Direct simulation of electron transfer using ring polymer molecular dynamics: Comparison with semiclassical instanton theory and exact quantum methods

The use of ring polymer molecular dynamics (RPMD) for the direct simulation of electron transfer (ET) reaction dynamics is analyzed in the context of Marcus theory, semiclassical instanton theory, and exact quantum dynamics approaches. For both fully atomistic and system-bath representations of condensed-phase ET, we demonstrate that RPMD accurately predicts both ET reaction rates and mechanisms throughout the normal and activationless regimes of the thermodynamic driving force. Analysis of the ensemble of reactive RPMD trajectories reveals the solvent reorganization mechanism for ET that is anticipated in the Marcus rate theory, and the accuracy of the RPMD rate calculation is understood in terms of its exact description of statistical fluctuations and its formal connection to semiclassical instanton theory for deep-tunneling processes. In the inverted regime of the thermodynamic driving force, neither RPMD nor a related formulation of semiclassical instanton theory capture the characteristic turnover in the reaction rate; comparison with exact quantum dynamics simulations reveals that these methods provide inadequate quantization of the real-time electronic-state dynamics in the inverted regime

Analytical Gradients for Projection-Based Wavefunction-in-DFT Embedding

Projection-based embedding provides a simple, robust, and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction method while the remainder of the system is described at the level of density functional theory. Here, we present the derivation, implementation, and numerical demonstration of analytical nuclear gradients for projection-based wavefunction-in-density functional theory (WF-in-DFT) embedding. The gradients are formulated in the Lagrangian framework to enforce orthogonality, localization, and Brillouin constraints on the molecular orbitals. An important aspect of the gradient theory is that WF contributions to the total WF-in-DFT gradient can be simply evaluated using existing WF gradient implementations without modification. Another simplifying aspect is that Kohn-Sham (KS) DFT contributions to the projection-based embedding gradient do not require knowledge of the WF calculation beyond the relaxed WF density. Projection-based WF-in-DFT embedding gradients are thus easily generalized to any combination of WF and KS-DFT methods. We provide numerical demonstration of the method for several applications, including calculation of a minimum energy pathway for a hydride transfer in a cobalt-based molecular catalyst using the nudged-elastic-band method at the CCSD-in-DFT level of theory, which reveals large differences from the transition state geometry predicted using DFT.Comment: 15 pages, 4 figure

Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results

We compute the pointwise asymptotics of orthogonal polynomials with respect to a general class of pure point measures supported on finite sets as both the number of nodes of the measure and also the degree of the orthogonal polynomials become large. The class of orthogonal polynomials we consider includes as special cases the Krawtchouk and Hahn classical discrete orthogonal polynomials, but is far more general. In particular, we consider nodes that are not necessarily equally spaced. The asymptotic results are given with error bound for all points in the complex plane except for a finite union of discs of arbitrarily small but fixed radii. These exceptional discs are the neighborhoods of the so-called band edges of the associated equilibrium measure. As applications, we prove universality results for correlation functions of a general class of discrete orthogonal polynomial ensembles, and in particular we deduce asymptotic formulae with error bound for certain statistics relevant in the random tiling of a hexagon with rhombus-shaped tiles. The discrete orthogonal polynomials are characterized in terms of a a Riemann-Hilbert problem formulated for a meromorphic matrix with certain pole conditions. By extending the methods of [17, 22], we suggest a general and unifying approach to handle Riemann-Hilbert problems in the situation when poles of the unknown matrix are accumulating on some set in the asymptotic limit of interest.Comment: 28 pages, 7 figure

Exact nonadditive kinetic potentials for embedded density functional theory

We describe an embedded density functional theory (DFT) protocol in which the nonadditive kinetic energy component of the embedding potential is treated exactly. At each iteration of the Kohn–Sham equations for constrained electron density, the Zhao–Morrison–Parr constrained search method for constructing Kohn–Sham orbitals is combined with the King-Handy expression for the exact kinetic potential. We use this formally exact embedding protocol to calculate ionization energies for a series of three- and four-electron atomic systems, and the results are compared to embedded DFT calculations that utilize the Thomas–Fermi (TF) and the Thomas–Fermi–von Weisacker approximations to the kinetic energy functional. These calculations illustrate the expected breakdown due to the TF approximation for the nonadditive kinetic potential, with errors of 30%–80% in the calculated ionization energies; by contrast, the exact protocol is found to be accurate and stable. To significantly improve the convergence of the new protocol, we introduce a density-based switching function to map between the exact nonadditive kinetic potential and the TF approximation in the region of the nuclear cusp, and we demonstrate that this approximation has little effect on the accuracy of the calculated ionization energies. Finally, we describe possible extensions of the exact protocol to perform accurate embedded DFT calculations in large systems with strongly overlapping subsystem densities

Supporting Career Development and Employment: Benefits Planning, Assistance and Outreach (BPA&O) and Protection and Advocacy for Beneficiaries of Social Security (PABSS)

This training curriculum is dedicated to increasing knowledge and understanding of the Social Security Administration\u27s disability and return to work programs and work incentive provisions as prescribed in the Social Security Act and Ticket to Work and Work Incentives Improvement Act of 1999 as well as other federal benefit programs. These informational resources were compiled and edited to provide continuing education and print materials for benefits specialists and protection and advocacy personnel on the interplay of these benefit programs and impact or employment

A Two-Coordinate Nickel Imido Complex That Effects C−H Amination

An exceptionally low coordinate nickel imido complex, (IPr*)Ni═N(dmp) (2) (dmp = 2,6-dimesitylphenyl), has been prepared by the elimination of N_2 from a bulky aryl azide in its reaction with (IPr*)Ni(η^6-C_7H_8) (1). The solid-state structure of 2 features two-coordinate nickel with a linear C−Ni−N core and a short Ni−N distance, both indicative of multiple-bond character. Computational studies using density functional theory showed a Ni═N bond dominated by Ni(dπ)−N(pπ) interactions, resulting in two nearly degenerate singly occupied molecular orbitals (SOMOs) that are Ni−N π* in character. Reaction of 2 with CO resulted in nitrene-group transfer to form (dmp)NCO and (IPr*)Ni(CO)_3 (3). Net C−H insertion was observed in the reaction of 2 with ethene, forming the vinylamine (dmp)NH(CH═CH_2) (5) via an azanickelacyclobutane intermediate, (IPr*)Ni{N,C:κ^2-N(dmp)CH_2CH_2} (4)

The Changing Financial Structure of the U.S. Farm Sector

Agricultural Finance,

Growth of the Northern Fur Seal Colony on Bogoslof Island, Alaska

Northern fur seal, Callorhinus ursinus, pups were first observed on Bogoslof Island, southeast Bering Sea, in 1980. By 1988 the population had grown at a rate of 57%/yr to over 400 individuals, including 80+ pups, 159 adult females, 22 territorial males, and 188 subadult males. Some animals originated from rookeries of the Commander Islands, whereas others are probably from the Pribilof Islands. In 1983 and 1985 over 50% of the females were estimated to be >6 years of age, based on vibrissae color. The rookery is in the same location where solitary male fur seals were seen in 1976 and 1979 and is adjacent to a large northern sea lion rookery.Key words: Bogoslof Island, northern fur seal, Callorhinus ursinus, northern sea lion, breeding colonyMots clés: île Bogoslof, otarie à fourrure nordique, Callorhinus ursinus, lion de mer nordique, colonie reproductric