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

Articles you may be interested in Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations

We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on selfconsistent 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 selfconsistent 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.PACS numbers: 71.15. Pd,31.15.Ew,31.15.Qg,34.10.+x Ab initio molecular dynamics based on Hartree-Fock or density functional theory [1,2,3,4,5,6,7,8,9] has become an important tool for simulations of an increasingly wider range of problems in geology, material science, chemistry, and biology. Ab initio molecular dynamics, where the atomic positions move along classical trajectories, can be categorized in two major groups: Lagrangian Car-Parrinello molecular dynamics and BornOppenheimer molecular dynamics [4,5,6,7,8,9,10,11,12]. The tremendous success of Car-Parinello molecular dynamics, invented two decades ago [4], is based on its low computational cost combined with the conserved Lagrangian properties of the dynamics. However, unless a Car-Parinello simulation is performed carefully, it may yield results different from Born-Oppenheimer molecular dynamics [5,6,13,14,15,16]. In BornOppenheimer molecular dynamics the atomic positions are propagated by forces that are calculated at the selfconsistent electronic ground state for each instantaneous arrangement of the ions. Born-Oppenheimer molecular dynamics is computationally expensive compared to Car-Parinello dynamics because of the requirement to reach a self-consistent field (SCF) solution in each timestep. However, the number of SCF cycles and thus the computational cost can be strongly reduced by using an initial guess for the electronic degrees of freedom ρ(t n+1 ) (here represented by the electron density), which is given by an extrapolation from previous time steps [5,8,9,17,18,19]. The electronic extrapolation scheme, combined with the SCF procedure, can be seen as an adiabatic propagation of the electronic degrees of freedom, * Corresponding author: Email amn@lanl.gov where(1)Unfortunately, this approach has a fundamental problem. Because of the non-linear and irreversible SCF procedure, which in practice never is complete, the timereversal symmetry of the electronic propagation is broken. This problem does not occur in Lagrangian Car-Parinello molecular dynamics [20], where both the nucl...

A new linear scaling method for computation of the Cartesian Gaussian-based Hartree-Fock exchange matrix is described, which employs a method numerically equivalent to standard direct SCF, and which does not enforce locality of the density matrix. With a previously described method for computing the Coulomb matrix [J. Chem. Phys. 106, 5526 (1997)], linear scaling incremental Fock builds are demonstrated for the first time. Microhartree accuracy and linear scaling are achieved for restricted Hartree-Fock calculations on sequences of water clusters and polyglycine α-helices with the 3-21G and 6-31G basis sets. Eightfold speedups are found relative to our previous method. For systems with a small ionization potential, such as graphitic sheets, the method naturally reverts to the expected quadratic behavior. Also, benchmark 3-21G calculations attaining microhartree accuracy are reported for the P53 tetramerization monomer involving 698 atoms and 3836 basis functions.

Thresholding criteria are introduced that enforce locality of exchange interactions in Cartesian Gaussian-based Hartree–Fock calculations. These criteria are obtained from an asymptotic form of the density matrix valid for insulating systems, and lead to a linear scaling algorithm for computation of the Hartree–Fock exchange matrix. Restricted Hartree–Fock/3-21G calculations on a series of water clusters and polyglycine α-helices are used to demonstrate the 𝒪(N) complexity of the algorithm, its competitiveness with standard direct self-consistent field methods, and a systematic control of error in converged total energies.