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Register a new userCanonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory
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We discuss the development and implementation of a constant temperature (NVT) molecular dynamics scheme that combines the Nose-Hoover chain thermostat with the extended Lagrangian Born-Oppenheimer molecular dynamics (BOMD) scheme, using a linear scaling density functional theory (DFT) approach. An integration scheme for this canonical-ensemble extended Lagrangian BOMD is developed and discussed in the context of the Liouville operator formulation. Linear scaling DFT canonical-ensemble extended Lagrangian BOMD simulations are tested on bulk silicon and silicon carbide systems to evaluate our integration scheme. The results show that the conserved quantity remains stable with no systematic drift even in the presence of the thermostat.
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While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical intersections are suitably regularized in the resulting nuclear particle motion and the associated Lorentz force involves a smoothened Berry curvature identifying a loop-dependent geometric phase. In turn, this geometric phase rapidly reaches the usual topological index as the loop expands away from the original singularity. This feature reproduces the phenomenology appearing in recent exact nonadiabatic studies, as shown explicitly in the Jahn-Teller problem for linear vibronic coupling. Likewise, a newly proposed regularization of the diagonal correction term is also shown to reproduce quite faithfully the energy surface presented in recent nonadiabatic studies.
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of DFT calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the contracted basis functions for closely related environments, e.g. in geometry optimizations or combined calculations of neutral and charged systems.
We present an efficient general approach to first principles molecular dynamics simulations based on extended Lagrangian Born-Oppenheimer molecular dynamics in the limit of vanishing self-consistent field optimization. The reduction of the optimization requirement reduces the computational cost to a minimum, but without causing any significant loss of accuracy or longterm energy drift. The optimization-free first principles molecular dynamics requires only one single diagonalization per time step and yields trajectories at the same level of accuracy as exact, fully converged, Born-Oppenheimer molecular dynamics simulations. The optimization-free limit of extended Lagrangian Born-Oppenheimer molecular dynamics therefore represents an ideal starting point for a robust and efficient formulation of a new generation first principles quantum mechanical molecular dynamics simulation schemes.
We introduce a method to carry out zero-temperature calculations within density functional theory (DFT) but without relying on the Born-Oppenheimer (BO) approximation for the ionic motion. Our approach is based on the finite-temperature many-body path-integral formulation of quantum mechanics by taking the zero-temperature limit and treating the imaginary-time propagation of the electronic variables in the context of DFT. This goes beyond the familiar BO approximation and is limited from being an exact treatment of both electrons and ions only by the approximations involved in the DFT component. We test our method in two simple molecules, H$_2$ and benzene. We demonstrate that the method produces a difference from the results of the BO approximation which is significant for many physical systems, especially those containing light atoms such as hydrogen; in these cases, we find that the fluctuations of the distance from its equilibrium position, due to the zero-point-motion, is comparable to the interatomic distances. The method is suitable for use with conventional condensed matter approaches and currently is implemented on top of the periodic pseudopotential code SIESTA.
Classical density functional theory for finite temperatures is usually formulated in the grand-canonical ensemble where arbitrary variations of the local density are possible. However, in many cases the systems of interest are closed with respect to mass, e.g. canonical systems with fixed temperature and particle number. Although the tools of standard, grand-canonical density functional theory are often used in an ad hoc manner to study closed systems, their formulation directly in the canonical ensemble has so far not been known. In this work, the fundamental theorems underlying classical DFT are revisited and carefully compared in the two ensembles showing that there are only trivial formal differences. The practicality of DFT in the canonical ensemble is then illustrated by deriving the exact Helmholtz functional for several systems: the ideal gas, certain restricted geometries in arbitrary numbers of dimensions and finally a system of two hard-spheres in one dimension (hard rods) in a small cavity. Some remarkable similarities between the ensembles are apparent even for small systems with the latter showing strong echoes of the famous exact of result of Percus in the grand-canonical ensemble.
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