Molecular modeling study on the water-electrode surface interaction in hydrovoltaic energy

The global energy problem caused by the decrease in fossil fuel sources, which have negative effects on human health and the environment, has made it necessary to research alternative energy sources. Renewable energy sources are more advantageous than fossil fuels because they are unlimited in quantity, do not cause great harm to the environment, are safe, and create economic value by reducing foreign dependency because they are obtained from natural resources. With nanotechnology, which enables the development of different technologies to meet energy needs, low-cost and environmentally friendly systems with high energy conversion efficiency are developed. Renewable energy production studies have focused on the development of hydrovoltaic technologies, in which electrical energy is produced by making use of the evaporation of natural water, which is the most abundant in the world. By using nanomaterials such as graphene, carbon nanoparticles, carbon nanotubes, and conductive polymers, hydrovoltaic technology provides systems with high energy conversion performance and low cost, which can directly convert the thermal energy resulting from the evaporation of water into electrical energy. The effect of the presence of water on the generation of energy via the interactions between the ion(s) and the liquid–solid surface can be enlightened by the mechanism of the hydovoltaic effect. Here, we simply try to get some tricky information underlying the hydrovoltaic effect by using DFT/B3LYP/6-311G(d, p) computations. Namely, the physicochemical and electronic properties of the graphene surface with a water molecule were investigated, and how/how much these quantities (or parameters) changed in case of the water molecule contained an equal number of charges were analyzed. In these computations, an excess of both positive charge and negative charge, and also a neutral environment was considered by using the Na+, Cl−, and NaCl salt, respectively.

www.nature.com/scientificreports/While the theoretical exploration of infinite graphene planes presents an intellectually engaging discourse, it is essential to acknowledge that the preponderance of graphene's practical implementations is based on finite-sized components.Consequently, despite the intrinsic limitations inherent to the finite nature of these graphene-based systems, the insights garnered from such studies continue to offer substantial value and applicability across multiple domains.
Until now, DFT computations in terms of molecular mechanics and dynamic perspective have been applied successfully to graphene/ graphite systems [26][27][28][29][30] such as doped by metal or transition metal, nanostructures, or graphene quantum dots, etc.For instance, the Density Functional Theory (DFT) based on first principles examined the impact of different impurities on the structure, electronics, and charge transfer in graphene to explore the possible usage for graphene in optoelectronics and other devices requiring switching capabilities 31 .Other first-principles DFT computations were reported to explore the gas-sensing performance of transition metal-doped graphene systems 32 .Furthermore, Kumar et al. employed DFT computations to examine the impact of doping graphene with platinum group elements (PGE); they calculated the energy gap, UV-vis absorption spectra, and Mulliken population to explore the potential uses in wearable electronics, optoelectronics, sensors, and solar cells 33 .Furthermore, the graphene oxide nanosheet (GON) was modified based on the Lerf-Klinowski model and investigated the impact of integrating Be, B, N, O, and F atoms on GON's properties by using the B3LYP-D3/6-31 + G(d,p) 34 .Also, the DFT calculations and MD simulations were utilized to investigate boronmodified graphane nanoparticles to determine the reactivity and hydrogen binding potencies to examine their optoelectronic properties, indicating potential applications in clean energy and materials science 35 .In another study on research of BX (X = N, P) doped twin-graphene, the authors utilized the DFT based on first-principle calculations to explore the possible potentials of the designed systems, which would produce clean energy 36 .
To understand the basic mechanism of the surface-based hydrovoltaic effect; it is necessary to understand the interactions and energy relations of water, ions, and electrons on the solid-liquid surface.In this direction, in our study, the physicochemical effects of a water molecule on the graphene surface as a typical model were investigated.In addition, it also analyzed how the physicochemical parameters change when the water molecule contains an equal number of charges, excess positive charge or excess negative charge.Our work serves as a significant step toward understanding the intricate dynamics at the solid-liquid interface, crucial for optimizing the hydrovoltaic effect in various applications.By providing detailed insights into the physicochemical interactions between the ions and water and finite graphene, we hope that the results of this work pave the way for future research aimed at enhancing the efficiency and performance of graphene-based hydrovoltaic devices.

DFT calculations
All electronic structure computations were performed by G09 37 package and analyses and representations of the results were made by using GaussView 6.0.16 38 .At first, the electronic structures of isolated molecules, ions, and salt were confirmed by the absence of no imaginary frequency following the geometry optimization by the default convergence criteria 39,40 , at B3LYP/6-311G** level 41,42 and basis set [43][44][45] .
The thermochemical and physical characteristics of all studied species were determined by the quantum statistical principles [46][47][48] .As known well, thermodynamic and thermochemical properties for the relevant systems are calculated by using the total partition function which depends on the freedom degrees of the translational (Q trans.), rotational (Q rot.), vibrational (Q vib.), and electronic (Q elec. ) movements 46,47 .For a general system, the molecular partition function is defined as The vibrational partition function for the asymmetric top molecules is given below, and the degrees of vibrational freedom contribution to the thermochemical quantities can be calculated by Eqs.(3)-(5) [46][47][48][49] .

