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

Case Report: Diverticulitis Involving a Meckel’s Diverticulum

We report a case of a 65-year-old female who presented with abdominal pain and was diagnosed with diverticulitis involving a Meckel‘s Diverticulum. The differential diagnosis of abdominal pain is vast, in this age group includes, but is not limited to appendicitis, diverticulitis, cholecystitis, and small bowel obstruction. In the absence of complicated features, conservative management with oral antibiotics and close outpatient follow is advised. However, in the case of complicated diverticulitis and a rare manifestation such as a Meckel’s Diverticulum, careful management is indicated

New Class of 4-Dim Kochen-Specker Sets

We find a new highly symmetrical and very numerous class (millions of non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the nature of their geometrical symmetries, they cannot be obtained from previously known ones. We generate the sets from a single set of 60 orthogonal spin vectors and 75 of their tetrads (which we obtained from the 600-cell) by means of our newly developed "stripping technique." We also consider "critical KS subsets" and analyze their geometry. The algorithms and programs for the generation of our KS sets are presented.Comment: 7 pages, 3 figures; to appear in J. Math. Phys. Vol.52, No. 2 (2011

A framework for priority effects

History of species arrival can influence plant community assembly. In this issue of the Journal of Vegetation Science, Sarneel et al. show that the strength of such historical contingency, or priority effects, varies with soil moisture in riparian plants. We discuss this study within a theoretical framework describing how and when priority effects occur via destabilizing and equalizing mechanisms.History of species arrival can influence plant community assembly. In this issue of the Journal of Vegetation Science, Sarneel et al. show that the strength of such historical contingency, or priority effects, varies with soil moisture in riparian plants. We discuss this study within a theoretical framework describing how and when priority effects occur via destabilizing and equalizing mechanisms.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/122424/1/jvs12434.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/122424/2/jvs12434_am.pd

Mixing Time Scales in a Supernova-Driven Interstellar Medium

We study the mixing of chemical species in the interstellar medium (ISM). Recent observations suggest that the distribution of species such as deuterium in the ISM may be far from homogeneous. This raises the question of how long it takes for inhomogeneities to be erased in the ISM, and how this depends on the length scale of the inhomogeneities. We added a tracer field to the three-dimensional, supernova-driven ISM model of Avillez (2000) to study mixing and dispersal in kiloparsec-scale simulations of the ISM with different supernova (SN) rates and different inhomogeneity length scales. We find several surprising results. Classical mixing length theory fails to predict the very weak dependence of mixing time on length scale that we find on scales of 25--500 pc. Derived diffusion coefficients increase exponentially with time, rather than remaining constant. The variance of composition declines exponentially, with a time constant of tens of Myr, so that large differences fade faster than small ones. The time constant depends on the inverse square root of the supernova rate. One major reason for these results is that even with numerical diffusion exceeding physical values, gas does not mix quickly between hot and cold regions.Comment: 23 pages, 14 figures that include 7 simulation images and 19 plots, accepted for publication at Ap

Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence

Hydrodynamic supersonic turbulence can only prevent local gravitational collapse if the turbulence is driven on scales smaller than the local Jeans lengths in the densest regions, a very severe requirement (Paper I). Magnetic fields have been suggested to support molecular clouds either magnetostatically or via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would form sheet-like clouds, the second mechanism not only could exert a pressure onto the gas counteracting the gravitational forces, but could lead to a transfer of turbulent kinetic energy down to smaller spatial scales via MHD wave interactions. This turbulent magnetic cascade might provide sufficient energy at small scales to halt local collapse. We test this hypothesis with MHD simulations at resolutions up to 256^3 zones, done with ZEUS-3D. We first derive a resolution criterion for self-gravitating, magnetized gas: in order to prevent collapse of magnetostatically supported regions due to numerical diffusion, the minimum Jeans length must be resolved by four zones. Resolution of MHD waves increases this requirement to roughly six zones. We then find that magnetic fields cannot prevent local collapse unless they provide magnetostatic support. Weaker magnetic fields do somewhat delay collapse and cause it to occur more uniformly across the supported region in comparison to the hydrodynamical case. However, they still cannot prevent local collapse for much longer than a global free-fall time.Comment: 32 pages, 14 figures, accepted by Ap