Boosting Photocatalytic Water Splitting of Polymeric C60 by Reduced Dimensionality from Two-Dimensional Monolayer to One-Dimensional Chain

The recent synthesis of monolayer fullerene networks (HouL., et al. Nature2022, 606, 50735705817 ) provides new opportunities for photovoltaics and photocatalysis because of their versatile crystal structures for further tailoring of electronic, optical, and chemical function. To shed light on the structural aspects of the photocatalytic water splitting performance of fullerene nanomaterials, we compare the photocatalytic properties of individual polymeric fullerene chains and monolayer fullerene networks from first-principles calculations. We find that the photocatalytic efficiency can be further optimized by reducing the dimensionality from two-dimensional (2D) to one-dimensional (1D). The conduction band edge of the polymeric C60 chain provides an external potential for the hydrogen reduction reaction much higher than that of its monolayer counterparts over a wider range of pH values, and there are 2 times more surface active sites in the 1D chain than in the 2D networks from a thermodynamic perspective. These observations identify the 1D fullerene polymer as a more promising candidate as a photocatalyst for the hydrogen evolution reaction in comparison to monolayer fullerene networks.

][3][4][5][6][7][8][9][10][11][12][13] Recently synthesised 2D fullerene networks 14,15 hold great promise for such applications owing to the benefits of (1) a suitable band gap to generate a large amount of electron-hole pairs, (2) high carrier mobility to separate electrons and holes, and (3) appropriate band edges to thermodynamically drive the hydrogen evolution reaction with the help of photoexcited electrons, and the computational predictions based on such microscopic mechanisms 16 have been recently confirmed experimentally . 17Among the different structural phases of polymeric C 60 monolayers, the quasi-1D quasi-tetragonal phase (qTP1) and the tightly bound quasi-tetragonal phase (qTP2) have enhanced photocatalytic water splitting performance over the quasi-hexagonal phase (qHP).However, monolayer qTP2 C 60 is thermodynamically less stable than monolayer qTP1 C 60 at room temperature, while monolayer qTP1 C 60 tends to split into individual 1D chains because of its low dynamic and mechanical stability . 18erefore, it is worth investigating the electronic, optical, transport and thermodynamic properties of the 1D fullerene polymer in the context of the photocatalysis of the hydrogen evolution reaction.
9][30][31][32] Additionally, polarons and self-trapped excitons can be formed in the 1D C 60 crystals, resulting in Jahn-Teller distortion that can be described by the Su-Shriffer-Heeger model . 33,346][37][38] However, it is unclear whether 1D fullerene polymers can be assessed as a possible photocatalyst of the hydrogen evolution reaction.In particular, the physical and chemical implications of reducing the dimensionality from 2D to 1D C 60 on photocatalysis are still uninvestigated.
In this work, we investigate the band structures of the 1D C 60 chain and 2D qTP2 C 60 networks using the unscreened hybrid functional, which accurately describes the effects of reduced dimensionality.Due to the similarities in their structures, a direct comparison between 1D C 60 and 2D qTP2 C 60 polymers is possible.The excitonic and transport properties of polymeric fullerene chains are also investigated to understand whether electrons and holes can be separated effectively upon photoexcitation.Finally, the free energy barrier for the intermediates in the hydrogen evolution reaction is calculated for all possible adsorption sites, which further confirms that 1D C 60 has much higher photocatalytic efficiency owing to twice the energetically favoured adsorption sites and larger surface area compared to their monolayer counterpart.The band structure calculations using the unscreened hybrid functional give a band gap of 2.46 and 2.13 eV for 1D and 2D C 60 respectively.The larger band gap of the 1D chain can be attributed to much weakened screening effects as the dimensionality is reduced from a 2D monolayer to a 1D chain.Compared to the band gap difference of about 0.6 eV between monolayer and bulk MoS 2 , ? the relatively small band gap difference between 1D and 2D C 60 of 0.33 eV is due to their similar dielectric screening.The static dielectric function ϵ ∞ of bulk MoS 2 is more than 3.5 times larger than its monolayer counterpart, whereas the ϵ ∞ of monolayer qTP2 C 60 is approximately 1.5 times the ϵ ∞ of 1D C 60 chains (for details, see the dielectric function in the Supporting Information).[41] Another requirement for photocatalysts is that the band edges must accommodate the redox potentials involved in the water splitting reaction.The calculated band edges for both systems are shown in Fig. 2, with the vacuum levels calculated by averaging the electrostatic potential as references.1D C 60 has a valence band maximum (VBM) at -6.30 eV and a conduction band minimum (CBM) at -3.84 eV with respect to the vacuum level.Both the CBM and VBM lie at the X point in the Brillouin zone, resulting in a direct band gap.On the other hand, 2D qTP2 C 60 has an indirect band gap with the VBM at Γ and the CBM at Y. The VBM of 2D C 60 at -6.08 eV is 0.22 eV higher than that of 1D C 60 , and its CBM at -3.95 is lower than that of 1D C 60 by 0.11 eV.
