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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
    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
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1488597
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  • 3
    Electronic Resource
    Electronic Resource
    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
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1398088
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1398089
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  • 5
    Electronic Resource
    Electronic Resource
    Reduced multireference coupled cluster method: Ro-vibrational spectra of N2 (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 9966-9977 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The reduced multireference (RMR) coupled cluster method with singles and doubles (CCSD), relying on four- and eight-dimensional reference spaces, is employed to generate the potential energy curve for the nitrogen molecule, using both the correlation-consistent polarized valence-triple-zeta (cc-pVTZ) and atomic natural orbital basis sets. The resulting potentials are then used to compute the ro-vibrational term values, which are compared with the available experimentally determined values. Moreover, a direct comparison with the measured spectral line frequencies, for both the fundamental rotational Raman band and the vibrationally excited Q branches, is also carried out. Comparisons with the single reference CCSD, as well as with the corresponding multireference configuration interaction results that serve as the external source for RMR CCSD, are also made. An excellent performance of RMR CCSD, and its systematic improvement with the increasing dimension of the reference space employed, is demonstrated for the cc-pVTZ basis set. The fundamental Raman band frequencies are computed with an error of less than 1 cm−1, while for the vibrationally excited bands a systematic deviation of about 7 cm−1 is found. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1323260
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  • 6
    Electronic Resource
    Electronic Resource
    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
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.449359
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  • 7
    Electronic Resource
    Electronic Resource
    Direct iterative solution of the generalized Bloch equation. II. A general formalism for many-electron systems (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 2594-2611 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A general nonperturbative formulation of the recently proposed [H. Meißner and E. O. Steinborn, Int. J. Quantum Chem. 61, 777 (1997); Part I] quadratic iterative scheme for the wave function expansion coefficients (WECs), enabling a direct solution of the generalized Bloch equation, is given for the ab initio electronic Hamiltonians, thus enabling the computation of the molecular electronic structure. The method exploits the concepts of a multidimensional reference or model space, a (non-Hermitian) effective Hamiltonian, and the generalized Bloch equation. The formulation in terms of WECs provides a considerable freedom in the design of various approximation schemes by combining direct iterations on WECs with their approximation by disconnected cluster components based on the exponential cluster ansatz for the wave operator. The resulting formalism is capable of handling a rather large class of both ground and excited states. While the general formulation represents a multiconfigurational, multireference scheme, a special attention is paid to its two-dimensional state selective or state specific version. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1305321
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  • 8
    Electronic Resource
    Electronic Resource
    Direct iterative solution of the generalized Bloch equation. III. Application to H2-cluster models (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 2612-2621 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A state-selective multiconfigurational single-reference method that was outlined in the preceding paper of this series (H. Meißner and J. Paldus, J. Chem. Phys. 113, 2594 (2000); preceding paper), and is based on a quadratic iterative algorithm enabling the direct solution of the generalized Bloch equation, is applied to several model systems consisting of interacting hydrogen molecules, nowadays referred to as the H4, S4, and H8 models. These exactly solvable models are often used to test the efficacy of post-Hartree–Fock methods in their ability to recover both the dynamic and nondynamic correlation energies, since they enable a continuous variation of the degree of quasidegeneracy from the degenerate to nondegenerate limit by varying a single geometrical parameter, while simulating the dissociation of one or more single bonds. Various approximation schemes that were outlined in Part II, as well as their combinations, are tested and their performance evaluated. The size-extensivity deviations of those approximations that do not rely on the exponential cluster ansatz for the wave operator are also examined using larger hydrogen molecule clusters. It is shown that the so-called BQ4 approximation performs extremely well in all cases and even outperforms the externally corrected, reduced multireference (RMR) CCSD in the quasidegenerate region of geometries. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1305322
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  • 9
    Electronic Resource
    Electronic Resource
    Direct iterative solution of the generalized Bloch equation. IV. Application to H2, LiH, BeH, and CH2 (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 2622-2637 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The state selective, one- and two-determinantal versions of the recently proposed direct iterative approach to the solution of the generalized Bloch equation [H. Meißner and J. Paldus, J. Chem. Phys. 113, 2612 (2000); Part II] are applied to the ground and excited states of several test molecular ab initio models for which the exact full configuration interaction results are available. Both closed- and open-shell states of different spin multiplicity are considered, as well as the excited states belonging to the same symmetry species as does the ground state. The versatility and flexibility of this approach stems from the possibility of introducing the cluster expansion based approximations of highly excited clusters at various levels of the iterative scheme, leading to a sequence of approximations including both the configuration interaction and coupled cluster methods with singles and doubles as a special case. Both the reliability and the efficiency of these various approximations is examined, and potentially promising approximation schemes are identified. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1305323
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  • 10
    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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