Practical and reliable approximation of nonadiabatic coupling terms between triplet electronic states using only adiabatic potential energies

An, Heesun; Baeck, Kyoung Koo

doi:10.1016/j.cplett.2018.02.036

Cited by 7 publications

(7 citation statements)

References 31 publications

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“…Details of their model are surveyed in Section II. Baeck and An's numerical tests for different molecules have indeed shown an outstanding agreement between this simple approximation and the exact nonadiabatic coupling 27,28 . Our goal in this paper is to expand and explore the Baeck-An (BA) model to be used in surface hopping dynamics.…”

Section: Introductionmentioning

confidence: 72%

Fewest switches surface hopping with Baeck-An couplings

Casal¹,

Toldo²,

Pinheiro³

et al. 2021

Open Res Europe

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In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

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Section: Introductionmentioning

confidence: 72%

Fewest switches surface hopping with Baeck-An couplings

Casal¹,

Toldo²,

Pinheiro³

et al. 2021

Open Res Europe

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“…The approximation of NAC vectors, as explained in the main text and adapted from Refs. [11,93,94], relies on the approximation of the Hessian from energy potentials between two states. It is especially powerful for ML models trained on quantum chemistry methods, where implementations of NAC vectors are largely missing, such as linear-response methods and here especially between the first excited state and the ground state, with the ADC(2) method being a prominent example [106].…”

Section: Nac Approximation and Timingmentioning

confidence: 99%

“…After singular value decomposition, the hopping direction can be computed as the eigenvector, v ij , of the largest nonzero eigenvalue 101,104,105 with the corresponding eigenvalue, λ ij , as the squared magnitude of the ML smooth coupling, C ̃ij NAC . The final approximated NAC vectors, C ij aNAC , between two states are then…”

Section: = ⟨ψ| ̂|ψ⟩mentioning

confidence: 99%

“…The squared energy-gap Hessian can be further obtained as the sum of two symmetric dyads, that define the branching space [90]. Hence, this Hessian can be employed to obtain the symmetric dyad of the smooth NACs via [11,93]:…”

mentioning

confidence: 99%

“…The squared energy-gap Hessian can be further obtained as the sum of two symmetric dyads, which define the branching space . Hence, this Hessian can be employed to obtain the symmetric dyad of the smooth NACs via , After singular value decomposition, the hopping direction can be computed as the eigenvector, v ij , of the largest nonzero eigenvalue ,, with the corresponding eigenvalue, λ ij , as the squared magnitude of the ML smooth coupling, C ̃ ij NAC . The final approximated NAC vectors, C ij aNAC , between two states are then …”

mentioning

confidence: 99%

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Combining SchNet and SHARC: The SchNarc Machine Learning Approach for Excited-State Dynamics

Westermayr

Gastegger

Marquetand

2020

J. Phys. Chem. Lett.

169

298

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In recent years, deep learning has become a part of our everyday life and is revolutionizing quantum chemistry as well. In this work, we show how deep learning can be used to advance the research field of photochemistry by learning all important properties for photodynamics simulations. The properties are multiple energies, forces, nonadiabatic couplings and spin-orbit couplings. The nonadiabatic couplings are learned in a phasefree manner as derivatives of a virtually constructed property by the deep learning model, which guarantees rotational covariance. Additionally, an approximation for nonadiabatic couplings is introduced, based on the potentials, their gradients and Hessians. As deep-learning method, we employ SchNet extended for multiple electronic states. In combination with the molecular dynamics program SHARC, our approach termed SchNarc is tested on a model system and two realistic polyatomic molecules and paves the way towards efficient photodynamics simulations of complex systems.1 Excited-state dynamics simulations are powerful tools to predict, understand and explain photo-induced processes, especially in combination with experimental studies. Examples of photo-induced processes range from photosynthesis, DNA photodamage as the starting point of skin cancer, to processes that enable our vision [1][2][3][4][5]. As they are part of our everyday lives, their understanding can help to unravel fundamental processes of nature and to advance several research fields, such as photovoltaics [6,7], photocatalysis [8] or photosensitive drug design [9].Since the full quantum mechanical treatment of molecules remains challenging, exact quantum dynamics simulations are limited to systems containing only a couple of atoms, even if fitted potential energy surfaces (PESs) are used [10][11][12][13][14][15][16][16][17][18][19][20][21][22][23][24][25][26]. In order to treat larger systems in full dimensions, i.e., systems with up to 100s of atoms, and on long time scales, i.e., in the range of several 100 picoseconds, excited-state machine learning (ML) molecular dynamics (MD), where the ML model is trained on quantum chemistry data, has evolved as a promising tool in the last couple of years [27][28][29][30][31][32][33].Such nonadiabatic MLMD simulations are in many senses analog to excited-state ab initio molecular dynamics simulations. The only difference is that the costly electronic structure calculations are mostly replaced by a ML model, providing quantum properties like the PESs and the corresponding forces. The nuclei are assumed to move classically on those PESs. This mixed quantum-classical dynamics approach allows for a very fast on-the-fly evaluation of the necessary properties at the geometries visited during the dynamics simulations.In order to account for nonadiabatic effects, i.e., transitions from one state to another, further approximations have to be introduced [34]. One method, which is frequently used to account for such transitions, is the surface-hopping method originally developed by Tully [35]...

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Dynamics of FHCl Including Two Bidirectional Dissociation Channels: Comparative Study Using Quantum Nuclear Wavepackets and Semiclassical Trajectory Surface Hopping

Ariyageadsakul,

Baeck

2024

J. Phys. Chem. A

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The dynamics starting from the charge transfer excited state of neutral FHCl includes two bidirectional dissociation channels, producing "FH" and "Cl" fragments or "F" and "HCl" fragments by electron-transfer (ET) or proton-transfer (PT) processes, respectively. The quantum features of its dynamics were studied using the quantum dynamics of nuclear wavepacket propagation and the semiclassical dynamics of trajectory surface hopping propagation. The MS-CASPT2(17,11)/aug-cc-pVTZ method was used for calculating the energies of electronic states. Two critical quantum features identified in previous studies were the dominance of PT over ET and the ∼80 fs time gap between the onset of the earlier PT and the later ET processes. These features, in contrast to classical anticipation, were confirmed again, and their classical interpretations were developed based on the results of semiclassical dynamics. The relative location of nonadiabatic regions with respect to the starting point of dynamics and the activation of angular motion altering the HFCl angle play crucial roles in governing the two quantum features.

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Practical and reliable approximation of nonadiabatic coupling terms between triplet electronic states using only adiabatic potential energies

Cited by 7 publications

References 31 publications

Fewest switches surface hopping with Baeck-An couplings

Fewest switches surface hopping with Baeck-An couplings

Combining SchNet and SHARC: The SchNarc Machine Learning Approach for Excited-State Dynamics

Dynamics of FHCl Including Two Bidirectional Dissociation Channels: Comparative Study Using Quantum Nuclear Wavepackets and Semiclassical Trajectory Surface Hopping

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