Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only

Baeck, Kyoung Koo; An, Heesun

doi:10.1063/1.4975323

Cited by 29 publications

(37 citation statements)

References 55 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%

“…Recently, Baeck and An 27 conjectured that nonadiabatic couplings near an energy crossing point could be estimated from the simple 1D model ( )…”

Section: Introductionmentioning

confidence: 99%

“…Baeck and An pointed out two potential limitations of their model 27 . First, it is strictly valid for molecular configurations coupling only two states.…”

Section: Introductionmentioning

confidence: 99%

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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%

“…Recently, Baeck and An 27 conjectured that nonadiabatic couplings near an energy crossing point could be estimated from the simple 1D model ( )…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fewest switches surface hopping with Baeck-An couplings

Casal¹,

Toldo²,

Pinheiro³

et al. 2021

Open Res Europe

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“…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, 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 …”

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confidence: 99%

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

Westermayr

Gastegger

Marquetand

2020

J. Phys. Chem. Lett.

167

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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Topological studies related to molecular systems formed during the Big Bang: H₃⁺ as an example

Mukherjee

Shamasundar

Adhikari

et al. 2019

Int J of Quantum Chemistry

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In the present article are analyzed the non‐adiabatic coupling terms (NACT) for two molecular systems, namely H3+ and H3. In contrast to previous occasions in which the NACTs are studied along (closed) circular contours usually surrounding conical intersections (ci), in the present article are studied distribution of the NACTs in (planar) configuration spaces (CS). The motivation for this study has to do with a novel idea being mentioned earlier (Molec. Phys., 116, 2435 [2018]; ArXiv:1801.00103) that NACTs are like a Glue (eventually) associated with the ability of creating molecules and/or protecting them from breaking up. It was found that the distributions of the NACTs due to the two molecules are similar as long as the attention is given to regions close to their equilateral cis, but then they behave significantly different in other regions. In case of H3+, the NACTs are distributed rather uniformly whereas, in case of H3 they become spiky the closer they approach the diatom axis. The main conclusion of this study is that the glue which has its origin in the NACTs is most likely to be effective in case of H3+ that explains the creation and later survival of this molecule.

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Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only

Cited by 29 publications

References 55 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

Topological studies related to molecular systems formed during the Big Bang: H₃⁺ as an example

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Practical approximation of the non-adiabatic coupling terms for same-symmetry interstate crossings by using adiabatic potential energies only

Cited by 29 publications

References 55 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

Topological studies related to molecular systems formed during the Big Bang: H3+ as an example

Contact Info

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Topological studies related to molecular systems formed during the Big Bang: H₃⁺ as an example