Orbital-Selective Photoinduced Polaron Dynamics in Na₂O₂: Ultrafast Asymmetric Charge Transport Modulation in Sodium–Air Batteries

Abstract

Understanding and controlling polaron dynamics are pivotal for improving charge transport in sodium–air batteries. Here, we employ real-time time-dependent density functional theory to investigate the ultrafast photoinduced dynamics of hole polarons (HPs) and electron polarons (EPs) in Na₂O₂ under femtosecond laser excitation. In the ground state, both polarons are highly localized and exhibit high dissociation barriers, 0.52 eV for HPs and 1.36 eV for EPs, limiting their thermally activated mobility. Upon photoexcitation, HP exhibits an increased occupation of π* antibonding orbitals, which weakens the O–O bond and drives coherent stretching oscillations. This process culminates in spontaneous, barrierless polaron dissociation with the release of mobile holes into the valence band, enabling enhanced charge delocalization and facilitating polaron hopping. In contrast, EP undergoes an additional population of σ* antibonding orbitals, further stabilizing the elongated O–O bond and increasing the dissociation barrier, thereby suppressing carrier mobility. This asymmetric photoresponse arises from an orbital-selective excitation pathway coupled to distinct bonding character at the polaron sites. These findings unveil a fundamental design principle for tuning polaronic conductivity via light and highlight the potential of optical modulation strategies for improving performance in metal–air batteries.

1. Introduction

Lithium-ion batteries (LIBs) have achieved remarkable maturity after decades of development and are now ubiquitous in consumer electronics, electric vehicles, and grid-scale energy storage systems. − Despite their widespread adoption, several intrinsic limitations continue to hinder their further advancement. First, a significant portion of the cell mass consists of electrochemically inactive materials (“dead mass”), which restricts the achievable energy density. − Second, the use of flammable and volatile organic electrolytes raises persistent safety concerns. − Third, self-discharge effects reduce the long-term operational efficiency of LIBs. , These challenges have driven increasing interest in next-generation battery chemistries that promise higher energy densities, improved safety, and enhanced durability. − Among the contenders, metal–air batteriesparticularly sodium–air (Na–air) systemshave emerged as promising candidates. −

Unlike LIBs, which rely on prestored active materials, metal–air batteries utilize ambient oxygen as a cathodic reactant, enabling significantly higher theoretical energy densities. However, practical application is limited by two key challenges: poor rechargeability and low round-trip efficiency. , These issues are largely attributed to the electrochemical instability of discharge productssuch as peroxides and superoxideswhich tend to undergo parasitic side reactions that form inactive byproducts during cycling.

Sodium–air batteries offer a distinct advantage in this regard. Owing to a more favorable single-electron transfer pathway, − they primarily form sodium superoxide (NaO₂) and sodium peroxide (Na₂O₂), both of which exhibit enhanced chemical stability and improved reversibility compared to their lithium counterparts. This intrinsic stability makes Na–air batteries more amenable to repeated charge–discharge cycles, providing a pathway toward practical, high energy density storage systems.

Despite these advantages, a critical challenge remains: the insulating nature of the discharge products, particularly Na₂O₂, which tend to accumulate on the cathode surface and inhibit electron transfer during charging. , In Na₂O₂, charge carriersboth electrons and holesdo not exhibit band-like conduction with high mobility (μ > 10 cm²/V·s) but rather localize as small polarons with extremely low mobility (μ < 0.01 cm²/V·s). − Consequently, charge transport occurs via thermally activated polaron hopping, involving site-to-site reorganization of local lattice distortions. ,− Improving the polaron conductivity is thus a key objective for enabling efficient charging in Na-air batteries. Traditional strategies include intrinsic material engineeringsuch as metal doping (e.g., Mg, Al) to reduce migration barriers − and extrinsic approaches like nanoscale heterojunction design to create more favorable hopping pathways. , In parallel, external environmental conditions can also modulate the hopping efficiency. While thermal activation can enhance hopping rates by increasing vibrational amplitudes, ,, such improvements are modest , and often impractical due to thermal management and device design constraints. ,

Recently, ultrafast laser excitation has emerged as a novel approach to controlling polaron dynamics. A theoretical study on Li₂O₂ demonstrated that coherent phonon activation via femtosecond laser pulses is predicted to enhance electron polaron (EP) mobility by up to 8 orders of magnitude. This finding offers an exciting new paradigm for light-assisted conductivity control in metal–air batteries. However, critical questions remain unresolved, including the selection of optimal photoexcitation conditions and the fundamentally distinct responses of EPs and hole polarons (HPs) to light. Addressing these questions is essential for developing targeted, highly efficient charging protocols.

