Grid-Based Projector Augmented Wave (GPAW) Implementation of Quantum Mechanics/Molecular Mechanics (QM/MM) Electrostatic Embedding and Application to a Solvated Diplatinum Complex.

A multiscale density functional theory-quantum mechanics/molecular mechanics (DFT-QM/MM) scheme is presented, based on an efficient electrostatic coupling between the electronic density obtained from a grid-based projector augmented wave (GPAW) implementation of density functional theory and a classical potential energy function. The scheme is implemented in a general fashion and can be used with various choices for the descriptions of the QM or MM regions. Tests on H2O clusters, ranging from dimer to decamer show that no systematic energy errors are introduced by the coupling that exceeds the differences in the QM and MM descriptions. Over 1 ns of liquid water, Born-Oppenheimer QM/MM molecular dynamics (MD) are sampled combining 10 parallel simulations, showing consistent liquid water structure over the QM/MM border. The method is applied in extensive parallel MD simulations of an aqueous solution of the diplatinum [Pt2(P2O5H2)4]4- complex (PtPOP), spanning a total time period of roughly half a nanosecond. An average Pt-Pt distance deviating only 0.01 Å from experimental results, and a ground-state Pt-Pt oscillation frequency deviating by <2% from experimental results were obtained. The simulations highlight a remarkable harmonicity of the Pt-Pt oscillation, while also showing clear signs of Pt-H hydrogen bonding and directional coordination of water molecules along the Pt-Pt axis of the complex.

Optimizing a parametrized Thomas-Fermi-Dirac-Weizsäcker density functional for atoms.

Because of issues with accuracy and transferability of existing orbital-free (OF) density functionals, OF functional development remains an active research area. However, due to numerical difficulties, all-electron self-consistent assessment of OF functionals is limited. Using an all-electron radial OFDFT code, we evaluate the performance of a parametrized OF functional for a wide range in parameter space. Specifically, we combine the parametrized Thomas-Fermi-Weizsäcker kinetic model (λ and γ for the fractions of Weizsäcker and Thomas-Fermi functionals, respectively) with a local density approximation (LDA) for the exchange-correlation functional. In order to obtain the converged results for λ values other than λ = 1, we use the potential scaling introduced in previous work. Because we work within a wide region in parameter space, this strategy provides an effective route towards better understanding of the parameter interplay that allows us to achieve good agreement with the Kohn-Sham (KS) model. Here, our interest lies in total energy, Euler equation eigenvalue, and electronic densities when the parameters are varied between 0.2 and 1.5. We observe that a one-to-one relation between λ and γ defines a region in parameter space that allows the atomic energies to be approximated with a very small average error (less than 3% percent for all the atoms studied) with respect to the KS reference energies. For each atom, the reference KS HOMO eigenvalue can also be reproduced with a similar error, but the one-to-one correspondence between λ and γ belongs to a different region of the same parameter space. Contrary to both properties, the atomic density behaves more smoothly and the error in reproducing the KS reference densities appears more insensitive to variation of the parameters (with mostly an average integrated difference of 0.15-0.20 |e| per electron). These results pave the way towards testing of parameter transferability and further systematic improvement of OF density functionals.

Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method.

Electronic structure calculations have become an indispensable tool in many areas of materials science and quantum chemistry. Even though the Kohn-Sham formulation of the density-functional theory (DFT) simplifies the many-body problem significantly, one is still confronted with several numerical challenges. In this article we present the projector augmented-wave (PAW) method as implemented in the GPAW program package (https://wiki.fysik.dtu.dk/gpaw) using a uniform real-space grid representation of the electronic wavefunctions. Compared to more traditional plane wave or localized basis set approaches, real-space grids offer several advantages, most notably good computational scalability and systematic convergence properties. However, as a unique feature GPAW also facilitates a localized atomic-orbital basis set in addition to the grid. The efficient atomic basis set is complementary to the more accurate grid, and the possibility to seamlessly switch between the two representations provides great flexibility. While DFT allows one to study ground state properties, time-dependent density-functional theory (TDDFT) provides access to the excited states. We have implemented the two common formulations of TDDFT, namely the linear-response and the time propagation schemes. Electron transport calculations under finite-bias conditions can be performed with GPAW using non-equilibrium Green functions and the localized basis set. In addition to the basic features of the real-space PAW method, we also describe the implementation of selected exchange-correlation functionals, parallelization schemes, ΔSCF-method, x-ray absorption spectra, and maximally localized Wannier orbitals.