<i>Ab initio</i>molecular dynamics: Analytically continued energy functionals and insights into iterative solutions

Arias, T. A.; Payne, M. C.; Joannopoulos, J. D.

doi:10.1103/physrevlett.69.1077

Cited by 239 publications

(138 citation statements)

References 11 publications

Supporting

Mentioning

135

Contrasting

Order By: Relevance

“…We have also found that 20 -25 % more computational effort is required for the calculation of interatomic forces in going from REF to MTMD. This is because the atoms move a longer distance at each MTMD step, as will be shown below, which makes the extrapolation of initial guesses less effective [50]. A similar effect was observed in our previous work on CMD [6].…”

Section: A Numerical Accuracysupporting

confidence: 64%

See 1 more Smart Citation

Ab initio mass tensor molecular dynamics

Tsuchida

2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

Mass tensor molecular dynamics was first introduced by Bennett [J. Comput. Phys. 19, 267 (1975)] for efficient sampling of phase space through the use of generalized atomic masses. Here, we show how to apply this method to ab initio molecular dynamics simulations with minimal computational overhead. Test calculations on liquid water show a threefold reduction in computational effort without making the fixed geometry approximation. We also present a simple recipe for estimating the optimal atomic masses using only the first derivatives of the potential energy.

show abstract

Section: A Numerical Accuracysupporting

confidence: 64%

“…The electronic states were quenched to the Born-Oppenheimer surface at each MD step with the limited-memory variant [47,48] of the quasi-Newton method [49]. The initial guesses were extrapolated from previous MD steps [50].…”

Section: Computational Detailsmentioning

confidence: 99%

Ab initio mass tensor molecular dynamics

Tsuchida

2011

The Journal of Chemical Physics

View full text Add to dashboard Cite

show abstract

“…(4) The expensive and inefficient evolution for the orbital rotations is now shifted to the matrix f ; this implies that the associated slow frequencies in the evolution of A have now been compressed to zero by the minimization condition. Subspace alignment [9] between subsequent orbital updates is also automatically enforced.…”

mentioning

confidence: 99%

Ensemble Density-Functional Theory forAb InitioMolecular Dynamics of Metals and Finite-Temperature Insulators

1997

Self Cite

View full text Add to dashboard Cite

A new method is presented for performing first-principles molecular-dynamics simulations of systems with variable occupancies. We adopt a matrix representation for the one-particle statistical operator Γ, to introduce a "projected" free energy functional G that depends on the Kohn-Sham orbitals only and that is invariant under their unitary transformations. The Liouville equation [Γ,Ĥ] = 0 is always satisfied, guaranteeing a very efficient and stable variational minimization algorithm that can be extended to non-conventional entropic formulations or fictitious thermal distributions.In recent years, the range of problems that can be studied with quantitative accuracy using the methods of computational solid state physics has expanded dramatically. It is now possible to calculate many materials properties with an accuracy that is often comparable to that of experiments. This degree of confidence is based on the fundamental quantum-mechanical treatment offered by density-functional theory (DFT) [1], coupled with the availability of increasingly powerful computers and with the development of algorithms tuned towards optimal performance [2].The application of these methods and techniques to metallic systems has nonetheless encountered several difficulties, that have made progress slower than for the case of semiconductors and insulators. The discontinuous variation of the orbital occupancies across the Brillouin zone (BZ) makes the occupation numbers rather ill-conditioned variables, and the self-consistent solution of the screening problem can suffer from several instabilities. The absence of a gap in the energy spectrum and the requirement of an exact diagonalization for the Hamiltonian matrix everywhere in the BZ (in order to assign the occupation numbers) introduce "slow frequencies" in the evolution of the orbitals towards the ground state and preclude the straightforward extension to metals of algorithms which performed well for insulators. Smearing the Fermi surface with a finite electronic temperature [3] allows for an improved BZ sampling, but only partially alleviates the problems alluded to above.In this Letter, we introduce a new approach which solves many of these problems in a natural way, and which provides a general and efficient framework for obtaining the ground state of a Kohn-Sham Hamiltonian at a finite electronic temperature. The typical context is the Mermin formulation for the Fermi-Dirac statistics [4], but the method also applies when generalized entropic functionals are introduced [5], as it is often the case for metallic systems. Other applications include DFT studies of insulators or semiconductors with thermally excited states [6], and fractional quantum Hall states [7]. The language of ensemble-DFT [8] is used, and an orbitalbased variational algorithm for the minimization to the ground state is developed and implemented. Dramatic improvements are obtained in the convergence of the energies and especially of the Hellmann-Feynman forces.Within ensemble-DFT, the Helmholtz free energy fun...

show abstract

“…Within the above approximations, we determine the quantum state of the system by minimizing the total energy over all possible sets of orthonormal electronic wavefunctions using the analytically-continued functional approach [16,23], which has been recently shown to be nearly optimal in a rigorous mathematical sense [24]. The calculations are performed within the DFT ++ formalism [25,26] which makes different physical descriptions (LDA, LSDA, SIC, Hartree-Fock, etc.)…”

Section: Methodsmentioning

confidence: 99%

Ab Initio Study of Magnetic Structure and Chemical Reactivity of Cr₂O₃ and Its (0001) Surface

2000

View full text Add to dashboard Cite

We present the first ab initio density functional theory study of the oxygen-terminated Cr2O3 (0001) surface within the local spin-density approximation (LSDA). We find that spin plays a critical role for even the most basic properties of Cr2O3 such as the structure and mechanical response of the bulk material. The surface exhibits strong relaxations and changes in electronic and magnetic structure with important implications for the chemical reactivity and unusual spin-dependent catalytic activity of the surface. Unlike the bulk, the outermost chromium bilayer is ferromagnetically ordered, and the surface oxygen layer exhibits appreciable net spin polarization in the opposite sense. Surprisingly, despite this ferrimagnetic order, the chemically important states near the Fermi level exhibit ferromagnetic order and thus favor electronic spin alignment of species interacting with the surface. Finally, we also find a high density of unoccupied electronic surface states available to participate in the chemical reactivity of the surface.

show abstract

Ab initiomolecular dynamics: Analytically continued energy functionals and insights into iterative solutions

Cited by 239 publications

References 11 publications

Ab initio mass tensor molecular dynamics

Ab initio mass tensor molecular dynamics

Ensemble Density-Functional Theory forAb InitioMolecular Dynamics of Metals and Finite-Temperature Insulators

Ab Initio Study of Magnetic Structure and Chemical Reactivity of Cr₂O₃ and Its (0001) Surface

Contact Info

Product

Resources

About

Ab initiomolecular dynamics: Analytically continued energy functionals and insights into iterative solutions

Cited by 239 publications

References 11 publications

Ab initio mass tensor molecular dynamics

Ab initio mass tensor molecular dynamics

Ensemble Density-Functional Theory forAb InitioMolecular Dynamics of Metals and Finite-Temperature Insulators

Ab Initio Study of Magnetic Structure and Chemical Reactivity of Cr2O3 and Its (0001) Surface

Contact Info

Product

Resources

About

Ab Initio Study of Magnetic Structure and Chemical Reactivity of Cr₂O₃ and Its (0001) Surface