Elucidating the Influence of Electric Fields toward CO2 Activation on YSZ (111)

Despite its high thermodynamic stability, the presence of a negative electric field is known to facilitate the activation of CO2 through electrostatic effects. To utilize electric fields for a reverse water gas shift reaction, it is critical to elucidate the role of an electric field on a catalyst surface toward activating a CO2 molecule. We conduct a first-principles study to gain an atomic and electronic description of adsorbed CO2 on YSZ (111) surfaces when external electric fields of +1 V/Å, 0 V/Å, and −1 V/Å are applied. We find that the application of an external electric field generally destabilizes oxide bonds, where the direction of the field affects the location of the most favorable oxygen vacancy. The direction of the field also drastically impacts how CO2 adsorbs on the surface. CO2 is bound by physisorption when a +1 V/Å field is applied, a similar interaction as to how it is adsorbed in the absence of a field. This interaction changes to chemisorption when the surface is exposed to a −1 V/Å field value, resulting in the formation of a CO3− complex. The strong interaction is reflected through a direct charge transfer and an orbital splitting within the Olatticep-states. While CO2 remains physisorbed when a +1 V/Å field value is applied, our total density of states analysis indicates that a positive field pulls the charge away from the adsorbate, resulting in a shift of its bonding and antibonding peaks to higher energies, allowing a stronger interaction with YSZ (111). Ultimately, the effect of an electric field toward CO2 adsorption is not negligible, and there is potential in utilizing electric fields to favor the thermodynamics of CO2 reduction on heterogeneous catalysts.


Introduction
Global energy demand has rapidly increased over the past decades due to the increase in world population and rapid economic development of developing countries [1,2]. It is expected that this increasing trend in the world energy demand will continue in the foreseeable future. In order to meet this energy demand, the consumption of fossil fuels has dramatically increased and is predicted to continuously increase as well [3]. Because fossil fuels produce large quantities of CO 2 when burned, their large consumption has negatively impacted our environments (e.g., global warming due to CO 2 accumulation in the atmosphere) [4,5]. Among various alternative and renewable energy technologies, hydrogen-based technologies are considered as one of the most promising strategies to replace conventional fossil fuel-based energy technologies because it only produces H 2 O byproducts when it combusts [6,7]. However, the majority of hydrogen is currently 2 of 13 produced via steam methane reforming (SMR). Thus, current hydrogen production is still bounded to non-renewable sources and generates a large amount of CO 2 emissions (e.g., 380-420 kg CO 2 /Nm 3 H 2 ) [8]. Biogas is considered a viable renewable source to produce hydrogen, as described in Figure 1. To produce green hydrogen from biogas at an economically feasible price (e.g., DOE target of US $4/kg of H 2 ), the raw biogas needs to be reformed without the CO 2 gas separation step. One of the technical challenges with reforming the raw biogas is its high tendency for coke formation, which eventually deactivates the catalyst [9]. In order to mitigate this coking issue, one can increase the steam-to-carbon (S/C) ratio for the raw biogas reforming process [8,9]. However, this high (S/C) operation increases the overall operating energy consumption requirement and cost to produce the hydrogen gas. Thus, it is highly desired to find new reforming technologies that can process raw biogas without using a large amount of steam and at a lower operating reaction temperature. H2O byproducts when it combusts [6,7]. However, the majority of hydrogen is currently produced via steam methane reforming (SMR). Thus, current hydrogen production is still bounded to non-renewable sources and generates a large amount of CO2 emissions (e.g., ~380-420 / ) [8].
Biogas is considered a viable renewable source to produce hydrogen, as described in Figure 1. To produce green hydrogen from biogas at an economically feasible price (e.g., DOE target of US $4/kg of H2), the raw biogas needs to be reformed without the CO2 gas separation step. One of the technical challenges with reforming the raw biogas is its high tendency for coke formation, which eventually deactivates the catalyst [9]. In order to mitigate this coking issue, one can increase the steam-to-carbon (S/C) ratio for the raw biogas reforming process [8,9]. However, this high (S/C) operation increases the overall operating energy consumption requirement and cost to produce the hydrogen gas. Thus, it is highly desired to find new reforming technologies that can process raw biogas without using a large amount of steam and at a lower operating reaction temperature. Recently, electric-field-assisted fuel reforming has been investigated in an attempt to prevent coking and to reduce the reaction temperature for the conventional steam methane reforming reaction [10][11][12]. By applying an external electric field, it is possible to manipulate both the thermodynamic (e.g., equilibrium constant) and kinetic (e.g., molecular orientation and electronic interaction between the reactive species and the catalyst) aspects of the steam methane reforming reaction [11]. For example, when a positive electric field is applied to the Ni catalyst surface during the steam methane reforming reaction, one can increase the adsorption rate of water molecules over the catalyst surface by aligning its dipole moment with the orientation of the external electric field that is applied [10,13]. As the local concentration of water molecules at the catalyst surface increases with the electric field strength, the formation of coke can be significantly mitigated even at the low S/C ratio of 2 [10]. Furthermore, methane conversion increases when the positive electric field is applied over the Ni catalytic surface by affecting the energetics of its key intermediates to influence its reaction pathways [11,12].
