detailed analysis of the suitability of Fluorenol and Fluorenone as nanoelectronic materials (Fig. 1). Using DFT, QTAIM, and Landauer transport theory, we investigate their electrical conductivity under various applied electric fields²⁵. As organic molecular fragments are highly suitable for medical implants and improving their performance, the results of this research will provide valuable insight into the potential of fluorenol and fluorenone in these applications.

Fig. 1.

Geometric structure of fluorenone (A) and fluorenol (B) in the absence of an electrode and after binding to a gold electrode (Au-A-Au and Au-B-Au).

Computational details

All structures were initially designed using GaussView and optimized using Gaussian 09W software. Figure 1 shows the structures studied in this work. The optimization was performed using DFT at the CAM-B3LYP/6-311 + G computational level. The CAM-B3LYP functional was chosen due to its well-documented accuracy in predicting molecular geometries, as emphasized in various literature sources^26,27. CAM-B3LYP is a range-separated hybrid functional that incorporates a mix of short-range hybrid exchange (B3LYP) and long-range Hartree–Fock (HF) exchange, reducing self-interaction errors (SIE) compared to traditional hybrid functionals²⁸. Previous studies have shown that CAM-B3LYP provides reasonable band gap predictions for π-conjugated and organic molecular systems, including molecular wires and switches, making it a practical choice for this study²⁹. Also, to verify the stability of the optimized structures, frequency calculations were conducted at the same theoretical level, and the absence of imaginary frequencies confirmed that all designed structures correspond to true local minima on the potential energy surface. An external electric field was also applied along the x-axis, and the electronic properties were analyzed computationally under these conditions. For gold atoms, which served as electrodes, the LANL2DZ pseudopotential was employed to accurately account for relativistic effects and core-electron interactions³⁰. Also, all calculations were done in the gas phase. This computational approach ensures a reliable and precise evaluation of the molecular and electronic properties of the designed structures.

The energy gap (HLG) was calculated using Eq. (1):

1

In this equation, E_HOMO is related to the energy of the HOMO frontier orbitals and E_LUMO is related to the energy of the LUMO frontier orbitals.

Landauer’s formula/theory (LT, Eqs. 2–4) was used to predict the current–voltage diagram (I–V curve) of this field-effect molecular wire³¹. In this regard, the temperature-independent direct-tunneling electric conduction (G) of a single-molecule nanoelectronics system can be evaluated using the Landauer formula as follows:

2

3

4

where is , is the potential barrier height for tunneling through the HOMO or the LUMO level, which is equivalent to the energy difference between the Fermi energy and the molecular HOMO or LUMO level, m* is the effective mass of the electron (m* = 0.16 m₀, m₀ is the free electron mass), and α is the symmetry parameter in the potential profile, in this symmetric case, α = 1³².

And finally, the dipole moment (), and polarizability () were calculated using Eqs. (5 and 6)³³.

5

6

The polarizability values reported in this study correspond to static polarizability (at zero frequency), calculated as the linear response of the molecular dipole moment to the applied electric field. While static polarizability provides a foundational understanding of the electronic response, we note that frequency-dependent polarizability (which accounts for orbital relaxation under dynamic perturbations via methods like coupled-perturbed self-consistent field (CPSCF) equations) could offer further insights for systems under oscillating fields. Such analyses are reserved for future studies to explore time-dependent effects in these molecular systems.

Results and discussion

Isolated structure

Energy of HOMO and LUMO molecular orbitals

Results Table 1 presents the HOMO and LUMO energies along with the HOMO–LUMO gap (HLG) for fluorenone and fluorenol, obtained using the CAM-B3LYP computational method.

Table 1.

HOMO/LUMO molecular orbital energies and energy gaps (HLG) calculated with CAM-B3LYP functional for fluorenone and fluorenol. (All values are in eV).

Method	Structure	LUMO	HOMO	HLG
CAM-B3LYP	Fluorenone	− 1.53	− 7.99	6.46
	Fluorenol	− 1.65	− 7.56	5.91

From the CAM-B3LYP results, fluorenone has a LUMO energy of − 1.53 eV and a HOMO energy of − 7.99 eV, resulting in a HLG of 6.46 eV. Fluorenol, on the other hand, has slightly lower orbital energies (− 1.65 eV for LUMO and − 7.56 eV for HOMO), leading to a smaller HLG of 5.91 eV. This indicates that fluorenol has a smaller electronic gap than fluorenone, suggesting that fluorenol may exhibit slightly better charge transport properties due to its reduced energy gap.

The PBEPBE and WB97XD results, while quantitatively different, follow the same trend. Although the absolute values differ significantly, the qualitative trend remains the same: fluorenol consistently has a lower HLG than fluorenone, regardless of the computational method used (Table S1).

Density of States (DOS) plots were used to highlight the differences in electronic structure between fluorenone and fluorenol. DOS diagrams are an excellent way to visualize the distribution of molecular orbital energies, particularly the HOMO–LUMO energy gap (HLG)³⁴.

The results obtained from the DOS plots confirm the energy gap trends reported in Tables 1 and S1 (in the Supplementary Data). In all three computational approaches (WB97XD, CAM-B3LYP, and PBEPBE), the DOS plots show that fluorenol consistently has a smaller energy gap than fluorenone, consistent with the numerical HLG values. This agreement between DOS plots and calculated energy levels validates the computational findings and reinforces the reliability of the observed trends (See Fig. 2 and Figure S1 (in the Supplementary Data)).

Fig. 2.

DOS diagram for fluorenone and fluorenol with CAM-B3LYP functional.

UV–Vis spectrum

Table 2 shows the excitation properties of fluorenone and fluorenol, including the wavelength of maximum absorption (λmax), oscillator strength (ƒ), excited state energy (Eex), and electronic transition assignment, calculated using the CAM-B3LYP computational method³⁵. The results obtained from the WB97XD and PBEPBE computational methods are reported in the Supplementary Data section (Table S2 and Fig S2).

Table 2.

Calculated values of λmax (nm), Eex (eV), ƒ and HOMO to LUMO assignments for Fluorenone and Fluorenol using CAM-B3LYP functional.

Methode	Structure	λmax	ƒ	Eex	Assignment
CAM-B3LYP	Fluorenone	348.00	0.0055	3.56	HOMO → LUMO (97%)
	Fluorenol	393.85	0.0125	3.14	HOMO → LUMO (90%)

The data in Table 2 demonstrate that a consistent qualitative trend emerges despite quantitative differences in the calculated optical properties of fluorenone and fluorenol across the PBEPBE, WB97XD, and CAM-B3LYP functionals. In all cases, fluorenol exhibits a significantly red-shifted absorption maximum (λmax) compared to fluorenone, indicating better optical properties for light absorption in the visible region (Fig. 3). For instance, WB97XD predicts λmax at 271.94 nm for fluorenone and 394.69 nm for fluorenol, while PBEPBE yields 348.06 nm and 451.11 nm, respectively. Similarly, CAM-B3LYP results in λmax values of 348.00 nm for fluorenone and 393.85 nm for fluorenol.

Fig. 3.

UV spectra for fluorenone and fluorenol using the CAM-B3LYP functional.

