Tests for balanced incomplete block ranked data with ties

We consider balanced incomplete block data when ties occur and propose new statistics for testing (a) differences in mean ranks, (b) differences in distributions of ranks, (c) differences in nonlinear effects of ranks and (d) linear contrasts. A sensory evaluation example where the data are ranks is give

First-Principles Modeling of Non-Covalent Interactions in Supramolecular Systems: The Role of Many-Body Effects

Supramolecular host-guest Systems play an important role for a wide range of applications in chemistry and biology. The prediction of the stability of host-guest complexes represents a great challenge to first-principles calculations Clue to, an interplay of a ride variety of covalent and noncovalent interactions in these systems. In particular van der Waals (vdW) dispersion interactions frequently play a prominent role in determining the structure, stability, and function of supramolecular systems. On the basis of the widely used benchmark case of the buckyball catcher complex (C-60@C60H28), we assess the feasibility of computing the binding energy of supramolecular host-guest complexes from first principles. Large-scale diffusion Monte Carlo (DMC) calculations are carried out to accurately determine the binding energy for the C-60@C60H28 complex (26 +/- 2 kcal/mol). On the basis of the DMC reference, we assess the accuracy of widely used and efficient density-functional theory (DFT) methods with dispersion interactions. The inclusion of vdW dispersion interactions in DFT leads to a large stabilization of the C-60@C60H28 complex. However, DFT methods including pairwise vdW interactions overestimate the stability of this complex by 9-17 kcal/mol compared to the DMC reference and the extrapolated experimental data. A significant part of this overestimation (9 kcal/mol) stems from the lack of dynamical dielectric screening effects in the description of the molecular polarizability in pairwise dispersion energy approaches. The remaining overstabilization. arises from the isotropic treatment of atomic polarizability tensors and the lack of Many-body dispersion interactions. A further; assessment of a different supramolecular system - glycine anhydride interacting with an amide macrocycle - demonstrates that both the dynamical screening and the many-body dispersion energy are complex contributions that are very sensitive to the underlying molecular geometry and type of bonding. We discuss the required improvements in theoretical methods for achieving ``chemical accuracy'' in the first-principles modeling of supramolecular systems

Benchmarking Calculated Lattice Parameters and Energies of Molecular Crystals Using van der Waals Density Functionals

The development of new functionals and methods to accurately describe van der Waals forces in density functional theory (DFT) has become popular in recent years, with the vast majority of studies assessing the accuracy of the energetics of collections of molecules, and to a lesser extent molecular crystalline systems. As the energies are a function of the atom positions, we assess the accuracy of DFT calculations from both a geometric and energetics point of view for the C21 reference data set of Otero-de-la-Roza and Johnson for molecular crystals, and a set of monosaccharide molecular crystals. In particular, we examine the performance of exchange-correlation functionals designed to handle van der Waals forces, including the vdW-DF, vdW-DF2, and XDM methods. We also assess the effect of using small and large basis sets, the choice of basis functions (local atomic orbitals using the SIESTA code versus planewaves using the Quantum ESPRESSO code), and the effect of corrections for basis set superposition errors. Finally, we examine the geometries and energies of the S22 reference set of molecular complexes. Overall, the most accurate geometries for both choices of basis functions are obtained with the vdW-DF2 functional, while the most accurate lattice energies are obtained using vdW-DF2 with local atomic orbitals and XDM with planewaves with mean absolute errors of less than 4 kJ/mol