| 1. |
- Odell, Anders, et al.
(författare)
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Higher-order symplectic integration in Born-Oppenheimer molecular dynamics
- 2009
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 131:24
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Tidskriftsartikel (refereegranskat)abstract
- The extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, C. J. Tymczak, and M. Challacombe, Phys. Rev. Lett. 100, 123004 (2008); Phys. Rev. Lett. 97, 123001 (2006)] enables the use of geometric integrators in the propagation of both the nuclear and the electronic degrees of freedom on the Born-Oppenheimer potential energy surface. Different symplectic integrators up to the sixth order have been adapted and optimized in the framework of ab initio self-consistent-field theory. It is shown how the accuracy can be significantly improved compared to a conventional Verlet integration at the same level of computational cost, in particular, for the case of very high accuracy requirements.
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| 2. |
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| 3. |
- Finkelstein, Joshua, et al.
(författare)
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Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective
- 2021
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 17:4, s. 2256-2265
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Tidskriftsartikel (refereegranskat)abstract
- We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for half-precision floating point operations on Nvidia’s A100 tensor core units. The second-order recursive Fermi-operator scheme is formulated in terms of a generalized, differentiable deep neural network structure, which solves the quantum mechanical electronic structure problem. We demonstrate how this network can be accelerated by optimizing the weight and bias values to substantially reduce the number of layers required for convergence. We also show how this machine learning approach can be used to optimize the coefficients of the recursive Fermi-operator expansion to accurately represent the fractional occupation numbers of the electronic states at finite temperatures.
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| 4. |
- Finkelstein, Joshua, et al.
(författare)
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Quantum-Based Molecular Dynamics Simulations Using Tensor Cores
- 2021
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 17:10, s. 6180-6192
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Tidskriftsartikel (refereegranskat)abstract
- Tensor cores, along with tensor processing units, represent a new form of hardware acceleration specifically designed for deep neural network calculations in artificial intelligence applications. Tensor cores provide extraordinary computational speed and energy efficiency but with the caveat that they were designed for tensor contractions (matrix-matrix multiplications) using only low-precision floating-point operations. Despite this perceived limitation, we demonstrate how tensor cores can be applied with high efficiency to the challenging and numerically sensitive problem of quantum-based Born-Oppenheimer molecular dynamics, which requires highly accurate electronic structure optimizations and conservative force evaluations. The interatomic forces are calculated on-the-fly from an electronic structure that is obtained from a generalized deep neural network, where the computational structure naturally takes advantage of the exceptional processing power of the tensor cores and allows for high performance in excess of 100 Tflops on a single Nvidia A100 GPU. Stable molecular dynamics trajectories are generated using the framework of extended Lagrangian Born-Oppenheimer molecular dynamics, which combines computational efficiency with long-term stability, even when using approximate charge relaxations and force evaluations that are limited in accuracy by the numerically noisy conditions caused by the low-precision tensor core floating-point operations. A canonical ensemble simulation scheme is also presented, where the additional numerical noise in the calculated forces is absorbed into a Langevin-like dynamics.
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| 5. |
- Finkelstein, Joshua, et al.
(författare)
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Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network
- 2022
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Ingår i: Journal of Chemical Theory and Computation. - : American Chemical Society (ACS). - 1549-9618 .- 1549-9626. ; 18:7, s. 4255-4268
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Tidskriftsartikel (refereegranskat)abstract
- Time-independent quantum response calculations are performed using Tensor cores. This is achieved by mapping density matrix perturbation theory onto the computational structure of a deep neural network. The main computational cost of each deep layer is dominated by tensor contractions, i.e., dense matrix–matrix multiplications, in mixed-precision arithmetics, which achieves close to peak performance. Quantum response calculations are demonstrated and analyzed using self-consistent charge density-functional tight-binding theory as well as coupled-perturbed Hartree–Fock theory. For linear response calculations, a novel parameter-free convergence criterion is presented that is well-suited for numerically noisy low-precision floating point operations and we demonstrate a peak performance of almost 200 Tflops using the Tensor cores of two Nvidia A100 GPUs.