In addition to influencing the CH4 and H2O chemistries during the raw biogas steam reforming process under the surface electric field condition, one also needs to efficiently convert CO2 into CO so that they can be further converted to valuable chemicals and fuels. Various pathways exist for the reduction of CO2 to CO. The redox-mechanism, where the reduction of CO2 and oxidation of the catalyst occurs simultaneously, has been proposed Recently, electric-field-assisted fuel reforming has been investigated in an attempt to prevent coking and to reduce the reaction temperature for the conventional steam methane reforming reaction [10][11][12]. By applying an external electric field, it is possible to manipulate both the thermodynamic (e.g., equilibrium constant) and kinetic (e.g., molecular orientation and electronic interaction between the reactive species and the catalyst) aspects of the steam methane reforming reaction [11]. For example, when a positive electric field is applied to the Ni catalyst surface during the steam methane reforming reaction, one can increase the adsorption rate of water molecules over the catalyst surface by aligning its dipole moment with the orientation of the external electric field that is applied [10,13]. As the local concentration of water molecules at the catalyst surface increases with the electric field strength, the formation of coke can be significantly mitigated even at the low S/C ratio of 2 [10]. Furthermore, methane conversion increases when the positive electric field is applied over the Ni catalytic surface by affecting the energetics of its key intermediates to influence its reaction pathways [11,12].
In addition to influencing the CH 4 and H 2 O chemistries during the raw biogas steam reforming process under the surface electric field condition, one also needs to efficiently convert CO 2 into CO so that they can be further converted to valuable chemicals and fuels. Various pathways exist for the reduction of CO 2 to CO. The redox-mechanism, where the reduction of CO 2 and oxidation of the catalyst occurs simultaneously, has been proposed for various catalysts [14,15]. Other well-known pathways are categorized as the association mechanism, where CO 2 adsorbs on the catalyst and reacts with protons to form  [16,17]. Either routes can occur on reducible oxides [18][19][20]. Regardless of the mechanism, however, the activation of CO 2 is consistently an energetically costly step, as it requires the transfer of an electron to the CO 2 adsorbate, forming a radical anion [21].
Recent work by Xiao et al. [22] has shown how the oxidation state of Cu influences the adsorption strength of CO. Furthermore, since water has a permanent dipole moment that either aligns or anti-aligns with the electric field vector (resulting in an increased or decreased adsorption strength, respectively) [13], we co-adsorbed water in the vicinity of a CO 2 molecule to see if one can find a similar enhancement effect of the electric field with regard to the adsorption of CO 2 . This would facilitate its dissociative adsorption into CO and O adspecies as suggested by Xiao et al. [22]. Unfortunately, our preliminary work shown in Figure 2 demonstrates that electric field effects were negligible toward CO 2 adsorption on Ni (111), as its adsorption energy remained weak between −0.16 eV and −0.04 eV. The adsorption of CO 2 is typically enhanced in the presence of active O, which can be provided by oxide-supported catalysts [16,20,23]. However, despite the high selectivity (90-99%) for CO 2 reduction, most conversion rates for the reversed water gas shift reaction are limited to below 20% over oxide-supported catalysts [16]. The potential for enhancing CO 2 activation using electric fields has been explored by Oshima et al. [24]. Further, recent field emission studies by Lambeets et al., where a high electric field is applied at the apex of a field Rh emitter tip, have also shown evidence of CO 2 activation [25]. This shows that even though CO 2 is a very stable molecule with no permanent dipole moment, it can be polarized under the applied electric field [26]. However, a theoretical study specifically investigating changes upon the catalyst's electronic structure induced by the electric field has not been done yet. for various catalysts [14,15]. Other well-known pathways are categorized as the association mechanism, where CO2 adsorbs on the catalyst and reacts with protons to form intermediate species such as formate, carboxyl, carbonate, and bicarbonate [16,17]. Either routes can occur on reducible oxides [18][19][20]. Regardless of the mechanism, however, the activation of CO2 is consistently an energetically costly step, as it requires the transfer of an electron to the CO2 adsorbate, forming a radical anion [21]. Recent work by Xiao et al. [22] has shown how the oxidation state of Cu influences the adsorption strength of CO. Furthermore, since water has a permanent dipole moment that either aligns or anti-aligns with the electric field vector (resulting in an increased or decreased adsorption strength, respectively) [13], we co-adsorbed water in the vicinity of a CO2 molecule to see if one can find a similar enhancement effect of the electric field with regard to the adsorption of CO2. This would facilitate its dissociative adsorption into CO and O adspecies as suggested by Xiao et al. [22]. Unfortunately, our preliminary work shown in Figure 2 demonstrates that electric field effects were negligible toward CO2 adsorption on Ni (111), as its adsorption energy remained weak between −0.16 eV and −0.04 eV. The adsorption of CO2 is typically enhanced