Matrix elements of U(2n) generators in a multishell spin-orbit basis. I. The del-operator MEs in a two-shell composite Gelfand-Paldus basis

This is the first in a series of three articles which aimed to derive the matrix elements of the U(2n) generators in a multishell spin-orbit basis. This is a basis appropriate to many-electron systems which have a natural partitioning of the orbital space and where also spin-dependent terms are included in the Hamiltonian. The method is based on a new spin-dependent unitary group approach to the many-electron correlation problem due to Gould and Paldus [M. D. Gould and J. Paldus, J. Chem. Phys. 92, 7394, (1990)]. In this approach, the matrix elements of the U(2n) generators in the U(n) x U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single Ll(n) adjoint tensor operator called the del-operator, denoted by Delta(j)(i) (1 less than or equal to i, j less than or equal to n). Delta or del is a polynomial of degree two in the U(n) matrix E = [E-j(i)]. The approach of Gould and Paldus is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. Hence, to generalize this approach, we need to obtain formulas for the complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The nonzero shift coefficients are uniquely determined and may he evaluated by the methods of Gould et al. [see the above reference]. In this article, we define zero-shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis which are appropriate to the many-electron problem. By definition, these are proportional to the corresponding two-shell del-operator matrix elements, and it is shown that the Racah factorization lemma applies. Formulas for these coefficients are then obtained by application of the Racah factorization lemma. The zero-shift adjoint reduced Wigner coefficients required for this procedure are evaluated first. All these coefficients are needed later for the multishell case, which leads directly to the two-shell del-operator matrix elements. Finally, we discuss an application to charge and spin densities in a two-shell molecular system. (C) 1998 John Wiley & Sons.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. II. The two-shell nonzero shift ACCs and U(2n) generator MEs

This is the second in a series of articles whose ultimate goal is the evaluation of the matrix elements (MEs) of the U(2n) generators in a multishell spin-orbit basis. This extends the existing unitary group approach to spin-dependent configuration interaction (CI) and many-body perturbation theory calculations on molecules to systems where there is a natural partitioning of the electronic orbital space. As a necessary preliminary to obtaining the U(2n) generator MEs in a multishell spin-orbit basis, we must obtain a complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. The zero-shift coefficients were obtained in the first article of the series. in this article, we evaluate the nonzero shift adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis. We then demonstrate that the one-shell versions of these coefficients may be obtained by taking the Gelfand-Tsetlin limit of the two-shell formulas. These coefficients,together with the zero-shift types, then enable us to write down formulas for the U(2n) generator matrix elements in a two-shell spin-orbit basis. Ultimately, the results of the series may be used to determine the many-electron density matrices for a partitioned system. (C) 1998 John Wiley & Sons, Inc.

Matrix elements of U(2n) generators in a multishell spin-orbit basis. III. General formulas

This is the third and final article in a series directed toward the evaluation of the U(2n) generator matrix elements (MEs) in a multishell spin/orbit basis. Such a basis is required for many-electron systems possessing a partitioned orbital space and where spin-dependence is important. The approach taken is based on the transformation properties of the U(2n) generators as an adjoint tensor operator of U(n) x U(2) and application of the Wigner-Eckart theorem. A complete set of adjoint coupling coefficients for the two-shell composite Gelfand-Paldus basis (which is appropriate to the many-electron problem) were obtained in the first and second articles of this series. Ln the first article we defined zero-shift coupling coefficients. These are proportional to the corresponding two-shell del-operator matrix elements. See P. J. Burton and and M. D. Gould, J. Chem. Phys., 104, 5112 (1996), for a discussion of the del-operator and its properties. Ln the second article of the series, the nonzero shift coupling coefficients were derived. Having obtained all the necessary coefficients, we now apply the formalism developed above to obtain the U(2n) generator MEs in a multishell spin-orbit basis. The methods used are based on the work of Gould et al. (see the above reference). (C) 1998 John Wiley & Sons, Inc.

