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Chávez M, Ernst M. Continuous Floquet theory in solid-state NMR. J Chem Phys 2024; 160:244111. [PMID: 38940539 DOI: 10.1063/5.0213078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2024] [Accepted: 06/10/2024] [Indexed: 06/29/2024] Open
Abstract
This article presents the application of continuous Floquet theory in solid-state nuclear magnetic resonance (NMR). Continuous Floquet theory extends the traditional Floquet theory to non-continuous Hamiltonians, enabling the description of observable effects not fully captured by the traditional Floquet theory due to its requirement for a periodic Hamiltonian. We present closed-form expressions for computing first- and second-order effective Hamiltonians, streamlining integration with the traditional Floquet theory and facilitating application in NMR experiments featuring multiple modulation frequencies. Subsequently, we show examples of the practical application of continuous Floquet theory by investigating several solid-state NMR experiments. These examples illustrate the importance of the duration of the pulse scheme regarding the width of the resonance conditions and the near-resonance behavior.
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Affiliation(s)
- Matías Chávez
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Department of Chemistry and Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Camenisch GM, Wili N, Jeschke G, Ernst M. Pulsed dynamic nuclear polarization: a comprehensive Floquet description. Phys Chem Chem Phys 2024; 26:17666-17683. [PMID: 38868989 PMCID: PMC11202326 DOI: 10.1039/d4cp01788a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/30/2024] [Accepted: 06/05/2024] [Indexed: 06/14/2024]
Abstract
Dynamic nuclear polarization (DNP) experiments using microwave (mw) pulse sequences are one approach to transfer the larger polarization on the electron spin to nuclear spins of interest. How the result of such experiments depends on the external magnetic field and the excitation power is part of an ongoing debate and of paramount importance for applications that require high chemical-shift resolution. To date numerical simulations using operator-based Floquet theory have been used to predict and explain experimental data. However, such numerical simulations provide only limited insight into parameters relevant for efficient polarization transfer, such as transition amplitudes or resonance offsets. Here we present an alternative method to describe pulsed DNP experiments by using matrix-based Floquet theory. This approach leads to analytical expressions for the transition amplitudes and resonance offsets. We validate the method by comparing computations by these analytical expressions to their numerical counterparts and to experimental results for the XiX, TOP and TPPM DNP sequences. Our results explain the experimental data and are in very good agreement with the numerical simulations. The analytical expressions allow for the discussion of the scaling behaviour of pulsed DNP experiments with respect to the external magnetic field. We find that the transition amplitudes scale inversely with the external magnetic field.
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Affiliation(s)
- Gian-Marco Camenisch
- Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich, Switzerland.
| | - Nino Wili
- Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry, Aarhus University, Aarhus, Denmark
| | - Gunnar Jeschke
- Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich, Switzerland.
| | - Matthias Ernst
- Department of Chemistry and Applied Biosciences, ETH Zürich, Zürich, Switzerland.
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Chen J, Wang Y, Dou W. Floquet nonadiabatic mixed quantum-classical dynamics in periodically driven solid systems. J Chem Phys 2024; 160:214101. [PMID: 38828807 DOI: 10.1063/5.0204158] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2024] [Accepted: 05/16/2024] [Indexed: 06/05/2024] Open
Abstract
In this paper, we introduce the Floquet mean-field dynamics and Floquet surface hopping approaches to study the nonadiabatic dynamics in periodically driven solid systems. We demonstrate that these two approaches can be formulated in both real and reciprocal spaces. Using the two approaches, we are able to simulate the interaction between electronic carriers and phonons under periodic drivings, such as strong light-matter interactions. Employing the Holstein and Peierls models, we show that strong light-matter interactions can effectively modulate the dynamics of electronic population and mobility. Notably, our study demonstrates the feasibility and effectiveness of modeling low-momentum carriers' interactions with phonons using a truncated reciprocal space basis, an approach impractical in real space frameworks. Moreover, we reveal that even with a significant truncation, carrier populations derived from surface hopping maintain greater accuracy compared to those obtained via mean-field dynamics. These results underscore the potential of our proposed methods in advancing the understanding of carrier-phonon interactions in various periodically driven materials.