The redox potentials of the relevant half reactions for pH values of 0 and 7 are also plotted in Fig. 2. The CBM of the 1D fullerene polymer is 0.60 eV above the reduction potential of the H 2 /H + half reaction at a pH of 0, and it reaches the reduction potential at a pH of 10.In monolayer qTP2 C 60 , the reduction potential of the H 2 /H + half reaction is higher than the CBM at a pH of 7.This renders both 1D and 2D C 60 polymers suitable for the photocatalysis of the hydrogen evolution reaction.However, at a pH of 8, photocatalysis is no longer activated in 2D C 60 , whereas the 1D fullerene polymer can still catalyse the reaction until pH = 10.Therefore the 1D fullerene polymer is able to function as an effective catalyst in a greater range of pH conditions than the 2D qTP2 monolayer.
The first step in photocatalysis is the photoexcitation of the catalysts to generate electronhole pairs.In this process, it is preferable that the optical absorption is strong enough to generate a large amount of electron-hole pairs, while the excitonic effects are not too strong so the electrons and holes can be separated effectively.The time-dependent Hartree-Fock calculations of excitonic effects reveal the two brightest excitons (with largest oscillator strength) near the band edges in 1D C 60 , and the electron-hole pair contributions are illustrated in Fig. 2 as circles, the radii of which reflect the contribution of a particular electron-hole pair to the brightest excitons.The two excitons have eigenenergies of 2.57 and 2.77 eV respectively, corresponding to the red and yellow circles in Fig. 2. The binding energies of the excitons are given by the difference between the independent-particle hybrid-functional eigenenergy and the exciton eigenenergy.The binding energies of the two brightest excitons are 157 and 44 meV respectively.Because the holes that contribute the most to the excitons are in much lower valence states than the VBM, carrier thermalisation always leads to the dissociation of the excitons.This process gives rise to effective electron-hole separation, and as a result, both the electrons and holes can proceed to involve themselves in their respective redox reactions.
To investigate whether the electrons and holes can transfer efficiently after the dissociation of the excitons following the carrier thermalisation, the carrier mobility of 1D and 2D C 60 is computed at different doping concentrations, as shown in Fig. 3.The carrier mobility shows similar trends with increasing concentrations for both systems, as the ionised impurity scattering becomes stronger with more dopants.However, even when the doping concentration is relatively high, i.e. at 10 −3 e/f.u.(charge per unit cell), good carrier mobility can still be obtained, which can be attributed to the delocalised π bonds formed near the band edges . 16 Adsorption sites for both systems, with the numbers from lower to higher corresponding to free energies of the intermediates from lower to higher.
There are two paths shown in Fig. 4(a) with zero and finite external potential U (in black and red respectively).The U = 0 reaction path in black corresponds to catalysis without photoexcitation.From the free energy diagram, it can be seen that without photoexcitation to provide an external potential, the production of diatomic hydrogen via the hydrogen evolution reaction described above is not spontaneous, i.e. the energy barrier posed by the intermediate is not negative as is suitable for effective catalysis.The existence of twice the energetically favourable adsorption sites in the 1D chain suggests a greater reaction rate, which renders 1D polymeric fullerene chain a promising candidate as a photocatalyst for the hydrogen evolution reaction.Additionally, the 1D chain is thermodynamically more stable than monolayer qTP2 fullerene networks , 18 indicating that the 1D fullerene polymer is a better candidate compared to the 2D qTP2 monolayer as a photocatalyst.
In conclusion, the electronic structures, excitonic effects, transport properties and thermodynamics for the hydrogen evolution reaction of 1D fullerene polymers are investigated in the context of its application as a photocatalyst compared with monolayer fullerene networks.
We find that reducing dimensionality from monolayer to chain boosts the photocatalytic per-

