Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

Alborzpour, Jonathan P.; Tew, David P.; Habershon, Scott

doi:10.1063/1.4964902

Cited by 56 publications

(55 citation statements)

References 88 publications

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“…This subset is defined by the choice of DVR and it is the configuration subspace defined by this selection in which the GPR approximation 180 of the PES is constructed. With regards to the GPR, we note that we used α=0.5 in all simulations reported here (see equation (5)); earlier work has shown that variation of this parameter within a reasonable range should give give little overall 185 change in the results presented below [38].…”

Section: Methodsmentioning

confidence: 99%

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Richings

Habershon

2017

Chemical Physics Letters

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100

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We present a method for performing non-adiabatic, grid-based nuclear quantum dynamics calculations using diabatic potential energy surfaces (PESs) generated "on-the-fly". Gaussian process regression is used to interpolate PESs by using electronic structure energies, calculated at points in configuration space determined by the nuclear dynamics, and diabatising the results using the propagation diabatisation method reported recently [J. Phys. Chem. A, 119, 12457 -12470 (2015)]. To test this new method, the nuclear dynamics on the ground and first electronic excited states of the butatriene cation is studied using a grid-based method. The evolution of diabatic state populations is in very good agreement with those produced using a fitted potential. Overall, our scheme offers a route towards accurate quantum dynamics on diabatic PESs learnt on-the-fly.Keywords: Direct-dynamics, Diabatisation, Grid-based quantum dynamics, Butatriene 2010 MSC: 00-01, 99-00The study of nuclear quantum dynamics of nuclei is of great importance in helping to understand of the time-evolution of molecular systems upon excitation of the electronic degrees-of-freedom (DOFs); such simulations can make direct connections to the states. [6,7] One can model these non-adiabatic transitions using classical mechanics, as in the trajectory surface hopping (TSH) algorithm, [2,[8][9][10] but as the dynamics are inherently quantum mechanical, it is better to use a quantum mechani-25 cal method such as the multi-configuration timedependent Hartree (MCTDH) approach [1, 11,12] where possible.The major bottleneck in performing quantum dynamics calculations is usually not the wavefunc-30 tion time-propagation, but the creation of an appropriate PES on which to run the dynamics. As quantum mechanics is non-local, one needs a PES which is known everywhere in the configuration space of the nuclear motion prior to running the 35 dynamics. For the fully quantum mechanical study of non-adiabatic systems it is usually necessary to convert the PESs from the adiabatic representation to a diabatic representation. The adiabatic representation of the potential is an energy-ordered set 40 of PESs, and corresponds to the energies generated by electronic structure programs. However, at points in configuration space where adiabatic surfaces become degenerate, such as at conical interePreprint submitted to Chemical Physics Letters December 20, 2016 sections (CIs), there is a discontinuity in the gradi-45 ent of the states, such that the adiabatic states are no longer smooth; furthermore, the coupling between the states at these points is also infinite. Neither property of the adiabatic PESs is conducive to performing wavepacket dynamics, so transforma-50 tion to the diabatic representation is performed, resulting in smoothly varying surfaces with finite couplings. Diabatic representations are not unique for a given set of adiabatic states, so an appropriate diabatisation scheme must be chosen before the 55 PES can be used in a dynamics calculation. PESs are usua...

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Section: Methodsmentioning

confidence: 99%

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Richings

Habershon

2017

Chemical Physics Letters

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100

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“…One can then Taylor expand the electronic energy and/or nonadiabatic coupling about this centroid and evaluate the resulting integral analytically. 113,127,[139][140] As an example, we consider the expansion of the intrastate coupling term -containing the electronic energybetween two TBFs k and i with centroid position R ki…”

Section: Ab Initio Multiple Spawningmentioning

confidence: 99%

Ab Initio Nonadiabatic Quantum Molecular Dynamics

2018

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The Born-Oppenheimer approximation underlies much of chemical simulation and provides the framework defining the potential energy surfaces that are used for much of our pictorial understanding of chemical phenomena. However, this approximation breaks down when the dynamics of molecules in excited electronic states are considered. Describing dynamics when the Born-Oppenheimer approximation breaks down requires a quantum mechanical description of the nuclei. Chemical reaction dynamics on excited electronic states is critical for many applications in renewable energy, chemical synthesis, and bioimaging. Furthermore, it is necessary in order to connect with many ultrafast pump-probe spectroscopic experiments. In this review, we provide an overview of methods that can describe nonadiabatic dynamics, with emphasis on those that are able to simultaneously address the quantum mechanics of both electrons and nuclei. Such ab initio quantum molecular dynamics methods solve the electronic Schrödinger equation alongside the nuclear dynamics and thereby avoid the need for precalculation of potential energy surfaces and nonadiabatic coupling matrix elements. Two main families of methods are commonly employed to simulate nonadiabatic dynamics in molecules: full quantum dynamics, such as the multiconfigurational time-dependent Hartree method, and classical trajectory-based approaches, such as trajectory surface hopping. In this review, we describe a third class of methods that is intermediate between the two: Gaussian basis set expansions built around trajectories.

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“…31,37 Since the Hessians are not needed for the propagation of the classical trajectory, additional speed-up is achieved through parallel computation of the Hessians after the full trajectory is known. Note that other Hessian approximations, such as the Hessian update schemes [38][39][40] and Gaussian process regression 41,42 have been developed in the context of ab initio simulations. The considerable cost of multiple Hessian evaluations has also inspired various semiclassical approximations, 43 including the prefactor-free, 22 adiabatic, 44,45 harmonic, 43 and "poor person's" 46 variations of the Herman-Kluk propagator.…”

Section: Hessian Interpolationmentioning

confidence: 99%

Single-Hessian thawed Gaussian approximation

Begušić

Cordova

Vaníček

2019

The Journal of Chemical Physics

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To alleviate the computational cost associated with on-the-fly ab initio semiclassical calculations of molecular spectra, we propose the single-Hessian thawed Gaussian approximation, in which the Hessian of the potential energy at all points along an anharmonic classical trajectory is approximated by a constant matrix. The spectra obtained with this approximation are compared with the exact quantum spectra of a one-dimensional Morse potential and with the experimental spectra of ammonia and quinquethiophene. In all cases, the single-Hessian version performs almost as well as the much more expensive on-the-fly ab initio thawed Gaussian approximation and significantly better than the global harmonic schemes. Remarkably, unlike the thawed Gaussian approximation, the proposed method conserves energy exactly, despite the time dependence of the corresponding effective Hamiltonian, and, in addition, can be mapped to a higher-dimensional time-independent classical Hamiltonian system.We also provide a detailed comparison with several related approximations used for accelerating prefactor calculations in semiclassical simulations.

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Efficient and accurate evaluation of potential energy matrix elements for quantum dynamics using Gaussian process regression

Cited by 56 publications

References 88 publications

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Direct grid-based quantum dynamics on propagated diabatic potential energy surfaces

Ab Initio Nonadiabatic Quantum Molecular Dynamics

Single-Hessian thawed Gaussian approximation

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