Evaluating Hellmann–Feynman forces within non-local pseudopotentials

Novák, Matyáš; Vackář, Jiří; Cimrman, Robert

doi:10.1016/j.cpc.2019.107034

Cited by 8 publications

(3 citation statements)

References 31 publications

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“…The transpiler and einsum expression based weak form implementations are available in SfePy from version 2021.1, allowing a rapid prototyping of multi-physical finite element models and subsequent calculations in various fields such as biomechanics [30] or solid state physics [22]. All data used in preparation of this paper are available online [8].…”

Section: Discussionmentioning

confidence: 99%

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Cimrman

2021

Preprint

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In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit loops, using a single tensor contraction expression by employing the Einstein summation convention. To automate this process and leverage existing high performance codes, we first introduce a notation allowing trivial differentiation of multi-linear finite element forms. Based on that we propose and describe a new transpiler from Einstein summation based expressions, augmented to allow defining multi-linear finite element weak forms, to regular tensor contraction expressions. The resulting expressions are compatible with a number of Python scientific computing packages, that implement, optimize and in some cases parallelize the general tensor contractions. We assess the performance of those packages, as well as the influence of operand memory layouts and tensor contraction paths optimizations on the elapsed time and memory requirements of the finite element form evaluations. We also compare the efficiency of the transpiled weak form implementations to the C-based functions available in the finite element package SfePy.

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Section: Discussionmentioning

confidence: 99%

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Cimrman

2021

Preprint

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“…The spin-dependent density of states (DOS) and band structures are visualized with a denser 48 × 48 × 1 Γ centered k -grid. The trilayer is relaxed after fixing the lattice parameters of the supercell until the Hellmann–Feynman force on all atoms is less than 10 –3 eV Å –1 . A vacuum separation of 20 Å is considered along the aperiodic z -axis to avoid interactions between neighboring images .…”

Section: Simulation Methodsmentioning

confidence: 99%

Effect of Magnetic Tuning and Induced Charge Transfer Isotropy in a CrI₃-Based 2D Trilayer Heterostructure

Chakraborty

Ravikumar

2022

J. Phys. Chem. C

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We predict the induction/suppression of Chern insulating states in graphene and semiconductor to metal phase transition in MoS 2 under the influence of magnetic tuning of CrI 3 from a ferromagnetic (FM) case to an antiferromagnetic (AFM) one. We examine the spin-dependent electronic structure of the trilayer constructed with a 2D magnetic insulator (CrI 3 ) sandwiched between graphene and MoS 2 using first principle calculations. We observe that the induced σ z lattice strain breaks the symmetry of graphene's Dirac cone (which shows a bandgap of ∼0.47 eV), and the interlayer charge transfer results in a metallic trilayer. In the ferromagnetic case, for the spin-down channel, the Dirac cone split lies in the bandgap of CrI 3 , inducing Chern insulating states of graphene. As we switch to an antiferromagnetic case, graphene loses its Chern insulating states and hybridizes with the substrate in both of the spin channels. When spin−orbit coupling interactions are considered, the Dirac cone split of graphene is preserved which now lies in the bandgap of CrI 3 , enhancing its Chern insulating properties. Hexagonal MoS 2 however shows a semiconductor to metal transition in both the FM and the AFM cases which we believe has not been reported previously. Under the effect of spin− orbit coupling, the valence bands of MoS 2 shift above the Fermi level, retaining the semiconductor to metal transition. The effects examined in this work could lead to the design of CrI 3 -based 2D MOS-like devices with potential applications in ultrathin supercapacitors and quantum transistors.

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“…The original concept of the Hellman-Feynman force uniquely identifies atomic nuclei in molecules 28,29 :…”

Section: Introduction: the Search For Atomsmentioning

confidence: 99%

Monitoring Evolution of Atoms and Bonds on a Reaction Path by the Reaction Fragility Method

Ordon

Komorowski

2022

Preprint

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. The theoretic foundations of the novel method for the comprehensive studies on the mechanism of the evolution of the electronic structure in a chemical reaction have been presented. Our method provides quantification for both the sequence of bond forming and breaking and the degree of bond (order) modifications along the chemical reaction path. The new Density Functional Connectivity Matrix has been introduced: its elements are the divergences of the Hellmann–Feynman forces for atoms in a molecule over the atomic displacements. They have been proved to describe to what extend atoms in a molecule are actually connected with chemical bonds or bonding interactions. The matrix provided foundation for the Reaction Fragility Method. (i) With the use of the Conceptual Density Functional Theory we have completed the road map to characterization of the properties of atoms and bonds in a molecule. We have derived the new gradient theorem, essential for demonstrating the direct link between divergences of the Hellman-Feynman forces on the nuclei and the linear response function of electron density. (ii) The vibrational energy of a system has been decomposed into the atomic fragility modes through diagonalization of the DF Connectivity Matrix, by analogy with the formalism of the normal modes. We present numerical results for the evolution of the atomic fragility modes on the reaction path in the test reaction of the internal proton transfer in H2N-CHO molecule. The visualization of the involvement of bonds and/or contacts between individual atoms on consecutive steps of the reaction has been demonstrated. (iii) The bond fragilities introduced in previous works clearly deliver description of the anharmonic effects for all bonds/contacts in the reacting system. Here we demonstrate how the bond fragilities provide a unique measure of the anharmonic effects in the system, reflecting the response of the vibrational electronic energy to changes in the distances between atoms. The additive contributions from all bonds are combined to the unique global anharmonicity parameter, the third electron energy derivative over the reaction progress. This quantity can be used as a measure of the global changes in a molecule, when they are triggered step by step along a specific reaction path.

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Evaluating Hellmann–Feynman forces within non-local pseudopotentials

Cited by 8 publications

References 31 publications

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Effect of Magnetic Tuning and Induced Charge Transfer Isotropy in a CrI₃-Based 2D Trilayer Heterostructure

Monitoring Evolution of Atoms and Bonds on a Reaction Path by the Reaction Fragility Method

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Evaluating Hellmann–Feynman forces within non-local pseudopotentials

Cited by 8 publications

References 31 publications

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Effect of Magnetic Tuning and Induced Charge Transfer Isotropy in a CrI3-Based 2D Trilayer Heterostructure

Monitoring Evolution of Atoms and Bonds on a Reaction Path by the Reaction Fragility Method

Contact Info

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Effect of Magnetic Tuning and Induced Charge Transfer Isotropy in a CrI₃-Based 2D Trilayer Heterostructure