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  • 1
    Electronic Resource
    Electronic Resource
    Influence on isotope effect calculations of the method of obtaining force constants from vibrational data (1982)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 86 (1982), S. 659-663 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100394a014
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  • 2
    Electronic Resource
    Electronic Resource
    Improving the convergence and estimating the accuracy of summation approximants of 1/D expansions for Coulombic systems (1998)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 39 (1998), S. 5112-5122 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The convergence of large-order expansions in δ=1/D, where D is the dimensionality of coordinate space, for energies E(δ) of Coulomb systems is strongly affected by singularities at δ=1 and δ=0. Padé–Borel approximants with modifications that completely remove the singularities at δ=1 and remove the dominant singularity at δ=0 are demonstrated. A renormalization of the interelectron repulsion is found to move the dominant singularity of the Borel function F(δ)=∑jEj′/j!, where Ej′ are the the expansion coefficients of the energy with singularity structure removed at δ=1, farther from the origin and thereby accelerate summation convergence. The ground-state energies of He and H2+ are used as test cases. The new methods give significant improvement over previous summation methods. Shifted Borel summation using Fm(δ)=∑jEj′/Γ(j+1−m) is considered. The standard deviation of results calculated with different values of the shift parameter m is proposed as a measure of summation accuracy. © 1998 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532561
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  • 3
    Electronic Resource
    Electronic Resource
    A linear algebraic method for exact computation of the coefficients of the 1/D expansion of the Schrödinger equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 101 (1994), S. 5987-6004 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The 1/D expansion, where D is the dimensionality of space, offers a promising new approach for obtaining highly accurate solutions to the Schrödinger equation for atoms and molecules. The method typically employs an asymptotic expansion calculated to rather large order. Computation of the expansion coefficients has been feasible for very small systems, but extending the existing computational techniques to systems with more than three degrees of freedom has proved difficult. We present a new algorithm that greatly facilitates this computation. It yields exact values for expansion coefficients, with less roundoff error than the best alternative method. Our algorithm is formulated completely in terms of tensor arithmetic, which makes it easier to extend to systems with more than three degrees of freedom and to excited states, simplifies the development of computer codes, simplifies memory management, and makes it well suited for implementation on parallel computer architectures. We formulate the algorithm for the calculation of energy eigenvalues, wave functions, and expectation values for an arbitrary many-body system and give estimates of storage and computational costs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.467314
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  • 4
    Electronic Resource
    Electronic Resource
    Dimensional scaling for hydrogen molecule(1+) without the Born-Oppenheimer approximation (1993)
    s.l. : American Chemical Society
    The @journal of physical chemistry 〈Washington, DC〉 97 (1993), S. 2464-2466 
    Details
    Source: ACS Legacy Archives
    Topics: Chemistry and Pharmacology , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1021/j100112a057
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  • 5
    Electronic Resource
    Electronic Resource
    A summation procedure that improves the accuracy of the fourth-order Møller–Plesset perturbation theory (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 6461-6464 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A procedure is demonstrated for summing the Møller–Plesset many-body perturbation expansion based on the ability of quadratic summation approximants to locate branch point singularities in the complex plane of the perturbation parameter. Accuracy comparable to that from CCSDT coupled-cluster calculations is obtained using fourth-order perturbation theory. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1318740
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  • 6
    Electronic Resource
    Electronic Resource
    Convergent summation of Møller–Plesset perturbation theory (2000)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 4901-4909 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Rational and algebraic Padé approximants are applied to Møller–Plesset (MP) perturbation expansions of energies for a representative sample of atoms and small molecules. These approximants can converge to the full configuration–interaction result even when partial summation diverges. At order MP2 (the first order beyond the Hartree–Fock approximation), the best results are obtained from the rational [0/1] Padé approximant of the total energy. At MP3 rational and quadratic approximants are about equally good, and better than partial summation. At MP4, MP5, and MP6, quadratic approximants appear to be the most dependable method. The success of the quadratic approximants is attributed to their ability to model the singularity structure in the complex plane of the perturbation parameter. Two classes of systems are distinguished according to whether the dominant singularity is in the positive half plane (class A) or the negative half plane (class B). A new kind of quadratic approximant, with a constraint on one of its constituent polynomials, gives better results than conventional approximants for class B systems at MP4, MP5, and MP6. For CH3 with the C–H distance at twice the equilibrium value the quadratic approximants yield a complex value for the ground-state electronic energy. This is interpreted as a resonance eigenvalue embedded in the ionization continuum. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.481044
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  • 7
    Electronic Resource
    Electronic Resource
    On the use of algebraic approximants to sum divergent series for Fermi resonances in vibrational spectroscopy (1999)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 110 (1999), S. 8205-8206 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Padé summation of large-order perturbation theory can often yield highly accurate energy eigenvalues for molecular vibrations. However, for eigenstates involved in Fermi resonances the convergence of the Padé approximants can be very slow. This is because the energy is a multivalued function of the perturbation parameter while Padé approximants are single valued, and Fermi resonances occur when a branch point lies close to the physical value of the parameter. Algebraic approximants are multivalued generalizations of Padé approximants. Using the (200) state of H2S and the (400) state of H2O as examples of Fermi resonances, it is demonstrated here that algebraic approximants greatly improve the summation convergence. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.478722
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  • 8
    Electronic Resource
    Electronic Resource
    Dimensional perturbation theory for vibration–rotation spectra of linear triatomic molecules (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 4099-4111 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A very efficient large-order perturbation theory is formulated for the nuclear motion of a linear triatomic molecule. All coupling between vibration and rotation is included. To demonstrate the method, all of the experimentally observed rotational energies, with values of J almost up to 100, for the ground and first excited vibrational states of CO2 and for the ground vibrational states of N2O and of OCS are calculated. The perturbation expansions reported here are rapidly convergent. The perturbation parameter is D−1/2, where D is the dimensionality of space. Increasing D is qualitatively similar to increasing the angular momentum quantum number J. Therefore, this approach is especially suited for states with high rotational excitation. The computational cost of the method scales only in proportion to JNv5/3, where Nv is the size of the vibrational basis set. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.474802
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  • 9
    Electronic Resource
    Electronic Resource
    Perturbation theory for coupled anharmonic oscillators (1997)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 106 (1997), S. 2681-2684 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Perturbation theory is applied to a pair of coupled oscillators with cubic anharmonicity. Large-order perturbation theory is shown to be more efficient computationally than numerical diagonalization of the Hamiltonian. Quadratic Padé summation of the energy expansions yields convergent results for the real and the imaginary parts of resonance eigenvalues. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.473370
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  • 10
    Electronic Resource
    Electronic Resource
    Extrapolating the coupled-cluster sequence toward the full configuration-interaction limit (2002)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 116 (2002), S. 6948-6956 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Extrapolation methods that accelerate the convergence of coupled-cluster energy sequences toward the full configuration–interaction (FCI) limit are developed and demonstrated for a variety of atoms and small molecules for which FCI energies are available, and the results are compared with those from Møller–Plesset (MP) perturbation theory. For the coupled-cluster sequence SCF, CCSD, CCSD(T), a method based on a continued-fraction formalism is found to be particularly successful. It yields sufficient improvement over conventional CCSD(T) that the results become competitive with, and often better than, results from the MP4-qλ method (MP4 summed with quadratic approximants and λ transformation). The sequence SCF, CCSD, CCSDT can be extrapolated with a quadratic approximant but the results are not appreciably more accurate than those from the CCSD(T) continued fraction. Singularity analysis of the MP perturbation series provides a criterion for estimating the accuracy the CCSD(T) continued fraction. © 2002 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1462620
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