Geometrical picture of the electron-electron correlation at the large-D limit.

In electronic structure calculations, the correlation energy is defined as the difference between the mean field and the exact solution of the non relativistic Schrödinger equation. Such an error in the different calculations is not directly observable as there is no simple quantum mechanical operator, apart from correlation functions, that correspond to such quantity. Here, we use the dimensional scaling approach, in which the electrons are localized at the large-dimensional scaled space, to describe a geometric picture of the electronic correlation. Both, the mean field, and the exact solutions at the large-D limit have distinct geometries. Thus, the difference might be used to describe the correlation effect. Moreover, correlations can be also described and quantified by the entanglement between the electrons, which is a strong correlation without a classical analog. Entanglement is directly observable and it is one of the most striking properties of quantum mechanics and bounded by the area law for local gapped Hamiltonians of interacting many-body systems. This study opens up the possibility of presenting a geometrical picture of the electron-electron correlations and might give a bound on the correlation energy. The results at the large-D limit and at D = 3 indicate the feasibility of using the geometrical picture to get a bound on the electron-electron correlations.

Thermodynamic feasibility of shipboard conversion of marine plastics to blue diesel for self-powered ocean cleanup.

Collecting and removing ocean plastics can mitigate their environmental impacts; however, ocean cleanup will be a complex and energy-intensive operation that has not been fully evaluated. This work examines the thermodynamic feasibility and subsequent implications of hydrothermally converting this waste into a fuel to enable self-powered cleanup. A comprehensive probabilistic exergy analysis demonstrates that hydrothermal liquefaction has potential to generate sufficient energy to power both the process and the ship performing the cleanup. Self-powered cleanup reduces the number of roundtrips to port of a waste-laden ship, eliminating the need for fossil fuel use for most plastic concentrations. Several cleanup scenarios are modeled for the Great Pacific Garbage Patch (GPGP), corresponding to 230 t to 11,500 t of plastic removed yearly; the range corresponds to uncertainty in the surface concentration of plastics in the GPGP. Estimated cleanup times depends mainly on the number of booms that can be deployed in the GPGP without sacrificing collection efficiency. Self-powered cleanup may be a viable approach for removal of plastics from the ocean, and gaps in our understanding of GPGP characteristics should be addressed to reduce uncertainty.

Dimensional Interpolation for Random Walk.

We employ a simple and accurate dimensional interpolation formula for the shapes of random walks at D = 3 and D = 2 based on the analytically known solutions at both limits D = ∞ and D = 1. The results obtained for the radius of gyration of an arbitrary shaped object have about 2% error compared with accurate numerical results at D = 3 and D = 2. We also calculated the asphericity for a three-dimensional random walk using the dimensional interpolation formula. The results agree very well with the numerically simulated results. The method is general and can be used to estimate other properties of random walks.

Dimensional interpolation for metallic hydrogen.

We employ a simple and mostly accurate dimensional interpolation formula using dimensional limits D = 1 and D = ∞ to obtain D = 3 ground-state energy of metallic hydrogen. We also present results describing the phase transitions for different symmetries of three-dimensional structure lattices. The interpolation formula not only predicts fairly accurate energies but also predicts a correct functional form of the energy as a function of the lattice parameters. That allows us to calculate different physical quantities such as the bulk modulus, Debye temperature, and critical transition temperature, from the gradient and the curvature of the energy curve as a function of the lattice parameters. These theoretical calculations suggest that metallic hydrogen is a likely candidate for high temperature superconductivity. The dimensional interpolation formula is robust and might be useful to obtain the energies of complex many-body systems.

Exploring Unorthodox Dimensions for Two-Electron Atoms.

Melding quantum and classical mechanics is an abiding quest of physical chemists who strive for heuristic insights and useful tools. We present a surprisingly simple and accurate treatment of ground-state two-electron atoms. It makes use of only the dimensional dependence of a hydrogen atom, together with the exactly known first-order perturbation value of the electron-electron interaction, both quintessentially quantum, and the D → ∞ limit, entirely classical. The result is an analytic formula for D-dimensional two-electron atoms with Z ≥ 2. For D = 3 helium, it gives accuracy better than 2 millihartrees, which is better than current density functional theory. A kindred explicit formula for correlation energy exploits interpolation between D → ∞ and D = 1 or 2; when added to the Hartree-Fock energy, it improves accuracy for D = 3 helium to better than 0.1 millihartrees.

Michael Polanyi: Patriarch of Chemical Dynamics and Tacit Knowing.

Connecting Science and the Humanities was the title of the symposium on Michael Polanyi that took place at the Technische Universität Berlin (Technical University of Berlin) in October 2016. This essay, which appraises the scientific and philosophical contributions of Michael Polanyi, is based on the presentation given by Dr. Herschbach on this occasion. In the photograph: Polanyi in 1931.

Theodore William Richards: apostle of atomic weights and Nobel Prize winner in 1914.

In recognition of his exact determinations of the atomic weights of a large number of the chemical elements, T. W. Richards received the Nobel Prize in Chemistry in 1914. His meticulous techniques resulted in "a degree of accuracy never before attained". This Essay follows Richards from his precocious youth to becoming a celebrated chemist and emphasizes his dedication to forseeing likely sources of error and how to avoid them.

Unique Properties of Thermally Tailored Copper: Magnetically Active Regions and Anomalous X-ray Fluorescence Emissions.

