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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 10096-10115 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The interaction between two HF molecules as a function of all six internal coordinates is reported as calculated for 3284 selected points in configuration space at counterpoise-corrected explicitly correlated levels and fitted to an analytical expression, which is described in detail. The unweighted rms deviation for all 3284 points is 21 cm−1. Empirical refinements are applied through mixing and scaling of the ab initio data, guided by the comparison of multidimensional nuclear quantum energy levels with experimental data. The resulting semiempirical pair potentials (labeled SC-2.9 and SO-3) contain 67 and 61 freely adjusted parameters and are combined with a four parameter monomer potential of generalized Pöschl–Teller type. Various minimum energy paths and cuts are investigated. Major improvements over earlier HF dimer potentials are demonstrated via multidimensional solutions of the nuclear Schrödinger equation. Comparison with other high level ab initio calculations and with various experimental data reveals very good overall consistency. The new potential suggests strong Coriolis coupling in the librational degrees of freedom. Best estimates of stationary points, of the dimer dissociation energy (De=19.1±0.2 kJ/mol), of the electronic barrier to hydrogen bond exchange (4.2±0.2 kJ/mol), of the electronic barrier to linearity (3.9±0.2 kJ/mol), and of the electronic barrier to hydrogen exchange (175±10 kJ/mol) are inferred. Based on accurate electric dipole functions for the monomer and distortion contributions calculated with a large basis at SCF level, a simple analytical six-dimensional electric dipole hypersurface is presented. © 1998 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 106 (1997), S. 9639-9646 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The basis-set convergence of the electronic correlation energy in the water molecule is investigated at the second-order Møller–Plesset level and at the coupled-cluster singles-and-doubles level with and without perturbative triples corrections applied. The basis-set limits of the correlation energy are established to within 2 mEh by means of (1) extrapolations from sequences of calculations using correlation-consistent basis sets and (2) from explicitly correlated calculations employing terms linear in the interelectronic distances rij. For the extrapolations to the basis-set limit of the correlation energies, fits of the form a+bX−3 (where X is two for double-zeta sets, three for triple-zeta sets, etc.) are found to be useful. CCSD(T) calculations involving as many as 492 atomic orbitals are reported. © 1997 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. 1077-1084 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An intermolecular potential energy surface was derived for the hydrogen-bonded water trimer as a function of the three torsional angles ω1, ω2, ω3, for energies up to 1300 cm−1 (3.7 kcal/mol) above the global minimum. The O...O distances and the intramolecular geometry of the H2O molecules are held fixed. This surface is based on the ab initio calculations presented in a companion paper [W. Klopper et al., J. Chem. Phys. 103, 1085 (1995)], which involve very large basis sets and the most extensive treatment of correlation energy for calculations of (H2O)3 so far. The 70 ab initio interaction energies, multiplied by six due to the S6 symmetry of the surface, were fitted using an analytical potential function, with an average error of ≈11 cm−1. This potential provides a rapidly computable analytical expression for use in calculations of torsional eigenfunctions and -values and other properties of this cluster. Also given is a classification of the low-lying torsional wave functions according to nodal properties. © 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
    Springer
    Theoretical chemistry accounts 97 (1997), S. 164-176 
    ISSN: 1432-2234
    Keywords: Key words: Coupled-cluster theory ; Triples corrections ; Multiple basis sets ; Natural orbitals ; Integral-direct methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Multiple basis sets are used in calculations of perturbational corrections for triples replacements in the framework of single-reference coupled-cluster theory. We investigate a computational procedure, where the triples correction is calculated from a reduced space of virtual orbitals, while the full space is employed for the coupled-cluster singles-and-doubles model. The reduced space is either constructed from a prescribed unitary transformation of the virtual orbitals (for example into natural orbitals) with subsequent truncation, or from a reduced set of atomic basis functions. After the selection of a reduced space of virtual orbitals, the singles and doubles amplitudes obtained from a calculation in the full space are projected onto the reduced space, the remaining set of virtual orbitals is brought into canonical form by diagonalizing the representation of the Fock operator in the reduced space, and the triples corrections are evaluated as usual. The case studies include the determination of the spectroscopic constants of N2, F2, and CO, the geometry of O3, the electric dipole moment of CO, the static dipole polarizability of F−, and the Ne⋯Ne interatomic potential.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 99 (1998), S. 265-271 
    ISSN: 1432-2234
    Keywords: Key words: Nitrogen molecule ; Electronic structure calculations ; Basis-set limit ; Binding energy ; Spectroscopic constants
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. Results obtained from nonrelativistic electronic structure calculations using finite Gaussian basis sets are extrapolated to the limit of a complete basis set, employing the results of explicitly correlated coupled-cluster calculations including singles and doubles substitutions (CCSD). For N2, the basis-set limits for the electronic binding energy, equilibrium bond length and harmonic vibrational wave number are established for the CCSD model including a perturbative correction for triples substitutions and for the internally contracted multireference configuration interaction method. The resulting numbers are in good agreement with experimental values.
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