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  • 1
    Electronic Resource
    Electronic Resource
    Valence universal exponential ansatz and the cluster structure of multireference configuration interaction wave function (1989)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 90 (1989), S. 2714-2731 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A rigorous algebraic formulation of open-shell coupled-cluster theory is presented. This formulation yields explicit formulas exhibiting the relationship between open-shell cluster amplitudes and linear coefficients of multireference CI wave functions. When the valence-universal exponential ansatz is used, the CI coefficients of states with n valence electrons contribute to the n-body and higher-order cluster operators. The implications of cluster conditions, requiring that the four-body cluster amplitudes be small, are investigated. It is shown that for valence-universal theories these conditions lead to approximate relations involving CI coefficients for states of systems differing in the number of electrons. For Lindgren's ansatz these relations are linear in the CI coefficients corresponding to states with the largest electron number. For the valence-nonuniversal exponential ansatz of Jeziorski and Monkhorst, the cluster conditions do not mix wave functions for systems which differ in the number of electrons and are formally identical to those of the single-reference coupled-cluster theory. A detailed relationship between the cluster amplitudes of the valence-universal and valence-nonuniversal theories is also derived and discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.455919
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  • 2
    Electronic Resource
    Electronic Resource
    Relationship between SN and U(n) isoscalar factors and higher-order U(n) invariants (1990)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 31 (1990), S. 1589-1599 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: General relationships expressing U(n) and SN coupling and transformation isoscalar factors in terms of U(n) Racah and 9λ coefficients are derived. The absolute values of U(n) Racah coefficients involving at most k-column irreducible representations are shown to be identical with SU(k) Racah coefficients. In particular, an explicit relationship is established between the U(n) and SU(2) approaches to the many-electron correlation problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.528700
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  • 3
    Electronic Resource
    Electronic Resource
    A unitary group based open-shell coupled cluster study of vibrational frequencies in ground and excited states of first row diatomics (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 9555-9562 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The performance of recently introduced coupled cluster (CC) method exploiting the unitary group approach (UGA) to many-electron systems, truncated at the first order interacting space level [UGA-CCSD(is)] and using the 6-31G* basis set, in computations of equilibrium bond lengths and harmonic vibrational frequencies, is examined for a series of open-shell (OS) states of the first row diatomics and hydrides. Altogether, 48 distinct electronic states are considered for 9 diatomic hydrides (BeH, BH, CH, CH+, NH, NH+, OH, OH+ and FH) and 18 diatomics (BeF, BN, BO, C2, C2+, C2−, CN, CO, CO+, CF, N2+, NO, NO−, NF, O2, O2+, OF and F2+), involving both high and low spin cases. Very good agreement with the available experimental data is found in all cases, except when the experimental values are marked as "uncertain'' or where only the ΔG(1/2) values of harmonic frequencies are available. For the so-called "difficult'' systems, namely NO(X 2Π), O2(X 3Σg−), O2+(X 2Πg), OF (X 2Π) and F2+ (X 2Πg), the geometries and vibrational frequencies are also calculated using the TZ2P [5s4p2d] basis sets, and the results are compared with both the experiment and existing perturbation theory and CC results. All results indicate that UGA CCSD(is) represents a versatile, reliable and computationally affordable method that can handle a great variety of OS states, including OS singlets. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471697
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  • 4
    Electronic Resource
    Electronic Resource
    Spin-adapted open-shell state-selective coupled cluster approach and doublet stability of its Hartree–Fock reference (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 2013-2023 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The performance of the unitary group based state-selective coupled cluster approach, in both linear and quadratic approximations, is examined for the case of doublet ground states of the first two alkaline earth hydrides in the whole range of internuclear separation. It is shown that the doublet instability of the restricted open-shell Hartree–Fock wave functions is responsible for the singular behavior of the linear coupled cluster potential energy curves, as well as for slight discontinuity in these curves when the bilinear terms are included. The effect of using different types of orbitals is investigated and the results are compared with full or very precise limited configuration interaction results as well as with the coupled cluster results employing the unrestricted Hartree–Fock reference, which is free of the instability problems in open shell systems. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468766
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  • 5
    Electronic Resource
    Electronic Resource
    Unitary group based state-selective coupled-cluster method: Comparison of the first order interacting space and the full single and double excitation space approximations (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 8897-8905 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A unitary group based state selective coupled-cluster method, truncated at the first order interacting space and at the full single and double excitation space levels, has been applied to examine a complete dissociation (atomization) of the OH, NH2, CH3, and CN radicals. These molecules were chosen to model various bond breaking processes, including the dissociation of one, two, and three single bonds as well as of a multiple (triple) bond. In all cases the coupled-cluster expansion employing the full single and double excitation space represents an improvement over the interacting space approximation. Although this improvement is more significant for geometries involving stretched bonds than for the equilibrium ones, it is found to be rather small in all cases that were examined. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468943
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  • 6
    Electronic Resource
    Electronic Resource