The excitation energies (Eex) further support this observation, with fluorenol consistently showing lower Eex values (3.14 eV for WB97XD, 2.74 eV for PBEPBE, and 3.14 eV for CAM-B3LYP) compared to fluorenone (4.55 eV, 3.56 eV, and 3.56 eV, respectively). This indicates that fluorenol requires less energy for electronic transitions, aligning with its superior optical characteristics. Additionally, the oscillator strengths (ƒ) vary between the methods, but the key takeaway is that fluorenol consistently exhibits a bathochromic shift relative to fluorenone. This shift can be attributed to the hydroxyl (–OH) group in fluorenol, which influences electronic transitions by stabilizing the excited state and reducing the energy gap.

Thus, despite the quantitative discrepancies introduced by different computational approaches, the qualitative conclusion remains unchanged: fluorenol possesses more favorable optical properties than fluorenone, regardless of the functional group used. This consistency underscores the reliability of the observed trend across theoretical methods.

Non- isolated structure (electrode-molecule-electrode)

Structural properties

Bond length

The performance of nanoelectronic devices often relies on precise control over nanoscale material properties. Changes in molecular length under an electric field can affect the overall behavior of these materials. By studying this effect, the performance and efficiency of the device can be optimized³⁶. For this purpose, the effect of electric field at different intensities on the length of the molecules under study was investigated (Fig. 4). Changes in the length of the molecules from S₁ to S₂ atoms were considered. Changes in the length of the Fluorenone at the intensity of electric fields 0, 20 × 10⁻⁴ (a.u.), 40 × 10⁻⁴ (a.u.), 60 × 10⁻⁴ (a.u.), 80 × 10⁻⁴ (a.u.) and 100 × 10⁻⁴ (a.u.) were obtained as 10.5208 (A), 10.5154 (A), 10.5059 (A), 10.4995 (A), 10.4890 (A) and 10.4827 (A) respectively.

Fig. 4.

Changes in the length of the molecule in the intensity of different electric fields (zero electric field was used as a reference).

Also, changes in the length of the Fluorenol at the intensity of electric fields 0, 20 × 10⁻⁴ (a.u.), 40 × 10⁻⁴ (a.u.), 60 × 10⁻⁴ (a.u.), 80 × 10⁻⁴ (a.u.) and 100 × 10⁻⁴ (a.u.) were obtained as 10.4890 (A), 10.4832 (A), 10.4787 (A), 10.4766 (A), 10.4673 (A) and 10.4679 (A) respectively.

The obtained results show that the applied electric fields do not significantly affect the length of the molecule. The results indicate a relatively favorable stability along the length of the molecule.

Maintaining a stable molecular length under the influence of an electric field ensures reliability, efficiency, and predictable device performance in electronics and nanotechnology^35,36.

Vibrational analysis

The provided IR spectra display the vibrational characteristics of Fluorenone (top row) and Fluorenol (bottom row) under varying electric field (EF) strengths, specifically EF = 0, 40 × 10⁻⁴ a.u., and 100 × 10⁻⁴ a.u (Fig. 5). The spectra are plotted with IR activity on the y-axis and frequency (cm⁻¹) on the x-axis, ranging from 4000 to 0 cm^-1.

Fig. 5.

Vibrational analysis (IR spectrum) for each studied structure in the presence/absence of an electric field.

For Fluorenone (top row), in the absence of an electric field (EF = 0), distinct peaks are observed throughout the frequency range, particularly around 1700 cm^-1, corresponding to the C=O stretching vibration characteristic of the carbonyl group. As the electric field increases to 40 × 10⁻⁴ a.u., the intensity of the IR absorption bands increases, indicating enhanced IR activity due to the polarization effects induced by the field. This trend is more pronounced at EF = 100 × 10⁻⁴ a.u., where IR activity amplifies significantly, with peak intensities increasing substantially, especially for the carbonyl stretching mode. This suggests that the electric field enhances the dipole moment changes associated with vibrational transitions, leading to stronger IR absorption.

For Fluorenol (bottom row), the IR spectrum without an electric field (EF = 0) shows characteristic O–H stretching vibrations around 3200–3500 cm⁻¹ and C-H stretching modes slightly below 3000 cm⁻¹. Like Fluorenone, applying an electric field (40 × 10⁻⁴ a.u.) increases the intensity of several peaks, particularly in the fingerprint region (1500–500 cm^-1). At EF = 100 × 10⁻⁴ a.u., the IR activity is further amplified, with notable increases in the O–H stretching region and C-H bending modes. This indicates that the electric field significantly affects the vibrational dynamics of the O–H bond, likely due to increased polarization effects.

Comparing both molecules, Fluorenone shows a more substantial change in IR activity with increasing electric field, particularly in the carbonyl stretching region. This could be due to the highly polar nature of the C=O bond, making it more sensitive to external electric fields. In contrast, Fluorenol exhibits a more distributed enhancement across different vibrational modes, reflecting the diverse nature of its functional groups.

Overall, the spectra reveal that applying an electric field enhances the IR activity of both Fluorenone and Fluorenol, with the extent and distribution of this enhancement depending on the molecular structure and the nature of the vibrational modes involved. This suggests potential applications in tuning vibrational properties through external electric fields, particularly in molecular electronics and sensing technologies.

Cohesive energy

Cohesive energy (E_coh) is a measure of the energy required to break a substance into its constituent atoms³⁷. Cohesive energy analysis provides valuable information to predict the stability of studied compounds^38,39. The adhesion energy values in the presence/absence of the electric field were calculated using Eq. (7).

7

where E_tot, E_i and n_i represent the total energy of all designed molecules, the atomic energy, and the number of atoms in each molecule, respectively, with n being the total number of atoms.

The cohesive energy values for the studied structure due to the application of the electric field with different intensities are shown in Fig. 6.

Fig. 6.

Cohesive energy values at different electric field intensities.

The E_coh for Fluorenone in the intensity of electric fields 0, 20 × 10⁻⁴ (au), 40 × 10⁻⁴ (au), 60 × 10⁻⁴ (au), 80 × 10⁻⁴ (au), and 100 × 10⁻⁴ (au), were obtained as 73.2 (Kcal.mol^-1), 72.4 (Kcal.mol^-1), 71.05 (Kcal.mol^-1), 70.12 (Kcal.mol^-1), 69.11 (Kcal.mol^-1), and 68.17 (Kcal.mol^-1), respectively.

Also, The E_coh for Fluorenol in the intensity of electric fields 0, 20 × 10⁻⁴ (au), 40 × 10⁻⁴ (au), 60 × 10⁻⁴ (au), 80 × 10^–4 (au), and 100 × 10⁻⁴ (au) were obtained 74.5 (Kcal.mol^-1), 73.6 (Kcal.mol^-1), 72.1 (Kcal.mol^-1), 71.45 (Kcal.mol^-1), 70.62 (Kcal.mol^-1), and 69.38 (Kcal.mol^-1), respectively.

According to the obtained results, after applying the electric field, there was no significant change in the cohesive energy values, which indicates the acceptable stability of each structure in the presence of the electric field. However, a comparison of the two molecules shows that fluorenol has a higher binding energy than fluorenone, indicating greater structural stability under high-intensity electric fields. These findings suggest that fluorenol may be more suitable for applications that require greater stability in environments with varying electric field strength. Cohesive energy stability ensures that the studied structure can maintain its structural integrity over a long time^40,41. This property is very important for applications that require long-term stability, such as nanoelectronic devices (such as wires, switches, or molecular transistors).