Speciation and absolute bioavailability: risk assessment of arsenic-contaminated sites in a residential suburb in Canberra

Watson is a fully developed suburb of some 30 years in Canberra (the capital city of Australia), A plunge dip using arsenical pesticides for tick control was operated there between 1946 and 1960, Chemical investigations revealed that many soil samples obtained from the study area contained levels of arsenic exceeding the current health-based investigation levels of 100 mg kg(-1) set by the National Health and Medical Research Council in Australia, For the speciation study, nine composite samples of surface and sub-surface soils and a composite sample of rocks were selected. ICP-MS analysis showed that arsenic levels in these samples ranged from 32 to 1597 mg kg(-1), Chemical speciation of arsenic showed that the arsenite (trivalent) components were 0.32-56% in the soil and 44.8% in the rock composite samples. Using a rat model, the absolute bioavailability of these contaminated soils relative to As3+ or As5+ ranged from 1.02 to 9.87% and 0.26 to 2.98%, respectively, An attempt was made to develop a suitable leachate test as an index of bioavailability. However, the results indicated that there was no significant correlation between the bioavailability and leachates using neutral pH water or 1 M HCl. Our results indicate that speciation is highly significant for the interpretation of bioavailability and risk assessment data; the bioavailable fractions of arsenic in soils from Watson are small and therefore the health impact upon the environment and humans due to this element is limited.

Changes in estimated coronary risk in the 1980s: data from 38 populations in the WHO MONICA Project

The World Health Organization (WHO) MONICA Project is a 10-year study monitoring trends and determinants of cardiovascular disease in geographically defined populations. Data were collected from over 100 000 randomly selected participants in two risk factor surveys conducted approximately 5 years apart in 38 populations using standardized protocols. The net effects of changes in the risk factor levels were estimated using risk scores derived from longitudinal studies in the Nordic countries. The prevalence of cigarette smoking decreased among men in most populations, but the trends for women varied. The prevalence of hypertension declined in two-thirds of the populations. Changes in the prevalence of raised total cholesterol were small but highly correlated between the genders (r = 0.8). The prevalence of obesity increased in three-quarters of the populations for men and in more than half of the populations for women. In almost half of the populations there were statistically significant declines in the estimated coronary risk for both men and women, although for Beijing the risk score increased significantly for both genders. The net effect of the changes in the risk factor levels in the 1980s in most of the study populations of the WHO MONICA Project is that the rates of coronary disease are predicted to decline in the 1990s.

Sources of information about HIV/AIDS and perceived risk of infection among heterosexual young adults: 1989 and 1994

This paper reports a study of sources of information about HIV/AIDS and trust of the sources among heterosexuals in 1989 (113 females and 91 males) and 1994 (185 females and 66 males). We also examined whether perceived personal risk of HIV infection was predicted by sources of information about HIV/AIDS, trust of the sources, how informed about AIDS people believed they were, and perceived risk of infection to others, as well as whether there was a relationship between perceived personal risk and safe sex behaviour Participants received most of their information about AIDS/HIV from magazines, newspapers, and television, but placed most trust on sources such as doctors and HIV/AIDS organisations. Perceived personal risk was influenced most by perceived risk to friends and to people with the same sexual practices. In the 1994 sample, perceived personal risk was correlated with the amount of condom use among participants with sexual experience. These results indicate ther has been. relative stability across a five-year period. They also point to the continuing discrepancy among young heterosexuals between the most-used and most-trusted sources of information, as well as to the importance of peer influence on perceptions of personal risk of HIV infection.

Refining the risk-benefit equation for thrombolysis: How to identity the low risk patient before administering thrombolytic therapy

In view of the relative risk of intracranial haemorrhage and major bleeding with thrombolytic therapy, it is important ro identify as early as possible the low risk patient who may not have a net clinical benefit from thrombolysis in the setting of acute myocardial infarction. An analysis of 5434 hospital-treated patients with myocardial infarction in the Perth MONICA study showed that age below 60 and absence of previous infarction or diabetes, shock, pulmonary oedema, cardiac arrest and Q-wave or left bundle branch block on the initial ECG identified a large group of patients with a 28 day mortality of only 1%, and one year mortality of only 2%. Identification of baseline risk in this way helps refine the risk-benefit equation for thrombolytic therapy, and may help avoid unnecessary use of thrombolysis in those unlikely to benefit.

Expokit: A software package for computing matrix exponentials

Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear ODEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.