Embedded density functional theory for covalently bonded and strongly interacting subsystems

Embedded density functional theory (e-DFT) is used to describe the electronic structure of strongly interacting molecular subsystems. We present a general implementation of the Exact Embedding (EE) method [J. Chem. Phys. 133, 084103 (2010)] to calculate the large contributions of the nonadditive kinetic potential (NAKP) in such applications. Potential energy curves are computed for the dissociation of Li^+–Be, CH_3–CF_3, and hydrogen-bonded water clusters, and e-DFT results obtained using the EE method are compared with those obtained using approximate kinetic energy functionals. In all cases, the EE method preserves excellent agreement with reference Kohn–Sham calculations, whereas the approximate functionals lead to qualitative failures in the calculated energies and equilibrium structures. We also demonstrate an accurate pairwise approximation to the NAKP that allows for efficient parallelization of the EE method in large systems; benchmark calculations on molecular crystals reveal ideal, size-independent scaling of wall-clock time with increasing system size

Density functional theory embedding for correlated wavefunctions: Improved methods for open-shell systems and transition metal complexes

Density functional theory (DFT) embedding provides a formally exact framework for interfacing correlated wave-function theory (WFT) methods with lower-level descriptions of electronic structure. Here, we report techniques to improve the accuracy and stability of WFT-in-DFT embedding calculations. In particular, we develop spin-dependent embedding potentials in both restricted and unrestricted orbital formulations to enable WFT-in-DFT embedding for open-shell systems, and we develop an orbital-occupation-freezing technique to improve the convergence of optimized effective potential (OEP) calculations that arise in the evaluation of the embedding potential. The new techniques are demonstrated in applications to the van-der-Waals-bound ethylene-propylene dimer and to the hexaaquairon(II) transition-metal cation. Calculation of the dissociation curve for the ethylene-propylene dimer reveals that WFT-in-DFT embedding reproduces full CCSD(T) energies to within 0.1 kcal/mol at all distances, eliminating errors in the dispersion interactions due to conventional exchange-correlation (XC) functionals while simultaneously avoiding errors due to subsystem partitioning across covalent bonds. Application of WFT-in-DFT embedding to the calculation of the low-spin/high-spin splitting energy in the hexaaquairon(II) cation reveals that the majority of the dependence on the DFT XC functional can be eliminated by treating only the single transition-metal atom at the WFT level; furthermore, these calculations demonstrate the substantial effects of open-shell contributions to the embedding potential, and they suggest that restricted open-shell WFT-in-DFT embedding provides better accuracy than unrestricted open-shell WFT-in-DFT embedding due to the removal of spin contamination.Comment: 11 pages, 5 figures, 2 table

Far Term Noise Reduction Technology Roadmap for a Large Twin-Aisle Tube-And-Wing Subsonic Transport

Interest in unconventional aircraft architectures has steadily increased over the past several decades. However, each of these concepts has several technical challenges to overcome before maturing to the point of commercial acceptance. In the interim, it is important to identify any technologies that will enhance the noise reduction of conventional tube-and-wing aircraft. A technology roadmap with an assumed acoustic technology level of a 2035 entry into service is established for a large twin-aisle, tube-and-wing architecture to identify which technologies provide the most noise reduction. The noise reduction potential of the architecture relative to NASA noise goals is also assessed. The current roadmap estimates only a 30 EPNdB cumulative margin to Stage 4 for this configuration of a tube-and-wing aircraft with engines under the wing. This falls short of reaching even the 2025 Mid Term NASA goal (32 EPNdB) in the Far Term time frame. Specifically, the lack of additional technologies to reduce the aft fan noise and the corresponding installation effects is the key limitation of the noise reduction potential of the aircraft. Under the same acoustic technology assumptions, unconventional architectures are shown to offer an 810 EPNdB benefit from favorable relative placement of the engine when integrated to the airframe

Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present results from a new method that reconstructs maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type $\ell_1$-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass-mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on illustrative examples, before applying the developed formalism to two observational datasets of the Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of individual local massive substructure at significant confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data

Intended and Unintended Consequences: The 2006 Fair Minimum Wage Amendment of the Ohio Constitution

This Article first provides a brief overview of federal and Ohio minimum wage law. The Article then examines the text of the 2006 Amendment. The third section delves into the provisions of HB 690 and the differences between HB 690 and the Amendment. The final section explores litigation issues arising from these differences