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  • 1
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new approximation strategy, split-amplitude strategy, useful within the framework of the coupled-cluster (CC) methodology is proposed. It consists in representing the individual cluster amplitudes as a sum of two components, one of fixed value, which may be obtained from external sources, and the other determined from a set of modified CC equations. This approach provides new possibilities of absorbing information concerning the values of cluster amplitudes from independent calculations. By properly choosing the fixed amplitude components, one may substantially reduce the magnitudes of the most significant amplitudes to be determined for the state considered, which in turn causes that the known approximation procedures are more justifiable when applied to the modified CC equations than to the equations of the standard CC approaches. The split-amplitude strategy has been employed to setting up several almost-linear CC (AL-CC) approaches of a single reference type corresponding to the basic CC methods. These low-cost approaches seem to be useful in theories of processes involving nondynamically correlated (quasidegenerate) states. The AL-CC methods have been applied to the ground states for various geometries of the following molecular systems: H8, H2O, BH, and HF. It is found that the energies obtained for a given AL-CC approach are very close to those for the corresponding basic CC method, which is true even for strongly quasidegenerate states. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-5001
    Keywords: GATA-1 ; protein-protein interactions ; solution structure ; zinc finger
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Chemistry and Pharmacology
    Notes: Abstract Zinc fingers (ZnFs) are generally regarded as DNA-binding motifs. However, a number of recent reports have implicated particular ZnFs in the mediation of protein-protein interactions. The N-terminal ZnF of GATA-1 (NF) is one such finger, having been shown to interact with a number of other proteins, including the recently discovered transcriptional co-factor FOG. Here we solve the three-dimensional structure of the NF in solution using multidimensional 1H/15N NMR spectroscopy, and we use 1H/15N spin relaxation measurements to investigate its backbone dynamics. The structure consists of two distorted β-hairpins and a single α-helix, and is similar to that of the C-terminal ZnF of chicken GATA-1. Comparisons of the NF structure with those of other C4-type zinc binding motifs, including hormone receptor and LIM domains, also reveal substantial structural homology. Finally, we use the structure to map the spatial locations of NF residues shown by mutagenesis to be essential for FOG binding, and demonstrate that these residues all lie on a single face of the NF. Notably, this face is well removed from the putative DNA- binding face of the NF, an observation which is suggestive of simultaneous roles for the NF; that is, stabilisation of GATA-1 DNA complexes and recruitment of FOG to GATA-1-controlled promoter regions.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 2483-2505 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schrödinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schrödinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials. The introduced formalism amounts to a generalization of the classical methods for linearization of nonlinear differential equations such as the Carleman embedding technique and Koopman approach. © 1997 American Institute of Physics.
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  • 4
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The impact of approximations to the form of the cluster operator on the structure and physical significance of the complete set of geometrically isolated solutions to the coupled-cluster (CC) equations has been studied for the first time. To systematically study the correspondence of solutions obtained at various levels of the approximation process, a continuation procedure based on a set of β-nested equations (β-NE) has been proposed and applied. Numerical studies based on a homotopy method for obtaining full solutions to sets of polynomial equations have been performed for the H4 and P4 models which belong to the simplest realistic many-electron model systems. Two examples of approximation procedures have been considered. The first one involved, for the P4 model, the approximation leading from the full CC (FCC) method to the CC method based on double excitations (CCD). As a result of this approximations the number of solutions has increased from 8 to 20. In the second example, for H4, we have studied the approximation leading from the CCSD method to the CCD one. To complete these studies, we have for the first time obtained the full set of geometrically isolated solutions for a CCSD equations which consists of 60 solutions. Only a small subset of this set might have some physical significance. During the approximation process considered, the number of solution decreases from 60 to 12. This radical drop of the numbers of solutions is a consequence of the absence of the third and fourth powers of the unknowns in the CCD equations. © 1999 American Institute of Physics.
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  • 5
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: To gain more insight into the physical and mathematical content of the equations of the coupled–cluster (CC) method, comprehensive numerical studies have been performed for various geometries of the H4 model which belongs to the simplest and best understood among the realistic many–electron model systems. These studies are for the first time based on the knowledge of the complete sets of geometrically isolated solutions of the relevant equations that are obtained when using a special version of the homotopy methods. The equations of the CC method including two–electron excitations (CCD) both in the spin–orbital and spin–symmetry–adapted versions are considered. To establish the correspondence of the solutions attained with those of the configuration interaction (CID) method, we have for the first time solved the unabridged characteristic equations (CE) of T. P. Zivkovic and H. J. Monkhorst [J. Math. Phys. 19, 1007 (1978)]. The complete sets of solutions to the spin–orbital and spin–symmetry–adapted versions of the CCD equations and CEs consist of 20 and 12 solutions, respectively. Their structures turned out to be unexpectedly simple, which makes it possible to understand the physical and mathematical significance of the individual solutions. Moreover, this simplicity rises hopes that the most serious irregularities previously found for low dimensional simulations of the CEs can be avoided for realistic systems. The present results confirm most of the findings of previous research. Attention is paid to studies of the impact of using mixed–symmetry cluster operators on the structure of solutions to the CC equations. The specific part played by the components of the cluster amplitudes corresponding to other spin–symmetry than that of the reference function has been demonstrated for the first time. © 1999 American Institute of Physics.
