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. 2024 Sep 18;9(39):40446–40455. doi: 10.1021/acsomega.4c02889

Molecular Dynamics Simulation Model of Alkali Metal Reduction of Gaseous Halides and Reaction Mechanism Analysis

Bin Zhang 1, Kun Yang 1,*, Danyang Liu 1, Yiwen Xiao 1, Kaining Zhang 1, Tuo Yang 1, Jianying Lu 1, Junying Wu 1, Lang Chen 1
PMCID: PMC11447739  PMID: 39371985

Abstract

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The reaction of gaseous hydrogen halides with alkali metals provides a new pathway for producing hydrogen. The structure and reactivity of alkali metals are crucial for the reduction of gaseous halides. However, traditional gas-phase reaction models fail to provide insights into the dynamic processes occurring during alkali metal reactions. In this paper, based on the reaction between Hydrogen fluoride (HF) and alkali metal sodium (Na), we have established a metallic Na slab. HF molecules were randomly inserted above the surface of the Na slab, creating a reaction model for the reduction of HF by metallic Na. The reaction of HF on the Na surface was calculated using first-principles molecular dynamics. The configuration and reaction of the Na surface and HF molecules at different times were judged by analyzing the radial distribution function and mean squared displacement. Na atoms reacted with HF to produce intermediate NaFH, and then the F–H bond broke to form NaF and H. The F–H bond breaking of intermediate NaFH was the key step, and the kinetic parameters of this key step were calculated.

1. Introduction

Electrochemical water splitting and metal-based direct hydrogen production are two promising technologies for hydrogen generation.1 However, hydrogen production by electrolysis of water has the disadvantages of high cost and scarce catalyst resources.2 The reaction of metals and water has the advantages of on-site and on-demand hydrogen production.3 However, the hydroxide or oxide produced by the reaction tends to be deposited on the metal surface, preventing the continuous process of the reaction.4 Metals can also react with small molecular gaseous hydrides to produce H, such as the reaction of the alkali metal sodium (Na) with hydrogen fluoride (HF), which can also produce H.5 Therefore, research on the reaction of Na and HF to produce H could provide a new technical approach to hydrogen production.

Polanyi et al. studied the reaction kinetics of HF and Na using a chemiluminescence depletion method and analyzed the dependence of the reaction rate on the HF vibrational excited state. The results indicated that the reaction rate increased rapidly with the increase in HF vibrational excited states.5 The researchers also investigated the influence of the rotationally excited state of HF on the reaction rate using the same experimental method. They found that the reaction rate decreased first and then increased with the increase in the rotationally excited state of the HF.6 Lee et al. used the cross-molecular beam method to make HF and Na collide with each other in a vacuum and found that the ground-state HF and Na atom did not react.7 Düren et al. detected the reaction product sodium fluoride (NaF) for the first time using a cross-molecular beam method and a more sensitive detector.8 They controlled the collision velocity of Na and HF by changing the temperature and pressure and then analyzed the relationship between the collision energy and the reaction probability. The results indicated that the reaction integral cross section was still diminutive, and the reaction probability was low, even when the reaction collision energy was high.9 Despite extensive experimental studies on the reaction probability of HF with the Na atom in different electronic states, the reaction characteristics such as the potential energy surface cannot be obtained experimentally.