in the presence of active O, which can be provided by oxide-supported catalysts [16,20,23]. However, despite the high selectivity (90-99%) for CO2 reduction, most conversion rates for the reversed water gas shift reaction are limited to below 20% over oxide-supported catalysts [16]. The potential for enhancing CO2 activation using electric fields has been explored by Oshima et al. [24]. Further, recent field emission studies by Lambeets et al., where a high electric field is applied at the apex of a field Rh emitter tip, have also shown evidence of CO2 activation [25]. This shows that even though CO2 is a very stable molecule with no permanent dipole moment, it can be polarized under the applied electric field [26]. However, a theoretical study specifically investigating changes upon the catalyst's electronic structure induced by the electric field has not been done yet. The first step in overcoming the energetic costs of CO2 reduction on heterogeneous catalysts is the activation of CO2. In this study, we investigated the effect of applying an electric-field over YSZ (111) on CO2 adsorption using density functional theory (DFT)based calculations. Ultimately, by understanding how both the thermodynamics and kinetics of CO2 reduction chemistry are influenced by the surface electric field and combining this knowledge with existing knowledge on the applied field effect over CH4 steam The first step in overcoming the energetic costs of CO 2 reduction on heterogeneous catalysts is the activation of CO 2 . In this study, we investigated the effect of applying an electric-field over YSZ (111) on CO 2 adsorption using density functional theory (DFT)-based calculations. Ultimately, by understanding how both the thermodynamics and kinetics of CO 2 reduction chemistry are influenced by the surface electric field and combining this knowledge with existing knowledge on the applied field effect over CH 4 steam reforming chemistry, we can develop an economically feasible surface electric-field-assisted raw biogas reforming technology that could operate at a lower temperature and S/C ratio than the conventional raw biogas reforming technology.

Field-Assisted Oxygen Vacancy Formation on YSZ (111)
An electric field induces charge polarization within the system, which in turn affects the chemical properties of the surface. On the clean YSZ (111) surface, a negative electric field induces charge accumulation toward the surface, while the opposite effect occurs when a positive electric field is applied. We probed the surface reducibility through a water formation reaction, as detailed in the Methods section. The presence of an external electric field was found to decrease the vacancy formation energy values, as compared to when the electric field was absent, by 0.3 and 0.5 eV when we applied a field value of −1 V/Å and +1 V/Å, respectively. This indicates that regardless of the field direction, its presence destabilizes the surface ions. Interestingly, the most favorable oxygen vacancy forms in the O terminal site in the absence of field and in the presence of a −1 V/Å field value, but forms on the O sublattice site for the +1 V/Å field case, as shown in Figure 3. reforming chemistry, we can develop an economically feasible surface electric-field-assisted raw biogas reforming technology that could operate at a lower temperature and S/C ratio than the conventional raw biogas reforming technology.

Field-Assisted Oxygen Vacancy Formation on YSZ (111)
An electric field induces charge polarization within the system, which in turn affects the chemical properties of the surface. On the clean YSZ (111) surface, a negative electric field induces charge accumulation toward the surface, while the opposite effect occurs when a positive electric field is applied. We probed the surface reducibility through a water formation reaction, as detailed in the Methods section. The presence of an external electric field was found to decrease the vacancy formation energy values, as compared to when the electric field was absent, by 0.3 and 0.5 eV when we applied a field value of −1 V/Å and +1 V/Å, respectively. This indicates that regardless of the field direction, its presence destabilizes the surface ions. Interestingly, the most favorable oxygen vacancy forms in the Oterminal site in the absence of field and in the presence of a −1 V/Å field value, but forms on the Osublattice site for the +1 V/Å field case, as shown in Figure 3. To aid our understanding on the effects of field direction toward the reducibility of YSZ (111), we investigated electronic structure analysis through a partial density of states (PDOS) analysis of the underlying 2 oxygen anions (Oterminal and Osublattice) and the Y-cation that lies in between these two anions, as shown in Figure 4. The PDOS of the Y-cation dstate produces a shallow broad peak between −5 eV and the Fermi level ( Figure 4a) with similar fillings of 0.94, 0.98, and 1.22 for the 0 V/Å, +1 V/Å, and −1 V/Å cases, respectively (Table 1). Our Bader charge analysis shown in Table 2 corroborates this calculation, as the partial charge of the Y-cation remains the same for all three cases at ~2.20 electrons, indicating that the oxidation state of the cation is unchanged in the presence of an external field. As compared to when the electric field is absent, an applied field of +1 V/Å smears the bonding d-states (Figure 4a.2), while a negative field value of −1 V/Å shifts both the bonding and the antibonding d-states to slightly lower energy values (Figure 4a.3). We additionally see an increase of antibonding states for the −1 V/Å case, where the U/Nd ratio increases from 