To address this gap, we employ real-time time-dependent density functional theory (rt-TDDFT) to investigate the photoinduced dynamics of EPs and HPs in Na₂O₂ under ultrafast femtosecond laser pulses. In the ground state, both HPs and EPs exhibit significant dissociation barriers of 0.52 and 1.36 eV, respectively, indicating that thermal activation alone is insufficient to drive efficient polaron transport. Upon photoexcitation, a striking asymmetry emerges: for HP, the population of the π* antibonding orbital weakens the O–O bond, lowers the dissociation barrier, and promotes spontaneous polaron dissociation. This not only releases the hole into the valence band (VB) as a mobile carrier but also facilitates the subsequent hopping events, thereby enhancing conductivity. In contrast, photoexcitation of the EP populates the σ* antibonding orbital, which further elongates the already weakened O–O bond at the EP site, exacerbates lattice distortion, and raises the dissociation barrier, thereby suppressing polaron migration. Our results reveal a microscopic mechanism that connects the nature of antibonding orbital occupation (π* vs σ*) to light-induced conductivity modulation. These findings establish a fundamental principle for the orbital-selective control of polaron transport via tailored photoexcitation, offering a rational design strategy for optoelectronic tuning of sodium–air battery materials.

2. Computational Methodology

We performed rt-TDDFT simulations within the Ehrenfest (mean-field) electron–ion dynamics framework , using norm-conserving pseudopotentials and the local density approximation (LDA) , as implemented in the PWmat code. , Starting from the 12-atom hexagonal unit cell of α-Na₂O₂ (a = 6.19 Å, c = 4.46 Å), we constructed a 24-atom tetragonal supercell via a lattice transformation matrix M:

$$M=\left[\begin{array}{ccc}1& 1& 0\\ -1& 1& 0\\ 0& 0& 1\end{array}\right]$$ 1

This supercell was further expanded to a 1 × 2 × 3 supercell containing 144 atoms. A Γ-centered 2 × 2 × 2 Monkhorst–Pack k-point mesh and a plane-wave energy cutoff of 50 Ry were used. To accurately describe the localized electronic structure of the peroxide units, we adopted the LDA+U method. An electron was removed or added to the 144-atom supercell to generate the HPs and EPs, respectively, followed by structural relaxation under a range of U values. The resulting O–O bond lengths at both polaronic and nonpolaronic sites in Na₂O₂ are reported in Tables S1 (HPs) and S2 (EPs), and benchmarked against hybrid functional results obtained using HSE06. , The optimal U values were determined to be 7 eV for HP and 2 eV for EP.

For the HP system, a 500 fs ab initio molecular dynamics (AIMD) simulation with a 0.05 fs time step within the NVT ensemble was first conducted to generate thermally equilibrated nuclear structures and velocities. Subsequently, a linearly polarized laser pulse was applied to initiate an excited-state rt-TDDFT simulation in the NVE ensemble for 250 fs. The laser pulse had a photon energy of 6.0 eV (207 nm), a peak electric field of 0.67 V/Å at 10 fs, a Gaussian pulse width (σ) of 4 fs, and a total pulse duration of 20 fs. From 50 fs onward, a Boltzmann factor was applied to mimic hot carrier cooling via restoration of detailed balance. , The laser pulse parameters and excitation statistics are shown in Figure S1a. An identical protocol was employed for the EP system with the photon energy adjusted to 3.0 eV (413 nm). Corresponding laser parameters are shown in Figure S1b. In particular, the PWmat code adopts a linear time-dependent Hamiltonian scheme that enables a much larger integration step (typically 0.1–0.2 fs) than conventional rt-TDDFT methods requiring sub-attosecond resolution. In this work, both electrons and ions were propagated with a 0.05 fs time step, ensuring numerical stability and good energy conservation throughout the 250 fs trajectory.

3. Results and Discussion

3.1. Geometric and Electronic Structures of HP

The HP configuration was constructed by removing an electron from the 144-atom Na₂O₂ supercell. Upon geometry relaxation, a self-trapped HP spontaneously emerged. Side views of the relaxed geometry and the corresponding trapped hole density along the z- and x-axes are shown in Figure a,b, respectively. At the HP site, the O–O bond undergoes significant contraction to 1.25 Å, in contrast to the 1.41–1.42 Å bond lengths observed at nonpolaronic sites. The hole is highly localized around the shortened O–O bond, forming a compact polaronic state. The associated positive charge exerts a strong Coulomb repulsion on nearby Na⁺ ions, leading to pronounced lattice distortions. In particular, the three nearest Na⁺ ions (highlighted in blue) are displaced away from the HP center, increasing the nearest-neighbor Na–Na distance from ∼3.59 Å in the pristine lattice to 4.21 Å. The strong localization of the hole and the substantial local geometric distortion confirm that the employed supercell is sufficiently large to avoid spurious interactions between periodic images of the polaron.