Result and discussion
Molecule geometry and physicochemical properties.The confirmed structures of the possible interactions between Graphene and anionic, cationic, salt, and water were presented in Fig. 1.Also, the calculated geometric data for each system designed were summarized in Table 1.
From Table 1, all C-C lengths for systems G (isolated graphene) and S1 (with water on the Graphene surface) were calculated as 1.42 Å whereas this bond for S3 and S4 was determined as 1.43 Å.In the past, the C-C length for the graphene unit was determined in the range of 1.34-1.49Å 26,28,31,[59][60][61][62] depending on the type of the doped atom.Namely, the C-C bond length for the Mg-doped graphene core was calculated as 1.34-1.44Å 31 , whereas for the O-doped Graphene, the nearest C-C length was predicted as 1.49 Å 33 .On the other hand, this length for the isolated graphene core was mostly determined as 1.42-1.43Å 59 .Also, the neighbor C-C bond lengths for the B, N, O, and F-doped graphene structures were estimated at 1.403, 1.416, 1.485, and 1.353 A, respectively 63 .Also, the O-H-C1 length for all systems was calculated as 2.50, 2.23, 2.29, and 5.57 Å: the oxygen distance to the graphene surface did grow longer with the presence of the salt (NaCl) while it did narrow with the existence of the ions (Na + or Cl − ).The geometric parameters show that the electronic attraction force between the Na + ion and the graphene surface is larger than the other systems, and therefore the Na + ion (S3) is placed parallel to the graphene surface.On the other hand, the distance between the Cl -ion and the graphene surface increased due to the electronic repulsion forces between the charge density on the graphene surface and the charge cloud of the Cl -ion, and Cl --H-C1 length was calculated as 2.61 Å.Also, Na + -C3 and Cl --C3 lengths were calculated at 4.38 and 4.10 Å, respectively, whereas the Na + -C2 and Cl --C2 distances were calculated at 2.71 and 4.78 Å.The C1-C2 -Na + and C8-C4-Na angles for S3, which the placement of the Na + ion on the graphene-like layer, were calculated as 120.9° and 75.7°, respectively.Moreover, the C4-C2-O angle for S1 was calculated as 179.0° which implied that the water molecule was positioned approximately at the same plane with the graphene structure, whereas this angle for S4 was calculated as 72.1° which was a sign that the water molecule (existence of the salt) was placed on the surface at an angle.In addition, the C2-C5-O angle for systems S1-S4 was calculated at 99.5°, 108.2°, 98.3°, and 61.7°, respectively.From Table 1, all C-C-C angles for the single-layer graphene unit were calculated in the range of 118.8-122.5°,as can be expected from sp 2 hybridization.
Also, the calculated physical and thermochemical properties were summarized in Table 2. Accordingly, the dipole moment and polarizability values of systems S2 and S4 were calculated higher than those of the other systems because of the existence of the electronegative chlorine atom.Namely, the order of the dipole moments of G and S1-S4 (in D unit) was determined as 22.172 (S2) > 10.172 (S4) > 9.727 (S3) > 2.358 (S1) > 0.000 (G), whereas the polarizability values of them (in au) were determined as 308.940 (S4) > 308.878 (S2) > 291.786 (S3) > 288.305 (S1) > 279.745 (G).In the context of molecular electronic properties, our findings underscore a notable variability among the studied systems.Specifically, state S2 demonstrates the most pronounced dipole moment, standing at 22.172 D. This places S2 as the most polar entity within the studied set, implying a substantial charge separation within the molecule 64 .Contrastingly, state S4 exhibits the highest polarizability, with a measure of 308.940 atomic units.This suggests a heightened response of the electron cloud to perturbations in the external electric field, indicative of a more deformable electronic distribution under the influence of an external field [65][66][67] .Remarkably, ground state G is characterized by the least values for both dipole moment and polarizability, revealing its lower polarity and relative electron cloud rigidness.This set of observations facilitates a deeper understanding of the electronic characteristics of the various states, potentially driving further investigations into their interactive behaviors and reactivity profiles.
where ΔE SYS is the total energy of the defined systems; ΔE G is the energy of the isolated graphene; ΔE F is the sum of the energies of each isolated fragment.Similarly, ΔH ads .and ΔG ads .are defined similarly.Here, the negative Figure 1.The optimized systems of the possible interaction(s) of Graphene.The atom numbering scheme of the four systems is the same as those of the Graphene (G) core structure (The optimized structures were visualized by using the GaussView 6.0.16 38 software, took a screenshot, and arranged by the word (MS) tools).
energy value implied the stable adsorbate/graphene system.By using the thermochemical data given in Table 2, the calculated energies of assumed systems (S1-S4) were presented in Table 3.It should be expressed that each system and isolated adsorbates were optimized and confirmed to predict the thermochemical data.It is clear from Table 3 that the adsorption processes are exothermic for all systems designed here, but the energy released in the S3 process is greater than in the others.Namely, the enthalpy change (in kJ/mol) for the assumed systems was calculated as S1 (−12.08)< S2 (−113.94)< S4 (−119.03)< S3 (−176.71); the presence of the cation Na + made the enthalpy change of lowered.Furthermore, the adsorption-free energy changes indicated that the adsorption processes would occur spontaneously for the designed systems S2-S4.From Table 3, the adsorption-free energies of systems S2-S4 were determined as S2 (−52.86)< S4 (−57.45)< S3 (−115.86),while the free energy changing for S1 was determined as 14.84 kJ/mol, which indicated the adsorption system could not occur spontaneously.

