Christoph R. Jacob

The structures of small gold cluster anions as determined by a combination of ion mobility measurements and density functional calculations

A combined experimental and theoretical study of small gold cluster anions is performed. The experimental effort consists of ion mobilitymeasurements that lead to the assignment of the collision cross sections for the different cluster sizes at room temperature. The theoretical study is based on ab initiomolecular dynamics calculations with the goal to find energetically favorable candidate structures. By comparison of the theoretical results with the measured collision cross sections as well as vertical detachment energies (VDEs) from the literature, we assign structures for the small Au n − ions (n<13) and locate the transition from planar to three-dimensional structures. While a unique assignment based on the observed VDEs alone is generally not possible, the collision cross sections provide a direct and rather sensitive measure of the cluster structure. In contrast to what was expected from other metal clusters and previous theoretical studies, the structural transition occurs at an unusually large cluster size of twelve atoms.

Subsystem density‐functional theory

Subsystem density‐functional theory (subsystem DFT) has developed into a powerful alternative to Kohn–Sham DFT for quantum chemical calculations of complex systems. It exploits the idea of representing the total electron density as a sum of subsystem densities. The optimum total density is found by minimizing the total energy with respect to each of the subsystem densities, which breaks down the electronic‐structure problem into effective subsystem problems. This enables calculations on large molecular aggregates and even (bio‐)polymers without system‐specific parameterizations. We provide a concise review of the underlying theory, typical approximations, and embedding approaches related to subsystem DFT such as frozen‐density embedding (FDE). Moreover, we discuss extensions and applications of subsystem DFT and FDE to molecular property calculations, excited states, and wave function in DFT embedding methods. Furthermore, we outline recent developments for reconstruction techniques of embedding potentials arising in subsystem DFT, and for using subsystem DFT to incorporate constraints into DFT calculations.

Accurate frozen-density embedding potentials as a first step towards a subsystem description of covalent bonds

The frozen-density embedding (FDE) scheme [Wesolowski and Warshel, J. Phys. Chem. 97, 8050 (1993)] relies on the use of approximations for the kinetic-energy component v(T)[rho(1),rho(2)] of the embedding potential. While with approximations derived from generalized-gradient approximation kinetic-energy density functional weak interactions between subsystems such as hydrogen bonds can be described rather accurately, these approximations break down for bonds with a covalent character. Thus, to be able to directly apply the FDE scheme to subsystems connected by covalent bonds, improved approximations to v(T) are needed. As a first step toward this goal, we have implemented a method for the numerical calculation of accurate references for v(T). We present accurate embedding potentials for a selected set of model systems, in which the subsystems are connected by hydrogen bonds of various strength (water dimer and F-H-F(-)), a coordination bond (ammonia borane), and a prototypical covalent bond (ethane). These accurate potentials are analyzed and compared to those obtained from popular kinetic-energy density functionals.

Spin in density‐functional theory

The accurate description of open-shell molecules, in particular of transition metal complexes and clusters, is still an important challenge for quantum chemistry. Although density-functional theory (DFT) is widely applied in this area, the sometimes severe limitations of its currently available approximate realizations often preclude its application as a predictive theory. Here, we review the foundations of DFT applied to open-shell systems, both within the nonrelativistic and the relativistic framework. In particular, we provide an in-depth discussion of the exact theory, with a focus on the role of the spin density and possibilities for targeting specific spin states. It turns out that different options exist for setting up Kohn–Sham DFT schemes for open-shell systems, which imply different definitions of the exchange–correlation energy functional and lead to different exact conditions on this functional. Finally, we suggest possible directions for future developments.

A flexible implementation of frozen‐density embedding for use in multilevel simulations

A new implementation of frozen‐density embedding (FDE) in the Amsterdam Density Functional (ADF) program package is presented. FDE is based on a subsystem formulation of density‐functional theory (DFT), in which a large system is assembled from an arbitrary number of subsystems, which are coupled by an effective embedding potential. The new implementation allows both an optimization of all subsystems as a linear‐scaling alternative to a conventional DFT treatment, the calculation of one active fragment in the presence of a frozen environment, and intermediate setups, in which individual subsystems are fully optimized, partially optimized, or completely frozen. It is shown how this flexible setup can facilitate the application of FDE in multilevel simulations.

Calculation of local excitations in large systems by embedding wave-function theory in density-functional theory

We present a simple and efficient embedding scheme for the wave-function based calculation of the energies of local excitations in large systems. By introducing an embedding potential obtained from density-functional theory (DFT) it is possible to describe the effect of an environment on local excitations of an embedded system in wave-function theory (WFT) calculations of the excitation energies. We outline the implementation of such a WFT-in-DFT embedding procedure employing the ADF, Dalton and DIRAC codes, where the embedded subsystem is treated with coupled cluster methods. We then evaluate this procedure in the calculation of the solvatochromic shift of acetone in water and of the f-f spectrum of NpO22+ embedded in a Cs2UO2Cl4 crystal and find that our scheme does effectively incorporate the environment effect in both cases. A particularly interesting finding is that with our embedding scheme we can model the equatorial Cl- ligands in NpO2Cl42- quite accurately, compared to a fully wavefunction-based calculation, and this opens up the possibility of modeling the interaction of different ligands to actinyl species with relatively high accuracy but at a much reduced computational cost.

Localizing normal modes in large molecules

We show how vibrational spectra obtained from quantum chemical calculations can be analyzed by transforming the calculated normal modes contributing to a certain band in the vibrational spectrum to a set of localized modes. This is achieved by determining the unitary transformation that leads to modes which are maximally localized with respect to a suitably defined criterion. We demonstrate that these localized modes are more appropriate for the analysis of calculated vibrational spectra of polypeptides and proteins than the normal modes, which are usually delocalized over the whole system. Both the frequencies at which the bands in the vibrational spectra appear and the total intensities of these bands can be interpreted in terms of the localized modes. Furthermore, we show how coupling constants for the interaction between the localized modes, which can be employed to rationalize the observed band shapes, can be extracted from the calculations.

A subsystem density-functional theory approach for the quantum chemical treatment of proteins

We present an extension of the frozen-density embedding (FDE) scheme within density-functional theory [T. A. Wesolowski and A. Warshel, J. Phys. Chem. 97, 8050 (1993)] that can be applied to subsystems connected by covalent bonds, as well as a practical implementation of such an extended FDE scheme. We show how the proposed scheme can be employed for quantum chemical calculations of proteins by treating each constituting amino acid as a separate subsystem. To assess the accuracy of the extended FDE scheme, we present calculations for several dipeptides and for the protein ubiquitin.

Exact functional derivative of the nonadditive kinetic-energy bifunctional in the long-distance limit

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 H2O...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.

Can DFT Accurately Predict Spin Densities? Analysis of Discrepancies in Iron Nitrosyl Complexes.

Iron nitrosyl complexes are a particularly challenging case for density functional theory. In particular, for the low-spin state, different exchange-correlation functionals yield very different spin densities [ Conradie , J. ; Ghosh , A. J. Phys. Chem. B 2007 , 111 , 12621 - 12624 ]. Here, we investigate the origin of these differences in detail by analyzing the Kohn-Sham molecular orbitals. Furthermore, to decide which exchange-correlation functionals yield the most accurate spin densities, we make comparisons to CASSCF calculations. To ensure that the spin densities are converged with respect to the size of the active space, this comparison is performed for [Fe(NO)](2+) as a model system. We find that none of the investigated exchange-correlation functionals are able to reproduce the CASSCF spin densities accurately.