arXiv subjects

Anders M. N. Niklasson

Publications and source records attributed to Anders M. N. Niklasson.

49 records · Page 3Linked to original sources

arXiv2012

Fast method for quantum mechanical molecular dynamics

With the continuous growth of processing power for scientific computing, first principles Born-Oppenheimer molecular dynamics (MD) simulations are becoming increasingly popular for the study of a wide range of problems in materials science, chemistry and biology. Nevertheless, the computational cost still remains prohibitively large in many cases, particularly in comparison to classical MD simulations using empirical force fields. Here we show how to circumvent the major computational bottleneck in Born-Oppenheimer MD simulations arising from the self-consistent-charge optimization. The optimization-free quantum mechanical MD method is demonstrated for density functional tight-binding theory. The molecular trajectories are almost indistinguishable from an "exact" microcanonical Born-Oppenheimer MD simulation even when linear scaling sparse matrix algebra is used. Our findings drastically reduce the computational gap between classical and quantum mechanical MD simulations.

cond-mat.mtrl-sci↗

arXiv2011

Extended Lagrangian free energy molecular dynamics

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 eigenfunctions 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.

physics.chem-ph↗

arXiv2010

Wavefunction extended Lagrangian Born-Oppenheimer molecular dynamics

Extended Lagrangian Born-Oppenheimer molecular dynamics [Niklasson, Phys. Rev. Lett. 100 123004 (2008)] has been generalized to the propagation of the electronic wavefunctions. 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 self-consistency convergence. An implementation of the method within the planewave basis set is presented and the accuracy and efficiency is demonstrated both for semi-conductor and metallic materials.

cond-mat.mtrl-sci↗

arXiv2008

Cache oblivious storage and access heuristics for blocked matrix-matrix multiplication

We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the submatrix multiplications that leads to a speedup of up to four times for small block sizes. This is in contrast to results for single matrix elements showing that contiguous memory allocation quickly becomes irrelevant as the blocksize increases.

cs.DS↗

arXiv2008

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.

cond-mat.mtrl-sci↗

arXiv2008

Extended Lagrangian formulation of time-reversible Born-Oppenheimer molecular dynamics for higher-order symplectic integration

A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett. vol. 97, 123001 (2006)] is proposed. The 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. 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 extended Born-Oppenheimer molecular dynamics improves the accuracy by over an order of magnitude compared to previous formulations at the same level of computational cost.

cond-mat.mtrl-sci↗

arXiv2006

Time-reversible Born-Oppenheimer molecular dynamics

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 non-linearity and incompleteness of the self-consistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.

cond-mat.mtrl-sci↗

arXiv2005

Non-Orthogonal Density Matrix Perturbation Theory

Density matrix perturbation theory [Phys. Rev. Lett. Vol. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of response properties [Phys. Rev. Lett. Vol. 92, 193002 (2004)]. In this article, we generalize density matrix perturbation theory to include properties computed with a perturbation dependent non-orthogonal basis. Such properties include analytic derivatives of the energy with respect to nuclear displacement, as well as magnetic response computed with a field dependent basis. The non-orthogonal density matrix perturbation theory is developed in the context of recursive purification methods, which are briefly reviewed.

physics.comp-ph↗

arXiv2004

Higher Order Response in ${\cal O}(N)$ by Perturbed Projection

Perturbed projection for linear scaling solution of the coupled-perturbed self-consistent-field equations [Weber, Niklasson and Challacombe, Phys. Rev.\ Lett. {\bf 92}, 193002 (2004)] is extended to the computation of higher order static response properties. Although generally applicable, perturbed projection is developed here in the context of the self-consistent first and second electric hyperpolarizabilities of three dimensional water clusters at the Hartree-Fock level of theory. Non-orthogonal, density matrix analogues of Wigner's $2n+1$ rule are given up to fourth order. Linear scaling and locality of the higher order response densities under perturbation by a global electric field are demonstrated.

cond-mat.mtrl-sci↗

arXiv2003

Density Matrix Perturbation Theory

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation of the Hamiltonian. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N_pert.), and as O(1) with the total system size. It also allows direct computation of the density matrix response functions to any order with linear scaling effort. Energy expressions to 4th order based on only first and second order density matrix response are given.

cond-mat.mtrl-sci↗

arXiv2003

Implicit Purification for Temperature-Dependent Density Matrices

An implicit purification scheme is proposed for calculation of the temperature-dependent, grand canonical single-particle density matrix, given as a Fermi operator expansion in terms of the Hamiltonian. The computational complexity is shown to scale with the logarithm of the polynomial order of the expansion, or equivalently, with the logarithm of the inverse temperature. The system of linear equations that arise in each implicit purification iteration is solved efficiently by a conjugate gradient solver. The scheme is particularly useful in connection with linear scaling electronic structure theory based on sparse matrix algebra. The efficiency of the implicit temperature expansion technique is analyzed and compared to some explicit purification methods for the zero temperature density matrix.

cond-mat.mtrl-sci↗

arXiv2002

Expansion algorithm for the density matrix

A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix multiplications compared to existing methods at low (<10%) and high (>90%) occupancy. The expansion can be used with a fixed chemical potential in which case it is an asymmetric generalization of and a substantial improvement over grand canonical McWeeny purification. It is shown that the computational complexity, measured as number of matrix multiplications, essentially is independent of system size even for metallic materials with a vanishing band gap.

cond-mat.mtrl-sci↗

arXiv2002

Modeling the actinides with disordered local moments

A first-principles disordered local moment (DLM) picture within the local-spin-density and coherent potential approximations (LSDA+CPA) of the actinides is presented. The parameter free theory gives an accurate description of bond lengths and bulk modulus. The case of $δ$-Pu is studied in particular and the calculated density of states is compared to data from photo-electron spectroscopy. The relation between the DLM description, the dynamical mean field approach and spin-polarized magnetically ordered modeling is discussed.

cond-mat.mtrl-sci↗