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Affiliation(s)
- Jingqi Chen
- Fudan University, 220 Handan Road, Shanghai 200433, China
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
| | - Yu Wang
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
- Department of Physics, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
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Mosallanejad V, Wang Y, Dou W. Floquet non-equilibrium Green's function and Floquet quantum master equation for electronic transport: The role of electron-electron interactions and spin current with circular light. J Chem Phys 2024; 160:164102. [PMID: 38651810 DOI: 10.1063/5.0184978] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/28/2023] [Accepted: 04/03/2024] [Indexed: 04/25/2024] Open
Abstract
The non-equilibrium Green's function (NEGF) and quantum master equation (QME) are two main classes of approaches for electronic transport. We discuss various Floquet variances of these formalisms for transport properties of a quantum dot driven via interaction with an external periodic field. We first derived two versions of the Floquet NEGF. We also explore an ansatz of the Floquet NEGF formalism for the interacting systems. In addition, we derived two versions of Floquet QME in the weak interaction regime. With each method, we elaborate on the evaluation of the expectation values of the number and current operators. We examined these methods for transport through a two-level system that is subject to periodic driving. The numerical results of all four methods show good agreement for non-interacting systems in the weak regime. Furthermore, we have observed that circular light can introduce spin current. We expect these Floquet quantum transport methods to be useful in studying molecular junctions exposed to light.
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Affiliation(s)
- Vahid Mosallanejad
- Department of Chemistry, Westlake University, Hangzhou, Zhejiang 310024, China and Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Yu Wang
- Department of Chemistry, Westlake University, Hangzhou, Zhejiang 310024, China and Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Wenjie Dou
- Department of Chemistry, Westlake University, Hangzhou, Zhejiang 310024, China and Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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Wang Y, Mosallanejad V, Liu W, Dou W. Nonadiabatic Dynamics near Metal Surfaces with Periodic Drivings: A Generalized Surface Hopping in Floquet Representation. J Chem Theory Comput 2024; 20:644-650. [PMID: 38197260 DOI: 10.1021/acs.jctc.3c01263] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
With light-matter interaction extending into the strong regime, as well as rapid development of laser technology, systems subjecting to a time-periodic perturbation have attracted broad attention. Floquet theorem and Floquet time-independent Hamiltonian are powerful theoretical frameworks to investigate the systems subjected to time-periodic drivings. In this study, we extend the previous generalized surface hopping (SH) algorithm near a metal surface (J. Chem. Theory Comput. 2017, 13, 6, 2430-2439) to the Floquet space, and hence, we develop a generalized Floquet representation-based SH (FR-SH) algorithm. Here, we consider an open quantum system with fast drivings. We expect that the present algorithm will be useful for understanding the chemical processes of molecules under time-periodic driving near the metal surface.
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Affiliation(s)
- Yu Wang
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Vahid Mosallanejad
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Wei Liu
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
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Wang Y, Dou W. Nonadiabatic dynamics near metal surface with periodic drivings: A Floquet surface hopping algorithm. J Chem Phys 2023; 158:2895265. [PMID: 37290089 DOI: 10.1063/5.0148418] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2023] [Accepted: 05/23/2023] [Indexed: 06/10/2023] Open
Abstract
We develop a Floquet surface hopping approach to deal with nonadiabatic dynamics of molecules near metal surfaces subjected to time-periodic drivings from strong light-matter interactions. The method is based on a Floquet classical master equation (FCME) derived from a Floquet quantum master equation (FQME), followed by a Wigner transformation to treat nuclear motion classically. We then propose different trajectory surface hopping algorithms to solve the FCME. We find that a Floquet averaged surface hopping with electron density (FaSH-density) algorithm works the best as benchmarked with the FQME, capturing both the fast oscillations due to the driving and the correct steady-state observables. This method will be very useful to study strong light-matter interactions with a manifold of electronic states.