Electronic properties

Energy of HOMO/LUMO frontier orbitals and energy gap

Investigating the energy of HOMO/LUMO boundary orbitals and the energy gap between them in nanoelectronic devices (such as wires, switches, and molecular transistors) after applying an electric field is crucial for optimizing device performance, understanding the fundamental properties of materials, and searching for new capabilities. Examining these properties enables researchers to use quantum effects to create new molecule properties^42–45. Table 3 shows the obtained values for the energy of HOMO/LUMO orbitals and the energy gap between them.

Table 3.

The obtained values of the energy of HOMO/LUMO boundary orbitals and the energy gap in the intensity of different electric fields (All values are in eV).

Field strength (10−4 a.u.)	Au-A-Au				Au-B-Au
	LUMO	HOMO	HLG	LUMO	HOMO	HLG
0	− 2.69	− 7.01	4.32	− 2.76	− 6.74	3.98
20	− 2.93	− 6.98	4.05	− 2.76	− 6.25	3.49
40	− 3.19	− 6.94	3.74	− 3.35	− 5.80	2.45
60	− 3.53	− 6.81	3.28	− 3.53	− 5.54	2.01
80	− 3.80	− 6.75	2.94	− 3.74	− 5.59	1.85
100	− 4.08	− 6.68	2.60	− 4.16	− 5.79	1.63

The energy gap value for Au-A-Au in the absence of electric field was calculated to be 2.57 eV. In the presence of electric fields 20 × 10⁻⁴ (a.u.), 40 × 10⁻⁴ (a.u.), 60 × 10⁻⁴ (a.u.), 80 × 10⁻⁴ (a.u.), and 100 × 10⁻⁴ (a.u.), the energy gap value was 4.05 eV, 3.74 eV, 3.28 eV, 2.94 eV and 2.60 eV, respectively.

Also, the energy gap value for Fluorenol in the absence of an electric field was calculated to be 1.25 eV. In the presence of electric fields (for Fluorenol structure) 20 × 10⁻⁴ (a.u.), 40 × 10⁻⁴ (a.u.), 60 × 10⁻⁴ (a.u.), 80 × 10⁻⁴ (a.u.), and 100 × 10⁻⁴ (a.u.), the energy gap value was 3.49 eV, 2.45 eV, 2.01 eV, 1.85 eV, and 1.63 eV, respectively.

The obtained values show that the energy gap decreases as the intensity of the electric field increases, and there is a non-linear relationship between the energy gap and the intensity of the applied electric field (Fig. 7). According to the values obtained in Table 1, applying an electric field causes a perturbation in the distribution of electrons and energy levels. This has a significant effect on the energy gap between HOMO and LUMO, which is often called the energy gap. A smaller energy gap typically means that electrons can more easily move between different molecular orbitals. This enhances charge transport properties, allowing for better conductivity or mobility of charge carriers within the molecule. This is crucial for creating efficient electronic devices where rapid and efficient electron transfer is desired. Also, reducing the energy gap due to the application of an electric field facilitates the phenomenon of quantum tunneling between the electrode and the molecule and increases the conductivity of the molecule. This feature helps to design suitable materials (such as wire and molecular switches) for use in nanoelectronic circuits^47–51.

Fig. 7.

Equipment for experiments. (a) generator K2004E01 Kit; (b) scanning head model PSV-I-500, version GEO CO.

The density of states (DOS) plot is an excellent visual tool for showing the energy gap in a molecular system⁴⁶. To better understand the effect of the external electric field on the energy gap of the studied structures, DOS plots for Fluorenol and Fluorenone are presented in Fig. 8. These plots illustrate how the density of electronic states shifts in response to varying electric field intensities. It is clearly observed that applying an external electric field reduces the energy gap for both molecules. This effect is more pronounced in Fluorenol, where the HOMO and LUMO levels move closer together, resulting in a narrower gap. The enhanced response of Fluorenol can be attributed to its extended conjugation and higher polarizability due to the presence of the hydroxyl group, which facilitates stronger interactions with the electric field.

Fig. 8.

DOS plot for each studied structure in the absence of an electric field (EF = 0) and the presence of electric fields of 40 × 10⁻⁴ (a.u.) and 100 × 10⁻⁴ (a.u.).

The DOS plots confirm the results reported in Table 1, where a decreasing trend in the energy gap with increasing electric field intensity was documented. The consistency between the DOS visualization and the numerical data strengthens the reliability of the findings, highlighting Fluorenol’s superior electronic properties, such as improved conductivity and enhanced charge transfer efficiency under external electric fields.

According to the obtained results, the smaller energy gap of fluorenol makes electron transfer and conductivity more efficient and contributes to superior electronic performance compared to fluorenone. The lower energy gap in Fluorenol allows for easier charge transfer and electron flow, which is a critical factor in molecular electronics. Devices made from materials with lower energy gaps can operate at lower voltages and exhibit faster response times. Significant reduction of the energy gap in fluorenol facilitates the phenomenon of quantum tunneling between the electrode and the molecule^53,54. In this case, electron transfer along the length of the molecule occurs easily and the conductivity of the structure increases.

Dipole moment and polarizability

Investigating dipole moment and polarizability is crucial in designing nanoelectronic devices, including molecular wires, as these properties directly influence charge transport, electronic interactions, and device performance^47,48. The dipole moment determines how a molecule interacts with external electric fields and neighboring molecules. A higher dipole moment can lead to stronger intermolecular interactions, affecting charge mobility and stability in molecular junctions. Controlling dipole moments in nanoelectronic applications like medical implants ensures efficient signal transmission and minimizes unwanted charge trapping or dissipation^49–55. Polarizability describes a molecule’s ability to redistribute its electron cloud in response to an external electric field. Higher polarizability enhances charge delocalization, reducing resistance and improving conductivity in molecular wires. Additionally, molecules with high polarizability can better adapt to environmental fluctuations, which is critical for ensuring stable performance in biological or electronic systems^56,57.

Therefore, by optimizing the dipole moment and polarizability, molecular wires can be designed with better conductivity, stability, and response to external stimuli, producing more efficient and reliable nanoelectronic devices. For this purpose, the dipole moment and polarizability were calculated for each studied structure, and its results are shown in Fig. 9.

Fig. 9.

Effect of external field on dipole moment (left) and polarizability (right) of each molecular system.

As the field strength increases from 0 to 100 × 10⁻⁴ a.u., the dipole moment and polarizability show a rising trend for both Au-A-Au and Au-B-Au configurations. Without an external field, the Au-A-Au system has a lower dipole moment (2.02 Debye) than Au-B-Au (5.56 Debye), indicating that Au-B-Au possesses a stronger intrinsic polarization. However, with increasing field strength, both systems experience an enhancement in their dipole moments, with Au-B-Au consistently maintaining higher values. At the maximum field strength of 100 × 10⁻⁴ a.u., the dipole moment for Au-A-Au reaches 6.05 Debye, while that of Au-B-Au rises to 10.02 Debye.

