An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and “magnetic” forces

Miao, Gaohan; Bellonzi, Nicole; Subotnik, Joseph E.

doi:10.1063/1.5088770

Cited by 36 publications

(55 citation statements)

References 71 publications

(102 reference statements)

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“…FSSH dictates motion along adiabats and the algorithm will not predict any bending or reflection; for this reason, in Ref. 37, we have recommended augmenting FSSH dynamics with the Berry force F B (in Eq. 6) in order to better agree with the QCLE and capture the correct quantum dynamics.…”

Section: Discussion: Implications For Semiclassical Dynamicsmentioning

confidence: 99%

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A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians

Subotnik

Miao

Bellonzi

et al. 2019

The Journal of Chemical Physics

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Although the quantum classical Liouville equation (QCLE) arises by cutting off the exact equation of motion for a coupled nuclear-electronic system at order 1 (1 = 0 ), we show that the QCLE does include Berry's phase effects and Berry's forces (which are proportional to a higher order, = 1 ). Thus, the fundamental equation underlying mixed quantum-classical dynamics does not need a correction for Berry's phase effects and is valid for the case of complex Hamiltonians. Furthermore, we also show that, even though Tully's surface hopping model ignores Berry's phase, Berry's phase effects are included automatically within Ehrenfest dynamics. These findings should be of great importance if we seek to model coupled nuclearelectronic dynamics for systems with spin-orbit coupling, where the complex nature of the Hamiltonian is

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Section: Discussion: Implications For Semiclassical Dynamicsmentioning

confidence: 99%

“…Unfortunately, preliminary evidence suggests that the algorithms in Ref. 37 are not yet optimal; perhaps the different form of the QCLE (as present in Eqs. 5 and A1) will be useful for future derivations.…”

Section: Discussionmentioning

confidence: 99%

A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians

Subotnik

Miao

Bellonzi

et al. 2019

The Journal of Chemical Physics

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“…Recent dynamical work has suggested that the imaginary component of NADCs can yield very rich new physical behaviors. 42 In particular, whenever the derivative coupling d is complex, such complexity automatically introduces nontrivial Berry phase effects, 72,73 whereby a given trajectory moving on adiabat J with momentum ⃗ p should feel a force, 42,74…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless, one must presume that semiclassical mechanics are possible with complex NADCs, and a recent work has explored various ansätze for the extension of FSSH with complex-valued NADCs. 42 Since the overall phases of the adiabats are not well defined, the total phase of the derivative coupling is not well-defined, and choosing a direction of momentum rescaling is not obvious. Previous work in Ref.…”

Section: Article Scitationorg/journal/jcpmentioning

confidence: 99%

“…Previous work in Ref. 42 has suggested that one possible choice for momentum rescaling is the direction of the NADC between the participating states, as rotated to have the maximum norm in the real-valued component; and yet, (unpublished) data suggest that this ansatz may not be completely general. To date, the optimal direction for rescaling momenta likely remains unknown.…”

Section: Article Scitationorg/journal/jcpmentioning

confidence: 99%

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TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

Bellonzi

Alguire

Fatehi

et al. 2020

The Journal of Chemical Physics

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We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S 1 /T 2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde.

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Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy

Bian

Teh

et al. 2022

J. Chem. Theory Comput.

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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 “m s ” 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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An extension of the fewest switches surface hopping algorithm to complex Hamiltonians and photophysics in magnetic fields: Berry curvature and “magnetic” forces

Cited by 36 publications

References 71 publications

A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians

A demonstration of consistency between the quantum classical Liouville equation and Berry’s phase and curvature for the case of complex Hamiltonians

TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy

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