1.

Side views of the relaxed HP structure and associated hole density along the (a) z-axis and (b) x-axis, showing pronounced localization at the HP site. The O–O bond length shortens significantly to 1.25 Å at the HP site, compared to 1.41–1.42 Å at nonpolaronic pristine sites, confirming the formation of a localized HP. This localized positive charge exerts strong Coulomb repulsion on nearby Na⁺ ions (highlighted in blue), increasing the nearest-neighbor Na–Na distance from ∼3.59 Å (pristine) to 4.21 Å. (c) Spin-resolved band structure showing a direct bandgap of 4.12 eV at the Γ point and (d) atomic-orbital-resolved PDOS of the HP configuration. (e) Orbital hybridization diagram of the peroxide anion. The red lines correspond to the spin-split states induced by localized HP, including π _x *↓@HP, π _x *↑@HP, and π _y *@HP. The trapped hole occupies the π _x *↓@HP state, which lies 0.52 eV above the Fermi level. Two dominant photoexcitation channels under 6.0 eV illumination are highlighted: (i) π* → σ* and (ii) π → π _x *↓@HP. The laser pulse parameters and the corresponding proportion of excited valence electrons are detailed in Figure S1a.

The spin-resolved band structure of the HP configuration is shown in Figure c with spin-up and spin-down components denoted by red and blue curves, respectively. In pristine Na₂O₂, the system is nonmagnetic and exhibits spin-degenerate VB and conduction band (CB) with calculated direct bandgap of 4.12 eV at the Γ point (U = 7 eV). The atomic-orbital-resolved density of states (DOS) shown in Figure d confirms this observation. The energy diagram of the binding configuration of the peroxide anion is schematically depicted in Figure e. Each O^– contributes five 2p electrons, one of which is donated by a nearby Na⁺ ion, as indicated by the dashed arrow. Therefore, the valence electrons in O₂ ^2– occupy the σ bonding, π bonding, and π* antibonding molecular orbitals, leaving the σ* antibonding orbital empty and placing the Fermi level above the filled π* band.

Upon hole trapping at a peroxide dimer, the process can be described by a redox reaction:

$${{\mathrm{O}}_2}^{2-}+{\mathrm{h}}^{+}\to {{\mathrm{O}}_2}^{-}$$ 2

According to the hole charge density (Figure a,b) and atomic-orbital resolved DOS (Figure d), the hole localizes at the highest-energy π* antibonding orbital, specifically the spin-down π _x * state. This state detaches from the VB and appears 0.52 eV above the Fermi level, denoted as π _x *↓@HP. The removal of an electron from the π* orbital reduces the antibonding character, thereby strengthening the O–O bond and resulting in a significant bond contraction to 1.25 Å. The associated local geometric distortion induces further splitting and reordering of nearby orbitals at the HP site. Notably, the π _x *↑@HP and π _y *@HP states shift in energy, as indicated by the short red lines in Figure e and highlighted in Figure d. These geometric and electronic signatures are consistent with prior theoretical studies, reinforcing the validity of the localized HP model in Na₂O₂.

3.2. Ultrafast Dynamics of HP under a Laser Field

A polaron arises when a localized charge carrier becomes strongly coupled to the surrounding lattice distortion. Consequently, any laser-induced redistribution of electronic occupation reshapes the local potential energy surface experienced by the nuclei. The subsequent excited-state evolution therefore reflects the coupled nonequilibrium dynamics of the charge–lattice composite rather than a purely electronic response. Figure shows the ultrafast dynamics of the HP in Na₂O₂ in response to photoexcitation by a femtosecond Gaussian laser pulse with a photon energy of 6.0 eV. The temporal profile of the pulse and the corresponding proportion of excited valence electrons are shown in Figure S1a. This excitation primarily activates two carrier transition pathways: (i) from the top of the π* band to the σ* band and (ii) from the top of the π band to the localized π _x *↓@HP state, as schematically depicted in Figure e. In addition to electronic excitations, the laser pulse simultaneously drives coherent lattice vibrations, resulting in a strong nonequilibrium carrier–phonon coupling that critically modulates HP dynamics.

2.