Similarly, polarizability increases with field strength for both systems. Initially, Au-A-Au exhibits a lower polarizability (287.86 a.u.) than Au-B-Au (428.53 a.u.), but both structures respond significantly to the applied field. By 100 × 10⁻⁴ a.u., the polarizability of Au-A-Au increases to 721.60 a.u., while Au-B-Au reaches 772.26 a.u., maintaining a higher overall value. These trends suggest that Au-B-Au is more sensitive to the external field in terms of dipole moment and polarizability than Au-A-Au.

According to the results, applying an external electric field caused the separation of positive and negative charge centers and changed the dipole moment and polarizability in the studied molecular system (Fig. 5). When an external electric field is applied, the dipole moment of Au-A-Au and Au-B-Au increases because the field causes more charge separation. However, the effect of the field on the dipole moment and polarizability of Au-B-Au is more significant. The hydroxyl group in fluorenol contributes to higher polarizability, enabling the molecule to adapt more effectively to external fields and strengthen the dipole moment.

Electronic spatial extent (ESE) analysis

Examining ESE is essential in nanoelectronic device design to harness quantum effects, optimize performance, and ensure efficient operation at the nanoscale^58,59.

The results of this study indicate that the increase in the ESE in Au-B-Au is more significant than in Au-A-Au after applying an external electric field (Fig. 10). This observation can be attributed to Fluorenol’s structural and electronic characteristics, particularly the extension of its conjugated bond system, which plays a critical role in facilitating charge delocalization and enhancing electronic properties.

Fig. 10.

Changes in ESE due to application of electric field with different intensities.

In Au-B-Au, the presence of the hydroxyl group (–OH) introduces additional electronic interactions through hydrogen bonding and resonance effects. This functional group can donate electrons via the lone pair on the oxygen atom, which interacts with the π-conjugated system of the fluorenyl backbone. As a result, the conjugation is extended beyond the typical π-system found in Fluorenone, allowing for more extensive electron delocalization. When an external electric field is applied, this extended conjugation in Fluorenol becomes more pronounced, enabling electrons to distribute over a larger molecular region. This enhanced delocalization reduces electron localization, increases the ESE, and facilitates smoother charge transport across the molecule.

In contrast, Fluorenone contains a carbonyl group (C=O) that acts as an electron-withdrawing moiety. While this group participates in the conjugated system, its electron-withdrawing nature limits the extent of delocalization compared to the electron-donating hydroxyl group in Fluorenol. The carbonyl group tends to localize electron density around itself, creating a more confined electron distribution. Consequently, the ability of Fluorenone to expand its electronic spatial extent under an external electric field is less pronounced. The significant increase in ESE observed in Fluorenol has important implications for its electronic performance. The extended conjugation and enhanced delocalization reduce electron scattering and promote higher charge carrier mobility, which is crucial for the efficiency of nanoelectronic devices. This property contributes to Fluorenol’s superior conductivity and better thermoelectric performance, as evidenced by its higher current response and lower Joule/Peltier heating effects in this study (See Section "Joule/Peltier heating (intramolecular coefficients)").

In conclusion, the more significant increase in ESE in Fluorenol compared to Fluorenone under the influence of an external electric field is primarily due to the extension of the conjugated bond system facilitated by the hydroxyl group. This structural feature promotes greater electron delocalization, improving charge transport properties and making Fluorenol a more promising candidate for applications in molecular nanoelectronics.

I–V curve

Studying a molecule’s Current–Voltage (I–V) characteristics using DFT is crucial in understanding its electronic transport properties^60–64. DFT provides a theoretical framework to calculate molecules’ electronic structure and properties, and I–V curves offer insights into the conductance behavior^65,66. Analysis of the I–V curve reveals valuable information about the electronic/quantum properties of the molecular structure, such as electrical conductivity, energy levels, and potential applications of the molecule in electronic devices (such as molecular junctions or nanoscale electronics)^67,68. For this purpose, the I–V curve of the studied molecular system was studied computationally (Fig. 11).

Fig. 11.

I–V curve of the studied structure in the intensity of applied currents.

The voltage-current (I–V) curve illustrates the electrical behavior of two molecular junctions, Au-A-Au and Au-B-Au, where A represents fluorenone, and B represents fluorenol. Both structures exhibit nearly linear I–V characteristics, indicating an ohmic response with a steady increase in current as voltage increases. However, the Au-B-Au system (fluorenol-based) demonstrates a higher current at equivalent voltages compared to the Au-A-Au system (fluorenone-based). This suggests that fluorenol provides a lower resistance pathway for electron transport, leading to enhanced electrical conductivity.

The difference in conductivity between the two systems can be attributed to the electronic properties of fluorenone and fluorenol. Fluorenone contains a conjugated ketone functional group, which influences electron delocalization differently than fluorenol, which has a hydroxyl (-OH) group. The ketone in fluorenone withdraws electron density through an electron-withdrawing effect, potentially disrupting π-electron delocalization and increasing resistance. In contrast, the hydroxyl group in fluorenol can engage in hydrogen bonding and electron-donating impact, which may facilitate better charge transport by stabilizing charge carriers and improving molecular orbital overlap.

A key factor influencing the voltage response and electrical conductivity in these molecular junctions is the role of π-electrons. π-electrons in conjugated systems, such as fluorenone and fluorenol, enable charge delocalization, which is crucial for efficient electron transport. In extended π-systems, electrons can move more freely across the molecular framework, reducing resistance and enhancing conductivity. The extent of π-conjugation and the molecular energy levels play a crucial role in determining the ease of charge transport.

In the case of Au-B-Au, fluorenol’s electronic structure likely facilitates better π-electron overlap, leading to improved conductivity and higher current values at equivalent voltages compared to Au-A-Au. The presence of π-electrons in both systems supports charge delocalization, but the structural and electronic differences between fluorenone and fluorenol contribute to the observed variations in electrical performance. Thus, the superior conductivity of Au-B-Au suggests that fluorenol provides a more favorable electronic environment for charge transport, likely due to its electronic effects and interaction with gold electrodes. These characteristics indicate the application of these structures in molecular electronics as a wire or molecular sensor.

Mulliken population analysis

The study of Mulliken charge distribution is critical in designing molecular nanoelectronic devices to investigate the behavior of atoms and orbitals in charge redistribution in response to external electric fields. This analysis helps better understand the role of different atoms in charge transfer and their overall electronic behavior in quantum nanoelectronic systems (Table 4)^69,70.

Table 4.

Mulliken population analysis for each of structures Au-A-Au and Au-B-Au in the presence/absence of electric fields of different intensities.