In terms of theoretical calculation, Shapiro et al. obtained the potential energy surface of HF and Na atom by the semiempirical calculation method and analyzed the relationship between the height and position of the reaction barrier and the Na–F–H bond angle.10 Gargano et al. used the stereodirected representation, the preferred attack angle method, and the examination of attack angle distribution methods to calculate the relationship between the reaction probability and the relative position of the atom. They found that the reaction probability strongly depended on the collision angle between HF and Na atom when the rotationally excited state of HF was 0.11 Laganà et al. constructed the global potential energy surface of HF and Na atoms by the polynomial expansion of two-body terms and three-body terms using the ab initio calculation method. They calculated the reaction probability of HF and Na atom under different vibration-excited states.12 They also used a more accurate calculation basis set to construct a new global potential energy surface and found that there was a large bend in the transition state region of the potential energy surface and that the shape of the intermediate product was linear.13 Based on the constructed global potential energy surface, Laganà et al. analyzed the influence of the rotational excited state of HF on the reaction rate;14 the calculation results were consistent with those reported by Polanyi and Trulhar et al., who calculated the ground and several excited-state adiabatic potential surfaces of the NaFH. They found that when the Na atom reacted with HF, either in the ground state or the excited state, it would first generate a metastable complex and then dissociate into NaF and H, or HF and Na.15 Yan et al. analyzed the reaction between HF and the excited Na atom using the Chebyshev real wave packet propagation scheme. They found that for reactions producing ground-state products (NaF and H) or reactants (Na and HF), the reaction integral cross sections decreased rapidly with the increase in collision energy and finally remained stable. The whole process was dominated by the formation of NaF and H.16 Bickelhaupt et al. studied the structure and thermochemistry of the NaF monomer and (NaF)4 cubic tetramer using density functional theory. The results indicated that the Na–F bond was not only strongly polar but also had a truly ionic bonding mechanism. The bond overlap-derived stabilization contributed only little to the bond strength.17 Yu et al. investigated the reaction mechanism of HF and Na and the adsorption of HF on a NaF monomer and (NaF)4 cubic tetramer. Na interacted with HF to form a complex NaFH, and the approaching of the F atom to Na resulted in a transition state H···F···Na. Accompanied by the broken of the H–F bond, the bond formed between F and Na atoms as NaF, and then the product NaF was yielded due to the removal of the H atom. NaF could form (NaF)4 cubic tetramer. NaF and (NaF)4 further adsorbed HF to form a strong complex.18

The experimental and theoretical studies mentioned above constitute an exhaustive analysis of the reaction between a gaseous HF molecule and a Na atom from the perspective of collision rate and collision cross section. The properties of the ground state and excited electronic state were described by constructing the potential energy surface of the reaction system between the gaseous HF molecule and the Na atom. The properties of typical chemical bonds (such as the Na–F bond) during the reaction were also obtained by analyzing the structures of intermediate products and final products. However, traditional gas-phase reaction models fail to provide insights into the dynamic processes occurring during alkali metal reactions. Studying the reaction between HF and condensed sodium will inevitably involve analyzing the gas–solid interfacial interaction between gaseous HF molecules and the sodium surface. The reaction between the gas HF molecules and the crystalline Na surface could be considered as a possible means of producing hydrogen.

In this paper, the reaction model for the reduction of gaseous HF by metallic Na was established based on the reaction characteristics of solid Na and gaseous HF molecules. Subsequently, the reaction mechanism of metals Na and HF was studied. First, the metal Na slab model was established, and HF molecules were randomly inserted above the surface of the Na slab, forming the reaction model of metal Na reduction of gaseous HF. Then, the reaction of HF on the Na surface was studied by first-principles molecular dynamics. Based on the research by Yan et al.,16,19 and to accelerate the reaction for observable results within the computational time, the reaction temperatures of 300, 1000, and 2000 K were finally selected. According to the positions of each atom at various times, the types of species were determined to reveal the reaction pathways of HF and solid Na. Finally, the reaction kinetic parameters of the key step between HF and Na were calculated.

2. Computational Methods

All density functional theory simulations were performed in the Quickstep module of CP2K software.20 First, the reaction model of HF and Na was established. The reaction between HF and Na was then analyzed at 300, 1000, and 2000 K.

2.1. Verification of Basis Sets and Pseudopotential Applicability

The accuracy of the first-principles calculation depends on the exchange–correlation functional, the corresponding pseudopotentials, and the basis sets. Therefore, it is necessary to verify the applicability of the selected exchange–correlation functional and its corresponding pseudopotential and basis sets. The PADE functional in the local density approximation, the Perdew–Burke–Ernzerhof functional (PBE) in the generalized gradient approximation, the Becke–Lee–Yang–Parr functional (BLYP), the B3LYP functional, and the PBE0 functional were verified and compared.21−25 The convergence criteria of the calculation results are: the maximum geometric displacement of the adjacent two steps is less than 3.0 × 10–3 bohr; the maximum root-mean-square of the displacement is less than 1.5 × 10–3 bohr; the interatomic force is less than 4.5 × 10–4 C–1 hartree bohr; the maximum root-mean-square of the force is less than 3.0 × 10–4 hartree bohr–1; and the pressure residual is less than 100 Pa. The bond length of HF and the Ecoh of Na crystal were calculated by using different functional, basis sets, and pseudopotential. The calculated values were compared with the experimental values to verify the rationality of the selected basis set and pseudopotential. The Ecoh of Na crystal was calculated by the following equation:26