FMO (frontier molecular orbital) analysis.
The possible reactivity identifiers of the isolated molecules and designed systems S1-S4 were given in Table 4. Here, the chlorinated graphene surface can be said that the less likely to interact with an external system due to the smallest energy gap value (1.592 eV), and vice versa for the isolated graphene (4.018 eV).Considering the effect of the anion, cation, or salt on the graphene reactivity, the Na + cation can be said that makes the graphene more reactive to the outer system(s) with the ΔE gap value of 3.794 eV that was greater than those of the Cl -and NaCl salt.As can be expected, the Na + ion (1s 2 2s 2 2p 6 ), with the electron deficiency, made the graphene more electrophile, while the water molecule made it less electrophile.From Table 4, the electrophilicity indexes (in eV) of G and systems S1-S4 were calculated in the order of S2 (0.040) < S1 (0.117) < G (0.125) < S4 (0.175) < S3 (0.441).Also, the calculated Δε back-donat.values revealed that the water molecule made G more stable via back donation whereas the Cl -made it less stable.The order of Δε back-donat.values (in eV) for systems S1-S4 was calculated as -0.501 (S1) < −0.474 (S3) < −0.452 (S4) < −0.199 (S2).In Table 4, the calculated ionization energy and electron affinity values of H 2 O, Cl-, Na, and NaCl species were given for the prediction/direction of the possible electronic movement between the surface and each of the chemical species.Here the frontier molecular orbital densities for the isolated molecules and designed systems were visualized in Figs. 2 and 3, respectively.As can be seen, the HOMO density for the systems S2-S4 expanded       www.nature.com/scientificreports/ on the Cl -ion and which was a pictorial proof of the electronic movement from the HOMO of Cl -ions to the LUMO of graphene.
To predict the direction of possible electron, transfer between the graphene surface and the considered ions and salts, the energy ranges for each designed system were calculated using the equations below, and the results are given in Table 5.From the results obtained, it can be said that the presence of water adsorbed on the Graphene surface facilitates electron transfer from HOMO to LUMO between the surface and the related chemical species since shortened energy gap.As can be expected from past reports, it is clear from the calculated results that electronic movement from the graphene molecule (HOMO) to the water molecule (LUMO) is more likely.Namely, it was calculated as 6.462 eV and was smaller than that of the inverse scenario (6.484 eV).Without water, the energy gap for the electron movement from the chlorine ion (HOMO) to the graphene surface (LUMO) was determined as 1.154 eV, while it was calculated at 1.268 eV for the same electronic motion in the presence of water.Similarly, the energy gap values for the possible electronic movement from HOMO (Graphene) to LUMO (Na + ) were calculated as 1.405 eV (without water) > 1.279 eV (with water).On the other hand, for the electrically neutral environment (NaCl salt), it can be said that the electronic movement from the HOMO of Graphene to the LUMO of NaCl is more likely than the opposite version.The energy ranges for these two possible electronic transition scenarios were calculated as follows: ΔE 2 (3.561 eV) < ΔE 1 (4.635 eV).
Without water,

Conclusions
In this study, we attempted to evaluate the presence of water on a solid surface about how higher hydrovoltaic energy can be obtained with which charged ion.Here, the computational results indicate that hydrovoltaic nanogenerators with higher voltage output can be produced on cation-rich water-included surfaces.The adsorption-free energies of systems S2-S4 were determined as S2 (−52.86)< S4 (−57.45)< S3 (−115.86),which indicated the adsorption process could occur spontaneously.Also, the energy range values strongly implied that the charge transfer could be towards from the HOMO of the S1 to LUMO of the Na + due to the order of it as ΔE 2 (1.279 eV) < ΔE 1 (37.833eV).The results showed that the positively charged Na + ion makes the Graphenewater system have higher energy and thus it is time to be focused on the positively charged G-water systems to produce the next-generation energy.

Figure 2 .Figure 3 .
Figure 2. HOMO & LUMO (isoval:0.02)plots of the main components of the designed systems S1-S4 at B3LYP/6-311G** level in gas (The HOMO & LUMO densities were analyzed and then visualized by using the GaussView 6.0.16 38 software, took a screenshot, and arranged by the Word (MS) tools).

Table 1 .
The selected optimized parameters for the systems S1-S4 and G at B3LYP/6-311G(d,p) basis set.

Table 3 .
The calculated adsorption energies (in kJ/ mol) of the designed systems at B3LYP/6-311G(d,p) basis set.

Table 4 .
The chemical reactivity values of the systems S1-S4 and fragments at B3LYP/6-311G(d,p) basis set.

Table 5 .
The energy range values (eV) for the possible electronic movements from HOMO to LUMO for designed systems.