Extended Lagrangian Born–Oppenheimer molecular dynamics: from density functional theory to charge relaxation models

Niklasson, Anders M. N.

doi:10.1140/epjb/s10051-021-00151-6

Cited by 9 publications

(56 citation statements)

References 176 publications

(356 reference statements)

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“…The corresponding Kohn-Sham expressions are generated by replacing the universal energy functional with its orbital-dependent Kohn-Sham energy functional [26]. Generalization to Hartree-Fock theory and semi-empirical methods, as well as to coarse-grained orbital-free flexible charge models, should be straightforward [17].…”

Section: Generalized Shadow Functionals and Potentialsmentioning

confidence: 99%

“…The universal energy functional, F [ρ], includes all the electronelectron interactions and the kinetic energy term. To keep it general, we may also assume ensemble generalizations where F [ρ] accounts for thermal effects, including the entropy contribution at finite electronic temperatures [17,24,27,28,30,66,67]. In the corresponding Kohn-Sham DFT the thermal effects introduces fractional occupation numbers of the Kohn-Sham orbitals [27,28], which is important to be able to describe, for example, metallic systems at finite temperatures and to stabilize calculations of systems with a small or vanishing electronic energy gap.…”

Section: A Born-oppenheimer Potentialmentioning

confidence: 99%

“…Shadow molecular dynamics was originally introduced in the context of classical molecular mechanics. More recently, the concept of a shadow dynamics has been applied also to non-linear self-consistent field (SCF) theory in quantum-mechanical Born-Oppenheimer molecular dynamics (QMD) simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics (XL-BOMD) [10][11][12][13][14][15][16][17]. The idea of a shadow molecular dynamics has been applied also to the non-linear timedependent dynamics of superfluidity [18], as well as to flexible charge equilibration models [17,19].…”

Section: Introductionmentioning

confidence: 99%

“…In regular QMD simulations [17,20,21] the Born-Oppenheimer potential and the interatomic forces are calculated on-the-fly from the ground-state electronic structure, which is determined from an iterative SCF optimization of some constrained non-linear energy functional, that is given, for example, from Hartree-Fock or DFT [22][23][24][25][26][27][28][29][30]. In practice the iterative SCF optimization is never fully converged and always approximate.…”

Section: Introductionmentioning

confidence: 99%

“…In XL-BOMD the iterative SCF optimization procedure is avoided by including the electronic degrees of freedom as extended dynamical variables, in the spirit of Car-Parrinello molecular dynamics [17,36], in addition to the atomic positions and velocities. However, in contrast to Car-Parrinello molecular dynamics, a constrained optimization is still required to calculate the exact electronic ground state, but the optimization is performed for an approximate shadow energy functional.…”

Section: Introductionmentioning

confidence: 99%

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Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

Niklasson¹,

Negre²

2023

Preprint

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In Born-Oppenheimer molecular dynamics (BOMD) simulations based on density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which in practice never is fully converged. The calculated energies and the forces are therefore only approximate, which may lead to an unphysical energy drift and instabilities. Here we discuss an alternative shadow BOMD approach that is based on a backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies and forces, but for an underlying approximate shadow BO potential energy surface. In this way the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stability. We show how such shadow BO potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional there is a corresponding ground state BO potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "0th-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock or semi-empirical methods, as well as to coarse-grained flexible charge models.

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Section: Generalized Shadow Functionals and Potentialsmentioning

confidence: 99%

Section: A Born-oppenheimer Potentialmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

Niklasson¹,

Negre²

2023

Preprint

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Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Kulichenko

Barros

Lubbers

et al. 2023

J. Chem. Theory Comput.

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Extended Lagrangian Born–Oppenheimer molecular dynamics (XL-BOMD) in its most recent shadow potential energy version has been implemented in the semiempirical PyTorch-based software PySeQM. The implementation includes finite electronic temperatures, canonical density matrix perturbation theory, and an adaptive Krylov subspace approximation for the integration of the electronic equations of motion within the XL-BOMB approach (KSA-XL-BOMD). The PyTorch implementation leverages the use of GPU and machine learning hardware accelerators for the simulations. The new XL-BOMD formulation allows studying more challenging chemical systems with charge instabilities and low electronic energy gaps. The current public release of PySeQM continues our development of modular architecture for large-scale simulations employing semi-empirical quantum-mechanical treatment. Applied to molecular dynamics, simulation of 840 carbon atoms, one integration time step executes in 4 s on a single Nvidia RTX A6000 GPU.

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Shadow Molecular Dynamics and Atomic Cluster Expansions for Flexible Charge Models

Goff

Zhang

Negre

et al. 2023

J. Chem. Theory Comput.

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A shadow molecular dynamics scheme for flexible charge models is presented where the shadow Born−Oppenheimer potential is derived from a coarse-grained approximation of rangeseparated density functional theory. The interatomic potential, including the atomic electronegativities and the charge-independent short-range part of the potential and force terms, is modeled by the linear atomic cluster expansion (ACE), which provides a computationally efficient alternative to many machine learning methods. The shadow molecular dynamics scheme is based on extended Lagrangian (XL) Born−Oppenheimer molecular dynamics (BOMD) [Eur. Phys. J. B 2021, 94, 164]. XL-BOMD provides stable dynamics while avoiding the costly computational overhead associated with solving an all-to-all system of equations, which normally is required to determine the relaxed electronic ground state prior to each force evaluation. To demonstrate the proposed shadow molecular dynamics scheme for flexible charge models using atomic cluster expansion, we emulate the dynamics generated from self-consistent charge density functional tight-binding (SCC-DFTB) theory using a second-order charge equilibration (QEq) model. The charge-independent potentials and electronegativities of the QEq model are trained for a supercell of uranium oxide (UO 2 ) and a molecular system of liquid water. The combined ACE+XL-QEq molecular dynamics simulations are stable over a wide range of temperatures both for the oxide and for the molecular systems and provide a precise sampling of the Born−Oppenheimer potential energy surfaces. Accurate ground Coulomb energies are produced by the ACE-based electronegativity model during an NVE simulation of UO 2 , predicted to be within 1 meV of those from SCC-DFTB on average during comparable simulations.

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Extended Lagrangian Born–Oppenheimer molecular dynamics: from density functional theory to charge relaxation models

Cited by 9 publications

References 176 publications

Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

Shadow Energy Functionals and Potentials in Born-Oppenheimer Molecular Dynamics

Semi-Empirical Shadow Molecular Dynamics: A PyTorch Implementation

Shadow Molecular Dynamics and Atomic Cluster Expansions for Flexible Charge Models

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