Extended Lagrangian Born–Oppenheimer molecular dynamics with dissipation

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. Stability and dissipation in the propagation of the electronic degrees of freedom in time-reversible extended Lagrangian Born-Oppenheimer molecular dynamics ͓Niklasson et al., Phys. Rev. Lett. 97, 123001 ͑2006͒; Phys. Rev. Lett. 100, 123004 ͑2008͔͒ 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. Extended Lagrangian Born-Oppenheimer molecular dynamics with dissipation

Linear-scaling first-principles molecular dynamics of complex biological systems with the Conquest code

“…In practice, for the numerical propagation of the matrix X, we use an equation of motion with a dissipative term to maintain the numerical stability of the matrix X. 34) In our previous study, we clarified the effects of control parameters used in the DMM method in the FPMD simulations. We found that, even when the total energy is not fully converged, MD trajectories are almost the same as those in more accurate MD simulations.…”

Stabilization ofAb InitioMolecular Dynamics Simulations at Large Time Steps

“…This algorithm may also be used in conjunction with other methods to accelerate the simulations even further, such as the Langevin dynamics [5][6][7][8] , linear scaling method [24][25][26] and mass scaling method 27 . …”

Extended Lagrangian free energy molecular dynamics

“…14,15,60,64 In this paper, first principles free energy molecular dynamics schemes were developed based on extended Lagrangian Born-Oppenheimer molecular dynamics. 3,4,10,34 The formulation was given both for density matrix and plane wave representations. The density matrix formulation has numerically convenient expressions for the electronic forces as well as a recursive Fermi operator expansion that are well suited for reduced complexity calculations.…”

“…This term corresponds to a weak coupling to an external system that removes numerical error fluctuations, but without any significant modification of the microcanonical trajectories and the free energy. 34 A few optimized examples of the dimensionless parameter, δt 2 ω 2 , the c k coefficients and α are given in Table I (see Ref. 34 for details). The integration coefficients in Table I are optimized under the condition of stability under incomplete, approximate SCF convergence.…”

“…that includes a weak external dissipative force that removes the accumulation of numerical noise, 34 has the following form:…”