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  • 1
    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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  • 2
    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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  • 3
    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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  • 4
    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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  • 5
    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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  • 6
    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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  • 7
    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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  • 8
    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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  • 9
    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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  • 10
    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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