    Unitary group based open-shell coupled cluster approach and triplet and open-shell singlet stabilities of Hartree–Fock references (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 6536-6547 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The performance of recently introduced state-selective coupled-cluster method, based on the unitary group approach to the many-electron correlation problem and enabling a properly spin-adapted treatment of open-shell states, is examined for open-shell singlet and triplet states having unstable restricted Hartree–Fock solutions that serve as a reference. The study employs an ab initio model at the double-zeta-plus-polarization level of approximation describing the dissociation of the methylene radical in its lowest triplet and open-shell singlet states into the CH and H fragments in their ground states. It is shown that the spin restricted Hartree–Fock equations have different solutions in the bonding and nonbonding regions, which coexist in a small transition region, where the corresponding potential energy curves intersect, and which is determined by the vanishing of the lowest root of the stability problem for each solution. These instabilities are then responsible for a slight discontinuity in the potential energy curves in the transition region when the correlation effects are accounted for. It is shown that the overall performance of the unitary group based coupled cluster method gives very satisfactory results at a moderate cost. Finally, the possible pitfalls of the spin orbital coupled cluster method employing the unrestricted Hartree–Fock reference are illustrated for the triplet ground state dissociation model of methylene. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.470380
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  • 7
    Electronic Resource
    Electronic Resource
    Molecular quadrupole moment functions of HF and N2. I. Ab initio linear-response coupled-cluster results (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 4699-4715 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The orthogonally spin-adapted linear-response coupled-cluster (LRCC) theory with singly and doubly excited clusters (CCSD) was employed to calculate quadrupole moment functions of the HF and N2 molecules in their ground electronic states. We also calculated several potential energy curves for both systems using various CC and non-CC methods, ranging from the limited and full configuration interaction (CI) and first-order CI (FOCI) to finite-order many-body perturbation theory. FOCI and related complete active space self-consistent field (CASSCF) methods were used in both energy and quadrupole moment calculations. Most of the calculations were performed using the medium-size basis set of TZ+2P quality devised by Sadlej [A. Sadlej, Coll. Czech. Chem. Commun. 53, 1995 (1988)] for high-level ab initio calculations of electrostatic molecular properties. In addition, a number of model CC calculations using small basis sets were performed, for which the exact full CI results, both for the energy and multipole moments, are available. It was demonstrated that the CCSD approach provides a realistic description of quadrupole moment functions, for all relevant geometries in the case of HF and for internuclear separations up to 1.5 times the equilibrium bond length for N2. The results of this study will be used for the analysis of the rovibrational dependence of quadrupole moments and for the calculation of quadrupole transition moments for both HF and N2. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471164
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  • 8
    Electronic Resource
    Electronic Resource
    Molecular quadrupole moment functions of HF and N2. II. Rovibrational effects (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 4716-4727 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Relying on the molecular quadrupole moment functions of the HF and N2 molecules in their electronic ground state, as obtained by the ab initio calculations at various levels of approximation of the coupled cluster method, as well as on the corresponding theoretical and experimental potential energy functions, the effective rovibrational averages and transition moments were evaluated over a wide range of values for the vibrational and rotational quantum numbers. The reliability of the ab initio data was also checked by evaluating the theoretical vibrational energies and comparing them with the experimental ones. The predicted quadrupole moments were found to be in close agreement with the available (rather scarce) experimental data, indicating the reliability of the calculated effective quadrupole moments for the broad range of rovibrational levels where no experimental data are available. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471165
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  • 9
    Electronic Resource
    Electronic Resource
    Orthogonally spin-adapted state-universal coupled-cluster formalism: Implementation of the complete two-reference theory including cubic and quartic coupling terms (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 5875-5890 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The complete orthogonally spin-adapted Hilbert-space (or state-universal) coupled-cluster (CC) theory involving singly and doubly excited clusters for a model space spanned by two closed-shell configurations is considered. Explicit expressions for the previously neglected cubic and quartic coupling terms are derived using diagrammatic methods of many-body perturbation theory and graphical methods of spin algebras. The resulting formalism has been implemented and the general purpose ab initio program has been written using newly developed procedure for improving the convergence of the reduced linear equation method. Results of the pilot calculations for the two lowest singlet states of the minimum basis set and double zeta plus polarization basis H4 models as well as for the CH2 molecule at equilibrium and displaced geometries are presented and compared with the available single-reference CC and configuration interaction data. They indicate negligible role of the cubic and quartic coupling terms, which justifies the validity of approximations considered so far.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467304
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  • 10
    Electronic Resource
    Electronic Resource
    Automation of the implementation of spin-adapted open-shell coupled-cluster theories relying on the unitary group formalism (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 8812-8826 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new implementation of the orthogonally spin-adapted open-shell (OS) coupled-cluster (CC) formalism that is based on the unitary group approach to many-electron correlation problem is described. Although the emphasis is on the so-called state specific single-reference but multiconfigurational OS CC approach, the developed algorithms as well as the actual codes are also amenable to multireference CC applications of the state-universal type. A special attention is given to simple OS doublets and OS singlet and triplet cases, the former being applicable to the ground states of radicals and the latter to the excited states of closed shell systems. The encoding of the underlying formalism is fully automated and is based on a convenient decomposition of the Hamiltonian into the effective zero-, one-, and two-orbital contributions as well as on the general strategy that focuses on the excitation operator driven evaluation of individual absolute, linear, quadratic, etc., coupled cluster coefficients, rather than on the standard molecular (spin) orbital driven algorithms. In this way unnecessary duplications are avoided and efficient codes are developed both for the general formula generation and final executable modules. A thorough testing of this procedure on a number of model cases is described and several illustrative applications at the ab initio level are provided.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.468074
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