Ultrafast dynamics of HP under a laser field. (a) Energy evolution and (b) occupation dynamics of the VB/CB edges, along with the HP-localized π _x *↓@HP at the Γ point. During the laser pulse (orange shaded region, 0–20 fs), the π _x *↓@HP state becomes transiently populated, reaching an occupation of approximately 20%. Between 100 and 140 fs, this state merges with the VB, accompanied by a rapid increase in its population beyond 80%, indicating significant hole delocalization. (c) Time-evolution of the O–O bond length at the HP site and (d) Na–Na distance adjacent to the HP site. Lattice-averaged values are shown for comparison with vertical lines indicating standard deviations. The O–O bond exhibits a marked elongation to 1.57 Å at ∼30 fs, followed by pronounced coherent oscillations persisting up to ∼100 fs. Beyond this point, the oscillations diminish and the bond length relaxes toward the lattice average (∼1.42 Å) after 140 fs. The Na–Na distance adjacent to the HP site, initially increases due to Coulombic repulsion from the localized hole, gradually decreases over time and converges to the bulk average beyond 140 fs. This behavior is consistent with local charge neutralization and signifies the eventual dissociation of the HP.

Figure a,b shows the time evolution of the energy levels and occupations of the VB and CB edge states and π _x *↓@HP at the Γ point. The duration of the laser pulse is marked by the orange-shaded region. Within the first 20 fs, the pulse populates the π _x *↓@HP state with its occupation stabilizing at ∼20% around 30 fs. This transient population significantly enhances the antibonding character of the O–O bond at the HP site. Between 30 and 100 fs, the π _x *↓@HP state exhibits pronounced oscillations in both energy and occupation, while gradually approaching the VBM. In the 100–140 fs window, nonadiabatic transitions become prominent, as the π _x *↓@HP state energetically couples with the VBM and VBM–1 states. After 140 fs, the π _x *↓@HP state merges into the VB, and its occupation exceeds 80%, indicating that the hole initially localized at the HP site has been delocalized and reabsorbed into the VB as a mobile carrier.

Figure c,d shows the time evolution of the O–O bond length and the nearest-neighbor Na–Na distance at the HP site compared with their lattice-averaged values (standard deviations indicated by vertical lines). Following photoexcitation, the O–O bond undergoes rapid elongation to 1.57 Å by 30 fs, well beyond typical values, and exhibits strong stretching coherent oscillations between 1.14 Å and 1.57 Å up to 100 fs, indicative of laser-induced phonon excitation. During this period, the Na–Na distance at the HP site remains significantly longer than that at nonpolaronic sites, reflecting continued Coulombic repulsion from the localized hole. From 100 to 140 fs, the O–O bond oscillations gradually diminish. After 140 fs, the bond length progressively relaxes to the 1.39–1.49 Å rangecomparable to pristine peroxide unitssignaling structural recovery. At the same time, the Na–Na distance shortens and converges toward the averaged value, consistent with charge neutralization. These geometric features suggest the dissociation of the HP and the restoration of the pristine lattice configuration. For comparison, Figure S2 shows the nuclear dynamics in the absence of laser pulses, where the HP configuration remains stable throughout the simulation. This contrast unequivocally confirms that photoexcitation is the driving force for HP dissociation, enabling both the release of trapped holes and enhanced charge transport via polaron unbinding and migration.

Integrating the carrier and nuclei dynamics, Figure a illustrates the key stages of the photoinduced HP evolution. Within the first 30 fs, laser excitation increases the occupation of the π _x *↓@HP state while simultaneously driving coherent lattice vibrations, leading to a rapid elongation of the O–O bond to 1.57 Å. This configuration corresponds to an O–O Elongation Intermediate (OEI). By 100 fs, strong oscillations of the O–O bond continue, during which the π _x *↓@HP state shifts toward the VB edge. Between 100 and 140 fs, the trapped hole is released into the VB, coinciding with the attenuation of the vibrational amplitude and the gradual relaxation of displaced Na⁺ ions, as exemplified by the structure at 120 fs. Ultimately, after 140 fs, the HP fully dissociates and the system relaxes to the pristine Na₂O₂ configuration, as represented by the structure at 200 fs.

3.