Methods
All calculations are performed using ab initio methods as implemented by vasp . 42,43The projector augmented wave (PAW) potential is used 44,45 with the PBEsol exchange-correlation functional under the generalised gradient approximation (GGA) . 46A plane wave cut-off of 800 eV is used with a k-mesh of 5 × 1 × 1 and 5 × 5 × 1 for 1D and 2D C 60 respectively.Both the lattice constants and internal coordinates are fully relaxed, until the energy is converged at 10 −6 eV for the self-consistent loop and the force is converged at 10 −2 eV/Å for the ge-ometry optimisation.A 1D fullerene polymer is modelled as a 3D lattice in which the b and c lattice constants are chosen to be 28 Å so that there is negligible interaction between any two 1D fullerene polymers in the 3D lattice.Similarly, for monolayer fullerene networks the c lattice constant is chosen as 24 Å.
The band structures are calculated using the unscreened hybrid functional, in which the Hartree-Fock and PBEsol exchange energies are mixed in a 1:3 ratio along with the full PBEsol correlation energy , [47][48][49] because it provides better descriptions of the measured electronic and optical band gaps [14][15][16][17] (for details, see the band gaps obtained by different levels of theory in the Supporting Information).Following this, the transport properties are calculated by utilising the hybrid-functional eigenenergies and eigenstates in a k-mesh of 10×1×1 and 8 × 8 × 1 for 1D and 2D C 60 respectively, with an interpolation factor of 100.The scat- tering rates for acoustic deformation potential and ionised impurity scattering are obtained using the amset package , 50 with the elastic tensor coefficients computed using the finite differences method 51,52 and the static dielectric constant computed using density functional perturbation theory . 53Excitonic effects are considered using the time-dependent Hartree-Fock calculations, which solve the Casida equation using the eigenenergies and wavefunction computed from the unscreened hybrid functional as inputs . 54,55A k-mesh of 10 × 1 × 1 and 8 × 8 × 1 is used for 1D and 2D C 60 respectively with the highest eight valence bands and the lowest eight conduction bands included as the basis to converge the computed exciton eigenenergies within 3 meV.
For the thermodynamics of the hydrogen evolution reaction, geometry optimisation consistently leads to the adsorption of a hydrogen atom on the top site for all symmetry irreducible carbon atoms (except those involved in the [2 + 2] cycloadditional bond that are chemically saturated).To avoid the interactions between hydrogen atoms in neighbouring cells, a supercell of 2 × 1 × 1 and 2 × 2 × 1 is used for 1D and 2D C 60 , respectively, with an electronic k-point grid of 3 × 1 × 1 and 3 × 3 × 1.All atoms undergo full relaxation, including both the lattice constants and internal atomic coordination.A significant con-tribution to the free energy of the system is the vibrational energy, and we compute the vibrational energies of both the hydrogen atom and the neighbouring carbon atoms within a radius of 2.5 Å of the adsorbed hydrogen atom.The vibration contribution to the free energy at room temperature is computed by the vaspkit package . 56The Gibbs free energy of the initial system is calculated using the energy per C 60 supercell, the energy of half a hydrogen molecule and half the vibrational energy associated with a free H 2 .Then, the total energy of the intermediate * H is calculated, with the change in vibrational energy between the adsorbate form and pure form included.
Supporting Information: Table S1.Calculated band gaps (eV) of bilayer and monolayer qHP, monolayer qTP2 and 1D C 60 using different levels of theory.

Figure 1
Figure 1 shows the crystal structures of polymeric fullerene chains and monolayer qTP2 fullerene networks.Both structures have inversion symmetry and are mirror symmetric with respect to the (100), (010) and (001) planes, with C 2 rotational symmetry along the [100], [010] and [001] axes.For 1D C 60 , each C 60 cage is connected by the in-plane [2 + 2] cycloaddition bonds along the a direction; in 2D qTP2 C 60 , the C 60 cages along a and b are linked by the vertical and in-plane [2 + 2] cycloaddition bonds respectively.Structural relaxation leads to the lattice constants a = 9.062 Å for 1D C 60 and a = 9.097 Å, b = 9.001 Å for 2D qTP2 C 60 respectively.

Figure 1 :
Figure 1: Crystal structures of 1D and 2D C 60 from the top view.