2.1. 1

where Ecoh is defined as the difference between the energy per atom in the bulk (Ebulk) and the ground-state energy per atom of a system of free atoms at rest far apart from each other (Eatom).

2.2. Calculation for the Reaction of the HF on the Na Surface

Figure 1 is a calculation model for the reaction of HF on the Na(001) surface. First, the initial Na unit cell was obtained from the Crystallography Open Database27 and relaxed at the same convergence criterion to obtain the stable structure with the lowest potential energy. The optimized Na unit cell parameters a, b, c, α, β, and γ were 4.264 4.264, and 4.264 Å, 90.000, 90.000, and 90.000°, respectively. The calculated results were consistent with the experimental parameters (4.225, 4.225, 4.225 Å, 90.000, 90.000, and 90.000°) with a maximum error of 0.91%.28 The stable structure of the Na unit cell was then enlarged 4 times along the a, b, and c directions to construct a 4 × 4 × 4 supercell using Materials Studio software.29 The Na supercell was cut to establish the (001) surface, and a 20 Å thick vacuum layer was inserted above the surface so that the parameters of the constructed box were 17.059 17.059, 32.282 Å, 90.000, 90.000, and 90.000°. The Na(001) surface had 5 atomic layers, and each layer contained 16 Na atoms. Compared with the atoms in the bulk phase, the coordination number of the surface atoms decreased, and the atomic layer spacing changed. Therefore, the constructed Na(001) surface was relaxed using the same convergence criteria as those for Na unit cell relaxation.

Figure 1.

Figure 1

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Calculation model for the reaction of HF on the Na(001) surface. (a) Scheme of the distance between the HF molecule and the Na(001) surface; (b) scheme of the position of the HF molecule on the Na(001) surface. Blue, red, and white spheres represent the Na, F, and H atoms, respectively.

Then, multiple HF molecules in the reaction mixture were optimized. A computational domain with lattice parameters a, b, c, α, β, and γ of 17.059, 17.059, 32.282, 90.000, 90.000, and 90.000° was constructed using Materials Studio software. At the horizontal plane, 13.0 Å from the bottom of the computational domain, four HF molecules were inserted to construct the HF gas molecule system. The system was first relaxed at 0 Pa to obtain the equilibrium structure with the lowest potential energy by using CP2K software. The optimized 4 HF molecule system was then placed into the vacuum layer above the Na(001) surface. Thus, the reaction model for HF on the Na(001) surface was constructed. Using the same convergence criterion, the reaction model was optimized to minimize its potential energy and form a stable structure.

Based on the canonical ensemble (NVT), the reactions of HF with Na atoms on the Na(001) surface were calculated at 300, 1000, and 2000 K, respectively. A Nosé–Hoover thermostat was used to maintain the reaction temperature in the calculation. The damping constant of the thermostat was 100 fs, the convergence accuracy of the self-consistent field was 10–6, and the calculation time step was 0.2 fs, which satisfied the convergence criterion of the self-consistent calculation and the energy conservation of the integration process. Atomic positions were recorded every 10 fs for a total calculation time of 5 ps.

The radial distribution function (RDF) is often used to study interatomic or intermolecular interactions.30 Through the change of RDF, the interaction between atoms in the reaction process of HF and Na was analyzed, and then, the formation and breakage of chemical bonds were judged. To further determine the reaction mechanism between HF and solid Na, each molecule undergoing chemical bond changes was traced to obtain a detailed reaction path.