Photoinduced dynamics and potential energy evolution of the HP. (a) Snapshots at representative time points (0, 30, 140, and 200 fs) show the key stages of photoinduced HP dynamics. At 0 fs, the HP retains its ground-state geometry. Upon photoexcitation, the population of the π _x *↓@HP state increases, leading to a significant elongation of the O–O bond to 1.57 Å at 30 fs. This transient, photoexcited configuration is denoted as the OEI. By 100 fs, the O–O bond undergoes strong coherent stretching vibrations, while surrounding Na⁺ ions are repelled due to increased Coulombic interaction. Between 100 and 140 fs, the length of the O–O bond relaxes toward the lattice average, vibrational amplitudes dampen, and the hole delocalizes into the VB, allowing Na⁺ to relax toward their equilibrium positions. This intermediate relaxation is represented by the snapshot at 120 fs. By 200 fs, the HP fully dissociates and the system recovers its pristine lattice configuration. (b) The PESs along the HP–OEI–Pristine transition pathway at 0, 30, 140, and 200 fs, where the x-axis represents a generalized configuration coordinate. The ground–state PES at 0 fs (black, aligned to the left axis) features a 0.52 eV barrier to HP dissociation (gray dashed arrow accompanied by a red cross mark indicating the inhibited process), primarily associated with the elongation of the O–O bond, which renders spontaneous dissociation energetically unfavorable. In contrast, the excited-state PES at 30 fs (pink, aligned to the right axis) significantly lowers this barrier to 0.06 eV, enabling facile bond elongation while maintaining hole localization at the π _x *↓@HP state. As the system evolves to 120 fs (blue), the HP to OEI barrier remains at 0.07 eV, and the OEI to Pristine path only has a 0.10 eV barrier between the local minimum and the pristine state. At 200 fs (green), the PESs reveal a progressive stabilization of the pristine lattice configuration, indicating spontaneous HP dissociation (solid purple arrow). This process also corresponds to the release of hole to the VB. The subsequent dynamics (dashed purple arrow) involve carrier recombination and retrapping of the hole at a different lattice site, completing a full cycle of the HP hopping event. This mechanism contributes to enhancing the electronic conductivity by generating mobile charge carriers and promoting HP hopping.

To further elucidate the energy profile along this photoinduced dynamic pathway, potential energy surfaces (PESs) were computed at 0, 30, 120, and 200 fs along the HP–OEI–Pristine structural pathway (Figure b). The horizontal axis denotes a generalized configuration coordinate that interpolates the nuclear geometries along this dynamic pathway; details of its construction are provided in the Supporting Information. On the ground-state PES (black) at 0 fs, HP dissociation requires overcoming an energy barrier of approximately 0.52 eV, mainly due to the cost of elongating the O–O bond. This barrier indicates that spontaneous dissociation is thermally inaccessible in the absence of photoexcitation. In contrast, the excited-state PES at 30 fs (pink) demonstrates a dramatic reduction in the barrier for the elongation of the O–O bond, down to just 0.06 eV, facilitated by the occupation of the π _x *↓@HP state, which weakens the O–O bond. However, at this stage, the hole remains localized, exerting strong Coulombic repulsion on the adjacent Na⁺ ions. As a result, the subsequent transition from OEI to the pristine configuration still requires surmounting an additional barrier of about 0.25 eV associated with Na⁺ repositioning. As the system evolves to 120 fs (blue), the hole becomes increasingly delocalized, weakening the lattice distortion that stabilizes the HP and OEI minima. Consequently, the HP to OEI barrier remains ∼0.07 eV, whereas the OEI to Pristine segment becomes downhill overall, with only a small barrier of ∼0.10 eV separating the shallow OEI local minimum from the fully restored pristine structure. By 200 fs (green), the PES shows that Na⁺ relaxation becomes barrierless, allowing spontaneous recovery of the pristine lattice. This evolution demonstrates that photoexcitation effectively drives HP dissociation by sequentially lowering energetic barriers along the pathway (solid purple arrow) over sub-picosecond time scales. We anticipate that, over longer time scales, electron–hole recombination may restore the system to the ground-state PES, potentially enabling HP reformation at a new site. This process constitutes a full polaron hopping event (dashed purple arrow).

The simulation shows that photoexcitation enhances hole transport in Na₂O₂ through two synergistic mechanisms: (i) promoting the release of the trapped hole into the VB as a free carrier and (ii) facilitating the spontaneous structural dissociation of the HP, thus accelerating the cycle of polaron hopping events.

3.3. Geometric and Electronic Structures of EP

Side views of the relaxed geometry and corresponding trapped electron density along the z- and x-axis are shown in Figure  a,b. The injected electron exhibits strong spatial localization, leading to a pronounced elongation of the O–O bond at the EP site to 2.36 Å, while the other O–O bonds remain unaffected at 1.48–1.49 Å. This localized negative charge exerts a significant Coulombic attraction on nearby Na⁺ ions, reducing their mutual separation to 3.18 Å, compared to the pristine Na–Na distance of 3.59 Å, as highlighted by the blue atoms in Figure a,b. These structural and electronic perturbations remain confined within a single unit cell, again verifying that the selected supercell size effectively eliminates artificial interactions between EP periodic images.

