Alternative sampling for variational quantum Monte Carlo

Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous publication it has been shown that for the simplest, most commonly applied strategy in continuum Quantum Monte Carlo, the random error in the resulting estimates is not well controlled. At best the Central Limit theorem is valid in its weakest form, and at worst it is invalid and replaced by an alternative Generalised Central Limit theorem and non-Normal random error. In both cases the random error is not controlled. Here we consider a new `residual sampling strategy' that reintroduces the Central Limit Theorem in its strongest form, and provides full control of the random error in estimates. Estimates of the total energy and the variance of the local energy within Variational Monte Carlo are considered in detail, and the approach presented may be generalised to expectation values of other operators, and to other variants of the Quantum Monte Carlo method.Comment: 14 pages, 9 figure

Accurate structure factors from pseudopotential methods

Highly accurate experimental structure factors of silicon are available in the literature, and these provide the ideal test for any \emph{ab initio} method for the construction of the all-electron charge density. In a recent paper [J. R. Trail and D. M. Bird, Phys. Rev. B {\bf 60}, 7863 (1999)] a method has been developed for obtaining an accurate all-electron charge density from a first principles pseudopotential calculation by reconstructing the core region of an atom of choice. Here this method is applied to bulk silicon, and structure factors are derived and compared with experimental and Full-potential Linear Augmented Plane Wave results (FLAPW). We also compare with the result of assuming the core region is spherically symmetric, and with the result of constructing a charge density from the pseudo-valence density + frozen core electrons. Neither of these approximations provide accurate charge densities. The aspherical reconstruction is found to be as accurate as FLAPW results, and reproduces the residual error between the FLAPW and experimental results.Comment: 6 Pages, 3 figure

Core reconstruction in pseudopotential calculations

A new method is presented for obtaining all-electron results from a pseudopotential calculation. This is achieved by carrying out a localised calculation in the region of an atomic nucleus using the embedding potential method of Inglesfield [J.Phys. C {\bf 14}, 3795 (1981)]. In this method the core region is \emph{reconstructed}, and none of the simplifying approximations (such as spherical symmetry of the charge density/potential or frozen core electrons) that previous solutions to this problem have required are made. The embedding method requires an accurate real space Green function, and an analysis of the errors introduced in constructing this from a set of numerical eigenstates is given. Results are presented for an all-electron reconstruction of bulk aluminium, for both the charge density and the density of states.Comment: 14 pages, 5 figure

Hydrogen incorporation and charge balance in natural zircon

The water and trace element contents of natural igneous zircons were determined to constrain the mechanism of hydrogen incorporation. The low radiation-damage zircons were derived from Fe–Ti oxide gabbros from the Vema Fracture Zone (11°N, Mid-Atlantic Ridge). They contain up to 1212 ppmw H2O, 1.9 wt.% Y2O3 and 0.6 wt.% P2O5 and are generally strongly zoned. REE + Y are partially charge-balanced by P (Y, REE3+ + P5+ = Zr4+ + Si4+), but a large REE excess is present. On an atomic basis, this excess is closely approximated by the amount of H present in the zircons. We therefore conclude that H is incorporated by a charge-balance mechanism (H+ + REE3+ = Zr4+). This interpretation is consistent with FTIR data of the Vema zircons, which shows a strongly polarised main absorption band at ca. 3100 cm−1, similar to experimentally grown Lu-doped hydrous zircon. The size of this 3100 cm−1 band scales with H and REE contents. Apart from a small overlapping band at 3200 cm−1, no other absorption bands are visible, indicating that a hydrogrossular-type exchange mechanism does not appear to be operating in these zircons. Because of charge-balanced uptake of H, P and REE in zircon, the partitioning of these elements into zircon is dependent on each of their concentrations. For instance, DREEzrc/melt increases with increasing H and P contents of the melt, whereas DHzrc/melt increases with increasing REE content but decreases with increasing P content. In addition, H–P–REE systematics of sector zoning indicate kinetic effects may play an important role. Hence, using H in zircon to determine the water content of melts is problematic, and REE partitioning studies need to take into account P and H2O contents of the melt

Density-functional embedding using a plane-wave basis

The constrained electron density method of embedding a Kohn-Sham system in a substrate system (first described by P. Cortona, Phys. Rev. B {\bf 44}, 8454 (1991) and T.A. Wesolowski and A. Warshel, J. Phys. Chem {\bf 97}, 8050 (1993)) is applied with a plane-wave basis and both local and non-local pseudopotentials. This method divides the electron density of the system into substrate and embedded electron densities, the sum of which is the electron density of the system of interest. Coupling between the substrate and embedded systems is achieved via approximate kinetic energy functionals. Bulk aluminium is examined as a test case for which there is a strong interaction between the substrate and embedded systems. A number of approximations to the kinetic-energy functional, both semi-local and non-local, are investigated. It is found that Kohn-Sham results can be well reproduced using a non-local kinetic energy functional, with the total energy accurate to better than 0.1 eV per atom and good agreement between the electron densities.Comment: 11 pages, 4 figure

Pervasive remagnetization of detrital zircon host rocks in the Jack Hills, Western Australia and implications for records of the early geodynamo

It currently is unknown when Earth's dynamo magnetic field originated. Paleomagnetic studies indicate that a field with an intensity similar to that of the present day existed 3.5 billion years ago (Ga). Detrital zircon crystals found in the Jack Hills of Western Australia are some of the very few samples known to substantially predate this time. With crystallization ages ranging from 3.0–4.38 Ga, these zircons might preserve a record of the missing first billion years of Earth's magnetic field history. However, a key unknown is the age and origin of magnetization in the Jack Hills zircons. The identification of >3.9 Ga (i.e., Hadean) field records requires first establishing that the zircons have avoided remagnetization since being deposited in quartz-rich conglomerates at 2.65–3.05 Ga. To address this issue, we have conducted paleomagnetic conglomerate, baked contact, and fold tests in combination with U–Pb geochronology to establish the timing of the metamorphic and alteration events and the peak temperatures experienced by the zircon host rocks. These tests include the first conglomerate test directly on the Hadean-zircon bearing conglomerate at Erawandoo Hill. Although we observed little evidence for remagnetization by recent lightning strikes, we found that the Hadean zircon-bearing rocks and surrounding region have been pervasively remagnetized, with the final major overprinting likely due to thermal and/or aqueous effects from the emplacement of the Warakurna large igneous province at ∼1070 million years ago (Ma). Although localized regions of the Jack Hills might have escaped complete remagnetization, there currently is no robust evidence for pre-depositional (>3.0 Ga) magnetization in the Jack Hills detrital zircons