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  • Articles  (14)
  • American Institute of Physics (AIP)  (14)
  • Cambridge University Press
  • 1990-1994  (14)
  • Chemistry and Pharmacology  (14)
  • Mathematics
  • Geosciences
  • 1
    Electronic Resource
    Electronic Resource
    Bifurcation analysis of chemical reaction mechanisms. I. Steady state bifurcation structure (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 3083-3095 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The vocabulary and techniques of numerical bifurcation analysis are described, with an emphasis on steady state bifurcations of codimension one and two. The direct computation of bifurcation sets is shown to be of considerable utility in analyzing and comparing complex chemical reaction mechanisms. The systems chosen for analysis are the chlorite–iodide and the mixed Landolt reactions. The calculation of a simple hysteresis loop for a mechanism of the chlorite–iodide reaction using both numerical bifurcation analysis and numerical integration begins an extended comparison between the methods advocated in this paper and more familiar methods. The systematic identification of the existence of isolated branches of steady states is described for a second mechanism of the chlorite–iodide reaction. Two mechanisms for the mixed Landolt system are contrasted. It is found that the alternative negative feedback pathway mechanism, which reproduces the periodic behavior more successfully at a selected point in parameter space, is less satisfactory than the EOE mechanism in describing the overall bifurcation behavior of the system in the parameter plane for which experimental data are available. Finally, we examine another mechanism for the chlorite–iodide reaction. This mechanism was designed with the intent of suppressing oscillatory behavior on a subset of parameter space. Numerical integration revealed only bistability of steady states, as desired, but numerical bifurcation analysis reveals a sizeable region in the previously investigated subset of parameter space on which oscillatory behavior exists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459831
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  • 2
    Electronic Resource
    Electronic Resource
    Quadratic response functions for a multiconfigurational self-consistent field wave function (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 1174-1190 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We describe an efficient implementation of the quadratic response function for a multiconfiguration self-consistent field reference wave function. The quadratic response function determines the hyperpolarizability and its residues determine the two-photon transition matrix elements and the transition matrix elements between excited states. We report sample calculations for the hyperpolarizability of Ne and for the two-photon transition matrix elements of Ne and H2.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463245
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  • 3
    Electronic Resource
    Electronic Resource
    Finite-element multiconfiguration Hartree–Fock calculations on the excitation energies and the ionization potential of oxygen (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 5229-5232 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The 3P, 1D, and 1S states of oxygen and the 4S ground state of the oxygen cation have been studied using large numerical multiconfiguration Hartree–Fock calculations with systematically increased active spaces. The nonrelativistic valence limits for the excitation energies are 1.968 and 4.181 eV for E(3P–1D) and E(3P–1S), respectively. The nonrelativistic valence limit for the ionization potential is 13.593 eV.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462733
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  • 4
    Electronic Resource
    Electronic Resource
    Large multiconfiguration Hartree–Fock calculations on the hyperfine structure of B(2P) and the nuclear quadrupole moments of 10B and 11B (1991)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 94 (1991), S. 5051-5055 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The hyperfine parameters for B(2P) are studied using numerical multiconfiguration Hartree–Fock (MCHF) calculations. A newly developed finite-element MCHF program allowing very large configuration–interaction expansions is used. The magnetic hyperfine parameters obtained are 0.0879(28), 0.7817(11), and −0.1675(3) a.u. for the Fermi contact term, the orbital term, and the spin–dipolar term, respectively, as compared to the experimental values of 0.1016(62), 0.7783(16), and −0.1686(5) a.u. The nuclear quadrupole moments obtained by comparing computed electric field gradients with experimental nuclear quadrupole couplings constants are Q(10B)=0.084 59(24) b and Q(11B)=0.040 59(10) b.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.460540
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  • 5
    Electronic Resource
    Electronic Resource
    Spin polarization in restricted electronic structure theory: Multiconfiguration self-consistent-field calculations of hyperfine coupling constants (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 3412-3419 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: It is shown that the isotropic hyperfine coupling constant Aiso associated with the Fermi contact interaction can be accurately calculated from conventional multiconfiguration self-consistent-field wave functions if, in addition to the expectation value of the contact operator, one also includes the terms originating from the response of the wave function. These response terms are nonvanishing only for perturbation operators that are nonsymmetric in spin space. Calculations of Aiso for N and BH2 illustrate the importance of the response terms and also indicate that a good estimate of the spin polarization of the core orbitals may be obtained from the response terms without correlating the core.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462977
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  • 6
    Electronic Resource
    Electronic Resource
