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arXiv:1812.00011 · Physical Review Letters

Multiset Matrix Product State Calculations Reveal Mobile Franck-Condon Excitations Under Strong Holstein-Type Coupling

Benedikt Kloss, David R. Reichman, Roel Tempelaar

Published Sep 16, 2019• 58 citations
arXivHTMLPDF

Abstract

We show that the dynamics of (vertical) Franck-Condon excitations in the regime where Holstein-coupled vibrational modes mix strongly with electronic degrees of freedom sharply contrasts with the known self-localized behavior of vibrationally relaxed excitations. Instead, the strongly coupled modes are found to periodically induce resonances between interacting electronic sites, during which effective excitation transfer occurs, allowing Franck-Condon excitations to attain substantial mean square displacements under conditions where relaxed excitations are essentially trapped to a single site. In demonstrating this behavior, we employ a multiset matrix product state formalism. We find this tensor network state method to be a remarkably efficient and accurate approach for the notoriously difficult problem posed by the Holstein model in the regime where the electronic coupling, the vibrational quantum, and the vibrational reorganization energy are comparable in magnitude.

DOI
10.1103/physrevlett.123.126601

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We show that the dynamics of (vertical) Franck-Condon excitations in the regime where Holstein-coupled vibrational modes mix strongly with electronic degrees of freedom sharply contrasts with the known self-localized behavior of vibrationally relaxed excitations. Instead, the strongly coupled modes are found to periodically induce resonances between interacting electronic sites, during which effective excitation transfer occurs, allowing Franck-Condon excitations to attain substantial mean square displacements under conditions where relaxed excitations are essentially trapped to a single site. In demonstrating this behavior, we employ a multiset matrix product state formalism. We find this tensor network state method to be a remarkably efficient and accurate approach for the notoriously difficult problem posed by the Holstein model in the regime where the electronic coupling, the vibrational quantum, and the vibrational reorganization energy are comparable in magnitude.
We develop a multiset matrix product state (MPS) approach based on the time-dependent variational principle to solve the hierarchical equations of motion (HEOM) for the fermionic bath and apply it to inelastic vibrational scattering on metal surfaces. By using a Newns-Anderson model with two nuclear degrees of freedom, we investigate the vibrational energy relaxation of NO scattering on Au(111) and Ag(111) surfaces. Our results show that the extent of vibrational relaxation depends strongly on both incident energy and molecule-surface coupling strength. Vibrational relaxation on the Au(111) surface is enhanced with increasing incident energy due to greater transient electron transfer. The dependence on molecule-surface coupling strength and effective metal bandwidth is more complex. In the case of scattering on the Au(111) surface with low initial vibrational excitation, the landscape of the adiabatic potential energy surface plays an important role. Stronger coupling enhances transient electron transfer and leads to more pronounced vibrational relaxation. However, for high initial vibrational excitation, the extent of transient electron transfer remains similar. Larger coupling strength increases adiabaticity and reduces vibrational relaxation. The vibrational relaxation on the Ag(111) surface is found to be more pronounced than on the Au(111) surface, consistent with experimental observations. Our study provides detailed insights into the nonadiabatic dynamics during molecule-surface scattering and demonstrates the utility of the multiset MPS-HEOM approach for studying such processes.
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Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n-mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. We expand the existing vibrational DMRG formalism by applying the n-mode quantization to all potential energy surfaces entering the Hamiltonian as well as to all off-diagonal coupling terms. This is accompanied by the introduction of a novel matrix product state architecture employing tailored local site operators, which allow an effective encoding of the vibronic wave function in a tensor-train format. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited-state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n-mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.
High Resolution Image Download MS PowerPoint Slide Theoretical predictions of photochemical processes are essential for interpreting and understanding spectral features. Reliable quantum dynamics calculations of vibronic systems require precise modeling of anharmonic effects in the potential energy surfaces and off-diagonal nonadiabatic coupling terms. In this work, we present the n -mode quantization of all vibronic Hamiltonian terms comprised of general high-dimensional model representations. We expand the existing vibrational DMRG formalism by applying the n -mode quantization to all potential energy surfaces entering the Hamiltonian as well as to all off-diagonal coupling terms. This is accompanied by the introduction of a novel matrix product state architecture employing tailored local site operators, which allow an effective encoding of the vibronic wave function in a tensor-train format. This results in a second-quantized framework for accurate vibronic calculations employing the density matrix renormalization group algorithm. We demonstrate the accuracy and reliability of this approach by calculating the excited-state quantum dynamics of maleimide. We analyze convergence and the choice of parameters of the underlying time-dependent density matrix renormalization group algorithm for the n -mode vibronic Hamiltonian, demonstrating that it enables accurate calculations of complex photochemical dynamics.
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