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| 6. |
- Gómez, M.M., et al.
(författare)
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Dye-sensitized sputtered titanium oxide films for photovoltaic applications : influence of the O2/Ar gas flow ratio during the deposition
- 2003
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Ingår i: Solar Energy Materials and Solar Cells. - 0927-0248 .- 1879-3398. ; 76:1, s. 37-56
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Tidskriftsartikel (refereegranskat)abstract
- Titanium oxide films were prepared by reactive DC magnetron sputtering onto SnO2:F coated glass substrates. The O-2/Ar gas flow ratio was kept at a constant value Gamma during the deposition, and a series of films were deposited with 0.050 < Gamma < 0.072. Structural studies were performed by X-ray diffraction and transmission electron microscopy; the structure displayed penniform features with a clear dependence on F. Charge transport in the films was evaluated by use of time-resolved photocurrents; a diffusion model was fitted to the experimental data and two different transport mechanisms were proposed depending on the film stoichiometry. Dye sensitization in cis-dithiocyanato-bis(2,2'-bipyridyl-4,4'-dicarboxylate) ruthenium (II) was performed to evaluate incident photon-to-current conversion efficiency and solar cell properties of the films. These parameters showed a clear dependence on Gamma. Optical measurements gave evidence for the presence of polaron absorption for the film deposited at Gamma = 0.050.
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| 7. |
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| 8. |
- Niklasson, Anders M. N., et al.
(författare)
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Extended Lagrangian Born-Oppenheimer molecular dynamics with dissipation
- 2009
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Ingår i: JOURNAL OF CHEMICAL PHYSICS. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 130:21, s. 148075-
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Tidskriftsartikel (refereegranskat)abstract
- Stability and dissipation in the propagation of the electronic degrees of freedom in time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics [Niklasson , Phys. Rev. Lett. 97, 123001 (2006); Phys. Rev. Lett. 100, 123004 (2008)] are analyzed. Because of the time-reversible propagation the dynamics of the extended electronic degrees of freedom is lossless with no dissipation of numerical errors. For long simulation times under "noisy" conditions, numerical errors may therefore accumulate to large fluctuations. We solve this problem by including a dissipative external electronic force that removes noise while keeping the energy stable. The approach corresponds to a Langevin-like dynamics for the electronic degrees of freedom with internal numerical error fluctuations and external, approximately energy conserving, dissipative forces. By tuning the dissipation to balance the numerical fluctuations the external perturbation can be kept to a minimum.
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| 9. |
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| 10. |
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| 11. |
- Odell, Anders, et al.
(författare)
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Geometric integration in Born-Oppenheimer molecular dynamics
- 2011
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 135:22, s. 224105-
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Tidskriftsartikel (refereegranskat)abstract
- Geometric integration schemes for extended Lagrangian self-consistent Born-Oppenheimer moleculardynamics, including a weak dissipation to remove numerical noise, are developed and analyzed.The extended Lagrangian framework enables the geometric integration of both the nuclear and electronicdegrees of freedom. This provides highly efficient simulations that are stable and energy conservingeven under incomplete and approximate self-consistent field (SCF) convergence. We investigatethree different geometric integration schemes: (1) regular time reversible Verlet, (2) secondorder optimal symplectic, and (3) third order optimal symplectic. We look at energy conservation,accuracy, and stability as a function of dissipation, integration time step, and SCF convergence. Wefind that the inclusion of dissipation in the symplectic integration methods gives an efficient dampingof numerical noise or perturbations that otherwise may accumulate from finite arithmetics in aperfect reversible dynamics.
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| 12. |
- Odell, Anders, 1979-, et al.
