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  • 1
    ISSN: 1432-2234
    Keywords: Key words: Spin projection ; Coupled-cluster theory including single and double excitations ; Spin contamination
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ 2. Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators  s+ 1 and Âs+2. The computational cost of such a projection scales with O(M 6) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair.
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  • 2
    ISSN: 1432-2234
    Keywords: Coupled cluster methods ; Perturbation analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Various coupled cluster (CC) and quadratic CI (QCI) methods are compared in terms of sixth, seventh, eighth, and infinite order Møller-Plesset (MPn, n=6, 7, 8, ∞) perturbation theory. By partitioning the MPn correlation energy into contributions resulting from combinations of single (S), double (D), triple (T), quadruple (Q), pentuple (P), hextuple (H), etc. excitations, it has been determined how many and which of these contributions are covered by CCSD, QCISD, CCSD(T), QCISD(T), CCSD(TQ), QCISD(TQ), and CCSDT. The analysis shows that QCISD is inferior to CCSD because of three reasons: a) With regard to the total number of energy contributions QCI rapidly falls behind CC for largen. b) Part of the contributions resulting from T, P, and higher odd excitations are delayed by one order of perturbation theory. c) Another part of the T, P, etc. contributions is missing altogether. The consequence of reason a) is that QCISD(T) covers less infinite order effects than CCSD does, and QCISD(TQ) less than CCSD(T), which means that the higher investment on the QCI side (QCISD(T) :O(M 7), CCSD :O(M 6), QCISD(TQ) :O(M 8), CCSD(T) :O(M 7),M: number of basis functions) does not compensate for its basic deficiencies. Another deficiency of QCISD(T) is that it does not include a sufficiently large number of TT coupling terms to prevent an exaggeration of T effects in those cases where T correlation effects are important. The best T method in terms of costs and efficiency should be CCSD(T).
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 88 (1994), S. 47-67 
    ISSN: 1432-2234
    Keywords: Coupled cluster methods ; Size-extensive CI ; Quadratic CI ; QCISDT ; QCISDTQ
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary A procedure is developed that leads from CI to size-extensive CI (ECI) by stepwise cancellation of disconnected terms in the CI equations. The ECI methods thus obtained are identical with the corresponding coupled cluster (CC) methods with the exception of CISD and CISDT, which convert to size-extensive quadratic CI (QCISD) and ECISDT. The latter method has similar properties as CCSDT, but does not offer any significant time-savings as compared to CCSDT. Therefore, the idea of extending CI methods to size-extensive CI methods does not lead to a hierarchy of independent CC methods. However, the procedure of obtaining ECI methods lays the basis for deriving QCI methods that are truly size-extensive. This is accomplished by (a) deleting the first linear term of thep-fold CI excitation equations (p ≥ 3) since this term always represents a disconnected term and (b) including just the connected part of appropriate quadratic correction terms in all but the energy equation. In this way, size-extensive QCISDT and QCISDTQ are obtained and their properties are discussed in comparison with QCISD(T) and CCSDT.
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  • 4
    ISSN: 1432-2234
    Keywords: Key words: Fourth-order Møller ; Plesset spectrum ; Complete-basis-set energies ; Basis set dependence ; Three-electron correlation effects ; Electron correlation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Fourth-order Møller–Plesset (MP4) correlation energies are computed for 28 atoms and simple molecules employing Dunning's correlation-consistent polarized-valence m-zeta basis sets for m=2, 3, 4, and 5. Extrapolation formulas are used to predict MP4 energies for infinitely large basis sets. It is shown that both total and partial MP4 correlation energies can be extrapolated to limit values and that the sum of extrapolated partial MP4 energies equals the extrapolated total MP4 correlation energy within calculational accuracy. Therefore, partial MP4 correlation energies can be presented in the form of an MP4 spectrum reflecting the relative importance of different correlation effects. Typical trends in calculated correlation effects for a given class of electron systems are independent of the basis set used. As first found by Cremer and He [(1996) J Phys Chem 100:6173], one can use MP4 spectra to distinguish between electron systems with well-separated electron pairs and systems for which electrons cluster in a confined region of atomic or molecular space. MP4 spectra for increasing size of the basis set reveal that smaller basis set calculations underestimate the importance of three-electron correlation effects for both classes by overestimating the importance of pair correlation effects. The minimum size of a basis set required for reliable MP4 calculations is given by a valence triple-zeta polarized basis, which even in the case of anions performs better than a valence double-zeta basis augmented by diffuse functions.
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  • 5
    ISSN: 1432-2234
    Keywords: Key words: Quasi-degenerate perturbation theory ; Multireference methods ; Correlation energy ; Single excitations ; Orbital coherence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. In multiconfiguration perturbation theory, the generalized Brill⊙uin theorem is normally fulfilled, which imposes constraints on the matrix elements involved in the description of single excitations. This can be considered as guaranteeing coherence of the configurations and orbitals describing the zeroth order wavefunction. In quasi-degenerate perturbation theory (QDPT) single excitations are treated independently, which causes a loss of coherence. It is argued that a loss of orbital coherence leads to unreasonable QDPT correlation energies.
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  • 6
    ISSN: 0948-5023
    Keywords: Keywords Bond energy(BE), Intrinsic bond energy(IBE), Bond dissociation energy(BDE), Force constants, Adiabatic internal mode
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The bond energy (BE) of a polyatomic molecule cannot be measured and, therefore, determination of BEs can only be done within a model using a set of assumptions. The bond strength is reflected by the intrinsic BE (IBE), which is related to the intrinsic atomization energy (IAE) and which represents the energy of dissociation under the provision that the degree of hybridization is maintained for all atoms of the molecule. IBE and BE differ in the case of CC and CH bonds by the promotion, the hybridization, and the charge reorganization energy of carbon. Since the latter terms differ from molecule to molecule, IBE and BE are not necessarily parallel and the use of BEs from thermochemical models can be misleading. The stretching force constant is a dynamical quantity and, therefore, it is related to the bond dissociation energy (BDE). Calculation and interpretation of stretching force constants for local internal coordinate modes are discussed and it is demonstrated that the best relationship between BDEs and stretching force constants is obtained within the model of adiabatic internal modes. The valence stretching force constants are less suitable since they are related to an artificial bond dissociation process with geometrical relaxation effects suppressed, which leads to an intrinsic BDE (IBDE). In the case of AX n molecules, symmetric coordinates can be used to get an appropriate stretching force constant that is related to the BE. However, in general stretching force constants determined for symmetry coordinates do not reflect the strength of a particular bond since the related dissociation processes are strongly influenced by the stability of the products formed.
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  • 7
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
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  • 8
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
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  • 9
    ISSN: 1520-6904
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
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  • 10
    ISSN: 1520-5126
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology
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