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  • 1
    Digitale Medien
    Digitale Medien
    A unitary group formulation of the complete active space configuration interaction method. II. An approach based on the subgroup chain U(n=n0+n1+n2) = U(n0)×U(n1 +in2) = U(n0)×U(n1)×U(n2) (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 5261-5271 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.462711
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  • 2
    Digitale Medien
    Digitale Medien
    A unitary group formulation of the complete active space configuration interaction method. I. General formalism (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 3680-3685 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A group theoretical formulation of the complete active space CI (CASCI) method is presented based on the subgroup chain U(n=n1+n2)&supuline;U(n1)×U(n2), where n1 is the number of active orbitals and n2 the number of external orbitals. The internal-external factorization of the U(n) generator matrices and the isolation of all singly, doubly (and higher) excited states fall out naturally in our approach. Moreover it is shown that the matrix elements of arbitrary products of U(n) generators may be obtained from simple products of the single generator matrices, to any order of excitation. The method is ideally suited to modern vector array processors and affords sufficient flexibility to allow core excitations and partitioning of the active space. Further simplifications occur in the all singles and doubles case, which will be discussed in the second (and final) paper of the series.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.455825
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  • 3
    Digitale Medien
    Digitale Medien
    Spin-dependent unitary group approach. I. General formalism (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 92 (1990), S. 7394-7401 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A new spin-dependent unitary group approach to the many-electron correlation problem is investigated. It is demonstrated that the matrix elements of the U(2n) generators, in the U(n)×U(2) adapted electronic Gel'fand basis, are determined by the matrix elements of a single U(n) adjoint tensor operator, herein denoted by Δij(1≤i, j≤n), where Δ is a polynomial of degree two in the U(n) matrix E=[Eij]. The method is then applied, in the second paper of the series, to derive a simple segment level formula for the matrix elements of all U(2n) generators. The advantages of this new procedure for computer implementation are discussed and the central role played by the matrix Δ for the determination of molecular spin densities is highlighted.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.458225
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  • 4
    Digitale Medien
    Digitale Medien
    Unitary group approach to reduced density matrices (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 4142-4153 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A fully spin-adapted approach to many-electron density matrices is developed in the context of the unitary group approach to many-electron systems. An explicit expression for the single-electron spin-density operator, as a polynomial of degree two in the orbital U(n) generators, is derived for the case of spin-independent systems. Extensions to spin-dependent systems are also considered, leading to the appearance of total-spin transition densities, whose general properties are investigated. A corresponding formalism for the two-electron density matrix, which is capable of further generalization, is also developed. The results of this paper, together with recent developments on the matrix elements of the U(2n) generators in the electronic Gel'fand basis, afford a versatile method for the direct calculation of one- and two-body density matrices in the unitary group approach framework.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.458747
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  • 5
    Digitale Medien
    Digitale Medien
    Matrix elements and Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1008-1022 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: In this series of papers the fundamental Wigner coefficients and the matrix elements of the generators for the quantum group Uq[gl(n)] are derived. The Uq[gl(n)]:Uq[gl(n−1)] reduced Wigner coefficients and reduced matrix elements are determined algebraically as eigenvalues of certain Uq[gl(n−1)] invariants in the quantum group Uq[gl(n)]. The matrix elements of the elementary quantum group generators, in the Gel'fand–Tsetlin basis, are derived below, while all fundamental Wigner coefficients are derived in the second paper of the series.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529986
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  • 6
    Digitale Medien
    Digitale Medien
    Reduced Wigner coefficients for Uq[gl(n)] (1992)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 33 (1992), S. 1023-1031 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: This is the second paper in a series concerned with the Racah–Wigner calculus for the quantum group Uq[gl(n)]. In this approach all reduced Wigner coefficients are determined algebraically by the eigenvalues of certain generalized Casimir invariants. Here the method is applied to evaluate all fundamental Wigner coefficients and reduced Wigner coefficients for Uq[gl(n)].
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529764
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  • 7
    Digitale Medien
    Digitale Medien
    Classification of all star and grade star irreps of gl(n||1) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1524-1534 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A method for inducing nondegenerate forms on irreducible gl(m||n) modules that implies some general results on star and grade star representations is investigated. These results are applied to obtain a complete classification, in terms of highest weights, of the irreducible star and grade star representations of gl(n||1). It is demonstrated that while gl(n||1) admits a large class of star representations the irreducible grade star representations are comparatively rare. Moreover, for n≠2 all grade star irreducible representations are also star representations and, for n〉2, are atypical. The superalgebra gl(2||1) proves to be a special case and admits a two-parameter family of four-dimensional typical grade star irreducible representations that are not star representations. In particular, typical grade star irreducible representations of gl(n||1) exist only for n=1,2.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.528695
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  • 8
    Digitale Medien
    Digitale Medien
    Classification of star and grade-star representations of C(n+1) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1889-1897 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: The two types of * and grade-* representations of the Lie superalgebra C(n+1) are classified. A type (1) irreducible *-representation is characterized by the single condition (Λ,αs)≥0, Λ and αs being the highest weight and the odd simple root, respectively, while the type (2) *-representations are duals of type (1) *-representations. For n〉1, only the identity and vector representations of C(n+1) are shown to be grade -*. The superalgebra C(2) proves to be an exception and admits several classes of nontrivial irreducible grade -* representations.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.528687
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  • 9
    Digitale Medien
    Digitale Medien
    Branching rules for a class of typical and atypical representations of gl(m||n) (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 2803-2810 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: The irreducible representations of the Lie superalgebra gl(m||n) with highest weights of the form Λ=(λ1,λ2,...λm||ω(overdot)) are investigated using a recently introduced induced module construction for atypical modules. The gl(m||n)↓gl(m||n−1) branching rules are obtained and a suitable Gel'fand–Tsetlin basis is introduced. The class of representations considered includes some multiply atypical irreducible representations of gl(m||n) and all irreducible representations of gl(m||1).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.528983
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  • 10
    Digitale Medien
    Digitale Medien
    Universal R matrices and invariants of quantum supergroups (1991)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 32 (1991), S. 3261-3267 
    Details
    ISSN: 1089-7658
    Quelle: AIP Digital Archive
    Thema: Mathematik , Physik
    Notizen: A general method is developed for constructing invariants of quantum supergroups using universal R matrices. Applied to Uq(gl(2/1)), this method yields the invariants of this quantum supergroup in explicit form. The eigenvalues of these invariants in arbitrary irreducible highest weight representations are computed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.529487
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