2.3. Calculation for Reaction Kinetic Parameters

We used Gaussian 16 software to analyze further the structures of the initial reactants, intermediates, and products, whose structures came from the calculation of the reaction between HF and Na at high temperatures.31

The ωB97X-D functional and the 6-311+G** basis set were used to calculate the transition state.32,33 Additional calculations using other functionals were also carried out to verify the applicability of the ωB97X-D functional. Table 1 lists the reaction enthalpy and Gibbs free energy of the Na + HF → TS reaction at 300 K calculated using different functionals. It can be seen that the calculated result using the ωB97X-D functional was the closest to the computed value calibrated at the complete basis set (CBS) level.

Table 1. Reaction Enthalpy and Gibbs Free Energy of the Na + HF → TS Reaction at 300 K and the Imaginary Frequency of Transition State.

functional ΔHr (kJ mol–1) ΔGr (kJ mol–1) imaginary frequency
ωB97X-D 77.96 95.95 188.68i
B3LYP 78.05 96.14 134.67i
M062X 78.12 96.23 132.48i
B2PLYP 80.09 99.52 114.53i
CBS 77.06 95.49  
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The simple harmonic oscillation frequency of the transition state was also calculated to determine whether there was a unique imaginary frequency in the transition state. Based on the calculated transition state and simple harmonic vibration frequency, the zero-point energy was corrected using the Shermo program with a correction factor of 0.9710.34

The reaction rate constant was calculated using the Eyring equation35

2.3. 2

where k(T) is the reaction rate constant, kB is the Boltzmann constant, h is the Planck constant, T is the reaction temperature, ΔSr is the entropy of reaction for the transition state (TS), ΔHr is the enthalpy of reaction for TS, and R is the universal gas constant. ΔSr and ΔHr were calculated by the Shermo program.

3. Results and Discussion

3.1. Verification Results of Basis Sets and Pseudopotential

Table 2 shows the calculated bond length of the HF molecule and the cohesion energy (Ecoh) of the Na crystal using different exchange–correlation functionals and their difference with the experimental value. It can be seen that when using the PBE and B3LYP functionals, the calculated HF bond lengths were 0.9273 and 0.9280 Å, respectively. The disparities from the experimental values were 0.0105 and 0.0112 Å, which were relatively close to the experimental value. Furthermore, when the PBE functional was employed, the calculated Ecoh of −117.7 kJ mol–1 was the closest to the experimental value. Therefore, the PBE functional, the corresponding GTH-PBE pseudopotential, and the DZVP-MOLOPT-SR-GTH basis set were used to calculate the reaction between HF and solid Na.

Table 2. Calculated Bond Length of HF Molecule and Cohesion Energy (Ecoh) of Na Crystal Using Different Exchange–Correlation Functionals and Their Difference with the Experimental Valuea.

XC RH–F (Å) ΔR (Å) Ecoh (kJ mol–1) ΔE (kJ mol–1)
Pade 0.9367 0.0199 –96.4 12.6
PBE 0.9273 0.0105 –117.7 –8.7
BLYP 0.9402 0.0234 –91.8 17.2
B3LYP 0.9280 0.0112 –120.5 –11.5
PBE0 0.9358 0.0190 –121.2 –12.2
experimental value 0.9168   –109.0  
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a

RH–F represents the bond length of HF; ΔR represents the difference between the calculated value and the experimental value of HF bond length; Ecoh represents the cohesion energy of Na crystal; and ΔE represents the difference between the calculated value and the experimental value of the cohesion energy.

3.2. Reaction Process and Mechanism of HF with Solid Na

We first analyzed the reaction of HF with Na atoms on the Na(001) surface at room temperature. Figure 2 shows the radial distribution function (RDF) with the distance for the reaction system at 300 K. At 1 ps, the main peak positions of RDF were 0.95, 3.75, 4.27, 6.07, and 7.06 Å, closely resembling the initial positions of main peaks 0.92, 3.73, 4.28, 6.03, and 7.08 Å. The RDF of the reaction system at 1 ps and the initial time almost overlap, indicating that the structure of the reaction system does not change; HF does not react with solid Na at room temperature.

Figure 2.

Figure 2

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Curves of the radial distribution function with distance for the reaction system at 300 K.

