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 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.

Extended Lagrangian Born-Oppenheimer molecular dynamics with dissipation

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 (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.

Density matrix perturbation theory

An orbital-free quantum perturbation theory is proposed. It gives the response of the density matrix upon variation of the Hamiltonian by quadratically convergent recursions based on perturbed projections. 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. The method allows efficient high order perturbation expansions, as demonstrated with an example involving a 10th order expansion. Density matrix analogs of Wigner's 2n+1 rule are also presented.

Ab initio linear scaling response theory: electric polarizability by perturbed projection

A linear scaling method for calculation of the static ab initio response within self-consistent field theory is developed and applied to the calculation of the static electric polarizability. The method is based on the density matrix perturbation theory [Phys. Rev. Lett. 92, 193001 (2004)]], obtaining response functions directly via a perturbative approach to spectral projection. The accuracy and efficiency of the linear scaling method is demonstrated for a series of three-dimensional water clusters at the RHF/6-31G(**) level of theory. The locality of the response under a global electric field perturbation is numerically demonstrated by the approximate exponential decay of derivative density matrix elements.

Time-reversible ab initio molecular dynamics

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.

Linear scaling computation of the Fock matrix. VII. Parallel computation of the Coulomb matrix

We present parallelization of a quantum-chemical tree-code for linear scaling computation of the Coulomb matrix. Equal time partition is used to load balance computation of the Coulomb matrix. Equal time partition is a measurement based algorithm for domain decomposition that exploits small variation of the density between self-consistent-field cycles to achieve load balance. Efficiency of the equal time partition is illustrated by several tests involving both finite and periodic systems. It is found that equal time partition is able to deliver 91%-98% efficiency with 128 processors in the most time consuming part of the Coulomb matrix calculation. The current parallel quantum chemical tree code is able to deliver 63%-81% overall efficiency on 128 processors with fine grained parallelism (less than two heavy atoms per processor).

Nonorthogonal density-matrix perturbation theory

Recursive density-matrix perturbation theory [A.M.N. Niklasson and M. Challacombe, Phys. Rev. Lett. 92, 193001 (2004)] provides an efficient framework for the linear scaling computation of materials response properties [V. Weber, A.M.N. Niklasson, and M. Challacombe, Phys. Rev. Lett. 92, 193002 (2004)]. In this article, we generalize the density-matrix perturbation theory to include properties computed with a perturbation-dependent nonorthogonal 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 theory is developed in the context of linear scaling purification methods, which are briefly reviewed.

The quasi-independent curvilinear coordinate approximation for geometry optimization

This paper presents an efficient alternative to well established algorithms for molecular geometry optimization. This approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate system, allowing separation of the 3N-dimensional optimization problem into an O(N) set of quasi-independent one-dimensional problems. Each uncoupled optimization is developed by a weighted least squares fit of energy gradients in the internal coordinate system followed by extrapolation. In construction of the weights, only an implicit dependence on topologically connected internal coordinates is present. This new approach is competitive with the best internal coordinate geometry optimization algorithms in the literature and works well for large biological problems with complicated hydrogen bond networks and ligand binding motifs.

Higher-order response in O(N) by perturbed projection

Perturbed projection for linear scaling solution of the coupled-perturbed self-consistent-field equations [V. Weber, A.M.N. Niklasson, and M. Challacombe, Phys. Rev. Lett. 92, 193002 (2004)] is extended to the computation of higher-order static response properties. Although generally applicable, perturbed projection is further developed here in the context of the self-consistent first and second electric hyperpolarizabilities at the Hartree-Fock level of theory. Nonorthogonal, density-matrix analogs of Wigner's 2n+1 rule valid for linear one-electron perturbations 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 for three-dimensional water clusters.