Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices within DIIS. This differs from the traditional DIIS of Pulay, which uses an object function derived from the commutator of the density and Fock matrices. Our results show that the present algorithm, abbreviated ADIIS, is more robust and efficient than the energy-DIIS (EDIIS) approach. In particular, several examples demonstrate that the combination of ADIIS and DIIS ("ADIIS+DIIS") is highly reliable and efficient in accelerating SCF convergence.

Convergence of numerical time-averaging and stationary measures via Poisson equations

Numerical approximation of the long time behavior of a stochastic di.erential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the stationary behavior of the numerical method converges to that of the SDE. The error analysis is based on using an associated Poisson equation for the underlying SDE. The main advantages of this approach are its simplicity and universality. It works equally well for a range of explicit and implicit schemes, including those with simple simulation of random variables, and for hypoelliptic SDEs. To simplify the exposition, we consider only the case where the state space of the SDE is a torus, and we study only smooth test functions. However, we anticipate that the approach can be applied more widely. An analogy between our approach and Stein's method is indicated. Some practical implications of the results are discussed. Copyright © by SIAM. Unauthorized reproduction of this article is prohibited.

North atlantic deepwater temperature change during late pliocene and late quaternary climatic cycles

Variations in the ratio of magnesium to calcium (Mg/Ca) in fossil ostracodes from Deep Sea Drilling Project Site 607 in the deep North Atlantic show that the change in bottom water temperature during late Pliocene 41,000-year obliquity cycles averaged 1.5°C between 3.2 and 2.8 million years ago (Ma) and increased to 2.3°C between 2.8 and 2.3 Ma, coincidentally with the intensification of Northern Hemisphere glaciation. During the last two 100,000-year glacial-to-interglacial climatic cycles of the Quaternary, bottom water temperatures changed by 4.5°C. These results show that glacial deepwater cooling has intensified since 3.2 Ma, most likely as the result of progressively diminished deep-water production in the North Atlantic and of the greater influence of Antarctic bottom water in the North Atlantic during glacial periods. The ostracode Mg/Ca data also allow the direct determination of the temperature component of the benthic foraminiferal oxygen isotope record from Site 607, as well as derivation of a hypothetical sea-level curve for the late Pliocene and late Quaternary. The effects of dissolution on the Mg/Ca ratios of ostracode shells appear to have been minimal.