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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 1985-2001 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The matrix elements needed in a CI-SD, CEPA, MP2, or MP3 calculation with linear r12-dependent terms for closed-shell states are derived, both exactly and in a consistent approximate way. The standard approximation B guarantees that in the atomic case the error due to truncation of the basis at some angular momentum quantum number L goes as ∼L−7, at variance with L−3 in conventional calculations (without r12 terms). Another standard approximation A has errors ∼L−5, but is simpler and—for moderate basis sets—somewhat better balanced. The explicit expressions for Møller–Plesset perturbation theory of second and third order with linear r12 terms (MP2-R12 and MP3-R12, respectively) are explicitly given in the two standard approximations.
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2002-2019 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The MP2-R12 method in approximations A and B as outlined in part I of this series is applied to the ground states of the closed-shell atoms He, Be, Ne, Mg, Ar, Ca, Cu+, Zn2+, and Kr, in terms of both STO and GTO basis sets. For He, Be, and Ne the partial wave increments of the various pairs are documented and compared with their conventional counterparts. The fast convergence of the partial wave increments, that go as (l+ (1)/(2) )−8 in the MP2-R12/B scheme, is demonstrated. From the MP2-R12 calculations more accurate estimates of the exact MP2 energies are possible than from the conventional partial wave expansion. The actually calculated values differ generally by a fraction of a 1% from the estimated basis sets limits if STO basis sets with l≤5 (in some cases l≤6) are used, while errors of typically 1% are obtained with GTO basis sets and l≤3.
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2020-2030 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The MP2-R12 method (Møller–Plesset second-order perturbation theory with terms linear in the interelectronic coordinate r12) in the approximations A and B as outlined in paper I of this series is applied to the ground states of the molecules H2, LiH, HF, H2O, NH3, CH4, Be2, N2, F2, C2H2, and CuH in their experimental equilibrium geometry, and to the van der Waals interaction between two He atoms. In all cases MP2 correlation energies are obtained that are supposed to differ by at most a few percent from the basis set limit. For CH4 the dependence of the energy on the symmetric stretching coordinate is studied, which together with other information leads to a recommended bond length of 1.086 A(ring) for the CH bond length. For He2 and F2 the canonical and localized descriptions are compared. The latter is superior for the K-shell contributions, otherwise there is a little difference. For He2 in the localized representation rather good results for the dispersion interaction are obtained. The potential curve of Be2 is significantly improved in MP2-R12 as compared to conventional MP2. The examples C2H2 and CuH show that the method is not limited to very small systems.
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 6397-6410 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: In explicitly correlated Møller–Plesset (MP2-R12) methods, the first-order wave function is expanded not only in terms of products of one-electron functions—that is, orbitals—but also in terms of two-electron functions that depend linearly on the interelectronic coordinates rij. With these functions, three- and four-electron integrals occur, but these integrals can be avoided by inserting a resolution of the identity (RI) in terms of the one-electron basis. In previous work, only one single basis was used for both the electronic wave function and the RI approximation. In the present work, a new computational approach is developed that uses an auxiliary basis set to represent the RI. This auxiliary basis makes it possible to employ standard basis sets in explicitly correlated MP2-R12 calculations.© 2002 American Institute of Physics.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 761-765 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is difficult, if not impossible, to extrapolate the helium pair potential to the limit of a complete basis to within the accuracy needed to improve significantly on existing, directly computed potentials. Even though the basis-set convergence of calculations in a correlation-consistent basis with cardinal number X is dominated by the X−3 term, it is important to account for energy terms that converge more rapidly than ∝X−3. The electron-correlation contribution to the potential will be overestimated noticeably when these terms are not properly taken into account. © 2001 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 9957-9965 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The equations of the original ab initio scalar-relativistic zeroth-order regular approximation (ZORA) and the infinite-order regular approximation (IORA) are expanded in orders of 1/c2. It is shown that previous ZORA/IORA implementations in ab initio quantum chemistry programs were not correct to order 1/c2, but contained imperfections leading to fictitious self-interactions. These errors can be avoided by adding exchange-type terms (coupling the large and small components) to the relativistic ZORA correction to the Hamiltonian, yielding improved ab initio relativistic zeroth- and infinite-order regular approximations that are correct to order 1/c2. The new methods have been tested numerically by computing the total energies, orbital energies, and static electric dipole polarizabilities of the rare gas atoms He through Xe. © 2000 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 7356-7363 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Starting from the Lévy-Leblond equation, which is the four-component nonrelativistic limit of the Dirac equation, a direct perturbation theory of magnetic properties and relativistic corrections is developed and implemented for point-charge and finite nuclei. The perturbed small components are regularized by projecting them onto an auxiliary small-component basis of Gaussian functions. The relevant operators and matrix elements are derived for the point-nuclear and Gaussian nuclear models. It is demonstrated how the usual paramagnetic spin-orbit, Fermi-contact, and spin-dipole integrals of Ramsey's theory can be evaluated in the same manner as field and field-gradient integrals—that is, as derivatives of potential-energy integrals. A few illustrative calculations are performed. © 2001 American Institute of Physics.
