Tensor decomposition in post-Hartree-Fock methods. II. CCD implementation.

In a previous publication, we have discussed the usage of tensor decomposition in the canonical polyadic (CP) tensor format for electronic structure methods. There, we focused on two-electron integrals and second order Møller-Plesset perturbation theory (MP2). In this work, we discuss the CP format for Coupled Cluster (CC) theory and present a pilot implementation for the Coupled Cluster Doubles method. We discuss the iterative solution of the CC amplitude equations using tensors in CP representation and present a tensor contraction scheme that minimizes the effort necessary for the rank reductions during the iterations. Furthermore, several details concerning the reduction of complexity of the algorithm, convergence of the CC iterations, truncation errors, and the choice of threshold for chemical accuracy are discussed.

Interaction of platinum nanoparticles with graphitic carbon structures: a computational study.

The interaction of platinum nanoparticles from a size of a few atoms up to 1 nm with extended carbon structures is studied by using quantum chemical methods. The aim is to obtain a deeper insight into the basic interactions between metal particles and carbon structures. For this purpose focus is placed on the type and strength of the interactions as well as the possibility to increase the adhesive forces by introducing chemical modifications (linker atoms) and defect sites or distortions of the support. The calculations show that there is a transition between an interaction with covalent character for smaller clusters and a dispersion-dominated interaction for larger particles. Furthermore, introduced linker atoms increase the covalent character of the interactions but also increase the distance between the cluster and the support, thereby leading to a lower interaction energy. This has implications for the design of chemical linkers or surface modifications to improve the durability of catalyst systems.

The impact of spectator species on the interaction of H2O2 with platinum--implications for the oxygen reduction reaction pathways.

The impact of electrolyte constituents on the interaction of hydrogen peroxide with polycrystalline platinum is decisive for the understanding of the selectivity of the oxygen reduction reaction (ORR). Hydrodynamic voltammetry measurements show that while the hydrogen peroxide reduction (PRR) is diffusion-limited in perchlorate- or fluoride-containing solutions, kinetic limitations are introduced by the addition of more strongly adsorbing anions. The strength of the inhibition of the PRR increases in the order ClO4(-)≈ F(-) < HSO4(-) < Cl(-) < Br(-) < I(-) as well as with the increase of the concentration of the strongly adsorbing anions. Electronic structure calculations indicate that the dissociation of H2O2 on Pt(111) is always possible, regardless of the coverage of spectator species. However, the adsorption of H2O2 becomes strongly endothermic at high coverage with adsorbing anions. A comparison of our observations on the inhibition of the PRR by spectators with previous studies on the selectivity of the ORR shows that oxygen is reduced to H2O2 only under conditions at which the PRR kinetics is significantly limited, while the ORR proceeds with a complete four-electron reduction only when the PRR is sufficiently fast. Therefore, only a H2O2-mediated pathway that includes a competition between the dissociation and the spectator coverage-dependent desorption of the H2O2 intermediate is enough to explain and unify all the observations that have been made so far on the selectivity of the ORR.

Modelling electrified interfaces in quantum chemistry: constant charge vs. constant potential.

The proper description of electrified metal/solution interfaces, as they occur in electrochemical systems, is a key component for simulating the unique features of electrocatalytic reactions using electronic structure calculations. While in standard solid state (plane wave, periodic boundary conditions) density functional theory (DFT) calculations several models for describing electrochemical environments exist, for cluster models in a quantum chemistry approach (atomic orbital basis, finite system) this is not straightforward. In this work, two different approaches for the theoretical description of electrified interfaces of nanoparticles, the constant charge and the constant potential model, are discussed. Different schemes for describing electrochemical reactions including solvation models are tested for a consistent description of the electrochemical potential and the local chemical behavior for finite structures. The different schemes and models are investigated for the oxygen reduction reaction (ORR) on a hemispherical cuboctahedral platinum nanoparticle.

Hydrogen peroxide electrochemistry on platinum: towards understanding the oxygen reduction reaction mechanism.

