Tools for analysing configuration interaction wavefunctions

The configuration interaction (CI) approach to quantum chemical calculations is a well-established means of calculating accurately the solution to the Schrodinger equation for many-electron systems. It represents the many-body electron wavefunction as a sum of spin-projected Slater determinants of orthogonal one-body spin-orbitals. The CI wavefunction becomes the exact solution of the Schrodinger equation as the length of the expansion becomes infinite, however, it is a difficult quantity to visualise and analyse for many-electron problems. We describe a method for efficiently calculating the spin-averaged one- and two-body reduced density matrices rho(psi)((r) over bar; (r) over bar' ) and Gamma(psi)((r) over bar (1), (r) over bar (2); (r) over bar'(1), (r) over bar'(2)) of an arbitrary CI wavefunction Psi. These low-dimensional functions are helpful tools for analysing many-body wavefunctions; we illustrate this for the case of the electron-electron cusp. From rho and Gamma one can calculate the matrix elements of any one- or two-body spin-free operator (O) over cap. For example, if (O) over cap is an applied electric field, this field can be included into the CI Hamiltonian and polarisation or gating effects may be studied for finite electron systems. (C) 2003 Elsevier B.V. All rights reserved.

Stable isomorphism of dual operator spaces

We prove that two dual operator spaces $X$ and $Y$ are stably isomorphic if and only if there exist completely isometric normal representations $phi$ and $psi$ of $X$ and $Y$, respectively, and ternary rings of operators $M_1, M_2$ such that $phi (X)= [M_2^*psi (Y)M_1]^{-w^*}$ and $psi (Y)=[M_2phi (X)M_1^*].$ We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being stably isomorphic. We apply these operator space results to prove that certain dual operator algebras are stably isomorphic if and only if they are isomorphic. We provide examples motivated by CSL algebra theory.

Proton pumping by complex I (NADH : ubiquinone oxidoreductase) from Yarrowia lipolytica reconstituted into proteoliposomes

The mechanism of energy converting NADH:ubiquinone oxidoreductase (complex 1) is Still unknown. A current controversy centers around the question whether electron transport of complex I is always linked to vectorial proton translocation or whether in some organisms the enzyme pumps sodium ions instead. To develop better experimental tools to elucidate its mechanism, we have reconstituted the affinity purified enzyme into proteoliposomes and monitored the generation of Delta pH and Delta psi. We tested several detergents to solubilize the asolectin used for liposome formation. Tightly coupled proteoliposomes containing highly active complex I were obtained by detergent removal with BioBeads after total solubilization or the phospholipids with n-octyl-beta-D-glucopyranoside. We have used dyes to monitor the formation of the two components of the proton motive force, Delta pH and Delta psi, across the liposomal membrane, and analyzed the effects of inhibitors, uncouplers and ionophores on this process. We show that electron transfer of complex I of the lower eukaryote Y. lipolytica is clearly linked to proton translocation. While this study was not specifically designed to demonstrate possible additional sodium translocating properties of complex 1, we did not find indications for primary or secondary Na+ translocation by Y lipolytica complex I. (c) 2005 Elsevier B.V. All rights reserved.

Many-body theory calculations of positron binding to negative ions

A many-body theory approach developed by the authors [Phys. Rev. A 70, 032720 (2004)] is applied to positron bound states and annihilation rates in atomic systems. Within the formalism, full account of virtual positronium (Ps) formation is made by summing the electron-positron ladder diagram series, thus enabling the theory to include all important many-body correlation effects in the positron problem. Numerical calculations have been performed for positron bound states with the hydrogen and halogen negative ions, also known as Ps hydride and Ps halides. The Ps binding energies of 1.118, 2.718, 2.245, 1.873 and 1.393 eV and annihilation rates of 2.544, 2.482, 1.984, 1.913 and 1.809 ns^{-1}, have been obtained for PsH, PsF, PsCl, PsBr and PsI, respectively.

Calbindin 2 (CALB2) Regulates 5-Fluorouracil Sensitivity in Colorectal Cancer by Modulating the Intrinsic Apoptotic Pathway

The role of the calcium binding protein, Calbindin 2 (CALB2), in regulating the response of colorectal cancer (CRC) cells to 5-Fluorouracil (5-FU) was investigated. Real-time RT-PCR and Western blot analysis revealed that CALB2 mRNA and protein expression were down-regulated in p53 wild-type and p53 null isogenic HCT116 CRC cell lines following 48 h and 72 h 5-FU treatment. Moreover, 5-FU-induced apoptosis was significantly reduced in HCT116 and LS174T CRC cell lines in which CALB2 expression had been silenced. Further investigation revealed that CALB2 translocated to the mitochondria following 5-FU treatment and that 5-FU-induced loss of mitochondrial membrane potential (Delta psi(m)) was abrogated in CALB2-silenced cells. Furthermore, CALB2 silencing decreased 5-FU-induced cytochrome c and smac release from the mitochondria and also decreased 5-FU-induced activation of caspases 9 and 3/7. Of note, co-silencing of XIAP overcame 5-FU resistance in CALB2-silenced cells. Collectively, these results suggest that following 5-FU treatment in CRC cell lines, CALB2 is involved in apoptosis induction through the intrinsic mitochondrial pathway. This indicates that CALB2 may be an important mediator of 5-FU-induced cell death. Moreover, down-regulation of CALB2 in response to 5-FU may represent an intrinsic mechanism of resistance to this anti-cancer drug.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.

Sets of multiplicity and closable multipliers on group algebras

We undertake a detailed study of the sets of multiplicity in a second countable locally compact group G and their operator versions. We establish a symbolic calculus for normal completely bounded maps from the space B(L-2(G)) of bounded linear operators on L-2 (G) into the von Neumann algebra VN(G) of G and use it to show that a closed subset E subset of G is a set of multiplicity if and only if the set E* = {(s,t) is an element of G x G : ts(-1) is an element of E} is a set of operator multiplicity. Analogous results are established for M-1-sets and M-0-sets. We show that the property of being a set of multiplicity is preserved under various operations, including taking direct products, and establish an Inverse Image Theorem for such sets. We characterise the sets of finite width that are also sets of operator multiplicity, and show that every compact operator supported on a set of finite width can be approximated by sums of rank one operators supported on the same set. We show that, if G satisfies a mild approximation condition, pointwise multiplication by a given measurable function psi : G -> C defines a closable multiplier on the reduced C*-algebra G(r)*(G) of G if and only if Schur multiplication by the function N(psi): G x G -> C, given by N(psi)(s, t) = psi(ts(-1)), is a closable operator when viewed as a densely defined linear map on the space of compact operators on L-2(G). Similar results are obtained for multipliers on VN(C).