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Affiliation(s)
- Yu Wang
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024, Zhejiang, China
- Department of Physics, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
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Arunachalam V, Sharma K, Mote KR, Madhu PK. Asynchronising five-fold symmetry sequence for better homonuclear polarisation transfer in magic-angle-spinning solid-state NMR. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2023; 124:101858. [PMID: 36796278 DOI: 10.1016/j.ssnmr.2023.101858] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/03/2022] [Revised: 01/28/2023] [Accepted: 01/30/2023] [Indexed: 06/18/2023]
Abstract
Recoupling, decoupling, and multidimensional correlation experiments in magic-angle-spinning (MAS) solid-state NMR can be designed by exploiting the symmetry of internal spin interactions. One such scheme, namely, C521, and its supercycled version SPC521, notated as a five-fold symmetry sequence, is widely used for double-quantum dipole-dipole recoupling. Such schemes are generally rotor synchronised by design. We demonstrate an asynchronous implementation of the SPC521 sequence leading to higher double-quantum homonuclear polarisation transfer efficiency compared to the normal synchronous implementation. Rotor-synchronisation is broken in two different ways: lengthening the duration of one of the pulses, denoted as pulse-width variation (PWV), and mismatching the MAS frequency denoted as MAS variation (MASV). The application of this asynchronous sequence is shown on three different samples, namely, U-13C-alanine and 1,4-13C-labelled ammonium phthalate which include 13Cα-13Cβ, 13Cα-13Co, and 13Co-13Co spin systems, and adenosine 5'- triphosphate disodium salt trihydrate (ATP⋅3H2O). We show that the asynchronous version performs better for spin pairs with small dipole-dipole couplings and large chemical-shift anisotropies, for example, 13Co-13Co. Simulations and experiments are shown to corroborate the results.
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Affiliation(s)
- Vaishali Arunachalam
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
| | - Kshama Sharma
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
| | - Kaustubh R Mote
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
| | - P K Madhu
- Tata Institute of Fundamental Research Hyderabad, 36/P Gopanpally Village, Ranga Reddy District, Hyderabad, 500046, India.
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Chávez M, Ernst M. Interaction frames in solid-state NMR: A case study for chemical-shift-selective irradiation schemes. SOLID STATE NUCLEAR MAGNETIC RESONANCE 2022; 122:101834. [PMID: 36327552 DOI: 10.1016/j.ssnmr.2022.101834] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2022] [Revised: 09/27/2022] [Accepted: 10/03/2022] [Indexed: 06/16/2023]
Abstract
Interaction frames play an important role in describing and understanding experimental schemes in magnetic resonance. They are often used to eliminate dominating parts of the spin Hamiltonian, e.g., the Zeeman Hamiltonian in the usual (Zeeman) rotating frame, or the radio-frequency-field (rf) Hamiltonian to describe the efficiency of decoupling or recoupling sequences. Going into an interaction frame can also make parts of a time-dependent Hamiltonian time independent like the rf-field Hamiltonian in the usual (Zeeman) rotating frame. Eliminating the dominant term often allows a better understanding of the details of the spin dynamics. Going into an interaction frame can also reduces the energy-level splitting in the Hamiltonian leading to a faster convergence of perturbation expansions, average Hamiltonian, or Floquet theory. Often, there is no obvious choice of the interaction frame to use but some can be more convenient than others. Using the example of frequency-selective dipolar recoupling, we discuss the differences, advantages, and disadvantages of different choices of interaction frames. They always include the complete radio-frequency Hamiltonian but can also contain the chemical shifts of the spins and may or may not contain the effective fields over one cycle of the pulse sequence.
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Affiliation(s)
- Matías Chávez
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093, Zürich, Switzerland.
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Chávez M, Ernst M. A continuous approach to Floquet theory for pulse-sequence optimization in solid-state NMR. J Chem Phys 2022; 157:184103. [DOI: 10.1063/5.0109229] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022] Open
Abstract
We present a framework that uses a continuous frequency space to describe and design solid-state nuclear magnetic resonance (NMR) experiments. The approach is similar to the well-established Floquet treatment for NMR, but it is not restricted to periodic Hamiltonians and allows the design of experiments in a reverse fashion. The framework is based on perturbation theory on a continuous Fourier space, which leads to effective, i.e., time-independent, Hamiltonians. It allows the back-calculation of the pulse scheme from the desired effective Hamiltonian as a function of spin-system parameters. We show as an example how to back-calculate the rf irradiation in the MIRROR experiment from the desired chemical-shift offset behavior of the sequence.
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Affiliation(s)
- Matías Chávez
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Matthias Ernst
- Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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