(författare)
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Geometric integration in extended lagrangian self consistent tight-binding molecular dynamics
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- Geometric integration schemes for extended Lagrangian self-consistent tight-binding molecular dynamics, including a weak dissipation to remove numerical noise, are developed and analyzed. The extended Lagrangian framework enables the geometric integration of both the nuclear andelectronic degrees of freedom. This provides highly effcient simulations that are stable and energy conserving even under incomplete and approximate self-consistent field (SCF) convergence. We investigate three different geometric integration schemes: i) regular time reversible Verlet, ii) secondorder optimal symplectic, and iii) third order optimal symplectic. We look at energy conservation, accuracy and stabilitty as a function of dissipation, integration time step, and SCF convergence. We find that the inclusion of dissipation in the symplectic integration methods gives an efficient damping of numerical noise or perturbations that otherwise may accumulate from finite arithmetics in a perfect reversible dynamics. The modification of the integration breakes symplecticity and introduces a global energy drift. The systematic drift in energy and the broken symplecticity can be kept arbitrarily small without significant perturbations of the molecular trajectories. However, we have yet to find a formalism for the inclusion of the dissipation in higher-order symplectic integration methods with a more optimal balance between efficient damping and minimal global energy drift.
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| 13. |
- Bergman, Anders, et al.
(författare)
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Magnetism of Fe clusters embedded in a Co matrix from first-principles theory
- 2004
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - 1098-0121 .- 1550-235X. ; 70:17, s. 174446-
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Tidskriftsartikel (refereegranskat)abstract
- We have calculated spin and orbital moments for Fe clusters of sizes up to 700 atoms embedded as impurities in a bcc Co matrix. The calculations have been carried out using relativistic first-principles real-space density functional theory, and we have made a comparison with earlier experimental studies. For Fe atoms close to theFeCo interface, the spin moments are found to increase while atoms far from the interface exhibit bulklike moments. The Co moments remain essentially unchanged and close to the moment of bulk bcc Co. With increasing cluster size, the average moments of the cluster atoms decrease due to the decreased surface to volume ratio. The orbital moments of both Fe and Co are calculated to be small and they stay almost constant regardless of cluster size. Our results for spin moments agree with experimental data but the calculated orbital moments are slightly underestimated. A simplified model indicates that a compound of close-packed Fe clusters surrounded by Co show higher average total moments compared to bulk and multilayer systems with a similar concentration. This increase seems to disappear when cluster-cluster interactions are taken into account. The general trend is that for a given alloy concentration of FexCo1−x, clustering tends to lower the average magnetic moment compared to that of ordered structures and random alloys.
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| 14. |
- Henning, Patrick, 1983-, et al.
(författare)
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Shadow Lagrangian Dynamics For Superfluidity
- 2021
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Ingår i: Kinetic and Related Models. - : American Institute of Mathematical Sciences (AIMS). - 1937-5093 .- 1937-5077. ; 14:2, s. 303-321
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Tidskriftsartikel (refereegranskat)abstract
- Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrodinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrodinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.
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| 15. |
- Niklasson, Anders M. N., et al.
(författare)
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Canonical density matrix perturbation theory
- 2015
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Ingår i: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. - 1539-3755 .- 1550-2376. ; 92, s. 063301:1-8
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Tidskriftsartikel (refereegranskat)
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| 16. |
- Niklasson, Anders M. N.
(författare)
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Extended Born-Oppenheimer molecular dynamics
- 2008
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 100:12, s. 123004-
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Tidskriftsartikel (refereegranskat)abstract
- A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics Niklasson et al. [Phys. Rev. Lett. 97, 123001 (2006)] is proposed. The formulation enables the application of higher-order symplectic or geometric integration schemes that are stable and energy conserving even under incomplete self-consistency convergence. It is demonstrated how the accuracy is improved by over an order of magnitude compared to previous formulations at the same level of computational cost. The proposed Lagrangian includes extended electronic degrees of freedom as auxiliary dynamical variables in addition to the nuclear coordinates and momenta. While the nuclear degrees of freedom propagate on the Born-Oppenheimer potential energy surface, the extended auxiliary electronic degrees of freedom evolve as a harmonic oscillator centered around the adiabatic propagation of the self-consistent ground state.
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| 17. |
- Niklasson, Anders M. N.