Atom	Field (10−4 a.u.)
	0	20	40	60	80	100
Au-A-Au
C1	− 0.182035	− 0.169766	− 0.157938	− 0.146520	− 0.135510	− 0.124855
C2	0.520506	0.505144	0.490869	0.477602	0.465484	0.454481
C3	− 0.657876	− 0.660144	− 0.662929	− 0.666115	− 0.669786	− 0.673864
C4	0.457172	0.467395	0.478484	0.490472	0.503378	0.517179
C5	0.513862	0.524238	0.534760	0.545468	0.556407	0.567610
C6	− 0.150958	− 0.147581	− 0.144514	− 0.141729	− 0.139206	− 0.136913
H7	0.221281	0.226953	0.232626	0.238300	0.243973	0.249644
H8	0.308903	0.303597	0.298335	0.293107	0.287910	0.282735
H9	0.238079	0.247457	0.256758	0.265981	0.275121	0.284179
C10	− 0.555333	− 0.564098	− 0.573760	− 0.584384	− 0.596073	− 0.608927
C11	0.456743	0.459054	0.461691	0.464648	0.467955	0.471625
C12	− 0.657328	− 0.666217	− 0.675842	− 0.686131	− 0.697082	− 0.708669
C13	0.520351	0.500656	0.483078	0.467341	0.453227	0.440569
C14	− 0.182393	− 0.165221	− 0.148836	− 0.133128	− 0.118016	− 0.103437
C15	− 0.150851	− 0.147693	− 0.144632	− 0.141640	− 0.138684	− 0.135735
C16	0.513411	0.525091	0.536815	0.548623	0.560581	0.572730
H17	0.308902	0.305865	0.302945	0.300142	0.297461	0.294903
H18	0.221279	0.231193	0.241049	0.250843	0.260569	0.270224
H19	0.238079	0.246241	0.254360	0.262433	0.270457	0.278430
O20	− 0.354937	− 0.367698	− 0.380312	− 0.392765	− 0.405043	− 0.417129
S21	− 0.388678	− 0.378444	− 0.368372	− 0.358609	− 0.349288	− 0.340563
S22	− 0.388576	− 0.359872	− 0.332015	− 0.305011	− 0.278872	− 0.253639
Au23	− 0.424772	− 0.462410	− 0.500165	− 0.537985	− 0.575800	− 0.613508
Au24	− 0.424834	− 0.453738	− 0.482454	− 0.510939	− 0.539161	− 0.567071
Au-B-Au
C1	− 0.027755	− 0.015690	− 0.003890	0.007652	− 0.152166	0.030139
C2	0.870011	0.851226	0.833398	0.816703	− 0.371896	0.786700
C3	− 0.681581	− 0.682585	− 0.684093	− 0.686115	− 0.211616	− 0.691614
C4	0.025089	0.033370	0.042009	0.050939	− 0.000370	0.069471
C5	0.460244	0.467675	0.475115	0.482596	0.057658	0.497778
C6	− 0.034856	− 0.031300	− 0.028024	− 0.024993	− 0.217953	− 0.019544
H7	0.214512	0.220079	0.225666	0.231271	0.243729	0.242534
H8	0.254370	0.248777	0.243249	0.237776	0.210001	0.226982
H9	0.236240	0.245529	0.254759	0.263926	0.235058	0.282061
C10	− 0.809553	− 0.815311	− 0.821162	− 0.827124	0.364166	− 0.839463
C11	0.471697	0.478240	0.485101	0.492334	0.041874	0.508061
C12	− 0.734138	− 0.743781	− 0.754250	− 0.765525	− 0.191876	− 0.790370
C13	0.551541	0.530749	0.512043	0.495125	− 0.397514	0.465724
C14	− 0.193333	− 0.176426	− 0.160376	− 0.145084	− 0.145370	− 0.116386
C15	− 0.137676	− 0.134825	− 0.132056	− 0.129346	− 0.216575	− 0.124005
C16	0.500000	0.510798	0.521619	0.532525	0.053584	0.554765
H17	0.293406	0.290138	0.286978	0.283936	0.241913	0.278215
H18	0.213480	0.223473	0.233403	0.243265	0.260688	0.262764
H19	0.233812	0.242075	0.250288	0.258448	0.238815	0.274606
O20	− 0.358370	− 0.363522	− 0.368466	− 0.373203	− 0.590935	− 0.382049
S21	− 0.378959	− 0.368820	− 0.358959	− 0.349567	0.222303	− 0.332753
S22	− 0.387375	− 0.358543	− 0.330647	− 0.303686	0.348580	− 0.252682
Au23	− 0.466902	− 0.504609	− 0.542380	− 0.580155	− 0.371215	− 0.655393
Au24	− 0.451997	− 0.480934	− 0.509665	− 0.538153	− 0.046524	− 0.594217
H25	0.338092	0.334218	0.330339	0.326454	0.395644	0.318673

In both structures, the Mulliken charges for the atoms change as the external electric field increases, indicating that charge redistribution occurs. The oxygen atom (O20) in both structures shows a clear trend of accumulating more negative charge with increasing field strength. In Au-A-Au, the charge on the oxygen atom decreases from − 0.354937 at 0 to − 0.417129 at 100 (10^–4 a.u.), reflecting a progressive negative charge accumulation. A similar but less pronounced shift is observed in Au-B-Au, where the oxygen charge decreases from − 0.358370 at 0 (10⁻⁴ a.u.) to − 0.382049 at 100 (10⁻⁴ a.u.). This indicates that the oxygen atom is involved in charge redistribution under the influence of the external electric field, with a more significant effect in the Au-A-Au structure.

Sulfur atoms (S21 and S22) in both structures also show charge redistribution in response to the external field. In Au-A-Au, sulfur atoms exhibit a modest decrease in charge as the field increases. For instance, S21 starts at − 0.388678 at 0 (10⁻⁴ a.u.) and decreases to − 0.340563 at 100 (10⁻⁴ a.u.), while S22 begins at − 0.388576 and shifts to − 0.253639 at 100 (10⁻⁴ a.u.). In Au-B-Au, the charge redistribution on sulfur atoms is more pronounced. S21 starts at − 0.378959 at 0 (10⁻⁴ a.u.) and shifts to − 0.332753 at 100 (10⁻⁴ a.u.), while S22 changes from − 0.387375 at 0 (10⁻⁴ a.u.) to − 0.252682 at 100 (10⁻⁴ a.u.). These larger shifts in the sulfur atom charges suggest that sulfur atoms in the Au-B-Au structure are more sensitive to the applied electric field compared to those in Au-A-Au.

In contrast, the carbon (C) and hydrogen (H) atoms in both structures show charge redistribution, but the changes are less significant compared to oxygen and sulfur. Carbon atoms (e.g., C1, C3, C10, etc.) in both structures exhibit small shifts in charge with increasing field strength, but the overall trends are weaker. Hydrogen atoms (e.g., H7, H8, H9, etc.) also show minor shifts, though these are much smaller than those observed in the oxygen and sulfur atoms.

When comparing the two structures, Au-A-Au (fluorenone) exhibits a more prominent redistribution of charge on the oxygen and sulfur atoms, indicating that fluorenone’s electronic structure is more influenced by the external electric field. In this structure, the oxygen atoms show a consistent negative charge accumulation, suggesting their central role in the charge redistribution. On the other hand, Au-B-Au (fluorenol) shows a smaller change in the charge of the oxygen atom but a more significant redistribution of charge on the sulfur atoms, with S21 and S22 exhibiting larger shifts compared to the Au-A-Au structure. This indicates that sulfur atoms in the fluorenol structure are more responsive to the external field.

