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Climent C, Schelter EJ, Waldeck DH, Vinogradov SA, Subotnik JE. On the circularly polarized luminescence of individual triplet sublevels. J Chem Phys 2023; 159:134304. [PMID: 37791627 DOI: 10.1063/5.0159932] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2023] [Accepted: 09/17/2023] [Indexed: 10/05/2023] Open
Abstract
We discuss the possibility of using circularly polarized luminescence (CPL) as a tool to probe individual triplet spin sublevels that are populated nonadiabatically following photoexcitation. This study is motivated by a mechanism proposed for chirality-induced spin selectivity in which coupled electronic-nuclear dynamics may lead to a non-statistical population of the three triplet sublevels in chiral systems. We find that low-temperature CPL should aid in quantifying the exact spin state/s populated through coupled electronic-nuclear motion in chiral molecules.
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Affiliation(s)
- Clàudia Climent
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Eric J Schelter
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - David H Waldeck
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Sergei A Vinogradov
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Zhou Z, Wu Y, Bian X, Subotnik JE. Nonadiabatic Dynamics in a Continuous Circularly Polarized Laser Field with Floquet Phase-Space Surface Hopping. J Chem Theory Comput 2023; 19:718-732. [PMID: 36655857 DOI: 10.1021/acs.jctc.2c00948] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Nonadiabatic chemical reactions involving continuous circularly polarized light (cw CPL) have not attracted as much attention as dynamics in unpolarized/linearly polarized light. However, including circularly (in contrast to linearly) polarized light allows one to effectively introduce a complex-valued time-dependent Hamiltonian, which offers a new path for control or exploration through the introduction of Berry forces. Here, we investigate several inexpensive semiclassical approaches for modeling such nonadiabatic dynamics in the presence of a time-dependent complex-valued Hamiltonian, beginning with a straightforward instantaneous adiabatic fewest-switches surface hopping (IA-FSSH) approach (where the electronic states depend on position and time), continuing to a standard Floquet fewest switches surface hopping (F-FSSH) approach (where the electronic states depend on position and frequency), and ending with an exotic Floquet phase-space surface hopping (F-PSSH) approach (where the electronic states depend on position, frequency, and momentum). Using a set of model systems with time-dependent complex-valued Hamiltonians, we show that the Floquet phase-space adiabats are the optimal choice of basis as far as accounting for Berry phase effects and delivering accuracy. Thus, the F-PSSH algorithm sets the stage for future modeling of nonadiabatic dynamics under strong externally pumped circular polarization.
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Affiliation(s)
- Zeyu Zhou
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph Eli Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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Wu Y, Subotnik JE. A quantum-classical Liouville formalism in a preconditioned basis and its connection with phase-space surface hopping. J Chem Phys 2023; 158:024115. [PMID: 36641414 DOI: 10.1063/5.0124835] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
We revisit a recent proposal to model nonadiabatic problems with a complex-valued Hamiltonian through a phase-space surface hopping (PSSH) algorithm employing a pseudo-diabatic basis. Here, we show that such a pseudo-diabatic PSSH (PD-PSSH) ansatz is consistent with a quantum-classical Liouville equation (QCLE) that can be derived following a preconditioning process, and we demonstrate that a proper PD-PSSH algorithm is able to capture some geometric magnetic effects (whereas the standard fewest switches surface hopping approach cannot capture such effects). We also find that a preconditioned QCLE can outperform the standard QCLE in certain cases, highlighting the fact that there is no unique QCLE. Finally, we also point out that one can construct a mean-field Ehrenfest algorithm using a phase-space representation similar to what is done for PSSH. These findings would appear extremely helpful as far as understanding and simulating nonadiabatic dynamics with complex-valued Hamiltonians and/or spin degeneracy.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Fransson J. The Chiral Induced Spin Selectivity Effect What It Is, What It Is Not, And Why It Matters. Isr J Chem 2022. [DOI: 10.1002/ijch.202200046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- J. Fransson
- Department of Physics and Astronomy Uppsala University Box 516, 751 21 Uppsala Sweden
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Bian X, Wu Y, Rawlinson J, Littlejohn RG, Subotnik JE. Modeling Spin-Dependent Nonadiabatic Dynamics with Electronic Degeneracy: A Phase-Space Surface-Hopping Method. J Phys Chem Lett 2022; 13:7398-7404. [PMID: 35926097 DOI: 10.1021/acs.jpclett.2c01802] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Nuclear Berry curvature effects emerge from electronic spin degeneracy and can lead to nontrivial spin-dependent (nonadiabatic) nuclear dynamics. However, such effects are not captured fully by any current mixed quantum-classical method such as fewest-switches surface hopping. In this work, we present a phase-space surface-hopping (PSSH) approach to simulate singlet-triplet intersystem crossing dynamics. We show that with a simple pseudodiabatic ansatz, a PSSH algorithm can capture the relevant Berry curvature effects and make predictions in agreement with exact quantum dynamics for a simple singlet-triplet model Hamiltonian. Thus, this approach represents an important step toward simulating photochemical and spin processes concomitantly, as relevant to intersystem crossing and spin-lattice relaxation dynamics.