Understanding the hydrogen peroxide electrochemistry on platinum can provide information about the oxygen reduction reaction mechanism, whether H(2)O(2) participates as an intermediate or not. The H(2)O(2) oxidation and reduction reaction on polycrystalline platinum is a diffusion-limited reaction in 0.1 M HClO(4). The applied potential determines the Pt surface state, which is then decisive for the direction of the reaction: when H(2)O(2) interacts with reduced surface sites it decomposes producing adsorbed OH species; when it interacts with oxidized Pt sites then H(2)O(2) is oxidized to O(2) by reducing the surface. Electronic structure calculations indicate that the activation energies of both processes are low at room temperature. The H(2)O(2) reduction and oxidation reactions can therefore be utilized for monitoring the potential-dependent oxidation of the platinum surface. In particular, the potential at which the hydrogen peroxide reduction and oxidation reactions are equally likely to occur reflects the intrinsic affinity of the platinum surface for oxygenated species. This potential can be experimentally determined as the crossing-point of linear potential sweeps in the positive direction for different rotation rates, hereby defined as the "ORR-corrected mixed potential" (c-MP).

Tensor decomposition in post-Hartree-Fock methods. I. Two-electron integrals and MP2.

A new approximation for post-Hartree-Fock (HF) methods is presented applying tensor decomposition techniques in the canonical product tensor format. In this ansatz, multidimensional tensors like integrals or wavefunction parameters are processed as an expansion in one-dimensional representing vectors. This approach has the potential to decrease the computational effort and the storage requirements of conventional algorithms drastically while allowing for rigorous truncation and error estimation. For post-HF ab initio methods, for example, storage is reduced to O(d·R·n) with d being the number of dimensions of the full tensor, R being the expansion length (rank) of the tensor decomposition, and n being the number of entries in each dimension (i.e., the orbital index). If all tensors are expressed in the canonical format, the computational effort for any subsequent tensor contraction can be reduced to O(R(2)·n). We discuss details of the implementation, especially the decomposition of the two-electron integrals, the AO-MO transformation, the Møller-Plesset perturbation theory (MP2) energy expression and the perspective for coupled cluster methods. An algorithm for rank reduction is presented that parallelizes trivially. For a set of representative examples, the scaling of the decomposition rank with system and basis set size is found to be O(N(1.8)) for the AO integrals, O(N(1.4)) for the MO integrals, and O(N(1.2)) for the MP2 t(2)-amplitudes (N denotes a measure of system size) if the upper bound of the error in the l(2)-norm is chosen as ε = 10(-2). This leads to an error in the MP2 energy in the order of mHartree.

Beyond Cassie's law: a theoretical and experimental study of mixed alkyl monolayers.

Within this study, the influence of ester groups in mixed monolayers on the surface properties will be discussed. Detailed investigations on the macroscopic and microscopic characteristics on mixed monolayers with different content of ester groups in an alkyl surrounding are done by contact angle measurements and atomic force spectroscopy. Density functional theory (DFT) calculations show a statistical distribution and a directed orientation of the ester molecules. In the experiments an increasing amount of ester groups leads to a fast increasing polarity followed by a nearly constant polarity in the regime of 25% and 40% of ester in the monolayer and a further increase at higher amounts of ester groups, which clearly differ from the behavior expected by Cassie. By DFT calculations it can be shown that water molecules form ring-like structures around the ester group. These solvent shells increase the hydrophilic fraction on the surface explaining the disproportional growth in the polarity of the monolayer. This rise in polarity is maximal for single ester groups (monomers) or dimers of esters. The amount of these monomers and dimers is estimated by Monte Carlo simulation showing clearly that the linear regime at fractions between 0.25 and 0.4 are caused by the transition from mainly monomers to mainly dimers. Thus, we show for the first time that adsorbed water molecules forming a solvent shell around hydrophilic groups in hydrophobic surroundings influence the surface properties of mixed monolayers on a macroscopic and microscopic scale which therefore must be taken into account when preparing, investigating, using and understanding such monolayers.

Optimization of augmentation functions for correlated calculations of spin-spin coupling constants and related properties.

A new hierarchy of augmented basis sets optimized for the calculation of molecular properties such as indirect spin-spin coupling constants is presented. Based on the Dunning hierarchy of cc-pVXZ (X = D, T, Q, and 5) basis sets augmentation functions with tight exponents have been optimized for coupled-cluster calculations of indirect spin-spin coupling constants. The optimal exponents for these tight functions have been obtained by optimizing the sum of the absolute values of all contributions to the coupling constant. On the basis of a series of test cases (CO, HF, N(2), F(2), H(2)O, NH(3), and CH(4)) we propose a set of tight s, p, and d functions to be added to the uncontracted Dunning basis sets, and, subsequently, to recontract. The resulting ccJ-pVXZ (X = D, T, Q, and 5) basis sets demonstrate excellent cost efficiency in benchmark calculations. These new basis sets should generally be applicable for the calculation of spin-spin coupling constants and other properties that have a strong dependence on powers of 1r or even contain a delta distribution for correlated ab initio methods.