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 6127-6132 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Explicitly correlated coupled cluster (CCSDT-1a-R12) results were obtained for the He2 interatomic potential from a new, integral-direct implementation. With the new code, Gaussian basis sets as large as 11s8p6d5f4g3h could be employed, and the potential energy curve was calculated over a wide range using a basis of the type 11s8p6d5f4g.This curve is very close to represent the basis set limit of the CCSDT-1a approach. At the internuclear separation R=5.6 a0, the CCSDT-1a limiting value for the interaction energy is −10.68 K. As the effect of quadruple substitutions can be estimated as −0.32 K, this limiting value is perfectly consistent with the accurate quantum Monte Carlo calculation of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], who reported a well depth of −11.01±0.10 K. On the other hand, however, CCSDT-1a-R12 calculations of the He2 potential energy curve strongly indicate that the most recent semiempirical potentials available in the literature are slightly too repulsive for short (R≤4.0 a0) interatomic distances. © 1995 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 6114-6126 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The global and local minima, stationary points, and torsional rearrangement processes of cyclic homodromic (H2O)4 were studied on its four-dimensional torsional intermolecular potential energy surface. Eight different energetically low-lying torsional stationary point structures were found by ab initio theory, and fully structure-optimized at the second-order Møller–Plesset level, using large basis sets. Second-order energies close to the one-particle basis set limit were obtained at these geometries using the explicitly correlated Møller–Plesset method. The effects of higher-order correlation energy terms were investigated by coupled cluster theory, and terms beyond second order were found to cancel in good approximation. The S4 symmetric global minimum has a square and almost planar O...O...O...O arrangement with free O–H bonds alternating "up'' and "down'' relative to this plane, with two isometric versions of this structure. Another torsional conformer with two neighboring up O–H bonds followed by two neighboring down O–H bonds is a local minimum, 0.93 kcal/mol above the global minimum. The four versions of this structure are connected to the global minima via two distinct but almost degenerate first-order torsional saddle points, which occur as two sets of eight isometric versions each, both about 1.24 kcal/mol above the global minimum. Yet another set of eight second-order saddle points lies at 1.38 kcal/mol. The structure with three O–H bonds up and one down is not a stationary point, while the structure with all four O–H bonds on the same side of the plane is a first-order saddle point.The fully planar C4h symmetric structure is a fourth-order stationary point 2.8 kcal/mol above the minimum. The torsional interconversion paths between this multitude of points are complex, and are discussed in three-dimensional spaces of symmetry-adapted torsional coordinates, and also in a network representation. The torsional normal-mode eigenvectors point fairly directly along the torsional interconversion pathways, but the harmonic frequencies are well below the corresponding barriers. Tunneling interconversion between torsional conformers is, hence, less important than for the water trimer. © 1995 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 309-320 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: To study the reliability of the recently developed explicitly correlated coupled cluster method (CCSDT1-R12) we have performed calculations on the four-electron systems Be, Li−, and LiH on various levels of perturbation theory and coupled cluster theory with and without explicit linear rij terms. The convergence of the total energy with increasing size of the basis is much faster than for the conventional coupled cluster approach. Our CCSDT1-R12 energies of −14.667261 Eh for Be and −7.500671 Eh for the Li− ground state are the best ones computed so far and are close to previous estimates of the CCSDT 1 basis set limits. The Be result differs from the "experimental'' nonrelativistic energy by ca. 0.1 mEh, mainly due to neglect of quadruple excitations. Our Born–Oppenheimer energy of LiH at the equilibrium distance of −8.070487 Eh is close to the experimental nonrelativistic energy. The binding energy (D0) of LiH with respect to Li+ and H− is calculated as −7.152 eV, in agreement with the experimental value within a meV. For LiH the harmonic vibrational frequencies and other related spectroscopic constants are studied in their basis dependence as well. The equilibrium distance and the harmonic vibrational frequency of LiH are much less sensitive to the inclusion of terms that explicitly depend on the interelectronic coordinates. Basis set superposition errors are much smaller in the R12 approach than in the conventional calculations, especially for the smaller basis sets. © 1995 American Institute of Physics.
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