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  • Articles  (178)
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  • Articles  (178)
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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. 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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  • 2
    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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  • 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 99 (1993), S. 5167-5177 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A principal source of error in electronic structure calculations is the inability of conventional CI (configuration interaction) expansions to describe the electron–electron cusp. This manifests itself in the slow convergence of correlation treatments with finite basis sets which are commonly applied in traditional ab initio quantum chemistry. In this paper we describe results obtained by adding special n-particle functions, which have terms linear in the interelectronic coordinate r12, to the usual trial wave function, which is an expansion in terms of Slater determinants. A vectorized and efficient computer program has been written for putting into practice second-order Møller–Plesset perturbation theory with linear r12 terms (MP2-R12): the sore program. It exploits both direct integral evaluation strategies and techniques that permit the full (also nonabelian) use of molecular point group symmetry. These two ingredients to the program allow for the use of very large Gaussian basis sets in conjunction with the linear r12 terms. As a result we are now able to press into new territories of accuracy. Calculations on Be and Mg clusters illustrate applications of the program. Binding energies are discussed with regard to basis set saturation and with some emphasis on the basis set superposition error (BSSE). The combination of our MP2 basis set limits on one hand with results from CCSD(T) and MRCI calculations with standard basis sets on the other leads to reliable estimates of the binding energies of Be3 (27 kcal/mol), Be4 (88 kcal/mol), Mg3 (8 kcal/mol), and Mg4 (28 kcal/mol). The most extensive MP2-R12 calculations have been performed with very large uncontracted Cartesian Gaussian basis sets. Also, core–core and core–valence correlation effects have been accounted for. In this work we present the results of the first real large-scale calculations employing Hylleraas-type coordinates which have been performed so far on many-electron, polyatomic molecules.
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 8830-8839 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The CISD-R12 method is applied to the ground states of H2 and H+3 at their equilibrium configurations, with both bare nuclear Hamiltonian (BNH) and self-consistent field (SCF) references with eight basis sets that range from 10 s (i.e., ten contracted s-type Gaussians) to 30s20p12d9f. With the largest basis set, the energy of H2 is obtained with an error of 2μEh, while for H+3, the error is probably smaller and the best calculated energy of −1.343 835Eh is supposed to be accurate to all indicated figures. The BNH reference is always superior to the SCF reference. The relativistic corrections are evaluated at the SCF level by means of "direct perturbation theory'' both for H2 and H+3. The Hylleraas-SCF methods and related concepts for the construction of an optimum reference function are discussed in the Appendix.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 102 (1995), S. 6168-6179 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Limiting values for Møller–Plesset second-order (MP2) correlation energies are provided for the ten-electron systems Ne, HF, and H2O, for the N2 molecule, and for the weak He...He interatomic interaction energy. These limiting values were obtained by the MP2-R12 approach. This approach differs from traditional MP2 theory by employing first-order wave functions which explicitly depend on the interelectronic coordinates rij. With the MP2-R12 method, the atomic orbital (AO) basis set limits for the systems under study are reached. The calculations provide insight into AO basis set requirements for methods with linear rij dependence (R12 methods), e.g., for coupled cluster methods, or multireference configuration interaction methods. Moreover, it is expected that the results have the potential to serve as valuable benchmarks for further developments in the field of explicitly correlated wave functions, for example for expansions in terms of Gaussian geminals (Gaussian functions which depend on rij). The present calculations on HF, H2O, and N2 provide the most accurate second-order correlation energies to date for these systems. © 1995 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 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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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 1085-1098 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A torsional potential energy surface for the cyclic water trimer was calculated at the level of second-order Møller–Plesset perturbation theory. For the construction of this ab initio surface, the first-order wave function was expanded in a many-electron basis which linearly depends on the interelectronic coordinates r12. The one-electron basis of Gaussian orbitals was calibrated on the water monomer and dimer to ensure that the ab initio surface computed represents the (near- ) basis set limit for the level of theory applied. The positions of the free O—H bonds are described by three torsional angles. The respective three-dimensional torsional space was investigated by 70 counterpoise corrected single-point calculations for various values of these angles, providing a grid to fit an analytical representation of the potential energy surface. The four symmetry unique stationary points previously found at the Hartree–Fock and conventional Møller–Plesset levels [Schütz et al., J. Chem. Phys. 99, 5228 (1993)] were studied in detail: Relative energies of the structures were calculated by applying second-order Møller–Plesset and coupled cluster methods; harmonic vibrational frequencies were calculated at the second-order Møller–Plesset level with a 6-311++G(d,p) basis set at these stationary points. It is expected that the present torsional potential energy surface for the water trimer will play an important role in the understanding of the vibrational transitions observed by far-infrared vibration–rotation–tunneling spectroscopy in terms of a nearly free pseudorotational interconversion on a cyclic vibrational–tunneling path. © 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. 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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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 2231-2243 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The potential energy surface (PES) of the H+3 ground state is computed by means of the single and double excitation configuration interaction with an explicit linear r12 term in the wave function (CISD-R12) developed recently by the present authors, with a nearly saturated basis set. The points of the PES suggested by Meyer, Botschwina, and Burton (MBB) were chosen and the fitting procedure of the same authors was followed. The present PES has both on an absolute and a relative scale (i.e., relative to the minimum) an error of a few microhartrees (μEh) in the relevant region, an accuracy that has never before been achieved in a quantum chemical calculation for a triatomic molecule. From the fit the vibrational term values for the fundamental bands and some overtones of H+3, H2D+, HD+2, and D+3 were computed by means of the TRIATOM package of Tennyson and Miller. The computed frequencies are in better agreement with experiment (maximum error ∼0.5 cm−1) than those of all previous ab initio calculations (without empirical adjustment). To achieve this accuracy, it is necessary to go beyond the Born–Oppenheimer approximation and to take care of the finite mass ratio between nuclei and electrons.
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