(författare)
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Extended Lagrangian Born-Oppenheimer molecular dynamics using a Krylov subspace approximation
- 2020
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Ingår i: Journal of Chemical Physics. - : AMER INST PHYSICS. - 0021-9606 .- 1089-7690. ; 152:10
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Tidskriftsartikel (refereegranskat)abstract
- It is shown how the electronic equations of motion in extended Lagrangian Born-Oppenheimer molecular dynamics simulations [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008); J. Chem. Phys. 147, 054103 (2017)] can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born-Oppenheimer molecular dynamics. The low-rank approximation of the Jacobian is directly related to Broyden's class of quasi-Newton algorithms and Jacobian-free Newton-Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.
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| 18. |
- Niklasson, Anders M N, et al.
(författare)
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Extended Lagrangian free energy molecular dynamics
- 2011
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Ingår i: Journal of Chemical Physics. - : American Institute of Physics (AIP). - 0021-9606 .- 1089-7690. ; 135:16, s. 164111-
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Tidskriftsartikel (refereegranskat)abstract
- Extended free energy Lagrangians are proposed for first principles molecular dynamics simulations at finite electronic temperatures for plane-wave pseudopotential and local orbital density matrix-based calculations. Thanks to the extended Lagrangian description, the electronic degrees of freedom can be integrated by stable geometric schemes that conserve the free energy. For the local orbital representations both the nuclear and electronic forces have simple and numerically efficient expressions that are well suited for reduced complexity calculations. A rapidly converging recursive Fermi operator expansion method that does not require the calculation of eigenvalues and eigen-functions for the construction of the fractionally occupied density matrix is discussed. An efficient expression for the Pulay force that is valid also for density matrices with fractional occupation occurring at finite electronic temperatures is also demonstrated.
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| 19. |
- Niklasson, Anders M. N., et al.
(författare)
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Linear scaling density matrix perturbation theory for basis-set-dependent quantum response calculations : An orthogonal formulation
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 127:6, s. 064105-
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Tidskriftsartikel (refereegranskat)abstract
- Linear scaling density matrix perturbation theory [A. M. N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] is extended to basis-set-dependent quantum response calculations for a nonorthogonal basis set representation. The generalization is achieved by a perturbation-dependent congruence transform, derived from the factorization of the inverse overlap matrix, which transforms the generalized eigenvalue problem to an orthogonal, standard form. With this orthogonalization transform the basis-set-dependent perturbation in the overlap matrix is included in the orthogonalized Hamiltonian, which is expanded in orders of the perturbation. In this way density matrix perturbation theory developed for an orthogonal representation can be applied also to basis-set-dependent response calculations. The method offers an alternative to the previous solution of the basis-set-dependent response problem, based on a nonorthogonal generalization of the density matrix perturbation theory, where the calculations are performed within a purely nonorthogonal setting [A. M. N. Niklasson , J. Chem. Phys. 123, 44107 (2005)].
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| 20. |
- Niklasson, Anders M. N., et al.
(författare)
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Time-reversible ab initio molecular dynamics
- 2007
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 126:14, s. 144103-
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Tidskriftsartikel (refereegranskat)abstract
- Time-reversible ab initio molecular dynamics based on a lossless multichannel decomposition for the integration of the electronic degrees of freedom [Phys. Rev. Lett. 97, 123001 (2006)] is explored. The authors present a lossless time-reversible density matrix molecular dynamics scheme. This approach often allows for stable Hartree-Fock simulations using only one single self-consistent field cycle per time step. They also present a generalization, introducing an additional "forcing" term, that in a special case includes a hybrid Lagrangian, i.e., Car-Parrinello-type, method, which can systematically be constrained to the Born-Oppenheimer potential energy surface by using an increasing number of self-consistency cycles in the nuclear force calculations. Furthermore, in analog to the reversible and symplectic leapfrog or velocity Verlet schemes, where not only the position but also the velocity is propagated, the authors propose a Verlet-type density velocity formalism for time-reversible Born-Oppenheimer molecular dynamics.
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| 21. |
- Niklasson, Anders M. N., et al.
