Exploring non-adiabaticity to CO reduction reaction through ab initio molecular dynamics simulation

Non-adiabatic chemical reaction refers to the electronic excitation during reactions. This effect cannot be modeled by the ground-state Born–Oppenheimer molecular dynamics (BO-MD), where the electronic structure is at the ground state for every step of ions’ movement. Although the non-adiabatic effect has been explored extensively in gas phase reactions, its role in electrochemical reactions, such as water splitting and CO2 reduction, in electrolyte has been rarely explored. On the other hand, electrochemical reactions usually involve electron transport; thus, a non-adiabatic process can naturally play a significant role. In this work, using one-step CO2 reduction as an example, we investigated the role of the non-adiabatic effect in the reaction. The reaction barriers were computed by adiabatic BO-MD and non-adiabatic real-time time dependent density functional theory (rt-TDDFT). We found that by including the non-adiabatic effect, rt-TDDFT could increase the reaction barrier up to 6% compared to the BO-MD calculated barrier when the solvent model is used to represent water. Simulations were carried out using explicit water molecules around the reaction site under different overpotentials, and similar non-adiabatic effects were found.

phase catalytic reactions on surfaces to understand the contribution from the NA effect. 30-35 48 For example, the NA simulation with fewest-switches surface-hopping algorithm has shown 49 the strong NA effect for spin flipping and transition during the O 2 disssociative adsorption on 50 Al and Pd surface, with the estimated rate consistent to the experiments. 36, 37 The reverse 51 process associative desorption of N 2 on Ru(001) further shows the NA effect from an ab 52 initio simulation indirectly. 38 In that work, consistent agreement between the simulation 53 and the experiments can be obtained only after including the NA effect in the calculation. A 54 comprehensive theoretical study has been made to explore the NA effect of H 2 /Cu (110) and 55 N 2 /W (110). However, their simulation has shown a marginal effect of the non-adiabaticity to 56 diatomic molecules adsorption process. 37 Based on these examples, the role of the NA effect 57 seems to depend on specific reaction types. However, for electrochemical reactions under 58 aqueous condition such as heterogenous catalysis, the NA effect has been rarely studied. 59 Electrochemical reactions necessitate the transfer of charge from one place to another, thus 60 it is more likely a NA process. Besides the question of excited state induced by the reaction 61 dynamics, another possibility is the charge transfer bottleneck, which also makes the process 62 NA. One recent work focusing the initial CO 2 adsorption to various metal surfaces has shown 63 very fast electronic hybridization compared to the adsorption, 21 showing the adiabatic nature 64 of the chemical adsorption process. Different from the initial adsorption process for CO 2 Meanwhile, the excitation of the electronic structure may drive the ions movement differently 85 compared to the ground-state electronic structure. With this capability, rt-TDDFT has been 86 widely used to simulate various NA processes such as optical excitations, 42 proton-assisted 87 chemical reactions, 43 and ion sputtering. 27,44 Different from other TDDFT algorithms where 88 a very small time step (∆t∼0.001fs) has to be used to evolve the charge density, the imple-89 mentation we have adopted here uses the adiabatic states (φ j (t)) as the basis to expand the 90 wavefunction. These adiabatic states are solved from the Hamiltonian at each ion's step t n 91 with time-step ∆t = t n+1 − t n ≤ 0.1fs. The time-dependent wavefunction is expanded as: where adiabatic state φ j (t) is solved by diaganolizing the Hamiltonian H at step t: H(t)φ j (t) = 93 j (t)φ j (t). The coefficient C ij (t) for the wavefunction is evolved from t n to t n+1 non-94 adiabatically following the Schrödinger's equation i∂ψ(t) ∂t = H(t)ψ(t) using a much smaller lation from H(t n ) to H(t n+1 ). However, since the adiabatic states (size∼100) are used as 97 basis to construct the wavefunction and Hamiltonian instead of plane-waves, the evolution 98 of wavefunction from t n to t n+1 involves only a small size matrix, its cost becomes negligi-99 ble. This method allows us to evolve wavefunction and ions' dynamics of a complex system 100 with hundreds of atoms such as the surface chemical reaction presented here. In this work, 101 the reaction is simulated with CO molecule adsorbed on copper [111] surface, and it is at-102 tacked by H 3 O + to form COH on copper. We find that the BO-MD and rt-TDDFT with 103 the same initial setups can reveal opposite results: near the reaction barrier, BO-MD allows 104 the reaction to happen, while rt-TDDFT fails to proceed the reaction to form ⋆COH but 105 return back to ⋆CO. Such difference clearly demonstrates the role of the non-adiabaticity to 106 electrochemical reactions in aqueous conduction. The reaction barrier change caused by the 107 non-adiabaticity is estimated, which is up to 6% correction compared to the ground-state 108 method calculated barriers. We also explored the reaction with the explicit solvent model 109 and with different electrode potentials, and we find similar NA effects.   Distance ( )

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During the simulation, the proton does not move across the reaction barrier, but it returns 179 back to water molecules re-forming the initial structure. We also perform rt-TDDFT up to 180 70 fs to confirm that the reaction does not happen during this time. and II are calculated as: bonding to ⋆CO to make the reaction successful (thus rt-TDDFT has a higher initial velocity than BO-MD). b) Measured change of total charge counted above the plane. This horizontal plane has its z-value in the middle between C and top Cu layer. Here, simulation-"TDDFT reaction fail" has the same initial velocity to "BO-MD reaction success", while "TDDFT reaction success" has higher initial velocity than "BO-MD reaction success". c) Eigen-energy of the adiabatic states for "BO-MD reaction success" and "TDDFT reaction success". The bottom isosurface is the state I charge density difference of BO-MD and rt-TDDFT at t = 20 fs (charge density at "Red" dot minus "Blue" dot). Yellow color in the isosurface indicates positive; blue indicates negative.
13 of the closer distance between H and CO. This can be shown in Fig. 4c is not sufficient, in some cases, for the BO-MD simulation, after the proton exchange, the 248 system can become spin-polarized. We expect this could be a real case if CO is sitting in 249 small Cu cluster instead of bulk Cu (see SI Fig. 4). This spin-polarization however, will never 250 be developed in rt-TDDFT, since such spin flip is impossible without spin-orbit coupling.

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Even with spin-orbit, the time of the reaction discussed here will not be enough to make 252 such spin flip.

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As afore discussed, the implicit solvent model reproduces the energetic of the solvation 254 effect to ions. However, it does has its disadvantages, 55 primarily as an averaged contin-  influence the reaction. We believe this is one of the first few works to directly illuminate 305 the NA effect in electrochemical reaction with the electrolytes. In this reaction, the proton 306 of hydronium is attacking ⋆CO to form ⋆COH. By tuning initial velocity of the proton and 307 monitoring the reaction using ground-state BO-MD, we can identify the adiabatic reaction 308 barrier to be the initial kinetic energy of the proton, which just let the reaction to finish.

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However, by using the same initial kinetic energy and structure, although BO-MD can finish the reaction, rt-TDDFT simulation involving the NA effect disallow the reaction to finish 311 but return the proton back to hydronium. A higher kinetic energy must be supplied to drive Nitrogen-Doped Graphenes as Efficient Active Centers for Water Splitting: A Theoret-