When high-purity copper (>/=99.98%(wt)) is melted, held in its liquid state for a few hours with iterative thermal cycling, then allowed to resolidify, the ingot surface is found to have many small regions that are magnetically active. X-ray fluorescence analysis of these regions exhibit remarkably intense lines from "sensitized elements" (SE), including in part or fully the contiguous series V, Cr, Mn, Fe, and Co. The XRF emissions from SE are far more intense than expected from known impurity levels. Comparison with blanks and standards show that the thermal "tailoring" also introduces strongly enhanced SE emissions in samples taken from the interior of the copper ingots. For some magnetic regions, the location as well as the SE emissions, although persistent, vary irregularly with time. Also, for some regions extraordinarily intense "sensitized iron" (SFe) emissions occur, accompanied by drastic attenuation of Cu emissions.

Manipulation of slow molecular beams by static external fields.

Deflection by magnetic or electric field gradients has long been used to analyze or to alter the translational trajectories of neutral gas-phase atoms or molecules. Recent work has developed sources of slow, cold molecular beams that offer means to enhance markedly the attainable deflections, which are inversely proportional to the translational kinetic energy. The sensitivity and resolution can thus be much increased, typically by factors of 10(2)-10(4). We illustrate ways to exploit this enhanced deflection capability, particularly when balancing electric and magnetic deflections. Chemical scope can be greatly extended by utilizing feeble but ubiquitous interactions, especially the induced electric dipole due to the molecular polarizability and magnetic moments resulting from molecular rotation or nuclear spins. We also examine the effect of non-Maxwellian velocity distributions produced by supersonic expansions or by quantum statistics (pertinent for ultracold beams). Generic plots are provided, employing dimensionless variables, to facilitate the design and interpretation of experiments with deflections amplified by low kinetic energy.

Simple and surprisingly accurate approach to the chemical bond obtained from dimensional scaling.

We present a new dimensional scaling transformation of the Schrödinger equation for the two electron bond. This yields, for the first time, a good description of the bond via D scaling. There also emerges, in the large-D limit, an intuitively appealing semiclassical picture, akin to a molecular model proposed by Bohr in 1913. In this limit, the electrons are confined to specific orbits in the scaled space, yet the uncertainty principle is maintained. A first-order perturbation correction, proportional to 1/D, substantially improves the agreement with the exact ground state potential energy curve. The present treatment is very simple mathematically, yet provides a strikingly accurate description of the potential curves for the lowest singlet, triplet, and excited states of H2. We find the modified D-scaling method also gives good results for other molecules. It can be combined advantageously with Hartree-Fock and other conventional methods.

Bohr's 1913 molecular model revisited.

It is generally believed that the old quantum theory, as presented by Niels Bohr in 1913, fails when applied to few electron systems, such as the H(2) molecule. Here, we find previously undescribed solutions within the Bohr theory that describe the potential energy curve for the lowest singlet and triplet states of H(2) about as well as the early wave mechanical treatment of Heitler and London. We also develop an interpolation scheme that substantially improves the agreement with the exact ground-state potential curve of H(2) and provides a good description of more complicated molecules such as LiH, Li(2), BeH, and He(2).

High-pressure vibrational spectroscopy of sulfur dioxide.

Solid sulfur dioxide was investigated by vibrational spectroscopy over a broad pressure and temperature range, extending to 32.5 GPa at 75-300 K in diamond anvil cells. Synchrotron infrared spectra provided the first measurements of the pressure dependence of the lattice modes in the far-IR region. Below 17.5 GPa, two fundamentals exhibit splittings enhanced by pressure. The asymmetric stretching mode of SO(2) exhibits a remarkable pressure-induced softening. The observations are consistent with the ambient pressure Raman measurements indicating that SO(2) crystallizes in an acentric cell, but are inconsistent with a previously proposed interpretation that the structure of the high-pressure phase consists of (SO(2))(3) clusters. Dramatic changes in the Raman spectra are found above 17.5 GPa at room temperature. These indicate major changes in structure and possible formation of SO(2) clustering with an enlarged unit cell. The behavior at low temperature differs from that at room temperature. These findings provide constraints on the phase diagram of sulfur dioxide.

Generation of methane in the Earth's mantle: in situ high pressure-temperature measurements of carbonate reduction.

We present in situ observations of hydrocarbon formation via carbonate reduction at upper mantle pressures and temperatures. Methane was formed from FeO, CaCO(3)-calcite, and water at pressures between 5 and 11 GPa and temperatures ranging from 500 degrees C to 1,500 degrees C. The results are shown to be consistent with multiphase thermodynamic calculations based on the statistical mechanics of soft particle mixtures. The study demonstrates the existence of abiogenic pathways for the formation of hydrocarbons in the Earth's interior and suggests that the hydrocarbon budget of the bulk Earth may be larger than conventionally assumed.

Electron localization-delocalization transitions in dissociation of the C4- anion: a large-D analysis.

We present a study, employing high level ab initio methods, of electron localization-delocalization transitions along the dissociation path of the C4- anion to C2 and C2-. We find that at the equilibrium geometry, the symmetrical and nonsymmetrical configurations of the linear C4- anion are almost isoenergetic. However, along a collinear dissociation path, the dipole moment drops abruptly to zero when the separation between the two middle carbon nuclei reaches about R = 2.15 angstroms. The dipole moment remains zero until about R = 2.78 angstroms, and then continuously increases as dissociation proceeds. This behavior is analogous to critical phenomena: The abrupt drop to zero of the dipole moment resembles a first-order phase transition, the later steady rise resembles a continuous phase transition. We show that a simple sub-Hamiltonian model, corresponding to the large-dimension limit for an electron in the field of four collinear carbon atoms, exhibits both kinds of phase transitions along the dissociation path.