In conclusion, the redistribution of charge in both structures is predominantly influenced by the oxygen and sulfur atoms. The oxygen atoms show a consistent trend of accumulating more negative charge with increasing external field, particularly in the Au-A-Au structure. The sulfur atoms, especially in Au-B-Au, exhibit more substantial charge shifts, making them more sensitive to the electric field. These observations highlight that oxygen and sulfur atoms play a key role in the charge response to the external electric field.

Natural bond orbitals (NBOs) analysis

Considering Natural Bond Orbital (NBO) analysis in designing molecular wires is crucial because it provides detailed insights into a molecule’s electronic structure, charge distribution, and delocalization. NBO analysis helps identify the most relevant donor–acceptor interactions, which is essential for understanding charge transport properties in molecular wires. One key parameter derived from NBO analysis is the stabilization energy, denoted as E^(2)71,72.

Stabilization energy (E⁽²⁾), which arises from second-order perturbation theory within NBO analysis, plays a significant role in the design of field-effect molecular wires. E⁽²⁾ quantifies the energetic stabilization resulting from donor–acceptor interactions, indicating the extent of charge delocalization and electronic coupling between molecular orbitals⁷³. A higher E⁽²⁾ value suggests stronger electronic interactions, enhancing charge mobility and reducing resistance in molecular wires⁷⁴. In the context of field-effect molecular wires, where external electric fields modulate charge transport, understanding and optimizing E⁽²⁾ helps design molecules with high responsiveness to field variations. This leads to improved efficiency and sensitivity in molecular electronic devices, such as transistors and sensors, where precise control over charge flow is essential. Thus, NBO analysis and E⁽²⁾ stabilization energy provide critical parameters for tailoring molecular architectures to achieve optimal electrical performance⁷⁵. The donor orbital occupancy (qi), off-diagonal elements (Ei and Ej), and diagonal NBO Fock matrix elements (F_i.j) are used to calculate the stabilization energy (E⁽²⁾) and can be expressed as follows (Eq. 8):

8

A higher E(2) value indicates a stronger interaction between electron donors, signifying enhanced charge delocalization and increased conjugation throughout the entire molecular system⁷⁶. This increased conjugation facilitates efficient charge transport, which is particularly crucial in field-effect molecular wires, where the conductivity and response to an external electric field depend on the degree of electronic coupling. A higher E⁽²⁾ value suggests that the molecule can sustain a more extended π-system, reducing charge recombination and increasing charge carrier mobility, thereby improving the overall performance of molecular electronic devices⁷⁷.

In this regard, the analysis of Natural Bond Orbitals (NBOs) for the designed molecules was performed using DFT to gain deeper insights into their electronic structure. The fundamental electronic transitions derived from the NBO analysis were reported in Table 5, providing essential information on the charge transfer pathways and the extent of orbital delocalization, which directly influence the field-effect properties of the molecular wire.

Table 5.

Values of NBOs analysis for Au-A-Au and Au-B-Au.

Donor (i)	Type	Acceptor (j)	Type	E(2) kcal.mol-1	E(j)-E(i) a.u	F(i,j) a.u
Au-B-Au
EF = 0
C11- C12		C10-O20		18.13	0.35	0.074
C12-H17		S22-Au24		10.82	0.49	0.065
C13-C14		C11-C12		27.85	0.38	0.093
C11-C12		C10-O20		18.13	0.35	0.074
S 22	LP (1)	C11—C12		2.37	0.82	0.043
Au24	LP (2)	S21 -Au23		8.72	0.28	0.044
EF = 40 × 10−4 a.u
C12-C13		S22-Au24		13.43	0.68	0.086
S22-Au24		C10-O20		14.29	0.91	0.102
C10-O20		C3-C4		40.37	0.04	0.077
C3-C4		C5-C6		27.32	0.40	0.094
S 22	LP (1)	C10-O20		38.42	1.24	0.195
Au24	LP (1)	S21 -Au23		9.35	0.26	0.044
EF = 60 × 10−4 a.u
C12-C13		S22-Au24		13.42	0.69	0.086
S22-Au24		C13-C14		51.91	0.57	0.153
C5-C6		C1-C2		31.91	0.34	0.094
C15-C16		C11—C12		29.32	0.38	0.094
S22	LP (1)	C10-O20		38.89	1.24	0.196
Au24	LP (2)	S21-Au23		9.71	0.25	0.044
EF = 100 × 10−4 a.u
C10-O20		C11—C12		18.83	0.72	0.114
C12-C13		S22 -Au24		30.20	0.89	0.147
C10-O20		C11-C12		56.35	0.04	0.044
C 5-C6		C1-C2		33.36	0.34	0.095
S22	LP (1)	C10-O20		63.87	1.22	0.250
S22	LP (2)	C14-C15		14.81	1.33	0.129
Au-A-Au
EF = 0
C10-O20		S21-Au23		30.46	3.09	0.388
C11-C16		C3-C4		69.18	6.45	0.847
C15-C16		C10-C11		20.01	0.27	0.105
C3-C4		C12-C13		21.58	1.62	0.244
S 22	LP (1)	C12-C13		10.82	0.94	0.478
Au24	LP (2)	C5-C16		2.33	0.69	0.051
EF = 40 × 10−4 a.u
C1-H7		C3-C4		20.75	1.44	0.218
C10-O20		S21-Au23		179.70	2.32	0.819
C10-C11		C15-C16		30.52	0.13	0.108
C3-C4		C12-C13		22.08	1.66	0.251
S21	LP (1)	C1- C2		11.39	0.34	0.086
O20	LP (2)	C4-C10		4.73	1.20	0.095
EF = 60 × 10−4 a.u
C1-H7		S21-Au23		19.17	2.54	0.279
C3-C4		S21-Au23		1.48	2.46	0.076
C3-C4		C12-C13		31.83	1.64	0.248
C10-C11		C3-C4		17.61	0.38	0.110
O20	LP (1)	C12-C13		18.52	0.97	0.128
S22	LP (2)	C13-C14		5.99	0.48	0.069
EF = 100 × 10−4 a.u
C3-H8		C3-C4		9.59	1.19	0.135
C1-C6		C3-C4		42.70	2.33	0.398
C10-O20		C12-C13		10.57	1.35	0.171
C12-C13		C10-C11		32.03	0.26	0.131
O20	LP (1)	C3-C4		22.56	1.32	0.218
S22	LP (2)	C13-C14		9.35	1.08	0.130

In general, the possible types of electronic transitions include σ → σ*, π → π*, LP(2) → σ*, and LP(1) → π*. Among these, π → π* transitions are the most dominant, primarily due to the presence of an extended π-conjugation system, which facilitates efficient electron delocalization. In contrast, σ → σ* transitions tend to be weaker since they involve sigma bonds requiring higher excitation energy. Meanwhile, LP(2) → σ* and LP(1) → π* transitions are relatively less significant, contributing only minimally to the overall excitation process^78,79.

Analyzing the data from Table 5 for the Au-A-Au and Au-B-Au structures under different electric field (EF) conditions, we observe significant variations in stabilization energy (E⁽²⁾) values for different electronic transitions.

For Au-B-Au, at EF = 100 × 10⁻⁴ a.u., the most dominant π → π* transition is C10-O20 → C11-C12 with an E(2) value of 56.35 kcal.mol⁻¹, indicating strong conjugation and charge delocalization. Additionally, the lone pair (LP) interaction S22 → C10-O20 π* shows a stabilization energy of 63.87 kcal.mol⁻¹, further supporting the molecule’s high potential for charge transport under an applied field.

