We have tested the performance of a large set of kinetic energy density functionals of the local density approximation (LDA), the gradient expansion approximation (GEA), and the generalized gradient approximation (GGA) for the calculation of interaction energies within a subsystem approach to density functional theory. Our results have been obtained with a new implementation of interaction energies for frozen-density embedding into the Amsterdam Density Functional program. We present data for a representative sample of 39 intermolecular complexes and 15 transition metal coordination compounds with interaction energies spanning the range from -1 to -783 kcal/mol. This is the first time that kinetic energy functionals have been tested for such strong interaction energies as the ligand-metal bonds in the investigated coordination compounds. We confirm earlier work that GGA functionals offer an improvement over the LDA and are particularly well suited for weak interactions like hydrogen bonds. We do, however, not find a particular reason to prefer any of the GGA functionals over another. Functionals derived from the GEA in general perform worse for all of the weaker interactions and cannot be recommended. An unexpectedly good performance is found for the coordination compounds, in particular with the GEA-derived functionals. However, the presently available kinetic energy functionals cannot be applied in cases in which a density redistribution between the subsystems leads to strongly overlapping subsystem electron densities.

Abstract:Applications of quantum chemistry have evolved from single or a few calculations to more complicated workflows, in which a series of interrelated computational tasks is performed. In particular multiscale simulations, which combine different levels of accuracy, typically require a large number of individual calculations that depend on each other. Consequently, there is a need to automate such workflows. For this purpose we have developed PyAdf, a scripting framework for quantum chemistry. PyAdf handles all steps necessary in a typical workflow in quantum chemistry and is easily extensible due to its object-oriented implementation in the Python programming language. We give an overview of the capabilities of PyAdf and illustrate its usefulness in quantum-chemical multiscale simulations with a number of examples taken from recent applications.

We have investigated the functional derivative of the nonadditive kinetic-energy bifunctional, which appears in the embedding potential that is used in the frozen-density embedding formalism, in the limit that the separation of the subsystems is large. We have derived an exact expression for this kinetic-energy component of the embedding potential and have applied this expression to deduce its exact form in this limit. Comparing to the approximations currently in use, we find that while these approximations are correct at the nonfrozen subsystem, they fail completely at the frozen subsystem. Using test calculations on two model systems, a H 2 O¯Li + complex and a cluster of aminocoumarin C151 surrounded by 30 water molecules, we show that this failure leads to a wrong description of unoccupied orbitals, which can lead to convergence problems caused by too low-lying unoccupied orbitals and which can further have serious consequences for the calculation of response properties. Based on our results, a simple correction is proposed, and we show that this correction is able to fix the observed problems for the model systems studied.

We have assessed the accuracy of a representative set of currently available approximate kinetic-energy functionals used within the frozen-density embedding scheme for the NgAuF (Ng=Ar, Kr, Xe) molecules, which we partitioned into a Ng and a AuF subsystem. Although it is weak, there is a covalent interaction between these subsystems which represents a challenge for this subsystem density functional theory approach. We analyzed the effective-embedding potentials and resulting electron density distributions and provide a quantitative analysis of the latter from dipole moment differences and root-mean-square errors in the density with respect to the supermolecular Kohn-Sham density functional theory reference calculation. Our results lead to the conclusion that none of the tested approximate kinetic-energy functionals performs well enough to describe the bond between the noble gas and gold adequately. This observation contributes to the growing evidence that the current procedure to obtain approximate kinetic-energy functionals by reparametrizing functionals obtained via the "conjointness" hypothesis of Lee, Lee, and Parr [Phys. Rev. A 44, 768 (1991)] is insufficient to treat metal-ligand interactions with covalent character.

We employed an explicit expression for the dispersion (D) energy in conjunction with Kohn-Sham (KS) density functional theory and frozen-density embedding (FDE) to calculate interaction energies between DNA base pairs and a selected set of amino acid pairs in the hydrophobic core of a small protein Rubredoxin. We use this data to assess the accuracy of an FDE-D approach for the calculation of intermolecular interactions. To better analyze the calculated interaction energies we furthermore propose a new energy decomposition scheme that is similar to the well-known KS bond formation analysis [F. M. Bickelhaupt and E. J. Baerends, Rev. Comput. Chem. 15, 1 (2000)], but differs in the electron densities used to define the bond energy. The individual subsystem electron densities of the FDE approach sum to the total electron density which makes it possible to define bond energies in terms of promotion energies and an explicit interaction energy. We show that for the systems considered only a few freeze-and-thaw cycles suffice to reach convergence in these individual bond energy components, illustrating the potential of FDE-D as an efficient method to calculate intermolecular interactions.