Fawzi Mohamed

Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach

Abstract We present the Gaussian and plane waves (GPW) method and its implementation in Quickstep which is part of the freely available program package CP2K. The GPW method allows for accurate density functional calculations in gas and condensed phases and can be effectively used for molecular dynamics simulations. We show how derivatives of the GPW energy functional, namely ionic forces and the Kohn–Sham matrix, can be computed in a consistent way. The computational cost of computing the total energy and the Kohn–Sham matrix is scaling linearly with the system size, even for condensed phase systems of just a few tens of atoms. The efficiency of the method allows for the use of large Gaussian basis sets for systems up to 3000 atoms, and we illustrate the accuracy of the method for various basis sets in gas and condensed phases. Agreement with basis set free calculations for single molecules and plane wave based calculations in the condensed phase is excellent. Wave function optimisation with the orbital transformation technique leads to good parallel performance, and outperforms traditional diagonalisation methods. Energy conserving Born–Oppenheimer dynamics can be performed, and a highly efficient scheme is obtained using an extrapolation of the density matrix. We illustrate these findings with calculations using commodity PCs as well as supercomputers.

The influence of temperature and density functional models in ab initio molecular dynamics simulation of liquid water

The performance of density functional theory methods for the modeling of condensed aqueous systems is hard to predict and validation by ab initio molecular simulation of liquid water is absolutely necessary. In order to assess the reliability of these tests, the effect of temperature on the structure and dynamics of liquid water has been characterized with 16 simulations of 20 ps in the temperature range of 280-380 K. We find a pronounced influence of temperature on the pair correlation functions and on the diffusion constant including nonergodic behavior on the time scale of the simulation in the lower temperature range (which includes ambient temperature). These observations were taken into account in a consistent comparison of a series of density functionals (BLYP, PBE, TPSS, OLYP, HCTH120, HCTH407). All simulations were carried out using an ab initio molecular dynamics approach in which wave functions are represented using Gaussians and the density is expanded in an auxiliary basis of plane waves. Whereas the first three functionals show similar behavior, it is found that the latter three functionals yield more diffusive dynamics and less structure.

Efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer molecular dynamics.

We present a new method which combines Car-Parrinello and Born-Oppenheimer molecular dynamics in order to accelerate density functional theory based ab initio simulations. Depending on the system a gain in efficiency of 1 to 2 orders of magnitude has been observed, which allows ab initio molecular dynamics of much larger time and length scales than previously thought feasible. It will be demonstrated that the dynamics is correctly reproduced and that high accuracy can be maintained throughout for systems ranging from insulators to semiconductors and even to metals in condensed phases. This development considerably extends the scope of ab initio simulations.

An Efficient Real Space Multigrid QM/MM Electrostatic Coupling.

A popular strategy for simulating large systems where quantum chemical effects are important is the use of mixed quantum mechanical/molecular mechanics methods (QM/MM). While the cost of solving the Schrödinger equation in the QM part is the bottleneck of these calculations, evaluating the Coulomb interaction between the QM and the MM part is surprisingly expensive. In fact it can be just as time-consuming as solving the QM part. We present here a novel real space multigrid approach that handles Coulomb interactions very effectively and implement it in the CP2K code. This novel scheme cuts the cost of this part of the calculation by 2 orders of magnitude. The method does not need very fine-tuning or adjustable parameters, and it is quite accurate, leading to a dynamics with very good energy conservation. We exemplify the validity of our algorithms with simulations of water and of a zwitterionic dipeptide solvated in water.

An Efficient Linear-Scaling Electrostatic Coupling for Treating Periodic Boundary Conditions in QM/MM Simulations

A new linear-scaling method based on a multigrid approach to treat long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics (QM/MM) simulations is described. The scheme has been implemented in the context of a QM calculation based on density functional theory (DFT). The method is tested on an analytical model to validate the new algorithm. Two realistic problems in α-quartz crystals and a zwitterionic dipeptide (GLY-ALA) in water have been chosen as further tests. Results from QM/MM calculations with periodic boundary conditions (PBC) show that the use of PBC is essential when studying highly ordered crystal structures, unless a carefully designed MM crystal is used for the calculation. With a general shaped MM subsystem, the absence of PBC leads to an incorrect description of Kohn-Sham band gaps and charge density. The present method allows periodic boundary conditions to be used in molecular simulations of biological and material science systems.

Resolution of identity approximation for the Coulomb term in molecular and periodic systems.

A new formulation of resolution of identity approximation for the Coulomb term is presented, which uses atom-centered basis and auxiliary basis functions and treats molecular and periodic systems of any dimensionality on an equal footing. It relies on the decomposition of an auxiliary charge density into charged and chargeless components. Applying the Coulomb metric under periodic boundary conditions constrains the explicit form of the charged part. The chargeless component is determined variationally and converged Coulomb lattice sums needed for its determination are obtained using chargeless linear combinations of auxiliary basis functions. The lattice sums are partitioned in near- and far-field portions which are treated through an analytical integration scheme employing two- and three-center electron repulsion integrals and multipole expansions, respectively, operating exclusively in real space. Our preliminary implementation within the TURBOMOLE program package demonstrates consistent accuracy of the method across molecular and periodic systems. Using common auxiliary basis sets the errors of the approximation are small, in average about 20 muhartree per atom, for both molecular and periodic systems.

A new glance at HCl-monohydrate spectroscopy, using on-the-fly dynamics

On-the-fly dynamics is used to analyze the remarkably anharmonic infrared spectroscopy of crystalline HCl monohydrate, an ionic solid composed of H3O+ and Cl-. The dominant intense infrared feature is shown to originate from specific sections of the hydronium trajectory, in which one of the H-atoms interacts strongly with a neighboring Cl-.

Solvation states of HCl in mixed ether:acid crystals: a computational study.

Acid solvation states are investigated in the recently discovered mixed ether:acid crystalline solids. The solids are simulated using on-the-fly molecular dynamics as implemented in the density functional code QUICKSTEP employing Gaussian basis sets. The solids are shown to display a remarkably broad range of acid solvation states, depending on the ether:acid ratio, including proton sharing in the 1:1 case, proton transfer to the ether in 1:2, and perturbed molecular acid in 1:6. The observed variation of the infrared spectra with the composition is accounted for qualitatively with the help of the calculations.