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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 5261-5271 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In this paper, we examine some aspects of complete active space configuration interaction (CASCI) calculations where excitations from the core are taken into account. We show that it is appropriate to work in a basis for the irreducible representations (irreps) of the orbital unitary group symmetry adapted to the subgroup U(n0)×U(n1)×U(n2) (where n0, n1, and n2 are the number of core, active, and external orbitals, respectively, and n=n0+n1+n2). We demonstrate that this approach has the following advantages; (i) it allows the efficient isolation of single, double, and higher excitations from the reference space; (ii) it demonstrates explicitly the internal–external factorization of generator matrix elements; (iii) it allows the determination of the matrix elements of arbitrary generator products by simple matrix multiplications.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 5112-5133 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This is the first in a series of papers which derives the matrix elements of the spin-dependent U(2n) generators in a multishell spin–orbit basis, i.e., a spin adapted composite Gelfand–Paldus basis. The advantages of such a multishell formalism are well known and well documented. The approach taken exploits the properties of the U(n) adjoint tensor operator denoted by Δij(1≤i,j≤n) as defined by Gould and Paldus [J. Chem. Phys. 92, 7394 (1990)]. Δ is a polynomial of degree two in the U(n) matrix E=[Eij]. The unique properties of this operator allow the construction of adjoint coupling coefficients for the zero-shift components of the U(2n) generators. The Racah factorization lemma may then be applied to obtain the matrix elements of all the U(2n) generators.In this paper we investigate the underlying formalism of the approach and discuss its advantages and its relationship to the shift operator method of Gould and Battle [J. Chem. Phys. 99, 5961 (1993)]. The formalism is then applied, in the second paper of the series, to calculate the matrix elements of the del operator in a two-shell spin–orbit basis. This immediately yields the zero-shift adjoint coupling coefficients in such a basis. The del-operator matrix elements are required for the calculation of spin densities in a two-shell basis. In the third paper of the series we derive the remaining nonzero shift adjoint coupling coefficients all of which are required for the multishell case. We then use these coupling coefficients to obtain formulas for the matrix elements of the U(2n) generators in a two-shell spin–orbit basis. This result is then generalized, in the fourth paper, to the case of the multishell spin–orbit basis. Finally, we demonstrate that in the Gefand–Tsetlin limit the formula obtained is equivalent to that of Gould and Battle for a single-shell system. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1573-2932
    Keywords: Alberta ; British Columbia ; climate change ; chilling requirement ; coniferous forests ; frost tolerance ; gap model ; temperature response ; succession ; ZELIG
    Source: Springer Online Journal Archives 1860-2000
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: Abstract We enhanced the forest patch model, Zelig, to explore the implications of 2×CO2 climate change scenarios on several forest regions in British Columbia and Alberta, Canada. In addition to the processes and phenomena commonly represented in individual-based models of forest stand dynamics, we added some species-specific phenology and site-specific frost events. The consideration of bud-break heat sum requirements, growing season limits, and chilling requirements for the induction of dormancy and cold hardiness slightly improved the ability of Zelig to predict the present composition of B.C. forests. Simulations of the predicted effects of future climatic regimes (based on the averaged predictions of four general circulation models) include some major shifts in equilibrial forest composition and productivity. Lowland temperate coastal forests are predicted to be severely stressed because indigenous species will no longer have their winter chilling requirements met. High-elevation coastal forests are expected to increase in productivity, while interior subalpine forests are expected to remain stable in productivity but will gradually be replaced by species currently characteristic of lower elevations. Dry, interior low-elevation forests in southern B.C. are likely to persist relatively unchanged, while wet interior forests are expected to support dramatic increases in yield, primarily by western hemlock. Northern interior sub-boreal forests are likewise expected to increase in productivity through enhanced growth of lodgepole pine. Conversely, the precipitous collapse of spruce stands in the true boreal forests of northeastern B.C. is expected to be associated with reduced productivity as they are replaced by pine species. Boreal-Cordilleran and Moist Boreal Mixedwood forests in Alberta are less likely to undergo compositional change, while becoming somewhat more productive. We believe these model enhancements to be a significant improvement over existing formulations, but the resulting predictions must still be viewed with caution. Model limitations include: (1) the current inability of climate models to predict future variation in monthly temperature and precipitation; (2) sparse information on the phenological behaviour of several important tree species; and (3) a poor understanding of the degree to which growth is constrained by different suboptimal climatic events.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Medical & biological engineering & computing 20 (1982), S. 375-382 
    ISSN: 1741-0444
    Keywords: Blood-gas transducers ; Foetal scalp ; Mass spectrometry ; Transducers
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology , Medicine
    Notes: Abstract A number of authors have described the design of transducers to be used with mass spectrometers for the skin-surface measurement of gases in newborn infants and adults. We have also previously considered the feasibility of designing a transducer for attachment to the foetal scalp during labour. This paper describes the problems which have been encountered in producing a practical transducer design for foetal scalp use. The major problem has been that of achieving adequate signal-to-noise ratio for the low oxygen levels encountered in the human foetus. A mathematical model is described, and results of the use of the model in optimising critical transducer design parameters are presented. Typical recordings obtained during labour are shown for O2, CO2 and N2O.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 66 (1998), S. 323-343 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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) × U(2)-adapted electronic Gelfand basis are determined by the matrix elements of a single U(n) adjoint tensor operator called the del-operator, denoted by Δji (1 ≤ i, j ≤ n). Δ or del is a polynomial of degree two in the U(n) matrix E = [Eji]. 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) × 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 be 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.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 323-343, 1998
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 66 (1998), S. 345-363 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 345-363, 1998
    Type of Medium: Electronic Resource
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  • 7
    Electronic Resource
    Electronic Resource
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 66 (1998), S. 365-375 
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: 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)×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. In 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. In 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).   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66: 365-375, 1998
    Type of Medium: Electronic Resource
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