For Au-A-Au, at EF = 40 × 10⁻⁴ a.u., the highest stabilization energy is observed in the σ → σ* transition C10-O20 → S21-Au23, reaching 179.70 kcal.mol⁻¹, which is remarkably high and suggests strong electronic coupling. However, in terms of π → π* transitions, the highest energy transition is C10-C11 → C15-C16 at 30.52 kcal.mol⁻¹, which is lower than the dominant π → π* transition in Au-B-Au.

Comparing both structures, Au-B-Au exhibits more significant π → π* interactions and LP → π* transitions under applied fields, which are crucial for effective charge transport in molecular wires. The presence of strong conjugation and hyperconjugative interactions in the Au-B-Au system, particularly at higher electric fields, suggests that it has superior charge delocalization and electronic stability.

The Au-B-Au structure is the best candidate as a molecular wire due to its higher stabilization energy for π → π* and LP → π* transitions, which are essential for efficient charge transfer. Its superior performance under an applied electric field makes it a more promising option for molecular electronic applications.

Joule/Peltier heating (intramolecular coefficients)

Understanding Joule and Peltier heating in nanoelectronic systems is vital, as these thermal effects play a key role in determining device performance, stability, and lifespan^80,81. As electronic components are scaled down to the nanoscale, heat dissipation becomes more challenging, making efficient thermal management essential for maintaining device efficiency. In such systems, excessive Joule/Peltier heating can lead to overheating, which not only reduces performance but may also cause irreversible damage to delicate components^82,83. Proper control of these thermal effects is, therefore, critical for ensuring the durability and reliable operation of nanoelectronic devices⁸⁴. The Joule and Peltier heating effects for the studied structures were analyzed computationally using QTAIM to address this.

When a molecular model is exposed to an external electric field (with intensity ε), it can be divided into electron donor and acceptor regions, similar to n-p junctions. This division facilitates a detailed analysis of charge and energy transfer under the influence of the electric field⁸⁵. To investigate pseudo-thermoelectric behavior in a molecular nanoelectronic system, the model must be segmented into distinct molecular regions, as shown in Fig. 12. This study divided the molecular system into left (SL) and right (SR) sections, akin to the partitioning seen in n/p-type semiconductor thermoelectric systems. This segmentation is essential for analyzing the molecule’s heat flow and thermoelectric properties when subjected to an external electric field. This perspective facilitates the interpretation of heat generation and transfer mechanisms within molecular nanoelectronics and provides insights into optimizing molecular structures for efficient energy management. By introducing a temperature gradient or applying a potential difference within the E-M-E molecular system, charge and energy transfer between the molecule and the electrode may occur, potentially leading to thermoelectric-like effects within the molecule⁸⁶.

Fig. 12.

Division of the studied molecular structures into two distinct intramolecular regions: the left segment (S_L) and the right segment (S_R).

Considering that Joule’s heat is an even function and Peltier’s heat is an odd function with respect to the change in the direction of the applied field (f/r), Therefore, similar to n/p-thermoelectric-like systems, the Joule-like heat ()and Peltier-like heat (),the intramolecular thermoelectric systems, can be given by (Eq. 9)⁸⁷:

9

where the superscripts and r correspond, respectively, to the forward and reverse biases. These definitions make it possible to discriminate between symmetrical and asymmetrical heat flow contributions to the IMTLCs. In analogy with Eq. (9), the intramolecular Joule-like (symmetric) heating, , and intramolecular Peltier-like (asymmetric) heating, , for any pair of sections corresponding to the coordinate q, can be defined as (Eq. 10)⁸⁸:

10

The total IMTLC can be considered to be constituted additively from two components and corresponding, respectively, to the electronic and vibrational degrees of freedom, which can be evaluated for any pair of IMTLSs , i,e. (Eq. 11)⁸⁹,

11

In many cases, the applied voltage is time-independent, and thus the thermoelectric coefficients and consequently thermoelectric figure of merit are (ZT) time-independent. In this picture, starting from this linear law, the intramolecular thermoelectric-like coefficient  can be introduced as (Eq. 12):

12

where is the kinetic energy (as heat) transferred between the two main IMTLS of interest located along the q direction due to the application of electric force . The electric force is measured in terms of the EF strength ε (i.e., ) whose components are defined as with V being the applied voltage along the q direction and l _q the projection of the length of the molecular system along that direction (i.e., distance between the two poles or terminals of the circuit). Macroscopically, EF intensity is measured and reported in volts/m while in atomic units it has the units of 1 au = 514.224 V/nm. To make our numerical results compatible with the macroscopic thermoelectric coefficients, the IMTLCs are in K/mV units, When the EF is applied in the x direction only (i.e.,  εy = εz = 0 ) Eq. (11) is reduced to (Eq. 13):

13

Accordingly, using Eq. (22), the IMTLC can be divided into two parts, symmetrical () and asymmetrical () IMTLCs, which describe the intramolecular Joule (or Joule-like) and Peltier (or Peltier-like) effects, respectively. We can, therefore, write (Eqs. 14 and 15):

14

15

in which and are the overall IMTLC corresponding to the thermoelectric process with forward and reverse biases, respectively. Obviously, we have ⁹⁰.

To calculate and analyze IMTLCs  and for both directions, parallel (q = x) and perpendicular (q = y) to the applied EF, in a model molecular system, EF effect on the atomic basin electronic and vibrational energies, and the resulting density and energy transfers between different sections of the molecule should be computed and analyzed. Variations of the calculated (intramolecular Joule-like) and (intramolecular Peltier-like) IMTLCs for both (S_L,S_R) pairs of IMTLSs with the intensity of the EF calculated for the electronic and vibrational degrees of freedom are demonstrated in Fig. 13.

Fig. 13.

Effect of external electric field on Peltier/Joule (Q_P/Q_J) coefficients in the studied structures. The right figure corresponds to Au-B-Au and the left figure corresponds to Au-A-Au.

Based on the results presented in Fig. 13, it is evident that the Joule and Peltier heating values for Au-B-Au are significantly lower than those for Au-A-Au. This reduction in heating suggests that Au-B-Au offers superior thermal management, making it particularly suitable for applications where minimizing heat generation is critical. Au-B-Au lower heating values present a clear advantage in medical devices, such as implants, where temperature control is essential to prevent tissue damage and ensure device longevity. Its ability to maintain cooler operating temperatures enhances its potential as a nanowire material in biomedical applications, where reliable performance and biocompatibility are key requirements for devices implanted in the body. Therefore, Au-B-Au is a promising candidate for developing advanced nanoelectronic medical implants.

ELF and LOL analysis

The Electron Localization Function (ELF) analysis provides valuable insights into charge transport behavior in molecular nanoelectronics, particularly in evaluating the performance of different molecular junctions^91,92. While fluorenone (A) exhibits a more delocalized π-system, the superiority of the Au-B-Au system can be argued based on key electronic characteristics that favor efficient charge injection, enhanced stability, and tunability under an external electric field (Fig. 14).

Fig. 14.

ELF contours for isolated and non-isolated Fluorenol (A) and Fluorenone (B) in the presence/absence of an electric field.