4.

Side views of the relaxed EP geometry and associated electron density along the (a) z-axis and (b) x-axis show a strongly localized excess electron at the EP site. The length of the O–O bond at the EP site is significantly elongated to 2.36 Å, compared to 1.48–1.49 Å in pristine Na₂O₂, indicating EP formation. The localized negative charge induces strong Coulomb attraction to nearby Na⁺ ions (blue spheres), resulting in a contraction of the nearest-neighbor Na–Na distance to 3.18 Å, in contrast to ∼3.59 Å in the pristine lattice. (c) Band structure of the EP configuration showing a direct band gap of 2.64 eV at the Γ point and (d) atomic-orbital-resolved PDOS of the EP configuration. (e) Orbital hybridization diagram of the peroxide anion in the EP system. The red lines correspond to the spin-split states induced by the localized EP, including σ*↑@EP, σ*↓@EP, and π _xy *@EP. Electronic structure analysis indicates that the excess electron occupies the σ*↓@EP state, while the σ*↑@EP state remains unoccupied, residing 1.13 eV above the Fermi level. Under 3 eV photoexcitation, two dominant excitation pathways are identified (yellow arrows): (i) π* → σ*, and (ii) π* → σ*↑@EP transitions. Detailed laser pulse parameters and excitation fractions are provided in Figure S1b.

The spin-resolved band structures and atomic-orbital-resolved PDOS of the relaxed EP configuration are presented in Figure  c,d, respectively. For pristine Na₂O₂, the calculated direct bandgap at the Γ point is 2.64 eV using a Hubbard U parameter of 2 eV. In contrast to the HP case (Figure c,d), the EP configuration breaks orbital degeneracy, which is expected to significantly influence both formation and relaxation dynamics of the polaron. This behavior can be rationalized from the orbital hybridization of the peroxide anion, as illustrated in Figure e. Upon electron injection, the peroxide ion undergoes reduction:

$${{\mathrm{O}}_2}^{2-}+{\mathrm{e}}^{-}\to {{\mathrm{O}}_2}^{3-}$$ 3

The excess electron localizes at the EP site, predominantly occupying the spin-down σ* antibonding orbital (σ*↓@EP), derived from O p _z orbitals. This behavior is confirmed by the real-space charge density distributions (Figure  a,b) and the PDOS (Figure  d). Occupation of the antibonding σ*↓ state weakens the O–O bond, leading to a notable elongation to 2.36 Å. This local structural distortion perturbs surrounding bonding and antibonding state manifolds, giving rise to well-defined spin-split polaronic states such as σ*↑@EP and π _xy *@EP, energetically separated from the host bands, as shown in Figure  c,e. Among these states, σ*↑@EP remains unoccupied and is located approximately 1.13 eV above the Fermi level. These structural and electronic signatures constitute the distinctive fingerprints of the EP in Na₂O₂, in agreement with prior theoretical studies.

3.4. Ultrafast Dynamics of EP under a Laser Field

Figure shows the real-time EP dynamics in Na₂O₂ under photoexcitation by the same femtosecond Gaussian laser pulse previously used for the HP with a photon energy of 3.0 eV. The detailed laser parameters and the corresponding excitation rates of the valence electrons are presented in Figure S1b. At this excitation energy, two primary electronic transitions are activated: (i) from the top of the π* VB group to the σ* CB and (ii) from the bottom of the π* VB group to the σ*↑@EP, as illustrated in Figure e.

5.

Ultrafast dynamics of EP under photoexcitation. (a) Energy evolution and (b) occupation dynamics of the VB and CB edges along with the σ*↑@EP state at the Γ point. During the laser pulse (orange shaded region, 0–20 fs), the σ*↑@EP state undergoes pronounced Rabi oscillations and transiently stabilizes within the bandgap. The occupation of this state peaks at ∼40% during excitation and subsequently stabilizes at 14–20%. In contrast, the electron-trapped σ*↓@EP state remains well separated from the bandgap and unperturbed, indicating robust electron localization throughout the simulation. (c) The evolution of the O–O bond length at the EP site and (d) Na–Na distance adjacent to the EP site. Lattice-averaged values are shown for comparison with vertical lines indicating standard deviations. The O–O bond length exhibits slight fluctuations during photoexcitation, followed by a gradual elongation to 2.49 Å by 250 fs. This behavior indicates further bond weakening without triggering coherent oscillations. The nearest Na–Na distance initially shows a transient expansion during 75–150 fs, likely driven by thermal fluctuations; however, the distances quickly recontract, highlighting the persistent Coulomb attraction by the localized electron. Overall, these results confirm that photoexcitation stabilizes the EP configuration by deepening the localization of the excess electron and elongating the O–O bond. This behavior stands in stark contrast to the dissociation dynamics observed for HP under analogous conditions.