Figure 2 :
Figure 2: Band structures of 1D fullerene chain and 2D fullerene networks computed using the unscreened hybrid functional.The red and yellow circles drawn on the 1D band structures indicate the contributions of the corresponding electron-hole pairs to the two brightest excitons near the band edges.The radii of these circles represent their corresponding oscillator strength.

Figure 3 :
Figure 3: Carrier mobility of 1D and 2D C 60 at different doping concentrations.

Figure 4 :
Figure 4: (a) Gibbs free energy changes associated with the hydrogen evolution reaction in the 1D fullerene chain and 2D fullerene networks at a pH of 0 under room temperature, showing the energy barrier posed by the intermediate adsorbate and the effect of photoexcitation in creating a more favourable Gibbs energy in both the intermediates and the products.(b)Adsorption sites for both systems, with the numbers from lower to higher corresponding to free energies of the intermediates from lower to higher.
The other path of a non-zero potential U in red indicates that the photoexcited electron lowers the free energy barrier by U .With photoexcitation and the production of electronhole pairs, electrons in the conduction band can be at high enough energy for the reaction to become spontaneous.During the reaction, the photoexctied electrons combine with protons to form the reaction intermediate * H.In 1D C 60 , an external potential U = 0.60 eV is generated by the difference between the CBM and the reduction potential of the H 2 /H + half reaction, the free energy change of the intermediate becomes negative for six adsorption sites.In 2D C 60 , U = 0.49 eV upon photoexcitation, and the free energy change becomes negative for only three adsorption sites at a pH of 0 under room temperature.For the 1D polymer, the lowest energy intermediate is that for which the hydrogen atom is adsorbed on the carbon atom that is nearest to the [2 + 2] cycloaddition bonds.The energy profiles of the reaction involving each of the symmetry irreducible adsorption sites in the 1D polymer in Fig.4(a) correspond to the numbers in Fig. 4(b), with lower numbers indicating lower Gibbs free energies of the intermediates.Only two adsorption sites among eight symmetry irreducible carbon atoms are not thermodynamically favourable, as marked by 7 and 8 in light grey in Fig. 4(b).For the 2D polymer, only three adsorption sites out of seven are energetically favourable for the hydrogen evolution reaction, with two of them being the nearest neighbouring carbon atoms to the [2 + 2] cycloaddition bonds.Additionally, the remaining four sites, marked by 4 − 7 in light grey in Fig. 4(b), have much larger energy barriers of at least 0.12 eV, which are much larger than the thermal fluctuation energy k B T at room temperature (0.026 eV) and are therefore not thermally accessible.
formance of polymeric fullerene.The band structures show that the band edges of 1D C 60 accommodate the reduction potentials of the hydrogen evolution reaction over a wider range of pH conditions than 2D qTP2 C 60 .Time-dependent Hartree-Fock calculations on excitonic effects indicate effective separation of electron-hole pairs in 1D polymeric fullerene chains upon carrier thermalisation, and such separation can further be enhanced by the high carrier mobility.The calculated Gibbs free energy also demonstrates that the 1D fullerene polymer is able to function as a photocatalyst of the hydrogen evolution reaction on two times more adsorption sites than the 2D qTP2 monolayer, as photoexcitation in 1D C 60 sufficiently reduces the energy barrier posed by the reaction intermediate.Overall, 1D C 60 can be a much better photocatalyst with higher efficiency and more thermodynamic stability than monolayer C 60 .

AcknowledgementB
.P. acknowledges support from the Winton Programme for the Physics of Sustainability, and from Magdalene College Cambridge for a Nevile Research Fellowship.The calculations were performed using resources provided by the Cambridge Service for Data Driven Discovery (CSD3) operated by the University of Cambridge Research Computing Service (www.csd3.cam.ac.uk), provided by Dell EMC and Intel using Tier-2 funding from the Engineering and Physical Sciences Research Council (capital grant EP/T022159/1), and DiRAC funding from the Science and Technology Facilities Council (www.dirac.ac.uk), and by the Cambridge Tier-2 system, operated by the University of Cambridge Research Computing Service (www.hpc.cam.ac.uk) and funded by EPSRC Tier-2 capital grant EP/P020259/1, as well as with computational support from the U.K. Materials and Molecular Modelling Hub, which is partially funded by EPSRC (EP/P020194), for which access is obtained via the UKCP consortium and funded by EPSRC grant ref.EP/P022561/1.