The ELF contours for the Au-B-Au system at EF = 0 indicate pronounced electron localization at the gold (Au) and sulfur (S) anchoring sites, suggesting strong metal–molecule interactions. This enhanced coupling is crucial for efficient charge injection, as the molecular orbitals interact more effectively with the electrodes, reducing contact resistance. The localization of electron density near Au in the Au-B-Au system implies that electron transfer between the molecule and the metal is more favorable than in the Au-A-Au system, where electron delocalization may lead to weaker coupling and reduced charge injection efficiency.

Under an applied electric field (EF = 40 × 10⁻⁴ a.u.), the ELF distribution in the Au-B-Au system exhibits notable polarization effects, indicating significant reorganization of electron density. This response suggests that Au-B-Au is more sensitive to external fields, a desirable characteristic for molecular electronic devices where tunability is essential. The enhanced localization of electrons in response to the field suggests a greater ability to modulate conductivity, allowing for improved performance in field-effect transistors and other nanoelectronic applications.

While fluorenone (A) has a more delocalized π-system, which can sometimes enhance conductivity, excessive delocalization can lead to increased electronic decoherence and instability in molecular junctions. The fluorenol (B)-based Au-B-Au system benefits from a more controlled electron distribution, which reduces leakage currents and enhances charge retention, making it a superior candidate for stable and reliable nanoelectronic devices. The presence of the hydroxyl (-OH) group in fluorenol contributes to localized interactions, preventing excessive electronic dispersion and maintaining consistent charge flow.

The ELF analysis supports the argument that while Au-A-Au benefits from greater intrinsic delocalization, the Au-B-Au system demonstrates superior charge injection, stronger field responsiveness, and greater stability, making it a more practical choice for molecular nanoelectronics. The strong coupling between the molecule and gold electrodes ensures efficient charge transfer, while the enhanced polarization response under an electric field suggests improved tunability. These characteristics make Au-B-Au a more adaptable and robust candidate for next-generation molecular wire applications.

The analysis of Localized Orbital Locator (LOL) contours provides crucial insights into molecular systems’ electronic structure and charge distribution, particularly in the context of molecular nanoelectronics^93,94. The provided LOL plots compare fluorenone (A) and fluorenol (B) in their pristine forms, as well as their Au-A-Au and Au-B-Au configurations when attached to gold electrodes, both in the absence and presence of an external electric field (EF) (Fig. 15). This comparison allows for a detailed assessment of charge localization, transport properties, and stability under electronic perturbations, ultimately determining the most suitable configuration for molecular wire applications⁹⁵.

Fig. 15.

The LOL contours for pristine fluorenone (A), pristine fluorenol (B), and Au-A-Au and Au-B-Au (attached to a gold electrode) in the presence/absence of an electric field.

In the pristine states of fluorenone (A) and fluorenol (B), the LOL distributions indicate strong electron localization around the atomic centers, particularly in the conjugated carbon backbone and oxygen functional groups. Fluorenol (B) exhibits a slightly higher localization around its hydroxyl (-OH) group, which influences its electronic structure compared to fluorenone (A). These intrinsic electronic differences impact the molecular interactions when coupled to gold electrodes.

When the molecules are attached to gold electrodes in the Au-A-Au and Au-B-Au structures, significant modifications in the electronic structure are observed. The Au-B-Au structure demonstrates a more continuous and well-defined electronic localization pattern along the molecular backbone, indicating efficient charge delocalization. In contrast, the Au-A-Au system exhibits relatively fragmented localization, suggesting weaker electronic coupling and possible charge scattering effects that could hinder conductivity. The presence of sulfur (S) and gold (Au) atoms in the metal–molecule junctions further influences the charge transport characteristics. The Au-B-Au structure maintains a more symmetrical and evenly distributed localization across its framework, favoring stable electron transport pathways.

Under the application of an external electric field (EF = 40 × 10⁻⁴ a.u.), the robustness of electronic localization becomes a key determinant of structural superiority. The Au-B-Au system continues to exhibit strong electronic retention along the molecular backbone, whereas the Au-A-Au structure shows more noticeable distortions in its LOL distribution. This indicates that Au-B-Au is more resilient to external perturbations, an essential feature for molecular nanoelectronic devices operating under varying voltage conditions.

The observed electronic characteristics highlight the superiority of the Au-B-Au configuration over Au-A-Au. The enhanced charge delocalization, more uniform electronic distribution, and improved stability under an electric field suggest that Au-B-Au offers better conductivity and reliability for molecular electronic applications. These findings establish Au-B-Au as the more suitable candidate for molecular wire implementations, where efficient charge transport and stability are critical for device performance.

Conclusion

This study systematically analyzed the electronic properties of fluorenone (A) and fluorenol (B) using DFT, QTAIM, and Landauer theories to assess their potential applications in molecular nanoelectronics. The results demonstrated that fluorenol consistently exhibited superior charge transport properties compared to fluorenone, primarily due to its lower HOMO–LUMO gap and enhanced electronic interactions under applied electric fields. Specifically, the energy gap of fluorenol was found to be 5.91 eV (CAM-B3LYP) and 1.94 eV (PBEPBE), which were lower than those of fluorenone at 6.46 eV and 2.44 eV, respectively, indicating fluorenol’s higher conductivity. Under increasing electric field intensity, the HOMO–LUMO gap for Au-B-Au (fluorenol) decreased from 3.98 eV at zero fields to 1.63 eV at 100 × 10⁻⁴ a.u. In contrast, Au-A-Au (fluorenone) dropped from 4.32 eV to 2.60 eV, confirming the stronger field response of fluorenol. Cohesive energy analysis further highlighted the stability of both molecules under applied fields, with fluorenol maintaining a slightly higher cohesive energy (74.5 kcal.mol⁻¹ at zero field) than fluorenone (73.2 kcal.mol⁻¹), suggesting its greater structural resilience. The I–V characteristics revealed that Au-B-Au achieved higher current values at equivalent voltages than Au-A-Au, reinforcing its suitability for efficient charge transport.

Additionally, dipole moment and polarizability analyses demonstrated that fluorenol exhibited a more pronounced response to the electric field, with its dipole moment increasing from 5.56 Debye to 10.02 Debye at 100 × 10⁻⁴ a.u., compared to fluorenone’s increase from 2.02 Debye to 6.05 Debye. Furthermore, ELF and LOL analyses supported the greater electron delocalization and charge stability in fluorenol, which improved conductivity and molecular wire potential. Lastly, Joule and Peltier’s heating values were significantly lower for Au-B-Au, indicating better thermal management, making fluorenol a more promising candidate for nanoelectronic applications, particularly in biomedical devices where thermal stability is critical. These findings confirm that fluorenol is a superior material for molecular nanoelectronics, offering enhanced conductivity, stability, and tunability under external fields compared to fluorenone.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Author contributions

Hashem O. Alsaab: Methodology, Conceptualization, Writing-original draft, Validation, Supervision, Writing—review & editing.

Funding

This research was funded by Taif University, Saudi Arabia, Project No. (TU-DSPP-2024–30).

Data availability

All required data are provided in the text of the manuscript.

Declarations

Competing interest

The authors declare no competing interests.