0.74 to 0.76 as compared to when the field is absent (see Table 1). We thus hypothesize that the presence of the electric field causes intra-atomic transitions within the Y-cation d-states, which is a common finding for partially filled d-bands [27]. To aid our understanding on the effects of field direction toward the reducibility of YSZ (111), we investigated electronic structure analysis through a partial density of states (PDOS) analysis of the underlying 2 oxygen anions (O terminal and O sublattice ) and the Ycation that lies in between these two anions, as shown in Figure 4. The PDOS of the Y-cation d-state produces a shallow broad peak between −5 eV and the Fermi level ( Figure 4a) with similar fillings of 0.94, 0.98, and 1.22 for the 0 V/Å, +1 V/Å, and −1 V/Å cases, respectively (Table 1). Our Bader charge analysis shown in Table 2 corroborates this calculation, as the partial charge of the Y-cation remains the same for all three cases at~2.20 electrons, indicating that the oxidation state of the cation is unchanged in the presence of an external field. As compared to when the electric field is absent, an applied field of +1 V/Å smears the bonding d-states (Figure 4a.2), while a negative field value of −1 V/Å shifts both the bonding and the antibonding d-states to slightly lower energy values (Figure 4a.3). We additionally see an increase of antibonding states for the −1 V/Å case, where the U/N d ratio increases from 0.74 to 0.76 as compared to when the field is absent (see Table 1). We thus hypothesize that the presence of the electric field causes intra-atomic transitions within the Y-cation d-states, which is a common finding for partially filled d-bands [27].     Table 3 indicate that the +1 V/Å and −1 V/Å field values induce a higher occupancy of the bonding states. We hypothesize that one of the ways the +1 V/Å field value enhances the surface reducibility is by rearranging the p-states to higher energies. The highest-energy state at −0.5 eV intensifies when a field value of +1 V/Å is applied, resulting in weaker bounded states and a lower gap between the occupied and the non-occupied states ( Figure  4b.2). We qualitatively could see the same effects with regard to Oterminal when a field value of +1 V/Å is applied. We hypothesize that the Osublattice site is more easily reducible than Oterminal under the +1 V/Å field due to a charge accumulation at the Osublattice site (5.24 vs. 3.28 electrons/vol in Table 3), destabilizing the O-anion. When a field value of −1 V/Å is applied, we can see a general shift of the O-anion p-states to lower energies, similar to the Y-cation d-states (Figure 4b Table 3 indicate that the +1 V/Å and −1 V/Å field values induce a higher occupancy of the bonding states. We hypothesize that one of the ways the +1 V/Å field value enhances the surface reducibility is by rearranging the p-states to higher energies. The highest-energy state at −0.5 eV intensifies when a field value of +1 V/Å is applied, resulting in weaker bounded states and a lower gap between the occupied and the nonoccupied states (Figure 4b.2). We qualitatively could see the same effects with regard to O terminal when a field value of +1 V/Å is applied. We hypothesize that the O sublattice site is more easily reducible than O terminal under the +1 V/Å field due to a charge accumulation at the O sublattice site (5.24 vs. 3.28 electrons/vol in Table 3), destabilizing the O-anion. When a field value of −1 V/Å is applied, we can see a general shift of the O-anion p-states to lower energies, similar to the Y-cation d-states (Figure 4b.3,c.3). While O terminal remains the most reducible O-anion when a field value of −1 V/Å is applied, its higher-intensity peak at −2 eV shown in Figure 4b.2 weakens the binding of the O-anion with respect to the case when the field is absent. In summary, the presence of an external electric field results in a rearrangement of the bonding states and affects the total number of available states at the ionic sites as well. As a result, the reducibility of YSZ (111) increases in the presence of an electric field, where a positive field value destabilizes the surface O-anions most strongly.

Elucidating the Influence of an Electric Field toward CO 2 Activation on YSZ (111)
We tested 10 distinct sites for the adsorption of CO 2 as detailed in the Methods section. Generally, CO 2 bonded more strongly in a Y-cation site, as seen in the Supplementary Materials Figures S1-S3. The adsorption energies of CO 2 in the absence of an electric field were weak, the strongest being −0.21 eV at Site B2 as depicted in the Supplementary Materials Figure S1. The most favorable adsorption configuration is presented again in Figure 5, where the binding is correlated with a differential charge visualization. All evidence points that in the absence of an electric field, no direct charge transfer occurs between CO 2 and the Y-cation. As seen by the charge distribution of the CO 2 molecule and the 3 Å bond length to the YSZ (111) surface, the bonding predominantly comes from a weak dipole-dipole interaction with CO 2 . The larger ionic radius of the Y-dopant is hypothesized to induce strain and weaken electronic binding within the surface, making the vicinity of the dopant more strongly bonded to the CO 2 reactant.  In summary, the presence of an external electric field results in a rearrangement of the bonding states and affects the total number of available states at the ionic sites as well. As a result, the reducibility of YSZ (111) increases in the presence of an electric field, where a positive field value destabilizes the surface O-anions most strongly.