Figure a,b shows the time evolution of electronic energy levels and occupations at the Γ point, focusing on the VB and CB edge states and the σ*↑@EP state. Within the initial 20 fs of laser irradiation (shaded in orange), carriers are rapidly excited into the σ*↑@EP state, reaching a maximum occupation of ∼40%. This transient population undergoes Rabi oscillations before stabilizing at 14–20% (Figure b), accompanied by substantial fluctuations in the energy level (Figure a). Notably, no significant nonadiabatic transitions are observed from the σ*↑@EP state, and the occupied σ*↓@EP state level does not migrate into the bandgap, suggesting that, unlike in the HP case, photoexcitation cannot delocalize or release the trapped electron.

The associated photoinduced structural response of the EP is shown in Figure c,d, which tracks the evolution of the O–O bond lengths and Na–Na distances at the EP site relative to lattice-averaged values. The O–O bond at the EP is substantially weakened, exhibiting suppressed vibrational amplitude and an absence of coherent oscillations. From the onset of photoexcitation up to ∼150 fs, the length of the O–O bond at the EP site fluctuates mildly within 2.29–2.38 Å, followed by a gradual elongation to 2.49 Å by 250 fs, significantly longer than the average bond length across the lattice. Meanwhile, the localized electron continues to attract nearby Na⁺ ions. Although the Na–Na distance transiently returns to near-average values during 75–150 fs due to its intrinsic fluctuations (as indicated by the large standard deviation in Figure d), it contracts again afterward, particularly with the Na1–Na2 pair shortening to 3.19 Å at 200 fs. These observations demonstrate that, in contrast to the HP case, the EP preserves its local lattice distortion and remains robust against photoinduced delocalization. For comparison, Figure S3 shows the nuclear dynamics in the absence of photoexcitation, where the EP configuration is also well preserved, but without the progressive O–O elongation observed under illumination.

By integrating the carrier and structural dynamics, Figure a summarizes the photoinduced evolution pathway of EP in Na₂O₂. Upon laser excitation, partial occupation of the σ*↑@EP state induces a modest O–O bond elongation but fails to trigger significant coherent oscillations or structural dissociation. The geometry at 250 fs, characterized by a 2.49 Å O–O bond length, is denoted as the OEI of the EP case. Importantly, the EP configuration cannot revert to the pristine Na₂O₂ structure during this process.

6.

Photoinduced dynamics and potential energy evolution of the EP. (a) The key stages of the photoinduced EP dynamics at 0 and 250 fs, compared with the pristine structure. Following photoexcitation, the O–O bond at the EP site gradually elongates, reaching 2.49 Å at 250 fs, while the adjacent Na⁺ ion remains strongly attracted to the localized electron. This metastable configuration is labeled OEI. Notably, no dissociation of the EP into the pristine lattice is observed throughout the simulation. (b) The PESs along the Pristine–EP–OEI structural pathway at 0, 20, and 250 fs, where the x-axis represents a generalized configuration coordinate. The 0 fs PES (black, aligned to the left axis) corresponds to the ground-state energy landscape, while the PESs at 20 fs (pink) and 250 fs (blue) represent photoexcited states (aligned to the right axis). On the ground-state PES, dissociation of the EP into the pristine lattice (gray dashed arrow accompanied by a red cross mark indicating the inhibited process) requires overcoming a substantial energy barrier of 1.36 eV, associated with O–O bond contraction and Na⁺ rearrangement. Upon photoexcitation, this barrier increases significantly to 2.35 eV at 20 fs and remains elevated at 1.93 eV at 250 fs, effectively stabilizing the EP configuration and suppressing its reversion to the pristine structure. In contrast, the energy gradient from EP toward the OEI is considerably lower, making this structural evolution energetically favorable (solid purple arrow), regardless of whether the system is in the ground or excited state. These results collectively indicate that photoexcitation reinforces EP stability by energetically penalizing dissociation while facilitating relaxation toward the OEI configuration.