(författare)
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Time-reversible Born-Oppenheimer molecular dynamics
- 2006
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Ingår i: Physical Review Letters. - 0031-9007 .- 1079-7114. ; 97:12, s. 123001-
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Tidskriftsartikel (refereegranskat)abstract
- We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the nonlinearity and incompleteness of the self-consistent field procedure. With a time-reversible lossless propagation the simulated dynamics is stabilized with respect to a systematic long-term energy drift and the number of self-consistency cycles can be kept low thanks to a good initial guess given from the electronic propagation. The proposed molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation, which preserves a detailed balance between propagation forwards and backwards in time.
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| 22. |
- Olovsson, Weine, et al.
(författare)
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Interface core-level shifts as a probe of embedded thin-film quality
- 2011
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - : American Physical Society. - 1098-0121 .- 1550-235X. ; 84:8, s. 085431-
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Tidskriftsartikel (refereegranskat)abstract
- We use first-principles calculations of layer-resolved core-level binding energy shifts (CLSs) within density functional theory as away to characterize the interface quality and thickness in embedded thin-film nanomaterials. A closer study of interfaces is motivated as properties specific to nanostructures can be related directly to the interface environment or indirectly as interference effects due to quantum confinement. From an analysis based on the Cu 2p(3/2) CLS for Cu embedded in Ni and Co fcc (100) and Fe bcc (100), with the interfaces represented by intermixing profiles controlled by a single parameter, we evaluate layer-resolved shifts as a probe of the thin-film quality. The core-level shifts in the corresponding disordered alloys, as well as local environment effects, are studied for comparison. We also discuss the possibility of detecting interface states by means of core-level shift measurements.
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| 23. |
- Rubensson, Emanuel H., et al.
(författare)
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Interior eigenvalues from density matrix expansions in quantum mechanical molecular dynamics
- 2014
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Ingår i: SIAM Journal on Scientific Computing. - : Society for Industrial & Applied Mathematics (SIAM). - 1064-8275 .- 1095-7197. ; 36, s. B147-B170
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Tidskriftsartikel (refereegranskat)abstract
- An accelerated polynomial expansion scheme to construct the density matrix in quantum mechanical molecular dynamics simulations is proposed. The scheme is based on recursive density matrix expansions, e. g., [A. M. N. Niklasson, Phys. Rev. B, 66 (2002), 155115], which are accelerated by a scale-and-fold technique [E. H. Rubensson, J. Chem. Theory Comput., 7 (2011), pp. 1233-1236]. The acceleration scheme requires interior eigenvalue estimates, which may be expensive and cumbersome to come by. Here we show how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost. Our method is illustrated with density functional tight-binding Born-Oppenheimer molecular dynamics simulations, where the computational effort is dominated by the density matrix construction. In our analysis we identify two different phases of the recursive polynomial expansion, the conditioning and purification phases, and we show that the acceleration represents an improvement of the conditioning phase, which typically gives a significant reduction of the computational cost.
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| 24. |
- Rubensson, Emanuel H., 1979-, et al.
(författare)
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Recursive inverse factorization
- 2008
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 128:10, s. 104105-
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Tidskriftsartikel (refereegranskat)abstract
- A recursive algorithm for the inverse factorization S−1=ZZ* of Hermitian positive definite matrices S is proposed. The inverse factorization is based on iterative refinement [A.M.N. Niklasson, Phys. Rev. B 70, 193102 (2004)] combined with a recursive decomposition of S. As the computational kernel is matrix-matrix multiplication, the algorithm can be parallelized and the computational effort increases linearly with system size for systems with sufficiently sparse matrices. Recent advances in network theory are used to find appropriate recursive decompositions. We show that optimization of the so-called network modularity results in an improved partitioning compared to other approaches. In particular, when the recursive inverse factorization is applied to overlap matrices of irregularly structured three-dimensional molecules.
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| 25. |
- Souvatzis, Petros, et al.