Elucidating the Influence of an Electric Field toward CO2 Activation on YSZ (111)
We tested 10 distinct sites for the adsorption of CO2 as detailed in the Methods section. Generally, CO2 bonded more strongly in a Y-cation site, as seen in the Supplementary Materials Figures S1-S3. The adsorption energies of CO2 in the absence of an electric field were weak, the strongest being −0.21 eV at Site B2 as depicted in the Supplementary Materials Figure S1. The most favorable adsorption configuration is presented again in Figure  5, where the binding is correlated with a differential charge visualization. All evidence points that in the absence of an electric field, no direct charge transfer occurs between CO2 and the Y-cation. As seen by the charge distribution of the CO2 molecule and the 3 Å bond length to the YSZ (111) surface, the bonding predominantly comes from a weak dipoledipole interaction with CO2. The larger ionic radius of the Y-dopant is hypothesized to induce strain and weaken electronic binding within the surface, making the vicinity of the dopant more strongly bonded to the CO2 reactant. The orientation of the electric field evidently plays a crucial role toward the capability of the YSZ (111) surface to activate CO2. We find that the binding configuration of CO2 drastically changes when an external electric field of −1 V/Å is applied, where its well- The orientation of the electric field evidently plays a crucial role toward the capability of the YSZ (111) surface to activate CO 2 . We find that the binding configuration of CO 2 drastically changes when an external electric field of −1 V/Å is applied, where its wellknown linear shape changes to a trigonal planar configuration with a bending angle of~128 • ( Figure 5). Here, CO 2 bonds to a lattice O, which acts as a Lewis base center as charge accumulates on the surface ions [17]. The configuration alone indicates that the CO 3 − orbitals are sp 2 hybridized. As a result, the binding of CO 2 is significantly strengthened from −0.21 eV (in the absence of a field) to −0.93 eV at Site T3 as shown in the Supplementary Materials Figure S2. The chemisorption of CO 2 is in turn accompanied by a lengthening of the C-O bond length by 0.1 Å. This also results in a Bader charge change of −0.06 electrons ( Figure 5) with respect to when the field was absent and demonstrates that a field value of −1 V/Å transfers charge from the surface to the adsorbed CO 2 molecule, in agreement with the characteristics of an activated CO 2 molecule [16,21]. These results present the potential of harnessing electric fields to tune the thermodynamic conditions for CO 2 activation.
When a +1 V/Å field was applied, the bonding between CO 2 and YSZ (111) remains limited due to the dipole-dipole interaction, as shown in Figure 5. Our calculations show, however, that the effect of a positive field value is non-negligible, since it enhances the adsorption strength of CO 2 to −0.43 eV at the same adsorption site (Site B2 in Supplementary Materials Figure S3). All adsorption configurations in the presence of an external field are displayed in Supplementary Materials Figures S2 and S3. We can see that the interaction between the molecule and the surface remained negligible within the vicinity of the Zr cation sites.
A density of states analysis of the adsorption of CO 2 on YSZ (111) is shown in Figure 6a. In the absence of an electric field, the bonding and the antibonding states are present as the −3.6 and 4.8 eV peaks, respectively (Figure 6a.1). When an electric field of +1 V/Å is applied, the peaks shift to higher energies, along with a decrease in the total number of states, illustrated by the shallow peaks in Figure 6a.2. We hypothesize that applying a field of +1 V/Å pulls electrons away from the CO 2 molecule, resulting in the destabilization of the CO 2 molecular orbitals to higher energies. The weakened binding of electrons within CO 2 thus allows for the stronger interaction with YSZ (111). The partial density of states of the Y-d states in Figure 6b display negligible changes upon the application of a +1 V/Å field strength. This further supports that the stronger adsorption induced by the +1 V/Å field indeed mainly stems from the response of CO 2 when a field is applied. s 2021, 11, 271 7 of 13 known linear shape changes to a trigonal planar configuration with a bending angle of ~128° ( Figure 5). Here, CO2 bonds to a lattice O, which acts as a Lewis base center as charge accumulates on the surface ions [17]. The configuration alone indicates that the CO3 − orbitals are sp 2 hybridized. As a result, the binding of CO2 is significantly strengthened from −0.21 eV (in the absence of a field) to −0.93 eV at Site T3 as shown in the Supplementary Materials Figure S2. The chemisorption of CO2 is in turn accompanied by a lengthening of the C-O bond length by 0.1 Å. This also results in a Bader charge change of −0.06 electrons ( Figure 5) with respect to when the field was absent and demonstrates that a field value of −1 V/Å transfers charge from the surface to the adsorbed CO2 molecule, in agreement with the characteristics of an activated CO2 molecule [16,21]. These results present the potential of harnessing electric fields to tune the thermodynamic conditions for CO2 activation. When a +1 V/Å field was applied, the bonding between CO2 and YSZ (111) remains limited due to the dipole-dipole interaction, as shown in Figure 5. Our calculations show, however, that the effect of a positive field value is non-negligible, since it enhances the adsorption strength of CO2 to −0.43 eV at the same adsorption site (Site B2 in Supplementary Materials Figure S3). All adsorption configurations in the presence of an external field are displayed in Supplementary Materials Figures S2 and S3. We can see that the interaction between the molecule and the surface remained negligible within the vicinity of the Zr cation sites.
