DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green’s functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

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.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics Niklasson et al. [Phys. Rev. Lett. 97, 123001 (2006)10.1103/PhysRevLett.97.123001] 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.

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

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...

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

Four different numerical algorithms suitable for a linear scaling implementation of time-dependent Hartree-Fock and Kohn-Sham self-consistent field theories are examined. We compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures to solve the random-phase approximation (RPA) (non-Hermitian) and Tamm-Dancoff approximation (TDA) (Hermitian) eigenvalue equations in the molecular orbital-free framework. Semiempirical Hamiltonian models are used to numerically benchmark algorithms for the computation of excited states of realistic molecular systems (conjugated polymers and carbon nanotubes). Convergence behavior and stability are tested with respect to a numerical noise imposed to simulate linear scaling conditions. The results single out the most suitable procedures for linear scaling large-scale time-dependent perturbation theory calculations of electronic excitations.

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