(författare)
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Extended Lagrangian Born-Oppenheimer molecular dynamics in the limit of vanishing self-consistent field optimization
- 2013
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 139:21, s. 214102-
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Tidskriftsartikel (refereegranskat)abstract
- We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The reduction of the optimization requirement reduces the computational cost to a minimum, but without causing any significant loss of accuracy or long-term energy drift. The optimization-free first principles molecular dynamics requires only one single diagonalization per time step, but is still able to provide trajectories at the same level of accuracy as "exact," fully converged, Born-Oppenheimer molecular dynamics simulations. The optimization-free limit of extended Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal starting point for robust and efficient first principles quantum mechanical molecular dynamics simulations.
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| 26. |
- Souvatzis, Petros, et al.
(författare)
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First principles molecular dynamics without self-consistent field optimization
- 2014
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 140:4, s. 044117-
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Tidskriftsartikel (refereegranskat)abstract
- We present a first principles molecular dynamics approach that is based on time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] in the limit of vanishing self-consistent field optimization. The optimization-free dynamics keeps the computational cost to a minimum and typically provides molecular trajectories that closely follow the exact Born-Oppenheimer potential energy surface. Only one single diagonalization and Hamiltonian (or Fockian) construction are required in each integration time step. The proposed dynamics is derived for a general free-energy potential surface valid at finite electronic temperatures within hybrid density functional theory. Even in the event of irregular functional behavior that may cause a dynamical instability, the optimization-free limit represents a natural starting guess for force calculations that may require a more elaborate iterative electronic ground state optimization. Our optimization-free dynamics thus represents a flexible theoretical framework for a broad and general class of ab initio molecular dynamics simulations. (C) 2014 AIP Publishing LLC.
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| 27. |
- Steneteg, Peter, et al.
(författare)
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Wave function extended Lagrangian Born-Oppenheimer molecular dynamics
- 2010
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Ingår i: Physical Review B. Condensed Matter and Materials Physics. - : American Physical Society. - 1098-0121 .- 1550-235X. ; 82:7, s. 075110-
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Tidskriftsartikel (refereegranskat)abstract
- Extended Lagrangian Born-Oppenheimer molecular dynamics [A. M. N. Niklasson, Phys. Rev. Lett. 100, 123004 (2008)] has been generalized to the propagation of the electronic wave functions. The technique allows highly efficient first principles molecular dynamics simulations using plane wave pseudopotential electronic structure methods that are stable and energy conserving also under incomplete and approximate selfconsistency convergence. An implementation of the method within the plane-wave basis set is presented and the accuracy and efficiency is demonstrated both for semiconductor and metallic materials.
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| 28. |
- Weber, Valery, et al.
(författare)
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Direct energy functional minimization under orthogonality constraints
- 2008
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Ingår i: Journal of Chemical Physics. - : AIP Publishing. - 0021-9606 .- 1089-7690. ; 128:8, s. 084113-
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Tidskriftsartikel (refereegranskat)abstract
- The direct energy functional minimization problem in electronic structure theory, where the single-particle orbitals are optimized under the constraint of orthogonality, is explored. We present an orbital transformation based on an efficient expansion of the inverse factorization of the overlap matrix that keeps orbitals orthonormal. The orbital transformation maps the orthogonality constrained energy functional to an approximate unconstrained functional, which is correct to some order in a neighborhood of an orthogonal but approximate solution. A conjugate gradient scheme can then be used to find the ground state orbitals from the minimization of a sequence of transformed unconstrained electronic energy functionals. The technique provides an efficient, robust, and numerically stable approach to direct total energy minimization in first principles electronic structure theory based on tight-binding, Hartree-Fock, or density functional theory. For sparse problems, where both the orbitals and the effective single-particle Hamiltonians have sparse matrix representations, the effort scales linearly with the number of basis functions N in each iteration. For problems where only the overlap and Hamiltonian matrices are sparse the computational cost scales as O(M-2 N), where M is the number of occupied orbitals. We report a single point density functional energy calculation of a DNA decamer hydrated with 4003 water molecules under periodic boundary conditions. The DNA fragment containing a cis-syn thymine dimer is composed of 634 atoms and the whole system contains a total of 12 661 atoms and 103 333 spherical Gaussian basis functions.
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