Transforming high-dimensional potential energy surfaces into a canonical polyadic decomposition using Monte Carlo methods

Schröder, Markus

doi:10.1063/1.5140085

Cited by 40 publications

(77 citation statements)

References 58 publications

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“…The kinetic energy operators are in the sum-of-products form, while potential energy operators must be expanded in the product form representation. Within the MCTDH code, 55 the POTFIT approach 62 is the default procedure to transform low-dimensional PESs to the product form, while for treating systems of larger dimensionality, alternatives, such as the n -mode representation, 63 the multigrid POTFIT, 64 Monte Carlo POTFIT (MCPOTFIT), 65 or those reported more recently, such as the Monte Carlo canonical polyadic decomposition (MCCPD) 66 and the rectangular collocation MCTDH (RC-MCTDH) 67 methods are used.…”

Section: Computational Detailsmentioning

confidence: 99%

Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features

Carrillo‐Bohórquez

Valdés

Prosmiti

2021

J. Chem. Theory Comput.

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We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational–rotational–vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C 60 fullerene by means of such a systematic approach that includes all nine degrees of freedom of H 2 O@C 60 and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n -mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H 2 O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H 2 O@C 60 are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest–host interactions.

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Section: Computational Detailsmentioning

confidence: 99%

Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features

Carrillo‐Bohórquez

Valdés

Prosmiti

2021

J. Chem. Theory Comput.

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“…Schröder has recently introduced new ideas for making CP PESs. 238 An important advantage of EXPNN is that its memory cost is low. It can be used for molecular systems for which a tensor product grid would be so large that the potential could not be stored on the grid.…”

Section: Sop Nnmentioning

confidence: 99%

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

2020

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We review progress in neural network (NN) based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods which impose structure (such as a multi-body representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions, including dimensionality reduction. We consider NN based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

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“…If the Hamiltonian does not have the required form it can, at the cost of some extra calculations, be replaced by an operator that is approximately equal to the original Hamiltonian, but does have the required form. [44][45][46][47][48] For many molecules with more than five atoms, the best available PES is a SOP. 49 a variational calculation, it requires a lot of computer time.…”

Section: Introductionmentioning

confidence: 99%

Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

Kallullathil

Carrington

2021

Preprint

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Present day computers do not have enough memory to store the high-dimensional tensors required when using a direct product basis to compute vibrational energy levels of a polyatomic molecule with more than about 5 atoms. One way to deal with this problem is to represent tensors using a tensor format. In this paper, we use CP format. Energy levels are computed by building a basis from vectors obtained by solving linear equations. The method can be thought of as a CP realization of a block inverse iteration method with multiple shifts. The CP rank of the tensors is fixed and the linear equations are solved with an Alternating Least Squares method. There is no need for rank reduction, no need for orthogonalization, and tensors with rank larger than the fixed rank used to solve the linear equations are never generated. The ideas are tested by computing vibrational energy levels of a 64-D bilinearly coupled model Hamiltonian and of acetonitrile(12-D).

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Transforming high-dimensional potential energy surfaces into a canonical polyadic decomposition using Monte Carlo methods

Cited by 40 publications

References 58 publications

Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features

Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

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Transforming high-dimensional potential energy surfaces into a canonical polyadic decomposition using Monte Carlo methods

Cited by 40 publications

References 58 publications

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

Computing vibrational energy levels by solving linear equations using a tensor method with an imposed rank

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Product

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Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features

Encapsulation of a Water Molecule inside C₆₀ Fullerene: The Impact of Confinement on Quantum Features