A density of states analysis of the adsorption of CO2 on YSZ (111) is shown in Figure  6a. In the absence of an electric field, the bonding and the antibonding states are present as the −3.6 and 4.8 eV peaks, respectively (Figure 6a.1). When an electric field of +1 V/Å is applied, the peaks shift to higher energies, along with a decrease in the total number of states, illustrated by the shallow peaks in Figure 6a.2. We hypothesize that applying a field of +1 V/Å pulls electrons away from the CO2 molecule, resulting in the destabilization of the CO2 molecular orbitals to higher energies. The weakened binding of electrons within CO2 thus allows for the stronger interaction with YSZ (111). The partial density of states of the Y-d states in Figure 6b display negligible changes upon the application of a +1 V/Å field strength. This further supports that the stronger adsorption induced by the +1 V/Å field indeed mainly stems from the response of CO2 when a field is applied.  On the other hand, when a negative electric field is applied, strong chemisorption of CO 2 occurs, which is also consequently reflected in its total density of states. As shown in Figure 6a evident by the increased total number of bonding states within CO 2 , from 3.76 electrons to 9.22 electrons/vol, with respect to when the field is absent. We also observe a smearing of the CO 2 states within the −5 and 0 eV range, which implies that the electronic state energy levels were now more closely spaced.
The partial density of states of the p-states within the CO 2 -bounded lattice O highlighted in yellow (O bind ) is given in Figure 6c. We can see that the electronic states of O bind lie between −5 and 0 eV in the absence of a field (Figure 6c.1). Upon the chemisorption of CO 2 when a −1 V/Å field was applied, a splitting of the p-orbitals occurs, as revealed by the emergence of a new peak at −6.24 eV (Figure 6c.2). Ultimately, the chemisorption between O bind and the CO 2 molecule is reflected through changes within their density of states.

Computational Methods
Electronic structure calculations were done under the density functional theory framework using the Vienna Ab initio Software Package (VASP) [28,29]. We used a planewave basis, through the Projector Augmented Wave (PAW) approach, using the PAW potentials that were released in 2015 [30], to expand the one-electron orbital wavefunctions for the electron density [31]. The kinetic cutoff energy for the planewave basis was 500 eV. The exchange-correlation function employed was the Perdew, Burke, and Ernzerhof (PBE) model within the generalized gradient approximation (GGA) level of theory [32]. Spinpolarized calculations were conducted to provide degrees of freedom for the electron filling. The Gaussian smearing method was used to treat the Fermi level with a width of 0.1 eV. The optimization criterion for the self-consistent field (SCF) cycle and ionic relaxation were 10 −6 eV and 10 −2 eV/Å, respectively. As previously reported, the optimized bulk lattice constant of ZrO 2 was 5.12 Å [33].
To examine the effects of the external electric field toward CO 2 adsorption, we used a 35-atom (1 × 1) YSZ (111) surface consisting of 3 stoichiometric layers, based on the unit cell proposed by Shishkin and Ziegler displayed in Figure 7 [34]. In this calculational setup, the bottom two stoichiometric layers were fixed at their bulk positions, while the first top layer was allowed to relax. The elementary building unit of YSZ closely resembles 9 mol% concentration of Yttria, where an oxygen vacancy compensates the charge imbalance induced from substituting a single formula unit of Y 2 O 3 into a cubic ZrO 2 lattice [34]. A Monkhorst-Pack [35] mesh with a grid of (4 × 4 × 1) k-points was chosen for the Brillouin zone integration for the 7.24 × 6.27 Å unit cell. The level of the theory of the model was justified from previous studies, as the choice between PBE and DFT + U did not change trends induced by external electric fields [33,36].
On the other hand, when a negative electric field is applied, strong chemisorption of CO2 occurs, which is also consequently reflected in its total density of states. As shown in Figure 6a.3, the bonding of CO2 to the lattice O results in a lowering of the bonding states in the presence of a negative electric field. In addition, the antibonding states are now below the Fermi energy. Charge transfer occurs from the lattice O, which was also evident by the increased total number of bonding states within CO2, from 3.76 electrons to 9.22 electrons/vol, with respect to when the field is absent. We also observe a smearing of the CO2 states within the −5 and 0 eV range, which implies that the electronic state energy levels were now more closely spaced.