However, there is still an interaction between HF and Na atoms on the Na(001) surface. Figure 3 shows the weak interactions of HF and Na atoms on the Na(001) surface, generated using Multiwfn software and the independent gradient model based on the Hirshfeld partition (IGMH) method.36,37 It could be observed that an obvious green isosurface between F atoms and Na atoms on the Na(001) surface indicated the existence of attractive interaction between them.

Figure 3.

Figure 3

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Colored isosurface of the weak interactions between HF and Na atoms on the Na(001) surface by IGMH analysis.

Figure 4 shows the snapshots at various times of the reaction system at 1000 K. At 0.08 ps, HF moved toward the Na(001) surface, and the distance between the HF molecule and Na(001) surface atoms decreased. At 0.25 ps, the HF molecule entered the Na(001) surface and reacted with the Na atom to form NaFH. Additionally, HF decomposed into F and H, while F reacted with Na and HF to form NaFHF. At 0.26 ps, NaFH decomposed into NaF and H atom. After that, NaF remained stable, and there was no further decomposition of NaFHF during the computational time. Figure 5 shows the electron density difference of the reaction system. The value of isosurfaces was set to 0.005, and two surfaces were generated, with the blue and yellow spheres representing the deprivation and accumulation of charge, respectively. When HF reacted with the Na atom, the Na atom lost electrons, and electrons were concentrated on the F atom. The Na–F bond, a typical ionic bond, was dominated by an electrostatic interaction. At the same time, some electrons were transferred to H, causing the H–F bond to break and eventually decompose to produce an H atom.

Figure 4.

Figure 4

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Snapshots at various times of the reaction system at 1000 K. Blue, red, and white spheres represent the Na, F, and H atoms, respectively. The solid gray line in the snapshot represents the periodic boundary.

Figure 5.

Figure 5

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Electron density difference of the reaction system at (a) 0.25 and (b) 0.26 ps at 1000 K. The blue and yellow spheres represent the deprivation and accumulation of charge, respectively.

Figure 6 shows snapshots at various times of the reaction system at 2000 K. At 0.05 ps, some HF decomposed into H and F atoms. At 0.14 ps, HF reacted with Na to form NaFH, and F atom reacted with Na and HF to produce NaFHF. At 0.18 ps, the F–H bond in NaFH was broken to form NaF and H atom. At 1.45 ps, the F–H bond of NaFHF was broken to form NaFH and F atom, and then F reacted with Na to form NaF. At 1.56 ps, NaFH decomposed to form NaF and H atom, which was the end of the simulation.

Figure 6.

Figure 6

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Snapshots at various times of the reaction system at 2000 K. Blue, red, and white spheres represent the Na, F, and H atoms, respectively. The solid gray line in the snapshot represents the periodic boundary.

Figure 7 shows the mean squared displacement (MSD) of the Na(001) surface at different times. At room temperature, MSD increased slowly with time to 0.25 Å and then remained stable. At 1000 K, the MSD experienced a rapid increase, reaching 0.7 Å within 0.3 ps at a rate of 2.3 Å ps–1, followed by a gradual increase at a rate of 0.54 Å ps–1. At 2000 K, MSD underwent a swift ascent to 2.3 Å at a rate of 4.2 Å ps–1 within 0.54 ps, subsequently increasing at a rate of 1.4 Å ps–1. Obviously, the MSD at high temperatures was significantly greater than that at room temperature, indicating a substantial change in the Na(001) structure under elevated temperatures. The higher the temperature, the more significant the rate of MSD variation, reflecting a more pronounced and drastic transformation in the Na(001) structure. Combining the snapshots from Figures 4 and 6, it could be observed that at room temperature, the HF molecule remained stable on the Na(001) surface and did not react with the Na atom. As the temperature increased to 1000 K, Na atom on the Na(001) surface gradually became disordered but did not escape from the surface. HF molecule diffused to the surface layer and formed NaFH with Na atom (which subsequently decomposed to generate the final products NaF and H). At 2000 K, Na atom gradually escaped from the Na(001) surface, and the HF molecule reacted quickly with the escaped Na atom.

Figure 7.

Figure 7

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Mean squared displacement (MSD) of the Na(001) surface at different times.