To assess the energetic accessibility of different structural transformations, we computed PESs at three key time frames (0, 20, and 250 fs) along the PristineEPOEI pathway (Figure b), where the x-axis represents a generalized configuration coordinate. On the ground-state PES at 0 fs (black), the relaxation from the EP configuration to the pristine structure requires O–O bond contraction and the surrounding Na⁺ ions repositioning, involving a substantial energy barrier of approximately 1.36 eV. This barrier is significantly higher than that in the HP case, consistent with previous reports, and indicates the high thermal stability of the EP. In contrast, the PES along the EP to OEI pathway is remarkably flat, suggesting that thermal elongation of the O–O bond is energetically accessible. Upon photoexcitation, the excited-state PES at 20 fs (pink curve) remains similar in shape but exhibits further destabilization of the O–O bond due to partial occupation of the antibonding σ*↑@EP state. As a result, the energy barrier for EP → pristine transformation increases to ∼2.35 eV, about 70% higher than in the ground state. At 250 fs, the excited-state PES (blue curve) still exhibits a significant dissociation barrier of ∼1.93 eV, indicating persistent inhibition of structural relaxation to the pristine geometry.

The simulations reveal that both ground- and excited-state PESs energetically favor O–O bond elongation at the EP site (as indicated by the purple arrow in Figure b), while strongly inhibiting polaron dissociation. Notably, photoexcitation further stabilizes the localized EP state by raising its dissociation barrier, thereby suppressing EP hopping and reducing the electronic conductivity in Na₂O₂.

The fundamentally different light responses of HP and EP in Na₂O₂ highlight a promising strategy for modulating the polaronic conductivity via controlled photoexcitation. The key factor governing this response lies in the interplay between orbital-selective excitations and electronic occupancy at the polaron site. For the HP, the localized hole shortens and strengthens the O–O bond; photoexcitation promotes an electron into the corresponding antibonding orbital, weakening the bond, destabilizing the localized distortion, and restoring the lattice back toward the pristine geometry. This reduction in lattice trapping increases carrier delocalization and enhances hopping. In contrast, the EP features a trapped electron that already occupies an antibonding orbital, leading to O–O bond elongation and structural distortion. Additional excitation pushes the electron into higher antibonding states, further reinforcing the distortion and suppressing polaron dissociation. As a result, charge transport becomes less efficient. Thus, the degree of antibonding-orbital occupation emerges as the principal determinant of photoinduced polaron dynamics. These results demonstrate that photoexcitation offers an effective and controllable means of tuning carrier mobility, an effect recently corroborated by experiment. From a device-design perspective, in cathodic regions where hole transport limits performance, photoresponsive surface layers or localized femtosecond modulation could transiently release hole polarons and improve charge extraction. Conversely, in electron-transport-dominated regions, minimizing optical exposure or engineering structures that suppress antibonding-state occupation mitigate electron overlocalization. Overall, these insights provide actionable principles for implementing light-assisted conductivity control in peroxide-based electrode architectures.

4. Conclusions

We have performed rt-TDDFT simulations to elucidate the ultrafast, orbital-selective photoinduced dynamics of HPs and EPs in Na₂O₂, a key intermediate discharge product in sodium–air batteries. In the ground state, both polaron types are structurally stable with substantial dissociation barriers of 0.52 eV for HPs and 1.36 eV for EPs, respectively, confirming their highly localized nature and intrinsically low mobility. Upon femtosecond laser excitation, we reveal a pronounced asymmetry in their dynamic responses governed by the orbital selectivity of the photoexcitation. In the HP case, photoexcitation increases the occupation of π* antibonding orbitals, destabilizing both the O–O bond and localized polaron state. This triggers coherent bond-stretching oscillations and leads to barrierless polaron dissociation, releasing mobile holes into the VB and promoting polaron hopping, thereby enhancing conductivity. In contrast, excitation of the EP system populates higher σ* antibonding orbitals, which further elongate the already weakened O–O bond and raise the dissociation barrier, thereby stabilizing the localized polaron and suppressing its mobility. These results demonstrate that the occupation of antibonding orbitals (π* vs σ*) is the principal factor in photoinduced polaron evolution. By correlating local bonding environments with excitation pathways, our work provides mechanistic insight into the light-responsive behavior of polarons and establishes a framework for controlling polaronic transport in peroxide-based metal–air battery materials. This understanding offers a promising strategy for enhancing the performance in sodium–air batteries through targeted photonic modulation of charge carrier dynamics.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacsau.5c01348.

• LDA+U parameter benchmark, laser pulse parameters, nuclear dynamics in the absence of a laser pulse, and construction of potential energy profiles along the dynamic pathway (PDF)

The authors declare no competing financial interest.