The partial density of states of the p-states within the CO2-bounded lattice O highlighted in yellow (Obind) is given in Figure 6c. We can see that the electronic states of Obind lie between −5 and 0 eV in the absence of a field (Figure 6c.1). Upon the chemisorption of CO2 when a −1 V/Å field was applied, a splitting of the p-orbitals occurs, as revealed by the emergence of a new peak at −6.24 eV (Figure 6c.2). Ultimately, the chemisorption between Obind and the CO2 molecule is reflected through changes within their density of states.

Computational Methods
Electronic structure calculations were done under the density functional theory framework using the Vienna Ab initio Software Package (VASP) [28,29]. We used a planewave basis, through the Projector Augmented Wave (PAW) approach, using the PAW potentials that were released in 2015 [30], to expand the one-electron orbital wavefunctions for the electron density [31]. The kinetic cutoff energy for the planewave basis was 500 eV. The exchange-correlation function employed was the Perdew, Burke, and Ernzerhof (PBE) model within the generalized gradient approximation (GGA) level of theory [32]. Spin-polarized calculations were conducted to provide degrees of freedom for the electron filling. The Gaussian smearing method was used to treat the Fermi level with a width of 0.1 eV. The optimization criterion for the self-consistent field (SCF) cycle and ionic relaxation were 10 −6 eV and 10 −2 eV/Å, respectively. As previously reported, the optimized bulk lattice constant of ZrO2 was 5.12 Å [33].
To examine the effects of the external electric field toward CO2 adsorption, we used a 35-atom (1 × 1) YSZ (111) surface consisting of 3 stoichiometric layers, based on the unit cell proposed by Shishkin and Ziegler displayed in Figure 7 [34]. In this calculational setup, the bottom two stoichiometric layers were fixed at their bulk positions, while the first top layer was allowed to relax. The elementary building unit of YSZ closely resembles 9 mol% concentration of Yttria, where an oxygen vacancy compensates the charge imbalance induced from substituting a single formula unit of Y2O3 into a cubic ZrO2 lattice [34]. A Monkhorst-Pack [35] mesh with a grid of (4 × 4 × 1) k-points was chosen for the Brillouin zone integration for the 7.24 × 6.27 Å unit cell. The level of the theory of the model was justified from previous studies, as the choice between PBE and DFT + U did not change trends induced by external electric fields [33,36]. A uniform electric field was applied in our DFT-based model using the approach proposed by Neugebauer and Scheffler [37]. The method consists of modeling an artificial dipole sheet in the vacuum center. A 15 Å vacuum was introduced to the unit cell to avoid "charge sloshing" from the interaction between periodic unit cells [38]. We considered three electric field scenarios in our system: −1.0, 0.0, and +1.0 V/Å. The direction of the negative electric field was defined to point perpendicularly toward the surface, causing charge to be accumulated on the surface, as annotated in Figure 7. The reverse convention is true for the positive electric field.
Charge polarization within the slab induced by an external electric field is bound to change the chemical properties of the surface. The effect of an external electric field on YSZ (111) was applied perpendicularly to its surface, → F = Fẑ. The surface reducibility was probed using the water formation reaction, with the reaction energy defined in Equation (1): where E YSZ (111) and E H 2 (g) ( → F ) are total energies of isolated gas-phase water and hydrogen molecules, respectively, with an orientation that is perpendicular to the externally applied electric field. A negative vacancy formation energy means that the reaction is exothermic, and a positive value indicates the reverse.
To investigate effects of the electric field toward the adsorption of CO 2 on YSZ (111), we compared their adsorption energies as defined in Equation (2): where E CO 2 /YSZ(111) (  A uniform electric field was applied in our DFT-based model using the appr proposed by Neugebauer and Scheffler [37]. The method consists of modeling an arti dipole sheet in the vacuum center. A 15 Å vacuum was introduced to the unit cell to a "charge sloshing" from the interaction between periodic unit cells [38]. We consid three electric field scenarios in our system: −1.0, 0.0, and +1.0 V/Å. The direction o negative electric field was defined to point perpendicularly toward the surface, cau charge to be accumulated on the surface, as annotated in Figure 7. The reverse conven is true for the positive electric field. Charge polarization within the slab induced by an external electric field is boun change the chemical properties of the surface. The effect of an external electric fiel YSZ (111) was applied perpendicularly to its surface, . The surface reducibility probed using the water formation reaction, with the reaction energy defined in Equ (1): where and are the field-dependent total energies of the YSZ (111) slab with and without an additional oxygen vacancy, respectively, and are total energies of isolated gas-phase water and hydr molecules, respectively, with an orientation that is perpendicular to the externally ap electric field. A negative vacancy formation energy means that the reaction is exothe and a positive value indicates the reverse.