Figure 8 shows a radial distribution function (RDF) with distance for Na–Na, Na–F, and F–H at 1000 and 2000 K. At 1000 K (Figure 8(a)), the main peak positions of Na–Na and F–H at 0.25 ps were the same as the initial time, and Na–F has a sharp peak at 1.48 Å. At 2 ps, the main peak position of Na–Na moved to 3.23 Å, indicating that the distance between Na atoms changed significantly. The main peak position of F–H increased from 1.05 Å at the initial moment to 1.25 Å, which was due to the obvious elongation of the F–H bond length during the entire simulation period. For Na–F, the main peak moved to 1.79 Å. At 2000 K (Figure 8(b)), and the main peak position of Na–Na at 0.14 ps moved from 3.75 Å at the initial moment to 3.41 Å. The main peak position of F–H was 1.04 Å, which was the same as the initial moment. The main peak of Na–F appeared at 1.67 Å. At 1.56 ps, and the main peak position of Na–Na moved to 2.91 Å. The significant change in the RDF peak position indicated that the distance between Na atoms changed significantly. This change was attributed to the increase in the motion speed of Na atoms caused by a high temperature. Due to the accelerated motion, the Na(001) surface underwent obvious changes. The main peak position of F–H finally moved to 1.36 Å, which may be caused by the complete breakage of the F–H bond after the reaction of HF and Na. The position of the main peak of Na–F was the same as that at 0.14 ps, indicating that Na–F remained stable during the simulation time. The above results indicated that the arrangement of Na atoms gradually became disordered at 1000 K. HF reacted with Na atom on the Na(001) surface, forming a Na–F bond. As the reaction progressed, the H–F bond eventually broke, while the Na–F bond remained stable. At 2000 K, the motion of the Na atom became more violent. According to the snapshots in Figure 6, it could be observed that the Na atom gradually escaped from the Na(001) surface and then reacted with HF to form Na–F. Subsequently, the F–H bond gradually stretched until it was completely broken. Therefore, combining the snapshots from Figures 4 and 6, the reaction between Na atoms and HF could be illustrated as

3.2. S1
3.2. S2
3.2. S3
3.2. S4
3.2. S5

where the double dagger designates the intermediate.

Figure 8.

Figure 8

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Curves of radial distribution function with distances for Na–Na, Na–F, and F–H. (a) Curves of radial distribution function with distance at 1000 K; (b) curves of radial distribution function with distance at 2000 K. The dashed line represents the main peak position, and the orange arrow indicates the movement direction of the main peak at different times.

The calculated results showed that the final products for the reaction between HF and Na atom were NaF and H, and the intermediate species included NaFH and NaFHF. To further elucidate the mechanism of the reaction between HF and Na atom, we investigated the reaction pathway and calculated the Gibbs free energy of the reaction (ΔGr) of each step. Figure 9 presents the schematic diagram of reaction pathways and Gibbs free energy (ΔGr) for the reaction at 2000 K. The calculation of ΔGr was based on the energies of the escaped Na atom and HF, whose stoichiometric coefficient was 2, respectively. It can be seen that the reaction of HF and Na involved two different pathways. The first reaction pathway comprised HF combining with Na to generate NaFH, and ΔGr was 237.2 kJ mol–1. The F–H bond in NaFH was then broken to produce the transition state (TS), whose ΔGr was 165.3 kJ mol–1. Finally, the H atom gradually moved away to generate the final products NaF and H, and ΔGr decreased by 295.0 kJ mol–1.

Figure 9.

Figure 9

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Schematic diagram of reaction pathways and Gibbs free energy (ΔGr) for the reaction between HF and Na at 2000 K. ΔGr was based on the energies of Na and HF, whose stoichiometric coefficients were 2, respectively.

The second reaction pathway involved the decomposition of HF to produce free F, which reacted with another HF molecule and Na atom to form NaFHF, with a ΔGr of 220.8 kJ mol–1. The F–H bond of NaFHF was then broken to generate NaFH and F. The F atom continued to react with the Na atom to generate NaF. The F–H bond in NaFH was broken to produce the TS, which eventually generated NaF and H. Obviously, the same TS stage was experienced in both reaction pathways. The F–H bond of NaFH was broken in this step, which was an endothermic reaction. Therefore, F–H bond cleavage in NaFH (Stage S5) was the key step in forming the final products.

