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The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models. [ABSTRACT FROM AUTHOR]

Excess hazard models became the preferred modelling tool in population-based cancer survival research. In this setting, the model is commonly formulated as the additive decomposition of the overall hazard into two components: the excess hazard due to the cancer of interest and the population hazard due to all other causes of death. We introduce a flexible Bayesian regression model for the log-excess hazard where the baseline log-excess hazard and any non-linear effects of covariates are modelled using low-rank thin plate splines. Using this type of splines will ensure that the log-likelihood function retains tractability not requiring numerical integration. We demonstrate how to derive posterior distributions for the excess hazard and for net survival, a population-level measure of cancer survival that can be derived from excess hazard models. We illustrate the proposed model using survival data for patients diagnosed with colon cancer during 2009 in London, England. [ABSTRACT FROM AUTHOR]