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  • 6
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: To establish the existence and origin of the nonalgebraic irregularities of solutions to coupled-cluster (CC) equations and to indicate ways of their elimination, we have revisited the two analytically solvable characteristic equations (CE) studied by Zivkovic and Monkhorst [J. Math. Phys. 19, 1007 (1978)]. The results of these studies have strongly influenced the general conclusions concerning the possible types of singularities. We present some arguments that the most serious irregularities—the nonnormal and resonance ones—are a result of the special structures of the CEs considered. The CE employed for the demonstration of resonance solutions is not physically representable, which raises the hope that such solutions will not appear in quantum-chemical applications of the coupled-cluster method. It is proved that the presence of nonnormal solutions is a consequence of the existence of such passive diagonal blocks of the Hamiltonian matrix which share a common eigenvalue. Such blocks can be eliminated by taking into account the symmetry species of the basis functions involved, which is most effectively done by proceeding to a symmetry-adapted formulations. Therefore, one may eliminate or at least reduce the number of nonnormal solutions to the CC equations by proceeding to their symmetry-adapted versions. © 1999 American Institute of Physics.
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  • 7
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The structure and physical significance of the full set of solutions to coupled-cluster (CC) equations at various stages of the dissociation process and the impact of the choice of reference functions on these solutions have been studied for the first time. The equations for the CC method involving double excitations (CCD) are obtained for the P4 model consisting of two H2 molecules in a rectangular nuclear configuration determined by a geometry parameter α. We consider equations for the reference states |ΦA〉, |ΦQ〉, and |ΦB〉 corresponding to the lowest, highest, and intermediate Hartree–Fock (HF) energies, respectively. The first two states provide a size-consistent description of the dissociation process. For the compact-molecule geometries (α〈10.0) the sets of complete solutions to the standard CCD equations [based on molecular orbitals (MOs) of D2h symmetry] in the spin–orbital and spin–symmetry-adapted versions always consist of 20 and 12 entries, respectively. For |ΦA〉 and |ΦB〉 in the dissociation limit (α→∞) only for the latter version the solutions can be attained by homotopy method. In this case we have reformulated the standard spin–symmetry-adapted CCD equations to a version based on the use of localized orbitals (LO) which is extremely simple and can be solved analytically providing an understanding of the unexpected peculiarities of the solutions for α→∞. For |ΦA〉 and |ΦQ〉, there are only two regular solutions. For the remaining 10 solutions, the CCD wave functions are meaningless despite the fact that the corresponding CCD energies are equal to the exact values. © 1999 American Institute of Physics.
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  • 8
    ISSN: 0020-7608
    Keywords: Computational Chemistry and Molecular Modeling ; Atomic, Molecular and Optical Physics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Single-reference coupled-cluster (SR-CC) methods parametrized with respect to four alternative reference-state configurations and orbital sets are applied to the simple H4 model system in which the degree of quasi-degeneracy of the electronic states can be varied in a wide range. Both the ground state and 10 excited states are considered with the aim of numerically studying the attainability and properties of multiple solutions of the system of nonlinear equations for the cluster amplitudes. Comparisons of up to four alternative descriptions of a given state in terms of various solutions of the SR-CC equations are made. It is found that for some excited states different parametrizations yield very close results and that the classification of the solutions into standard and nonstandard ones may not be straightforward. © 1995 John Wiley & Sons, Inc.
    Additional Material: 12 Tab.
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  • 9
    ISSN: 0020-7608
    Keywords: coupled-cluster theory ; electron correlation effects ; molecular orbital choice ; reference determinant choice ; quasi-degenerate states ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: The impact of the choice of molecular orbital sets on the results of single-reference-state coupled-cluster (CC) methods was studied for the H4 model. This model offers a straightforward way of taking into account all possible symmetry-adapted orbitals. Moreover, the degree of quasi-degeneracy of its ground state can be varied over a wide range by changing its geometry. The CCD, CCSD, and CCSDT approaches are considered. Surfaces representing the dependence of the energy on the parameters defining the orbitals are obtained. It is documented that for every method there exist alternative orbital sets which allow one to obtain more accurate energies than the standard (HF, BO, and NO) ones. However, for many of the former orbital sets, one obtains relatively large one-body amplitudes or one may encounter problems with solving the CC equations by conventional methods. An interesting variety of orbitals which might be useful for studies of quasi-degenerate states by the CCD method was found.   © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 205-219, 1998
    Additional Material: 5 Ill.
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