To investigate effects of the electric field toward the adsorption of CO2 on YSZ ( we compared their adsorption energies as defined in Equation (2): where and are field-dependent total energies of the CO sorbed and clean YSZ (111) surfaces, respectively. is the field-dependent energy of CO2 in the gas phase. A negative value of indicates stronger bindi the molecule with the surface, while a positive value points to a repulsive interaction adsorption sites tested in this study are labeled in Figure 8, consisting of the variou (T), bridge (B), and hollow (H) sites.  Charge exchange upon the adsorption of CO 2 on YSZ (111) was visualized in VESTA by calculating the frozen charge density difference at the optimized bonding geometry, described in Equation (3). In this paper, we refer to this as the differential charge analysis.
where n x is the notation for charge distribution of an optimized structure indicated by the subscripts. Within the visualization, a negative charge accumulation is displayed by a yellow electron density cloud, and charge loss is signified in blue. Quantification of the partial charge transfer is then conducted through a Bader charge analysis employing the algorithm proposed by Henkelman et al. [39]. A negative Bader charge is associated with negatively charged ions. It must be noted that while Bader charge correlates directly to oxidation number, it has also been established that the Bader charge alone cannot determine the exact oxidation state of the ion [40]. We also investigated the changes within the surface electronic structures through the analysis of their density of states. The ratio of antibonding/total states and total number of electronic states can be calculated using Equations (4) and (5), respectively, where the latter is simply an integration under the curve [41]: where E is the energy level, ρ(E) is the density of electronic states at a given energy, and E Fermi is the Fermi energy. Finally, the computational setup for the calculations shown in Figure 2 on Ni (111) was previously reported in our previous work [42]. These calculations were performed in a p (3 × 3) supercell. A Monkhorst-Pack [35] mesh with a grid of (4 × 4 × 1) k-points was chosen for the Brillouin zone integration. The adsorption energy as plotted is defined as

Conclusions
To harness electric fields for enhancing CO 2 reduction, we first need an understanding of its effects toward CO 2 activation. As CO 2 is inherently inert, chemisorbing CO 2 is typically one of the most energetically costly processes for heterogeneous catalysts [17]. We conducted a DFT study focusing on the electronic interactions between CO 2 and YSZ (111) under the influence of a positive (+1 V/Å) and a negative electric field (−1 V/Å) and compared our results to when the field is absent.
By comparing the oxygen formation energies within these three cases, we found that an electric field destabilizes surface O-ions on YSZ (111), where a +1 V/Å field value increases the reducibility of the surface by the largest extent. Destabilization was further reflected in a surface ion PDOS analysis by either increasing the density of higher-energy bonding states or by shifting bonding states closer to the Fermi energy. We also found that by inverting the direction of the electric field vector toward the surface (i.e., applying a −1 V/Å field value), the most favorable oxygen vacancy site changes from the O anion in the first layer (O terminal ) to O in the second atomic layer (O sublattice ). Ultimately, our studies show that an external electric field influences the surface states of YSZ (111).
Upon the adsorption of CO 2 on YSZ (111), we generally found that it binds more favorably within the vicinity of the Y-cation. Without the presence of an electric field, CO 2 binds with the surface through a weak dipole-dipole interaction. When a −1 V/Å field value is applied, CO 2 becomes chemisorbed to the surface and forms a CO 3 − complex with the surface O. The strong interaction is reflected upon the direct charge transfer to the adsorbate (through the gain of 0.06 electrons) and the orbital splitting observed within the O lattice p-states. While CO 2 remains physisorbed when a +1 V/Å field value is applied, our total density of states analysis indicates that a positive field pulls charge away from the adsorbate resulting in a shift of its bonding and antibonding peaks to higher energies, allowing a stronger interaction with YSZ (111). This explains why the adsorption energy of CO 2 was relatively stronger by 0.2 eV. Ultimately, the effect of an electric field toward CO 2 adsorption is not negligible, and there is potential in utilizing electric fields to favor the thermodynamics of CO 2 reduction.
Supplementary Materials: The following are available online at https://www.mdpi.com/2073-434 4/11/2/271/s1; Figure S1: Comparison of CO2 adsorption sites and their corresponding adsorption energies on YSZ (111) in the absence of an electric field. Highlighted in pink is the most favorable adsorption site; Figure S2: Comparison of CO2 adsorption sites and their corresponding adsorption energies on YSZ (111) when a −1 V/Å external electric field is applied. Highlighted in pink is the most favorable adsorption site. The legend for each species is shown in Figure S1; Figure S3: Comparison between the CO2 adsorption sites and their corresponding adsorption energies on YSZ (111) when a +1 V/Å external electric field is applied. Highlighted in pink is the most favorable adsorption site. The legend for each species is shown in Figure S1.

Data Availability Statement:
The data presented in this study are available upon request from the corresponding author.