A recently described symmetrical windowing methodology [S. J. Cotton and W. H. Miller, J. Phys. Chem. A 117, 7190 (2013)] for quasi-classical trajectory simulations is applied here to the Meyer-Miller [H.-D. Meyer and W. H. Miller, J. Chem. Phys. 70, 3214 (1979)] model for the electronic degrees of freedom in electronically non-adiabatic dynamics. Results generated using this classical approach are observed to be in very good agreement with accurate quantum mechanical results for a variety of test applications, including problems where coherence effects are significant such as the challenging asymmetric spin-boson system.
An approach has been developed for extracting approximate quantum stateto-state information from classical trajectory simulations which "quantizes" symmetrically both the initial and final classical actions associated with the degrees of freedom of interest using quantum number bins (or "window functions") which are significantly narrower than unit-width. This approach thus imposes a more stringent quantization condition on classical trajectory simulations than has been traditionally employed, while doing so in a manner that is time-symmetric and microscopically reversible.To demonstrate this "symmetric quasi-classical" (SQC) approach for a simple real system, collinear H + H 2 reactive scattering calculations were performed [1] with SQC-quantization applied to the H 2 vibrational degree of freedom (DOF). It was seen that the use of window functions of approximately 1 2 -unit width led to calculated reaction probabilities in very good agreement with quantum mechanical results over the threshold energy region, representing a significant improvement over what is obtained using the traditional quasiclassical procedure.The SQC approach was then applied [2] to the much more interesting and challenging problem of incorporating non-adiabatic e↵ects into what would otherwise be standard classical trajectory simulations. To do this, the classical Meyer-Miller (MM) Hamiltonian was used to model the electronic DOFs, with SQC-quantization applied to the classical "electronic" actions of the MM model-representing the occupations of the electronic states-in order to extract the electronic state population dynamics. It was demonstrated that if one ties the zero-point energy (ZPE) of the electronic DOFs to the SQC windowing 1 function's width parameter this very simple SQC/MM approach is capable of quantitatively reproducing quantum mechanical results for a range of standard benchmark models of electronically non-adiabatic processes, including applications where "quantum" coherence e↵ects are significant. Notably, among these benchmarks was the well-studied "spin-boson" model of condensed phase nonadiabatic dynamics, in both its symmetric and asymmetric forms-the latter of which many classical approaches fail to treat successfully.The SQC/MM approach to the treatment of non-adiabatic dynamics was next applied [3] to several recently proposed models of condensed phase electron transfer (ET) processes. For these problems, a flux-side correlation function framework modified for consistency with the SQC approach was developed for the calculation of thermal ET rate constants, and excellent accuracy was seen over wide ranges of non-adiabatic coupling strength and energetic bias/exothermicity. Significantly, the "inverted regime" in thermal rate constants (with increasing bias) known from Marcus Theory was reproduced quantitatively for these models-representing the successful treatment of another regime that classical approaches generally have di culty in correctly describing. Relatedly, a model of photoinduced proton coupled electron...
In adult humans, the net absorption of dietary copper is approximately 1 mg/d. Dietary copper joins some 4-5 mg of endogenous copper flowing into the gastrointestinal tract through various digestive juices. Most of this copper returns to the circulation and to the tissues (including liver) that formed them. Much lower amounts of copper flow into and out of other major parts of the body (including heart, skeletal muscle, and brain). Newly absorbed copper is transported to body tissues in two phases, borne primarily by plasma protein carriers (albumin, transcuprein, and ceruloplasmin). In the first phase, copper goes from the intestine to the liver and kidney; in the second phase, copper usually goes from the liver (and perhaps also the kidney) to other organs. Ceruloplasmin plays a role in this second phase. Alternatively, liver copper can also exit via the bile, and in a form that is less easily reabsorbed. Copper is also present in and transported by other body fluids, including those bathing the brain and central nervous system and surrounding the fetus in the amniotic sac. Ceruloplasmin is present in these fluids and may also be involved in copper transport there. The concentrations of copper and ceruloplasmin in milk vary with lactational stage. Parallel changes occur in ceruloplasmin messenger RNA expression in the mammary gland (as determined in pigs). Copper in milk ceruloplasmin appears to be particularly available for absorption, at least in rats.
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