First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems

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First-Principles Approach for Coupled Quantum Dynamics of Electrons and Protons in Heterogeneous Systems

Jianhang Xu, Ruiyi Zhou, Volker Blum, Tao E. Li, Sharon Hammes-Schiffer, and Yosuke Kanai

Phys. Rev. Lett. 131, 238002 – Published 7 December 2023

Abstract

The coupled quantum dynamics of electrons and protons is ubiquitous in many dynamical processes involving light-matter interaction, such as solar energy conversion in chemical systems and photosynthesis. A first-principles description of such nuclear-electronic quantum dynamics requires not only the time-dependent treatment of nonequilibrium electron dynamics but also that of quantum protons. Quantum mechanical correlation between electrons and protons adds further complexity to such coupled dynamics. Here we extend real-time nuclear-electronic orbital time-dependent density functional theory (RT-NEO-TDDFT) to periodic systems and perform first-principles simulations of coupled quantum dynamics of electrons and protons in complex heterogeneous systems. The process studied is an electronically excited-state intramolecular proton transfer of o-hydroxybenzaldehyde in water and at a silicon (111) semiconductor-molecule interface. These simulations illustrate how environments such as hydrogen-bonding water molecules and an extended material surface impact the dynamical process on the atomistic level. Depending on how the molecule is chemisorbed on the surface, excited-state electron transfer from the molecule to the semiconductor surface can inhibit ultrafast proton transfer within the molecule. This Letter elucidates how heterogeneous environments influence the balance between the quantum mechanical proton transfer and excited electron dynamics. The periodic RT-NEO-TDDFT approach is applicable to a wide range of other photoinduced heterogeneous processes.

Received 9 June 2023
Accepted 1 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.238002

Physics Subject Headings (PhySH)

Interfaces Molecules

Density functional theory Quantum chemistry methods Time-dependent DFT

Condensed Matter, Materials & Applied PhysicsPolymers & Soft MatterAtomic, Molecular & Optical

Authors & Affiliations

Jianhang Xu and Ruiyi Zhou

Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA

Volker Blum

Thomas Lord Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina, USA and Department of Chemistry, Duke University, Durham, North Carolina, USA

Tao E. Li and Sharon Hammes-Schiffer ^*

Department of Chemistry, Yale University, New Haven, Connecticut, USA

Yosuke Kanai ^†

Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA and Department of Physics and Astronomy, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA

^*sharon.hammes-schiffer@yale.edu
^†ykanai@unc.edu

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Issue

Vol. 131, Iss. 23 — 8 December 2023

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Images

Figure 1
The geometries of (a) the isolated oHBA molecule (with the quantum proton highlighted using a white isosurface) and (b) a snapshot of the oHBA molecule solvated in liquid water from the FPMD simulation. The isosurfaces show the molecular HOMO state (yellow) and the molecular LUMO state (blue). (c) Distances between the position expectation value of the transferring proton and the donor (blue) and acceptor (red) oxygen atoms in the oHBA molecule as a function of the time. The circles represent the isolated oHBA molecule in vacuum, and the solid lines represent the solvated oHBA molecule in water. The shaded areas along the solid lines indicate the standard deviation for the ensembles using six different snapshots from the FPMD simulation.
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Figure 2
(a) Geometry of the oHBA molecule directly chemisorbed on a hydrogen-terminated Si(111) surface. Isosurfaces for one of the three hybridized HOMO (hyb-HOMO) states (yellow) and the hybridized LUMO (hyb-LUMO) state (blue) are also shown. Molecular structures of the oHBA molecule with a hyb-HOMO state (yellow) and hyb-LUMO state (blue) are shown for (b) the direct attachment and (c) the attachment with a - $C \equiv C$ - linker group in between. (d) The density of electronic states for the direct attachment (solid line) and with the linker group (dashed line). The Fermi energy, defined here as the VBM of the equilibrium ground state, is at 0 eV, and the hyb-HOMO states and hyb-LUMO state are highlighted in yellow and blue, respectively.
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Figure 3
(a) Distances from the position expectation value of the transferring proton to the donor oxygen atom ( $O_{D}$ ) (red) and the acceptor oxygen atom ( $O_{A}$ ) (blue) as a function of the time for the isolated oHBA in vacuum (circles) and the oHBA on the Si surface with the direct attachment (solid lines) and with the linker group (dashed lines). (b) The percentage of the hole (red) and the excited electron (blue) spatially localized on the oHBA molecule based on Mulliken population analysis with the direct attachment (solid lines) and with the linker group (dashed lines). The shaded areas along the lines indicate the standard deviation for the initial particle-hole excitation from the three different hyb-HOMO states.
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Figure 4
The time-dependent probability amplitudes of the excited electron and hole in terms of the Kohn-Sham eigenstates of the ground-state system with direct attachment (a),(b) and with the linker group (c),(d). (a),(c) and (b),(d) are for the excited electron and the hole, respectively.
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