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Affiliation(s)
- Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Jonathan Rawlinson
- Department of Mathematics, University of Manchester, Manchester M13 9PL, U.K
| | - Robert G Littlejohn
- Department of Physics, University of California, Berkeley, California 94720, United States
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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Wu Y, Bian X, Rawlinson JI, Littlejohn RG, Subotnik JE. A phase-space semiclassical approach for modeling nonadiabatic nuclear dynamics with electronic spin. J Chem Phys 2022; 157:011101. [DOI: 10.1063/5.0093345] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Chemical relaxation phenomena, including photochemistry and electron transfer processes, form a vigorous area of research in which nonadiabatic dynamics plays a fundamental role. However, for electronic systems with spin degrees of freedom, there are few if any applicable and practical quasiclassical methods. Here, we show that for nonadiabatic dynamics with two electronic states and a complex-valued Hamiltonian that does not obey time-reversal symmetry (as relevant to many coupled nuclear-electronic-spin systems), the optimal semiclassical approach is to generalize Tully’s surface hopping dynamics from coordinate space to phase space. In order to generate the relevant phase-space adiabatic surfaces, one isolates a proper set of diabats, applies a phase gauge transformation, and then diagonalizes the total Hamiltonian (which is now parameterized by both R and P). The resulting algorithm is simple and valid in both the adiabatic and nonadiabatic limits, incorporating all Berry curvature effects. Most importantly, the resulting algorithm allows for the study of semiclassical nonadiabatic dynamics in the presence of spin–orbit coupling and/or external magnetic fields. One expects many simulations to follow as far as modeling cutting-edge experiments with entangled nuclear, electronic, and spin degrees of freedom, e.g., experiments displaying chiral-induced spin selectivity.
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Affiliation(s)
- Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
| | - Jonathan I. Rawlinson
- School of Mathematics, The University of Manchester, Oxford Rd., Manchester M13 9PL, United Kingdom
| | - Robert G. Littlejohn
- Department of Physics, University of California, 366 Physics North MC 7300, Berkeley, California 94720-7300, USA
| | - Joseph E. Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
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Mališ M, Vandaele E, Luber S. Spin-Orbit Couplings for Nonadiabatic Molecular Dynamics at the ΔSCF Level. J Chem Theory Comput 2022; 18:4082-4094. [PMID: 35666703 DOI: 10.1021/acs.jctc.1c01046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A procedure for the calculation of spin-orbit coupling (SOC) at the delta self-consistent field (ΔSCF) level of theory is presented. Singlet and triplet excited electronic states obtained with the ΔSCF method are expanded into a linear combination of singly excited Slater determinants composed of ground electronic state Kohn-Sham orbitals. This alleviates the nonorthogonality between excited and ground electronic states and introduces a framework, similar to the auxiliary wave function at the time-dependent density functional theory (TD-DFT) level, for the calculation of observables. The ΔSCF observables of the formaldehyde system were compared to reference TD-DFT values. Our procedure gives all components (energies, gradients, nonadiabatic couplings, and SOC terms) at the ΔSCF level of theory for conducting efficient, full-atomistic nonadiabatic molecular dynamics with intersystem crossing, particularly in condensed phase systems.
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Affiliation(s)
- Momir Mališ
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Eva Vandaele
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
| | - Sandra Luber
- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, 8057 Zürich, Switzerland
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Bian X, Wu Y, Teh HH, Subotnik JE. Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy. J Chem Theory Comput 2022; 18:2075-2090. [PMID: 35263116 DOI: 10.1021/acs.jctc.1c01103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "ms" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.
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Affiliation(s)
- Xuezhi Bian
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Yanze Wu
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Hung-Hsuan Teh
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
| | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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Abstract
Surface hopping has seen great success in describing molecular phenomena where electronic excitations tend to be localized, but its application to materials with band-like electronic properties has remained limited. Here, we derive a formulation of fewest-switches surface hopping where both the quantum and classical equations of motion are solved entirely in terms of reciprocal-space coordinates. The resulting method is directly compatible with band structure calculations and allows for the efficient description of band-like phenomena by means of a truncation of the Brillouin zone. Using the Holstein and Peierls models as examples, we demonstrate the formal equivalence between real-space and reciprocal-space surface hopping and assess their accuracy against mean-field mixed quantum-classical dynamics and numerically exact results. Having very similar equations of motion, reciprocal-space surface hopping can be straightforwardly incorporated in existing (real-space) surface hopping implementations.
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Affiliation(s)
- Alex Krotz
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
| | - Roel Tempelaar
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, USA
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