Then, we further analyzed the thermodynamic parameters at different temperatures for the overall reaction process and the key reaction steps, which are shown in Figure 10. From Figure 10(a,b), it could be observed that for the overall reaction Na+HF → NaF+H, the enthalpy of reaction (ΔHr) increased with rising temperature, whereas ΔGr decreased with temperature. This indicated that the increase in temperature was beneficial to the reaction. Figure 10(c) demonstrates that the entropy of the reaction (ΔSr) was consistently positive at different temperatures, indicating that the reaction was an entropy-increasing process, and as the temperature increased, ΔSr became larger. In the case of Na + HF → TS, which represented the key step of the reaction, ΔHr decreased with the temperature while ΔGr increased linearly with the temperature. ΔSr was negative at different temperatures, indicating that this process was entropy-decreasing. In conclusion, these findings suggested that higher temperatures promote the overall reaction Na + HF → NaF + H, leading to increased ΔHr and a decrease in ΔGr. Moreover, the reaction was characterized by an entropy-increasing process. As for the key step of the reaction, Na + HF → TS, demonstrating a decrease in ΔHr with temperature and an increase in ΔGr while exhibiting an entropy-decreasing behavior.

Figure 10.

Figure 10

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Thermodynamic parameter for the reaction between HF and Na. (a) Enthalpy of reaction (ΔHr) of TS and products at various temperatures; (b) Gibbs free energy of reaction (ΔGr) of TS and products at various temperatures; and (c) entropy of reaction (ΔSr) of TS and products at various temperatures.

3.3. Reaction Kinetic Parameters

We further calculated the kinetic parameters for the reaction between HF and Na. The reaction rate constants are listed in Figure 11(a). The reaction rate constant at 300 K was almost 0. In the temperature range of 300–1000 K, the reaction rate constant increased slowly with temperature and reached 1.17 × 106 s–1 at 1000 K. In the temperature range 1000–1500 K, the reaction rate constant increased gradually, then increased rapidly with the temperature above 1500 K, reaching 2.31 × 108 s–1 at 2000 K. The quantum tunneling effect may have an impact on the kinetics of the reaction.38,39 When the temperature was lower than 940 K, the threshold energy of the reaction was larger than the barrier height, which means that the tunneling effect was inefficient.16 This may be because the F atom to be exchanged was relatively heavy. Meanwhile, the reaction rate was very small at 940 K, and no reaction products were detected experimentally at this temperature.16 Therefore, at lower temperatures, it was believed that HF and Na hardly react. However, the reaction rates of HF and Na increased rapidly as the temperature increased. The reaction rate constants at different temperatures were fitted using linear relations, as shown in Figure 11(b). Based on the slope of the fitted straight line and the Arrhenius law, the activation energy and pre-exponential factor were 83.16 kJ mol–1 and 2.88 × 1010 s–1, respectively.

Figure 11.

Figure 11

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Kinetic parameters for the reaction between HF and Na. (a) Reaction rate constant at various temperatures; (b) logarithm of the reaction rate constant (ln(k)) against inverse temperature (1/T).

4. Conclusions

This paper overcame the problem that the gaseous reaction model cannot describe the structural changes when alkali metals reacted at high temperatures, established the reaction model for the reduction of HF by metallic Na, and realized a first-principles molecular dynamics calculation of the reduction of HF by metallic Na. The reaction mechanism between HF and solid Na was determined by tracking the molecules with chemical bonds that changed. At different temperatures, the surface of metallic Na changed in different forms. At lower temperatures, the atomic arrangement on the Na(001) surface gradually became disordered; HF entered the Na(001) surface and reacted with Na atom. As the temperature increased, Na atoms escaped from the surface and then reacted with HF. The reaction paths of Na and HF were the same at different temperatures. The cleavage of the F–H bond in the intermediate product NaFH was the key step in the reaction, and the kinetic parameters were calculated. The reaction mechanism of HF and solid Na elucidated in this article provides a theoretical basis for the study of hydrogen production by the reaction between HF and Na.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (grant No. 11832006) and the China Postdoctoral Science Foundation (grant No. 2024M754097).

The authors declare no competing financial interest.

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