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  • 1
    Digitale Medien
    Digitale Medien
    Reduced multireference CCSD method: An effective approach to quasidegenerate states (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 6257-6269 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: Standard multireference (MR) coupled cluster (CC) approaches are based on the effective Hamiltonian formalism and generalized Bloch equation. Their implementation, relying on the valence universal or state universal cluster Ansatz, is very demanding and their practical exploitation is often plagued with intruder state and multiple solution problems. These problems are avoided in the so-called state selective or state specific (SS) MR approaches that concentrate on one state at a time. To preserve as much as possible the flexibility and generality offered by the general MR CC approaches, yet obtaining a reliable and manageable algorithm, we propose a novel SS strategy providing a size-extensive CC formalism, while exploiting the MR model space and the corresponding excited state manifold. This strategy involves three steps: (i) The construction of a variational configuration interaction (CI) wave function within the singly (S) and doubly (D) excited state manifold, (ii) the cluster analysis of this CI wave function providing the information about the higher than pair cluster amplitudes, and (iii) the exploitation of these amplitudes in the so-called externally corrected CCSD procedure. This approach is referred to as the reduced MR (RMR) SS CCSD method and is implemented at the ab initio level and applied to several model systems for which the exact full CI results are available. These include two four electron H4 systems (usually referred to as the H4 and S4 models), an eight electron H8 model and the singlet-triplet separation problem in CH2. It is shown that the RMR CCSD approach produces highly accurate results, is free from intruder state problems, is very general and effective and applicable to both closed and open shell systems. © 1997 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.474289
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  • 2
    Digitale Medien
    Digitale Medien
    Reduced multireference couple cluster method. II. Application to potential energy surfaces of HF, F2, and H2O (1998)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 637-648 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The so-called reduced multireference (RMR) coupled cluster method restricted to singly and doubly excited clusters (CCSD) [see X. Li and J. Paldus, J. Chem. Phys. 107, 6257 (1997)] is employed to compute potential energy surfaces for the HF, F2 and H2O molecules over a wide range of geometries using basis sets of a double zeta (DZ) and DZ plus polarization (DZP) quality. The RMR-CCSD method belongs to a class of externally corrected CCSD approaches, which rely on a suitable non-CC wave function that is flexible enough to describe the dissociation process at hand and is used as a source of 3- and 4-body cluster amplitudes. These amplitudes are in turn used to achieve a more appropriate decoupling of the full CC chain of equations than that leading to the standard CCSD equations. The RMR-CCSD method employs for this purpose a MR-CISD wave function obtained with a relatively small active or model space. To illustrate the capabilities of this approach, the computed potential energy curves for the HF, F2 and H2O molecules are compared with the exact full CI or highly accurate large scale CI results, as well as with the MR-CISD results that are used as a source of 3- and 4-body amplitudes in the RMR-CCSD method. In all cases, the RMR-CCSD energies are far better than the standard CCSD energies or MR-CISD energies obtained with the same active space. The paper clearly demonstrates that the RMR-CCSD method provides very accurate data, while requiring only a modest increase in the computational effort over that of the standard CCSD method. © 1998 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.475425
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  • 3
    Digitale Medien
    Digitale Medien
    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
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.471697
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  • 4
    Digitale Medien
    Digitale Medien
    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
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.468766
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  • 5
    Digitale Medien
    Digitale Medien
    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
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.468074
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  • 6
    Digitale Medien
    Digitale Medien
    Alternancy symmetry: A unified viewpoint (1985)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 83 (1985), S. 1722-1735 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: A general formulation of the alternancy symmetry adaptation for the semiempirical Pariser–Parr–Pople (PPP) type Hamiltonians is presented at both the spin-orbital and spin-adapted many-electron levels. The derivation of the general form of the alternancy symmetry conjugation operators is based solely on the tight-binding approximation for the short range one-particle part of the Hamiltonian considered. It starts by a simple formulation of the desired invariance properties of the PPP type Hamiltonian. Using algebraic properties of the unitary group generators and of their particle number nonconserving extensions, it leads to a completely explicit and general form for the alternancy symmetry conjugation operators. In this way the prior descriptions, which become special cases of this general formulation, are interrelated and unified. The spin and quasispin character of certain components of these operators are also pointed out and explicitly derived. The spin-adapted version is based on the unitary group formulation of the valence bond-type approach. A completely general formulation is given which applies to many-electron states of an arbitrary multiplicity of neutral systems, either of the normal kind with an identical number of starred and nonstarred sites, or of the radicaloid character with different numbers of starred and nonstarred sites. An explicit form of the dependence of the relative phase factor of the alternancy symmetry conjugation operator on the total spin, total electron number and on the number of starred and nonstarred sites is also given. General rules for the construction of spin and alternancy symmetry-adapted states are illustrated on a few simple examples. Finally, a brief discussion of the implications of the alternancy symmetry is presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.449359
