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  • 1
    Electronic Resource
    Electronic Resource
    Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 1985-2001 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459921
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  • 2
    Electronic Resource
    Electronic Resource
    Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. II. Second-order Møller–Plesset (MP2-R12) calculations on closed-shell atoms (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2002-2019 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459922
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  • 3
    Electronic Resource
    Electronic Resource
    Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. III. Second-order Møller–Plesset (MP2-R12) calculations on molecules of first row atoms (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 2020-2030 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459923
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  • 4
    Electronic Resource
    Electronic Resource
    Potential energy surface of the H+3 ground state in the neighborhood of the minimum with microhartree accuracy and vibrational frequencies derived from it (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 2231-2243 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467663
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  • 5
    Electronic Resource
    Electronic Resource
    MP2-R12 calculations on the relative stability of carbocations (1990)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 94 (1990), S. 5625-5630 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100377a040
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  • 6
    Electronic Resource
    Electronic Resource
    Towards the one-particle basis set limit of second-order correlation energies: MP2-R12 calculations on small Ben and Mgn clusters (n=1–4) (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 5167-5177 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.466018
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  • 7
    Electronic Resource
    Electronic Resource
    Configuration interaction calculations with terms linear in the interelectronic coordinate for the ground state of H+3. A benchmark study (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 99 (1993), S. 8830-8839 
    Details
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465551
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  • 8
    Electronic Resource
    Electronic Resource
    Computation of some new two-electron Gaussian integrals (1992)
    Springer
    Theoretical chemistry accounts 83 (1992), S. 441-453 
    Details
    ISSN: 1432-2234
    Keywords: Molecular two-electron integrals ; r 12 methods ; Cartesian Gaussians ; Hermite functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary The evaluation of a new form of two-electron integrals is required if the interelectronic distancer 12 is used as a variable in then-electron functions of electron correlation methods. The McMurchie-Davidson algorithm for the generation of molecular integrals over Gaussian-type functions is ideally suited to this. The new Gaussian integrals are formed from Hermite integrals overr 12 (rather than 1/r 12) by standard techniques. The Hermite integrals overr 12 itself are generated by a simple procedure with negligible computational effort. The key results are discussed in the context of general recursion formulas.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01113067
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  • 9
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    MP2-R12 calculations on the relative stability of carbocations (1990)
    American Chemical Society
    Details
    Publication Date: 1990-07-01
    Print ISSN: 0022-3654
    Electronic ISSN: 1541-5740
    Topics: Chemistry and Pharmacology , Physics
    Published by American Chemical Society
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  • 10
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    Configuration interaction calculations with terms linear in the interelectronic coordinate for the ground state of H+3. A benchmark study (1993)
    American Institute of Physics
    Details
    Publication Date: 1993-12-01
    Print ISSN: 0021-9606
    Electronic ISSN: 1089-7690
    Topics: Chemistry and Pharmacology , Physics
    Published by American Institute of Physics
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