    Spin–orbit coupling constants in a multiconfiguration linear response approach (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 96 (1992), S. 2118-2126 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Spin–orbit coupling constants between singlet and triplet states are evaluated as residues of multiconfiguration linear response functions. In this approach, the spin–orbit coupling constants are automatically determined between orthogonal and noninteracting states. Sample calculations are presented for the X 3Σ−g–b 1Σ+g transition in O2 and the 1A1–3B1 transition in CH2. The convergence of the coupling constants is examined as a function of basis set and level of correlation. An exotic behavior is observed in the correlation of the 1A1 state for CH2 when increasing the active space, demonstrating an intricate coupling between the dynamic and static correlation. In general, the results indicate that reliable spin–orbit coupling constants between valence states may be obtained with a 4s3p2d1f basis set for first row atoms and a modest active orbital space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.462063
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  • 7
    Electronic Resource
    Electronic Resource
    C6 dispersion coefficients in multiconfiguration self-consistent field linear response theory (1990)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 93 (1990), S. 7256-7263 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: An algorithm for the evaluation of correlated dipole–dipole dispersion coefficients by direct MCSCF linear response theory is presented. Stepwise construction of a pseudo-state basis using eigenvectors of successive (Cauchy) moments of the linear response function gives an efficient scheme for obtaining polarizabilities at imaginary frequency. The scheme is also useful for polarizabilities on the real axis below the frequency of the first dipole-allowed transition. Sample calculations of C6 coefficients are described for a range of two-electron (H−, He, Li+, Be2+, H2, and H+3 ) and many-electron (Be, N, N2 ) closed- and open-shell systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.459448
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  • 8
    Electronic Resource
    Electronic Resource
    Multiconfigurational quadratic response functions for singlet and triplet perturbations: The phosphorescence lifetime of formaldehyde (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 9178-9187 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A formalism is presented for the calculation of quadratic response functions of multiconfigurational self-consistent field reference wave functions. The formalism is general in the sense that it applies equally well to singlet and triplet perturbations and it does not assume any permutational symmetry in the integrals of the perturbational operators. This formalism can be used to derive expressions for various properties related to singlet or triplet quadratic response functions and their residues. We focus on the spin-forbidden dipole transitions between singlet and triplet electronic states responsible for the long lifetime of phosphorescent states. The singlet–triplet transition moments are evaluated as the residues of quadratic response functions. Sample calculations are presented for the formaldehyde molecule.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463344
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  • 9
    Electronic Resource
    Electronic Resource
    First-order nonadiabatic coupling matrix elements from multiconfigurational self-consistent-field response theory (1992)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 97 (1992), S. 7573-7584 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A new scheme for obtaining first-order nonadiabatic coupling matrix elements (FO-NACME) for multiconfigurational self-consistent-field (MCSCF) wave functions is presented. The FO-NACME are evaluated from residues of linear response functions. The residues involve the geometrical response of a reference MCSCF wave function and the excitation vectors of response theory. Advantages of the method are that the reference state is fully optimized and that the excited states, represented by the excitation vectors, are strictly orthogonal to each other and to the reference state. In a single calculation the FO-NACME between the reference state and several excited states may be obtained simultaneously. The method is most well suited to describe situations where the dominant configurations for the two states differ mainly by a single electron replacement. When the dominant configurations differ by two electrons many correlating orbitals are required in the MCSCF reference state calculation to accurately describe the FO-NACME. FO-NACME between various states of H2, MgH2, and BH are presented. These calculations show that the method is capable of giving quantitatively correct results that converge to the full configuration interaction limit. Comparisons are made with state-averaged MCSCF results for MgH2 and finite-difference configuration interaction by perturbation with multi-configurational zeroth-order wave function reflected by interactive process (CIPSI) results for BH.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.463477
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  • 10
    Electronic Resource
    Electronic Resource
    Bifurcation analysis of chemical reaction mechanisms. II. Hopf bifurcation analysis (1993)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 98 (1993), S. 2805-2822 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: One- and two-parameter Hopf bifurcation behavior is analyzed for several variants of the Citri–Epstein mechanism of the chlorite–iodide reaction. The coefficients of an equation for the amplitude of oscillations (the universal unfolding of the Hopf bifurcation) are evaluated numerically. Local bifurcation diagrams and bifurcation sets are derived from the amplitude equation. Sub- and supercritical Hopf bifurcations are identified for the general case of a nondegenerate (codimension one) bifurcation. At degenerate (codimension two) points, the necessary higher-order terms are included in the unfolding, and features such as locally isolated branches of periodic orbits and bistability of a periodic orbit and a steady state are found. Inferences about the global periodic orbit structure and the existence of nearby codimension three Hopf bifurcation points are drawn by piecing together the local information contained in the unfoldings. Hypotheses regarding the global periodic orbit structure are tested using continuation methods to compute entire branches of orbits. A thorough discussion of the application of these methods is presented for one version of the mechanism, followed by a comparison of the complete two-parameter steady state bifurcation structure of three versions of the mechanism. In all cases, the potential for experimental verification of the predicted dynamics is examined.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.465049
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