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  • 7
    Digitale Medien
    Digitale Medien
    Energy versus amplitude corrected coupled-cluster approaches. II. Breaking the triple bond (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 5774-5783 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: We examine the effectiveness of various energy corrections to the standard CCSD and to the reduced multireference (RMR) CCSD methods. These corrections are based on the asymmetric energy formula, but instead of projecting onto the reference configuration, as in the standard CCSD method, we employ for this purpose either the MR CISD wave function that is based on a suitable model space of the kind used in RMR CCSD, or simply the zero-order wave function in that model space. Both full complete-active-space and severely-truncated model spaces are employed. The method is applied to the prototypical case of the triple-bond dissociation, namely, to the exactly solvable double-zeta model of the N2 molecule. It is shown that in this way we can eliminate the breakdown of the standard CCSD method in the region of highly stretched geometries and obtain reliable potential energy curves. The comparison with the recently proposed renormalized CCSD(T) and variational CCD methods is also briefly addressed. © 2001 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.1398089
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  • 8
    Digitale Medien
    Digitale Medien
    Energy versus amplitude corrected coupled-cluster approaches. I (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 5759-5773 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: In the spirit of recently proposed renormalized CCSD(T) and CCSD(TQ) methods [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 5644 (2000), and references therein], we explore the additive, noniterative energy corrections for both the standard and reduced multireference (RMR) CCSD approaches. Our study is based on a simple asymmetric energy expression of the standard single reference (SR) coupled cluster theory and casts a new light on the RMR CCSD method and its relationship with the corresponding MR CISD and SR reference CCSD methods, thus interrelating the amplitude and energy corrected schemes. These developments are illustrated on two exactly solvable model systems, namely, on the DZP models of the H4 system and of the HF molecule. We find that appropriately projected CCSD provides an almost identical energies as does the RMR CCSD method. © 2001 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.1398088
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  • 9
    Digitale Medien
    Digitale Medien
    Energy- versus amplitude-corrected coupled-cluster approaches. III. Accurate computation of spectroscopic data exemplified on the HF molecule (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 117 (2002), S. 1941-1955 
    Details
    ISSN: 1089-7690
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: The so-called energy-corrected coupled-cluster method with singles and doubles (CCSD), which is closely related to the recently proposed method of moments of Kowalski and Piecuch, accounts for the nondynamic correlation effects, which are missing in the standard single-reference CCSD, by projecting onto the modest-size multireference (MR) configuration-interaction SD (CISD) wave function when evaluating the energy, rather than onto the single-determinantal CCSD reference. The ability of this approach to generate reliable potential energy curves (PECs) or surfaces over a wide range of geometries is examined using a realistic ab initio model of the HF molecule. The PECs obtained with the correlation-consistent polarized valence double (triple, quadruple) zeta cc-pVXZ (T,Q) basis sets are used, together with the PEC extrapolated to the complete basis set limit, to compute the rotational and vibrational levels, which are then compared with the experimentally determined values as well as with the directly measured vibrational frequencies. A comparison is also made with the earlier results [X. Li, J. Mol. Struct.: THEOCHEM 547, 69 (2001)] that were obtained with the amplitude-corrected CCSD method, namely the so-called reduced MR CCSD that exploits the same MR CISD wave function, as well as with recently published renormalized CCSD(T) results [P. Piecuch et al., J. Chem. Phys. 115, 5796 (2001)]. It is shown that both the amplitude- and energy-corrected CCSD PECs may be used to generate highly accurate and reliable spectroscopic data once the basis set limit is achieved. © 2002 American Institute of Physics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.1488597
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  • 10
    Digitale Medien
    Digitale Medien
    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
    Quelle: AIP Digital Archive
    Thema: Physik , Chemie und Pharmazie
    Notizen: 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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1063/1.455919
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